Reducing non-uniqueness of inverting bimodal soil Kosugi hydraulic parameters

Hydrological models use soil hydraulic parameters to describe the storage and transmission of water in soils. Hydraulic parameters define the water retention, θ(ψ), and the hydraulic conductivity, K(θ), functions. These functions are usually obtained by fitting experimental data to the corresponding θ(ψ) and K(θ) functions. The drawback of deriving the hydraulic parameters by inverse modelling is that they suffer from equifinality or non-uniqueness, and the optimal hydraulic parameters are non-physical (Pollacco et al., 2008). To reduce the non-uniqueness, it is necessary to invert the hydraulic parameters simultaneously from observations of both θ(ψ) and K(θ), and ensure the measurements cover the full range of θ from fully saturated to oven dry, which requires expensive, labour-intensive measurements.  

We present a novel procedure to derive a unique, physical set of bimodal or dual permeabilityKosugi hydraulic functions, θ(ψ) and K(θ), from inverse modelling. The Kosugi model was chosen given its parameters have direct physical meaning to the soil pore-size distribution. The challenge of using bimodal functions is they require double the number of parameters (Pollacco et al., 2017), exacerbating the problem of non-uniqueness. To address this shortcoming, we (1) derive residual soil water content from the matrix Kosugi standard deviation, (2) derive macropore hydraulic parameters from the soil water pressure boundary between macropore and matrix, and (3) dynamically constraint the matrix Kosugi hydraulic parameters. We successfully reduce the number of hydraulic parameters to optimize and constrain the hydraulic parameters without compromising the fit of the θ(ψ) and K(θ) functions.

The robustness of the methodology is demonstrated by deriving the hydraulic parameters exclusively from θ(ψ) and K_sdata, enabling satisfactory prediction of K(θ) without having measured K(θ) data. Moreover, having a reduced number of hydraulic parameters that are physical allows an improved characterization of hydraulic properties of soils prone to preferential flow, which is a fundamental issue regarding the understanding of hydrological processes.

 

References

Pollacco, J.A.P., Ugalde, J.M.S., Angulo-Jaramillo, R., Braud, I., Saugier, B., 2008. A linking test to reduce the number of hydraulic parameters necessary to simulate groundwater recharge in unsaturated soils. Adv Water Resour 31, 355–369. https://doi.org/10.1016/j.advwatres.2007.09.002

Pollacco, J.A.P., Webb, T., McNeill, S., Hu, W., Carrick, S., Hewitt, A., Lilburne, L., 2017. Saturated hydraulic conductivity model computed from bimodal water retention curves for a range of New Zealand soils. Hydrol. Earth Syst. Sci. 21, 2725–2737. https://doi.org/10.5194/hess-21-2725-2017