Research Summary

Evaluation and Development of a Stochastic Precipitation Model
Jim Hughes, Peter Guttorp
We consider the use of stochastic models of precipitation in assessing climate variability and climate change and in downscaling (doing sub-grid scale simulation) of general circulation models of global climate. Technically, our method involves fitting non-stationary hidden Markov models to sequences of multi-station precipitation data. The states of the model are identified as "weather states'' and daily observations from atmospheric fields drive the transitions between weather states.

Thus far, assessment of fitted non-stationary hidden Markov models has involved comparison of model simulated rainfall statistics to historical rainfall statistics. Another approach to the assessment of such models is to compare precipitation probability forecasts based on the model to the forecasts made by meteorologists. To generate forecasts with the NHMM we would utilize recent rainfall history and forecast atmospheric field data. We propose to do such a comparison. We also intend to compare our forecasts to some produced by direct meteorological weather state models that have been developed in Atmospheric Sciences.

One of the important aspects of the fitting of this type of modelsis the choice of the number of weather states. This can be done using Bayes factor computations, but these require sophisticated numerical schemes to be evaluated. We have so far limited our selection procedures to the Bayes Information Criterion, which is a crude approximation to the Bayes factor. We therefore propose to develop algorithms for computing Bayes factors in this type of models. We will compare the efficacy of the Bayes Information Criterion to the use of Bayes factors with simulation studies.

While probability forecasting of precipitation is a useful tool, it is equally important to be able to include amounts in the model. Current methods in this context use resampling or modeling of amounts conditional upon the estimated weather state and the simulated occurrence pattern. A more natural approach is to include a spatial model for amounts directly into the fitting procedure (rather than first fitting a model for precipitation occurrence, and then a subsequent model for amounts, given that precipitation occurs). We propose to develop such a model.

LOCAL CONNECTIONS: This work is closely connected to the NSF project "Atmospheric Sciences and Statistics" with co-investigators from Statistics, Biostatistics, Applied Physics Laboratory, and Atmospheric Sciences. It is also closely connected to Dennis Lettenmaier's EPA-funded research on climate model assessment.