{"text_format":"1","workbook":"xlsx","n_sheets":8,"sheets":["Results","Reference values","ReadMe","Model","pS1","pS2","ps3","pS4"],"not_rendered":{"charts":1,"images":5,"macros":1,"external_links":0,"defined_names":1,"comments":1,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Results","index":0,"n_rows":18,"n_cols":15,"rows_kept":18,"cut":false,"hidden":false,"merged":[[13,13,16,14],[1,14,2,14],[0,0,2,7],[1,13,2,13]]}
["This spreadsheet will calculate the height of a groundwater mound beneath an stormwater infiltration BMP. \nMore information can be found in the U.S. Geological Survey Scientific Investigations Report 2010-5102 \n\"Simulation of groundwater mounding beneath hypothetical stormwater infiltration basins\"."]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Distance from center of infiltration BMP (m)","Ground-water mounding (m)"]
[]
["Go to the USGS report",null,null,null,null,null,null,null,null,null,null,null,null,0,{"$f":"Model!F57-$B$12","v":1.8012080837150393}]
[null,"Input Values",null,null,null,null,null,null,null,null,null,null,null,1,{"$f":"Model!F58-$B$12","v":1.8009008282825825}]
["Recharge (infiltration) rate (m/day)",0.15,"R",null,null,null,null,null,null,null,null,null,null,2.5,{"$f":"Model!F59-$B$12","v":1.7971781384627921}]
["Specific yield, Sy (dimensionless)",7.0000000000000007E-2,"Sy",null,null,null,null,null,null,null,null,null,null,5,{"$f":"Model!F60-$B$12","v":1.7205123811808036}]
["Horizontal hydraulic conductivity, Kh  (m/day)",8.6400000000000001E-3,"K",null,null,null,null,null,null,null,null,null,null,7.5,{"$f":"Model!F61-$B$12","v":0.9163014292065963}]
["1/2 length of basin (x direction, in m)",7.5,"x",null,null,null,null,null,null,null,null,null,null,10,{"$f":"Model!F62-$B$12","v":7.9512880921290829E-2}]
["1/2 width of basin (y direction, in m)",0.75,"y",null,null,null,null,null,null,null,null,null,null,12.5,{"$f":"Model!F63-$B$12","v":4.7941293448516831E-3}]
["Duration of infiltration period (days)",2,"t",null,null,null,null,null,null,null,null,null,null,15,{"$f":"Model!F64-$B$12","v":1.4846093549643058E-3}]
["Initial thickness of saturated zone (m)",10,"hi(0)",null,null,null,null,null,null,null,null,null,null,17.5,{"$f":"Model!F65-$B$12","v":1.428841367674849E-3}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,20,{"$f":"Model!F66-$B$12","v":1.428535290358468E-3}]
[]
[]
[]
[]
["maximum groundwater mounding \nbeneath center of basin at end of infiltration period",{"$f":"Model!F68-$B$12","v":-2.7194493085308009},"Δh(max)"]

{"sheet":"Reference values","index":1,"n_rows":7,"n_cols":5,"rows_kept":7,"cut":false,"hidden":false,"merged":[[1,2,1,4],[1,1,2,1]]}
[]
[null,null,"Specific Yield"]
[null,null,"Max","Min","Mean"]
[null,"Clay",{"$f":"5/100","v":0.05},0,{"$f":"2/100","v":0.02}]
[null,"Sandy clay",{"$f":"12/100","v":0.12},{"$f":"3/100","v":0.03},{"$f":"7/100","v":7.0000000000000007E-2}]
[null,"Silt",{"$f":"19/100","v":0.19},{"$f":"3/100","v":0.03},{"$f":"18/100","v":0.18}]
[null,"Fine sand",{"$f":"28/100","v":0.28000000000000003},{"$f":"10/100","v":0.1},{"$f":"21/100","v":0.21}]

{"sheet":"ReadMe","index":2,"n_rows":12,"n_cols":1,"rows_kept":12,"cut":false,"hidden":false,"merged":[[0,0,10,14],[11,0,13,14]]}
