app10_storm_ty

app10_storm_ty - Application Example 10 (Joint, marginal...

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Application Example 10 (Joint, marginal and conditional distributions) RELATION BETWEEN STORM DURATION AND PRECIPITATION INTENSITY Hydrologists are much interested in the statistical characteristics of precipitation events. Such characteristics are for example used to assess the variability of river flow, evaluate the risk of floods, and design river regulation structures. The two most important storm characteristics are duration T and average precipitation intensity Y. The product TY gives the total precipitation volume V during the storm. The random variables T and Y are probabilistically dependent. For example, the intensity Y is much more variable for short than for long-lasting storms. Whether a storm with characteristics (T, Y) is critical for a given river basin depends on the characteristics of the basin: large basins have a slow response and are mainly affected by long-lasting precipitation events, even though the intensity may have relatively low. By contrast, small basins have rapid response and for them, intense short storms produce the highest floods. Simple models of precipitation in time use the joint distribution of T and Y to probabilistically describe the generic rainfall event as a “rectangular pulse” of random duration T and random intensity Y. The simplest models also assume that storms occur at Poisson times and ignore seasonality effects by assuming that (a) the rate λ of arrival of storms is constant throughout the year, and (b) the random vectors (T,Y) i that describe the characteristics of different storms i are independent and identically distributed. This is called the (stationary) Poisson Rectangular Pulse (or PRP) model; see Figure 1.
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app10_storm_ty - Application Example 10 (Joint, marginal...

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