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WQMCAL version 2 user manual

1. ss nsseesseessessseeeseeesssttsseessessseersseesssresseesseesseesseeeessees 32 The trans versal mix ine model saisan a ieee Ea A s k 36 LAKE MODEES sicasicescersaserenteaatvonsesaenensregoreaieasnseacenveseaeorsnsenousensonoysy anor EARE 40 Introduction to basic lake ecosystem processes sscceesseceesteceeteeceeaeeceeaeeceeneeceeeeeceeeeeeeeaes 40 General introduction to lake models essicgi c ists teal meitie sete tca ieee ceed Maat ie citi aa 44 Input Toad model ejcscseeuicccaisegeaisasvasddeusnseaedaseaysanasedeadcaas aonede e EAEE A EEE E EEEak 46 Lake hydrology regulation model 5 44 cisarsscissaches seaesescsdes utes bewescesadaosbes daueacceauadetendeaeansetevere 48 Experimental lake model Lake model No 1 eeceessccesseceeeeceeaeeceeneeceeneecesaeeceeeeeeenaes 49 Dynamic nutrient budget model Lake model No 2 0 00 ceeeceeeeseceeeeececeteceeneeesseeeeneeeenas 51 P balance model with sediment interaction Lake model No 3 0 0 ccceeeeeecesccccesseneeeees 53 P budget model coupled with experimental eutrophication model Lake Model No 4 56 Dynamic algae growth model Lake model NO 5 0 ceescccessseceesseceeeeceeneeceeneeceeneeceeneeenaees 58 Waterdual o imit valle Se i ent eto eet e rte E ee at eee er annie reer se re see tre rere 62 Exercises for using the programme for teaching learning sees eseseeeeeseeneeeeseeeeseeseeseeneenes 63 Testing your kKnGWwled se J to 42 h0i0 ais tors asso sate hau eiuh
2. C concentration of the pollutant in the waste water ML Qb discharge rate of flow of the river upstream of the effluent outfall L T qs the effluent discharge C T D 255 Or as a distributed source by adding a constant or time and or space varying input to each elementary water body The most simple example is the input to the fully mixed reactor type lake models where the input load is divided by the volume of the lake After these considerations one can define the following most frequently used river and lake model versions 13 Table I Basic river and lake model forms and their uses General equation oC oC oC Vx Vy Vz t Ox Oy Oceans seas large ce O 3 OC F 0 T5 R lakes SAR ay Oy As AS y s J intemal not used in this form E Ox 3 D models Wind induced 2 D horizontal circulation in lakes river or lake not used in this form models C transversal mixing in Ox oc oc oc ee 2 D river model Eye Ey FSC Yy t E Sintemal Mis meot pouant Spe e ans eral Ot Ox Oy Oy plume mixing model rivers oc a oc 2 D vertical Ct Vy y vg Wind induced currents plane lake in deep lakes in a cross not used in this software models Ta 9 Dy g 2 v c Sy Z t Sintemal section Oy Oy Oz OZ ec ao C 2 es A See in menu block 1 D river models Longitudinal dispersion Accidental pollution 3 was F wave model
3. Fixed boundary classification Pin mg m3 655 8 Reduced C Lake PC Sediment P CAB Chha meanP mg m3 80 4 Eutrophic Qin m3 s 0 412 Pin mg m3 2623 Time horizon years T0 Bee mean Chha mg m3 16 3 Eutrophic Lptkg day OO Lptkovday 00 4 max Chka mg m3 30 9 Eutrophic Lnps kg day 23 4 Lrps kg day 93 2 3 Probabiity distibution Total load kg day 23 4 Totalload kg day 9 3 Chka concentration in the lake water mg m3 CvemeaP ORTHA Ove max Cha Land use fractions 9 Utra oligotrophic 1 Dligotiophic 16 Mesotiophic S 7 25 62 Eutrophic WS 21 Hipertrophic WN 7 Probability distibution for trophic categories KS Load proportions kg day Na y 14 0 Figure 19 a 60 Water Quality Modelling CAL Fle View Window Help i on Graph Input load model El lt E1 Graph Trophic categories Results of input load mod p Graph settings p Fired boundary classification Pin mg m3 681 6 Reduced C LakeP CSedimentP CAB Chk meanP mg m3 86 2 Eutrophic Qin m3 s 0 431 Pin mg m3 2726 Time horizon years TO pl mean Chra mg m3 37 9 Hypertrophic Lpt kg da OO Lptkg days 00 m max Chka mg m3 74 5 Eutrophic Lnps kg day 25 4 Lnps kg day 10 2 Probabiliy Getibution Land use fractions LLLE Total load kg day 25 4 Total load kg day 10 2 Chia concentration in the lake water
4. v Water Quality Modelling CAL BEES File View Window Help Oo k 5 El Fa D Wait Click to practice gt Inputmodel Hydrology 2nd lake model and lake dlas Practice Dynamic nutrient LP E3 Graph Lake model result FE E3 Graph Trophic categories ME Model parameters r Graph settings r Fired boundary classification PLO mg m3 250 Cake mean P mg m3 HE E Time horizon years T0 Stop mean Cha mg m3 alculated D a uao 4 8 max Chla mg m3 Not calc 4 Tame gt 1 Ho lake Wak 7m Probability distribution otal P concentration in the lake water mg m G r vs mean c CKset yeart 0 00 250 9 ner ma E 0 Ultra oligotrophic 0 Olgotrophic LP mg m3 y 163 3241 0 80 3 Mesotrophic qyearl 1051 Kset year1 0 26 53 Eutrophic PLeg mg m3 124 WB 432 Hierop Probability distribution for trophic categories Equilibrium 20 Hypertrophic Eutrophic Mesotrophic Tligatrophie 8 9 10 a 1000 Time years P mean mg m3 hed Lake models Model No 2 Dynamic nutient model Practice Figure 13 Note that in each model block the result evaluation field Figure 10 also appears It is also to be noted that in each lake model block the option of directly entering the input model block and the hydrological model block is given This facilitates the entering of new basic data new lakes or exercising certain clean up strategies load reducti
5. 4T x n0 4x 4x Legend C is the concentration of the pollutant in the stream M L g m y is the transversal mixing coefficient L T m s Coo Co Go Vx h B C is the concentration of the pollutant in the waste water discharge M E g m qo is the rate of flow of the waste water discharge L T m s x is the distance downstream of the source of pollution m X X amp y Vx B y y B y is the distance from the river bank across the river Yo Y B Yo is the distance of the pollution source pipe outlet from the river bank m B is the width of the river m Parameter estimation of the transversal mixing model This equation estimates the value of the transversal mixing coefficient in function of the flow depth and the slope the shear velocity For more details see the chapter on the Basic theory the general description of dispersion models and the general description of transversal mixing models Eq 4 7 2 dh Sg sec Legend g is the acceleration of gravity 9 81 m sec S is the slope of the water surface dimensionless e g m m h is the average depth of flow m d is the experimental constant the value suggested by the authors for the purpose of this study is 0 7 39 LAKE MODELS Introduction to basic lake ecosystem processes As discussed under the General theory of water quality models all lake models included in this software are of the fully mixed re
6. Jm 1 3 Calculate the reduction of P load required for meeting the following criteria Chl amax lt 25 mg m Chl amean lt 8 mg m PP lt 176 gC m year Pinflow for Chl amax lt 25 mg m sel P21 DARA ug l Pinfiow for Chl mean lt 8 mg m 161 4200 ug l Pinflow for PP lt 176 gC m year 98 71 ug l using the first formula The original load how much 7568 6 kg year was assumed to include 15 direct point sources and 10 indirect point sources non sewered settlements while the rest was coming via the runoff load non point source input Do the calculations for the following situation 80 P reduction of direct point sources 60 of indirect point sources and 40 of non point sources How much is the feasibly reduced load Lreduced 0 24 0 15 0 2 0 24 0 1 0 4 0 24 0 75 0 6 0 1248 g s 3935 7 kg year Calculate the conditions achievable by this reduced load What is the mean P concentration of the inflow Pintlows 0 1248 0 3 1 000 416 0000 mg m Trophic values achievable by the load reduction Ximproved 126 13 mg m Chl amean 16 9 0 cceee mg m eutrophic Chlair AS n mg m eutrophic PP 417 2 426 6 gC m year eu polytrophic Compare the results with the categories 78 The lake remains eutrophic although the highly dangerous hypertrophic conditions were relieved Further improvement is only achievable by drastic measure
7. 157 5 ug l hypertrophic Chl a mean 19 2 ug l eutrophic Chl a max 70 3 ug l eutrophic Run the lake model No 2 Do not forget to reset original land use proportions and reduction values to 1 00 Set r 0 7 PLo 250 Simulate 15 years Fixed boundary evaluation 731 0 ug l hypertrophic Probabilistic evaluation 99 hypertrophic Make the realistic cleanup What is the result Fixed boundary evaluation 287 8 ug l hypertrophic Probabilistic evaluation 87 hypertrophic Run the lake model No 3 Reset original loads Set Pso 100 Pseg 500 r 0 7 Fixed boundary evaluation 749 4 ug l hypertrophic Probabilistic evaluation 100 hypertrophic Make the realistic cleanup What is the result Fixed boundary evaluation 295 1 ug l hypertrophic Probabilistic evaluation 88 hypertrophic Try highest possible reduction r 0 3 X p 0 1 X np 0 4 Fixed boundary evaluation 81 5 ug l eutrophic Probabilistic evaluation 64 eutrophic Run the lake model No 4 85 Reset original loads and reduction factors reset r to 0 7 Fixed boundary evaluation PL 749 4 l hypertrophic Chl a mean 118 4 hypertrophic Chl a max 425 6 ug l hypertrophic Probabilistic evaluation highest probability hypertrophic with 100 probability for PL 98 hypertrophic for Chl a mean 100 hypertrophic for Chl a max Make the realistic cleanup X p 0 2 X np 0 6 What is the result Fixed boundary evaluation PL 295 1 ug l hypertrophic Chl a mean 55
8. 2 p 2 50 Z t S x x Oy Oy Oz z yee aad appendix i When temperature dependent process kinetics should be also considered then the changes of temperature can be also described by the heat conservation equation as 4 or r T T 2 ar 2 z al a M y y y M K gt Ot Ox Oy Oz amp x Ox Oy y amp z Oz pc In equations 1 through 4 the following notations were used Vx Vy Vz components of flow velocity in x y and z coordinate directions respectively LTH p the density of fluid ML or FT L4 P pressure FL Exx Exy turbulent eddy diffusivity coefficients LTH Q the Coriolis parameter TH Fyx Fey surface wind friction forces FL Fox Foy Foz bottom friction forces FL C is the concentration of the pollutant ML Dx Dy Dz are coefficients of dispersion L T T is the water temperature temperature unit e g C F Kx Ky K combined heat exchange coefficients due to turbulent eddy diffusivity and molecular heat conductivity L T M inputs of heat at a given point thermal unit L T c specific heat thermal unit M temperature unit Terms in the above equations 1 a c have the following meanings First left hand side term local inertia instantaneous local acceleration of fluid at a point Second to fourth left hand side terms convective inertia acceleration of fluid when transported from one point to another one Fifth left hand side ter
9. 0 6 m s f 2 00 Mean flow depth h 2 5m Characteristic water temperature 21 C Use the dilution equation and calculate the initial values 11 654 mgO gt l DOo 6 925 mgOz 1 Do oxygen deficit 2 1 mgOo l The other source the town of Black Ferry is located on the Shiny Duck river 20 km upstream from the confluence with the River Shallow Rapids which is 27 km downstream from Great Groves The population of Black Ferry is 65 000 The per capita water consumption rate is 250 litre day and the water losses amount to 20 drinking bathing watering etc The design discharge August low flow of Shiny Duck river is 12 0 m s Other data are as follows Raw sewage strength BOD Ls2 550 mg O2 l Effluent discharge qs2 0 15 calculate m s Effluent DO DOg 2 5 mg0O7 1 River flow Qp2 12 0 m s Background BOD Ly2 6 0 mg O7 1 70 Background DO DO 7 0 mg O7 1 River flow velocity V2 0 4 m s slow river f 1 5 Average flow depth h 1 3 m Water temperature 21 C Use the dilution equation and calculate the initial values Lo 12 716 mgO7 1 DOo 6 944 mgO7 1 Do oxygen deficit 2 07 mgO7 l Downstream of the confluence with Shiny Duck the River Shallow Rapids is characterized by the following data flow velocity v3 0 5 m s water depth d 2 0 m The task is to analyse the oxygen household conditions over the entire river system and des
10. 1 ug l hypertrophic Chl a max 173 9 ug l hypertrophic Probabilistic evaluation highest probability hypertrophic with 88 probability for PL 85 hypertrophic for Chl a mean 95 hypertrophic for Chl a max Try highest possible reduction r 0 3 X p 0 1 X np 0 4 Fixed boundary evaluation PL 81 5 ug l eutrophic Chl a mean 19 2 ug l eutrophic Chl a max 50 6 ug l eutrophic Try additional forestation measures go back to input sub model set the following land use proportions Forest 50 Meadow 23 Agriculture 23 Fixed boundary evaluation PL 71 6 ug l eutrophic Chl a mean 17 3 ug l eutrophic Chl a max 44 6 ug l eutrophic Run Lake model No 5 Set AB ABo 830 r 0 7 rp 0 1 r 0 7 Set back reduction factors X to 1 00 in the input model Set back original land use proportions Simulate 15 years Do not change other parameters Gradually change maximum growth rate mumax until you achieve concentrations and trophic categories similar to those of the 4 model run What do you observe At maximum growth rate mumax 0 18 day you obtain Fixed boundary evaluation PL 749 4 l hypertrophic Chl a mean 134 9 Hypertrophic Chl a max 412 2 ug l hypertrophic Probabilistic evaluation highest probability hypertrophic with 100 probability for PL 99 hypertrophic for Chl a mean 100 hypertrophic for Chl a max Make the realistic cleanup X p 0 2 X np 0 6 What is the result Fixed boundary evaluation PL
11. 4 Lake eutrophication models spanning from simple experimental regression models to dynamic algae phosphorus models including a sub model for input load calculation and a lake water budget regulation model The authors wish to state that no existing commercially available river or lake water quality softwares have been utilized for writing this programme The authors have developed all model softwares presented below This means that the software is a genuine product involving no copyright matters whatsoever and that all property rights of this material and software programme stay with the authors and UNESCO The authors also wish to emphasise that the software and the models are not intended for use in practical work design water pollution control planning environmental impact assessment etc neither in the present nor in any of the future forms and serve solely for teaching purposes Therefore the authors wish to state that they do not assume any responsibility for failures faults or damages caused by such non intended use of the softwares and the programme Moreover the authors will consider such use when discovered the violation of their respective rights as owners of design softwares that relay on the same or similar principles This document and software is the second version of the earlier software by the same authors Basic River Water Quality Models WQMCAL version 1 1 expanded to deal also with the basics of lake wate
12. 428 57 m What is the value of the dispersion coefficient Dy 134 85 m s Find the place where the concentration decreases below alarm level exactly at 100 km downstream of the source There is a drinking water intake at 40 km downstream of the accident Hand calculate maximum concentration value of the pollution wave at 40 km downstream of the site of the accident 0 474 mg l When does the pollution peak arrive to this section ERA hours How much will be the pollutant concentration at the section of the water intake two hours earlier C40km 13 87 h sesisssssss 197 westsasees ug l t 49932 s How much lead time the operators of this waterworks have for action until the above calculated not yet critical concentration arrives your work as an experienced modelling specialist has taken 1 0 h and you were informed about the accident in half an hour Tead time for action 13 87 1 5 12 37 h After the event has passed you were given recorded data You certainly wish to process these data in order you update the knowledge on river parameters e g obtain correct values for the dispersion coefficient The reported measurement data are as follows At a station 10 km downstream C max 1 0 mg l while at another one at 25 km distance it was C2 max 0 6 mg l Find the appropriate formula in the lecture notes Calculate Di 113 78 m s Correct your prediction for the site where the ala
13. General description of BOD DO river models and the General description of the traditional oxygen sag curve The oxygen sag curve a screen outprint of the software is shown in Figure 6 19 Legend i Water Quality Modelling CAL Graph Oxygen Curve Traditional model Fl File View Window Help laj x a Sa k SE Ba STOP Wait r Oxygen model parameters LOmg 24 6 K1 1 day 0 30 DOsat mg 10 1 K2 1 day 0 75 DOO mg 5 8 tort day 1 35 DO mg 44 DOcrit mg l 3 59 m mg02A 02 Sag Curve DOSE t E O EEA T ETEA EEEL EEEE EPEL POETE 10 9 8 7 Class 1 6 Class 2 5 4 Class 3 Class 4 3 5 Class 5 2 1 0 0 1 2 3 4 5 6 7 8 3 10 11 12 13 14 15 16 17 18 19 Time days 3 BOD DO river models Traditional Oxygen Sag curve Oxygen Sag equation j F gg E m e Figure 6 D K Lo e a ekt Doe K K D is the oxygen deficit of water g 0 m see also equations 2 7 and 2 8 Do is the initial oxygen deficit in the water downstream of effluent outfall see also equations 2 6 and 2 7 Lo is the initial BOD concentration in the water g O m downstream of effluent discharge see also Eq 2 5 K is the rate coefficient of biochemical decomposition of organic matter es usually day K2 is the reaeration rate coefficient T t is the time that is the time of travel in the river interpreted as t x v where x is the distance downstream of the point of effluent
14. Skipping again some of the details of deriving the basic equation Jolankai 1979 Jolankai 1992 let us consider an elementary water body a cube of dx dy and dz dimensions as shown in Figure 4 The quality of water within this elementary water body depends on the mass of a polluting substance present there Water quality models then should describe the change of the mass of a polluting substance within this water body The change of the mass of this substance is calculated as the difference between mass flows mass fluxes entering and leaving this water body considering also the effects of internal sources and sinks of the substance if any The mechanism of mass transfer into and out of this water body includes the following processes Mass transported by the flow by the vx v and v components of the flow velocity vector This process is termed the advective mass transfer The transfer of mass that is the mass flux in mass per time M T dimension can be calculated in the direction x as C v dy dz where C is the concentration of the substance in the water in mass per volume dimension M L see also Equation 1 1 The other means of mass transfer is termed the dispersion or dispersive transport Here one has to explain this term because there is usually considerable confusion with the terms diffusion and dispersion in short dispersion is a term used for the combined effect of molecular diffusion and turbulent diffusion and both o
15. a substance and the velocity of flow in that spatial direction These are the terms used in writing the overall mass balance that is Eq 1 2 of an elementary water body as shown in Figure 4 Eq 1 1 B D 2E Mrr dx ADV Cv 3 ML T Legend Ex is the dispersive mass flux in the spatial direction x in M L T dimension with the assumption that the law of Fick holds for the joint effect of molecular diffusion and turbulent diffusion that is for dispersion ADV is the advective mass flux in the spatial direction x in M E T dimension C is the concentration the mass of the quality constituent in a unit volume of water mass per volume M L D is the coefficient of dispersion in the direction of spatial co ordinate x in surface area per time or units Vx is the component of the flow velocity in spatial directions x length per time L T The mass balance equation of an elementary water body This equation was derived by writing a mass balance of in and outflowing advective and dispersive mass fluxes of an elementary water body see Figure 4 and see explanation of the terms at Eq 1 1 and expressing the change of the mass of the substance with time The terms for one spatial direction include the inflowing mass flux and the outflowing mass flux which latter is the difference between inflowing flux and the change of the flux within the water body For more details see the General description of basic theory
16. as the quantity mass of oxygen consumed from a unit volume of water by microorganisms while they decompose organic matter during a specified period of time BOD is the amount of oxygen excreted by microorganisms into a unit volume of water during the decomposition of organic matter during a selected period of time correct answers use the Test menu 5 What the term oxygen deficit D means a b c It is the rate of oxygen consumption by the respiration of aquatic plants It is the loss of oxygen from water caused by molecular diffusion across the water surface It is the difference between the saturation dissolved oxygen content and the actual dissolved oxygen content of water correct answer use the Test menu 91 6 How would you calculate the initial concentration of a pollutant in the river downstream of a pollution discharge outlet for the steady state BOD DO models presented in this programme As the sum of pollutant mass fluxes of the river and the effluent discharge divided by the sum of river flow and waste water flow As the sum of the concentrations of the pollutant in the river and that in the waste water e g C tCy Expressing the concentration Co from a mass balance equation written for the selected downstream cross section e g by the dilution equation As the sum of background river mass flux of the pollutant plus the pollutant concentration in the sewage water correct answers use t
17. as to protect and save human life and the life of other living things which latter is a precondition of human life as well The management of water quality or the protection of the aquatic ecosystem in a broader sense means the control of pollution Water pollution originates from point and non point diffuse sources Figure 1 and it is always due to human action the author strongly believes that no such thing as natural pollution exists as sometimes advocated by other people Transport and transformation processes of pollutants in the ts gt atmosphere e Sin Toes Precipitation and deposition AAT TTT HH ny Waeeen f iS Ee ri fE ram le ey RO he Storage of pollutants in the soil De RAREZA Ground water Storage of pollutants in gound water HEHEH Figure 1 The control of water pollution the protection of aquatic systems is thus the control of human activities that result in pollution In addition to this man also should make efforts to enhance the capabilities of terrestrial and aquatic ecosystems in assimilating and reducing pollution This is one of the basic notions of the novel ecohydrological concept of managing water quality Figure 2 This also means the understanding and enhancement of the evolutionarily established resistance and resilience of freshwater ecosystems to stress This should be done first of all by understanding and quantifying the r
18. because you will need it later B 52 0 72 2 5 0 6 34 7 m Assume for non point source BOD runoff strength 20 mg l a good average estimate for larger populated watersheds with mixed land use and take its DO content as 4 0 mg l Set for the time being both benthic oxygen demand and photosynthesis respiration source sink term to zero note that P R can not be set to zero just near to zero to avoid division by zero Make observations on the resulting model run Can the water quality criteria be met without any control action 68 You observe that for BOD the desired Class I water quality would be reached after about 6 days time of travel only that corresponds to some 311 km river length which means that the entire river reach in concern would be polluted You also observe that the critical DO also falls below Class II it is about 4 7 mg l Design alternative cleanup measures for point and non point source pollution 1 Calculate the effect of 80 BOD removal at the effluent outfall of the city Go back to the respective menu item e g dilution equations You should enter 0 2x420 84 mg l for BOD strength Ls You will find that the critical DO is still below 6 mg l and BOD remains also high over a longer reach of the river Thus the task was not accomplished Assume point and non point source control strategies to be introduced over the entire catchment basin Assume 50 NPS BOD removal and only 25 improvement in the DO con