["This spreadsheet solving the Hantush (1967) equation for ground-water mounding beneath an infiltration basin is made available to the general public as a convenience for those wishing to replicate values documented in the USGS Scientific Investigations Report 2010-5102 \"Groundwater mounding beneath hypothetical stormwater infiltration basins\" or to calculate values based on user-specified site conditions. Any changes made to the spreadsheet (other than values identified as user-specified) after transmission from the USGS could have unintended, undesirable consequences. These consequences could include, but may not be limited to: erroneous output, numerical instabilities, and violations of underlying assumptions that are inherent in results presented in the accompanying USGS published report. The USGS assumes no responsibility for the consequences of any changes made to the spreadsheet. If changes are made to the spreadsheet, the user is responsible for documenting the changes and justifying the results and conclusions."]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Cosmetic changes were made (with permission from the original author) to this spreadsheet in 2017 by Toronto Region Conservation Authority. "]

{"sheet":"Model","index":3,"n_rows":68,"n_cols":12,"rows_kept":68,"cut":false,"hidden":true,"merged":[[41,6,44,13]]}
["Hantush's Solution for a rectangular infiltration basin to simulate mounding:"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,"ref: Hantush, M. ,1967, Growth and Decay of Groundwater Mounds in Response to Uniform Percolation,WRR v.3 no.1"]
[]
[null,null,null,null,null,null,"W = constant rate of percolation"]
[null,null,null,null,null,null,"K = hydraulic conductivity"]
[]
[null,null,null,null,null,null,null,null,null,null,{"$f":"A27*G40/A26","v":0.18822857142857141}]
[]
[]
[]
[]
[]
[]
["Input Values"]
[{"$f":"Results!B6","v":0.15},"w",null,"Percolation Rate (meters/day)"]
[{"$f":"Results!B7","v":7.0000000000000007E-2},"Sy",null,"Specific Yield",null,null,null,null,".02 < S < .3"]
[{"$f":"Results!B8","v":8.6400000000000001E-3},"K",null,"Horizontal Hydraulic Conductivity  (meters/day)",null,null,null,null,"K","10-1  -  10-3",null,"silt, sandy silt, clayey sand"]
[{"$f":"Results!B9","v":7.5},"l",null,"1/2 length of basin (meters)",null,null,null,null,null,"10-2 - 1",null,"sily sand  fine sand"]
[{"$f":"Results!B10","v":0.75},"a",null,"1/2 width of basin (meters)",null,null,null,null,null,"1 - 100",null,"well sorted sand"]
[null,null,null,null,null,null,null,null,null,"10 - 1000",null,"gravel"]
[{"$f":"0","v":0},"x",null,"x coordinate  (meters)"]
[0,"y",null,"y coordinate  (meters)"]
[{"$f":"Results!B11","v":2},"t",null,"time (days)"]
[]
[3.05,"hi(0)",null,"initial head    (meters)",null,null,null,"h(te) - h"]
[null,"h(te)",null,"head at end of simulation (meters)",null,null,null,{"$f":"A36-B47","v":-3.8465744902695547}]
[]
[null,null,null,"constant of linearization  "]
[]
[null,null,null,null,null,null,{"$f":"0.5*(A35+A36)","v":1.5249999999999999}]
["Output"]
[null,"Simpson",null,"Trapezoid",null,null,"note:  for manual calculations (that do not employ the macros associated with the \"Re-Calculate Now\" button on the Results worksheet), one needs to iterate between solution given in cell b47 and the value for the head needed for linearization cell a36.  Result only valid for X,Y obs point in G48, G49"]
