{"text_format":"1","workbook":"xlsx","n_sheets":10,"sheets":["Introduction","Solver details","1 layer","Plot-1 layer","2 layer","Plot-2 layer","3 layer","Plot-3 layer","4 layer","Plot-4 layer"],"not_rendered":{"charts":4,"images":8,"macros":1,"external_links":0,"defined_names":142,"comments":4,"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":"Introduction","index":0,"n_rows":17,"n_cols":14,"rows_kept":17,"cut":false,"hidden":false,"merged":[[1,3,1,11],[1,13,1,19],[16,13,16,19]]}
[]
[null,null,null,"FLUX-LM: MODEL OVERVIEW & INSTRUCTIONS",null,null,null,null,null,null,null,null,null,"HYPERLINKS TO OTHER SHEETS"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Last Edited"]
["2017-01-18"]
["by Barret Kurylyk"]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"WARNING"]

{"sheet":"Solver details","index":1,"n_rows":8,"n_cols":4,"rows_kept":8,"cut":false,"hidden":false,"merged":[]}
[null,null,null,"Solver must be:"]
[null,null,null,"(1) Turned on in Excel (see Step 1 below in figures)"]
[null,null,null,"(2) Accessible to Visual Basic (see Step 2 below in figures)"]
[]
[null,null,null,"*All screen shots are from MS Excel 2013; for other versions, a simple web search of 'turning "]
[null,null,null,"Solver on in Excel' and 'referencing Solver in Visual Basic' should yield appropriate information."]
[]
[null,null,null,"Step 1 progresses from left to right in the top row of figures. Step 2 is in the bottom row."]

{"sheet":"1 layer","index":2,"n_rows":2009,"n_cols":14,"rows_kept":2009,"cut":false,"hidden":false,"merged":[[0,2,0,3],[7,0,7,3],[7,5,7,7]]}
["1-Layer",null,"Summary of Results"]
[null,null,"Optimal Darcy flux (m s-1)",{"$f":"D3/365/24/60/60","v":-1.199245784995523E-8}]
[null,null,"Optimal Darcy flux (m yr-1)",-0.37819415075618812,"           Enter flux in m/yr",null,null,"Solve macro "]
[null,null,"RMSE (°C)",{"$f":"SQRT(AVERAGE(E10:E2109))","v":1.9739526072843495E-2},null,null,null,"minimizes cell D4"]
[null,null,"Peclet Number",{"$f":"ABS(D2*G12*G10/G11)","v":1.0192566358090742}]
[null,null,null,null,null,null,null,null,null,null,"To be hidden"]
[]
["Table 1: Field Data",null,null,null,null,"Table 2: Input Parameters",null,null,null,null,"Table 3: Calculated Equation Coefficient"]
["Depth (m)","Temperature (°C)","Adjusted Depth (m)","Calculated Temp. (°C)","Error2","Parameter","Value","Unit",null,null,"Parameter","Value","Units","Eq. # [in Kurylyk et al.]"]
