R-Groundwater: model user's manual for NERC Virtual Observatory
Contents
1. OR 11 059 Table 3 Format of observed groundwater level input file File contents Description dt gwl Header containing string dt gwl 1970 01 15 16 82 Date in yyyy mm dd format and groundwater level 1970 02 15 20 88 1970 03 15 22 40 A space separated file 1970 04 15 21 81 1970 05 15 21 91 1970 06 15 20 66 1970 07 15 19 46 1970 08 15 17 96 1970 09 15 16 68 1970 10 15 15 46 1970 11 15 14 28 1970 12 15 13 75 1971 01 15 14 39 1971 02 15 16 18 1971 03 15 19 42 etc Table 4 Format of rainfall and PE input file File contents Description dt pptn pe Header containing string dt pptn pe 1970 01 15 72 0 12 0 Date in yyyy mm dd format followed by rainfall mm and PE mm 1970 02 15 70 9 24 2 1970 03 15 65 0 40 6 A space separated file 1970 04 15 43 3 56 2 1970 05 15 90 8 82 8 1970 06 15 10 4 85 6 1970 07 15 14 0 92 8 1970 08 15 96 9 77 2 1970 09 15 52 3 61 4 1970 10 15 22 5 44 1 1970 11 15 46 0 26 4 1970 12 15 124 0 12 4 1971 01 15 47 6 11 0 etc 10 OR 11 059 Table 5 Example R file in which recharge model parameter ranges are defined Name of rainfall file Change the name inside the df Rain File read table Rainfall_ PE txt header T DO NOT MODIFY THE FOLLOWING 3 LINES dt Date In as POSIXct df Rain FileSdt nu Recharge In df Rain FileSpptn 1000 nu PE In df Rain FileSpe 1000 Parameters for the UZ transfer funtion Are the number of weights random or sp2. S is the storage coefficient Sh is the change in groundwater head L over time dt T and h is the groundwater head L The discharge term Q is calculated using an equation of the form __Tdy 0 5Ax Q Equation 10 where Ah L is the difference between the groundwater head and the elevation of an aquifer outlet point and T is the appropriately calculated transmissivity L T OR 11 059 Dx Figure 3 Basic structure of lumped catchment groundwater model Groundwater flow out of the aquifer is split into a series of discharges via outlets at different elevations Each of these outlets is associated with a vertical section of aquifer to which a value of hydraulic conductivity is specified Figure 4 The aquifer is drained by a stream with perennial Qp and intermittent Qw flow components A third discharge component Qa is added at the base of the system to represent groundwater discharge below the level of a perennial stream The groundwater level may fall beneath the level of the perennial stream hp but will always be above the base of the aquifer Zp Hydraulic conductivity is defined using three piecewise constant values The section of the aquifer discharging to the intermittent stream above hy is characterised by hydraulic conductivity Kw The perennial stream is fed by a zone with hydraulic conductivity Kp and the groundwater discharge zone below hp is controlled by a hydraulic conductivity K Th
3. 88 British Geological Survey 1835 NATURAL ENVIRONMENT RESEARCH COUNCIL R Groundwater model user s manual for NERC Virtual Observatory implementation Groundwater Science Programme Open Report OR 11 059 Actual Evaporation Precipitation Soil Moisture Model Runoff f FAO 56 soil landuse Potential recharge Soil drainage spread over n months according to Unsaturated Zone Transfer function Weibull distribution v Kw hw 1 t p 4 e Qw Kp pect EEEE bene _ hp 5 Qp Ka gl ha BRITISH GEOLOGICAL SURVEY GROUNDWATER SCIENCE PROGRAMME OPEN REPORT OR 11 059 R Groundwater model user s manual for NERC Virtual Observatory implementation The National Grid and other Ordnance Survey data are used with the permission of the Controller of Her Majesty s Stationery Office Licence No 100017897 2007 C R Jackson and L Wang Keywords Lumped groundwater model R code NERC Virtual Observatory Front cover Structure of R Groundwater model Bibliographical reference JACKSON C R AND WANG L 2011 R Groundwater model user s manual for NERC Virtual Observatory implementation British Geological Survey Open Report OR 11 059 19pp Copyright in materials derived from the British Geological Survey s work is owned by the Natural Environment Research Council NERC and or the authority that commissioned the work You may not copy or adapt this public
4. 9 1 1 SOIL MOISTURE BALANCE MODEL Potential recharge from the base of the soil zone is calculated using the FAO method FAO 1998 which describes soil moisture as a function of both vegetation root depth and the propensity of vegetation to withdraw available water from the soil Thus this approach can appropriately represent soil moisture response to contrasting land cover types In the FAO method soil moisture is calculated using a maximum root depth Z and moisture depletion fraction dp parameter which varies between vegetation and soil types The amount of water available to plants after a soil has drained to its field capacity is described as the total available water TAW TAW is defined as a function of the field capacity FC wilting point WP and maximum root depth Z such that TAW Z FC WP Equation 1 As the moisture content of the soil column decreases vegetation will find it more difficult to extract moisture from the soil matrix The fraction of TAW that can easily be extracted before this point is reached is described as readily available water RAW The value of RAW is related to TAW by a land cover defined depletion factor dp RAW dp TAW Equation 2 where Rf is the rainfall and SMD is the soil moisture deficit The intermediate soil moisture deficit SMD is then SMD SMD PE Rf Equation 3 where PE is the potential evaporation If in the above calculation SMD drops below RAW the evaporati
