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

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Abstract

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 \(\times \) 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.

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Acknowledgements

We thank the Associate Editor and two anonymous referees for very helpful and constructive comments and suggestions that helped improve earlier drafts of this paper. We gratefully thank Professor Kay E. Holekamp (Michigan State University) and the Kenya Meteorological Department (KMD) for providing the rainfall data as well as helpful advice. In particular, we are greatly indebted to Ms Christine Mahonga for her patience and excellent support in making the data available to us and coordinating the verification of the rainfall data at KMD. We are grateful to Mr. Gordon Ojwang (Directorate of Resource Surveys and Remote Sensing of Kenya) for his assistance in acquiring the data and to Chris Shitote of FEWS NET for his help in extracting the blended satellite-station rainfall and temperature data from the GEOCLIM TOOL. We are also grateful to Professor Sujit K. Sahu (University of Southampton) for suggestions that helped improve the spatio-temporal model and to Professor Norman Owen-Smith (University of the Witwatersrand) for providing valuable insights on understanding the rainfall pattern in Narok. JOO was supported by a grant from the German Research Foundation (Grant No. OG 83/1-1). This project has received funding from the European Union Horizon 2020 research and innovation programme under Grant Agreement No. 641918.

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Authors and Affiliations

  1. Biostatistics (340C), University of Hohenheim, Fruwirthstrasse 23, 70599, Stuttgart, Germany

    Sabyasachi Mukhopadhyay, Joseph O. Ogutu, Gundula Bartzke & Hans-Peter Piepho

  2. Indian Institute of Management, Udaipur, Balicha, Udaipur, Rajasthan, 313001, India

    Sabyasachi Mukhopadhyay

  3. Wasaa Conservation Centre, IUCN ESARO, P.O. Box 68200, Nairobi, 00200, Kenya

    Holly T. Dublin

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  1. Sabyasachi Mukhopadhyay
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  2. Joseph O. Ogutu
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Correspondence to Sabyasachi Mukhopadhyay.

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Mukhopadhyay, S., Ogutu, J.O., Bartzke, G. et al. Modelling Spatio-Temporal Variation in Sparse Rainfall Data Using a Hierarchical Bayesian Regression Model. JABES 24, 369–393 (2019). https://doi.org/10.1007/s13253-019-00357-3

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