DOI: 10.18419/darus-2382
title: Benchmarking in subsurface hydrological inversion: high-fidelity reference solution and EnKF replication data
title: Replication data for https://doi.org/10.5194/hess-2024-60

description: &lt;p&gt;&lt;strong&gt;Description:&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Dataset published with the paper "Towards a community-wide effort for benchmarking in subsurface hydrological inversion: benchmarking cases, high-fidelity reference solutions, procedure and a first comparison". You can use these data to generate the comparisons between the EnKF and the MCMC solution as seen in the &lt;a href="https://doi.org/10.5194/hess-2024-60"&gt;paper&lt;/a&gt;.&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Folder structure &amp; Nomenclature:&lt;/strong&gt;&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Each folder with &lt;strong&gt;reference&lt;/strong&gt; data starts with "&lt;strong&gt;ref_&lt;/strong&gt;", followed by the scenario identifier like for S0, "ref_S0". See the scenario description below for further explanation.
&lt;ul&gt;
&lt;li&gt;In each of the reference folders, the several MCMC chains are stored. Please refer to the publication for further information about the file.&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;Each folder with solutions that are not references, but just &lt;strong&gt;replications&lt;/strong&gt;, start with "&lt;strong&gt;rep_&lt;/strong&gt;", like for the S0 steady state EnKF, "rep_EnKF_S01".
&lt;ul&gt;
&lt;li&gt;In these folders, the datafiles including the solutions are stored. &lt;/li&gt;
&lt;li&gt;For your own references, we recommend creating your own folder called "rep_YourFolderName_ScenarioSpecifier".&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;&lt;strong&gt;Scenario description:&lt;/strong&gt;&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;S0 is the base case. It features a relatively strong degree of heterogeneity with &sigma;&theta; = 2, relatively accurate measurement data with &sigma;e = 0.05 [L], irregularly placed observations, and steady-state groundwater flow.&lt;/li&gt;
&lt;li&gt;S1 features the regular grid of observations instead of the random one. While irregular monitoring 375 networks are more realistic, the very close spacing of a few monitoring wells may pose a problem to some methods due to their high autocorrelation. Therefore, S1 is a fallback scenario.&lt;/li&gt;
&lt;li&gt;S2 is again like S0, but reduces the strength of heterogeneity from &sigma;&theta; = 2 to &sigma;&theta; = 1. While &sigma;&theta; = 2 is a more realistic degree of heterogeneity, it may already be challenging for methods that are explicitly or implicitly linearization-based. Therefore, S2 is a fallback scenario.&lt;/li&gt;
&lt;li&gt;S3 is again like S0, but increases the assumed level of observational errors from &sigma;e = 0.05 [L] to &sigma;e =0.1 [L]. Given the overall head difference of 20 [L] across the domain by the boundary conditions, these values can be classified as high and medium accuracy, respectively. Iterative or sampling-based methods may have problems with the accuracy requirement posed by the large accuracy in S0. Once again, S3 is a fallback solution. However, as posterior uncertainties will remain larger for smaller measurement accuracy, S3 may also trigger stronger non-linearities across the larger remaining postcalibration uncertainty ranges.&lt;/li&gt;
&lt;li&gt;S4 changes S0 to feature transient (instead of steady-state) groundwater flow. This is relevant for&lt;br /&gt;EnKF-type methods that work via transient data assimilation and that do not iterate.&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;&lt;strong&gt;Download and benchmarking:&lt;/strong&gt;&lt;/p&gt;
&lt;a href="https://github.com/LS3-university-of-stuttgart/hydrological-inversion-benchmarking"&gt;Github Package&lt;/a&gt;