Spatial-temporal rainfall modelling for flood risk estimation

Abstract

Some recent developments in the stochastic modelling of single site and spatial rainfall are summarised. Alternative single site models based on Poisson cluster processes are introduced, fitting methods are discussed, and performance is compared for representative UK hourly data. The representation of sub-hourly rainfall is discussed, and results from a temporal disaggregation scheme are presented. Extension of the Poisson process methods to spatial-temporal rainfall, using radar data, is reported. Current methods assume spatial and temporal stationarity; work in progress seeks to relax these restrictions. Unlike radar data, long sequences of daily raingauge data are commonly available, and the use of generalized linear models (GLMs) (which can represent both temporal and spatial non-stationarity) to represent the spatial structure of daily rainfall based on raingauge data is illustrated for a network in the North of England. For flood simulation, disaggregation of daily rainfall is required. A relatively simple methodology is described, in which a single site Poisson process model provides hourly sequences, conditioned on the observed or GLM-simulated daily data. As a first step, complete spatial dependence is assumed. Results from the River Lee catchment, near London, are promising. A relatively comprehensive set of methodologies is thus provided for hydrological application.

Estimating functions and the generalized method of moments

“…For the Poisson-based model described above, in fact it is possible to derive a joint distribution for the binary sequence defined by considering whether or not the rainfall in each time interval is zero: this can be used to define a marginal likelihood [17]. However, even this approach seems intractable for the more complex models that are needed for a realistic representation of observed rainfall structure (see [18] for a review of these models).…”

“…In view of the infeasibility and potential undesirability of likelihood-based inference for this class of rainfall models, parameters are usually chosen to achieve as close a match as possible, according to a weighted least-squares criterion, between the observed and fitted values of selected statistical properties [18]. Specifically, let T ¼ (T 1 .…”

“…In the hydrological literature, many authors have sought to address some of these questions empirically (e.g. [18,20]). However, EF theory provides direct answers to all of them.…”

“…To account for seasonality in rainfall data, these models are usually fitted separately to data for each calendar month [18,19]: data from different years are considered to provide independent replicates of the rainfall process. Each of our simulations represents 20 years' worth of data for a single calendar month: specifically, m ¼ 20 independent sets of 30 days' worth of hourly values are generated, each from a model with parameter vector u 0 ¼ (23.5 0 0 1.1) 0 .…”

Simulation of multisite precipitation using an extended chain‐dependent process

“…They make up the most important step in construction of weather generators, which have wide applications in agriculture and ecosystem simulations [Richardson, 1981] and have application in climate change studies [Wilks, 1992;Furrer and Katz, 2007;Brissette et al, 2007]. Although much progress has been achieved in the development of precipitation simulation tools, current challenges include the accurate representation of extremal behavior, the generation of multisite sequences with realistic spatial dependence, the need to represent realistic levels of interannual variability in the generated sequences, and the representation of complex dynamical structures within a relatively cheap computational framework [e.g., Wheater et al, 2005].…”