19. change thy hydrological and nutrient washoff parameters The reason is that in a later third stage of the software development the authors intend to include a relatively complex integrated catchment modelling block to add more flavours to the ecohydrological concept of this software It is to be noted that the ecohydrological objective will be fully met when this third part of the series is also made since two of the main objectives of the ecohydrology programme of IHP are i To develop a methodological framework through experimental research to describe and quantify flow paths of water sediments nutrients and pollutants through the surficial ecohydrological system of different temporal and spatial scales under different climatic and geographic conditions i To develop an integrated approach for managing the surficial eco hydrological environment including the non structural measures and this actually means the description integrated modelling of the transport and transformation of pollutants nutrients in the catchment and stream network That is a drainage basin modelling block of the CAL series should be also provided This is the intended future third version of this software series Introduction Water is life and thus the quality of water is an essential measure of the quality of life or rather the existence of life Consequently water quality management is or should be one of the most important activities of mankind so
20. chlorophyll and versus nutrients primary production versus P loading primary production versus in lake phosphorus and chlorophyll a etc In the relevant literature there were many attempts to modify improve or test the above models Rechkow 1979 Yeasted and Morel 1978 Hoare 1980 Golterman 1980 Kerekes 1983 Mahamat and Bhagat 1983 Salas and Martino 1991 exercising sometimes strong criticism over them One may however state that these empirical relationships are indispensable tools in assessing the fate of lake ecosystems especially when quick answers to lake recovery problems are required on the basis of 49 limited data but they must be used with due concern to their limitations perhaps together with parameter sensitivity and error analysis 50 Dynamic nutrient budget model Lake model No 2 Description Early lake eutrophication and nutrient budget models Vollenveider 1969 Lorenzen 1974 Sonzogni et al 1976 Thoman et al 1977 considered the phosphorus balance as the sum of external supply LP minus outflow and sedimentation assuming that the lake segment is fully mixed and the lake volume is constant while sedimentation is proportional to the P concentration of the lake see Figure 12 Outflow Figure 12 For a given retention ratio r O lt r lt 1 of phosphorus expressing the ratio of the lake equilibrium concentration Peq to the inflow concentration Pin the settling rate coefficient varies in
21. discharge and v is the mean flow velocity of the river reach in concern L T 20 The dilution equation for BOD This dilution equation computes the initial concentration of BOD in the river downstream of a point source sewage discharge with the assumption of instantaneous mixing For more details see the Basic theory the General description of BOD DO river models and the General description of the traditional oxygen sag curve Eq 2 5 Lo Ls q T Lo Q q Q Legend Lo is the initial concentration of BOD in the river downstream of the effluent discharge point ML e g mg Oy l Ls is the background concentration of BOD in the river ML e g mg O7 l L is the BOD content of the waste water ML Q discharge rate of flow of the river upstream of the effluent outfall L T q the effluent discharge iT The dilution equation for DO This dilution equation computes the initial concentration of dissolved oxygen in the river downstream of a point source sewage discharge with the assumption of instantaneous mixing For more details see the Basic theory the General description of BOD DO river models and the General description of the traditional oxygen sag curve Eq 2 6 _ DO g DOQ Q q DOo Legend DOo is the initial concentration of dissolved oxygen in the river downstream of the effluent discharge point ML e g mg O l DO is the background concentration of dissolved oxyg
22. distribution curves splitting the above distance into equal parts This value can be seen in the graph when you set the highlighted curve to a position which equals or is near to the distance in concern see Figure 7 a screen outprint of the software s Water Quality Modelling CAL Graph Wave model lef x Dil Fie View Window Help la x Click to practice gt Dx estimation Wave model parameters M kg 1000 Highlighted wave at Dx m2 s 4 49 0 0116 day s 1 km K 1 day 0 30 H v mss 10 Animation ral Clmax 1 419 Pollution Wave Model 20 Alaim level 0 1 2 3 4 5 6 T 8 8 10 11 Distance km ke Dispersion river models Longitudinal dispersion model Practice Figure 7 34 Eq 4 1 OC OC OC Dx vx KC t dx dx Eq 4 2 M x V t C x t exp Kt AJ4zD t 4D t Legend C is the concentration of the pollutant in the stream M LS g m M is the mass of the pollutant discharged instantaneously into the stream M grams D is the coefficient of longitudinal dispersion 7 T m s K is the reaction rate coefficient assuming first order decay as the transformation process Vx is the average flow velocity of the stream L jE m s t is the time T A is the wetted cross section area L also defined as Q v where Q is the rate of flow in the river reach concerned Model for estimating dispersion coefficient D T
23. eventually on the hydraulic parameters of the stream and a large number of experimental formulae have been presented in the literature along with reviews of these literature equations Gromiec 1983 Jol nkai 1979 1992 These expressions deviate from each other sometimes substantially For the purpose of this CAL programme we have developed a special equation on the basis of a number of literature published equations that give the value of K3 in function of flow velocity v and stream depth H by simply averaging the coefficient values of different authors when they were relatively close to each other The thus obtained formula is Equation 2 13 For the estimation of the value of K the Table of Fair ref Jol nkai 1979 can be used when knowing the value of Ks can be used This Table expresses the ratio f K2 K in function of the verbally described hydraulic condition of the stream as shown in Table 2 17 Table 2 Ratio f K K in function of the verbally described hydraulic condition of the stream Description of the water body range of f K K Small reservoir or lake 0 5 1 0 Slow sluggish stream large lake 1 0 2 0 Both the reaeration coefficient K and especially the decomposition rate coefficient K depend on the ambient water temperature For this latter the most widely accepted formula is Eq 2 14 One should note that reported literature values of K and K3 vary over wide ranges of which for this teaching aid progra
24. explanation of the term dispersion is given Thus to summarise dispersion is a transport process caused by the joint effect of molecular diffusion and turbulent diffusion The traditional concept of modelling diffusion and thus dispersion relies on Fick s law which states that the transport of the substance in a space direction is proportional to the gradient of the concentration of this substance in that direction the proportionality factor being the coefficient of diffusion dispersion Writing a mass balance equation for an elementary water body of dx dy dz dimensions considering the above dispersive and the advective mass fluxes plus external sources and internal sources and sinks of the substance one obtains the basic equation Eq 1 3 for the variation of the concentration of the substance with the time and space the reader user is kindly requested to consult the relevant literature if he she is interested in more details of the derivation of this basic equation In the practice many more or less simplified versions of this basic model equation are used for describing the fate of various substances within the rivers when introduced discharged into the water from natural or anthropogenic sources within the river Of these many possible applications we have selected for the purpose of this CAL programme two cases which represent probably the two most important applications of these dispersion models sometimes termed also mixing models be
25. function of the hydraulic washout rate q This retention ratio is built into the software Many modifications to this basic equation were developed and applied Equations Eq 5 4 dPL_ 1 Pin u P Kse dt A h Qn 20 t P LP P t P eo 1 _ eT Keak a d Ka Lp LinPin A q Q out h A h A Eq 5 5 LP P 1 Pia r Leq K set 2 i q Kse Pin r Legend PL is the total P concentration in the lake water ML gt mg m Pro is the initial total phosphorus concentration at time t 0 of the lake Peg is the equilibrium concentration of the lake for the given input load and settling rate Pinn is the mean inflow concentration of phosphorus Qin is the water inflow rate L TH m year 51 Qor is the water outflow rate L T m year h is the average depth of the lake L m A is the average surface area of the lake LI m3 LP is the volumnar P loading rate to the lake ML TY mg m year to be obtained as the loading rate of P MT divided by the lake volume V L q is the hydraulic washout rate TH year calculated as the water outflow rate L TH divided by the lake volume V L Ke is the sedimentation rate TI year r the retention ratio of phosphorus O lt r lt 1 expressing the ratio of the lake equilibrium concentration Pj eq to the inflow concentration Pin t is the time T Figure 13 shows a screen outprint of this model
26. given for a number of characteristic trophic parameters This work has been based on the experimental data of a large number of lakes A computer realisation of the slightly modified adapted distribution curves of this study an outprint of the software s screen is shown in Figures 10 This is the result evaluating screen that appears in each lake model showing the probabilities with which the lake in concern falls into a strophic state in respect to mean P Chlorophyll a mean and maximum values Water Quality Modelling CAL Graph Trophic categories 6 Water Quality Modelling CAL Graph Trophic categories v gt Water Quality Modelling CAL Graph Trophic categories MEE Fil File View Window Help lal x Fil Eie View Window Help Fil Eie View Window Help 18 xj i o Ai fo kyl ic zii fos kev cz I Bel hel se Se D A kel s Gal kel SS RA Wait Wait Wait Fixed boundary classification r Fired boundary classification r Fixed boundary classification mean P mg m3 100 0 Eutrophic mean P mg m3 100 0 Eutrophic mean P mg m3 100 0 Eutrophic mean Chl a mg m3 25 0 Eutrophic mean Chl a mg m3 25 0 Eutrophic mean Chl a mg m3 25 0 Eutrophic max Chl a mg m3 75 0 Eutrophic max Chra mg m3 75 0 Eutrophic max Chta mg m3 75 0 Eutrophic Probability distribution Probability distribution Probability distribution Cis meanA C vs mean Cha C vs max Cha Cvs meanP iys meanChka C vs max Ch
27. in days 28 The second expanded BOD DO model General description of 2 expanded BOD DO model The second expanded BOD DO model selected for this software programme is that of the model system SENSMOD Jolankai 1985 which has been developed by the authors of this CAL programme Although in this model the basic modelling concept has also been changed slightly the reader user is kindly requested to consult also the following topics General introduction of BOD DO models the General introduction of the traditional oxygen sag equation the General introduction of the Expanded BOD DO models and the General introduction of the first expanded BOD DO models The main differences of this modelling concept are as follows l Longitudinal variation of the mass flux the product of flow and concentration is expressed instead of expressing the variation of concentration with the time of travel thus allowing for the consideration of longitudinally varying river flow 2 The DO equation is written for the dissolved oxygen termed here Cox instead of the oxygen deficit D 3 Non point source input loads are also considered in terms of concentrations of BOD and DO in the lateral inflow here the term lateral inflow q L T refers to the increment of river flow Q L T over a unit downstream distance L of the river assuming uniform q values over a given river reach 4 Photosynthesis and respiration of aquatic plants are considered
28. indirect point sources and non point sources respectively LPyeduced LP 0 15 0 2 0 1 0 4 0 75 0 6 0 52 LP 0 0785 g m year Thus the problem cannot be solved with the available technologies although the result is better than what was obtained by the OECD regressions models You will have to look for additional treatment techniques such as the construction of pre treatment reservoirs filter ponds at the river inflow sections Calculate and plot the lake response curve in P lake concentration with and without load reduction for the following parameters P 0 3 mg l K 0 05 year Compose similar examples if you have more time left for this exercise Exercise 7a Analysis of lake eutrophication with the simple dynamic P budget model Lake Model No 2 A lake of 90 km area and 5 meters average depth has a drainage area of 1000 km The multiannual average runoff is 120 mm 82 Calculate the inflow to the lake Q 3 8 m s Enter the hydrology sub model set evaporation equalling precipitation Qou Qin Qout max hmin Nmax N 5 0 m Enter the input load menu Scarce data indicate that the multiannual average inflowing phosphorus concentration is Pmean 300 ug l The point source input is 20 kg day Set the phosphorus retention capacity of the lake to 30 a realistic value r 0 7 Set PLo to 90 mg m Simulate 15 years time horizon Run the model what do you observe Fixed boundary evaluat
29. separately that is rather with their difference e g P R The 2nd expanded BOD DO model selected for this programme software has essentially the same parameters as the first expanded BOD DO model and the same limitations refer to the possibilities of parameter estimation The differences are a the parameter q the lateral inflow that can be relatively easily obtained from the hydrological longitudinal profile For a given river reach of length x it obtained as the flow increment over the reach divided by the length of the reach b Concentrations of the constituents in the lateral inflow should be either estimated by another submodel this is done in the SENSMOD model system by the overland runoff transport submodel the NPS submodel or a literature estimate of runoff concentration of the respective substance must be used C Parameters of BOD decay rate K and reaeration rate K have slightly different values from those of the previous models due to the difference in modelling concept and thus in the exponents of the model equations A correction algorithm is built in the programme to facilitate conversion not shown in the written material so as to allow the use of the respective parameter estimation formulae and tables 29 In the calculation example of this CAL programme we will use pre defined ranges of parameter values within which the user may select one so as to see their effect on the final outcome of the model simula
30. stream downstream of the planned sewage outfall are set for the oxygen household conditions as follows Dissolved oxygen DO not less than 6 mg l Class II good in the critical low flow period flow of 80 duration in the summer months BOD less than 6 mgO I Class II good Data of the raw sewage of the city are as follows Background BOD concentration 6 mg O l Background DO 7 mg O 1 Effluent discharge 0 72 m s Estimated raw sewage strength BODs 420 mg O l Oxygen content of the effluent 1 5 mg l Stream velocity 0 6 m s large river of medium flow velocity Select f 2 0 Mean depth of stream 2 5 m The river temperature in the summer months is 21 C Critical summer flow upstream of the city 52 m s The river Blue Rapids has only several small non monitored tributaries over this 150 km length downstream of Seven Churches and you know from the hydrological flow profile data from that of the hydrographic station at Tricky Bridge that the corresponding flow there is 68 m s We do not have data on the pollution sources of the highly populated and agriculturally also cultivated watershed of Blue Rapids and consequently we must assume that they represent non point source input to the river Use the 2 Expanded BOD DO model from the menu which allows for NPS input loads Calculate lateral inflow q 68 52 0 72 150 000 0 000107 m7 s Also calculate width of the river downstream of Seven Churches
31. t What is the time until the peak concentration arrived t 46 5 h 167 400 sec What is the average flow velocity vx 0 6 m sec x t A 266 67 m D 62 93 m s Di M7 A Cmax 4 T t Choose the Accidental pollution wave model from the menu and enter the data Note that the maximum pollutant mass that can be entered is 10 tons because the programme was not designed to events of such magnitude and thus you will have to multiply all results by 10 Vary channel geometry parameters flow depth h channel width B and slope S within realistic ranges until you achieve the above calculated value Dx D1 62 54 at S 19 9 cm km and B 69 m Use the model for answering the following questions What was the likely CN maximum concentration near 10km to the source 103 mg l What could have been the CN maximum concentration at Cicirlua Nagysik rl 20 km from the source 73 1 mg l What was the CN maximum concentration at Caraseu Szamoskrass approximately 40 km from the source 51 7 mg l What was the likely CN maximum concentration at Satu Mare Szatm rn meti approximately 80 km from the source 36 5 mg l Can it be a correct value if the local authorities reported 7 8 mg l maximum concentration for Satu Mare Yes but they must have certainly missed the peak by several hours unless the Csenger value was wrong Calculate what could have been the corresponding sampling time the time lag when missing the peak Setting al
32. t2 20000 0 4 86400 0 578 days and exp K 2t2 0 771 t3 70000 0 5 86400 1 62 days and exp Kj3t3 0 625 Next the BOD concentration of the river Shallow Rapids at the end of the reach examined control point is calculated as Lmonitoring A 1 B Qpi qs1 T Cn2 D Qb2 qs2 exp K 3t3 Qbi qs Qb2 qs2 Combining the three equations you obtain Lmonitoring 5 2 n1 5 36 52 72 5 23 n2 4 57 12 15 0 625 52 72 12 15 2 64 n 0 612 n2 3 25 Thus for example 80 treatment at both plants would result in the following BOD concentration in the monitoring station 70 km downstream of the confluence of the two rivers Leotreatment 2 64 0 2 0 612 0 2 3 25 3 9 mg O7 1 Note that due to the higher multiplier of n the same BOD removal rate at the larger source will be more efficient in cleaning up the river than at the smaller source an evident result 12 Exercise 4 Analysis of an accidental pollution case The Case An oil transporter lorry has fallen into a river from over the bridge Its load of 2 tonnes of mineral oil has been instantaneously discharged into the river Use the longitudinal dispersion model of the CAL programme The river data are as follows River flow Q 300 m s Channel slope S 20 cm km River width B 60 m Flow velocity v 0 7 m s Set alarm concentration to 300 ug l Consider zero decay of the oil K 0 Calculate flow depth and cross section area H 7 14 m A
33. the framework of the IHP V projects teaching project 8 1 and ecohydrology projects 2 3 and 2 4 to aid university teachers and students in teaching respectively and learning the basis of river and lake water quality modelling The authors wish to express herewith their gratitude towards UNESCO Venice Office Regional Office for Science amp Technology for Europe for financially supporting the development of this recent version of the software They also wish to thank the support of the International Hydrological Programme of UNESCO for the publication of this document and the related software on CD ROM The authors wish to thank herewith the support of their home institution the Water Resources Research Centre VITUKI Budapest Hungary where the knowledge needed for the preparation of this software has been gained in the framework of actual water quality modelling and other environmental and hydrological projects during many decades Experiences gained by the first author during some 30 years of teaching subjects related to the Environmental Hydrology in various Hungarian and foreign universities and international courses have also been utilized to a great extent The authors also wish to emphasise that the software and the models are not intended for use in practical work design water pollution control planning environmental impact assessment etc and serve solely for teaching purposes Therefore the authors also wish to st
34. the river system Consider DO 5 0 mg O I for the treated effluent 5 Compose a treatment model for the overall case expressing the resultant BOD concentration of the monitoring point 70 km downstream of the confluence of the two rivers in function of the treatment efficiencies of the two plants in the form of 71 Linonitoring point 7 411 T bn2 d where n 2 are the treatment factors of the respective treatment plants fraction of BOD load remaining after treatment e g 80 efficiency corresponds to n 0 2 Write the dilution equations and use the BOD decay equation in formulating the model Determine model coefficients a b and c Use the model for checking various control removal options and variations Solution The BOD in Shallow Rapids upstream of the confluence with Shiny Duck river is obtained as Liy Lsi qsi exp Ky iti Qpitqsi n1 1 Qpi Loi exp Ky iti Qpitgsi A n B where A Lsi qsi1 exp Ky 1t1 Qpitqs1 420 0 72 0 906 52 0 72 5 2 and B Qp1 Lyi exp Ky 1t1 Qp1 Gs1 52 6 0 0 906 52 72 5 36 Similarly the BOD of Shiny Duck river upstream of the confluence with Shallow Rapids river will be La c2 qs2 exp K j 2t Qp2 ds2 M2 1 Qp2 Lyo exp K 12t2 Qb2 qs2 Cn2 D where C Ly qo exp K psts Qyo qgo 550 0 15 0 771 12 40 15 5 23 and D Qyo Lio exp K 12ts Qhotdo 12 6 0 771 12 15 4 57 Note that the times of travel are t 27000 0 6 86400 0 521 days and exp Kj t 0 906
35. 0 Go back to the Lake model No 1 and look at the results Try to change land use proportions for cleanup cleaning also up the point source What do you observe You find that the catchment model yields even more pessimistic conditions Note that the current built in catchment model is very rough and unrealistic and will be replaced by a complete set of sub models in the 3 version of this CAL software Go back to the input load menu item for the data to be entered alternative Change the Pin to 300 mg m Set point source input to 20 kg day Set back cleanup factors to 1 00 Check the trophic state both by the fixed category and by the probability distribution You still obtain eutrophic conditions Try the realistic and the possible maximum cleanup measures as above What do you find The realistic cleanup still leaves you with eutrophic conditions but the maximum cleanup results in mesotrophic ones 80 Exercise 7 Analysis of lake eutrophication with a simple lake model manual calculation Consider the lake of the previous example A lake of 10 km area and 5 m average depth has a drainage area of 100 km The multiannual average runoff is 94 6 mm Calculate the inflow to the lake Q 0 3 m s Scarce data indicate that the multiannual average inflowing phosphorus concentration is very high Pinean 800 ug l Use the following simple lake model P GF rby 5 dt where P is the P concentration of