[12.494,17.45,{"$f":"IF(A10-$A$10>=0,A10-$A$10,\"Past bottom boundary\")","v":0},{"$f":"IF(C10=\"Below bottom boundary\",#N/A,$L$12*EXP($D$2*C10/$L$10)+$L$13)","v":17.449999999999996},{"$f":"IF(ISERROR((D10-B10)^2),\"\",(D10-B10)^2)","v":1.2621774483536189E-29},"Total thickness (d)",{"$f":"INDEX(C:C,MATCH(9.99999999999999E+307,C:C))","v":35.972000000000001},"m",null,null,"σ1",{"$f":"G11/$G$12","v":4.2324246771879483E-7},"m2 s-1","NA"]
[12.715,17.48,{"$f":"IF(A11-$A$10>0,A11-$A$10,\"Below bottom boundary\")","v":0.22100000000000009},{"$f":"IF(C11=\"Below bottom boundary\",#N/A,$L$12*EXP($D$2*C11/$L$10)+$L$13)","v":17.479105465082821},{"$f":"IF(ISERROR((D11-B11)^2),\"\",(D11-B11)^2)","v":8.0019271805353601E-7},"Thermal conduct. (λ)",1.77,"W m-1 °C-1",null,null,"a",{"$f":"EXP(D2*(G10/L10))","v":0.36086309319436061},{"$f":"\"-\"","v":"-"},10]
[12.933999999999999,17.5,{"$f":"IF(A12-$A$10>0,A12-$A$10,\"Below bottom boundary\")","v":0.4399999999999995},17.507768299628218,{"$f":"IF(ISERROR((D12-B12)^2),\"\",(D12-B12)^2)","v":6.0346479113768646E-5},"Heat capacity of water (cwρw)",4182000,"J m-3 °C-1",null,null,"C11",{"$f":"(G14-G13)/(L11-1)","v":-4.662537819782349},"-",8]
[13.156000000000001,17.53,0.66200000000000081,17.53664280994623,4.412692398171318E-5,"Top thermal boundary (T0)",{"$f":"B10","v":17.45},"°C",null,null,"C12",{"$f":"((L11*G13)-G14)/(L11-1)","v":22.112537819782347},"-",7]
[13.298,17.54,0.80400000000000027,17.555017073987599,2.2551251114906237E-4,"Bottom thermal boundary (TB)",{"$f":"INDEX(B:B,MATCH(9.99999999999999E+307,B:B))","v":20.43},"°C"]
[13.442,17.55,0.9480000000000004,17.573574784948914,5.5577048538749325E-4]
[13.583,17.57,1.0890000000000004,17.591672654955957,4.6970397283995521E-4]
[13.798,17.59,1.3040000000000003,17.619129889605773,8.4855046844453522E-4]
[14.013999999999999,17.61,1.5199999999999996,17.646546908603842,1.3356765284976062E-3]
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[14.378,17.66,1.8840000000000003,17.69237169873281,1.0479268788477971E-3]
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[null,null,{"$f":"IF(A1996-$A$10>0,A1996-$A$10,\"Below bottom boundary\")","v":"Below bottom boundary"},{"$error":"#N/A"},""]
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[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
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{"sheet":"Plot-1 layer","index":3,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"2 layer","index":4,"n_rows":2009,"n_cols":14,"rows_kept":2009,"cut":false,"hidden":false,"merged":[[0,2,0,3],[7,0,7,3],[7,5,7,7]]}
["2-Layer",null,"Summary of Results"]
[null,null,"Optimal Darcy flux (m s-1)",{"$f":"D3/365/60/60/24","v":-2.1719535503996017E-6}]
[null,null,"Optimal Darcy flux (m yr-1)",-68.494727165401841,"           Enter flux in m/yr",null,null,"Solve macro "]
[null,null,"RMSE (°C)",{"$f":"SQRT(AVERAGE(E10:E2109))","v":{"$error":"#DIV/0!"}},null,null,null,"minimizes cell D4"]
[null,null,"Peclet Number",{"$f":"ABS(D2*G15*((G10/G13)+(G11/G14)))","v":{"$error":"#DIV/0!"}}]
[null,null,null,null,null,null,null,null,null,null,"To be hidden"]
[]
["Table 1: Field Data",null,null,null,null,"Table 2: Input Parameters",null,null,null,null,"Table 3: Calculated Equation Coefficient"]
["Depth (m)","Temperature (°C)","Adjusted Depth (m)","Calculated Temp. (°C)","Error2","Parameter","Value","Unit",null,null,"Parameter","Value","Units","Eq. # [in Kurylyk et al.]"]
