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M. Esteves, G. Nord

M. Esteves, G. Nord. PSEM_2D. A process-based soil erosion model at the plot scale. DYNAS Workshop Rocquencourt 6 th -8 th December 2004. Introduction. PRIM_2D P lot R unoff and I nfiltration M odel (1999) PSEM_2D P lot S oil E rosion M odel (2003) These models were designed

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M. Esteves, G. Nord

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  1. M. Esteves, G. Nord PSEM_2D A process-based soil erosion model at the plot scale DYNAS Workshop Rocquencourt 6th-8th December 2004 DYNAS Workshop, 6th-8th December 2004, INRIA

  2. Introduction PRIM_2D Plot Runoff and Infiltration Model (1999) PSEM_2D Plot Soil Erosion Model (2003) These models were designed • to dynamically couple hydrological and soil erosion processes • to predict the spatial pattern of overland flow hydraulics • to predict the spatial pattern of soil erosion • to be used in natural slopes conditions • to consider complex rainfall events The models work on a rainfall event basis PRIM_2D has been validated (Esteves et al., 2000, J. Hyd.,228) PSEM_2D model is still under evaluation (Nord and esteves, WRR, submitted) DYNAS Workshop, 6th-8th December 2004, INRIA

  3. Objectives The main goals are • to improve our understanding of local overland flow hydraulics • to develop a better understanding of soil erosion processes • to bring a better description of the spatial and temporal variability of soil erosion at the plot scale DYNAS Workshop, 6th-8th December 2004, INRIA

  4. Presentation outline • Description of PRIM_2D and PSEM_2D • Applications of PRIM_2D • Validation of the model by comparison with observed data • Effect of the micro-topography • Effect of soil surface features pattern (crusted soils) • Applications of PSEM_2D • Evaluation of the model by comparison with experimental data • Some numerical examples to show the capabilities of the model • As a conclusion: Future research DYNAS Workshop, 6th-8th December 2004, INRIA

  5. Model description DYNAS Workshop, 6th-8th December 2004, INRIA

  6. Model description The model has three major components • Overland flow (OF) is generated as infiltration excess rainfall (hortonian) • OF is routed using the depth averaged two dimensional unsteady flow equations on a finite difference grid • Rainfall and OF hydraulics are used to compute soil erosion A single representative particle size (D50) DYNAS Workshop, 6th-8th December 2004, INRIA

  7. Model description : Infiltration In the case of crusted soils the profile is divided in two layers The infiltration algorithm is based on the Green and Ampt equation (1911) Zf DYNAS Workshop, 6th-8th December 2004, INRIA

  8. Model description : Overland flow • Fully dynamic two dimensional unsteady flow equations (Barré de Saint-Venant) • Continuity equation: • Momentum equations: • g gravitational acceleration (m.s-2) • h flow depth (m) • R rainfall intensity (m s -1) • I rate of infiltration (m s -1) • Sox ground slope (x direction) • Soy ground slope (y direction) • Sfx friction slope (x direction) • Sfy friction slope (y direction) • u flow velocity (x direction) (m s -1) • v flow velocity (y direction) (m s -1) x direction: y direction: DYNAS Workshop, 6th-8th December 2004, INRIA

  9. Model description : Flow resistance • Friction is approximated using the Darcy-Weisbach equation • The Darcy-Weisbach friction factor is constant • For small depth flows (< 0.1 mm) the velocities are calculated using a kinematic wave approximation x direction: • g gravitational acceleration (m.s-2) • h flow depth (m) • Sfx friction slope (x direction) • Sfy friction slope (y direction) • u flow velocity (x direction) (m s -1) • v flow velocity (y direction) (m s -1) • f Darcy-Weisbach friction factor y direction: DYNAS Workshop, 6th-8th December 2004, INRIA

  10. Model description : soil erosion Detachment and re-detachment by raindrop impact Drd > 0 Deposition Dfd < 0 Dfd > 0 Transport by runoff Detachment by runoff Entrainment Tc> qs DYNAS Workshop, 6th-8th December 2004, INRIA

  11. Model description: Soil erosion • A covering Layer of loose sediment (Hairsine and Rose, 1991) • εis conceptualized as the percentage of a grid cell covered by a deposited layer of depth the median particle diameter D50. • Thereforeε is calculated as: DYNAS Workshop, 6th-8th December 2004, INRIA