["h2-hi2 =",{"$f":"((Model!$A$25/(2*Model!$A$27))*(Model!$K$17*Model!$A$33))*SUM(Model!B50:E50)","v":5.4936353091924852},"m2",{"$f":"((Model!$A$25/(2*Model!$A$27))*(Model!$K$17*Model!$A$33))*SUM(Model!B51:E51)","v":5.4936351740788538},"m2"]
[]
["h-hi=",{"$f":"SQRT(B43+(Model!$A$35)^2)-Model!$A$35","v":0.79657449026955485},"m",{"$f":"SQRT(D43+(Model!$A$35)^2)-Model!$A$35","v":0.79657447270670323},"m"]
[]
["h=",{"$f":"B45+Model!A35","v":3.8465744902695547},"m",{"$f":"D45+Model!A35","v":3.8465744727067031},"m",null,"Constants and variables needed for calculation"]
["Integral evaluation:",null,1E-3,"dt","fixed",null,{"$f":"Model!B67","v":0},"x","Location of observation point, x direction, meters"]
[null,"PS1","PS2","PS3","PS4",null,0,"y","Location of observation point, y direction, meters"]
["Simpson",{"$f":"'pS1'!L1014","v":0.42027811108576396},{"$f":"'pS2'!L1014","v":0.42027811108576396},{"$f":"'ps3'!L1014","v":0.42027811108576396},{"$f":"'pS4'!L1014","v":0.42027811108576396},null,{"$f":"(Results!B8*(0.5*(Results!B12+Model!G51)))/Results!B7","v":1.3454580699555903},"ν","average linear velocity, used in integration"]
["Trapezoidal",{"$f":"'pS1'!H1013","v":0.42027810074920197},{"$f":"'pS2'!H1013","v":0.42027810074920197},{"$f":"'ps3'!H1013","v":0.42027810074920197},{"$f":"'pS4'!H1013","v":0.42027810074920197},null,{"$f":"Model!C67","v":11.801403911317436},"h(te)","estimated  head"]
[null,null,null,null,null,null,{"$f":"((Results!$B$6/(2*Results!$B$8))*(Model!G50*Results!$B$11))*SUM(Model!B50:E50)","v":39.268512235141188},"h2-hi2 "]
["Calculations based on values input in Results worksheet are below",null,null,null,null,null,{"$f":"(SQRT(Model!$G$52+Results!$B$12^2))-Results!$B$12","v":1.8012080837150393},"h-hi","calculated  head"]
[null,null,null,null,null,null,{"$f":"G53+Results!B12","v":11.801208083715039},"h"]
[]
[null,null,"Hest","Hcalc","Hcalc - Hest","Hfinal"]
[null,{"$f":"Results!N4","v":0},11.801403911317436,{"$f":"Model!$G$54","v":11.801208083715039},{"$f":"D57-C57","v":-1.9582760239700292E-4},11.801208083715039,10.497,20.497]
[null,{"$f":"Results!N5","v":1},11.80109778878785,{"$f":"Model!$G$54","v":11.801208083715039},{"$f":"D58-C58","v":1.1029492718961365E-4},11.800900828282582,10.173,20.172999999999998]
[null,{"$f":"Results!N6","v":2.5},11.797379948126364,{"$f":"Model!$G$54","v":11.801208083715039},3.8281355886748969E-3,11.797178138462792]
[null,{"$f":"Results!N7","v":5},11.720675049370938,{"$f":"Model!$G$54","v":11.801208083715039},8.053303434410175E-2,11.720512381180804]
[null,{"$f":"Results!N8","v":7.5},10.916323667441194,{"$f":"Model!$G$54","v":11.801208083715039},0.88488441627384518,10.916301429206596]
[null,{"$f":"Results!N9","v":10},10.07951305952276,{"$f":"Model!$G$54","v":11.801208083715039},1.7216950241922788,10.079512880921291]
[null,{"$f":"Results!N10","v":12.5},10.004794145544473,{"$f":"Model!$G$54","v":11.801208083715039},1.7964139381705664,10.004794129344852]
[null,{"$f":"Results!N11","v":15},10.000714336304364,{"$f":"Model!$G$54","v":11.801208083715039},1.800493747410675,10.001484609354964]
[null,{"$f":"Results!N12","v":17.5},10.000714285717654,{"$f":"Model!$G$54","v":11.801208083715039},1.800493797997385,10.001428841367675]
[null,{"$f":"Results!N13","v":20},10.000914285714266,{"$f":"Model!$G$54","v":11.801208083715039},1.8002937980007729,10.001428535290358]
[null,{"$f":"Results!O14","v":0},11.801403911317436,{"$f":"Model!$G$54","v":11.801208083715039},-1.9582760239700292E-4,11.801208083715039]
