Comparison of two approaches for downscaling synoptic atmospheric patterns to multisite precipitation occurrence

The physical linkages between climate on the large scale and weather on the local scale allow the formulation of downscaling approaches for assessing the impact of climate variability at point locations. This paper presents a comparison between two such approaches applied for downscaling synoptic atmospheric patterns to point rainfall occurrences on a rain gauge network. The approaches evaluated are the parametric nonhomogenous hidden Markov model (NHMM) and the nonparametric k-nearest neighbor downscaling approach. The NHMM defines local-scale weather as a function of a discrete weather state that is Markovian and depends on predictor variables representing synoptic atmospheric patterns. As the model is defined parametrically, the number of parameters that need specification increases as one considers more discrete weather states. Consequently, parameter identification and generalization to ungauged sites becomes difficult. On the other hand, nonparametric resampling is attractive because of its efficiency and simplicity, being structured as a direct probabilistic relationship between the larger-scale climatic variables and the local-scale weather. Such a formulation offers a simpler alternative to the NHMM approach of using intermediate hidden weather state variables but is less capable of representing persistence introduced through Markovian assumptions in the NHMM. In the comparison presented here, we applied weather-state-based nonhomogeneous hidden Markov model and the k-nearest neighbor bootstrap to estimate precipitation occurrences at a network of 30 rain gauge locations around Sydney, Australia. Our results suggest that both the models perform well in representing spatial variations while they show a lack in representing temporal dependence at scales longer than a few days as exhibited through wet spell length characteristics. Local-scale features that are difficult to represent through the large-scale climate predictors are, as expected, not reproduced by either approach.