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1. one time every day and not being included in the parameter estimation Appropriate start values must be assigned to C FS amp and C_FS _ phase which are both activated for the parameter estimation Pay attention to the identifiability of these parameters Version date of change changed by replaces version of 7 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration Attention If C_FS_amp is activated for parameter estimation but it is still being assigned a value of 0 the algorithm fails Set C_FS_amp to an appropriate initial value gt 0 The complete definition for the concentration in the foul sewage is finally C FS C FS a C FS b Q FS C FS c Q FS 2 C FS amp sin C_FS _ freq t C_FS_ phase 2 pi To assure comparability between the different APUSS data sets I recommend assigning the following limits for the parameter estimation C_FS phase min 0 and max 1 C FS amp min 0 max is not relevant 3 1 3 Time spans that are considered for the parameter estimation fit_times fit times is a Real List Variable t It defines which spans of the measured time series C WW _ measured und Q WW_measured are used for the parameter estimation fit_times 1 this time span is considered for the parameter estimation fit_times 0 this time span is excluded from the parameter estimation Example In the example Sewer_Infiltration2. You will now need to modify the User Input 1 to 21 according to your data set and requirements All user inputs are explained in the file itself For a first trial it is recommend to not change these entries and perform a parameter estimation with the provided example data set However you must at least modify User Input 1 the working directory 3 Start the parameter estimation by copying the content of ChemHydSepMCS R to the R console Version date of change changed by replaces version of 15 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration 4 4 FAQ s on the R script file ChemHydSepMCS R This chapter aims to summarize answers to some of the most frequently asked questions FAQ s that were asked by users during the test runs of the scripts within the APUSS project 4 4 1 Output of statistical parameters Statistical information about the estimated total amount of infiltration during the considered span of time is obtained by pasting the lines Output of statistical parameters summary Total_inf MCS Total infiltration for the considered span of time summary X_Total_inf MCS Infiltration ratio for the considered span of time quantile Total_inf_ MCS probs c 0 025 0 975 95 confidence interval total infiltration quantile X_Total_inf_ MCS probs c 0 025 0 975 95 confidence interval infiltration ratio Remark The automatically generated
3. 3 1 9 Auxiliary variables 1 t is a Program Variable that refers to the programs internal time argument Time It is required to make the time argument available for the definitions of the Formula Variables Residulas C_WW is a Formula Variable that calculates the difference between C_WW and C_WW_ measured A visualization of these residuals can give a first control for the adequacy of the model structure Residulas C_WW can be exported for further statistical analyses and tests 3 1 10 Auxiliary variables 2 To offer the possibility for a basic evaluation of the influence of systematic measurement errors on the estimated parameter values four auxiliary variables are introduced These variables can be set manually in example to the maximum assumption for a systematic measurement error and therewith allow to investigate the maximum influence on the estimated parameters values that can be expected Version date of change changed by replaces version of 10 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration Q WW systerr_a offset error in the wastewater flow measurements This variable is assigned the value 0 if no offset error is assumed Q WW systerr_b constant relative error in the wastewater flow measurements This variable is assigned the value 1 if no relative error is assumed These two variables are introduced to the model by defi
4. SOP Stable Isotopes Method for the Quantification of Sewer Infiltration increase Therefore it is advisable to not exaggerate in building too complex models on a rather limited set of measured data The extend of the identifiable parameter set will also depend on the quality of the measured input data 6 Finally judge your results critically point 4 and 5 Time series data can now be exported to the spread sheet compatible text file xxy lis by the use of the Output data graphics Estimated model parameters and statistical information are finally stored to the xxy fit text file 3 3 Implemented graphics for visualization of the results Some standard graphical representations are implemented in the script and can be accessed by the View Results option The chart Input_data displays the raw input data series C_WW_measured and Q WW_ measured As these series are not altered by interpolation or smoothing they are useful for a fast overview Fit times informs about the periods that have chosen to be considered for the parameter estimation Concentrations displays the measured and modelled concentrations C WW _ measured C_WW_fit C_FS and C_ Inf Discharge displays the measured and modelled discharges Q WW Q Inf Q baseflow and Q FS Residuals visualises the differences between C WW and C_WW_measured Output_data is not a real graphical representation but rather i
