On the use of Markov chain models for drought class transition analysis while considering spatial effects

Prediction of drought class transitions has been received increasing interest in the field of water resource management. Markov chain models are effective prediction tools that are widely used to analyse drought class transitions by describing the temporal dependency of drought events. However, geophysical events or phenomena (such as drought events) can exhibit spatial effects resulting from spatial heterogeneity and/or dependency. This means that on the one hand the drought processes may vary over space, and on the other hand the state change of a drought event may not only depend on its previous state but also on the previous states of its neighbours, and it is thus unreasonable to directly apply Markov chain models without considering spatial effects. Therefore, this paper proposes a framework that considers spatial effects when employing drought class transition analysis. Three types of Markov chain models are introduced (traditional, local and spatial). To test for the existence of spatial effects, spatial clustering technology is selected to identify spatial heterogeneity, and aQstatistic is used to determine the existence of spatial dependency. Based on the results of these tests, a corresponding type of Markov chain models is then selected to analyse drought class transitions. Monthly rainfall time series data for Southwest China from 1951 to 2010 are employed in a case study, and the results show that spatial heterogeneity exists for both the 3- and 9-month SPI time series; however, the existence of spatial dependency is not confirmed. Forward and backward estimation rules are also obtained for drought class transitions using local Markov chain models.