36. 0 mg l What do you conclude Class IV water quality indicating hypertrophic conditions Consider the following management strategies and calculate the achievable load reduction Effluent concentration after P removal 1 0 mg l Efficiency of non point source management strategies for agricultural areas 40 P reduction Efficiency of non point source management strategies for urban areas 60 P reduction Lreducea_ 189 694 0 6 3400 0 05_ 0 6 0 4 0 5 3400 2800 0 05 0 5 3800 0 05_ 0 6 0 4 3800 0 5 0 4 0 1 3800 2 0 0 2 3000 0 05 0 6 0 7 3000 0 5 0 4 0 1 3000 2 0 0 4 0 4 1400 2 0 0 6 0 6 1400 0 5 3988 IEE S O 3 988 kg year TP edicao 0 418 mg l It still falls slightly into Class IV Continuation of exercise 9 In the reality washoff loads depend highly on the runoff while runoff changes substantially with the landuse Calculate weighed runoff values for the different landuse forms agriculture urban land forest with the help of the following runoff coefficients attention the total runoff volume must remain the same V measured 8 640 000 teere m year Oforest 0 05 Qagri 0 15 Qurban 0 4 V measured A R 8640000 m year Reorest T 24 8 sser mm year Ragi 74 65 mm year Rurban 199 1 sssess mm year Calculate unit area loading rates UAL in function of the runoff using the following formulas Jol nkai 1999 88 For forest 1 VAL owe Tox 5 92 0
37. 023 m s Cpt 8000 mg m Lpt 15 9 kg day Note that you can only enter 0 022 m s for Qpt and thus you obtain 15 2 kg day for the point source load Use the input model and select non point load calculation Enter the following data for land use proportions 41 forest 25 meadow 30 agriculture 4 urban land The multiannual precipitation of the area is 800 mm Take note of the total calculated inflow 0 327 m7 s Enter the hydrology sub model set outflow inflow set ho hmin hmax 2 0 m E P Set Qou to 0 3 m s and Qoutmax to 1 0 m s Run the Lake Model No 1 Fixed boundary evaluation PL 425 5 ug l hypertrophic Chl a mean 41 6 ug l hypertrophic Chl a max 171 9 ug l hypertrophic Probabilistic evaluation highest probability hypertrophic with 96 probability for PL 73 hypertrophic for Chl a mean 95 hypertrophic for Chl a max Make the realistic cleanup X p 0 2 X np 0 6 What is the result Fixed boundary evaluation PL 167 5 ug l hypertrophic Chl a mean 20 1 ug l eutrophic Chl a max 74 3 ug l hypertrophic Probabilistic evaluation highest probability hypertrophic with 61 probability for PL 58 eutrophic for Chl a mean 64 hypertrophic for Chl a max Try additional forestation measures go back to input sub model set the following land use proportions Forest 50 Meadow 23 Agriculture 23 Urban land 4 How much improvement can you achieve Fixed boundary evaluation PL
38. 1R For agricultural land amp ALa ri 7 ale 1 exp 4 4 0 018R For urban land 6 ALur a a PAL 1 exp 2 15 0 0053R UAL forest 0 03 1 0 0 kg ha year UALapgi 0 36 000006 kg ha year UALS 1 50 00 kg ha year Repeat the load assessment with the new UAL values Les 6518 kg year Calculate total flow including the point source discharges and the annual mean concentration of TP in the stream water Qout 0 302 m s TP Resa 0 684 mg 1 Compare this value with that of the water quality classes for waters to be impounded or discharged into a lake Hungarian Standards TP Class I 0 04 mg l Class H 0 2 mg l Class IH 0 4 mg l Class IV 1 0 mg l What do you conclude Calculate again the achievable load reduction liedje ers 3108 kg year EP rediced maen 0 326 mg l What is the final conclusion The runoff based more accurate model yields a little more favourable results because the estimated annual runoff was very low even in Hungarian conditions Calculate the runoff and the TP load for each of the five subcatchments Qi 0 048 m s Li 0 0175 9 s C1 0 365 mg l Qo 0 022 m s Ly 0 00275 g s Q 0 073 m s L3 0 0388 9 s Qu 0 081 m s L4 0 0673 9 s Qs 0 077 m s Ls 0 0802 9 s Draw the hydrological profile for the main stream between 1 and Gauge conside
39. 295 1 ug l hypertrophic Chl a mean 4 5 ug l mesotrophic Chl a max 9 7 ug l Mesotrophic Compare and evaluate the five model runs The five models give more or less the same results The small lake would be hypertrophic without cleanup measures Realistic cleanup measures reduces hypertrophy to eutrophy only by the forecast of lake model no l Lake model No 5 gives the best response to cleanup measures Highest possible reduction and cleanup would still result in eutrophic state Note that the oversimplified wired in catchment model the non point load estimate according to land use proportions might be responsible for these unrealistically bad conditions This will be improved in the 3 version of this software when realistic detailed catchment models will be included 86 Exercise 9 Analysis of the nutrient budget of a drainage basin The task is to calculate estimate the total phosphorus load leaving the catchment shown below and calculate the effect of management alternatives A 34km forest 60 agri 40 urban 0 A 28km forest 100 agri 0 urban 0 A 38km forest 50 agri 40 urban 10 aoe ae A DW a eee on Cage ee AE Renee t een E T Se al Seneeaeeeenee A 30km forest 20 agri 70 urban 10 g tay aay mney ea t A 14km forest 0 agri 60 urban 40 Gauge Total catchment area A 144 km Annual mean r
40. 83 Modelling of Non point Source Pollution In Application of Ecological Modelling in Environmental Management Editor J rgensen S E pp 283 379 Elsevier Scientific Publishing Company Amsterdam Jolankai G 1986 SENSMOD A Simple Experimental Non point Source Model System Proc Int Conf Water Quality Modelling in the Inland Natural Environment Bournemouth England 10 13 June pp 77 92 Jolankai G 1992 Hydrological Chemical and Biological Processes of Contaminant Transformation and Transport in River and Lake Systems UNESCO series Technical Documents in Hydrology WS 93 WS 15 UNESCO Paris p 147 Jolankai G Ajkay R Biro I 1991 Regional Water and Water Quality Management Decision Support System for Large Lakes Phase I in Hungarian VITUKI Res Rep No 7611 1 2034 J rgensen S E 1976 An eutrophication model for a lake Ecological Modeling No 2 1976 pp 147 165 J rgensen S E editor 1988 Fundamentals of Ecological Modeling Elsevier Science Publishers B V Amsterdam J rgensen S E Harleman D R F 1977 Summary Report of the MASA Workshop on Geophysical and Ecological Modeling of Deep Lakes and Reservoirs Laxenburg Austria Dec 12 15 1977 Kelly R A 1973 Conceptual ecological model of the Delaware Estuary Manuscript Quality of the Environment Program Resources for the Future Inc Washington D C Kelly R A Spofford W O 1977 Application of an Ecosystem Model to Water Quality M
41. Co operation and Development OECD 1982 utilizing the data of a large number of lakes also grouping these lakes into several categories e g Alpine Nordic Shallow etc A sample relationship from this study was used for this CAL programme Estimate of trophic state is given together with the probability of its occurrence based on the same study An important note is that parameters of the original model equations were slightly altered in order to avoid copy right problems on one hand and not to allow the user to use this software for actual design purposes but for the teaching learning of the techniques only Experimental OECD lake model equations Eq 5 2 Chl mean 0 37 X Hin 0 74 X PP 22 9 x or PP iom 48 0 X Eq 5 3 Z P in 1 yt Legend Chl means Chlmax are the average and maximum in lake chlorophyll a concentrations in mg m PP is the primary production rate in the lake gC m yr X is the flushing corrected average inflow concentration of phosphorus Pin is the annual mean inflow concentration of total phosphorus in mg m and tw is the mean residence time of water in the lake year Note that the primary production PP sub model is not included in the software to keep uniformity as the rest of the models do not calculate this Further remarks Other empirical relationships of the OECD study included nitrogen versus phosphorus biomass and in lake nutrient concentrations transparency versus
42. D DO model the oxygen sag curve General description of the traditional oxygen sag curve In this model the decomposition of biodegradable organic matter is expressed as the first order decay of BOD termed here L in function of the time where time is the time of travel t x v by Eq 2 1 and 2 2 see also the basic theory chapter 16 The oxygen line the oxygen sag curve is written for the oxygen deficit D is such a way that oxygen consumed by micro organisms adds to the oxygen deficit while the process of aeration or reaeration the uptake of oxygen across the water surface due to turbulence and molecular diffusion reduces this deficit Equations 2 3 and 2 4 In these equations the initial conditions e g L Lo and D Dp at x 0 t to should be calculated using the Dilution equation Eq 1 4 The substitution of waste water and river parameter values is relatively straight forward in the case of calculating Lo Eq 2 5 while for calculating Do first the initial oxygen concentration should be calculated Eq 2 6 and the result of this should be subtracted from the saturation DO concentration to achieve Do Eq 2 7 The saturation dissolved oxygen concentration of the water is temperature dependent and the respective values can be obtained either from tables published in the relevant literature or from experimental expressions In this teaching aid we will use the latter method in the form of Equation 2 8 Wang et al ref Gro
43. Graph Trophic categories lolx Model parameters r Graph settings r Fixed boundary classification PLO ma m3 250 PSO mg m3 500 CO LakeP SedimentP C Chl mean mean P ma m3 115 5 Hypertrophic 4 gt 4 Time horizon years 8 Stop mean Chia mg m3 25 5 Hypertrophic La ophi n 0 80 PSeq mg m3 500 4 max Chla mg m3 70 7 Eutrophic Probability distribution vs meanP C vs mean Cha C vs max Chha 0 Ultra oligotrophic 0 Diigotrophic 4 Mesotrophic Chi max concentration in the lake water mg m3 alpha 1 50 d m 0 10 151 E ff s C Kset year 1 0 00 a 57 Eutrophic 39 Hipettrophic ayeart 1 051 Kscu yeari 0 98 ia t 0 80 Kbur year 1 1 96 Kset year 1 0 39 PLeq mg m3 124 Probabiity distribution for trophic categories GEDLING pists or Max CHI Eutrophic 10 Mesotrophic 5 Diigotrophic 7 8 100 1000 Time years P mean mg m3 hed Lake models Model No 4 P budget with simple Chia Practice Figure 17 57 Dynamic algae growth model Lake model No 5 Explanation In this model the dynamic phosphorus budget model Lake model No 3 is coupled with an algae growth model Figure 18 Algae growth is assumed to be limited by phosphorus and temperature Light limitation is assumed to be included in the temperature limiting function and the limitation by other pla
44. M Elsevier Scientific Publishing Co pp 593 599 Niemi J 1979 Application of an Ecological Simulation Model to Lake Paijanne National Board of Waters Helsinki Finland p 39 OECD 1982 Eutrophication of Waters Monitoring and Assessment OECD Publications Office Paris Orlob G T 1977 Mathematical Modeling of Surface Water Impoundments Resource Management Associate Inc Lafayette Cal U S Dept of the Interior Project T 0006 p 119 Porter S K editor 1975 Nitrogen and Phosphorus Food Production Waste and the Environment Ann Arbor Science Publishers p 372 Rechkow K H 1979 Quantitative Techniques for the Assessment of Lake Quality EPA 440 5 79 015 p 146 Rossi G Premazzi G 1991 Delay in lake recovery caused by internal loading Water Research Vol 25 No 5 pp 567 575 Salas H J Martino P 1991 A simplified phosphorus trophic state model for warm water trophical lakes Water Research Vol 25 No 3 pp 341 350 Shanahan P Harleman D R F Somly dy L 1986 Wind induced water motion In Modeling and Managing Shallow Lake Eutrophication editors Somly dy L van Straten G Springer Verlag pp 204 256 Shanahan P and Harleman D R F 1986 Lake Eutrophication Model Coupled Hydrophysical Ecological Model In Modeling and Managing Shallow Lake Eutrophication editors Somly dy L va Straten G Springer Verlag pp 256 285 96 Streeter H W Phelps E B 1925 A Stud
45. OD less than 6 mgO I Class II good Water consumption in Prettybrooks is 250 litre cap day in average and the estimated water losses of the system in the summer months evaporation gardening losses leakage of the sewer system etc is 20 The environmental authority supplied the following background data for the river for this critical period Background BOD concentration L 6 mg O l Background DO 7 mg O Estimated raw sewage strength BODs 550 mg Ov l DOs 1 5 mg l Stream velocity 0 4 m s a slowly flowing stream Mean depth of stream 1 3 m The river temperature in the summer months is 19 C Model calculations Calculate cross section area and stream width Calculate sewage quantity 0 15 m s Use the Traditional BOD DO model from the menu of the CAL programme Calculate the dilution equations Enter the above data You find L 12 716 mg l DO 6 937 mg l Check Saturation oxygen level You find DO a 9 36 mg l Initial D oxygen deficit 2 4 mg l Enter stream data and calculate K you find 0 65 day Consider Little Lousy river as a large slow stream for the calculation of K by entering K2 K 1 8 You find K 0 36 day correct for temperature Kp 0 35 day 66 Check the BOD decay curve and compare to limit values above Calculate the length of river over which the quality criteria would be violated You find that it falls below Class II at about 2 2 days time of travel and this corre
46. Ox Quasi 1 D river O 4 8K 8 Steady state river See the BOD DO model ak models river models SO E S internal fully mixed reactor type lake models pollutant spill model 0 D lake models T See the lake models 15 BOD DO River Models General Description of BOD DO river models BOD DO river models deal with the oxygen household conditions of the river by considering some of the main processes that affect dissolved oxygen DO concentrations of the water These models are of basic importance since aquatic life and thus the existence of the aquatic ecosystem depend on the presence of dissolved oxygen in the water All river water quality models and thus the BOD DO models can be derived from the general basic water quality model equation Eq 1 3 For some details of this derivation procedure see the Chapter on Basic Theory on water quality modelling and on the Chapter on the Derivation of simple practical models from the basic model equation The main process that affect deplete the oxygen content of water is the oxygen consumption of micro organisms living in the water while they decompose biodegradable organic matter This means that the presence of biodegradable organic matter is the one that mostly affect the fate of oxygen in the water There are internal and external sources of such biodegradable organic matter Internal sources include organic matter that stem from the decay death of living organisms aquatic plant
47. P A 0 05 F 0 1 MP 0 2 Ag 0 7 U m s Non point source load model Laps A 0 01 F 0 2 MP 1 5 Ag 2 5 U kg year Point source load calcualtion Lot 0 0864 Cp Qpe kg day Total load model L 365 Lpt Laps kg year Calculation of Pin Pin 0 03171 L Q mg m 46 3 Load reduction models The user may enter load reduction treatment factors as follows 10 90 treatment efficiency for point sources multipliers X p 0 9 to 0 1 of Lp load 10 60 reduction efficiency for non point sources X np 0 9 0 4 The load reduction model Lreduced Xrp 3 65 Lpt X np Lnps kg year Pin 0 03 171 Lreduced Q Figure 11 shows the results of the input load model indicating also the effects of load reduction measures 4 Water Quality Modelling CAL File View Window Help Citra was Pin mg m3 6044 Reduced Qin m3 s 0 427 Pin mg m3 4461 Lptka day 35 Lp kg day C Data to be entered Non point load estimate oi r Input load model a we Thart we Load proportions kg day inp multipie 0 80 Reduced Lpt kg day 14 Reduced Lnps kg day 15 1 Reduced load kg day 16 5 hed Lake models Input load model Figure 11 Remark In the final version of this CAL programme the input load will be calculated for all lake and where appropriate also for str
48. WQMCAL Description of the CAL programme on Water Quality Modelling Version 2 Basic river and lake water quality models with an outlook to ecohydrological applications Final report prepared by Dr G za Jolankai with contribution by Istvan Bird in the framework of the IHP V Projects 8 1 2 3 and 2 4 of the United Nations Educational Scientific and Cultural Organization financed by UNESCO Venice Office Budapest May 2000 This written material is the hard copy of the text and equations of a Computer Aided Learning CAL programme Most of the text therefore appears separately from the equations and this may make the reading through this hard copy a little cumbersome On the screen however the presentation is better harmonised as the author hopes It is also hoped that lucidity and understanding will be even more enhanced by the graphs of the actual model runs that the user can control The author also wishes to emphasise that the software and the models are not intended for use in practical work design water pollution control planning environmental impact assessment etc and serve solely for teaching purposes The author therefore also wishes to state that he does not assume any responsibility for failures faults or damages caused by such non intended use of the software This is a computer aided learning software CAL which has been prepared by G za Jolankai and Istvan B r for UNESCO in
49. actor type This means that no transport processes are considered The main reason is that the literature of lake modelling has proven that hydraulically based transport and transformation models cannot generally give significantly better or more realistic simulations of the water quality of lakes than those of the fully mixed reactor models or the chain of such interconnected fully mixed box models which latter can be used for simulating various interconnected basins or bays of the lakes or reservoirs Nevertheless the hydraulic equations of fluid motion are also given in Appendix I as general information but they are not used in this programme Another simplification was that this programme does not deal with deeper thermally stratified lakes or reservoirs but only with shallow lakes and reservoirs The main reason to this approach was to avoid complications which would result from the consideration of a high number of additional model parameters and coefficients In discussing the pollutant transformation processes of standing water bodies one eventually has to focus on the problem of eutrophication as one of the most crucial environmental problems of our era The word eutrophy is generally taken to mean nutrient rich Jorgensen 1988 and is used sometimes as contrasted to dystrophic ill nourished Baxter et al 1992 Eutrophication known also as the natural ageing process of standing waters has dramatically increased since
50. al 1975 Niemi 1978 Vincon Leite and Tassin 1990 Knoblauch 1977 J rgensen and Harlemann 1977 some of them considering also vertical transport processes across the termocline Stochastic approaches might be also applied or coupled with any of the conceptual and deterministic models Canale and Effler 1989 Some of the latest approaches claim the necessity of using the techniques of artificial intelligence for the interpretation and qualification of the complex hydroecological processes involved Guerrin 1991 For any quantification however one has to deal first with the definition or modelling of inputs of flow and material to the lake This will be done in a very simple model block see input load models A more detailed integrated catchment modelling block will replace this simplified block in the third next phase of the development of this software Note that inputs will be calculated for phosphorus only wit the assuming that the lake in concern is phosphorus limited This was needed for keep the models within relatively easily manageable controllable frames Next a separate or joint model block is needed for the hydrology or the water budget of the lake implying also the definition of the basic lake geometry parameters This will be done in the block Lake hydrology and regulation 45 Input load model for eutrophication models Description Input loads of phosphorus are calculated for the eutrophicatio
51. anagement The Delaware Estuary In Models as Ecological Tools Theory and Case Histories editors Hall C A S and Day J W Wiley Interscience Inc New York pp 420 443 Kerekes J 1983 Predicting Tropic Response to Phosphorus addition in a Cape Breton Island Lake Proc N S Inst Sci Vol 33 pp 7 18 95 Knoblauch A 1977 Mathematische Simulation von Stoffkreislaufen stehender Gewasser aufgezeigt am Phosphorkreislauf der Wahnbachtalsperre Vom Wasser Vol 49 pp 55 70 Kutas T Herodek D 1986 A complex model for simulating the Lake Balaton ecosystem In Modeling and Managing Lake Eutrophication with application to Lake Balaton editors Somly dy L van Straten G Springer Verlag pp 309 323 Lewis S Nir A 1978 A study of parameter estimation procedures of a model for lake phosphorus dynamics Ecological Modeling Vol 4 pp 99 117 Lorensen M W 1973 Predicting the effects of nutrient diversion on lake recovery In Modeling the eutrophication process editors Middlebrooks E J Falkenborg D H Maloney T E Ann Arbor Science Publishers Inc Ann Arbor Michigan Lung W S Canale R P Freedman P L 1976 Phosphorus Models for Eutrophic Lakes Water Research Vol 10 pp 1101 1114 Mahamah D S Bhagat S K 1983 Use and Abuse of Empirical phosphorus models in lake management In Analysis of Ecological Systems State of the Art in Ecological Modeling editors Lauenroth W K Skogerobe G V Flug
52. arm level to 0 78 mg l you find that it intersects the curve of 80 km distance at about 7 km earlier which corresponds to about 3 2 h time lag 74 How the measurement date of the Hungarian authorities at Tunyogmatolcs approximately 120 km from the source when they reported a maximum concentration of 30 mg l can be confirmed by this calibrated model very much the simulated value is 29 8 mg l How the measurement date of the Hungarian authorities at Olcsvaapati approximately 145 km from the source when they reported 25 mg l maximum concentration can be confirmed by this calibrated model It is likely that they slightly missed the peak because the simulated value is 27 1 mg l Finally note that cyanide is a highly toxic compound The international limit value is 0 1 mg l in streams used for drinking water production 75 Exercise 5 Analysis of transversal mixing cases A large industrial discharger seeks to have license from the environmental authorities It is characterized by the following data qo 0 85 m s C 656 mg l COD The case is very special since there are water intakes just 1500 m downstream of the planned source Thus the water quality limit value should be set to Class I 12 mg COD D Data of the recipient river are h 2 m B 160 m v 0 7 m s S 40 cm km do not alter the value of d in the programme Analyse the case with the transversal mixing model Note that this model calculates in s
53. asic theory of water quality models General description In logical order the teaching of this topic should have started with the description of both the quantitative and qualitative state of the water body Nevertheless the audience of such environmental engineering courses has preferably a strong background on hydrology and hydraulics thus introduction to quantitative hydrodynamic modelling techniques is skipped here The more so since even the basic flow modelling techniques would fill a separate curriculum in itself Nevertheless the user can have an insight to the basic equations of fluid motion in Appendix I The programme however does not utilise these equations see the respective equations in Appendix I Consequently in the following sections of this programme all hydraulic and hydrological river parameters e g rate of flow flow velocity stream depth and width etc will be considered as given input data In the lake modelling block however a simple hydrological catchment model and a lake water budget model are also included to allow for the calculation of runoff and runoff induced diffuse loads and for the regulation of the lake water level both of which have an important bearing on the concentrations of substances in the lake water Thus we will start with the introduction of the basic mass transport and transformation processes relying on continuity and conservation of mass considerations E eur E xtevy dx Figure 4