5. Method for the Quantification of Sewer Infiltration In case of a repeated data export after a new simulation AQUASIM will not overwrite the text file xxy lis The new data will rather be annexed to the old file To avoid this you should give a new name to the new file or delete the old file before doing a new data export However unlike the xxy lis file the xxy fit file is overwritten whenever a new parameter estimation is performed After having effectually finished a parameter fit AQUASIM does not automatically perform a new simulation with the most recent parameter set Therefore it is necessary to initialize and start the simulation again manually to provide the actual data for the graphical representations and the data export Version date of change changed by replaces version of 14 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration 4 Use of the R Script file APUSS ChemHydSep r This chapter describes the principal use of the R Script files APUSS ChemHydSep r and APUSS_ ChemHydSep _biblio r 4 1 General Remarks The algorithms for data analysis have been programmed in the R language Ihaka et al 1996 and packed in the libraries APUSS ChemHydSep r front end for user defined entries and APUSS ChemHydSep _biblio r general library of underlying functions All libraries and code examples are available for pu
6. graphs somehow seem to overwrite the statistical results If this happens simply paste again these lines 4 4 2 Generating an output file A result file results txt for external postprocessing of the curves describing the hydrograph separation can be produced with the following code Results lt cbind t t Q_baseflow t Q_infiltration Q ww_measured write table Results file results txt Remark The part that produces a result file Results lt cbind t t Q_ baseflow t Q_ infiltration Q ww_measured write table Results file results txt is for the moment commented out That means the character causes the lines to be not considered as an executable code To generate a result file just remove the characters and paste the lines again 4 4 3 Time units and intervals The time unit is days The unit 1 equals one day In order to generate the example data set we have measured every minute The data were then interpolated with a time step of 0 004 days This results in a data point beeing available every 86400 0 004 seconds 4 4 4 Data range considered for the parameter estimation The estimation of the 8 model parameters Qpaseftow Qo interflow Krec a b c A and phase is based on the whole range of the measured data sets input_file Q ww and input file COD_ww In practice the control of the subset of data that is considered for the parameter estimation is done by preprocessing the two input
7. N APUSS NY Assessing Infiltration and Exfiltration on the Performance of Urban Sewer Systems Contract number EVK1 CT 2000 00072 APUSS Project homepage http Awww insa lyon fr Laboratoires URGC HU apuss DELIVERABLE 1 3 Standard Operation Procedure SOP Quantification of Infiltration by the Analysis of Pollutant Time Series as an Intrinsic Tracer O Kracht EAWAG March 2005 DRESDEN O wa EAWAG 7 e TH TECHNISCHE f Czech Technical University in Prague Q INSA dy UNIVERSITAT 19 Faculty of Civil Engineering LYON o Swiss Federal Institute for Environm ental Science and Technology DHIE gay VI onossEMSCHER WATER amp ENVIRONMENT vee MIDDLESEX 22 UNIVERSITY An EAWAG E SOP Stable Isotopes Method for the Quantification of Sewer Infiltration Standard Operation Procedure SOP Quantification of Infiltration by the Analysis of Pollutant Time Series as an Intrinsic Tracer Number Version No pages Author Date Changed at Valid from 2 19 Oliver Kracht oliver kracht eawag ch EAWAG Environmental Engineering Ueberlandstrasse 133 CH 8600 Duebendorf Switzerland 28 March 2005 28 March 2005 28 March 2005 Ta SOP Stable Isotopes Method for the Quantification of Sewer Infiltration Table of Content 1 General PrintipleSssssssssisssssssessssissossosiisossosss ossosotessi assossosas essossssi essoss s soss svss 4 1 1 Ir
8. NA COD fs_phase ini NA User Input 11 User Input 12 User Input 13 User Input 14 User Input 15 User Input 16 User Input 17 Would mean The model consists of a constant baseflow Q_baseflow and a polynomic description for the COD foul sewage COD fs a and COD fs_b Interflow and time dependency of COD foul sewage COD _ fs amp COD_fs_ phase are assumed to be not present Version 2 date of change 28 03 05 changed by replaces version of 02 06 2003 18 OK EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration Whilst performing the model structure selection it is recommended to set the number of Monte Carlo Simulations down to n 3 to save computing time 4 4 9 Direct output of the individual parameter estimates The 8 model parameters Qbaseflow Qozinterflows Krec a b c A and phase are fitted from the start values given in User Inputs 11 to 17 To obtain information about the final estimates i e the final values that have been found for Input 11 to 17 you need to paste the following lines of the R Sript to the R console Output of identified model parameters estimates MCS Matrix of estimates from all MCS runs summary estimates MCS Statistical summary of estimates from all MCS runs 4 4 10 Save and or load an R workspace image It can be useful to save an image of the R workspace after having conducted the script calculations This al
