Multiscale Bayesian Spatial Modelling And Mapping Of Soil Organic Carbon With The INLA-SPDE Approach

Soil organic carbon(SOC)is one of the key properties of soil.A knowledge of the characteristics of SOC such as its geographical distribution at different spatial scales,has an important role in a range of fields such as soil resource use,agricultural production,and climate change modeling research.In the past decades,Integrated nested Laplace approximation with stochastic partial differential equation(ESNLA-SPDE)have been developed which is based on the Bayesian frameworks for fast spatial modeling,prediction and mapping of geostatistical data.Although the INLA-SPDE approach has the advantage of using posterior probability distribution to express the prediction results,the literature pays scant attention on the use of 1NLA-SPDE in studies of digital mapping of SOC.The reasons lie in some key research problems which have not been addressed yet,such as(a)how to select or build the SOC covariates at field,regional and global scales?(b)how to quantitatively express the uncertainty with the prediction result of Bayesian model?and(c)how to solve the computational problems of large number of sample points,large amount of raster data of environmental covariates and large number of prediction points in Bayesian spatial modeling and prediction at global scale?To this end,the solonchak soil in Kongtailik,Aksu,Xinjiang province of China,agricultural soils in northern North Dakota,USA,and global surface soils were selected as research area at the field,regional and global scale,respectively,the INLA-SPDE Bayesian spatial modelling method was performed to prediction,mapping and uncertainty assessment of SOC contents at multiscale,in order to promote the Bayesian spatial statistics and its application in digital soil mapping and management of SOC and to provide a certain reference.The main research results and findings of this paper are as follows:(1)In the case of field scale,it is in a special conditions of sparse vegetation and flat desert terrain,and no covariates,spatial autocorrelation,as a spatial random effect,constitutes a Bayesian spatial model,which is the main basis for predicting SOC of desert solonchak soil.Total 144 sample points of desert solonchak soil(5-10 cm)in Kongtailik were used to perform this study,and 1/4 sample points as independent samples were used to validate the predictive performance of INLA-SPDE and Markov chain Monte Carlo(MCMC)simulation(The Bayesian spatial models with MCMC simulation was constructed with Python language PyMC library and R language spBayes package,respectively).The results showed that RMSE,RHengl2 and RAdhikari2 of INLA-SPDE were 1.15 g/kg,36%and 0.24,respectively.The predictive performance indicators(MAE,RMSE,RHengl2 and RAdhikari2)of INLA-SPDE and MCMC simulation for SOC were similar.INLA-SPDE prediction uncertainty(SOC posterior prediction standard deviation between 4.6 g/kg and 5.5 g/kg)was lower than that of spBayes and higher than that of PyMC.The posterior mean and standard deviation maps of SOC content with spatial resolution of 10 m×10 m were obtained.(2)Aimed the regional scale,spatial variability of SOC is consisted of trend components and spatial random components,meanwhile,there is more spatial heterogeneity on regional scale than that of field scale,how to not use other environmental covariates,only the information of the soil itself being used to express the trend of SOC variation,it is a challenge for a Bayesian spatial model having higher prediction accuracy.In this paper,based on 1081 sample points of agricultural soil(0-15 cm)in northern North Dakota,the INLA-SPDE Bayesian spatial model was constructed using 29 soil great group classes and clay content extracted from SSURGO soil survey geographic database and POLARIS soil database which is generated by SSURGO probability remapping,respectively,and they together constituted the covariates of fixed effect of INLA-SPDE model.The validity of the covariates was evaluated using the deviation information criterion(DIC).Using 270 samples as independent validation samples to evaluate the predictive performance of INLA-SPDE and POLARIS.The results showed that the predictive performance of INLA-SPDE(RMSE=6.73 g/kg,RHengl2=40.7%,RAdhikari2=0.52)was promising than that of POLARIS(RMSE=11.00 g/kg,RHengl2=-58.3%,RAdhikari2=0.08).In this study,a 100 m×100 m SOC content map and a quantitative expression map of uncertainty in northern North Dakota were obtained,which provided important spatial information for soil management and fertility improvement.(3)On global scale,if a single Bayesian model was used to predict SOC,it would face problems such as increasing spatial heterogeneity,the constrained refined Delaunay triangulation(MESH)being not easy to build,and computing problem of too many prediction points.Therefore,in this paper,the world land was divided into seven continents/regions:Africa,Europe,Oceania,North America,South America,North Asia and South Asia,and the MESH and INLA-SPDE Bayesian spatial model were constructed based on each continent/region,then the predicted results of them were merged to the global maps with 30"×30" spatial resolution.The 0-5 cm topsoil SOC data of 88157 profiles/sampling points were extracted from the WoSIS and LUCAS datasets.Fifteen environmental covariates were extracted from the raster maps of global topography,climate,vegetation and land use/land cover.The covariates going into the Bayesian spatial model were selected by the DIC and Occam's razor criterion.The results of 10-fold cross-validation showed that RHengl2 values of seven continents/regions ranged from 24.9%to 58%with global value of 43%,these values were slightly higher than the validation results(ranged from-19.4%to 22.9%)of other four global datasets(HWSD,GSDE,IGBP and SoilGridslkm)with the same spatial resolution,but lower than that of SoilGrids250m(63.5%)studied by other researchers.RMSE values of the seven continents/regions ranged from 21.9 g/kg to 94.8 g/kg with global value of 65.7 g/kg,these values were slightly higher than that of other five global datasets(SoilGrids250m,SoilGridslkm,HWSD,GSDE and IGBP)whose results ranged from 29.8 g/kg to 36.2 g/kg.The study developed a series of global maps with the 30"×30" spatial resolution.These maps included global SOC posterior prediction means and the prediction uncertainties,i.e.,the posterior prediction standard deviation,the upper and lower limits,and width of the 95%highest posterior density credible interval(95%HPD CI)and the prediction uncertainty of 95%HPD CI(the ratio of width of 95%HPD CI to the posterior prediction mean).This study proposed an integrated method and technology for global SOC mapping based on Alibaba Cloud computing,combined with using DIC and Occam's Razor criterion to select environmental covariates,bottom-up partitioning zone modelling SOC using INLA-SPDE.This integrated method and technology offers an alternative solution to the problems of spatial big data calculation faced by global digital mapping of SOC.(4)This paper analyzed the INLA-SPDE theory and method.We found that as the spatial scale expanded from field to regional and global,the nugget variance and range of SOC latent Gaussian field increased correspondently.The results of this study demonstrate that INLA-SPDE method is appropriate for Bayesian spatial modelling and digital mapping of SOC content at field,regional and global scales.Related drawing digital map products enrich SOC database.