54. ate that they do not assume any responsibility for failures faults or damages caused by such non intended use of the software and the programme Content page GT WOU ac ide che hel cde EAA 1 MIE OCAUE TON sess sts oentestetcoeuetatste siisii iiis SEE sE SESSE EEEE ESEE EEEE EESE EEEE EESE 3 Basic theory t water quality MOdels 2515505550003 sstosstoato sen non nann nen e a a 6 Mass transport terms for deriving the basic model nsessseeseeseseesesseseesesseseeseseesessesesesseseesessesee 8 The mass balance equation of an elementary water body eceeceesececeeseeeeeeseeeeeeseeeseeeeeaeeneeeaes 8 The basic water quality model equation 3 cccscccscccsecescanccacenseeaceuacesccesecucuenceddcadccuddarsesndervexseencesnseadene 10 Derivation of practical models from the basic model CquatiONn sees eeeseeseeseeseeseeseeseeeeseeaes 11 The most simple water quality modeleren inneni EA EA EE a 12 Ehe sencera RelUELie rain Wels Ucc1 sha Wemeenemnn came arteeeren aye teeter E I IIA 13 BOD DO Rivyer Models rrr eisie e E EE EREE eer RRR iS 16 General Description of BOD DO river models seesesseseeseeeseseesesssesressresreserssresseserssresee 16 The traditional BOD DO model the oxygen sag curve ooo eeeeeeesececeteceenteeetneeeenaeeeaes 16 Expanded modified BOD DO river models cece eesceesteceeneeceeaeeceeneeceeeeeceeneeceeneeeesaes 25 DISPERSION RIVER MODES gai a a a A ae ees 32 The longitudinal dispersion model
55. ater level variation is allowed With this conditions specified the lake water budget model will run until one of the regulation limits are reached then Qou is automatically adjusted to be equal to z Qin Where z is a correction element to counterbalance the difference between precipitation P and evaporation E This means that Qout is increased when the precipitation onto the lake surface exceeds evaporation and the actual h equals hmax and decreased when it equals hmin The opposite correction is applied when evaporation exceeds precipitation Model equations Eq 5 1 dh 1 O P E dt A lo O Qu Ont z when A gt A maV h lt hmin z P E A Legend h is the lake depth m Qin Qout are the inflow and outflow rates of the lake respectively m year A the average lake surface area m PandE are the precipitation and evaporation onto from the lake surface respectively m year 48 Experimental lake model Lake model No 1 Explanation These methods of predicting the nutrient concentrations and the associated trophic state of standing waters rely on the use of statistically defined empirical relationship between a state variable and one or more independent variables characterising the lake s hydrological hydraulic and input nutrient load conditions Based on the original concept of Vollenveider 1969 the perhaps most well known set of tools have been published in a comprehensive study by the Organization for Economic
56. c equation there is a general term the internal source sink term or internal reaction term that should be also discussed in somewhat more detail They are also called the transformation processes with the meaning that the substance in concern is being transformed by various physical chemical biochemical and biological processes resulting in the change of the quantity of the substance in an elemental water body This change is either a loss or sink term caused by processes such as settling chemical biochemical decomposition uptake by living organisms or a gain a source term such as scouring from the stream bed product of chemical biochemical reactions biological growth that is the build up of the substance in concern on the expense of other substances present in the system The actual form of these transformation processes will be presented in relation to concrete model equations such as the BOD DO models the models of the oxygen household and the plant nutrient phosphorus transformation processes of the lake models Eq 1 3 oc oc oc oc ah ger Yoga tyz Ox Oy ot OZ 0 oc 0 oC 0 oC ac 210 ac gt T Jese YZ t Sintemal Legend C is the concentration the mass of the quality constituent in a unit volume of water mass per volume M L D Dy D are the coefficients of dispersion in the direction of spatial co ordinates x y and z surface area per time LT Vx Vy Vz are the components of the flow velocit
57. cation is almost exclusively due to the over enrichment of phosphorus and nitrogen that is the result of increased external nutrient loads from a large variety of point and non point sources e g communal and industrial waste waters agricultural runoff water residential urban runoff waters atmospheric fallouts onto the lake surface From the view point of the sources this problem will be discussed in the 3 version of the software which will be dealing with hydrologically induced transport and transformation processes of pollutants In natural lake ecosystems one or some of the plant nutrients mostly phosphorus sometimes nitrogen and much more rarely silicon are present in 40 so low concentrations that it they limit the growth of phytoplankton thus exercising control over the aquatic ecosystem as a whole This growth limiting factor was for the majority of lakes phosphorus or more precisely the bioavailable forms of phosphorus The bioavailable form the P form that algae can take up is either taken as orthophosphate phosphorus PO P or termed the dissolved inorganic phosphorus DIP or just the bioavailable phosphorus BAP which is meant to include more than one phosphorus forms DIP a certain fraction of TP DIP Before discussing the quantification possibilities of the set of processes briefly discussed above the first task is to construct a scheme or flow diagram of the state variables and processes of lake ecosystems as indicate
58. cause what actually happens is that the pollutant mixes with the water upon the above briefly described dispersive and advective transport processes These two models are 1 The one dimensional longitudinal dispersion model and its probably most interesting use is when one wishes to study describe simulate downstream propagating pollution waves upon accidental pollution events instantaneous inputs of larger masses of pollutants Ze The transversal mixing model when one wishes to determine the spreading of a pollutant plume downstream of an effluent outfall that is to determine the concentration distribution of the pollutant across the river at any cross section downstream of the effluent outfall The longitudinal dispersion model General description of longitudinal dispersion models The reader user is kindly requested first to consult the following topics Basic theory of modelling river water quality and the General description of dispersion river models The first is dispersion advection river model selected for the purpose of this CAL programme is termed here the one dimensional longitudinal dispersion model and its probably most interesting use is when one wishes to study describe simulate downstream propagating pollution waves upon accidental pollution events instantaneous inputs of larger masses of pollutants In constructing this model we consider the river as a linear system in which transversal and vertical tra
59. d in Figure 9 Inputs Outflow Sediment Figure 9 Figure 9 is obviously a much simplified scheme a model of the actual processes and focuses on two of the perhaps most important chains of processes These are the aquatic food web termed also the foodchain and the main processes of the oxygen household Verbally the main processes are as follows i The growth of algae phytoplankton is governed mostly by the availability of the two main nutrients P and N plus light and temperature ii Algae are consumed grazed by herbivorous or omnivorous zooplankton which is the food for carnivorous zooplankton and non predatory fish which latter is in turn the prey of predatory fish iii After death all living organisms contribute to the dead organic matter compartment termed detritus which forms the substratum for bacteria Organic matter originates from external sources too iv Decomposition of organic matter by bacteria includes a carbonaceous phase CBOD and a nitrogenous phase NBOD The latter is termed the nitrification process in which ammonia and amine compounds are oxidised to nitrite and then to nitrate by nitrifying bacteria Nitrosomonas and Nitrobacter respectively thus recycling the nitrogenous food for algae NO3 N from the dead organic matter There is some evidence that a fraction of the phosphorus content of particulate dead organic matter is also recycled by bacteria feeders into solubl
60. dasagi Kiad Budapest p 289 Golterman H L 1980 Phosphate models a gap to bridge Hydrobiologia Vol 72 pp 61 71 Gromiec M J 1983 Biochemical Oxygen demand Dissolved Oxygen River Models In Application of Ecological Modelling in Environmental Management Editor Jorgensen S E pp 131 218 Elsevier Scientific Publishing Company Amsterdam Guerrin F 19910 Qualitative Reasoning about an ecological process interpretation in hydroecology Ecological Modeling Vol 59 pp 165 201 Harleman D R F 1973 Transport Processes in Water Quality Control Lecture notes No 1 77 Massachusetts Institute of Technology Department of Civil Engineering 94 Hoare R A 1980 The sensitivity to phosphorus and nitrogen loads of Lake Potorua New Zeland Prog Wat Tech Vol 12 pp 897 904 Imboden D M Gachter R 1978 A Dynamic Lake Model for Tropic State Prediction Ecological Modeling Vol 4 pp 77 98 Jolankai G Sz ll si Nagy A 1978 A simple eutrophication model for the bay of Keszthely Lake Balaton Proc IAHS AISH Symp Modeling the Water Quality of the Hydrological Cycle Sept 1978 Baden FRG pp 137 149 Jolankai G 1979 V zmin s gi modellez s Water Quality Modelling in Hungarian In Vizminos gszabalyozas a K6rnyezetv delemben In Water Pollution Control in Environmental Protection Editors Benedek P Literathy P Publisher M szaki K nyvkiad Budapest pp 173 214 Jolankai G 19
61. ditions note that all these actions will appear as NPS reduction in your model also note that overall catchment management measures can hardly exceed an efficiency of 50 reduction not even at high costs Enter 10 mg l for La and 5 mg l for Ca Observe and make notes on the results You find that DO sag curve remains just above the Class II level and that BOD also drops below Class II over relatively short time distance Considering the fact that overall catchment management measures are very expensive and cumbersome to accomplish although this must be the final solution you may wish to investigate the effects of less efficient overall strategies Consider 20 BOD removal only You enter 0 8x20 16 mg l for Ld and you observe a small violation of DO targets Try to think in terms of some stream aeration measures there are many technical means for it to improve the situation The P R term of the model can be used for this Calculate how much oxygen input you need to achieve WQ targets You find that giving low values for P R you will get good results e g the model is very sensitive to this term Calculate the amount of oxygen needed for 0 15 gO m day input This is 52x86 400x0 15 673 92 kg oxygen per day Try to consider some hydraulic river aeration means by assuming the increase of river flow velocity and the decrease of flow depth turn back to the menu item K estimating Note that flow velocity and depth are interrelated
62. e and bioavailable form Porter 1975 41 although it is generally claimed that there is a net loss of phosphorus from the water column to the lake bottom v While the decomposition of organic matter depletes the dissolved oxygen content aquatic plants phytoplankton and macrophytes contribute to it by their photosynthetic activity However out of the photoperiod during the night their respiration also depletes the oxygen content Thus the net difference of photosynthetic oxygen production rate P and respiratory oxygen consumption rate R e g P R will define the role of aquatic plants in the oxygen household process vi There are external inputs to practically all compartments via point sources inflowing water and atmospheric fallout while losses via outflow flushing burial in the sediment and via harvesting of fish and aquatic weeds provide the other arms of the mass balance vii Several natural and man influenced factors such as pH water temperature water depth suspended solids transparency wind and or temperature difference induced currents wind induced turbulence etc affect the rates of the above briefly described processes There remains however a question to be answered and this is the classification of water bodies into classes of various trophic levels Below two approaches will be briefly presented In the eutrophication manual of OECD OECD 1982 the probability distribution of five trophic categories are
63. e model can be used for any non conservative substance provided that the assumption of first order reaction kinetics holds In the case of the transversal mixing model the user can set a critical value for the pollutant investigated the violation of which at a pre selected downstream distance renders the situation for example the installation of a water intake work hazardous The user is kindly advised again to consult the water quality standard for drinking water intake for example of his her home country in order to gain a realistic case when a pollutant is named In the case of lake eutrophication models the quality classes wired in are those of the OECD report OECD 1982 and are not to be changed since the probability distributions which gives the final evaluation e g the probability of a value representing a given trophic category also originate from this report 62 Exercises for using the programme for teaching learning Below exercises numerical examples will be given for each of the main model blocks of the software together with the solution and some explanation on how to reach the solution These are to guide the teacher student in creating similar examples for using this software Important note The cases to be analysed include certain names of towns rivers etc They are mostly fantasy names The exception is the accidental pollutant spill case where we used the real names of the recent February 2000 cata
64. e selected two models for inclusion in this CAL programme The criteria of selection was that the model should take many or most of the above processes into consideration for the first model and it should also consider longitudinally varying flow and with this non point source external loads for the second model It is to be noted that we did not consider models that deal with dispersion and mixing since such models will be separately discussed later on 25 The first expanded BOD DO model General description of the 1st expanded BOD DO model This expanded BOD DO model is the modification of the traditional oxygen sag curve model and therefore the user should get acquainted with the General introduction of BOD DO models the General introduction of the traditional oxygen sag equation and the General introduction of the Expanded BOD DO models The first expanded BOD DO model selected for this software was developed by Camp 1963 and it involves the following processes in addition to the decay of organic matter BOD decay and reaeration Sedimentation of biodegradable organic matter Benthic oxygen demand e g the diffuse source of BOD represented by the decay of organic matter that had settled out earlier onto the channel bottom Internal oxygen source represented by the photosynthetic activity of aquatic plants In this case one should note that the term accounting for this process in the model is rather the balance be
65. e ye seisteanenia us iarahaeia ahaa ahaa eee aMaiNs 91 REFETENCES cela ha lor uh io hr a do fora hfe ha a fou ve bya for chabaudi Dha ere dhe bedi 94 Appendix I Pollutant transport processes in lakes cece eeeeeseeseeseceeeseeneeecseeseeseeseeseeseeseeneenes i Description of the CAL programme on Water Quality Modelling Basic river and lake water quality models Foreword This programme is the second extended version of the former computer aided learning software WQMCAL version 1 1 UNESCO series Technical Documents in Hydrology NO 13 SC97 WS 80 which has been prepared by the same authors for UNESCO in the framework of the IHP IV Project on the preparation of didactic materials in hydrology CAL to aid university teachers and students in teaching respectively and learning the basis of river water quality modelling This present CAL version which includes lake eutrophication models with an outlook to ecohydrological applications was made in such a way as to fit into the frames of UNESCO IHP s Ecohydrological programme Projects 2 3 and 2 4 of IHP V The basis or rather basics of river and lake water quality modelling means for the purpose of this programme and software 1 General theoretical background Basic theory 2 BOD DO models the traditional oxygen sag curve and two more sophisticated versions 3 Dispersion advection models a one dimensional pollutant spill model version and a 2D transversal mixing model
66. eam models with the help of a series of catchment modelling options Of these the first model will be similar to that wired in but not shown into this CAL using runoff coefficients and unit area loading rates for the various land use forms as specified also in this model block The most sophisticated one of these future models will be a kind of GIS based digital raster map based runoff and load calculation programme This will be an important part of the 3 version of this CAL as non point sources tend to dominate the pollution processes of our era 47 Lake hydrology regulation model Explanation In this model block the user defines the area A of the lake assuming that it does not change with the depth The initial water depth h at the start of the simulation is also given and the lake volume is calculated as V A h The water release rate Qout is specified it shall be higher or lower than Qin when the operator wishes to rise or sink the lake s water level respectively The discharge capacity of the outflow structure Qoutmax Shall also be given Note that for the two simple lake models 1 and 2 Qout Qin Where Qin is the inflow rate as was calculated or given in the input load modelling block For the rest of the models Qoutmax gt Qin aS regulation is only possible when the adjustable rate of outflow is higher than the inflow Regulation water level options shall be confined by giving hmax and hmin the range within which w
67. ecursively interactive hydrological and ecological processes of aquatic ecosystems in which the basics of lake eutrophication models can represent the essential very first step from the environmental engineering point of view Conceptual scheme of Ecohydrological processes with the indication of pollution sources Atmosphere air pollution land pollution anthropogenic wastes interception processes overland flow Terrestrial runoff ecosystem evaporation precipitation wet and dry deposition evapotranspiration erosion solutes filtration material uptake control of flow and water levels water pollution water abstraction transport Land and stream channel V Water Ecotons filtration uptake sedimentation resuspension advection capillary rise pollution infiltration I l i gol E l dispersion transport transformation unsaturated zone m Nn Aquatic adsorption desorption Ecosystem fa aie baseflow exfiltration rise of watertable pollution front percolation groundwater interaction with shallow solute transport groundwater groundwater storage long term storage of contaminants deep percolation Deep groundwaters One should also understand that the protection of the aquatic environment and within this the control of pollution is a profession and not an easy one A profession like designing a house a bridge a road or just the making of a pai
68. ed boundary and by the probability distribution You obtain eutrophic conditions with the exception of mean P for the fixed boundaries 101 8 hypertrophic and eutrophic conditions for the probabilistic classification Thus you have improved the trophic state by about one category Check whether the theoretically achievable best technology 90 point source and 60 non point source reduction could help You still remain in the eutrophic range Note that unfortunately it is a realistic scene and eutrophic conditions remain even after a major cleanup in cultivated agricultural land Switch over to the non point source estimate programme in the input model block the catchment model which calculates on the basis of fixed literature ranges runoff load on the basis of land use data to be entered Set up a realistic land use distribution e g 30 forest 50 agriculture 15 meadow and 5 urban land Try to achieve the same inflow 3 8 m s by adjusting precipitation Do not forget to enter the data for the catchment area Keep the point source load value 50 kg day unchanged by entering concentration Cpt and flow Qpt data for the point source Note that the 79 phosphorus concentration value of municipal point sources is several thousand ug l Vary precipitation in such a way as to obtain the same inflow Qin Cpt 2000 ug l Qpt 0 290 m3 s Lpt 50 1 kg day Prec 670 mm Qin 3 796 m3 s Set back cleanup factors to 1 0
69. ed for the purpose of this programme and thus serve solely for teaching learning purposes We wish you success in your teaching learning programme 63 Exercise 0 Design of sewage treatment efficiency a task which can be solved without any environmental engineering knowledge The village of P r ske is in the valley of the River Abakoppany The multiannual mean flow of the river is 3 0 m s Population of P r ske is 6000 The daily average water consumption is 250 litre capita day Water utilisation the water spent for watering gardens watering animals etc is 20 Sewers are built in the village and they plan the construction of a sewage treatment plant The local government also wishes to construct a small recreational reservoir downstream of the site of the planned effluent discharge Licensing getting the permit for constructions is under way but the local authority has to prove that the aquatic environment of the to be reservoir will not be impaired by the sewage discharge Thus the sewage treatment plant should be designed for phosphorus removal too in order to avoid eutrophication To achieve this the concentration of phosphorus in the inflow to the planned reservoir should meet the Class I water quality standard for phosphorus total phosphorus concentration TP smaller than 40 mg m We also know that the average TP of household sewage water is about 10 mg l C 10000 mg m and the TP concentration of the unpolluted river u
70. eglect for the time being all terms accounting for dispersion With this we assume that the system is fully mixed which means that any external material input load to the river or lake will be instantaneously and fully mixed with the water This is a very rough approximation and its consequences will be discussed in a subsequent sections dealing with dispersion and mixing problems However this approximation holds for long linear systems e g in the case of smaller rivers with continuous steady input loads waste water discharges It also holds or must be assumed for most of the lakes since neither measurement data of lake currents nor the spatial distribution of water quality monitoring points will usually allow the consideration of dispersion effects b In the case of a river let us average flow and concentrations over the cross section The only velocity component which remains in the basic equation is then v the average longitudinal flow velocity C In the case of a lake a standing water body neglect flow velocities and consider the water body fully mixed the fully mixed reactor concept In this case there remains only the internal source sink term on the right hand side of the basic equation Eq 1 3 d Consider one single water quality constituent with its concentration C and assume that it is subject to internal processes like decay decomposition and settling Assume that this process is proportional to the concentrat