9. aqu the time span from day 18 60 to day 18 85 is excluded from the parameter fit for the reason of a short breakdown of the flow measurement unit The data after day 26 7 are also excluded because of the initiation of a heavy rain event 3 1 4 Modelled concentration in the wastewater C_WW is a Formula Variable The modelled concentration in the wastewater is derived from a mixing of foul sewage and infiltration C WW C FS Q FS C Inf Q Inf Q WW C_WW is calculated for the whole modelled time span and can therefore be used for graphical representations In contrast the formula variable C_WW_fit is the modelled wastewater concentration that is used for the parameter fit For fit_times 1 it is automatically set to C_WW_fit C_WW In case of fit times 0 it is C_WW _ fit 0 therefore these periods have no influence on the parameter estimation It is also possible to use C_WW_fit instead of C_WW for the graphical representations It is then more clearly visualized which spans of time were used for the parameter estimation 3 1 5 Measured concentration in the wastewater C_WW_ measured is a Real List Variable t New data are imported by the use of the Read function use tab or comma separated text files The time argument must be a number that is strictly monotonic increasing from row to row Unfortunately it is not possible to read in real time and date formats We preferred the definition Version d
10. arameter space This problem will also be overcome by the foreseen Mont Carlo facility The relevance of the uncertainty of the estimated parameter values that is stemming from possible systematic errors which are embedded in the measurements of C_WW and or Q WW will also depend on the intended use of the examination findings As an example the over or underestimation of Q WW will of course lead to an over or underestimation of Q Infiltration However if the demanded result of the examination is not the absolute Q Infiltration but rather the fraction of infiltration in relation to the totally discharged wastewater volume X_Infiltration the larger part of the error will in turn be crossed out Nevertheless a certain part of error contribution will remain due to the nonlinear behaviour of the model and its parameter estimation functions 3 5 Practical hints for working with AQUASIM It is important to check if AQUASIM has really adjusted the parameters to the optimum Always restart the parameter fit to assure that the sum of squared residuals Chi2 does not reduce further If required repeat this procedure until the sum of squared residuals does not change anymore Similarly it is always advantageous to restart the parameter estimation with different initial conditions to control and confirm the first estimate Version date of change changed by replaces version of 13 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes
11. ate of change changed by replaces version of 8 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration of a time step of one to represent one day Pay attention to give an appropriate number of digits to not coarsen the temporal resolution Remark C_WW_ measured out is a Formula Variable It is only used for the data export This showed to be helpful for further data processing in spread sheet programs as it provides a time series with equal time steps which might not be the case with your input data It is simply C WW _ measured out C WW _ measured 3 1 6 Measured wastewater discharge quantity Q WW _ measured is a Real List Variable t Calculated from this the Formula Variable Q WW is the corrected measured wastewater discharge Q WW Q WW measured Q WW systerr b Q WW systerr_a The two auxiliary variables for the representation of possible systematic measurement are described at point Auxiliary variables 2 Remarks 1 It can be the case that several alternative time series Q WW_measured_1 Q WW_measured_2 OQ WW_measured_3 etc are available i e from alternative measuring principles In this case it is easy to set Q WW Q WW_measured_1 or Q WW Q _WW_measured_ 2 or Q WW OQ WW_measured_3 etc This definition of OQ WW allows narrowing down the amount of necessary changes to one single entry Thus it can
