Nonstationary spatial prediction of soil organic carbon: Implications for stock assessment decision making

Abstract

in order to provide contemporaneous measurements of soil organic carbon (SOC) across the US. Despite the broad extent of the RaCA data collection effort, direct observations of SOC are not available at the high spatial resolution needed for studying carbon storage in soil and its implications for important problems in climate science and agriculture. As a result, there is a need for predicting SOC at spatial locations not included as part of the RaCA project. In this paper, we compare spatial prediction of SOC using a subset of the RaCA data for a variety of statistical methods. We investigate the performance of methods with off-the-shelf software available (both stationary and nonstationary) as well as a novel nonstationary approach based on partitioning relevant spatially-varying covariate processes. Our new method addresses open questions regarding (1) how to partition the spatial domain for segmentation-based nonstationary methods, (2) incorporating partially observed covariates into a spatial model, and (3) accounting for uncertainty in the partitioning. In applying the various statistical methods we find that there are minimal differences in out-of-sample criteria for this particular data set, however, there are major differences in maps of uncertainty in SOC predictions. We argue that the spatially-varying measures of prediction uncertainty produced by our new approach are valuable to decision makers, as they can be used to better benchmark mechanistic models, identify target areas for soil restoration projects, and inform carbon sequestration projects.

Identifying regions of inhomogeneities in spatial processes via an M-RA and mixture priors

“…As already indicated by Risser et al (2019), SOC is characterized by a spatial dependence structure that is not homogeneous in space. The contribution of our paper is to present a novel statistical modeling approach that does not require a practitioner to determine a priori if a process is stationary or not, and can be used to model both stationary and non-stationary spatial processes.…”

“…The data are openly available in the R package soilDB. A subset of these data, relative to the Great Lakes region, was previously analyzed by Risser et al (2019) who demonstrated that, contrarily to previous analyses of SOC that assumed second-order stationarity, SOC is indeed a non-stationary spatial process with varying correlation ranges across the Great Lakes region.…”

“…As Figure 1(a) shows, raw SOC measurements are extremely right skewed, prompting us to work on the log scale, as did Risser et al (2019). Log-transforming the data yields a distribution that is more symmetric, as Figure 1(a) depicts.…”

“…Building upon previous modeling efforts focused mostly on spatial prediction (Risser et al, 2019;Mishra et al, 2009), in modeling the spatial process of SOC we expresse its mean function, µ(s), as a linear combination of three spatially-varying covariates -land use/land cover, drainage class, and elevation -known to influence levels of SOC. The first two, both categorical variables, are rather important from a geological point of view and refer, respectively, to: six different land use classifications according to the definition of the National Resources Inventory (namely: wetland, crop, pastureland, rangeland, forestland and land under a Conservation Reserve Program or CRP), and eight different classes that refer to the "frequency and duration of wet periods under conditions similar to those under which the soil developed" (NRCS Soil Survey Manual).…”

“…The decomposition of a spatial domain into areas with similar spatial dependence is one of the classical modeling approaches used to construct non-stationary covariance functions (Sampson, 2010), see for example Fuentes (2001), Kim et al (2005), Nott and Dunsmuir (2002), Pope et al (2018), Gramacy and Lee (2008), Konomi et al (2014), and, more recently, Risser et al (2019) who leverage information in the covariates to define the domain segmentation. Our model adds to this literature on non-stationary spatial processes, and it breaks with previous approaches in that it provides an alternative, computationally less challenging way to determine regions of local stationarity.…”