The early 1990s saw extreme flooding in parts of the Galway Bay region of Western Ireland, and this led to speculation of changing rainfall patterns in the area. A study was commissioned to investigate this, and to try and identify possible flood alleviation schemes to safeguard against future repetition. Using daily rainfall data from a network of raingauges in the area, and long monthly rainfall records where available, stochastic models for daily rainfall in the area were developed and used to identify the presence of long-term trends in the climate of the area. The use of Generalised Linear Models enabled uncertainty in these trends to be quantified via, for example, confidence intervals for trend parameters. The fitted models were simulated to obtain probability distributions for future climate scenarios in the area, which were subseqently used as input to hydrological models for assessing future flooding risk. In this talk, we give an overview of the rainfall modelling work involved in this study, and present some specimen predictions of future climate in the area derived from our simulations.

RICHARD CHANDLER
Department of Statistical Science
University College London
Gower Street
London WC1E 6BT, UK
richard@stats.ucl.ac.uk
 
 

Stochastic modeling of rainfall time series is an important topic with a rich history in applied hydrology. At short time scales, i.e., maximum resolution finer than a day, such models have usually been constructed by integrating stochastic point processes based on the Poisson point processes. In recent years, the use of scale-invariant models such as those based on multiplicative random cascades have been investigated since they hold the promise of a providing a more parsimonious way to parameterize the multiple scales of variation evident in the data. However, in either case, except in a few studies, the important fact that a rainfall time series is really a transect through an evolving, advecting space-time field is ignored.
      Simultaneous with the development and application of scale-invariant models to rainfall time series has been development and application of the same to spatial rain, and in the last few years, to space-time rain. In the last case, it was necessary to preserve the special properties of time by ensuring the causality of the evolution of the field in time, in other words, that the future depends only on the past and present. It was attempted in the development of these models to make them as simple as possible while maintaining the basic requirements of the problem. Nevertheless many of the models' properties are unknown, including basic properties of time series that may be extracted from the model. Exploring the properties of time series from such models is important, both because such time series make natural candidates for improved high resolution rainfall time series models, and because time series data (i.e., from rain gauges) is often the only record of the rain in a region, so if a space-time model is to be applied there, inferring its properties from the time series is a necessity.
      In this paper we will introduce a class of space-time causal multifractal rainfall models based on discrete random cascades, describe what is known regarding the properties of these models, emphasizing temporal properties, and compare these properties to those of data and Poisson point process-based models. The paper will conclude with a discussion of how one might estimate the parameters of such a model, again with an emphasis of the use of time series data.

THOMAS  M. OVER
Department of Civil Engineering
205K Wisenbaker
Texas A & M University
College Station, TX 77843-3136,USA
t-over@tamu.edu
 
 

In the past decade or so there has been growing a line of research on the investigation of scale-invariant statistical properties in various types of rainfall data, as a promising key concept to linking rainfall variability across various ranges of spatial and temporal scales. If such properties do indeed hold true, then the merits are at least two-fold. Firstly, one may make inferences about variability in one scale by exploiting information from measurements in another scale, according to the underlying statistical invariance up to a (possibly random) scaling factor. Secondly, one may explore the adequacy of various modelling approaches (physically based or purely stochastic) with respect to their compliance to the anticipated underlying scale-invariance. Both these potential merits are most valuable to applied sciences such as hydrology of ungauged river basins, and meteorology.
Most of the existing literature on scale-invariant statistical properties of rainfields focuses almost exclusively on either spatial features (e.g. spatial average of instantaneous rain rate over a given region, fractional area where rain rate exceeds a given threshold over a given region, spatial spectra of instantaneous rain rate maps), or on temporal features (e.g.  time averages across a time series of given length at a fixed location).
Provided that perhaps the most basic feature of rainfall phenomena is their intermittence in both space and time, then the questions of "where" and "when" does it rain, may be more fundamental than the question of "how much" does it rain. Paraphrasing slightly the questions of "where" and "when" to "for how long" and to "on how large a region" does it rain or does it not rain, the current study tries to link the potential answers to these two questions, hence the space-time approach.
Specifically, using a long series of TOGA-COARE radar scans of rain rate over a large tropical region (120x120 Km2), we explore various possibilities of scale-invariant behavior on the probability distributions of dry and wet epoch duration, as inferred by the lengths of dry and wet spells in time series of spatially averaged rain rate over sampled sub-regions of various spatial scales. Our investigation is based on both sample quantiles and sample moments of the marginal probability distributions, while the corresponding tail behavior is also explored and linked to the observed scaling behavior.

HARRY PAVLOPOULOS
Department of Statistics
Athens University of Economics and Business
76 Patission Str.
Athens, GR-10434, Greece
hgp@aueb.gr