12. be avoided to edit every single formula where Q WW occurs 2 OQ WW is helpful for further data processing in spread sheet programs instead of using OQ WW_measured directly in analogy to C WW measured _out 3 1 7 Modelled extraneous discharge quantity of infiltration Q Inf is a Formula Variable that is defined by multiple Constant Variables 1 In the most basic model case the quantity of infiltration is assumed to be constant over time baseflow Q Inf Q baseflow possible extensions are 2 We additionally introduce a virtual linear reservoir that additionally causes an exponential receding discharge component interflow after rain events Q Inf Q baseflow Q interflow with Q interflow Q 0 interflow exp k_interflow t t_0_interflow k_interflow recession constant that defines the shape of the receding interflow hydrograph Note that unit of k_interflow is defined as 1 days Version date of change changed by replaces version of 9 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration Q_ 0 interflow Discharge from the virtual interflow reservoir at the point in time t_0_interflow To open the possibility to account for the influence of multiple rain events within the time of investigation a set of multiple Q interflow_i is available Q interflow_1 Q interflow_2 and Q interflow_3 It is simply Q _interflow gt Q interfl
13. blic use As we see our role in the provision of a thorough functionality instead of a user friendly software design this implementation of the code relies completely on the user interface of R As we provided no GUI Graphical User Interface we recommend the use of convenient editors e g WinEdt or SciViews R 4 2 Working with R It is not necessary to have an understanding of R for the execution of the data analysis script However some basic knowledge on R s data structure and file handling is helpful for the data analysis The binary distribution of R comes with a documentation that is stored in the doc folder More useful documentation for a beginner can be found on www t project org in the Documentation Contributed section Help on specific problems can be sought at the R newsgroup see www r project org In general every S Plus documentation is also valid for R 4 3 Principal use of the R Script files A data analysis with the supplied R Script files will generally consist of the following steps 1 Copy the four files ChemHydSepMCS R ChemHydSepMCS biblio R COD_RL txt and Q_ RL txt to a folder on your hard disk the working directory Users may exchange the example data files COD_RL txt and Q RL txt by files containing their own data Remark both files have to be recorded with the same time steps same time data in the first column 2 Open the file ChemHydSepMCS R with a text editor e g WinEdt or SciViews R
14. d graphical output figure 1 Version date of change changed by replaces version of 17 2 28 03 05 OK 02 06 2003 S Ta Total Amount of Infiltration OP Stable Isotopes Method for the Quantification of Sewer Infiltration Average Infiltration Ratio gt 8 gt oS s gt 2 2 T T T T T T 1 5 2 j T T T T 1 0 0 e 00 4 0e 06 80et 06 1 2 e 07 0 0 0 2 0 4 0 6 0 8 1 0 Q total I X Infiltration Hydrograph Separation So 7 m Lo G b Wastewater Baseflow Interflow Separation o Infiltration Span for the calculation of totals Time days Data Fit Fo Es a og Oo 9 18 20 22 24 26 Time days Figure 1 Standard graphical output 4 4 7 graphical control of fit quality of the R script file ChemHydSepMCS R For a first control of model structure a plot is generated automatically that compares the modeled COD time series to the measured data figure 1 4 4 8 Control on the model definitions From version 1 1 or higher the model definition can easily be controlled by the User Inputs 11 to 17 If an initial value a number is entered here the parameter will be considered in the model and a parameter value will be estimated Alternatively the entry NA excludes the model part that is described by this parameter In example Q _baseflow ini 40 Q 0 interflow ini NA k_rec ini NA COD fs_a ini 700 COD_fs_b ini 10 COD _fs_amp ini
15. d wastewater discharge optional USC c ccccecsceesseceteceeeeeeeeeseeesseenteeeees 10 3 1 9 Auxiliary variables i cece ascanaGvaitacsieeenaansneancwnensensnnin cen catteonsanenceiasitnerunrexcisvanentencnaneanauats 10 3 410 Auxiliary variables 2 sccpstecesssevasessacencnnnecnnn atacand ence eaten aceite 10 3 2 Principle procedure for conducting a parameter estimation ccceeeeteeseeereeeeeeeeeeeeees 11 3 3 Implemented graphics for visualization of the results 00 0 0 cceeccecssceeseeeseeeeeeeeeeesaeeeeaees 12 3 4 Remarks on the uncertainties of the estimated parameter values ecceeceeeeeeeeteeeeeee 12 3 5 Practical hints for working with AQUASIM sssssssssssssessssessesersssessessrssressessrssresseeseeseessee 13 4 Use of the R Script file APUSS ChemHydSep r ccssssssssssssesssceeeeee 15 4 1 General Remarks cscs ere cleat wes natn eo caw ne ee E TAE 15 4 2 Wotking With ER sacwcsezcat vincesescccweuddsanncseuobutiss ncscausyanddehasenedusboaysubicesuesuoniacealdiededuasietiastinates 15 4 3 Principal use of the R Script files 0 scciss scvssissnestdessccensatecesassacctantsaunadeanecseiaandeussssaiveamnionss 15 44 FAQ s on the R seript file ChemHydSepMCS R scsccsesacecesinecetasssscisatsnncsseunteceuieenacavasstends 16 4 4 1 Output of statistical Parameters eis ciscessiccadciaacsaisessnncssonicnteranssadbesdhvaeasedianetsuandesaseaces 16 4 4 2 Generating an GOTO ING sede sntrsestsnndduuvinceverepsnesuceieecu