  12. Model description: Soil erosion • h water depth (m) • c sediment concentration (m3 m-3) • rs sediment particle density (kg m-3) • qx unit runoff discharge (x direction) (m2 s-1 ) • qy unit runoff discharge (y direction) (m2 s-1 ) • Drd soil detachment rate by rainfall (kg m-2 s-1 ) • Dfd soil detachment/deposition rate by runoff (kg m-2 s-1 ) • Sediment mass conservation equation (Bennet,1974) DYNAS Workshop, 6th-8th December 2004, INRIA

  13. Model description: Soil erosion Before sediment movement • Soil detachment by rainfall is a function of the rainfall intensity (Li, 1979) (kg m-2 s -1) a soil detachability coefficient by rainfall (kg m-2 mm-1) p an exponent set to 1.0 according to the results of Sharma et al. [1993] h water depth (m) ld loose sediment depth (m) zm the maximum penetration depth of raindrop splash (m) R rainfall intensity (m s-1) Damping effect of the water film at the soil surface where DYNAS Workshop, 6th-8th December 2004, INRIA

  14. Model description: Soil erosion After sediment movement • Soil detachment by rainfall Detachment (kg m-2 s -1) Re-detachment (kg m-2 s -1) e function of the area of the covering layer (0-1) a soil detachability coefficient by rainfall (kg m-2 mm-1) ad soil re-detachability coefficient by rainfall (kg m-2 mm-1) p an exponent (1.0) h water depth (m) zm the maximum penetration depth of raindrop splash (m) R rainfall intensity (mm h-1) DYNAS Workshop, 6th-8th December 2004, INRIA

  15. Model description: Soil erosion • Soil detachment or deposition by runoff : a model proposed by Foster and Meyer [1972] • When • qs<Tc, additional sediment detachment • qs>Tc, excessive sediment deposition (kg m-2 s-1) Tc sediment transport capacity of the flow (kg m-1 s-1) qs sediment discharge per unit flow width in the flow direction (kg m-1 s-1) DYNAS Workshop, 6th-8th December 2004, INRIA

  16. Model description: Soil erosion • When Tc>qs (Dfd>0) net erosion occurs and the detachment and entrainment rates are given by: Detachment (kg m-2 s -1) Entrainment (kg m-2 s -1) tfis the flow shear stress in the flow direction (Pa) tcis the critical shear stress of a spherical sediment particle [Yang, 1996] (Pa) tsoilthe critical shear stress of the soil (Pa) Kr is the rill erodibility parameter (s m–1) Tc sediment transport capacity of the flow (kg m-1 s-1) qs sediment discharge per unit flow width in the flow direction (kg m-1 s-1) DYNAS Workshop, 6th-8th December 2004, INRIA

  17. Model description: Soil erosion • When Tc<qs (Dfd<0) net deposition occurs and the deposition rates is given by [Foster et al., 1995]: (kg m-2 s -1) j is araindrop induced turbulence coefficient assigned to 0.5. Vf is the particle settling velocity (m s–1) q is the water dicharge per unit flow width in the flow direction (m 3 s-1 m-1) Tc sediment transport capacity of the flow (kg m-1 s-1) qs sediment discharge per unit flow width in the flow direction (kg m-1 s-1) DYNAS Workshop, 6th-8th December 2004, INRIA

  18. Model description: Soil erosion • Flow sediment transport capacity is based on the flow shear stress tf (Foster, 1982) (kg m-1 s-1) h coefficient of efficiency of sediment transport (m0.5 s2 kg –0.5 ) tf flow shear stress acting on the soil particles (Pa) tc critical shear stress of sediment (Pa) k an exponent taken as 1.5 (Finkner et al.,1989) DYNAS Workshop, 6th-8th December 2004, INRIA

  19. Model description: Numerical methods • Hydrological model and erosion model are treated independently since it is assumed that the flow dynamics are not affected by the suspended sediment • The Saint Venant equations are solved using the MacCormack scheme • The mass balance equation for sediment is solved using a second-order centered explicit finite difference scheme • For numerical stability of the scheme and computational efficiency the time step is optimised • Topographic elevations are re-estimated at each time step if there is runoff DYNAS Workshop, 6th-8th December 2004, INRIA