5. ated hydrograph for the Baydon Hole borehole Berkshire Downs 2 1 INPUT FILES The model requires five input text files containing 1 Model control parameters 2 A times series of observed groundwater levels against which the model is calibrated 3 Time series of rainfall and potential evaporation 4 An R file in which parameter value ranges for the soil moisture balance model and recharge transfer function are specified 5 An R file in which parameter value ranges for the saturated groundwater model component are specified The format of these files is presented in Table 2 to Table 6 OR 11 059 Table 1 Summary of model parameters Model Parameter Data informing parameter estimation component Runoff coefficient RO River base flow indices 1 BFI E s Field capacity FC FAO Irrigation and Drainage paper 56 FAO 1998 n o 5 Wilting point WP FAO Irrigation and Drainage paper 56 FAO 1998 g Te Maximum rooting depth Z FAO Irrigation and Drainage paper 56 FAO 1998 n Depletion factor dp FAO Irrigation and Drainage paper 56 FAO 1998 Number of months over which to distribute Cross correlation of monthly groundwater levels and lagged monthly rainfall g 5 potential recharge n FE Oo Weibull shape parameter k Calibration parameter but varied between values that allows a broad range of distributions to be tested aq B ree Weibull shape parameter A Calibration paramet
6. ation without first obtaining permission Contact the BGS Intellectual Property Rights Section British Geological Survey Keyworth e mail ipr bgs ac uk You may quote extracts of a reasonable length without prior permission provided a full acknowledgement is given of the source of the extract Maps and diagrams in this book use topography based on Ordnance Survey mapping NERC 2011 All rights reserved Keyworth Nottingham British Geological Survey 2011 BRITISH GEOLOGICAL SURVEY The full range of our publications is available from BGS shops at Nottingham Edinburgh London and Cardiff Welsh publications only see contact details below or shop online at www geologyshop com The London Information Office also maintains a reference collection of BGS publications including maps for consultation The Survey publishes an annual catalogue of its maps and other publications this catalogue is available from any of the BGS Sales Desks The British Geological Survey carries out the geological survey of Great Britain and Northern Ireland the latter as an agency service for the government of Northern Ireland and of the surrounding continental shelf as well as its basic research projects It also undertakes programmes of British technical aid in geology in developing countries as arranged by the Department for International Development and other agencies The British Geological Survey is a component body of the Natural Envi
7. e storativity of the aquifer is depth invariant The discharge terms Q are again calculated using Equation 3 where Ah L is the difference between the groundwater head and the elevation of the outlet below or the difference in elevation between two outlets depending on the current groundwater head and T is the appropriately calculated transmissivity L T OR 11 059 y Kw ed eee E S EE _ gt Qw Kp hp oo ee S S te P E spe tae ene E EN p Qp Ka ee eee ee eee gt Qa I Figure 4 Example lumped groundwater model structure for application to a Chalk aquifer OR 11 059 2 Application of the model The model is written in the R programming language Individual models of groundwater level hydrographs are calibrated through a Monte Carlo process in which parameter values are sampled from user defined ranges All of the model parameters can be defined as calibration parameters however some can be identified reasonably accurately based on hydrogeological judgment and are therefore fixed A summary of the parameters for the model shown in Figure 4 and the data used to determine Monte Carlo calibration ranges for them are listed in Table 1 An example comparison between an observed and simulated chalk hydrograph using this model is shown in Figure 5 A Validation Calibration Validation Obsarved Bast 50 000 modals I Groundwater Level m a 0 1975 120 1985 1980 1985 m0 m05 Figure 5 Observed and simul
