A hidden Markov model for downscaling synoptic atmospheric patterns to precipitation amounts

Abstract

Nonhomogeneous hidden Markov models (NHMMs) provide a relatively simple framework for simulating precipitation at multiple rain gauge stations conditional on synoptic atmospheric patterns. Building on existing NHMMs for precipitation occurrences, we propose an extension to include precipitation amounts. The model we describe assumes the existence of unobserved (or hidden) weather patterns, the weather states, which follow a Markov chain. The weather states depend on observable synoptic information and therefore serve as a link between the synoptic-scale atmospheric patterns and the local-scale precipitation. The presence of the hidden states simplifies the spatio-temporal structure of the precipitation process. We assume the temporal dependence of precipitation is completely accounted for by the Markov evolution of the weather state. The spatial dependence of precipitation can also be partially or completely accounted for by the existence of a common weather state. In the proposed model, occurrences are assumed to be conditionally spatially independent given the current weather state and, conditional on occurrences, precipitation amounts are modeled independently at each rain gauge as gamma deviates with gauge-specific parameters. We apply these methods to model precipitation at a network of 24 rain gauge stations in Washington state over the course of 17 winters. The first 12 yr are used for model fitting purposes, while the last 5 serve to evaluate the model performance. The analysis of the model results for the reserved years suggests that the characteristics of the data are captured fairly well and points to possible directions for future improvements.

Linking climate change modelling to impacts studies: recent advances in downscaling techniques for hydrological modelling

“…p(wet-wet) or mean wet day amount, associated with a given atmospheric circulation pattern (e.g. Bellone et al, 2000). Climate change is estimated by evaluating the change in the frequency of the weather classes simulated by the GCM.…”

MCMC implementation for Bayesian hidden semi-Markov models with illustrative applications

“…We anticipate this would be quite computationally intensive for networks where many hidden chains are involved. Of course any physical justification is ideal as in the case of Hughes et al (1999) and Bellone et al (2000) who model precipitation occurrences and the hidden states are linked to unobserved weather states which link synoptic-scale atmospheric patterns to local-scale precipitation.…”

“…A few examples of applications that have found use for HMMs include: climate modelling where HMMs are used for downscaling precipitation forecasts (Bellone et al, 2000), in economics HMMs are used to capture non-stationarity in share price return series (Rydén et al, 1998), in medical applications to model disease progression in cancer studies (Kozumi, 2000;Jouyaux et al, 2000), in genetics (Yau et al, 2011), in mechanical engineering (Jardine et al, 2006) and several others.…”

Untitled

“…Rather than restricting attention to indices that assume only a small number of states, it would be straightforward to condition on a continuous index (Woolhiser et al, 1993). Finally, an alternative approach that should result in much stronger relationships involves conditioning on high, instead of low, frequency information about circulation (i.e., smaller-scale circulation indices that vary on a daily time scale) (Bellone et al, 2000;Tebaldi, 2000).…”