  20. Model description Model description: Numerical methods Flow chart of PSEM_2D To avoid directional bias of the Mac Cormack scheme the order is reversed every time step (predictor-forward, corrector-backward then predictor-backward, corrector-forward). DYNAS Workshop, 6th-8th December 2004, INRIA

  21. Model description: Initial and boundary conditions u = 0 c = c_inward v = 0 h = h _ i n w a r d d u m m y c e l l s u p s l o p e v = 0 i n w a r d b o u n d a r i e s u = 0 u = 0 y d o w n s l o p e • Boundary conditions • In the plot version the boundaries are 3 non porous walls and an open boundary (outlet) • Dummy cells are added to model wall boundary • At the outlet no condition is required because the flow is supercritical • Initial condition • At the beginning of the simulation h(x,y,0) = 0 u(x,y,0) = 0 v(x,y,0) = 0 c(x,y,0) = 0 We consider that rainsplash transportation outside the plot is balanced by sediment coming from the area surrounding the plot. DYNAS Workshop, 6th-8th December 2004, INRIA

  22. Model description : Calibrated parameters Detachment and re-detachment by raindrop impact Drd > 0 Deposition Dfd < 0 a ad Dfd > 0 Transport by runoff Detachment by runoff h tsoil Kr Entrainment Tc> qs hf,f DYNAS Workshop, 6th-8th December 2004, INRIA

  23. Model description: Data • The model needs information on • Slopes and elevations (Digital Elevation Model) • Map of soil surface features distribution • Infiltration parameters (hf, initial WC,Kc,Ks) • Map of DW friction factor • Soil erosion parameters (h,Kr, tsoil, D50) • Map of a and ad, (ad=10 a) • Rainfall (time, intensities) DYNAS Workshop, 6th-8th December 2004, INRIA

  24. Model description: Parameter identfication • The parameter identification is carried out in three stages • We started with parameters estimation based on physical characteristics and published data • Some of soil erosion parameters are defined using data available in the literature (ds=0.047, tsoil is estimated using the WEPP soil database) • Calibration is undertaken for hf (crusted soils) and/or f on one rainfall event • Calibration is undertaken for h,Kr, tsoil using the ranges of values found in the literature WEPP: Water Erosion Prediction Project (US Dept. Agr.) DYNAS Workshop, 6th-8th December 2004, INRIA

  25. Applications of PRIM_2D DYNAS Workshop, 6th-8th December 2004, INRIA

  26. Examples of application PRIM_2D Two runoff plots located on the same hillslope • Homogeneous soil surface feature (ERO) • one type of crust: erosion • Heterogeneous surface feature (JAC) • erosion crust and sandy aeolian micro mounds • Grid resolution 0.25 by 0.25 m • Both plots have the same subsoil • Initial soil water content were obtained from neutron probe measurements • Verification runs DYNAS Workshop, 6th-8th December 2004, INRIA

  27. Examples of application PRIM_2D Homogeneous soil surface feature (ERO) Heterogeneous surface feature (JAC) Runoff plots in Niger (West Africa) DYNAS Workshop, 6th-8th December 2004, INRIA

  28. Examples of application PRIM_2D JAC Sandy mounds Erosion crusts ERO DYNAS Workshop, 6th-8th December 2004, INRIA

  29. PRIM_2D Validation An exemple of validation run DYNAS Workshop, 6th-8th December 2004, INRIA

  30. PRIM_2D Validation DYNAS Workshop, 6th-8th December 2004, INRIA

  31. PRIM_2D Validation DYNAS Workshop, 6th-8th December 2004, INRIA

  32. Plot scale results DYNAS Workshop, 6th-8th December 2004, INRIA

  33. Plot scale results Efficiency ERO : 0.879 Efficiency JAC : 0.913 DYNAS Workshop, 6th-8th December 2004, INRIA

  34. Distributed results Time 789 s (max discharge) JAC JAC Water depth (m) ERO ERO DYNAS Workshop, 6th-8th December 2004, INRIA

  35. Distributed results JAC JAC Time 789 s Shear velocities (m/s) Infiltration depth (m) ERO ERO DYNAS Workshop, 6th-8th December 2004, INRIA