16. ers may exchange the example files with their own data Version date of change changed by replaces version of 5 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration 2 Methodological Description The underlying theory of the pollutant time series method is described in detail in the scientific paper text Quantification of infiltration into sewers based on time series of pollutant loads Kracht and Gujer 2004 which is attached as a separate file This text is regarded to be a principal part of this SOP Version date of change changed by replaces version of 6 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration 3 Use of the AQUASIM model file Sewer_Infiltration aqu This chapter describes the use of the AQUASIM model file Sewer_Infiltration aqu It explains the concept of the script and gives the user the necessary information to run it on his own set of data For general information on the use of AQUASIM please refer to its manual Reichert 1998 The script is filled with an example data set that is meant to be overwritten by the users own data 3 1 Model description In the following the single elements of the model are described first Afterwards a short description of the principle procedure for conducting a parameter estimation for the quantification of infiltration i
17. files COD and Q the whole series contained in these two files will be the basis for t the parameter estimation To exclude certain time spans these parts need to be deleted from the read in files Version date of change changed by replaces version of 16 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration 4 4 5 Data range considered for the calculation of totals The date range that is considered for the calculation of totals Total Amount of Infiltration Average Infiltration Ratio is specified by t_start and t_end User Input 4 and User Input 5 Based on the estimates for Qbaseflow Qo interflow and krec the total volume of infiltration that was discharged within the span of time between t_start and t_end is integrated This result is made available by the R Script under the output variables name Total inf MCS Analogous the output variable X _ Total inf MCS relates the volumes of infiltration to the total amount of wastewater discharge within this considered span of time 4 4 6 Consideration of input uncertainties with respect to the two measured variables To quantify the effect of input uncertainties stemming from possible systematic errors embedded in the two measured variables on our estimates a Monte Carlo Simulation step is included in the R Script For both measured variables CODwastewater and Qwastewater a hypothetical consta
18. ion then start Simulation 4 Evaluate the results and the quality of the parameter fit critically a Use the build in graphic representations b Have a look at the text file xxy fit that is automatically produced by AQUASIM Besides the estimated values of the parameters also estimated standard errors and a correlation matrix of the parameters are given which should be your decisive factors to judge the identifiability of the parameters Remark Standard errors and correlation matrix are only calculated when using the secant algorithm In case of convergence problems it can be helpful to perform a preliminary parameter estimation with the simplex algorithm first and then to redo the parameter estimation again with the secant algorithm If the secant algorithm can not calculate standard errors this indicates a bad identifiabilty of the parameter set 5 You can now continue to refine the model by successively activating more of the offered parameters in the parameter estimation Control the model refinements by returning to point 4 Remark The use of a large quantity of parameters expands the flexibility of the model This improves the parameter fit and reduces the sum of squared residuals However as a matter of fact the identifiabilty of the individual parameters will be impaired and standard errors Version date of change changed by replaces version of 11 2 28 03 05 OK 02 06 2003 EAWAG T
19. lows accessing all variables later by reloading them to R without the time consuming need to conduct all R calculations again save image file imagefile Rdata compress TRUE load imagefile Rdata 4 4 11 Excluding parts of an R script In the script code the prefixing character causes a line to be not considered as executable code commenting out If you want to include lines of the script that are for the moment commented out you need to remove the characters This offers a possibility to include or exclude parts of a script from being executed Version date of change changed by replaces version of 19 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration 5 References Ihaka Ross and Gentleman Robert 1996 R A Language for Data Analysis and Graphics Journal of Computational and Graphical Statistics 5 3 299 314 Kracht O Gujer W 2004 Quantification of infiltration into sewers based on time series of pollutant loads Proceedings of the 4 International Conference on Sewer Processes and Networks Funchal Madeira Portugal 22 24 November 293 300 Reichert P 1998 AQUASIM 2 0 User Manual Technical report Swiss Federal Institute for Environmental Science and Technology EAWAG Diibendorf Switzerland Version date of change changed by replaces version of 20 2 28 03 05 OK 02 06 2003
