Point to Space: Data-driven Soil Moisture Spatial Mapping using Machine-Learning for Small Catchments in Western Germany
Authors: Boog Johannes , Kalbacher Thomas 
Published: March 2021

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&lt;p&gt;Soil moisture is a crucial variable in the earths critical zone. It depends on multiple factors such as climate,&amp;#160;&lt;span&gt;topographic conditions, soil characteristics and affects energy and water fluxes across the land-atmosphere&amp;#160;&lt;/span&gt;&lt;span&gt;interface and, therefore, is highly important for terrestrial ecosystems, ecosystem management and agriculture.&amp;#160;&lt;/span&gt;&lt;span&gt;The accurate mapping of soil moisture across time and space is challenging but highly desirable.&lt;/span&gt;&lt;/p&gt;
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&lt;p&gt;One option is to deploy ground-based moisture sensors at the point-scale and to interpolate and/or map the&amp;#160;&lt;span&gt;measurements into space.&amp;#160;&lt;/span&gt;&lt;span&gt;We have developed a data-driven approach to map the soil moisture in a reference&amp;#160;&lt;/span&gt;&lt;span&gt;area from point measurements at specific time points and the covariates: location, topographic conditions and&amp;#160;&lt;/span&gt;&lt;span&gt;soil characteristics. We tested the mapping capacity of different two machine-learning algorithms (Random&amp;#160;&lt;/span&gt;&lt;span&gt;Forest and Neural Networks) and compared those with Ordinary Kriging as standard method. Our questions&amp;#160;&lt;/span&gt;&lt;span&gt;were: 1) How accurate are the machine-learning methods for soil moisture mapping? 2) Which covariates are&amp;#160;&lt;/span&gt;&lt;span&gt;most important? 3) How does mapping accuracy vary with data density and temporal resolution?&amp;#160;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span&gt;We used soil moisture data from the TERENO experimental sites W&amp;#252;stebach and Rollesbroich located in&amp;#160;&lt;/span&gt;&lt;span&gt;western Germany. These small catchments are equipped with a dense network of soil moisture sensors using&amp;#160;&lt;/span&gt;&lt;span&gt;time domain reflectometry (TDR) that has been operated since 2010 (Bogena et al., 2010;&amp;#160;&lt;/span&gt;&lt;span&gt;Zacharias et al., 2011). From this, we created 2700 point-based soil moisture data sets at specific time points,&amp;#160;&lt;/span&gt;&lt;span&gt;specific depth and for various numbers of sensor locations. Then we merged these data sets with sampled data&amp;#160;&lt;/span&gt;&lt;span&gt;on soil texture and chemical composition (Qu et al., 2016; Gottselig, et al., 2017; ) as well as remote sensed&amp;#160;&lt;/span&gt;&lt;span&gt;terrain data.&amp;#160;&lt;/span&gt;&lt;span&gt;These time stamp specific point-based soil moisture measurements were mapped using Ordinary&amp;#160;&lt;/span&gt;&lt;span&gt;Kriging (OK), Random Forest (RF) and Neural Networks (ANN) using combinations of the soil and terrain&amp;#160;&lt;/span&gt;&lt;span&gt;attributes as well as geometric distances between sensor locations as covariates. Each model was trained (80%&amp;#160;&lt;/span&gt;&lt;span&gt;subset) and tested (20% subset) on the point-based data sets.&amp;#160;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span&gt;In general, average model accuracy across the methods and individual data set types (depth, number of sensor&amp;#160;&lt;/span&gt;&lt;span&gt;locations, temporal averaging) was relatively low with R2 values of approximately 0.2-0.5. This originated in&amp;#160;&lt;/span&gt;&lt;span&gt;the high variability of soil moisture. Surprisingly, models using the spatial structure of the domain (using&amp;#160;&lt;/span&gt;&lt;span&gt;distances between sensors as covariates) already yield an R2 of approximately 0.45. Further adding covariates&amp;#160;&lt;/span&gt;&lt;span&gt;such as soil and terrain attributes did not substantially improve the accuracy for these models. In comparison,&lt;/span&gt;&lt;span&gt;using only terrain attributes as covariates for RF and ANN did yield an accuracy of R2 of 0.25-0.27.&lt;/span&gt;&lt;span&gt;The trained&amp;#160;&lt;/span&gt;&lt;span&gt;models were then used to map soil moisture onto the entire study area. This resulted in maps with interesting&amp;#160;&lt;/span&gt;&lt;span&gt;patterns that differed between the individual methods&amp;#8212;even when using same covariate types.&lt;/span&gt;&lt;/p&gt;
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&lt;p&gt;&lt;span&gt;Finally, it can be concluded that for spatial interpolation of soil moisture the Random Forest algorithm using&amp;#160;&lt;/span&gt;&lt;span&gt;distance between sensor locations as covariates is a promising alternative to Ordinary Kriging from the point&amp;#160;&lt;/span&gt;&lt;span&gt;of accuracy and simplicity.&lt;/span&gt;&lt;/p&gt;
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