Spatial variability and uncertainty associated with soil moisture content using INLA-SPDE combined with PyMC3 probability programming.

Spatial variability and uncertainty associated with soil volumetric moisture content (SVMC) is crucial in moisture prediction accuracy, this paper sets out to address this point of SVMC by developing data-driven model. Grid samples of SVMC covered approximately a 3-ha field during the jointing growth stage of winter wheat, and SVMC were measured by Time Domain Reflectometry (TDR), located in North China Plain, China. Bayesian inference was performed to explore spatial heterogeneity, robustness, transparency, interpretability and uncertainty related to SVMC using python-based PyMC3 combined with Integrated Nested Laplace Approximation with the Stochastic Partial Differential Equation (INLA-SPDE) model. The results showed that the prediction surface of SVMC, the lower and upper limits of 95% credible intervals quantified uncertainty associated with SVMC, cauchy prior of the flexibility and adaptability to obtain state-of-the-art predictive performance is more robust than gaussian prior for SVMC prediction, the transparency and interpretability of SVMC prediction model were revealed by MCMC (Markov-Chain Monte-Carlo) trace plots, KDE (Kernel density estimates), and rank plots. The uncertainty associated with SVMC can explicitly be described using the highest-posterior density interval, the prediction lower and upper limits.