Chapter 11
Stochastic Modeling of
Precipitation with
Applications to Climate
Model Downscaling
by Dennis Lettenmaier
11.1 Introduction
Probabilistic models of precipitation are mathematical representations of the
probability distribution of precipitation without regard to time, that is
l
~+d~
prob (x < X < x + dx) = ~
Ix (r)dr,
(11.1)
where X might be, for instance, the total annual (or monthly) precipitation
occurring at a given station, or the maximum annual precipitation occurring
in a 24 hour period. Probabilistic models are useful for assessing risk, which,
in its simplest form, is the prob ability of an undesirable outcome. For instance, in an unirrigated agricultural area, it may be important to know the
Acknowledgements: The assistance of James P. Hughes and Larry W. Wilson in
assembling the review materials is greatly appreciated. Portions of this material have
previously appeared in a paper by the author included in the proceedings of the Conference
on Stochastic and Statistical Methods in Hydrology and Environmental Engineering (June,
1993, University of Waterloo).