The estimation of flow quantiles is a major focus of current hydrologic research. Probabilistic representations of a few individual quantiles, notably the annual flood and low flow, have been devised, and recently a few of the larger quantiles have been modeled. This research describes and demonstrates the use of a probability model for all flow quantiles in a river. A flow duration curve represents the annual flow frequency characteristics of rivers by depicting the cumulative frequencies for average ranked flows in a river. A model requiting only five parameters is developed, by combining the principles of order statistics and traditional flow frequency analyses, and applied to flow duration curves for rivers in the province of British Columbia, Canada. Streamflows in British Columbia are generated from a number of distinct physical processes operating in highly variable environments. The model presented incorporates the physical generating processes of streamflow in both the statistical representation of flow duration curves and their interpretation.Let X•, X2, "' , Xn denote a random sample from a parent population with continuous cumulative distribution function F x. Within that sample a unique ordered arrangement should exist: suppose that git ) denotes the largest of that sample; X(2) denotes the second largest, and so on; and X(n) denotes the smallest. Then X(•) > denotes the original random sample after arrangement in decreasing order of magnitude and are collectively termed the order statistics of the random sample, such that X(r), for 1 < r <-n, is the rth order statistic [Gibbons, 1985]. The annual flood, which is the maximum of the annual sample of daily streamflows in a year, will be denoted by X(•)' the 3535
The estimation of flow quantiles and the regionalization of hydrologic characteristics are two major foci of current hydrologic research. A flow-duration curve represents the annual flow-frequency characteristics of rivers by depicting the cumula tive frequencies for average ranked flows in a river. Generally the process requires the empirical estimation of the mean flow at each of 365 ranks. A model requiring only five parameters is developed by combining the principles of order statistics and traditional flow-frequency analyses and is applied to flow-duration curves for rivers in the province of British Columbia, Canada. Results from the model may be interpreted both statis tically and physically and allow the identification of hydrologically similar regions. Streamflows in British Columbia are generated from a number of distinct physical processes operating in highly diverse environments. The mixture of the streamflowgenerating processes requires that the statistical model be capable of encompassing the different flow-frequency regimes. Identification of hydrologic regions also depends on the inclusion of these generating processes. The model presented incorporates the physical generating processes of streamflow in both the statistical representation of flow-duration curves and their interpretation. Similarly, the spatial model presents hydrologic regions that correspond to the known physical environment. [
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