Modeling Depth of the Redox Interface at High Resolution at National Scale Using Random Forest and Residual Gaussian Simulation

Abstract

The management of water resources needs robust methods to efficiently reduce nitrate loads.Knowledge on where natural denitrification takes place in the subsurface is thereby essential. Nitrate is naturally reduced in anoxic environments and high-resolution information of the redox interface, that is, the depth of the uppermost reduced zone is crucial to understand the variability of the denitrification potential. In this study we explore the opportunity to use random forest (RF) regression to model redox depth across Denmark at 100-m resolution based on~13,000 boreholes as training data. We highlight the importance of expert knowledge to guide the RF model in areas where our conceptual understanding is not represented correctly in the training data set by addition of artificial observations. We apply random forest regression kriging in which sequential Gaussian simulation models the RF residuals. The RF model reaches a R 2 score of 0.48 for an independent validation test. Including sequential Gaussian simulation honors observations through local conditioning, and the spread of 800 realizations can be utilized to map uncertainty. Emphasis is put on adequate handling of nonstationarities in variance and spatial correlation of the RF residuals. The RF residuals show no spatial correlation for large parts of the modeling domain, and a local variance scaling method is applied to account for the nonstationary variance. Moreover, we present and exemplify a framework where newly acquired field data can easily be integrated into random forest regression kriging to quickly update local models.Plain Language Summary Nutrients, such as nitrogen in form of nitrate are essential for plant growth. Despite their benefits, nutrient surplus can cause adverse health and ecological effects. In fact, nitrate leaching from agricultural fields is one of the major water resources management challenges in today's agricultural landscapes. During the transport through the subsurface, nitrate can potentially be degraded in anoxic layers below the redox interface. This is referred to as denitrification and its potential varies spatially depending on the local landscape. The location of the redox interface is thus essential knowledge toward a spatially differentiated water resources management. We applied a machine learning method to model the redox depth at 100m spatial resolution across Denmark, based on redox data obtained from~13,000 boreholes and environmental variables that explain redox variability. We highlight the importance of expert knowledge in guiding the machine learning model by adding artificial observations in underrepresented landscapes. As an add-on, a geostatistical model is used to honor local data at grid scale and quantify the spatial uncertainty elsewhere. Lastly, we outline and exemplify a framework that allows an easy integration of newly acquired field data for updating local models of the depth to the redox interface.

Nation-wide estimation of groundwater redox conditions and nitrate concentrations through machine learning

“…Other studies on prediction of groundwater nitrate concentration determined uncertainties in a similar range (Ransom et al 2017, Rahmati et al 2019. Koch et al (2019) pointed out that the uncertainty can be significantly reduced with a more comprehensive data set. In line with this, we also tested a data set with additional monitoring sites (n = 13 038 for NO 3 ) operated by several federal states in Germany, which resulted in a reduced, but still high uncertainty (MPI = 41.9 mg l −1 ).…”

“…Such anaerobic conditions are characterised by an oxygen (O 2 ) concentration of ⩽1-2 mg l −1 and iron (Fe) concentration of ⩾0.1-0.2 mg l −1 (Kunkel et al 2004, Rivett et al 2008, Mcmahon and Chapelle 2008. Several studies dealt with the large-scale estimation of redox conditions in groundwater (Tesoriero et al 2015, Close et al 2016, Rosecrans et al 2017, Koch et al 2019 and Ransom et al (2017) identified it as one of the most important parameters for the estimation of nitrate concentrations.…”

“…In terms of the estimation of groundwater redox conditions, Close et al (2016) and Wilson et al (2018) performed linear discriminant analyses. Whereas, other studies also made use of ML for predicting groundwater redox conditions or the redox interface (Tesoriero et al 2015, Rosecrans et al 2017, Koch et al 2019, Friedel et al 2020.…”

“…As one of the few, Rahmati et al (2019) investigated the uncertainties in machine learning approaches for estimating groundwater nitrate concentrations and showed that it is important to consider both the performance and the uncertainty for model evaluation. Ransom et al (2017) used bootstrapping for a boosted regression tree model and Koch et al (2019) extended RF with geostatistics to assess uncertainties. By modifying RF to quantile random forest (QRF), Meinshausen (2006) provided a method to consider a full conditional distribution for the predictions instead of the mean only.…”

Enviromicsin breeding: applications and perspectives on envirotypic-assisted selection

“…One Step 1: Enviromental Index (EI): The phenotypic mean within the 50 experimental trials deployed in 231 the area is calculated and we subsequently generate values of this variable for the entire range of pixels 232 of the raster by using a Random Forest (RF) regression in R software (Liaw and Wiener 2002), a 233 nonparametric multivariate modeling technique that is well suited to capture nonlinear dependencies 234 that uses a common machine learning algorithm based on an enhanced utilization of regression trees. 235 According to Koch et al (2019), several studies from different geoscience fields have shown that RF has 236 overcome most other machine learning techniques available at the time. In our study, five hundred 237 decision trees (default arguments of the randomForest R function) were built to establish the 238 relationship between the mean performance of the genotypes within trial for the evaluated yield trait 239 and the 100 enviromic markers.…”