Compressing soil structural information

&amp;lt;p&amp;gt;The ability of correlation functions to describe structure (Karsanina et al., 2015; Karsanina et al., 2018) and provide means to reconstruct the structure based on correlation functions (Gerke and Karsanina, 2015; Karsanina and Gerke, 2018) alone was proposed as means to effectively compress and store structural information (Gerke et al., 2015). This is especially appealing considering the fact that truly multi-scale digital 3D soil structure model for a single genetic horizon even with the resolution not finer than 1 &amp;amp;#181;m will contain enormous amount (approx., up to 10^15 voxels or even more) of data. Effective management and pore-scale simulations based on such datasets does not seem feasible at the moment. Another approach would be to retrieve only a relevant part of the dataset and operate on it indirectly, in particular based on correlation functions or stochastic reconstructions. The main aim of this work was to investigate the possibility to compress soil structural data, as resulted from X-ray microtomography data and directional correlation functions computation (Gerke et al., 2014), into a very limited number of parameters, potentially with minimal information content loss. We show that with the help of the proposed technique it is possible to compress a 3D image of 900^3-1300^3 voxels into a set of correlation functions, that with the help of fitting of an analytical function in the form of the superposition of three different basis functions may help to map all these correlation functions in a vector of six parameters. We apply the proposed methodology to 16 different soil 3D images and discuss numerous important implications that can help to achieve the ultimate goal of building 3D multi-scale soil structure model from meter to nm. Such model would help in establishing a fully multi-scale hydrological model operating from first principles as opposed to coarse continuum scale models.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;This work was supported by Russian Science Foundation grant 19-72-10082 (correlation functions) and Russian Foundation for Basic Research grant 18-34-20131 &amp;amp;#1084;&amp;amp;#1086;&amp;amp;#1083;_&amp;amp;#1072;_&amp;amp;#1074;&amp;amp;#1077;&amp;amp;#1076; (soil data).&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;References:&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Karsanina, M. V., Gerke, K. M., Skvortsova, E. B., Ivanov, A. L., &amp;amp; Mallants, D. (2018). Enhancing image resolution of soils by stochastic multiscale image fusion. Geoderma, 314, 138-145.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Gerke, K. M., Karsanina, M. V., &amp;amp; Mallants, D. (2015). Universal stochastic multiscale image fusion: an example application for shale rock. Scientific reports, 5, 15880.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Karsanina, M. V., &amp;amp; Gerke, K. M. (2018). Hierarchical Optimization: Fast and Robust Multiscale Stochastic Reconstructions with Rescaled Correlation Functions. Physical Review Letters, 121(26), 265501.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Gerke, K. M., &amp;amp; Karsanina, M. V. (2015). Improving stochastic reconstructions by weighting correlation functions in an objective function. EPL (Europhysics Letters), 111(5), 56002.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Gerke, K. M., Karsanina, M. V., Vasilyev, R. V., &amp;amp; Mallants, D. (2014). Improving pattern reconstruction using directional correlation functions. EPL (Europhysics Letters), 106(6), 66002.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Karsanina, M. V., Gerke, K. M., Skvortsova, E. B., &amp;amp; Mallants, D. (2015). Universal spatial correlation functions for describing and reconstructing soil microstructure. PLoS ONE, 10(5), e0126515.&amp;lt;/p&amp;gt;