| 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.
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