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Evaluation of Model Complexity and Input Uncertainty of Field-Scale Water Flow and Salt Transport

Hydrology Program, Department of Land, Air and Water Resources (LAWR), University of California, Davis, CA 95616, USA; G. Schoups, Currently at Department of Geological and Environmental Sciences, Stanford University, Stanford, CA 94305, USA

View larger version (26K): [in a new window]   Fig. 1. Hypothesized relation between data availability and model complexity, and similarly between structural and model input uncertainty.

View larger version (33K): [in a new window]   Fig. 2. Schematic outline for calculating the different errors: observation error, model input error, and structural model error. f denotes the true or reference model, and is the approximate model.

View larger version (21K): [in a new window]   Fig. 3. Relative sums of squared errors (SSE) for the prediction of crop transpiration as a function of the coefficient of variation (CV) of net infiltration for different levels of vertical spatial discretization (i.e., 41, 21, 7, and 3 nodes, respectively). Triangles = SSEs; squares = SSEi. The number of point-scale measurements is n = 20. Crop parameters: c50 = 2 dS/m, h50 = –70 m and = 1.

View larger version (12K): [in a new window]   Fig. 4. Trade-off between optimal model complexity, expressed by the number of vertical nodes, and the level of model input uncertainty, expressed by the CV of net infiltration. Optimal model complexity corresponds to a relative SSEs = 50%. Diamonds = crop transpiration; squares = salt drainage. The number of point-scale measurements is n = 20. Crop parameters: c50 = 2 dS m–1, h50 = –70 m and = 1.

View larger version (21K): [in a new window]   Fig. 5. Contour plot of the number of nodes needed to achieve a relative SSEs of 50% as a function of the CV of net infiltration and log(n), which is the logarithm of the number of point-scale measurements. Crop parameters: c50 = 2 dS m–1, h50 = –70 m and = 1.

View larger version (31K): [in a new window]   Fig. 6. Dynamics of moisture content and salt concentration during the 150-d growing season: (a) reference numerical model at the soil surface ("top") and at the bottom of the root zone ("bottom"), (b) lumped model using daily boundary conditions ("Daily BC") and seasonally averaged boundary conditions ("Seasonal BC"). Crop parameters: c50 = 2 dS m–1, h50 = –70 m and = 1. Seasonal net infiltration is 0.8 m.

View larger version (22K): [in a new window]   Fig. 7. Contour plots of relative SSEs as a function of n and CV of net infiltration for field-scale prediction of crop transpiration with the lumped model using daily boundary conditions ("Daily BC") and seasonally averaged boundary conditions ("Seasonal BC"). Crop parameters: c50 = 2 dS m–1, h50 = –70 m and = 1.

View larger version (19K): [in a new window]   Fig. 8. Crop transpiration as a function of seasonal net infiltration predicted with the finely discretized numerical model and the lumped model using either daily boundary conditions ("Daily BC") or seasonally averaged boundary conditions ("Seasonal BC"). Crop parameters: c50 = 2 dS m–1, h50 = –70 m and = 1.

View larger version (35K): [in a new window]   Fig. 9. Effect of crop salt stress sensitivity (parameter c50) on relative SSEs as a function of n and CV of net infiltration for field-scale prediction of crop transpiration with the lumped model using daily boundary conditions ("Daily BC") and seasonally averaged boundary conditions ("Seasonal BC"). Crop parameters: h50 = –70 m and = 1.

View larger version (40K): [in a new window]   Fig. 10. Effect of crop water stress sensitivity (parameter h50) on relative SSEs as a function of n and CV of net infiltration for field-scale prediction of crop transpiration with the lumped model using daily boundary conditions ("Daily BC") and seasonally averaged boundary conditions ("Seasonal BC"). Crop parameters: c50 = 2 dS m–1 and = 1.

View larger version (36K): [in a new window]   Fig. 11. Effect of crop root distribution (parameter ) on relative SSEs as a function of n and CV of net infiltration for field-scale prediction of crop transpiration with the lumped model using daily boundary conditions ("Daily BC") and seasonally averaged boundary conditions ("Seasonal BC"). Crop parameters: c50 = 2 dS m–1 and h50 = –70 m.

View larger version (21K): [in a new window]   Fig. 12. Contour plots of relative SSEs as a function of n and CV of net infiltration for field-scale prediction of salt drainage with the lumped model using daily boundary conditions ("Daily BC") and seasonally averaged boundary conditions ("Seasonal BC). Crop parameters: c50 = 2 dS m–1, h50 = –70 m and = 0.1.