[null,0,7.2811035794483949,{"$f":"Model!$G$54","v":11.801208083715039},{"$f":"D68-C68","v":4.5201045042666443},7.2805506914691991]

{"sheet":"pS1","index":4,"n_rows":1014,"n_cols":12,"rows_kept":1014,"cut":false,"hidden":true,"merged":[]}
[]
[]
[]
[]
[]
[]
[]
[]
[]
["a",{"$f":"(Results!$B$9+Model!$G$48)/(SQRT(4*Model!$G$50*Results!B$11))","v":2.2860261075602146}]
["b",{"$f":"(Results!$B$10+Model!$G$49)/(SQRT(4*Model!$G$50*Results!B$11))","v":0.22860261075602148}]
["t","erf(a/sqrt(t))",null,"erf(b/sqrt(t))",null,"integrand",null,"trapezoidal integral O(h^2)","Simpson integral O(h^4)","kount",null,"Simpson total Sum"]
[0,1,null,1,null,{"$f":"B13*D13","v":1},null,0,0]
[{"$f":"Model!$C$48","v":1E-3},{"$f":"ERF($B$10/SQRT(A14))","v":1},null,{"$f":"ERF($B$11/SQRT(A14))","v":1},null,1,null,{"$f":"0.5*(F14+F13)*(A14-A13)+H13","v":1E-3},null,1]
[{"$f":"A14+Model!$C$48","v":2E-3},{"$f":"ERF($B$10/SQRT(A15))","v":1},null,{"$f":"ERF($B$11/SQRT(A15))","v":0.99999999999951361},null,0.99999999999951361,null,1.9999999999997572E-3,null,{"$f":"IF(J14=1,0,1)","v":0}]
[{"$f":"A15+Model!$C$48","v":3.0000000000000001E-3},{"$f":"ERF($B$10/SQRT(A16))","v":1},null,{"$f":"ERF($B$11/SQRT(A16))","v":0.99999999641952919},null,0.99999999641952919,null,2.9999999982092788E-3,{"$f":"(I13+((A16-A15)/3)*(F13+4*F14+2*F15))*J16","v":2.3333333333330091E-3},1,null,{"$f":"IF(J16=1,I16,I15)","v":2.3333333333330091E-3}]
[{"$f":"A16+Model!$C$48","v":4.0000000000000001E-3},1,null,0.99999968074395673,null,0.99999968074395673,null,3.9999998367910216E-3,{"$f":"(I15+((A17-A16)/3)*(4*F15+2*F16))*J17","v":0},0,null,{"$f":"IF(J17=1,I17,I16)","v":2.3333333333330091E-3}]
[{"$f":"A17+Model!$C$48","v":5.0000000000000001E-3},1,null,0.99999517029457952,null,0.99999517029457952,null,4.9999972623102898E-3,4.3333331157216857E-3,1,null,4.3333331157216857E-3]
[{"$f":"A18+Model!$C$48","v":6.0000000000000001E-3},1,null,0.99997002991825978,null,0.99997002991825978,null,5.9999798624167091E-3,0,0,null,4.3333331157216857E-3]
[{"$f":"A19+Model!$C$48","v":7.0000000000000001E-3},1,null,0.99988849561106319,null,0.99988849561106319,null,6.9999091251813708E-3,6.3333066960599652E-3,1,null,6.3333066960599652E-3]
[{"$f":"A20+Model!$C$48","v":8.0000000000000002E-3},1,null,0.99969910080648794,null,0.99969910080648794,null,7.9997029233901465E-3,0,0,null,6.3333066960599652E-3]
[{"$f":"A21+Model!$C$48","v":9.0000000000000011E-3},1,null,0.99934512688176391,null,0.99934512688176391,null,8.9992250372342743E-3,8.3329574240790429E-3,1,null,8.3329574240790429E-3]
[{"$f":"A22+Model!$C$48","v":1.0000000000000002E-2},1,null,0.99877472042759818,null,0.99877472042759818,null,9.9982849608889566E-3,0,0,null,8.3329574240790429E-3]
[{"$f":"A23+Model!$C$48","v":1.1000000000000003E-2},1,null,0.99794714388774552,null,0.99794714388774552,null,1.0996645893046629E-2,1.0331267406873129E-2,1,null,1.0331267406873129E-2]
[{"$f":"A24+Model!$C$48","v":1.2000000000000004E-2},1,null,0.99683506303545089,null,0.99683506303545089,null,1.1994036996508228E-2,0,0,null,1.0331267406873129E-2]
[{"$f":"A25+Model!$C$48","v":1.3000000000000005E-2},1,null,0.9954241174016456,null,0.9954241174016456,null,1.2990166586726777E-2,1.2326420307413759E-2,1,null,1.2326420307413759E-2]
[{"$f":"A26+Model!$C$48","v":1.4000000000000005E-2},1,null,0.99371107009931681,null,0.99371107009931681,null,1.398473418047726E-2,0,0,null,1.2326420307413759E-2]