8. ecfied S R keep the ch Calver Weights Choice R If R random give the range of the number of months over which potential recharge is spread nu Calver Range U c 12 12 If S specified then give the monthly weights Monthly weights for transfer function u nu U c 0 2 0 4 0 3 0 1 Are the Weibull distribution k and lambda random or specfied S R keep the ch Calver Weibull param Choice S Range for Weibull distribution shape parameter k nu Wk Range c 2 6 Range for Weibull distribution scale parameter lambda nu Wlambda Range c 1 8 3 0 Runoff coefficient value equals one minus the base flow index nu ROCoeff c 0 01 0 3 Soil parameter values ranges nu FC c 0 2904 0 2904 nu WP c 0 1529 0 1529 nu Zr c 0 5 1 3 nu dp c 0 02 0 2 nu SMDStart c 0 0 0 0 nu PEAEFrac c 0 1 0 1 11 OR 11 059 Table 6 Example R file in which groundwater model parameter ranges are defined SET PARAMETER RANGES BY CHANGING VALUES WITHIN c Length of aquifer nu Length c 4408 4408 Kw Hydraulic conductivity for heads gt Hw nu K High c 30 50 Kp Hydraulic conductivity for heads gt Hp nu K Low c 30 45 Ka Hydraulic conductivity for lt Hp nu K Base c 0 02 0 2 S Storage coefficient nu S Low c 0 01 0 03 Ha Base elevation of the aquifer nu H Low c 46 46 Hp Outlet elevation for perennial river nu H Mid c 4 8 Hw Outlet elevation for ephemeral rive
9. er but varied between values that allows a broad range of distributions to be tested Elevation of intermittent stream outlet hy DTM elevation of intermittent streams Elevation of Perennial stream outlet h DTM elevation of perennial streams Elevation of groundwater discharge outlet Geological and hydrogeological boreholes logs o 2 S Hydraulic conductivity of upper aquifer Calibration ranges based on pump test data and hydrogeological experience E above h Kw g E Hydraulic conductivity of middle aquifer Calibration ranges based on pump test data and hydrogeological experience A between hw and hp Kp Hydraulic conductivity of lower aquifer between h and ha Ka Calibration ranges based on pump test data and hydrogeological experience Storativity of aquifer S Calibration ranges based on pump test data and hydrogeological experience OR 11 059 Table 2 Format of main input file Input txt Line File contents Description 1 Using the output from a previous run Y or N Comment line 2 N Flag to determine if running previously calibrated models 3 If Y run all behavioural models i e that met error criterion Y or N Comment line 4 N Flag to determine if should re run all behavioural models 5 If N specify the number of best models to be used Comment line 6 10 If re running subset of behavioural models how many should be run 7 Recharge parameter input R file
10. les 7 References 13 FIGURES Figure 1 Structure of R Ground Water essseseesesseseesesseeeessestsesstseestssersessestesesseseesessesees 1 Figure 2 Example Weibull probability density function 000 0 eee eeeeeeete cee ceeeeeeeneeeeees 4 Figure 3 Basic structure of lumped catchment groundwater model ecceeeeeeeeeeeee 5 Figure 4 Example lumped groundwater model structure for application to a Chalk AOI Cis cseu coteedsdcoalardecthn dalscanash a ea a a e r aS 6 Figure 5 Observed and simulated hydrograph for the Baydon Hole borehole Berkshire DOWANS eaa a a a i a E ides E e AE aa EEEN 7 TABLES Table 1 Summary of model parameters csc scecasicctscssseevsludtesvee niece cispneieleddentiens 8 Table 2 Format of main input file Input txt aneuele siicktiscAaeaeacnted Sadie 9 Table 3 Format of observed groundwater level input file eee ee ceeeeeeeeteeeeseeees 10 Table 4 Format of rainfall and PE input file cece ccecceesceeseeeeeecnseceeeeeeeeeseeesaeenes 10 Table 5 Example R file in which recharge model parameter ranges are defined 11 Table 6 Example R file in which groundwater model parameter ranges are defined 12 OR 11 059 Summary This report describes the structure and usage of the R Groundwater model for implementation within the NERC Virtual Observatory project R Groundwater is a simple lumped catchment groundwater model written in the R programming language and run within the R environment It has been deve
11. loped to model groundwater level time series at observation boreholes by linking simple algorithms to simulate soil drainage the transfer of water through the unsaturated zone and groundwater flow Time series of flow through the outlets of the groundwater store are also generated which can be related to river flow measurements The model is calibrated through a Monte Carlo process by randomly selecting input parameter values from ranges specified by the user Simple text files are used to define the input to the model and to write the output OR 11 059 1 Structure of lumped catchment groundwater model The R Groundwater model consists of three components 1 A soil moisture balance model producing a time series of potential recharge soil drainage 2 A simple transfer function representing the delay in the time of the arrival of recharge from the base of the soil to the water table 3 A lumped catchment groundwater model based on a simple Darcian representation of flow out of a series of aquifer outlets Each of these components is described in the following subsections The structure of the model is shown in Figure 1 Actual Evaporation Precipitation Soil Moisture Model Runoff soil landuse Potential recharge Soil drainage spread over n months according to Weibull distribution Unsaturated Zone Transfer function Actual recharge Vv a ha Figure 1 Structure of R Groundwater OR 11 05