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[null,null,{"$f":"IF(A11-$A$10>0,A11-$A$10,\"Below bottom boundary\")","v":"Below bottom boundary"},{"$f":"IF(C11=\"Below bottom boundary\",#N/A,IF(C11<$G$10,$L$13*EXP($D$2*C11/$L$10)+$L$14,$L$15*EXP($D$2*C11/$L$11)+$L$16))","v":{"$error":"#N/A"}},{"$f":"IF(ISERROR((D11-B11)^2),\"\",(D11-B11)^2)","v":""},"Thickness of layer 2 (b2)",null,"m",null,null,"σ2",{"$f":"G14/$G$15","v":0},"m2 s-1","NA"]
[null,null,{"$f":"IF(A12-$A$10>0,A12-$A$10,\"Below bottom boundary\")","v":"Below bottom boundary"},{"$error":"#N/A"},"","Total thickness (d2)",{"$f":"INDEX(C:C,MATCH(9.99999999999999E+307,C:C))","v":0},"m",null,null,"a",{"$f":"EXP(D2*((G10/L10)+(G11/L11)))","v":{"$error":"#DIV/0!"}},{"$f":"\"-\"","v":"-"},10]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Thermal conduct. of layer 1 (λ1)",null,"W m-1 °C-1",null,null,"C11",{"$f":"(G17-G16)/(L12-1)","v":{"$error":"#N/A"}},"-",8]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Thermal conduct. of layer 2 (λ2)",null,"W m-1 °C-1",null,null,"C12",{"$f":"((L12*G16)-G17)/(L12-1)","v":{"$error":"#DIV/0!"}},"-",7]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Heat capacity of water (cwρw)",4182000,"J m-3 °C-1",null,null,"C21",{"$f":"L13*EXP(D2*G10*((1/L10)-(1/L11)))","v":{"$error":"#N/A"}},"-",9]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Top thermal boundary (T0)",{"$f":"B10","v":0},"°C",null,null,"C22",{"$f":"L14","v":{"$error":"#DIV/0!"}},"-",7]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Bottom thermal boundary (TB)",{"$f":"INDEX(B:B,MATCH(9.99999999999999E+307,B:B))","v":{"$error":"#N/A"}},"°C"]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Check message below to ensure congruence between "]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","layer thickness values and total adjusted depth of domain"]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"",{"$f":"IF(G12=SUM(G10:G11),\"Layer thickness values and entered depths match\",\"Combined layer thicknesses do not match entered depths!\")","v":"Layer thickness values and entered depths match"}]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
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[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$f":"IF(C75=\"Below bottom boundary\",#N/A,IF(C75<$G$10,$L$13*EXP($D$2*C75/$L$10)+$L$14,$L$15*EXP($D$2*C75/$L$11)+$L$16))","v":{"$error":"#N/A"}},{"$f":"IF(ISERROR((D75-B75)^2),\"\",(D75-B75)^2)","v":""}]
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[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
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[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$f":"IF(C1995=\"Below bottom boundary\",#N/A,IF(C1995<$G$10,$L$13*EXP($D$2*C1995/$L$10)+$L$14,$L$15*EXP($D$2*C1995/$L$11)+$L$16))","v":{"$error":"#N/A"}},{"$f":"IF(ISERROR((D1995-B1995)^2),\"\",(D1995-B1995)^2)","v":""}]
[null,null,{"$f":"IF(A1996-$A$10>0,A1996-$A$10,\"Below bottom boundary\")","v":"Below bottom boundary"},{"$error":"#N/A"},""]
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[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
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{"sheet":"Plot-2 layer","index":5,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"3 layer","index":6,"n_rows":2009,"n_cols":14,"rows_kept":2009,"cut":false,"hidden":false,"merged":[[0,2,0,3],[7,0,7,3],[7,5,7,7]]}
["3-Layer",null,"Summary of Results"]
[null,null,"Optimal Darcy flux (m s-1)",{"$f":"D3/365/24/60/60","v":3.1709779326850509E-8}]
[null,null,"Optimal Darcy flux (m yr-1)",0.9999996008515577,"           Enter flux in m/yr",null,null,"Solve macro "]
[null,null,"RMSE (°C)",{"$f":"SQRT(AVERAGE(E10:E2109))","v":4.3247289219469943E-7},null,null,null,"minimizes cell D4"]
[null,null,"Peclet Number",{"$f":"ABS(D2*G17*((G10/G14)+(G11/G15)+(G12/G16)))","v":9.8115095239598453}]
[null,null,null,null,null,null,null,null,null,null,"To be hidden"]
[]
["Table 1: Field Data",null,null,null,null,"Table 2: Input Parameters",null,null,null,null,"Table 3: Calculated Equation Coefficient"]
["Depth (m)","Temperature (°C)","Adjusted Depth (m)","Calculated Temp. (°C)","Error2","Parameter","Value","Unit",null,null,"Parameter","Value","Units","Eq. # [in Kurylyk et al.]"]
