210
Chapter 11: Stochastic Modeling of Precipitation
the atmospheric variables is a function only of the present value of the hidden state, and not the previous value. In one of the two examples explored,
Hughes found, using a Bayes Information Criterion to discriminate between
models, that the second model was the best choice.
In the other example, the full Markov dependence was retained.
In the two examples, Hughes evaluated the means of the weather variables
corresponding to the hidden states. He found that the large area characteristics were reasonable. For winter, the states with the most precipitation on
average corresponded to a low pressure system off the north Pacific coast, and
the cases with the least precipitation corresponded to a high pressure area
slightly inland of the coast. In the second example, with modeled precipitation occurrences at 24 stations in western Washington, transitional states
with differences in the surface and 500 hPa flow patterns were shown to result in partial precipitation coverage (precipitation at some stations, and not
at others). These results suggest that the NHMM may offer a reasonable
structure for transmitting the effects of large area circulation patterns to the
local scale.
11.5 Applications to Alternative Climate
Simulation
Although the development of most of the models reviewed above have been
motivated in part by the need for tools to simulate local precipitation for
alternative climate scenarios, there have only been a few applications where
climate model (GCM) scenarios have been downscaled using stochastic methods. Hughes et al. (1993) estiD;lated parameters of semi-Markov models from
five-year 1 x CO2 and 2 x CO2 GFDL simulations of surface pressure and 850
hPa temperature. From these five-year sequences, they computed the daily
weather states using algorithms developed from historical sea level pressure
observations (see Section 11.4.1), and fit semi-Markov models to the weather
states. The semi-Markov models were used to simulate 40-year weather state
sequences corresponding to the 1 x C02 and 2 x CO2 runs. Daily precipitation (and temperature maxima-minima, using the model described in Section
11.4.2) were then simulated for the 40-year period, and were used as input to
a hydrologic model which was used to assess shifts in flood risk that might
be associated with climate change.
Zorita et al. (1995) used a model similar to that of Hughes et al. (1993)
to simulate daily precipitation for four sites in the Columbia River basin.
They found that the model performed reasonably weIl in winter, but there
were difficulties in application of the CART procedure to determine climate
states in summer. When stations relatively far from the Pacific Co ast were
used in definition of the multistation rain states in the CART algorithm,
no feasible solutions resulted. This problem could be avoided by restricting
Chapter 11: Stochastic Modeling of Precipitation
the atmospheric variables is a function only of the present value of the hidden state, and not the previous value. In one of the two examples explored,
Hughes found, using a Bayes Information Criterion to discriminate between
models, that the second model was the best choice.
In the other example, the full Markov dependence was retained.
In the two examples, Hughes evaluated the means of the weather variables
corresponding to the hidden states. He found that the large area characteristics were reasonable. For winter, the states with the most precipitation on
average corresponded to a low pressure system off the north Pacific coast, and
the cases with the least precipitation corresponded to a high pressure area
slightly inland of the coast. In the second example, with modeled precipitation occurrences at 24 stations in western Washington, transitional states
with differences in the surface and 500 hPa flow patterns were shown to result in partial precipitation coverage (precipitation at some stations, and not
at others). These results suggest that the NHMM may offer a reasonable
structure for transmitting the effects of large area circulation patterns to the
local scale.
11.5 Applications to Alternative Climate
Simulation
Although the development of most of the models reviewed above have been
motivated in part by the need for tools to simulate local precipitation for
alternative climate scenarios, there have only been a few applications where
climate model (GCM) scenarios have been downscaled using stochastic methods. Hughes et al. (1993) estiD;lated parameters of semi-Markov models from
five-year 1 x CO2 and 2 x CO2 GFDL simulations of surface pressure and 850
hPa temperature. From these five-year sequences, they computed the daily
weather states using algorithms developed from historical sea level pressure
observations (see Section 11.4.1), and fit semi-Markov models to the weather
states. The semi-Markov models were used to simulate 40-year weather state
sequences corresponding to the 1 x C02 and 2 x CO2 runs. Daily precipitation (and temperature maxima-minima, using the model described in Section
11.4.2) were then simulated for the 40-year period, and were used as input to
a hydrologic model which was used to assess shifts in flood risk that might
be associated with climate change.
Zorita et al. (1995) used a model similar to that of Hughes et al. (1993)
to simulate daily precipitation for four sites in the Columbia River basin.
They found that the model performed reasonably weIl in winter, but there
were difficulties in application of the CART procedure to determine climate
states in summer. When stations relatively far from the Pacific Co ast were
used in definition of the multistation rain states in the CART algorithm,
no feasible solutions resulted. This problem could be avoided by restricting