Abstract
In order to help the design of flood protection schemes and so on it is often required that predictions should be made about the extreme levels of river flows or rainfall over a very long time. For example, it may be required to predict the rainfall level that may be exceeded once in perhaps 500 years. To make these predictions stochastic hydrologists tend to use the annual maxima series for river flow or rainfall level. However, these records tend to be of short duration and they may not be taken particularly close to the site of interest. To overcome this lack of data it is now usual to use some form of regional estimation technique. These techniques generally assume that data from a hydrologically homogeneous region may in some way be pooled and used to produce regional estimates of the river flow and rainfall quantiles. The quantiles at any particular site may then be found by scaling the regional quantiles using at-site data. The main points of the most commonly used regional estimation techniques are briefly discussed. One of the problems with these techniques is that they assume that within a region all the sites are independently distributed. After a review of previous work examining this problem of inter-site dependence a new method for modelling and examining inter-site dependence using the properties of min-stable processes is introduced. The problem of how to generate min-stable distributions is considered and the techniques required to fit these distributions are investigated using both simulated data and annual maxima rainfall data. Although the estimators are found to be rather inaccurate the model itself is shown to have great potential for use as a simulation tool for studying the effects of inter-site dependence.