[5,10,{"$f":"IF(A10-$A$10>=0,A10-$A$10,\"Past bottom boundary\")","v":0},{"$f":"IF(C10=\"Below bottom boundary\",#N/A,IF(C10<$G$10,$L$14*EXP($D$2*C10/$L$10)+$L$15,IF(C10<($G$10+$G$11),$L$16*EXP($D$2*C10/$L$11)+$L$17,$L$18*EXP($D$2*C10/$L$12)+$L$19)))","v":10},{"$f":"IF(ISERROR((D10-B10)^2),\"\",(D10-B10)^2)","v":0},"Thickness of layer 1 (b1)",50,"m",null,null,"σ1",{"$f":"G14/$G$17","v":1.9189383070301292E-7},"m2 s-1","NA"]
[6,10.000049251208376,{"$f":"IF(A11-$A$10>0,A11-$A$10,\"Below bottom boundary\")","v":1},{"$f":"IF(C11=\"Below bottom boundary\",#N/A,IF(C11<$G$10,$L$14*EXP($D$2*C11/$L$10)+$L$15,IF(C11<($G$10+$G$11),$L$16*EXP($D$2*C11/$L$11)+$L$17,$L$18*EXP($D$2*C11/$L$12)+$L$19)))","v":10.000049251379938},{"$f":"IF(ISERROR((D11-B11)^2),\"\",(D11-B11)^2)","v":2.9433629611568346E-20},"Thickness of layer 2 (b2)",25,"m",null,null,"σ2",{"$f":"G15/$G$17","v":7.6757532281205167E-7},"m2 s-1","NA"]
[7,10.000107352067166,{"$f":"IF(A12-$A$10>0,A12-$A$10,\"Below bottom boundary\")","v":2},10.000107352437288,1.3699008099608428E-19,"Thickness of layer 3 (b3)",25,"m",null,null,"σ3",{"$f":"G16/$G$17","v":1.5351506456241033E-6},"m2 s-1","NA"]
[8,10.000175892716292,3,10.000175893316129,3.5980397646944841E-19,"Total thickness (d3)",{"$f":"INDEX(C:C,MATCH(9.99999999999999E+307,C:C))","v":100},"m",null,null,"a",{"$f":"EXP(D2*((G10/L10)+(G11/L11)+(G12/L12)))","v":18242.50380027921},{"$f":"\"-\"","v":"-"},10]
[9,10.000256749018252,4,10.000256749883748,7.4908353238111283E-19,"Thermal conduct. of layer 1 (λ1)",0.80249999999999999,"W m-1 °C-1",null,null,"C11",{"$f":"(G19-G18)/(L13-1)","v":2.7410020877354798E-4},"-",8]
[10,10.000352133897884,5,10.00035213507048,1.3749819475194416E-18,"Thermal conduct. of layer 2 (λ2)",3.21,"W m-1 °C-1",null,null,"C12",{"$f":"((L13*G18)-G19)/(L13-1)","v":9.9997258997912262},"-",7]
[11,10.000464657907042,6,10.000464659434499,2.3331257171049437E-18,"Thermal conduct. of layer 3 (λ3)",6.42,"W m-1 °C-1",null,null,"C21",{"$f":"L14*EXP(D2*G10*((1/L10)-(1/L11)))","v":0.13462341247862336},"-",9]
[12,10.000597400671786,7,10.000597402609111,3.7532280282117194E-18,"Heat capacity of water (cwρw)",4182000,"J m-3 °C-1",null,null,"C22",{"$f":"L15","v":9.9997258997912262},"-",7]
[13,10.000753995177471,8,10.000753997587983,5.8105713724979555E-18,"Top thermal boundary (T0)",{"$f":"B10","v":10},"°C",null,null,"C31",{"$f":"L16*EXP(D2*(G10+G11)*((1/L11)-(1/L12)))","v":0.63375792359600891},{"$f":"\"-\"","v":"-"},9]