71. els can be calibrated against long records of past measurement data This means that parameter estimation sub models are also built in into the software Nevertheless the user will be allowed to change some of the parameters of this parameter estimation submodels like the assumed retention ratio parameters see later This was needed in this software to keep the models running as a free choice of reaction rate parameters would certainly result in the blow up of the models 44 Quantification of transformation processes in standing waters The quantification of lake processes described in the general introduction of lake ecosystem processes can be made in a large variety of ways starting with experimental and empirical relationships Vollenveider 1969 Chapra 1975 OECD 1982 and other simple nutrient mostly phosphorus budgeting type approaches Lorenzen 1975 Lewis and Nir 1978 Chapra and Canale 1991 Salas and Martino 1991 Rossi and Premazzi 1991 through various phosphorus phytoplankton models Thoman et al 1974 Imboden and Gachter 1975 Jolankai and Sz ll si Nagy 1978 Larsen and Mercier ref Orlob 1977 Jolankai 1991 and multiparameter dynamic lake ecosystem models J rgensen 1976 Di Toro et al 1977 Kelly and Spofford 1977 Kelly 1973 Bierman et al 1980 Di Toro and Conolly 1980 Kutas and Herodek 1986 Park et al 1974 including the multilayered epilymnion hypolymnion models of deep lakes Lung et
72. en in the river ML e g mg O l DO is the dissolved oxygen content of the waste water ML Q discharge rate of flow of the river upstream of the effluent outfall L T q the effluent discharge CTY 21 The initial oxygen deficit equation This set of equations is used to calculate the initial oxygen deficit of the water downstream of a point source sewage discharge as compared to the saturation dissolved oxygen concentration which latter is temperature dependent For more details see the Basic theory the General description of BOD DO river models and the General description of the traditional oxygen sag curve Eq 2 7 Do DO a DOo mgO litre Eq 2 8 DOgat 14 61996 0 4042 T 0 00842 T 0 00009 T Legend Do is the initial concentration of dissolved oxygen deficit in the river downstream of the effluent discharge point ML e g mg O7 1 DO is the initial concentration of dissolved oxygen in the river downstream of the effluent discharge point ML e g mg O7 1 see also Eq 2 6 DO a is the saturation oxygen concentration of water T is the water temperature C 22 Critical values of the oxygen sag curve This set of four equations is used to compute the lowest dissolved oxygen concentration highest oxygen deficit in the river water downstream of a single source of sewage water along with the corresponding time of travel and downstream distance For more details see the Basic
73. er values are available e g they are used for trying to explain unaccounted differences between measured and calculated in stream data That is when an observed BOD DO profile can not be simulated with reasonable parameter values of K and K then parameters B P and K can be used to account for unknown internal sources or sinks in a trial error manner 26 The first expanded BOD model These equations the differential equation and its solution describe the decomposition of organic matter BOD decay its sedimentation and the benthic source of it See also General introduction of BOD DO models the General introduction of the traditional oxygen sag equation and the General introduction of the Expanded BOD DO models Eq 3 1 dL qo Kit KB Eq 3 2 B B Delt K K t Lu GK OPE MK Ko K K Legend L is BOD in the water M E g O m Lo is the initial BOD in the stream downstream of the waste water discharge see also Eq 2 5 K is the rate coefficient of biochemical decomposition of organic matter T usually day K3 is the rate constant for BOD removal by sedimentation T usually day B is the benthic oxygen demand the rate of BOD addition to overlying water from the bottom sediment M T L usually gO m day t is the time of travel t x v expressed in days 27 The 1st expanded oxygen model The model describes the variation of the dissolved oxygen deficit of the water with the
74. es of lake models Simplified models Vertical or longitudinal Vertical plane horizontal single layer Circulation models Real 3 D multilayer Ekman type There are three basic reasons why we had to make this choice a Results of the literature dealing with the comparison of hydraulically based lake eutrophication models with the fully mixed reactor type chain of fully mixed reactor type models indicated that the latter gives fairly good approximation of the former Paul 1976 Shanahan and Harlemann 1986 That is hydraulic transport models would not significantly improve the simulation and prediction capability of 0 D eutrophication models b Usually available water quality monitoring and flow pattern data bases do not allow real spatial differentiation of the processes At the most one has information on the quality of various bays of larger lakes This latter can be well approximated by a chain of fully mixed reactor models C The transformation processes relevant to lake eutrophication are complex enough to form the subject of a teaching aid on the basics of lake modelling Several options are available even for modelling the basics of nutrient budget and nutrient algae growth models as will be indicated by the model blocks included in this software Important remark In the lake models shown below a built in mechanism cares for all state variables reaching an equilibrium state This mechanism kind of assumes that the mod
75. etention ratio of phosphorus that is r 0 8 for 20 retention while in the second one use K the retention rate coefficient with time dimension Combine the two equations and derive the K f q r relationship This relatively difficult task is for you to check whether you fully understood the mass balance concept and the meaning of the retention rate The formula that relates washout rate q to the retention ratio r 0 8 in the assumed case is derived as Q V Pin K Peq Q V Peq dividing the equation by Pin q rK rq from where K q rq r or K q r 1 r for the given case Calculate the load reduction efficiency that would be required for achieving the above defined water quality class with the new reduced retention rate K20 LPciass m lt 0 2 0 1892 0 047 0 047 sseeeesees Jm year What overall load reduction efficiency would be required to achieve this load NS esee 70 The required load reduction is X 0 152 0 047 X 0 31 and this corresponds to about 70 reduction of the load from the catchment Calculate the feasibly achievable load subject to the following considerations Assume that 15 and 10 of the total load originated from direct and indirect point sources respectively while the rest is non point source runoff load Check whether the overall removal rate can be achieved or not if your feasible management strategies allow 80 60 and 40 removal efficiencies for direct point sources
76. f these latter processes is caused by pulsating motion that is by the Brownian thermally induced motion of the molecule molecular diffusion and by the pulsation of the flow velocity around its mean value caused by turbulence called the turbulent diffusion The dispersive mass transfer Ex Ey E has the dimension of mass per time per area M die Bag and it is usually expressed by the law of Fick which states that the transport of the substance in a space direction is proportional to the gradient of the concentration of this substance in that direction the proportionality factor being the coefficient of dispersion as shown in equation 1 1 Mass transport terms for deriving the basic model These equations describe the dispersive and advective transport of a polluting substance from the x direction into an elementary water body The first term is actually the law of Fick which states that the diffusive dispersive transport of the substance in a space direction is proportional to the gradient of the concentration of this substance in that direction the proportionality factor being the coefficient of dispersion The user finds more information on dispersion in the general part of this basic theory chapter and on the programme part on dispersion river models The second term is the advective transport term which states that the specific per unit area transfer of mass to a spatial direction is the product of the concentration of
77. he Test menu What are the main source and sink terms of oxygen in the BOD DO process models Sources aeration reaeration caused by aerating devices such as aerator rotors and motorboat propellers Sinks photosynthesis by aquatic plants and the BOD decomposition Sources Reaeration across the water surface and the photosynthesis of aquatic plants Sinks Oxygen uptake by micro organisms while they decompose organic matter benthic oxygen demand and the respiration of aquatic plants Sources turbulence and wave motion plus molecular diffusion plus photosynthesis Sinks BOD decay process plus respiration of aquatic plants plus benthic oxygen demand correct answers use the Test menu What are the best ways of estimating model parameters such as K4 K2 DL Dm etc Selection of the most reliable experimental expression from the relevant literature Calibration of the respective model by fitting it to series of field measurement data Measurements should cover most changes of ambient conditions e g ranges of flow velocity and water depth temperature etc variations Using literature defined ranges tabulated values of the respective parameters correct answer use the Test menu What is simulated described by the Longitudinal dispersion model presented in this programme Concentration vs time curves in different cross sections of the river downstream of an instantaneous pollution source of pollutant mass M The longitud
78. he one where you wish to know the shape of the plume and the numerical concentration values at the river banks Cl concentration at the left bank Cr concentration at the right bank Note that when you select a very small distance downstream of the source as the modelled reach the concentration distribution curves might become erratic Also note that when you pull out the pipe from the river bed yo with negative values or larger than the river width B the model can not be run and you hear and see warning signals see Figures 8 a and 8 b a schematic view of the pollutant plume and its computer realisation the screen outprint of the software 37 Concentration C Distance x River flow Figure 8 a Water Quality Modelling CAL Graph Mixing model e x ile Vie iow Help la x Click to practice gt Epsy estimation Mixi Both Mixing model parameters CO mg l 250 Highlighted curve at 850m q0 m3 s O65 4 iH hi a Distance 8500m ym io L Ww Epsy m2 s 0 031 Transversal Mixing Model 01234567 B 8 1011121314 15 1617 1819 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 BO Distance from left bank m Dispersion river models Transversal mixing model Practice Figure 8 b 38 Eq 4 5 OC ac ac at ay ox Eq 4 6 m 9 9 262 Cx y Coo 5 a y 2n yy rel y 2nt y
79. hication with experimental regression models based on the OECD study A lake of 10 km area and 5 meters average depth has a drainage area of 100 km The multiannual average runoff is 94 6 mm Calculate inflow to the lake Q 0 3 m s Scarce data indicate that the multiannual average inflowing phosphorus concentration is very high Pinean 800 ug l Use the following experimental equations Mean chlorophyll a concentration mg m Chl amean 0 37 X Maximum Chl a concentration ug l Chl amax 0 74 X Primary production gC m year PP 22 9 X or PP 589X 48 X where X Pinflow 1 for and Pinflow average concentration of phosphorus in the inflow mg m t mean residence time of water in the lake in years average lake volume per average inflow Calculate the values E ZO etc year ae 242 Necciteietetias mg m Chl amean DE Snina mg m ie ee eee 98 1 mg m PP 617 5 491 Josssie gC m year Compare results with the following categories Table 1 Fixed trophic state categories of the OECD study 1 Trophic categories Indices of trophic state mg m Ultra oligotrophic 11 Trophic state categories Hungarian guidelines Felfoldy 1987 Degree of trophity Primary Algal count Chlorophyll a production gC m year 10 litre mg OAutrophic J 0 f 0 f O This means that the expectable state is hypertrophic or eu polytrophic polytrophic for primary production
80. his CAL programme we have rather arbitrarily selected a range of K for a most common parameter the COD For the estimation of D the literature offers a wide choice of experimental expressions that express Dx sometimes termed also D the L standing for the word longitudinal in function of the hydraulic parameters of the stream the slope S the hydraulic radius R the flow Q the shear velocity u the stream depth h and the channel width B and combinations thereof that affect turbulence which in turn mostly determine the process of dispersion Nevertheless when testing the available experimental expressions with real stream data the obtained values of D vary within an order of magnitude or even more This means that the only reliable method is to make field measurements tracer studies and or analysis of the data of actual pollution incidents both being rather cost and labour intensive experiments For the purpose of this CAL programme we have selected a formula the McQuivey Keefer formula which yield D values in about the middle of the range over which the results of other expressions vary Eq 4 3 33 The accidental pollution wave model This model a special case of longitudinal dispersion models describes the downstream propagation or travel of a pollution wave interpreted as a series of time vs concentration curves in selected downstream sections of the river at different distances x downstream of an accidental p
81. his equation is used for the estimation of the value of the reaeration rate coefficient K in function of the flow velocity and flow depth Note that this equation have been generated for the purpose of this programme and thus it differs from the many other formulas offered by the relevant literature For more details see the General description of BOD DO river models and the General description of the traditional oxygen sag curve Eq 2 13 Ko L 2 148 a be 48 23 Legend K2 is the reaeration rate coefficient the rate at which oxygen enters the water from the atmosphere day v is the average flow velocity in the river reach m sec H isthe average depth of flow over the river reach m Temperature correction formula for K This equation is used for the correction of the value of BOD decomposition rate coefficient K in function of the water temperature Note that this formula has been selected for this programme from among the many others offered by the relevant literature Also note that in the computer programme there is a built in algorithm that guides the selection of the value of K at 20 C temperature in function of the type and size of the river and of the already calculated value of Ky For more details see the the General description of BOD DO river models and the General description of the traditional oxygen sag curve Eq 2 14 Ki Kiewo 0470 Legend Kip is the value of rate coefficient K at water te
82. his model estimates the value of the dispersion coefficient Dx in function of the rate of flow the slope of the water surface and the river width The formula was chosen for the purpose of this CAL programme solely from among the many other ones offered by the relevant literature Eq 4 3 2 D 0 005394 L 1 SB sec Legend Q is the stream flow m s S is the slope of the water surface dimensionless eg in meter per meter B is the width of the stream m 35 The transversal mixing model General description of transversal mixing model The reader user is kindly requested first to consult the following topics Basic theory of modelling river water quality and the General description of dispersion river models One of the most frequently encountered practical use of dispersion mixing models is when one wishes to determine the spreading of a pollutant plume downstream of an effluent outfall that is to determine the concentration distribution of the pollutant across the river at any cross section downstream of the effluent outfall It can usually be assumed that vertical mixing takes place immediately It is also assumed in many cases that the transversal advective transport can be neglected or rather its effect is incorporated in the value of the transversal mixing coefficient This is needed mostly because there are no measurement data available for the transversal component of the flow velocity vector With this assumpti
83. ign the treatment efficiencies needed for meeting the limit values Make the following calculations 1 Calculate manually the BOD and DO concentrations for the section of the River Shallow Rapids just upstream of its confluence with the river Shiny Duck calculate values for the 27 km distance Also calculate the critical DO levels and their locations checking that whether they would occur within this 27 km or not Use the CAL programme or calculate all parameters manually using the manual of the CAL programme Equations 2 2 2 14 Ky 0 19 day 1 DOicri 5 37 Mg O2 1 BOD at 27 km 10 54 mg Oz l DO at 27 km 6 27 mg Oo l 2 Repeat the calculation with the data of Black Ferry and Shiny Duck River for the section upstream of the confluence 20 km Ky 0 45 day K 0 65 MENS day X2crit 90 45 KM te it 1 46 days not falling into the reach DO derit 4 44 Sea s mg O l BOD at 20 km 9 80 mg Oz l DO at 20 km 5 16 mg Oo l 3 Calculate the BOD DO conditions of the Shallow Rapids river reach downstream of the confluence of the Shiny Duck river Use again the dilution equation consider the Shiny Duck river as the effluent using the above calculated BOD and DO data Ky 0 29 day K3 0 42 T day X3crit 76 KM terit 1 76 days 4 Calculate the effect of 80 BOD removal at both treatment plants on the BOD DO conditions of
84. inal concentration profile of a pollutant upon the effect of an accidental input of pollutant mass M Pollutant concentration distribution curves across the river downstream of a source of accidental mass input correct answer use the Test menu What is simulated described by the Transversal Mixing Model presented in this programme Transversal and vertical concentration distributions of a pollutant downstream of a continuous source of that pollutant Depth averaged transversal concentration distribution curves of a pollutant downstream of its continuous point source The distance where full transversal mixing of the pollutant with the stream takes place correct answer use the Test menu 92 11 S v anoop _ 2 S v anoop What is the process of eutrophication Excessive growth of aquatic vegetation due to increased input loads of organic matter Processes due to the enrichment of water in plant nutrients Excessive growth of aquatic vegetation due to increased input loads of inorganic plant nutrients Processes due to increased temperature increased organic load and increased irradiation correct answers use the Test menu What can control limit the growth of algae Concentrations of organic matter phosphorus and other nutrients Either phosphorus or nitrogen Phosphorus nitrogen light and temperature Phosphorus nitrogen light temperature and long list of other elements which latter are us
85. ion PL 210 ug l hypertrophic Probabilistic evaluation highest probability hypertrophic with 74 probability Make a clean up Use realistic removal rates 80 for point sources X rp 0 2 and 40 for non point sources X mp 0 6 Fixed boundary evaluation PL 108 9 ug l hypertrophic Probabilistic evaluation highest probability eutrophic with 59 probability Check whether the theoretically achievable best technology 90 point source and 60 non point source reduction could help Fixed boundary evaluation PL 71 2 ug l eutrophic Probabilistic evaluation highest probability eutrophic with 63 probability Thus you have highly improved the conditions but the lake still remains eutrophic Check whether the ever reported best phosphorus retention 70 could improve the situation this is the lowest wired in limit value for r r 0 3 Fixed boundary evaluation PL 30 5 ug l mesotrophic Probabilistic evaluation highest probability mesotrophic with 63 probability Check what retention value would be sufficient for staying in the mesotrophic range r 0 34 You may repeat the same example with the 3 Jake model with sediment interaction you shall achieve the same results 83 Exercise 8 Lake eutrophication analysis with the dynamic algae P lake model of the CAL programme Lake model No 5 Note that in this model the number of parameters is already so high that you might not be able to fully reconstruc
86. ion of the constituent the pollutant and the coefficient of proportionality is K the decay decomposition settling etc rate coefficient Assumption of first order reaction kinetics When considering a river of steady state conditions with flow of the river and input material loads into the river not varying in time then we have arrived at the practically identical river and lake models of the form given in equations Eq 1 4 and Eq 1 5 Note that with these assumptions t x v the time of travel for the river this making the two equations identical 11 The most simple water quality models The most simple river model Vx KC dx The most simple lake model aC __ Ke dt where C is the concentration the mass of the quality constituent in a unit volume of water mass per volume M L vx is the mean flow velocity of a river reach investigated L T K is the reaction rate coefficient for first order kinetics T t is the time of travel interpreted as t x v x the distance downstream L Practically all water quality model equations used in the everyday practice can be derived in a similar way by adding one or more dispersion and advection terms and by coupling the reaction processes when more than one interacting water quality constituents pollutants are concerned This latter coupling of reactions is the key action of constructing water quality models and these techniques will be discussed when actuall
87. ion ratio of phosphorus in the lake 54 Figure 15 shows the screen outprint of the results of lake model No 3 w Water Quality Modelling CAL RHE STOP Model parameters PSO mg m3 500 Im E PSeqg mg m3 500 d m 0 10 PLO mg m3 250 r 0 80 alpha 1 50 Kset year 1 0 00 _ qyearl 1051 r 0 80 Kset year 1 0 39 PLeg mg m3 124 Kscu year 1 0 98 Kbur year 1 1 96 J Graph Lake model result r Graph settings C LakeP Sediment P Time horizon years g PS E3 _ Graph Trophic categories r Fixed boundary classification 115 5 Hypertrophic mean P mg m3 mean Chl a mg m3 Not calculated max Chla mg m3 Not calculated 750 700 650 600 550 500 Total Pigeneentison ithe sediment ma ms vs meanP vs mean Chia vs max Chia 0 Ultra oligotrophic 0 Oligotrophic 4 Mesotrophic 57 Eutrophic 39 Hipertrophic Probability dstibution for trophic categories hoo 95 aol 854 80 754 704 65 60 he 50 454 30 5 204 15 104 5 7 8 ya 10 700 1000 Time years P mean mg m3 Figure 15 55 P budget model coupled with experimental eutrophication model Lake Model No 4 Description One step forward in eutrophication modelling is when the nutrient budget m
88. ional model Fi File View Window Help 16 x Wait BOD model parameters LO mg 24 6 tcrit day 1 35 K1 1 day 0 30 mg02A Decay Curve 24 23 22 21 b i 2 3 4 5 6 7 8 3 io 1 12 3 14 i z3 BOD DO river models Traditional Oxygen Sag curve Decay equation Figure 5 The dissolved oxygen model The traditional dissolved oxygen model describes the fate the sag of the dissolved oxygen in the river as influenced by the decay of biodegradable organic matter and the reaeration process across the water surface For more details see the Basic theory the General description of BOD DO river models and the General description of the traditional oxygen sag curve Eq 2 3 K L kK D Legend D is the oxygen deficit of water g 02 m see also equations 2 7 and 2 8 L BOD in the water g O m K is the rate coefficient of biochemical decomposition of organic matter T usually day K2 is the reaeration rate coefficient T t is the time that is the time of travel in the river interpreted as t x v where x is the distance downstream of the point of effluent discharge The Oxygen Sag Curve model The traditional oxygen sag curve model describes the fate the sag of the dissolved oxygen in the river as influenced by the decay of biodegradable organic matter and the reaeration process across the water surface For more details see the Basic theory the
