Modelling Spatio-Temporal Variation in Sparse Rainfall Data Using a Hierarchical Bayesian Regression Model

Rainfall is a critical component of climate governing vegetation growth and production, forage availability and quality for herbivores. However, reliable rainfall measurements are not always available, making it necessary to predict rainfall values for particular locations through time. Predicting rainfall in space and time can be a complex and challenging task, especially where the rain gauge network is sparse and measurements are not recorded consistently for all rain gauges, leading to many missing values. Here, we develop a flexible Bayesian model for predicting rainfall in space and time and apply it to Narok County, situated in southwestern Kenya, using data collected at 23 rain gauges from 1965 to 2015. Narok County encompasses the Maasai Mara ecosystem, the northern-most section of the Mara-Serengeti ecosystem, famous for its diverse and abundant large mammal populations and spectacular migration of enormous herds of wildebeest, zebra and Thomson's gazelle. The model incorporates geographical and meteorological predictor variables, including elevation, distance to Lake Victoria and minimum temperature. Salient features of our model are the use of non-stationary covariance structures and the facility to handle excess zeros and many missing observations. We assess the efficiency of the model by comparing it empirically with the established Gaussian process, Kriging, simple linear and Bayesian linear models. We use the model to predict total monthly rainfall and its standard error for all 5 x 5 km grid cells in Narok County for each year from 1965 to 2015. Using the Monte Carlo integration method, we estimate seasonal and annual rainfall and their standard errors for 29 sub-regions of Narok for each of the 51 years spanning 1965-2015. The non-stationary model can handle data from a sparse network of observations with many missing values and performs at least as well as or better than four established and widely used models on the Narok rainfall data set. The model produces rainfall predictions consistent with expectation and in good agreement with blended station and satellite rainfall values. The predictions are precise enough for most practical purposes. The model is very general and applicable to other variables besides rainfall.