[{"$f":"A27+Model!$C$48","v":1.5000000000000006E-2},1,null,0.99170145750513206,null,0.99170145750513206,null,1.4977440444279486E-2,1.4316126510682165E-2,1,null,1.4316126510682165E-2]
[{"$f":"A28+Model!$C$48","v":1.6000000000000007E-2},1,null,0.98940727166439746,null,0.98940727166439746,null,1.5967994808864253E-2,0,0,null,1.4316126510682165E-2]
[{"$f":"A29+Model!$C$48","v":1.7000000000000008E-2},1,null,0.98684492989561223,null,0.98684492989561223,null,1.6956120909644257E-2,1.6297999968465274E-2,1,null,1.6297999968465274E-2]
[{"$f":"A30+Model!$C$48","v":1.8000000000000009E-2},1,null,0.98403361767953401,null,0.98403361767953401,null,1.7941560183431831E-2,0,0,null,1.6297999968465274E-2]
[{"$f":"A31+Model!$C$48","v":1.900000000000001E-2},1,null,0.98099400160917904,null,0.98099400160917904,null,1.8924073993076187E-2,1.8269815620112449E-2,1,null,1.8269815620112449E-2]
[{"$f":"A32+Model!$C$48","v":2.0000000000000011E-2},1,null,0.97774726874733509,null,0.97774726874733509,null,1.9903444628254444E-2,0,0,null,1.8269815620112449E-2]
[{"$f":"A33+Model!$C$48","v":2.1000000000000012E-2},1,null,0.9743144355685448,null,0.9743144355685448,null,2.0879475480412385E-2,2.0229639134756248E-2,1,null,2.0229639134756248E-2]
[{"$f":"A34+Model!$C$48","v":2.2000000000000013E-2},1,null,0.97071587024574391,null,0.97071587024574391,null,2.185199063331953E-2,0,0,null,2.0229639134756248E-2]
[{"$f":"A35+Model!$C$48","v":2.3000000000000013E-2},1,null,0.96697097863320269,null,0.96697097863320269,null,2.2820834057759004E-2,2.2175868962344806E-2,1,null,2.2175868962344806E-2]
[{"$f":"A36+Model!$C$48","v":2.4000000000000014E-2},1,null,0.96309801277110574,null,0.96309801277110574,null,2.3785868553461161E-2,0,0,null,2.2175868962344806E-2]
[{"$f":"A37+Model!$C$48","v":2.5000000000000015E-2},1,null,0.95911396907585611,null,0.95911396907585611,null,2.4746974544384643E-2,2.4107228942369816E-2,1,null,2.4107228942369816E-2]
[{"$f":"A38+Model!$C$48","v":2.6000000000000016E-2},1,null,0.9550345507261464,null,0.9550345507261464,null,2.5704048804285645E-2,0,0,null,2.4107228942369816E-2]
[{"$f":"A39+Model!$C$48","v":2.7000000000000017E-2},1,null,0.9508741748506423,null,0.9508741748506423,null,2.6657003167074041E-2,2.6022737268288389E-2,1,null,2.6022737268288389E-2]
[{"$f":"A40+Model!$C$48","v":2.8000000000000018E-2},1,null,0.94664600999867332,null,0.94664600999867332,null,2.7605763259498699E-2,0,0,null,2.6022737268288389E-2]
[{"$f":"A41+Model!$C$48","v":2.9000000000000019E-2},1,null,0.94236203317990763,null,0.94236203317990763,null,2.855026728108799E-2,2.7921666841421694E-2,1,null,2.7921666841421694E-2]
[{"$f":"A42+Model!$C$48","v":3.000000000000002E-2},1,null,0.93803309867599338,null,0.93803309867599338,null,2.9490464847015941E-2,0,0,null,2.7921666841421694E-2]
[{"$f":"A43+Model!$C$48","v":3.1000000000000021E-2},1,null,0.93366901303384087,null,0.93366901303384087,null,3.042631590287086E-2,2.980350495144557E-2,1,null,2.980350495144557E-2]
[{"$f":"A44+Model!$C$48","v":3.2000000000000021E-2},1,null,0.92927861230147668,null,0.92927861230147668,null,3.1357789715538521E-2,0,0,null,2.980350495144557E-2]
[{"$f":"A45+Model!$C$48","v":3.3000000000000022E-2},1,null,0.92486983879128781,null,0.92486983879128781,null,3.2284863941084901E-2,3.166791604369168E-2,1,null,3.166791604369168E-2]
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