Updating the Coupling Algorithm in HYDRUS Package for MODFLOW SAHILA BEEGUM Guided by Dr. K P Sudheer, Dr. Indumathi M Nambi & Dr. Jirka Šimunek Department of Civil Engineering, Indian Institute of Technology Madras 19 January 2018
Introduction: HYDRUS Package for MODFLOW (HPM) Seo et al. (2007) and Twarakavi et al. (2008) HYDRUS 1D Šimůnek et al., 2016 1D Richards equation MODFLOW Harbaugh et al., 2000 3D Groundwater flow 2
HPM: Spatial discretization HYDRUS- 1D MODFLOW 3
WT RF WT RF WT RF WT RF WT RF WT RF Start of simulation End of simulation HPM: Temporal discretization Time Time Time Time Time Time step 1 step 2 step 1 step 1 step 2 step 3 Stress period 1 Stress period 2 Stress period 3 MODLFOW Multiple time steps in HYDRUS-1D HYDRUS-1D Time step 1 Time step 2 Time step 1 Time step 1 Time step 2 Time step 3 Stress period 1 Stress period 2 Stress period 3 MODFLOW 4
Start of simulation End of simulation Depth (m) HPM: Limitations Inflow = 0.001 m/day 1 m 1 m 10 m Initial pressure head (m) -5-4 -3-2 -1 0 1 2 3 4 5 0 1 2 3 4 5 6 7 8 9 10 No flow boundaries: Sides and bottom 600 days No. of time steps: 6, Duration of each time step: 100 day 5
Cumulative bottom flux (m) Water table elevation (m) Bottom flux (m/day) HPM: Limitations 6 0.46 5 4 3 2 1 0.36 0.26 0.16 0.06 0 0-100 100-200 200-300 300-400 400-500 500-600 6-0.04 0 100 200 300 400 500 600 Eliminate the sudden variation in the The water table elevation after every MODFLOW time step. The flux at the bottom of the HYDRUS-1D profile. bottom flux from HYDRUS-1D 0 100 200 300 400 500 600 0.0-0.1-0.1-0.2-0.2-0.3-0.3-0.4 Cumulative bottom flux in the HYDRUS-1D profile.
Objectives To update the coupling algorithm between HYDRUS- 1D and MODFLOW to eliminate sudden fluxes when the groundwater table depth changes. To verify the coupling algorithm using HYDRUS- 2D/3D and analytical solution 7
Depth of soil Start of simulation End of simulation Updating the coupling algorithm between HYDRUS-1D and MODFLOW Update pressure head profile in the HYDRUS-1D column Time Time Time Time Time Time step 1 step 2 step 1 step 1 step 2 step 3 Stress period 1 Stress period 2 Stress period 3 Pressure head profile Steady state pressure Pressure head at the end of T 1 at the end of T 1 head profile Steady-state nodal fluxes adjusted before moving to T 2 compared with the nodal fluxes - - at T 1 If (relative difference between these two fluxes > 0.1% of the - flux); WT Pressure head values below this node = pressure heads WT WT obtained by the steady-state 8 profile q 1 + q + 1 Pressure head values above q 1 + this node = pressure heads h 1 h 2 = WT from h at T 2 1 MODFLOW 8
Coupling algorithm Steady state pressure head profile obtained using Darcy-Buckingham law q K h Kh i i 1 hi1 hi 1 zi zi 2 1 The above equation has to be solved for h i+1, while the value h i is known and q is equal to the bottom flux. Soil Hydraulic models Van Genuchten model Modified van Genuchten (Vogel and Cislerova) Brooks and Corey Van Genuchten with air entry value of 2 cm Log-normal (Kosugi) 9
Verification of the updated coupling algorithm Constant boundary condition Varying boundary conditions Different soil types Comparison with HYDRUS 2D/3D Comparison with Analytical solution 10
