A Bayesian statistical model for deriving the predictive distribution of hydroclimatic variables

Recent publications have provided evidence that hydrological processes exhibit a scaling behaviour, also known as the Hurst phenomenon. An appropriate way to model this behaviour is to use the Hurst-Kolmogorov stochastic process. The Hurst-Kolmogorov process entails high autocorrelations even for large lags, as well as high variability even at climatic scales. A problem that, thus, arises is how to incorporate the observed past hydroclimatic data in deriving the predictive distribution of hydroclimatic processes at climatic time scales. Here with the use of Bayesian techniques we create a framework to solve the aforementioned problem. We assume that there is no prior information for the parameters of the process and use a non-informative prior distribution. We apply this method with real-world data to derive the posterior distribution of the parameters and the posterior predictive distribution of various 30-year moving average climatic variables. The marginal distributions we examine are the normal and the truncated normal (for nonnegative variables). We also compare the results with two alternative models, one that assumes independence in time and one with Markovian dependence, and the results are dramatically different. The conclusion is that this framework is appropriate for the prediction of future hydroclimatic variables conditional on the observations.