20. newadiseavinedereensenmedenteunndisevieds 16 4 4 3 Tineunits ANG mterval Sessien ae EE A A aa 16 4 4 4 Data range considered for the parameter estimation cccccesceeeeeeeeeeteeceeeeteeeees 16 4 4 5 Data range considered for the calculation of totals cccccccesceeceeeeeeeteeeeteeeteeeees 17 4 4 6 Consideration of input uncertainties with respect to the two measured variables 17 4 4 7 graphical control of fit quality scesaaveccsskcnissavennednacesunesecnneaeaacasesbravensntvecunasbacenenrvacssaiees 18 4 4 8 Control on the model definitions ssssssessssseesessessesensessesesseseesessestesessesressssersessesss 18 4 4 9 Direct output of the individual parameter estimates s snsssnseesssesesseseessessresresseese 19 4 4 10 Save and or load an R workspace image ajscssiccvusinscadesnnsavsessntaveddunstiuiuseasui Mvedbvnesieas 19 4 4 11 Excluding parts of an R script ss ssesessseessesessressessresesseesrssresseeseestrsseeseserssesseseese 19 D ReferentesS sssssssssssessessssessossscsssssssosssossosessosssses ossssessossssessossssssosssss so sesssos ssssse0s 20 Version date of change changed by replaces version of 3 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration 1 General Principles 1 1 Introduction The following description gives a compendium for the quantification of infiltration into sewers by the analysis of pollutant time se
21. ng parameter estimation functions The algorithm that is employed calculates these derivatives using the finite difference approximation Di P V Ay Y OV Ay Where Ayx is chosen to be 1 of the standard error se yx The approximated standard errors se p of the estimated parameter values p are then derived from the diagonal elements of the covariance matrix Cov p by se p Cov p In consequence two aspects must be pointed out 1 This approximation of standard errors for the estimated parameter values only takes into account the random errors statistical scattering that are assigned to the measured data It must be underlined that the influence of systematic measurement errors on the estimated parameter values is not automatically calculated by the script Systematic errors are not included in the standard errors of the parameter estimates that are given in the xxy fit file It is foreseen to supply a Mont Carlo facility work of the next weeks to allow for an automated calculation of the total accuracy of measurement 2 Depending on your model definitions this means the parameters constant variable you have chosen to be active in the model the model results C_WW might show a distinct non linear dependency on the parameter values The employed linear approximation therefore limits the validity of the error estimation to a relatively small surrounding around the estimated parameter values within the p
22. ning the variable Q WW to Q WW Q WW _ measured Q WW systerr b Q WW systerr_a C_WW systerr_a offset error in the wastewater concentration measurements This variable is assigned the value 0 if no offset error is assumed C_WW systerr_b constant relative error in the wastewater concentration measurements This variable is assigned the value 1 if no relative error is assumed These two variables are introduced to the model by redefining the variable C WW to C_ WW C_FS Q FSC Inf Q Inf Q WW C WW systerr_a C WW _systerr_b 3 2 Principle procedure for conducting a parameter estimation 1 Read in the data for Q WW _ measured and C WW _measured 2 Start the parameterfit type basic with a simple model first In example with only C_FS_a and Q baseflow beeing active for the parameter estimation Pay attention to have correctly filled the entry in the Initial Time field that is accessible by the Edit Calculation for Parameter Estimation option gt start the parameter estimation routine Attention possible pitfall The other relevant parameters C_FS_b C_FS_c C_FS_amp and Q_interflow_i must be set to the value 0 Otherwise they are active in the model even if they are not active for the parameter estimation 3 Set the appropriate Output Steps and Initial Time in the Edit Calculation Definition of the simulation definition calc 1 Initialize the simulat
23. nt offset error a and a relative error is assumed COD wastewater measured a COD Oeics name at p O iienaa wastewater real The number of Monte Carlo Simulation runs to be performed is specified in User Input 21 n MCS The assumed statistical key parameters for the probability distributions of these error terms must be specified in User Input 18 syst_errors_means 19 syst_errors_ranges and 20 syst_errors_stdvs Details about the format of these inputs can be found in the scripts embedded comments According to these specifications the parameter estimation is repeated n MCS times Each of these estimations is based on a newly drawn random sample for the error parameters As an intermediate result we obtain a number of n MCS sets of estimates for Opaseftow Qo interflow ANA krec From these sets a number of n MCS simmulation results for the two output variables Total inf MCS and X_Total inf MCS is calculated The statistical key parameters of the probability distributions of Total_inf MCS and X Total inf MCS are made available by the following R code summary Total_inf MCS summary X_Total_inf MCS quantile Total_inf_ MCS probs c 0 025 0 975 quantile X_Total_inf_ MCS probs c 0 025 0 975 The distribution of Total inf MCS and X_Total_inf MCS is also graphically displayed in the two small histograms that are part of the implemented standar