[14,10.00093872719852,9,10.000938730155056,8.7411071833997652E-18,"Bottom thermal boundary (TB)",{"$f":"INDEX(B:B,MATCH(9.99999999999999E+307,B:B))","v":15},"°C",null,null,"C32",{"$f":"L17","v":9.9997258997912262},"-",7]
[15,10.001156652594123,10,10.001156656180424,1.2861555105894806E-17]
[16,10.001413735680096,11,10.001413739992362,1.8595638915136338E-17,"Check message below to ensure congruence between "]
[17,10.001717012463923,12,10.001717017612595,2.6508829535559645E-17,"layer thickness values and total adjusted depth of domain"]
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[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$f":"IF(C1995=\"Below bottom boundary\",#N/A,IF(C1995<$G$10,$L$14*EXP($D$2*C1995/$L$10)+$L$15,IF(C1995<($G$10+$G$11),$L$16*EXP($D$2*C1995/$L$11)+$L$17,$L$18*EXP($D$2*C1995/$L$12)+$L$19)))","v":{"$error":"#N/A"}},{"$f":"IF(ISERROR((D1995-B1995)^2),\"\",(D1995-B1995)^2)","v":""}]
[null,null,{"$f":"IF(A1996-$A$10>0,A1996-$A$10,\"Below bottom boundary\")","v":"Below bottom boundary"},{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
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[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
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[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
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{"sheet":"Plot-3 layer","index":7,"n_rows":0,"n_cols":0,"rows_kept":0,"cut":false,"hidden":false,"merged":[]}

{"sheet":"4 layer","index":8,"n_rows":2009,"n_cols":14,"rows_kept":2009,"cut":false,"hidden":false,"merged":[[7,5,7,7],[7,0,7,3],[0,2,0,3]]}
["4-Layer",null,"Summary of Results"]
[null,null,"Optimal Darcy flux (m s-1)",{"$f":"D3/365/24/60/60","v":0}]
[null,null,"Optimal Darcy flux (m yr-1)",null,"           Enter flux in m/yr",null,null,"Solve macro "]
[null,null,"RMSE (°C)",{"$f":"SQRT(AVERAGE(E10:E2109))","v":{"$error":"#DIV/0!"}},null,null,null,"minimizes cell D4"]
[null,null,"Peclet Number",{"$f":"ABS(D2*G19*((G10/G15)+(G11/G16)+(G12/G17)+(G13/G18)))","v":{"$error":"#DIV/0!"}}]
[null,null,null,null,null,null,null,null,null,null,"To be hidden"]
[]
["Table 1: Field Data",null,null,null,null,"Table 2: Input Parameters",null,null,null,null,"Table 3: Calculated Equation Coefficient"]
["Depth (m)","Temperature (°C)","Adjusted Depth (m)","Calculated Temp. (°C)","Error2","Parameter","Value","Unit",null,null,"Parameter","Value","Units","Eq. # [in Kurylyk et al.]"]
