Reducing non-uniqueness of inverting bimodal soil Kosugi hydraulic parameters
Authors: Fernández-Gálvez Jesús , Pollacco Joseph , McNeill Stephen , Carrick Sam , Lilburne Linda , Lassabatere Laurent , Angulo-Jaramillo Rafael 
Published: March 2021

&lt;p&gt;Hydrological models use soil hydraulic parameters to describe the storage and transmission of water in soils. Hydraulic parameters define the water retention, &lt;em&gt;&amp;#952;(&amp;#968;)&lt;/em&gt;, and the hydraulic conductivity, &lt;em&gt;K(&amp;#952;)&lt;/em&gt;, functions. These functions are usually obtained by fitting experimental data to the corresponding &amp;#952;(&amp;#968;) and K(&amp;#952;) 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 &lt;em&gt;et al.&lt;/em&gt;, 2008). To reduce the non-uniqueness, it is necessary to invert the hydraulic parameters simultaneously from observations of both&lt;em&gt; &amp;#952;(&amp;#968;)&lt;/em&gt; and &lt;em&gt;K(&amp;#952;&lt;/em&gt;), and ensure the measurements cover the full range of &lt;em&gt;&amp;#952;&lt;/em&gt; from fully saturated to oven dry, which requires expensive, labour-intensive measurements. &amp;#160;&lt;/p&gt;&lt;p&gt;We present a novel procedure to derive a unique, physical set of bimodal or dual permeabilityKosugi hydraulic functions,&lt;em&gt; &amp;#952;(&amp;#968;)&lt;/em&gt; and &lt;em&gt;K(&amp;#952;)&lt;/em&gt;, 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 &lt;em&gt;et al.&lt;/em&gt;, 2017), exacerbating the problem of non-uniqueness. To address this shortcoming, we&lt;strong&gt; (1) &lt;/strong&gt;derive residual soil water content from the matrix Kosugi standard deviation, &lt;strong&gt;(2) &lt;/strong&gt;derive macropore hydraulic parameters from the soil water pressure boundary between macropore and matrix, and &lt;strong&gt;(3)&lt;/strong&gt; 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 &lt;em&gt;&amp;#952;(&amp;#968;)&lt;/em&gt; and &lt;em&gt;K(&amp;#952;)&lt;/em&gt; functions.&lt;/p&gt;&lt;p&gt;The robustness of the methodology is demonstrated by deriving the hydraulic parameters exclusively from&lt;em&gt; &amp;#952;(&amp;#968;)&lt;/em&gt; and &lt;em&gt;K&lt;sub&gt;s&lt;/sub&gt;&lt;/em&gt;data, enabling satisfactory prediction of &lt;em&gt;K(&amp;#952;)&lt;/em&gt; without having measured K(&amp;#952;) 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.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;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&amp;#8211;369. https://doi.org/10.1016/j.advwatres.2007.09.002&lt;/p&gt;&lt;p&gt;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&amp;#8211;2737. https://doi.org/10.5194/hess-21-2725-2017&lt;/p&gt;