Statistical work in hydrology on the topic of riverflow time series is discussed. The theme is the "data-generation method" which in the present situation aims to produce simulations corresponding to a chosen historical riverflow series; they are required to resemble the historical data in respect of hydrologically important properties, such as runs of low flows. In practice the simulations are then used as input to a projected water resources system, but this aspect is not treated here. Capture of statistical resemblence entails a thorough statistical analysis of the historical series, and the paper describes the distinctive non-Gaussian and periodic features of typical riverflow series; it emphasizes the hydrological importance of seasonality, marginal distribution, dependence and crossing properties. The paper then describes hydrological adaptions and use of some of the traditional time series and shot noise models. It discusses the hydrologically motivated long memory fractional noise and broken line models; here the aim is to bring them to the attention of statisticians for appraisal while at the same time making their theory more accessible to hydrologists. Places where the presently used methodology needs consolidating are mentioned, as are areas where further statistical and mathematical work would be of value.
Abstract. We present a method of modeling the areal reduction factor (ARF) of storm rainfall. The ARF is widely used in reducing point rainfall to obtain areal average values for the same duration, probability of exceedance, and specified area. The concepts of scaling and multiscaling, developed in recent years, provide a powerful framework for studying spatial and temporal variability of hydrological processes. It is our view that ARF must reflect the scaling properties of rainfall in space and time. We develop a simple statistical approach to the ARF of extreme storm rainfall based on the scaling properties of the underlying process in space and time. We derive the scaling relations of mean rainfall intensity over an area A and for a duration T using the concepts of dynamic scaling and statistical self-affinity. A new physically based formula for the ARF is then obtained. Applications are made to observations from the metropolitan area of Milan, Italy, and to data in the United Kingdom, as given in the Natural Environmental Research Council Flood Studies Report. These studies indicate that storm rates in space and time are scaling for extreme events, and hence this concept is shown to provide a useful practical approach to the evaluation of design storms for specified areas.
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