Cumulative bottom flux (m) Water table elevation (m) Cumulative bottom flux (m) Water table elevation (m) Verification of the coupling algorithm: Constant 0 100 200 300 400 500 600 surface flux 0.0-0.1-0.2-0.3-0.4-0.5-0.6 0.0-0.1-0.2-0.3-0.4-0.5-0.6 Without pressure head modification With pressure head modification 0 100 200 300 400 500 600 6 TS, modified 6 TS, unmodified 60 TS, modified 60 TS, unmodified 600 TS, modified 600 TS, unmodified 8 7 6 5 4 3 2 1 0 6.8 6.6 6.4 6.2 6.0 5.8 5.6 5.4 5.2 5.0 0-100 100-200 With pressure head modification Without pressure head modification 200-300 - 300 400 6 TS, modified 6 TS, unmodified 60 TS, modified 60 TS, unmodified 600 TS, modified 600 TS, unmodified 11 400-500 500-600 0 100 200 300 400 500 600
Cumulative bottom flux (m) Water table elevation (m) Precipitation / Potential evapotranspiration (m/day) Verification of the coupling algorithm: Variable surface flux 0.00-0.05-0.10-0.15-0.20-0.25-0.30 0 50 100 150 200 250 300 350 10 TS, modified 10 TS, unmodified 20 TS, modified 20 TS, unmodified 30 TS, modified 30 TS, unmodified 365 TS, modified 365 TS, unmodified 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000 Precipitation (m/day) Potential evapotranspiration (m/day) 0 50 100 150 200 250 300 350 Time (day) 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 10 TS, modified 20 TS, modified 20 TS, unmodified 30 TS, modified 30 TS, unmodified 365 TS, modified 365 TS, unmodified 0 50 100 150 200 250 300 350 12
Verification of the coupling algorithm: Different soil types 20 18 16 14 12 10 8 6 4 2 0 0.078 0.057 0.045 0.43 0.41 0.43 Residual moisture content [-] Saturated soil moisture content [-] Loam Loamy sand Sand 3.6 12.4 14.5 Parameter alpha in the soil water retention function [L-1] 1.56 2.28 2.68 Parameter in the soil water retention function 3.502 7.128 0.2496 0.5 Saturated hydraulic conductivity [LT-1] 0.5 0.5 Tortuosity parameter in the conductivity function [-] 13
Bottom flux (m/day) Bottom flux (m/day) Bottom flux (m/day) 0.19 0.14 0.09 0.04-0.01-0.06 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 50 TS, unmodified 25 TS, unmodified 10 TS, unmodified 50 TS, modified 25 TS, modified 10 TS, modified Sand (K=7.128 m/day) 0.05 0.03 0.01-0.01-0.03-0.05 0.01 0.00-0.01-0.02-0.03-0.04 50 TS_unmodified 25 TS_unmodified 10 TS_unmodified 50 TS_modified 25 TS_modified 10 TS_modified 14-0.05 0 5 10 15 20 25 30 35 40 45 50 50 TS, unmodified 25 TS, unmodified 10 TS, unmodified 50 TS, modified 25 TS, modified 10 TS, modified Loamy sand (K= 3.502 m/day) Loam (K=0.2496 m/day)
Bottom flux (m/day) Verification of the modified HPM with HYDRUS 2D/3D Water table level (m) 0.0000-0.0002-0.0004-0.0006-0.0008-0.0010-0.0012 0 100 200 300 400 500 600 HPM HYDRUS-2D 5.300 5.250 5.200 5.150 5.100 5.050 5.000 HYDRUS-2D HPM 0 100 200 300 400 500 600 15
Water table elevation (m) Comparison with analytical solution 2 2 2 2 ( H2) ( H1) W 2 H ( x) ( H1) x ( lx x ) l K (Bear, 1972) 5.30 H 1 H 2 5.25 5.20 5.15 5.10 5.05 5.00 Analytical solution HYDRUS (2D/3D) HPM 0 25 50 75 100 125 150 175 200 x (m) 16
Summary and Conclusion The coupling algorithm between HYDRUS-1D and MODFLOW is updated in HPM The algorithm is verified for its functionality for Different boundary condition Different soil types HPM is verified by comparing the HPM results with the results obtained using HYDRUS-2D/3D and analytical solution 17