89. la Cvs meanP C vs mean Cha ivs max Chla 0 Ukra oligotrophic 0 Ulta oligotrophic 0 Ultra oligotrophic 0 Oligotrophic 0 Oligotrophic 0 Oligotrophic Z Mesotrophic 5 Mesotiophic 1 Mesotrophic E1 Eutrophic 50 Eutrophic 34 Eutrophic 31 Hipettrophic 44 Hipettrophic 64 Hipertrophic Probability distribution for trophic categories Probability distribution for trophic categories Probability distribution for trophic categories 1000 100 1000 100 1000 P mean mg m3 Average Chl a mg m3 Maximum Chha mg m3 ge Lake models Classification of water bodies peg Lake models Classification of water bodies eB Lake models Classification of water bodies Figures 10 42 The OECD study also presents a table showing the fixed categories of eutrophication The evaluation according to the fixed categories also appears in the heading of the trophic state evaluating screen Figure 10 above Table 3 Fixed trophic state categories of the OECD study 1982 Mesotrophic 10 30 2 5 8 0 8 0 25 ae ae Where P_ is the annual mean concentration of total phosphorus in the lake water Chlmean Chlmax are the mean and the maximum annual chlorophyll a concentrations in the lake water a measure of the phytoplankton e g algae concentration Felf6ldy 1987 presented a fairly detailed categorization of the trophic state on the basis of three parameter
90. lake surface respectively u is the growth rate of algae Umax is the maximum growth rate of algae Kp is the half saturation constant for algae growth P concentration at which the growth rate is half of the maximum TEMPLIM is the temperature limiting function 1 gt TEMPLIM gt 0 a function of the water temperature q is a proportionality factor between algae biomass and chlorophyll a set for the model as that of the recent average of the Keszthely Bay of Lake Balaton Hungary Chl a Chlorophyll a concentration Models of parameter estimation Explanation In order to keep the model parameters within realistic ranges they are estimated on the basis of certain assumptions The first assumption is that the model can be calibrated against measurement data of stabilised equilibrium state of the lake or data of an assumed planned state For the estimation of the parameters of the phosphorus budget part of this model see there lake models nos 2 3 For the algae growth model the half saturation parameter K is estimated with the assumption that at a very low phosphorus concentration for which we suggest the use of the upper limit value of Class I TP concentration and wired in the value of the Hungarian water quality standard the growth rate will be one tenth of the maximum growth rate or lower For the lumped algae loss rate coefficient K only a relationship with the maximum growth rate max can be derived for the known or plan
91. low to and outlet from the standing water body wind induced currents including wave motion and the pulsating turbulent motion caused by seiche wind setup density currents in deep thermally stratified lakes While inflow and outlet induced throughflow currents are of significance mostly in river impoundments and density difference dependent currents might be of interest in deep stratified lakes wind induced currents dominate the flow pattern in many or most of the lakes The transport of pollutants in lakes and reservoirs can be only described along with the description of the motion of fluid as caused by the above effects The conservation of momentum equation expressing the acceleration of fluid in a three dimensional space is written as 1 a O O O O 1 OP Ov O Ov Ye Vz ty Ye by WLT ope ifon a Exy v len X Fa Fo Ot Ox Oy OZ pox Ox x Oy Ov amp Oz 1 b O ee ee ee ee ee ee 2 y 7 ty 2 y 2 QOy E yx T Eyy 2 T Eyz a Fs Foy Ot Ox Oy Oz p oy Ox Ox Oy Ov O amp Oz 1 c Ova Ove Vra Sais 1 Ln ans eu 2 an a x22 F Oz pz p OZ ox ox oy Ov Oz Oz The corresponding equation of continuity for an incompressible fluid is 2 Ov Ovy v Ox Oy amp z 0 Next the transport process can be described by the conservation of mass equation similarly to Eq 1 3 3 oC oC oC OC Vx y y t x lay dz 2 p 2e 2 D oC
92. m acceleration caused by pressure forces Sixth left hand side terms Equations 1 a and 1 b acceleration caused by the Coriolis force due to the rotation of Earth First to third right hand side terms acceleration of fluid caused by the combined effects of viscosus friction forces and turbulent fluctuation forces with the assumption that the Boussinesq approximation of Reynold s stress terms is valid Sixth left hand side term Eq 1 c vertical acceleration of fluid caused by gravity force terms of the mass balance equation Eq 3 have been explained previously see Eq 3 in the main text For more details of the derivation of the above equations the reader is advised to consult the respective literatures Orlob 1977 Harleman et al 1972 Bengtsson 1978 Clements and Schnelle 1969 Although the above equations provide a fairly general description of the temporal and spatial variations of fluid properties there exist more general approaches for example when the variations of fluid density p f x y z t are also considered appendix ii In actual practical applications the choice of the lake circulation and material transport model depends on the problem to be solved and on the physical chemical and biological characteristics of the water body concerned The range of possible models to be developed on the basis of the above general approach can be well illustrated by classifying according to spatial representation as sh
93. mg m3 8 Futrophic Nonpoint reduction Mesoophic Cvs meanP iys mean Cha C vs max Chla 0 Ultra oligotrophic 0 Oligotrophic 1 Mesotrophic 30 Eutrophic 69 Hipettrophic Probability distribution for tophic categories BRSRSEFSASRAASRSRS 2 3 4 8 amp T 8 3 w Time years 700 Toog Average Chia mg m3 Practice EAT 63 Vea temp T I E3 Temperatur F J E3 Practice P f 1 E3 Practice A f J E3 Practice ETE hag Lake models Model No 5 Dynamic algae growth model Practice Figure 19 b Further remarks A very large variety of algae growth models exist in the relevant literature They also use a high variety of nutrient temperature and light limitation functions 61 Water quality limit values Water quality limit values can be entered through the respective menu of the programme WG limit values For BODs and DO the initial or default values of the programme those of the presently valid Hungarian surface water quality standard as of 1994 are used the user can enter the values of his her respective home country standard provided it consists also of five quality classes In the case of the longitudinal dispersion advection model the pollution wave model the user is kindly advised to consult the water quality standard of his her home country in order to gain a realistic case when a pollutant is named th
94. miec 1983 The oxygen sag curve which the user can see in the window when in the respective menu item has a critical point where the dissolved oxygen content of water is the lowest that is when the oxygen deficit is the highest The time of travel or the corresponding downstream distance can be expressed by finding the minimum of the sag curve It is obtained in the form of Eq 2 9 for terit Eq 2 10 for X crit and Eq 2 11 for Deit Thus the critical dissolved oxygen concentration is obtained as the difference between saturation oxygen concentration and the critical oxygen deficit Eq 2 12 For the practical use of the above simple model equations one should find estimate the values of the two model parameters K and K3 There are two basic ways of estimating values of the reaction rate parameters 1 If one has in stream measurement data of DO and BOD then one can calibrate the model by fitting the calculated curves to the measured ones This can be easily done for BOD for Kj expressing K from Eq 2 2 but the value of reaeration coefficient Ky can be found only by trial error model simulations or by using a respective fitting algorithm built in models of practical use not included in the model used for this teaching aid 2 If you do not have access to measurement data then you can estimate model parameters using formulae and tables published in the relevant literature The value of the reaeration coefficient K depends
95. mme we will consider the following domain K 0 1 1 7 day K2 0 2 1 2 day For this software we have discretised this domain at 0 1 day steps and the user can adjust the variation of the ratio f K2 Kj seeing also the corresponding description of the domain of river flow conditions From this table not shown here but included in the programme one cannot adopt values of f lower than 0 5 or higher than 5 0 The BOD decay model The BOD decay model describes the decomposition of biodegradable organic matter termed here L in function of the time which is the time of travel along the stream t x v In Equation 2 2 the initial conditions e g L Lo at x O t to are calculated by the Dilution equation For more details see the Basic theory the General description of BOD DO river models and the General description of the traditional oxygen sag curve Eq 2 1 K L dt Eq 2 2 L Le Legend L BOD in the water g O2 m Lo initial BOD in the stream below waste water discharge see also Eq 2 5 K is the rate coefficient of biochemical decomposition of organic matter T usually day t is the time that is the time of travel in the river interpreted as t x v where x is the distance downstream of the point of effluent discharge T given usually in days 18 The BOD decay curve is shown in Figure 5 a screen outprint from the software iv Water Quality Modelling CAL Graph BOD Curve Tradit
96. mperature T C Ki 20 c is the value of rate coefficient K at water temperature T 20 C 24 Expanded modified BOD DO river models General description of expanded models The reader user is kindly requested to get first acquainted with the General introduction of BOD DO models and the General introduction of the traditional oxygen sag equation In addition to the decay of organic matter and the process of reaeration discussed under the above headings there are many other processes in a stream which affect the fate the sag of the dissolved oxygen content These processes are without claiming completeness as follows Physical processes Effects of dispersion mixing spreading mixing diluting pollutants thus reducing BOD and increasing aeration a process that is to be included in the reaeration rate coefficient K2 Settling of particulate organic matter that reduces in stream BOD values Chemical biological and biochemical processes Effects of benthic deposits of organic matter e g the diffuse source of BOD represented by the decay of organic matter that had settled out earlier onto the channel bottom Sinks and sources of oxygen due to the respiration and photosynthesis of aquatic plants macrophytes phytoplankton algae and attached benthic algae oxygen consumption by oxidising biochemical processes such as nitrification Of the many modifications of the traditional oxygen sag curve we hav
97. n models in two ways 1 Either the data annual mean flow and concentration and the point source load are entered or 2 The runoff and the non point source load of the catchment basin is calculated by a very simple fixed model and the point source data are given This model is a rough substitute of the future catchment model series which shall be developed in the 3 version of this software Load reduction treatment efficiency options are also given 10 90 removal and 10 60 removal for point and non point sources respectively Models Model equations are not given in the software only a choice for the above two options then the respective scroll bars for the parameters to be entered plus a result field Options 1 Data to be entered P annual mean total P concentration in the inflow mg m Qin annual mean discharge of inflowing streams m s Lp sum of point source loads of phosphorus kg day Non point load estimate Lnps 0 0864 Pin Qin Lot kg day 2 Models A area of the catchment basin ha F fraction of forested land 0 lt F lt 1 MP fraction of meadow pasture 0 lt MP lt 1 Ag fraction of agricultural land 0 lt Ag lt 1 U fraction of urban land 0 lt U lt 1 F MP Ag U 1 00 PC precipitation mm Cp Basin averaged concentration of phosphorus in the point source discharges mg m Qp Total water discharge of point source dischargers m s Input load models Flow model Q 0 0000003171
98. ned equilibrium state of the system using retention ratios r of phosphorus and r for algae 59 Submodel equations Eq 5 13 _ Pi l r TA _ Pra TEMPLIM q r 1 Kp r Pp K p ete P Leq Legend K is the half saturation constant for algae growth in lake TP concentration at which the growth rate of algae is half of the maximum Ptc is the upper limit value of water quality Class I excellent for total phosphorus in lake water Tp is the fraction 0 1 gt x gt 0 a reduction multiplier of the maximum growth rate of algae their product e g Wow X Umax is the assumed growth rate at Class I TP concentration Pieq is the measured or desired new equilibrium annual mean total phosphorus concentration of the lake water Pteq r Pin Ta is the ratio of the desired maximum in lake algae biomass to the biomass in the in flow ra ABi ABteg max Figure 19 a and 19 b shows the results of algae phosphorus lake model No 5 for two situations with slight changes only in the forest agriculture land use proportions The dramatic effect of deforestation and increasing agricultural land is apparent in that the algae peaks does not seem to attenuate after the unfavourable changes Water Quality Modelling CAL File View Window Help SW H kea amp __ Graph Input load model P E32 Graph Lake model result l x Rees ox Results of input load model 7 Graph settings
99. nsport processes are considered as instantaneously completed ones With other words it means that 32 the contaminant discharged into the stream from any external source is being instantaneously mixed with an elementary water body of A dx volume Here A is the wetted cross section area of the river and dx is the elementary distance downstream It means that the level of contamination of the stream by the pollutant at any point x along the longitudinal profile is represented by the cross sectionally averaged concentration of that substance Using this assumption and considering a non conservative contaminating substance which is subject to decay decomposition as given in the decay equation Eq 1 5 one can simplify Equation 1 3 to Equation 4 1 This one dimensional dispersion advection model of a non conservative pollutant is solved for initial conditions of the input of pollutant mass M at x 0 The resultant solution describes the flattening out of time concentration pollutant waves along the river In this model the river flow is considered steady state e g neither the flow nor the river depth and flow velocity changes with the time or space Parameters of this model apart from the hydraulic ones are the reaction rate coefficient K and the longitudinal dispersion coefficient Dx Estimation of the reaction rate coefficient K depends on the pollutant concerned Thus it can not be made for a general case for the calculation example of t
100. nt nutrients is neglected This latter is usually a correct assumption for the nitrogen fixing blue green algae This model is also driven by the results of the Input load model and the lake water budget regulation model Outflow Figure 18 Model equations Eq 5 10 dP _ 1 d Pin Yin 7 117 AX set HE suPs gt y T gla Qin Pe Qoud Kea Pet Ksa Ps7 aPs he Pr KscuPs KourP dt d setl L scul s burl s dh 1l ijo 9 P E dt le OA and Eq 5 11 dAB 1 T 0 ABn ABQ uAB K AB dt y in 4B Qa AB K u u TEMPLIM Kp tP Chl a amp AB and 58 Eq 5 12 remem t exf 1 14 RER te to te to 0 if t gt te Legend Pi is the in lake P concentration mg m P is the P concentration in the sediment mg m h is the lake depth m d is the depth of the active or interactive sediment m Qin Qout are the inflow and outflow rates of the lake respectively m s Pin is the P concentration in the inflow mg m Kse is the sedimentation settling rate constant of phosphorus year Kscu is the phosphorus resuspension scouring rate constant year Kpur is the phosphorus burial coefficient year A the average lake surface area km AB is the concentration of algae biomass ABin algae biomass concentration in the inflow Ka isthe lumped algae loss rate constant mortality and zooplankton grazing P and E are the precipitation and evaporation onto from the
101. odel is coupled with an experimental regression model between the nutrient and an index of the trophic state usually chlorophyll a as indicated by Figure 16 Outflow Figure 16 The software programme is based on the following equations Model equations Eq 5 8 dP _ l d Fo LP in Gin 7 out KseP Th alle dt Ah P Qn P Q L h dP _h dt gee F K scu Ps KourPs dh 1 10 P E 7 7 On Dona and Eg 5 9 Chl mean 0 52 Pi Chl wax 0 74 P Legend Pi is the in lake P concentration mg m P is the P concentration in the sediment mg m h is the lake depth m d is the depth of the active or interactive sediment m Qin Qout are the inflow and outflow rates of the lake respectively m s Pin is the P concentration in the inflow mg m Kse is the sedimentation settling rate constant of phosphorus year 56 K u is the phosphorus resuspension scouring rate constant year Kpur is the phosphorus burial coefficient year A the average lake surface area km P and E are the precipitation and evaporation onto from the lake surface respectively m Chlmax Chlmean are the maximum and mean concentration of chlorophyll a respectively Figure 17 shows the result screen of Lake model No 4 Water Quality Modelling CAL BEES File View Window Help Click to practice gt Input model Hydrology li Practice P balance lake model lolx eea P E E3 1
102. oint source of pollution represented by a pollutant mass M discharged instantaneously into the river In constructing this model we consider the river as a linear system in which transversal and vertical transport processes are considered as instantaneously completed ones With other words it means that the contaminant discharged into the stream from any external source is being instantaneously mixed with an elementary water body of A dx volume Here A is the wetted cross section area of the river and dx is the elementary distance downstream It means that the level of contamination of the stream by the pollutant at any point x along the longitudinal profile is represented by the cross sectionally averaged concentration of that substance This model can be used for any non conservative substances the decay decomposition of which can be approximated by first order reaction kinetics see also Eqs 1 5 and 1 6 For more details see the the basic theory of water quality models the general description of dispersion river models and the general description of longitudinal dispersion models In the practice menu of this model you can set the length of the river reach to be modelled by the Distance scroll bar so as to be longer than the distance of a monitoring station or water intake where you want to know the actual value of the pollutant concentration with which the pollution wave arrives there The software calculates 10 time concentration
103. on the two dimensional vertically averaged longitudinal transversal dispersion advection model of a non conservative pollutant can be derived from Eq 1 1 in the form of Equation 4 4 A further simplification can be applied by combining longitudinal and transversal dispersion effects into a single mixing term Even further usual simplification is that the contaminant is considered a conservative one this can be assumed in most of the practical cases since the hydraulic transport dilution effects will dominate the fate of the concentration within the plume until the transversal mixing is completed With these further assumptions one obtains the simple transversal mixing model in the form of Equation 4 5 Although several analytical solutions of equations 4 4 and 4 5 and of several other model versions are known from the relevant literature for various initial conditions inlet discharge arrangements the one we selected Fisher 1979 for the purpose of this CAL programme is probably one of the most practical one for cases when we want to investigate also the effect of the point of discharge of the pollutant within the cross section For an effluent discharge of C pollutant concentration and qo flow rate released into the stream at the discharge point effluent outlet of yo m distance from the stream bank and at x x longitudinal distance the model formula of Equation 4 6 can be obtained Apart from the hydraulic and stream geometry paramete
104. ons or lake water level regulation 52 P balance model with sediment interaction Lake model No 3 Explanation One of the most widely used nutrient phosphorus budget models is the one where both the settling and resuspension of the nutrient is considered in the model In this model block the water budget is also calculated as it also has a strong bearing on the processes involved In the sediment phosphorus budget a burial reaction is also considered to account for sediment phosphorus which becomes non exchangeable This is a precondition if one wishes to consider the retention loss of phosphorus in the system Figure 14 There are two ways of using the model 1 either the user enters the settling scouring and burial rates of phosphorus or 2 the parameters are estimated by a sub model on the basis of de desired measured equilibrium in lake and sediment P concentrations and a retention ratio to be achieved Outflow Figure 14 Model equations Eq 5 6 E s E kua Pr Ksa Ps KowPs dh_1 a qOr Qoud P E Legend Pu is the in lake P concentration mg m P is the P concentration in the sediment mg m h is the lake depth m d is the depth of the active or interactive sediment m Qin Qout are the inflow and outflow rates of the lake respectively m s Pin is the P concentration in the inflow mg m Kse is the sedimentation settling rate constant of phosphorus year Kgcu is
105. own below after Shanahan et al 1986 Simplified models a OSOS Vertical or longitudinal 1 D Vertical plane horizontal single layer Circulation models Real 3 D multilayer Ekman type appendix iii
106. pertrophic for Chl a mean 87 hypertrophic for Chl a max Make a clean up Use realistic removal rates 80 for point sources X rp 0 2 and 40 for non point sources X rmp 0 6 Go back to the input load menu Fixed boundary evaluation PL 108 9 ug l hypertrophic Chl a mean 26 4 ug l hypertrophic Chl a max 56 6 ug l eutrophic Probabilistic evaluation highest probability eutrophic with 59 probability for PL 48 eutrophic for Chl a mean 48 48 hypertrophic and eutrophic for Chl a max Thus the algae phosphorus model yields at this given parameter set a similar answer than the other more simple lake models Note again that with slight changes of the input values and model parameters you might have very different results The more simple models are usually more realistic because they reflect earlier statistics while this model is highly sensitive to a larger number of model parameters 84 Exercise 8a Analysis of a small lake with various lake models Consider a small lake of 10 km area and 2 0 m average depth draining a catchment basin of 90 km The population in the area 10000 inhabitants has no sewage treatment and their sewage water is assumed to reach the recipient streams with approximately 8 mg l TP concentration The daily water consumption is 250 litre capita day The assumed water loss via garden watering and evaporation infiltration etc is 20 Calculate the point source load Qpt 0
