A Feasibility Study on Design-Based Estimation of Global Soil Organic Carbon Stock

By Antoon Meijer

Abstract
Large-scale anthropogenic CO2 emissions are causing a runaway global warming effect. One mitigation strategy could be to sequester carbon in the Earth's soil, as is the goal of recently launched initiatives such as "4p1000". However, there is no accurate estimate of the current global soil organic carbon stock and changes therein. There are two main approaches to inference: model-based and design-based. The model-based approach uses a model fitted to data to make inferences, usually resulting in a map. The design-based approach uses a probability sample to infer general statistics about the study area. Most global SOC stock estimation studies have used model-based methods, partly because no global probability sample exists, which is necessary for design-based inference. Design-based methods are deemed to be better suited for global SOC stock estimation because these do not rely on model assumptions. Therefore, this thesis aims to evaluate the feasibility of design-based estimation methods for estimating global SOC stock, i.e. the costs involved and the required probability sample size.

To determine the required estimation accuracy, the SOC sequestration targets of "4p1000" and "RECSOIL" were consulted. These five-year SOC sequestration targets were used as basis for the estimation accuracy, such that the methods proposed in this thesis can be used to detect five-year global SOC stock changes. From these targets, four levels of accuracy were calculated that were used throughout this research. This was done to enable the reader to choose their preferred level of accuracy. The estimation accuracy was expressed by the standard error. To calculate the required sample size, the SOC stock population variance must first be estimated. SOC stock data were derived from the WoSIS Soil Profile Database, yielding a total of 12,708 SOC stock observations across the globe. This sample was then used for population variance estimation. This estimation was done in two ways: a variogram-based method and a bootstrapping method. A variogram was created based on the WoSIS-derived SOC stock sample, to which a spherical model was fitted. The sill of this model was taken as population variance estimate. The bootstrapping method was used to estimate a "worst-case" variance by taking the 95th percentile value of the resulting variance distribution.

Then, required sample sizes and costs were calculated for three design-based estimators: simple random sampling (SRS), stratified simple random sampling (SSRS), and model-assisted estimation (MAE). Costs include only operational costs incurred for taking the soil samples. The largest part of costs, traveling costs to sampling locations, was estimated by using a global accessibility map that showed travel time to the nearest city. For SSRS, the study area was stratified twice, with the SoilGrids SOC stock map and with a global accessibility map. For MAE, the SoilGrids map was used as the auxiliary model to reduce variance.

For simplicity, costs and required sample sizes were reported here for a 95% confidence interval width of 7 gigatons of carbon. The range in reported results is a consequence of using two variance estimation methods. SRS returned a required sample size of 114-161 thousand with estimated costs of €220-310 million, SSRS requires a sample size of 54.2-99.3 thousand with estimated costs of €76.2-138 million, and MAE required 49.3-90.2 thousand samples with estimated costs of €94.8-173 million.

The most promising method seemed to be SSRS, as costs are lowest overall for this method. MAE is close behind, needing fewer samples but having a higher cost. This is due to SSRS minimizing sampling in high-cost strata.

However, only the combination of MAE and SRS was studied, and other combinations could further reduce costs and sample size. Further research is needed to evaluate other combinations, for example with SSRS.

Based on the results of this thesis, the global SOC stock could be estimated for €76.2-138 million, with a 95% confidence interval width of 7 gigatons carbon. This estimate would be much more accurate than current SOC stock estimates, and would provide a solid basis from which SOC stocks can be monitored in the future. Monitoring SOC stocks thus seems technically feasible and reasonably affordable, it is now up to the international community and soil monitoring organizations to put such a sampling campaign in place.