24. ntended for the data export by the list to file functionality It is used to export the relevant time series data to a spread sheet compatible text file xxy lis Output_data contains time series of the variables Q WW Q baseflow Q interflow C_WW_measured out C WW and C FS However remind that all other graphics have the possibility to be directly exported to a text file in the same way 3 4 Remarks on the uncertainties of the estimated parameter values The use of a frequentistic parameter estimation and error approximation has certain implications on the interpretation of the results that should shortly be summarized here The model parameters p that are represented by the means of constant variables are estimated by minimizing the sum of the squares of the weighted deviations between measurements and calculated model results 2 xv p gt Yk measured Yk p k 1 Yk measured Where Yk measured is the measured value at the point in time k of the time series and y p is the corresponding model result n is the total number of data points The standard deviations Oyk measured are used as the weighing factors Version date of change changed by replaces version of 12 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration The covariance matrix Cov p of the parameter estimates is derived by the use of a linear approximation of the correspondi
25. od 1615 16 0 Rpreee es mr ter E ee reer er pee eee re me eee ree eer ete 4 1 2 COME OF th exampl packa tes rocis iernii eiee A EEE ia 4 1 3 T rminolO pyansa ca ese ie e EA nls R E EE ARA R E ERTE 5 1 4 Principles of the pollutant time series method 2 0 0 0 cc ecccceseceeeceeeeeeeeceseeceseceteeeeeeesseeesaeens 5 1 5 Site description example data set R mlang CH s ssssensssoeseseesessseessrsensseesseserssressessees 5 2 Methodological Description ooeossooessooessoeessoosssoesesoosssseossoossssesesoossssocsesoosssssee 6 3 Use of the AQUASIM model file Sewer _Infiltration aqu soossssosessossss00 7 3 1 Model description sieisen E E EE E EEE EE ER TEE 7 3 1 1 Concentration in the infiltrating Water eeceesceesseceteceeeceeeceeseecsaecneeeeeeeeseeceaeens 7 3 1 2 Concentration in the foul sewage ie sacassccsansudnedacescalcantebeniensatahccteviglaeinencaeeamiends 7 3 1 3 Time spans that are considered for the parameter estimation fit_times 8 3 1 4 Modelled concentration in the Wastewatel ccccccscceeseessecsteceseceeeeeeseecsaeceeeeeeeeenees 8 3 1 5 Measured concentration in the wastewater ss ssessesesessesseesreseessesstesresstestesrnsseesee 8 3 1 6 Measured wastewater discharge quantity ss sssssessssseesseesseseesseesesreesseserssressessese 9 3 1 7 Modelled extraneous discharge quantity of infiltration 0sssenseeseesesseseesseesseseee 9 3 1 8 Modelle
26. ollutant concentrations and discharged wastewater The data analysis uses a mixing model describing the concentration of pollutants C in the wastewater in dependency of the quantity of wastewater flow Q and time t equation 3 The employed parameter set contains variables to consider time dependencies of the infiltration rate as well as temporal fluctuations of the pollutant concentration in the foul sewage equations 4 and 5 _ eee O firain i C Foul Sewage eq 3 Wastewater model O rasina with C roul sewaz TG O poul Sewage eq 4 and O mfitration O saseflow t Onterftow t eq 5 The parameters defining Qinfittration are Subsequently estimated by fitting a modelled time series of pollutant concentrations to the measured data 1 5 Site description example data set Riimlang CH The R Scripts are distributed with an example data set that has been derived from a measurement campaign conducted in the village of R mlang in the fall of 2003 Riimlang is a commune of about 5 400 inhabitants located to the north eastern boarder of the agglomeration of Zurich The total length of its sewer system amounts to 23 1 km R mlang has a mixed infrastructure with no predominant type of industry COD_RL txt and Q RL txt are example ASCI text files containing a COD and discharge time series respectively The in line measurements were conducted in a trunk sewer that connects the village to the regional treatment plant Us