  36. Point results Velocities A small pond Water depth B rill Shear velocities C rill D top Reynolds Rainfall DYNAS Workshop, 6th-8th December 2004, INRIA

  37. Effect of the microtopography The microtopography is represented by • the topographic map of the plot (JAC) • a plane surface with the same mean slope All other parameters are the same DYNAS Workshop, 6th-8th December 2004, INRIA

  38. Effect of the microtopography DYNAS Workshop, 6th-8th December 2004, INRIA

  39. Effect of the microtopography JAC PLAN Distributed results JAC PLAN Time 789 s Water depth (m) DYNAS Workshop, 6th-8th December 2004, INRIA

  40. Effect of the surface features distribution The soil surface features are represented by • the soil surface feature map (JAC) • the dominant surface feature (erosion crust) All the other parameters are the same DYNAS Workshop, 6th-8th December 2004, INRIA

  41. Effect of the surface features distribution DYNAS Workshop, 6th-8th December 2004, INRIA

  42. Effect of the surface features distribution JAC 1 SF JAC 2 SF Time 589 s • For this storm the time to ponding is • 390 s for erosion crust • 625 s for sandy mounds Water depth (m) DYNAS Workshop, 6th-8th December 2004, INRIA

  43. Key results • Even in low relief plots, OF is not a sheet of flowing water, uniform in depth and velocity across the slope. OF concentrates downslope into deeper flow pathways • Small surface feature may play a major role in the OF production from a plot • A good reproduction of discharges at the outlet of a plot does not imply that OF hydraulics is correctly simulated • Infiltration is not homogeneous all over the plot which is partly due to the effect of micro-topography • Large variations in the OF hydraulics are due to the variable rainfall rates and to the characteristics of the uphill areas DYNAS Workshop, 6th-8th December 2004, INRIA

  44. PSEM_2D Evaluation DYNAS Workshop, 6th-8th December 2004, INRIA

  45. Psem_2D Evaluation : Experimental data • Kilinc and Richardson (1973) experimental data • A 1.52 m wide × 4.58 m long flume with an adjustable slope and a rainfall simulator. Each run was one hour long • The flume was filled with compacted sandy soil composed of 90 % sand and 10 % silt and clay. • The soil had a non-uniform size distribution with a median diameter D50of 3.5 × 10-4 m. • The soil surface was levelled and smoothed before each run. DYNAS Workshop, 6th-8th December 2004, INRIA

  46. Psem_2D Evaluation : Experimental data • Kilinc and Richardson (1973) experimental data • The major controlled variables were rainfall intensity and soil surface slope. • Infiltration and erodibility of surface were supposed constant. • Six slopes (5.7, 10, 15, 20, 30, and 40 %) were tested • Four rainfall intensities (32, 57, 93, and 117 mm h-1). • Calibration was carried out using a run with 20 % slope and 93 mm h-1 rainfall intensity. DYNAS Workshop, 6th-8th December 2004, INRIA

  47. Psem_2D Evaluation : Experimental data • Data available • Flow discharge at the outlet of the flume • Mean sediment concentration in the flow at the outlet • Mean infiltration rate • No data were collected on microtopography and Overland flow hydraulics (water depth, velocity) DYNAS Workshop, 6th-8th December 2004, INRIA

  48. Psem_2D Evaluation : Results Rain intensity, 93 mm h-1. Slopes, 15, 20, and 30 % 0.05 Observed, 30 % slope PSEM_2D, 30 % slope 0.04 Govindaraju and Kavvas [1991], 30 % slope Observed, 20 % slope 0.03 PSEM_2D, 20 % slope Sediment discharge (kg/m/s) (CALIBRATED) Govindaraju and Kavvas [1991], 20 % slope 0.02 Observed, 15 % slope PSEM_2D, 15 % slope 0.01 Govindaraju and Kavvas [1991], 15 % slope 0 0 10 20 30 40 50 60 Time (min) DYNAS Workshop, 6th-8th December 2004, INRIA

  49. Psem_2D Evaluation : Results Rain intensity, 117 mm h-1. Slopes, 15, 20, and 30 % DYNAS Workshop, 6th-8th December 2004, INRIA

  50. Psem_2D Evaluation : Results Singer and Walker [1983] experiment Slope 9% D50of the soil: 2. 10-5 m DYNAS Workshop, 6th-8th December 2004, INRIA

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