107. pstream of P rdske is C 10 mg m You are the designer and shall calculate the following What TP concentration will characterize the water of the River Abakoppany after having the sewage water discharged into it Cfeeg mg m Does this value meet the Class I water quality If not what degree level of treatment should be secured for phosphorus what is the required treatment efficiency is percentage Note that the treatment efficiency is n 1 X 100 where X is the multiplier of the sewage load a number between zero and one For the solution of this task you must only know remembering the lectures that the basis of all water quality management calculations is the making of mass balances using mass flux values The mass flux or load value is obtained as the product of water discharge in volume per time dimension and concentration in mass per volume unit yielding the load value in mass per time units You have to the mass balance mass flux of the river background mass flux of the sewage discharge resultant mass flux downstream of the effluent discharge and express the reservoir s feed water concentration Creea from it Poroske village S Efficiency STP to be designed GaP C 40g Cpe Q 3 0m s C 10mg m 64 Solution to Exercise 0 The background load of the river is Q C 3 0 10 0 30 mg s The sewage discharge load is qs C 0 01388 10 000 138 8 mg
108. r of shoes This also means that no bridge designers or hydraulic engineers and no shoemakers and not even water chemists and aquatic ecologists can alone attempt the solving of water pollution control problems although sometimes they think they can Figure 2 A crucial element in the series of complex activities of planning and implementing water pollution control actions is the quantitative determination and description of the cause and effect relationships between human activities and the state the response of the aquatic system its quantity the hydrological and hydraulic processes and quality the chemical and biological processes These activities together can be termed the modelling of aquatic systems hydrological hydraulic and water quality modelling These activities are aimed at calculating the joint effect the impact of natural and anthropogenic processes on the state of water systems Figure 3 System approach to managing the aquatic environment Legal and Implementation of legal and administrative administrative control measures measures Input and hti Cost efficiency impact models i analysis l Input response Expectable state cause effect of the aquatic c Emission models environment Preventive Process Objectives ontrol etc oriented field measures studies Process models of aquatic systems Modification of control ae measures Modification of objectives Figure 3 The s
109. r quality modelling with special regard to plant nutrient budgets and eutrophication This also means that all important features of version 1 1 are also included although in an improved modified way This CAL was made in such a way as to fit into the frames of UNESCO IHP s Ecohydrological programme Projects 2 3 and 2 4 of IHP V In the view of the author one of the basic tasks of ecohydrology is to trace the fate of pollutants and especially of plant nutrients through the water hydrological and ecological systems In doing so a major task is to describe as quantitatively as possible the input response nutrient input trophic state response relationships of lakes and standing water bodies This means with other words eutrophication modelling the basics of which is included in this software Eutrophication models describing trophic state of standing waters in function of inflow outflow water level water volume with examples of analysing the likely outcome of management scenarios will be the ecohydrological core of this CAL programme In addition to this a very simple catchment watershed model is also included in order to facilitate the calculation of input load which drives the lake models and the proportion of point source and non point source components of this load This is also an important ecohydrological element of the software Nevertheless this watershed model is of the wired in or fixed type where the user cannot
110. reat Lakes Environmental Planning Study Contribution No 33 pp 126 Camp T R 1963 Water and Its Impurities Reinhold Publishing Corp Chapman amp Hall Ltd London Canale R P Effler S W 1989 Stochastic phosphorus model for Onondaga Lake Water Research Vol 23 No 8 pp 1009 1016 Chapra S C 1975 Comment on An Empirical Model for estimating the retention of phosphorus in lakes Water Resources Research Vol 11 pp 1033 1034 Chapra S C Canale R P 1991 Long term phenomenological model of phosphorus and oxygen for stratified lakes Water Research Vol 25 No 6 pp 707 715 Clements W C Schnelle K B 1969 Mathematical models of dynamic systems with applications to non ideal systems Vanderbilt University Nashville Tenn Technical report No 24 Di Toro D M Thomann R V O Connor D J Mancini J L 1977 Estuarine Phytoplankton Biomass Models Verification Analysis and Preliminary Applications In The Sea Ideas and Observations on Progress in the Study of the Seas editor Goldberg E D John Wiley Sons Inc pp 969 1019 Di Toro D M Conolly J P 1980 Mathematical Models of Water Quality in Large Lakes Part 2 Lake Erie EPA 600 3 80 065 pp 231 Fischer H B List E J Koch R C Imberger J s Brooks N H 1979 Mixing in Inland and Coastal Waters Academic Press Inc London Felf ldy L 1987 A vizek k rnyezettana ltal nos hidrobiol giai Water environment General hydrobiology Mezdogaz
111. ring the following subsequent section lengths from upstream to downstream 5 km 6 km and 4 km Do not forget that subcatchments 3 and 5 are direct watersheds to the main stream and thus their flow occurs as lateral inflow as the slope of the flow profile Draw also the longitudinal load profile showing the calculated values showing also the point source steps Attention the direct catchment loads appear again as slopes of the load profile as non point source inflow 89 Draw also the phosphorus concentration profile showing the above calculated values This will indicate whether there are sections upstream where a fishpond could be created without the danger of eutrophication Do not forget to use the dilution equation in calculating the concentrations downstream of junctions What other tasks might be performed to improve the overall catchment management analysis done ABOVE iiss oasistaietniuaiotents Development and inclusion of transformation submodels for accounting the retention delivery of phosphorus along the transportation routes x k k 90 Testing your knowledge 1 What is the time of travel a b C it is the time period elapsed between the points of time of taking two samples in a river during a longitudinal profile measurement study it is the average period of time of the movement of water pollutant particles between two selected cross sections of the river it is the distance between t
112. rm level is not exceeded Change only average stream width B 71 m D 113 96 alarm level is reached at 120 km 73 Exercise 4a Analysis of another accidental pollution event The Case You are to evaluate the likely near source circumstances of the catastrophic cyanide pollution spill which occurred at 22 00 p m on the 30 of January 2000 at the tailings pond of a gold mining company of Baia Mare Nagybanya Romania due to the failure of the dam of the pond The pollutant spill then flowed into the river Lapus in Romania then entered the River Somes Szamos which crosses the border to Hungary then enters the River Tisza which flows into the Danube and then the Black Sea The peak of the concentration wave arrived to Csenger station at the Hungarian Rumanian border with a cyanide CN concentration of Cmax 32 6 mg l at 20 30 p m on the 1 of February 2000 Csenger is located approximately 100 km downstream of the site of the spill The flow of the river Szamos at Csenger was Q 160 m s Cyanide is a relatively conservative substance not subject to decay K 0 Evaluating teams processing the stream measurement data of the entire river system estimated that the quantity of the pollutant spilled was about 100 tons of cyanide Estimate the longitudinal dispersion coefficient from these above data Model calculations Use the pollutant spill model equation and note that the maximum concentration of a pollutant wave is when x v
113. rs that are input data for the model application the value of the mixing coefficient ey should be estimated either by fitting the model to measurement data concentration distributions of the cross sections or by applying experimental expressions from the relevant literature While it is always the best solution to use field measurement data for parameter estimation in the case of the transversal mixing model the literature offers mostly the same type of equation and even the parameters of these experimental equations vary within relatively narrow ranges For the purpose of this CAL programme we have selected Equation 4 7 In the relevant literature the value of the coefficient d varies between 0 1 and 0 9 Our own practical experience indicated that the effects of mixing are underestimated with the lower values of the domain of d Thus we suggest the use of a higher value for example d 0 7 36 It should be mentioned that more precise model simulations can be achieved with models that are more complex than Eqs 4 2 and 4 3 with special regard to taking the distribution of flow velocity across the stream also into consideration instead of considering the cross sectionally averaged mean flow velocity vx only A 2D dispersion advection model This model is just an example for a two dimensional dispersion advection model for a non conservative substance For more details see the chapter on the Basic theory the general description of disper
114. s The sewage flow qs was obtained by multiplying water consumption with the population and the water utilisation rate converted to m s qs 250 0 8 6000 86400 1000 0 01388 m s On the basis of the conservation of mass the following mass balance equation can be written Q E Cp qs E C Creed Q qs from where Creed Q Cy qs Cy Qtqs 30 138 8 3 01388 56 00 mg m Thus the feed water of the planned lake would be higher than the desired Class I value that is 40 mg m The desired treatment efficiency n 1 X 100 is obtained as Ciimit 40 mg m Q Cy X qs Cs Q qs from where X 40 3 01388 30 138 8 0 652 This means that the minimum phosphorus removal efficiency should be n 35 65 Exercise 1 Analysis of a pollution case with the traditional BOD DO model 1 The case The town of Prettybrooks with a population of 65 000 wishes to build a sewage treatment plant they did not have one till now The local Environmental Authority demands an environmental impact assessment to be carried out for the project The water quality targets to be met in the recipient stream downstream of the to be sewage outfall are set for the oxygen household conditions as follows Dissolved oxygen DO not less than 6 mg l Class I good in the critical low flow period of 80 per cent duration in the summer months when the respective flow of the recipient river Little Lousy upstream of the to be plant is Q 12 m s B
115. s forestation banning certain agricultural practices declaration of nature conservation areas etc This situation is unfortunately a very realistic one in agricultural catchments Check whether this feasible solution is able to achieve the desired load How much is the desired load for Chlmax 1628 4 kg year Chl amean 1527 2 kg year PPri 933 9 kg year Exercise 6a Analysis of lake eutrophication with experimental regression models based on the OECD study Lake Model No 1 A lake of 90 km area and 5 meters average depth has a drainage area of 1000 km The multiannual average runoff is 120 mm Calculate inflow to the lake Q 3 8 m s Enter the hydrology sub model set evaporation equalling precipitation Qou Qin Qoutmax Amin hmax h 5 0 m Enter the input load menu Scarce data indicate that the multiannual average inflowing phosphorus concentration is very high P mean 600 ug l The point source input is roughly about 25 how much 3 8 0 6 86 4 25 49 2 kg day Enter 50 kg day for the point source Check the trophic state both by the fixed boundary and by the probability distribution You obtain hypertrophic conditions with the exception of mean Chl a for which both classification shows eutrophic conditions Make a clean up Use realistic removal rates 80 for point sources X rp 0 2 and 40 for non point sources X rnp 0 6 Check the trophic state both by the fix
116. s of pollution in the models There are two basic ways I Either as a point source an initial condition specifying the effect of the source in given point of the space and at a given point of time with an initial Co value This Co value is calculated usually with the dilution equation Example of this will be given in the various running model blocks see the river models for more detail 12 The general dilution equation This is one of the most important tools in water quality modelling a simple mass balance equation which is used when the pollution source is considered as an initial condition Considering a river and an effluent discharge of steady state conditions with flows and concentrations not varying in time and assuming instantaneous full cross sectional mixing of the sewage water with the river water the initial concentration Co downstream of an effluent outfall can be calculated by the dilution equation Eq 1 4 which stems from the balance equation of in and outflowing fluxes written for the section of the discharge point e g back ground river mass flux plus pollutant discharge mass flux equals the combined mass flow downstream of the point of discharge This equation is used very frequently in simple analytical water quality models for calculating the initial concentration of pollutants Eq 1 4 C Cq C Q q Q where Cb background concentration of the polluting substance in concern in the river ML
117. s and animals also termed detritus or dead organic matter Among external sources anthropogenic ones are of major concern and this includes wastewater sewage discharges and runoff induced non point source or diffuse loads of organic matter In the models biodegradable organic matter is taken into consideration by a parameter termed Biochemical oxygen demand BOD BOD is defined as the quantity mass of oxygen consumed from a unit volume of water by microorganisms while they decompose organic matter during a specified period of time Thus BOD is the five day biochemical oxygen demand that is the amount of oxygen that was used up by microorganisms in a unit volume of water during five days incubation time in the respective laboratory experiment Thus the unit of BOD is mass per volume e g gO m which equals mg O litre Another main process in the oxygen household of streams is the process of reaeration the uptake of oxygen across the water surface due to the turbulent motion of water and to molecular diffusion This process reduces the oxygen deficit D of water which is defined as the difference between saturation oxygen content and the actual dissolved oxygen level These two counteracting processes are considered in the traditional BOD DO model Streeter and Phelps 1925 in the mathematical form that you can see in the graph window of the Chapter The traditional BOD DO model the Oxygen sag curve The traditional BO
118. s as shown in Table below Table 4 Trophic state categories Hungarian guidelines Felf ldy 1987 Degree of trophity Primary Algal count Chlorophyll a production mg m gC m year 10 litre 1 Ultra oligotrophic 6 Eutrophic 1 10 In the models of this software the evaluation of the results of any model run will be automatically made with the help of the probability curves of the OECD and also by the fixed categories of OECD 43 General introduction to lake models In terms of the general theory of modelling transport and transformation processes of water bodies see the first Basic theory chapter lakes offer the consideration of a large variety of transport and transformation models For transport models see Eqs 1 2 and 1 3 the outputs of hydraulic or circulation models would be needed As mentioned before this hydraulic modelling of wind and or temperature difference induced models would need a teaching aid a CAL Programme of the magnitude of this present one Consequently we skipped this modelling phase but the user finds the relevant equations in Appendix 1 The developers have actually also skipped all kind of transport modelling and reduced the handling of the problem to the modelling of transformation processes This means that of the lake modelling options shown in Table 1 only the zero dimensional fully mixed reactor type models are discussed to a certain depth to their basics Table 5 Basic categori
119. sion models and the general description of transversal mixing models Note that this model is not utilized in this CAL programme and serves for illustration only Eq 4 4 oC ac ac c Dx D Vx KC t ax ay dx Legend C is the concentration of the pollutant in the stream M L gt g m D is the coefficient of longitudinal dispersion 7 he m s D is the coefficient of lateral dispersion 7 Tr m s K is the reaction rate coefficient of a non conservative substance assuming first order decay as the transformation process T Vx is the average flow velocity of the stream L TE m s t is the time T The transversal mixing model used in this programme This model calculates the concentration distribution of a conservative substance across a river of a given width at various distances downstream of a single point source in function of the hydraulic parameters and channel geometry parameters The distance of the point source from the river bank can also be varied For more details see the chapter on the Basic theory the general description of dispersion models and the general description of transversal mixing models In the practice menu of this model you can set the length of the river section to be modelled by the Distance scroll bar The software calculates 10 concentration distribution curves splitting the above distance into equal parts You can select then with the Highlighted curve scroll bar t
120. sponds to 76 km The conclusion is that requirements are not met Look at the oxygen sag curve Compare to above criteria Take note of critical time and DO concentration 1 47 days 5 3 mg O gt l You observe that DO criteria are also violated Design appropriate level of treatment Note that a relatively good biological sewage treatment system will remove about 80 of the influent BOD Enter the respective data using the Practice menu of the traditional BOD DO model Date to be entered is 550 0 2 110 mg l for sewage BOD Observe the effects of this control measure You find that DO stay above Class II limit 6 mg l over the entire length below the outfall and BOD drops below Class II within short time as well THUS THE CASE WAS SOLVED YOUR FIRST EXPERIENCE WAS SUCCESSFUL 67 Exercise 2 Analysis of a pollution case with an expanded BOD DO model 1 The Case The large city of Seven Churches is about to build treatment plant and the regional government the County Seat is responsible for the larger area Thus they will have to find a water pollution control solution for the entire catchment of the River Blue Rapids for its 150 km length downstream of Seven Churches until it joins the River Grand Shore at Tricky Bridge The local Environmental Authority demand an environmental impact assessment to be carried out for the sub catchment in concern The water quality targets to be meet over the entire 150 km length of the recipient
121. strophic cyanide spill of the Szamos Tisza Danube river system as it certainly was of world wide interest at the time of developing this version of the software Nevertheless the data and the simulation results presented below are of no scientific and even less political importance as the methods presented in this software are highly simplified and serve only for teaching purposes In this context the author wish to emphasise again that the software and the models are not intended for use in practical work design water pollution control planning environmental impact assessment etc and serve solely for teaching purposes This means that for the purpose of this CAL for the purpose of ensuring fail safe running of the models many such approximations simplifications and assumptions were made that would not be acceptable in the real life in practical water quality modelling activities Therefore the authors also wish to state that they do not assume any responsibility for failures faults or damages caused by such non intended use of the software and the programme The user can generate and handle many more similar water pollution control or environmental management situations with the use of this software Read more of the respective literature of water pollution control and of the management of aquatic ecosystems However be aware that you must not use this software for actual water pollution control calculations as the models are oversimplifi
122. sually m B is the benthic oxygen demand M T L here g O m day xX is the distance downstream along the river L usually in meters v is the mean flow velocity along the river reach in concern L T m s The 2nd expanded dissolved oxygen model The model describes the longitudinal variation of the dissolved oxygen content of the river as affected by point and non point sources of biodegradable organic matter BOD the decomposition process of organic matter the reaeration process and by the photosynthesis and respiration of aquatic plants For more details see also the following topics General introduction of BOD DO models the General introduction of the traditional oxygen sag equation the General introduction of the 30 Expanded BOD DO models the General introduction of the first expanded BOD DO models and the General description of the ane expanded BOD DO Model Legend Cox i Cox 0 S Coxa g Corsa E g Eq 3 7 lt Q 9X Conl q Cog Ki AL K2A G Cox A P R Eq 3 8 E Lat B E Ki Bi Ps Cox a Lf Bot F 2 g2 Henta HERO op 1 4000 Ru Py CF where g E E T A Ge 4 E Q qx Vv is the dissolved oxygen concentration of water referred to as DO in the former equations M Le gO m is the initial dissolved oxygen concentration downstream of the waste water discharge see also Eq 2 6 is the concentration of DO in the lateral inflow to the stream the diff
123. t the example given below A lake of 90 km area and 5 m average depth has a drainage area of 1000 km The multiannual average runoff is 120 mm Calculate the inflow to the lake Q 3 8 m s Enter the hydrology sub model set evaporation equalling precipitation Qou Qin Qout max 5 m s Amin hmax h 5 0 m Enter the input load menu Scarce data indicate that the multiannual average inflowing phosphorus concentration is Pmean 300 ug l The point source input is 20 kg day Set the phosphorus reduction capacity of the lake to 30 a realistic value r 0 7 Set PLo to 90 mg m Set Pso Pseqo 500 g l Set ra 0 7 r 0 7 rp 0 1 Set ABO ABin 830 1 Simulate 15 years time horizon Set reduction factors to 1 0 in the input submodel block Important Stop the model while you are entering new data because it takes time for running the model and the programme may be blown up when data are entered while the model is running Run the model by adjusting step by step the maximum growth rate umax mumax until you achieve similar values than what you had for the same example with the use of earlier lake models hypertrophic eutrophic conditions At mumax 0 29 day you will have the following results Fixed boundary evaluation PL 209 5 ug l hypertrophic Chl a mean 44 ug l hypertrophic Chl a max 124 4 ug l hypertrophic Probabilistic evaluation highest probability hypertrophic with 74 probability for PL 76 hy