[null,null,{"$f":"IF(A10-$A$10>=0,A10-$A$10,\"Past bottom boundary\")","v":0},{"$f":"IF(C10=\"Below bottom boundary\",#N/A,IF(C10<$G$10,$L$15*EXP($D$2*C10/$L$10)+$L$16,IF(C10<($G$10+$G$11),$L$17*EXP($D$2*C10/$L$11)+$L$18,IF(C10<($G$10+$G$11+$G$12),$L$19*EXP($D$2*C10/$L$12)+$L$20,$L$21*EXP($D$2*C10/$L$13)+$L$22))))","v":{"$error":"#N/A"}},{"$f":"IF(ISERROR((D10-B10)^2),\"\",(D10-B10)^2)","v":""},"Thickness of layer 1 (b1)",null,"m",null,null,"σ1",{"$f":"G15/$G$19","v":0},"m2 s-1","NA"]
[null,null,{"$f":"IF(A11-$A$10>0,A11-$A$10,\"Below bottom boundary\")","v":"Below bottom boundary"},{"$f":"IF(C11=\"Below bottom boundary\",#N/A,IF(C11<$G$10,$L$15*EXP($D$2*C11/$L$10)+$L$16,IF(C11<($G$10+$G$11),$L$17*EXP($D$2*C11/$L$11)+$L$18,IF(C11<($G$10+$G$11+$G$12),$L$19*EXP($D$2*C11/$L$12)+$L$20,$L$21*EXP($D$2*C11/$L$13)+$L$22))))","v":{"$error":"#N/A"}},{"$f":"IF(ISERROR((D11-B11)^2),\"\",(D11-B11)^2)","v":""},"Thickness of layer 2 (b2)",null,"m",null,null,"σ2",{"$f":"G16/$G$19","v":0},"m2 s-1","NA"]
[null,null,{"$f":"IF(A12-$A$10>0,A12-$A$10,\"Below bottom boundary\")","v":"Below bottom boundary"},{"$f":"IF(C12=\"Below bottom boundary\",#N/A,IF(C12<$G$10,$L$15*EXP($D$2*C12/$L$10)+$L$16,IF(C12<($G$10+$G$11),$L$17*EXP($D$2*C12/$L$11)+$L$18,IF(C12<($G$10+$G$11+$G$12),$L$19*EXP($D$2*C12/$L$12)+$L$20,$L$21*EXP($D$2*C12/$L$13)+$L$22))))","v":{"$error":"#N/A"}},"","Thickness of layer 3 (b3)",null,"m",null,null,"σ3",0,"m2 s-1","NA"]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Thickness of layer 4 (b4)",null,"m",null,null,"σ4",0,"m2 s-1","NA"]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Total thickness (d4)",{"$f":"INDEX(C:C,MATCH(9.99999999999999E+307,C:C))","v":0},"m",null,null,"a",{"$f":"EXP(D2*((G10/L10)+(G11/L11)+(G12/L12)+(G13/L13)))","v":{"$error":"#DIV/0!"}},{"$f":"\"-\"","v":"-"},10]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Thermal conduct. of layer 1 (λ1)",null,"W m-1 °C-1",null,null,"C11",{"$f":"(G21-G20)/(L14-1)","v":{"$error":"#N/A"}},"-",8]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Thermal conduct. of layer 2 (λ2)",null,"W m-1 °C-1",null,null,"C12",{"$f":"((L14*G20)-G21)/(L14-1)","v":{"$error":"#DIV/0!"}},"-",7]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Thermal conduct. of layer 3 (λ3)",null,"W m-1 °C-1",null,null,"C21",{"$f":"L15*EXP(D2*G10*((1/L10)-(1/L11)))","v":{"$error":"#N/A"}},"-",9]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Thermal conduct. of layer 4 (λ4)",null,"W m-1 °C-1",null,null,"C22",{"$f":"L16","v":{"$error":"#DIV/0!"}},"-",7]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Heat capacity of water (cwρw)",4182000,"J m-3 °C-1",null,null,"C31",{"$f":"L17*EXP(D2*(G10+G11)*((1/L11)-(1/L12)))","v":{"$error":"#N/A"}},{"$f":"\"-\"","v":"-"},9]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Top thermal boundary (T0)",{"$f":"B10","v":0},"°C",null,null,"C32",{"$f":"L18","v":{"$error":"#DIV/0!"}},"-",7]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Bottom thermal boundary (TB)",{"$f":"INDEX(B:B,MATCH(9.99999999999999E+307,B:B))","v":{"$error":"#N/A"}},"°C",null,null,"C41",{"$f":"L19*EXP(D2*(G10+G11+G12)*((1/L12)-(1/L13)))","v":{"$error":"#N/A"}},"-",9]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"",null,null,null,null,null,"C42",{"$f":"L20","v":{"$error":"#DIV/0!"}},"-",7]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","Check message below to ensure congruence between "]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"","layer thickness values and total adjusted depth of domain"]
[null,null,"Below bottom boundary",{"$error":"#N/A"},"",{"$f":"IF(G14=SUM(G10:G13),\"Layer thickness values and entered depths match\",\"Combined layer thicknesses do not match entered depths!\")","v":"Layer thickness values and entered depths match"}]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
[null,null,"Below bottom boundary",{"$error":"#N/A"},""]
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