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Soil Water Retention

II. Derivation and Application of Shape Index

^a Laboratoire d'Etude des Transferts en Hydrologie et Environnement, LTHE (UMR 5564, CNRS, INPG, UJF, IRD), BP 53X, 38041, Grenoble, Cedex 9, France
^b Instituto Mexicano de Tecnología del Agua (IMTA), Paseo Cuauhnáhuac 8532, Col. Progresso 62550 Jiutepec, Morelos, Mexico
^c CSIRO Land and Water, Indooroopilly, Qld. 4067, Australia

View larger version (36K): [in a new window]   Fig. 1. Outline of presentation of shape index with equation numbers for parameter conversion.

View larger version (25K): [in a new window]   Fig. 2. Shape index PvG computed for GRIZZLY according to Eq. [5] with k = 2, r = 0 as a function of clay and sand percentage.

View larger version (26K): [in a new window]   Fig. 3. Parametric shape index PBC according to Eq. [7] and PvG according to Eq. [9a], [10a], and [8], that is, the first- and second-order approximation and the exact expression, computed from optimized r, s, , m, and n as a function of the experimental shape index, P, using samples from UNSODA with a positive r. Coefficients for the correlation between all shape indices are provided in the insert.

View larger version (13K): [in a new window]   Fig. 4. Effect of r as an optimization parameter for k = 2 on 247 samples of GRIZZLY database: (a) mn2 as a function of mn0,2 and (b) PvG computed from optimization results with r > 0 versus results for r fixed at 0.

View larger version (11K): [in a new window]   Fig. 5. Parameter optimization to retention data from GRIZZLY with r = 0 using the BC and vG equations (k = 2): (a) 0 as a function of mn0,2 and (b) PBC as a function of PvG.

View larger version (17K): [in a new window]   Fig. 6. Optimizing vG equation to water content of 655 soils from GRIZZLY: RMSE if shape factor mn2 is independently predicted from BC equation with PBC = PvG versus RMSE if mn2 is included in the optimization.

View larger version (12K): [in a new window]   Fig. 7. Shape parameter 0 estimated from parameters of the vG equation, as a function of optimized 0 for 660 samples from GRIZZLY: (a) estimation from shape index, PvG, and (b) estimation with = mn1.

View larger version (15K): [in a new window]   Fig. 8. The effect of the user index, k, for optimizations of GRIZZLY data with r = 0: (a) shape parameters mn0,k for user index k = 0.5, 1, 3, 5, 7, and 10 as a function of mn0,2, and (b) shape index, PvG, for user index k = 0.5, 1, 3, 5, 7, and 10, as a function of PvG for k = 2.

View larger version (20K): [in a new window]   Fig. 9. The water retention shape index PvG as a function of mn0,k according to Eq. [5] for user index k = 0, 1, 2, 10 for the vG equation and k for the BC equation.

View larger version (34K): [in a new window]   Fig. 10. The effect of variations in r on shape parameters: (a) /0 and mn2/mn0,2 using a first- and second-order approximation (left-hand axis) and the distribution of samples with a nonzero r (right-hand axis) from GRIZZLY as a function of r/s and (b) mn2/mn0,2 using different m0,2 (left-hand axis) and the distribution of samples with a nonzero r (right-hand axis) from UNSODA.

View larger version (22K): [in a new window]   Fig. 11. Predictability of residual water content and shape factor with the first-order approximation of the shape index using Eq. [22]: (a) predicted versus optimized r/s and (b) predicted versus optimized mnk.