124. the mass transport terms for deriving the basic model and the General description of dispersion river models Eq 1 2 C axdydz v Ex dydz v C B dxdz v C B dxdy S 0 E EnO Baja os C Ey n Kv C elas dxdy 00 tet ivo EJz ayax Legend C is the concentration the mass of the quality constituent in a unit volume of water mass per volume M L Ex Ey Ez are the dispersive mass fluxes in the spatial directions x y and z in M L T dimension with the assumption that the law of Fick holds for the joint effect of molecular diffusion and turbulent diffusion that is for dispersion Vx Vy Vz are the components of the flow velocity in spatial directions x y and z length per time L T dx dy dz are the side lengths of an elementary cube an elementary water body as shown in Figure 4 The basic water quality model equation This equation forms the basis of all water quality models It was derived from Equations 1 1 and 1 2 by combining them carrying out the operations rearranging the result and dividing the equation by the elementary water volume dx dy dz and also by considering internal sources and sinks of the substance as well as external sources The basic equation describes the variation of the concentration of a quality constituent C with the time and space Apart from the advective and dispersive transport terms that were discussed in relation to Equations 1 1 and 1 2 in this basi
125. the phosphorus resuspension scouring rate constant year Kopu is the phosphorus burial coefficient year A the average lake surface area km 53 P and E are the precipitation and evaporation onto from the lake surface respectively m Parameter estimation sub model Description If one has information on the actual measured or desired planned in lake equilibrium phosphorus concentration and the actual or allowable planned equilibrium sediment P concentration in the upper active layer of the sediment then one can estimate first the burial rate then the sedimentation settling rate Kse and scouring rate K y that would be needed for achieving the actual planned conditions by the submodels shown here they can be derived from the basic balance equations sub model equations Eq 5 7 1 r P 1 ke i Kou 42 1 r pl 1 Kor 2 1 P Ksa 3 r Psa d Pin Pira h Legend Kse is the sedimentation settling rate constant of phosphorus year Kscu is the phosphorus resuspension scouring rate constant year Kow is the sediment phosphorus burial coefficient year q is the hydraulic washout rate inflow outflow Q divided by the lake volume V year Pieq is the equilibrium phosphorus concentration in the lake water mg m Pin is the average P concentration in the inflow mg m Pse is the equilibrium phosphorus concentration in the active sediment layer of d m depth r is the retent
126. the sixties mostly in industrialized countries with intensified agriculture due to the excessive anthropogenic input loads of plant nutrients phosphorus and nitrogen Therefore as contrasted to natural eutrophication the recent problem is termed anthropogenic or man made eutrophication It is usually observed as the excessive growth of phytoplankton that turns standing waters and sluggish streams into green known by the lay public as algae bloom a term frequently used by scientists as well It is frequently associated by the increased growth of attached algae or macrophytes Primary productivity the growth of phytoplankton expressed as carbon produced per unit area of the lake per unit period of time e g gCm yr is high leading to relatively high concentrations of dissolved organic matter DOM in the water This supports a population of heterotrophic bacteria that decompose organic matter and deplete the dissolved oxygen content of water In deep lakes in the hypolimnion this oxygen depletion might create anaerobic condition that gives rise to undesirable biological and chemical processes and may result in fish kills Nevertheless eutrophication is often associated with increased fish production but the species composition changes unfavourably Although about 16 20 elements are necessary for the growth of freshwater plants among others Carbon Silicon Calcium Potassium Magnesium Iron etc J rgensen 1988 anthropogenic eutrophi
127. theory the General description of BOD DO river models and the General description of the traditional oxygen sag curve Eq 2 9 l pK h Otek terit T l K K Ki Lo Ki Eq 2 10 Xerit V tcrit Eq 2 11 _ Ki Rare Dert Loe Kiterit K2 Eq 2 12 DOait DOaat E Dert Legend teir the critical time of travel time during which the water particle arrives to the point of lowest DO concentration in the stream Do is the initial concentration of dissolved oxygen deficit in the river downstream of the effluent discharge point ML e g mg O7 1 see also equations 2 7 and 2 8 Lo is the initial concentration of BOD in the river downstream of the effluent discharge point ML e g mg O l see also Equation 2 5 K is the rate coefficient of biochemical decomposition of organic matter the BOD decay rate T usually day K2 is the reaeration rate coefficient the rate at which oxygen enters the water from the atmosphere T Xcrit the critical distance downstream of the point of effluent discharge the point of lowest DO concentration L v is the average flow velocity of the river reach in concern L T Deri is the critical highest oxygen deficit in the water along the river ML e g mg O l DOzit is the critical lowest dissolved oxygen concentration of the water ML3 e g mg O gt l DO a _ is the saturation oxygen content of water see also equation 2 8 Equation for estimating K T
128. through the discharge and the relatively unchanged river width Q B h v Use fast flowing stream in estimating K You will find that there is a considerable improvement in the BOD DO conditions You should also observe that the building of hydraulic structures is also a very expensive measure in larger rivers and it may be obstacled by the requirements of navigation and environmental protection 69 Exercise 3 Analysis of a complex multiple source pollution situation with the simple BOD model The Case Consider a complex situation more realistic when there are 2 sources of pollution in the same river system See the corresponding Figure Black Ferry STP 20km Shiny Duck River Great Groves STP DO monitoring point a L Shallow Rapids River gt gt kr er 27km 70km The environmental authority requests the compliance with the following oxygen household limit values over the entire river system Dissolved oxygen gt 6 00 mg l Biochemical oxygen demand BODs lt 6 00 mg l The upstream background conditions of the main river and the planned sewage discharge of the town Great Groves are characterized by the following data Raw sewage strength BOD Ly 420 mg O gt l Effluent discharge qs 0 72 m s Effluent DO DO i 2 00 mg 07 1 River design flow Qb1 52 0 m s Background BOD Lyi 6 0 mg 07 1 Background DO DO 7 0 mg O I River flow velocity v
129. time of travel in function of the processes of reaeration decomposition decay of organic matter and oxygen production by photosynthesis For more details see also the following topics General introduction of BOD DO models the General introduction of the traditional oxygen sag equation and the General introduction of the Expanded BOD DO models as well as equations 3 1 and 3 2 Eq 3 3 dD K D K L P dt 2 1 Eq 3 4 K D Lo z l Ki Ks exp K K3 t exp K2t a I exp K2t Doexp Kat K Ki Ks Ki Legend D is the oxygen deficit of water M L e g gO m see also equations 2 7 and 2 8 Do is the initial oxygen deficit of water g O2 m downstream of the effluent discharge see also equations 2 6 and 2 7 L is BOD in the water M L g Oo m Lo is the initial BOD in the stream downstream of the waste water discharge see also Eq 2 5 K isthe rate coefficient of biochemical decomposition of organic matter rs usually day K gt isthe reaeration rate coefficient T usually day Ks isthe rate constant for BOD removal by sedimentation ar usually day B is the benthic oxygen demand the rate of BOD addition to overlying water from the bottom sediment M T L usually gO m day P is the rate of oxygen addition to water by the photosynthetic activity of aquatic plants MT L usually gOo m day t is the time of travel t x v expressed
130. tion The 2nd expanded BOD model The model equations describe the longitudinal variation profile of BOD in function of the decomposition process of organic matter non point source inputs represented by lateral inflow and a benthic source of BOD For more details see also the following topics General introduction of BOD DO models the General introduction of the traditional oxygen sag equation the General introduction of the Expanded BOD DO models the General introduction of the first expanded BOD DO models and the General description of the 2 expanded BOD DO Model Eq 3 5 d plore L qLa K AL B Eq 3 6 L x Lp phi Let BAM fpe E y F se B 1 Kgs 9 Legend L is BOD in the water M E g O m Lo is the initial BOD in the stream downstream of the wastewater discharge see also Eq 2 5 K _ is the rate coefficient of biochemical decomposition of organic matter T usually day La is the concentration of BOD in the lateral inflow to the stream the diffuse load components ML g On m Q is the rate of flow in the river L T usually m s Qo is the rate of flow at the beginning of the river reach just upstream of the wastewater discharge L T usually m s q is the lateral specific inflow rate to the river N T usually m s A is the wetted cross section area of the stream L defined as the rate of flow Q divided by the cross sectional mean flow velocity v u
131. tream concentrations which are due to the given source e g background concentration is considered zero 1 Analyse the case when the discharge is at the river bank Ccop at bank 13 8 mg l 2 Determine how far the source has to be moved towards the main streamline to meet the limit value Y source approximately 12 m 3 You have to be cautious with your proposal for the discharge permit Calculate the effluent COD and the required treatment efficiency for allowing discharge at the river bank C5 0 579 uoaa mg l n 12 65 4 To be on the safe side prescribe a distance from the bank which corresponds to zero concentration increase at the riverbank 1500 m downstream Y source 0 increase L00 sereas eea 00 Investigate a case when the given effluent would be discharged into a river of about ten times less flow Q 25 m s Leave depth h velocity v and slope S unchanged enter the width B that corresponds to the new Q B 17 85 18 m Consider that COD value must not exceed the Class H limit value 22 mg l after full mixing 5 How much is the COD concentration increase due to this source after full mixing COD igi 21 57 mg 1 6 What level of treatment is needed to meet the Class I limit value at 1500 m downstream at the river bank when the discharge point is yo 5 m Co 444 M8g l NS 32 3 70 76 Exercise 6 Analysis of lake eutrop
132. tween oxygen input via photosynthesis and oxygen consumption via the respiration of aquatic plants since respiration is not represented by a separate term in this model It is also worthwhile to mention that due to the diurnal variation of light the variation of the photosynthetic oxygen source can be best represented by a periodical function of the time as it is done in some other more complex models not discussed here There are three new parameters in this model the sedimentation rate constant K3 the benthic BOD B and the photosynthetic input of DO P Estimation of these parameters is rather difficult in the absence of measurement data measurement is also rather complicated the white black bottle method is used for measuring the net input of oxygen by photosynthesis a bell shaped device set into the bottom sediment is used for measuring the benthic oxygen demand and sedimentation of biodegradable organic matter is indicated by the change of the slope of a straight line in logarithmic paper showing the longitudinal variation of in stream BOD measurement data the user is advised to consult the literature for more details of these techniques when so required Nevertheless for the purpose of this programme we will set pre defined ranges of these model parameter values for the calculation example and for that only It will however indicate the way how such models are used in the practice when no field measurement data on the paramet
133. ually but not exclusively abundant correct answers use the Test menu What is the major process of phosphorus retention in lakes and reservoirs Sedimentation and subsequent burial when the deposited P becomes non exchangeable with the overlying water Uptake by aquatic macrophytes Uptake by algae then zooplankton then fish and the removal by fishing correct answers use the Test menu What is a possible ecohydrological eutrophication control option in reservoirs Rising of water levels and diluting the concentrations Excessive use of motor boats to provide oxygen input by the propellers which helps decomposing dead organic matter Provision of appropriate water level for the spawning of predator fish like pike perch which will predate on zooplankton feeding fish decreasing their number thus increasing zooplankton which latter will feed on algae thus reducing eutrophication Introduction of herbivorous fish which will eat macrophytes thus removing plant nutrients and organic matter correct answers use the Test menu 93 References Baxter R M Carey J H Lean D R S Burnison G K 1992 Influence of trophic status on the behavior of contaminants in aquatic systems J Contaminant Hydrology No 9 1992 pp 1 15 Bierman V J Dolan D M Stoermer E F Gannon J E Smith V E 1980 The Development and Calibration of a Spatially Simplified Multi class Phytoplankton model for Saginaw Bay Lake Huron G
134. ubject of this teaching aid is to introduce the basics of water quality modelling to the user Although the qualitative and quantitative modelling of water systems rivers lakes and reservoirs should be done simultaneously we will have to separate them for the purpose of this programme always assuming that the quantitative state the hydrological and hydraulic parameters of the water system is known and sufficiently well described With this we can focus on the quantitative mathematical description of processes that affect water quality although the equations of flow modelling are also given in the Appendix just for the shake of completeness but they are not made use of in this programme Even within water quality modelling we are going to deal in this second version of the software with the most essential basics of river and lake modelling with the hope that this CAL programme is only the second one in a series of similar softwares which would deal with more details of river and lake modelling including the basics of modelling non point source pollution a crucial problem of ever growing importance of our era This also means that the basic objectives of the ecohydrological approach the tracing of the fate of nutrients and other pollutants through the entire catchment and the aquatic ecosystem will only be achieved when the basics of integrated catchment modelling the likely next part of the series are also included in this software B
135. unoff R 60 mm Calculate the mean flow Q 0 274 m s Calculate the annual loads of the two point sources P discharge q1 0 006 m s TP concentration C 5 mg l load Lp 946 kg year P2 discharge q2 0 022 m s TP concentration Cp2 2 mg l load Lp1 1387 kg year Use the following model for calculating the total P load L Pi gt 9 UAL Ajr jx Where i j k L total annual load leaving the area kg year P annual load of the i th point source kg year UAL the Unit Area Loading rate of the k th land use form for which the following estimates were offered by relevant literature UALforest 0 05 kgP ha yr UAL ggri 0 5 kgP ha yr UALaurban 2 0 kgP ha yr Aj The area of the j th subcatchment ha Tjk ratio of the k th landuse form in the j th subcatchment fraction 0 1 L 946 1387 0 6 3400 0 05 0 4 0 5 3400 2800 0 05 0 5 3800 0 05 87 0 4 3800 0 5_ 0 1 3800 2 0 0 2 3000 0 05 0 7 3000 0 5 0 1 3000 2 0 0 4 1400 2 0 0 6 1400 0 5 8090 L 8090 kg year Calculate the total flow including the point source discharges and the annual mean concentration of TP in the stream water Qout 0 302 m s TPmean 0 849 mg 1 Compare this value with that of the water quality classes for waters to be impounded or discharged into a lake Hungarian Standards TP Class I 0 04 mg l Class H 0 2 mg l Class IM 0 4 mg l Class IV 1
136. use load component M Le gO m is the saturated dissolved oxygen concentration of water termed before also as DO gat see also Eq 2 8 is the initial BOD in the stream downstream of the wastewater discharge see also Eq 2 3 is the rate coefficient of biochemical decomposition of organic matter T usually day 1 is the reaeration rate coefficient T usually day is the concentration of BOD in the lateral inflow to the stream the diffuse load components M IZ g Oo m is the rate of flow in the river L TES usually m s is the rate of flow at the beginning of the river reach just upstream of the wastewater discharge L T usually m s is the lateral specific inflow rate to the river N TS usually m s is the wetted cross section area of the stream L defined as the rate of flow Q divided by the cross sectional mean flow velocity v usually m is the benthic oxygen demand M T L here g O2 m day is the distance downstream along the river L usually in meters is the net difference between oxygen production by the photosynthesis and oxygen consumption by the respiration of aquatic plants M T i gO gt m day is the mean stream flow velocity in the river section investigated L TE m s 31 DISPERSION RIVER MODELS General description of dispersion river models Here the reader user is kindly requested to consult also the Basic theory chapter of this material programme where a brief
137. water in the reservoir ML LP is the volumnar P loading rate to the lake ML T to be obtained as the loading rate of P MT divided by the lake volume V L q is the hydraulic washout rate TH calculated as the water outflow rate L T divided by the lake volume V L K is the sedimentation rate T1 t is the time T Solution of Eq 5 for initial conditions P P at t 0 is obtained as q Kyt LP 4 K t P t Poe e 6 The equilibrium concentration corresponding to a new LP load is thus obtained as paz g q K Calculate volumnar loading rate LP 0 1519 g m year Calculate washout rate q 0 18922 year Consider sedimentation rate K 0 1 year and calculate the expectable P concentration in the lake Try different K sedimentation rate values and check how the equilibrium lake concentration varies with different assumptions Calculate how much sedimentation rate would correspond to achieving class II 200 mgP m water quality K 0 5673 yr Use a much smaller sedimentation rate as you can not expect a lake to act as a permanent sink of this magnitude Try to derive a feasible or plausible sedimentation retention rate coefficient by assuming that 20 of the incoming load is retained in the lake Try to derive the necessary formula by writing the mass balance equations for a fully mixed lake where inflow equals outflow and only concentrations vary In 81 the mass balance use r P Pin the r
138. wo selected river cross sections divided by the cross sectionally and longitudinally averaged flow velocity of the river reach in concern that is t x v correct answers use the Test menu 2 What does the term mass flux mean a b C it is the concentration of a pollutant divided by time of travel it is the concentration of a pollutant multiplied by the rate of flow e g mass flux QXC frequently termed also as load Its is the rate of mass flow in a specified direction or across a given surface area the movement of mass during a unit period of time e g M T g sec kg day etc correct answers use the Test menu 3 What is dispersion a b C d dispersion is a transport process caused by the joint effect of molecular diffusion and turbulent diffusion Dispersion is a transport process in which the pollutant particles are moved by the pulsating motion of the flow velocity vector and by a similar thermally induced pulsating motion of the molecule Dispersion is a transport process when contaminant particles are moved jointly by hydraulic and wind forces Dispersion is the joint effect of wave and flow velocity induced motion correct answers use the Test menu 4 What is Biochemical Oxygen Demand BOD a It is the amount of oxygen produced by biological and chemical processes taking place in the water It is a measure of the biodegradable organic matter content of water BOD is defined
139. y in spatial directions x y and z length per time L T t is the time T S x y Z t denotes external sources and sinks of the substance in concern that may vary in both time and space mass per volume per time M L T D Sintemal denotes the internal sources and sinks of the substance M i T 10 Derivation of practical models from the basic model equation The basic three dimensional water quality model is seldom used in its original complex way Eq 1 3 mostly because three dimensional problems occur rarely For example river problems can be frequently reduced to one dimensional linear or two dimensional longitudinal transversal problems as it will be demonstrated in the programme Another example is the fully mixed reactor type or zero dimension lake models of this programme where no transport terms of the basic water quality models are included Another reason of using simplified models is that transversal or vertical velocity measurement data are seldom available The internal source sink terms that were only denoted in Eq 1 3 should be specified for each problem explicitly and they vary with the components considered Here it will be briefly demonstrated how can one derive the simple river and lake model versions of Eq 1 3 which can be used in the practice In order to arrive to some of the simple water quality models presented below we have to make first series of assumptions and approximations a N
140. y naming the parameters such as BOD DO and plant nutrients algae growth which the user will find in the menu A general remark however can also be added here The result of the decomposition decay consumption or settling of one constituent can be another one Examples are i The result of decomposition of biodegradable organic matter expressed in terms of BOD see more details in the menu block BOD DO models is the increase of oxygen deficit D in the water i Settling of a water quality constituent such as like phosphorus from the water phase will result in the increase of the same component in the bottom sediment iii The nitrification oxidation process will turn organic nitrogen into ammonium nitrogen then to nitrite nitrogen then to nitrate nitrogen iv Growth of algae will turn dissolved inorganic plant nutrients phosphorus and nitrogen of the water phase to organic matter of the algal body a process called primary production The most frequently used approach to the description simulation of these single and coupled reaction processes is the first order reaction kinetics The principle of first order reaction kinetics states that the decay decomposition uptake growth etc of a pollutant is proportional to the concentration of the pollutant and the factor of proportionality is K the rate coefficient T Another important aspect in the derivation of water quality models is how to consider the external source
141. y of the Pollutions and Natural Purification of the Ohio River Public Health Bulletin NO 146 U S Public Health Service Thomann R V Di Toro D M O Connor D J 1974 Preliminary Model of Potomac Estuary Phytoplankton J Environmental Engineering Division ASCE Vol 100 No EE2 pp 699 715 Velz C J 1970 Applied Stream Sanitation Wiley Interscience New York Vincon Leite B Tassin B 1990 Modelisation de la qualit des lacs profonds mod le thermique et biog ochimique du lac du Baurget La Huille Blanche No 3 4 1990 pp 321 236 Vollenwider R A 1976 Advances in defining critical loading levels for phosphorus in Lake Eutrophication Mem Ist Ital Idrobiol No 33 pp 58 83 Vollenwider R A Kerekes J 1981 Background and Summary Results of the OECD Cooperative Programme on Eutrophication Proc Int Symp on Inland Waters and Lake Restoration Sept 8 12 1981 Portland Maine USA EPA 440 5 81 110 pp 25 36 Yeasted J G Morel F M M 1978 Empirical insights into lake response to nutrient loading with application to models of phosphorus in lakes Environmental Science and Technology Vol 12 No 2 pp 195 201 97 Appendix I Pollutant transport processes in lakes In lakes and reservoirs the transport processes of particulate and dissolved constituents of water are related to water motion to currents that are induced by one or more of the following forces and phenomena currents caused by inf

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