Correspondence and Upscaling of Hydraulic Functions for Steady‐State Flow in Heterogeneous Soils

Soil hydraulic parameters at relatively large scales (e.g., remote sensing footprints) are important for land–atmosphere interaction and general circulation models as well as other applications. Within this context, we investigated two major issues involving soil hydraulic properties: (i) hydraulic parameter correspondence among some of the more commonly used soil hydraulic conductivity functions (i.e., the Gardner [G], Brooks–Corey [BC], and van Genuchten [VG] equations) and (ii) their application to upscaling of hydraulic properties for steady‐state flow in heterogeneous soils. We first establish parameter equivalence among the conductivity functions based on preserving macroscopic capillary lengths and predicting the same vertical water flux. Next we investigate the significance of parameter equivalence on averaging schemes for the hydraulic parameters to allow predictions of the ensemble characteristics for steady‐state flow. Results show that the hydraulic parameters correspond very well and that the same rules can be used for averaging the parameters of different hydraulic conductivity functions when predicting ensemble evaporation rates from heterogeneous soils having a relatively large suction at the soil surface (e.g., a dry surface condition and/or a shallow groundwater table). On the other hand, when the surface suction is finite (especially when the suction is relatively small and/or the groundwater table is deep), it is more difficult to obtain correspondence between the parameters of the different conductivity models. The hydraulic functions correspond especially poorly when infiltration is considered. Parameter equivalence between the hydraulic functions is always satisfied for the case of evaporation from a shallow water table, as long as the macroscopic capillary length is preserved.