Spatio-Temporal Prediction of Root Zone Soil Moisture Using Multivariate Relevance Vector Machines

Root zone soil moisture at one and two meter depths are forecasted four days into the future. In this article, we propose a new multivariate output prediction approach to root zone soil moisture assessment using learning machine models. These models are known for their robustness, efficiency, and sparseness; they provide a statistically sound approach to solving the inverse problem and thus to building statistical models. The multivariate relevance vector machine (MVRVM) is used to build a model that forecasts soil moisture states based upon current soil moisture and soil temperature conditions. The methodology combines the data at different depths from 5 cm to 50 cm, the largest of which corresponds to the depth at which the soil moisture sensors are generally operational, to produce soil moisture predictions at larger depths. The MVRVM test results for soil moisture predictions at 1 m and 2 m depth on the 4th day are excellent with RMSE = 0.0131 m3/m3 for 1 m; and RMSE = 0.0015 m3/m3 for 2 m forecasted values. The statistics of predictions for 4th day (CoE = 0.87 for 1 m and CoE = 0.96 for 2 m) indicate good model generalization capability and computations show good agreement with actual measurements with R2 = 0.88 and R2 = 0.97 for 1 m and 2 m depths, respectively. The MVRVM produces good results for all four days. Bootstrapping is used to check over/under-fitting and uncertainty in model estimates.