27. ow_i Usually t_0 interflow_iis manually set to an arbitrary point of time in between the start and the end of the corresponding rain event The end of a rain event would mean in this case the point in time when all inflow from direct surface runoff into the sewer has ceased Note the fact that t 0 interflow_i is generally not activated in the parameter estimation as it can not be estimated independently from Q 0 interflow and t_0 interflow The estimated Q 0 interflow and t_0_interflow are as the case may be purely virtual values not necessarily occurring in the real time series However the only important demand on these parameters is to adequately describe the discharging behaviour of the interflow reservoir during the investigated span of time It is recommended to initially set all Q 0_interflow_i to zero and therewith not include an interflow component in the model If required this part can successively be added later Pay attention to the identifiability of these parameters 3 1 8 Modelled wastewater discharge optional use Q WW _ modelled is a Formula Variable that is defined as Q WW modelled Q Inf Q FS Q WW systerr_a Q WW _systerr_b This variable is an additional option that allows for setting a second fit target Q WW modelled Q WW_ measured as it is defined in the parameterfit type extended This variable is not required for the parameter estimation with the by default parameterfit type basic
28. ries as an intrinsic tracer Pollutant Time Series Method Detailed background information on the underlying theory of the method and the required boundary conditions are described in a scientific paper text that was presented at the 4th International Conference on Sewer Processes and Networks Kracht and Gujer 2004 This text is attached as a separate file The method is based on a combined analysis of measured time series of pollutant concentrations and discharged wastewater It is suited to quantify the infiltration into a sewer system on catchment or subcatchment scale where a continuous discharge of wastewater can be assured A minimum amount of wastewater flow is required for the disturbance free operation of the measuring devices which may be critical during minimum night flow Furthermore predominant types of industrial effluents should be excluded as this may hinder a regular data analysis 1 2 Content of the example packages The example packages are meant for an exemplification of the described data analysis They consist of the following files 1 AQUASIM example package Sewer_Infiltration aqu Sewer _Infiltration aqu is an AQUASIM system definition file The example data sets are contained in the file 2 R Script example package APUSS_ChemHydSep r APUSS_ChemHydSep_biblio r COD_RL txt Q RL txt APUSS_ ChemHydSep r and APUSS_ChemHydSep_biblio r are R Script files The file name will be extended by a suffix indica
29. s given 3 1 1 Concentration in the infiltrating water C_Inf is a Constant Variable The concentration in the infiltrating water is assumed to be constant over time In the case of COD chemical oxygen demand the assumption C_Inf 0 is expected to be a good approximation 3 1 2 Concentration in the foul sewage C_FS is a Formula Variable that is defined by multiple Constant Variables 1 In the most basic model case the concentration in the foul sewage is assumed to be constant over time In this case it is simply C FS C FS a possible extensions are 2 The Concentration in the foul sewage is depending on the quantity of the foul sewage discharge C FS C FS a C FS b Q FS C FS c Q _ FS 2 It is recommended to start with the basic case C_FS C_FS a For this C FS _b and C FS are simply assigned the value 0 and are not included in the parameter estimation If required both parameters can then successively be added to the model Pay attention to the identifiability of these parameters 3 The Concentration in the foul sewage is depending on the time of day C_FS C _FS amp sin C_FS freq t C_FS_phase 2 pi It is recommended to start with a value C_FS_amp 0 and at first not to incorporate C_FS_ amp to the parameter estimation this is the basic case with a time invariant C_FS If required this part can then later be added to the model as follows C_FS_freq is recommended to be assigned the value 1
30. ting the version number Only ChemHydSepMCS R is foreseen to be edited by the user as it contains the model input definitions COD_RL txt and Q_RL txt are example ASCI text files containing a COD and discharge time series respectively Version date of change changed by replaces version of 4 2 28 03 05 OK 02 06 2003 EAWAG T SOP Stable Isotopes Method for the Quantification of Sewer Infiltration 1 3 Terminology The amount of discharged wastewater in a sewer generally shows a characteristic diurnal behaviour This hydrograph is composed of a variable volume of real foul sewage and a certain quantity of parasitic infiltration insisting Qeout Sewage O infiltration Equation 1 Infiltration is groundwater or other types of extraneous water that enters the sewer system through defective pipes cracks and fissures pipe joints couplings manholes and house connections In this text we do not distinguish this type of undeliberate infiltration from extraneous water stemming from creeks and drainages which were intentionally connected to the sewer system An often used expression is the amount of infiltration as a fraction of the total discharge of wastewater in the sewer infiltration ratio Q ntiltration Infiltration Equation 2 O wastewater 1 4 Principles of the pollutant time series method The fraction of infiltrating water is determined from a combined analysis of measured time series of p
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