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Chapter 11: Stochastic Modeling of Precipitation
11.4.2 Conditional Stochastic Precipitation Models
Hay et al. (1991) used a classification method (McCabe, 1990) based on wind
direction and cloud cover which was coupled with a semi-Markov model to
simulate temporal sequences of weather types at Philadelphia. Semi-Markov
models (Cox and Lewis, 1978) with seasonal transition probabilities and parameters of the sojourn time distribution, were used to simulate the evolution of the weather states. This step is not strictly necessary if a lengthy
sequence of variables defining the large-area weather states (the classification
used required daily wind direction and cloud cover data) is available. Where
such sequences are not available (sometimes the case for GCM simulations)
fitting a stochastic model to the weather states has the advantage that it
decouples the simulation of precipitation, and other local variables, from a
particular GCM simulation sequence. The method of simulating daily precipitation conditional on the weather state used by Hay et al. was as follows.
For each weather state and each of 11 weather stations in the region, the
unconditional probability of precipitation was estimated from the historie
record. Then, conditional on the weather state (but unconditional on precipitation occurrence and amount at the other stations and previous time) the
precipitation state was selected based on the unconditional precipitation occurrence prob ability. Precipitation amounts were drawn from the product of
a uniform and exponential distribution. Retrospective analysis of the model
showed that those variables explicitly utilized for parameter estimation (conditional precipitation occurrence probabilities, mean precipitation amounts)
were reproduced by the model. An analysis of dry period lengths suggested
that the length of extreme dry periods was somewhat underestimated.
Bardossy and Plate (1991) also used a semi-Markov model to describe the
structure of the daily circulation patterns over Europe, with circulation types
based on synoptic classification. They developed a model of the corresponding rainfall occurrence process that was Markovian within a weather state
(circulation type), but independent when the weather state changed. Precipitation occurrences were assumed spatially independent. Bardossy and Plate
(1991) applied the model to simulate the precipitation occurrences at Essen,
Germany. For this station, they found that the persistence parameter in the
occurrence model was quite small, so that the model was almost conditionally
independent (that is, virtually all of the persistence in the rainfall occurrence
process was due to persistence in the weather states). The model reproduced
the autocorrelations of the rainfall occurrences, as weIl as the distributions
of dry and wet days, reasonably weIl. This is somewhat surprising, since
other investigators (e.g., Hughes et al. , 1993) have found that conditionally
independent models tend to underestimate the tail of the dry period duration
distribution. However, this finding is likely to depend on both the structure
of the weather state process, and the precipitation occurrence process, which
is regionally and site-specific. Bardossy and Plate (1992) extended the model
of Bardossy and Plate (1991) to incorporate spatial persistence in the rain-
Chapter 11: Stochastic Modeling of Precipitation
11.4.2 Conditional Stochastic Precipitation Models
Hay et al. (1991) used a classification method (McCabe, 1990) based on wind
direction and cloud cover which was coupled with a semi-Markov model to
simulate temporal sequences of weather types at Philadelphia. Semi-Markov
models (Cox and Lewis, 1978) with seasonal transition probabilities and parameters of the sojourn time distribution, were used to simulate the evolution of the weather states. This step is not strictly necessary if a lengthy
sequence of variables defining the large-area weather states (the classification
used required daily wind direction and cloud cover data) is available. Where
such sequences are not available (sometimes the case for GCM simulations)
fitting a stochastic model to the weather states has the advantage that it
decouples the simulation of precipitation, and other local variables, from a
particular GCM simulation sequence. The method of simulating daily precipitation conditional on the weather state used by Hay et al. was as follows.
For each weather state and each of 11 weather stations in the region, the
unconditional probability of precipitation was estimated from the historie
record. Then, conditional on the weather state (but unconditional on precipitation occurrence and amount at the other stations and previous time) the
precipitation state was selected based on the unconditional precipitation occurrence prob ability. Precipitation amounts were drawn from the product of
a uniform and exponential distribution. Retrospective analysis of the model
showed that those variables explicitly utilized for parameter estimation (conditional precipitation occurrence probabilities, mean precipitation amounts)
were reproduced by the model. An analysis of dry period lengths suggested
that the length of extreme dry periods was somewhat underestimated.
Bardossy and Plate (1991) also used a semi-Markov model to describe the
structure of the daily circulation patterns over Europe, with circulation types
based on synoptic classification. They developed a model of the corresponding rainfall occurrence process that was Markovian within a weather state
(circulation type), but independent when the weather state changed. Precipitation occurrences were assumed spatially independent. Bardossy and Plate
(1991) applied the model to simulate the precipitation occurrences at Essen,
Germany. For this station, they found that the persistence parameter in the
occurrence model was quite small, so that the model was almost conditionally
independent (that is, virtually all of the persistence in the rainfall occurrence
process was due to persistence in the weather states). The model reproduced
the autocorrelations of the rainfall occurrences, as weIl as the distributions
of dry and wet days, reasonably weIl. This is somewhat surprising, since
other investigators (e.g., Hughes et al. , 1993) have found that conditionally
independent models tend to underestimate the tail of the dry period duration
distribution. However, this finding is likely to depend on both the structure
of the weather state process, and the precipitation occurrence process, which
is regionally and site-specific. Bardossy and Plate (1992) extended the model
of Bardossy and Plate (1991) to incorporate spatial persistence in the rain-