12. name Comment line 8 Recharge_Model_Parameters txt Name of recharge model parameter input file 9 Groundwater parameters input R file name Comment line 10 Groundwater_Model_Parameters txt Name of recharge model parameter input file 11 Simulation start end date format DD MM YYYY Comment line 12 15 01 1970 Simulation start date in dd mm yyyy format 13 15 12 1989 Simulation end date in dd mm yyyy format 14 Initial groundwater level Comment line 15 16 8175 Initial groundwater head m 16 Number of Monte Carlo calibration runs Comment line 17 1000000 Number of simulations in Monte Carlo run 18 Rainfall and PE data file name Comment line 19 Rainfall_ PE txt Name of rainfall and PE input file 20 Groundwater level file name Comment line 21 Groundwater_levels txt Name of input file containing observed groundwater levels 22 Input directory Comment line 23 E NERC_VO_VERSION Input directory path 24 Output directory Comment line 25 E NERC_VO_VERSION Results Output directory path must exist before model is run 26 Run name Comment line 27 Example Name of run which forms start of output file names 28 Error measure flag 1 RMSE 2 COREL 3 RMSE of extreme values 4 NSE Comment line 29 1 Flag specifying which error measure to use 30 Error measure value only those meeting criterion are stored Comment line 31 1 7 Error measure limiting criterion value for identifying behavioural models
13. on AE will take place at a lower rate determined by the equation 70 2 AE pe TAW SMD when SMD gt RAW Equation 4a TAW RAW AE PE when SMD lt RAW Equation 4b AE 0 when SMD gt TAW Equation 4c The calculation of SMD at the end of each timestep is then made with respect to the above such that SMD t SMD AE PE Equation 5 OR 11 059 The excess water EXW or the amount of water that is available for surface runoff and potential groundwater recharge is calculated as the amount of precipitation remaining after losses through interception evapotranspiration and soil moisture replenishment such that EXW Rf AE SMD _ SMD when SMD 0 Equation 6a t 1 EXW SMD when SMD lt 0 Equation 6b The potential recharge PR is then calculated as PR BFIx EXW Equation 7 where BFI is the baseflow index The parameters for FAO method can be based on those given in the FAO Irrigation and Drainage Paper 56 FAO 1998 1 2 UNSATURATED ZONE TRANSFER FUNCTION A commonly applied transfer function as used by Calver 1997 is the basis for the transfer of potential recharge from the base of the soil zone through the unsaturated zone to the water table Potential recharge from the base of the soil in each month is applied to the water table over the current month and a number of subsequent months The total number of months n over which recharge is distributed is a model parameter The distribution of
14. r nu H High c 6 23 5 DO NOT ALTER DATA BELOW HERE Dummy variables nu T Low c 10 500 nu T High c 500 5000 nu S High c 0 003 0 003 nu H Mid2 c 120 140 12 OR 11 059 References CALVER A 1997 Recharge Response Functions Hydrology and Earth System Sciences 1 47 53 FAO 1998 Crop evapotranspiration guidelines for computing crop water requirements FAO Irrigation and Drainage Paper 56 Rome 301 pp 13
15. recharge over the n months is specified using a two parameter Weibull probability density function Equation 8 where k gt 0 is the shape parameter and gt 0 is the scale parameter of the distribution The resulting distribution is scaled such that the area under the curve is equal to unity and consequently the recharge for each time step is simply spread over the selected n number of months This Weibull function can represent exponentially increasing exponentially decreasing and positively and negatively skewed distributions as illustrated in Figure 2 It is used because it is smooth and considered to be more physically justifiable than randomly selected monthly weights OR 11 059 2 5 Peep reer umeo n a A A m A 2 0 15 1 0 0 5 Q S 0 9 0 5 1 0 1 5 2 9 2 3 Figure 2 Example Weibull probability density function 1 3 LUMPED CATCHMENT GROUNDWATER MODEL Flow of saturated groundwater is represented by a rectangular block of aquifer In the following description the aquifer is assumed to be unconfined but different aquifer conceptualisations can easily be accommodated A simple explicit mass balance calculation is performed at each time step to calculate the new groundwater head With reference to Figure 3 this mass balance is formulated as R Ax Ay Q S Ax Ay h t Equation 9 where R is recharge LT Ax and Ay are the length and width of the aquifer L Q is the groundwater discharge L T
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