Spatio-temporal variability in observed and simulated rainfall fields

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How can we ensure that everybody has enough safe water to drink? What can be done to protect our towns and cities from flooding? Ultimately, the answers to such questions depend on how much it rains (or not!). Rainfall affects many other aspects of modern life in less obvious ways - for example, it affects radio communications, so that communications engineers need to consider rainfall when designing new technology.In planning for the future it is unwise to rely solely on past observations, because the weather is never exactly the same from day to day: the future is guaranteed to be different from the past (even without accounting for changes in the earth's climate). It is therefore useful to be able to use a computer to simulate pseudo-rainfall data that allows for random variation. Hydrologists can use these simulated data to test their plans and designs.One way of simulating rainfall data is by treating it as a random process in space and time, and building a probabilistic model for this process. Such a model should produce simulated rainfall sequences that have the right kind of structure. However, it is not always clear what is meant by this, or how to measure it. This is because, typically, the rainfall process is organised in a complex way in both time and space; some features of this organisation will be very important in controlling the effect of a particular rainfall event, while others might be less so. Within this context, the proposed research aims to develop ways of summarising the complex structure in observed rainfall fields, and to apply these summaries to rainfall models that are currently being developed for national application in the UK. The summaries considered are based on scaling ideas, whereby the structure of the rainfall process at one space or time scale can be related to that at another. Two particular class of summary measures will be considered:1. Spectral multiscaling of spatially averaged rain rate (SARR) processes. This is a means of linking the properties of rainfall sequences observed over different spatial areas. For example, an hourly sequence of average rainfall over an area of 100 square kilometres will typically look very different from an hourly sequence for an area of 10,000 square kilometres; spectral multiscaling describes the relationships between the properties of the two sequences. 2. Scaling properties of wet and dry periods at different spatial scales. For example, dry periods are likely to be shorter at large spatial scales than over small areas, since it is more likely to be raining somewhere in a large region than in a small area.3. Relationships between SARR and the fraction of area (in the region of aggregation) where rain rate exceeds a given threshold. A lot of previous work has shown that remarkably stable relationships exist, across a range of spatial scales, for rainfall observed in the tropics. One of the aims of the proposed research is to determine, through analyses of data from weather radar stations and rain gauges in the UK, whether these relationships hold more generally. If so, this would open up exciting possibilities - for example, the results could be used to recreate rainfall data at a fine space or time scale from observations at a much coarser scale.A further aspect of the proposed work is to determine whether these relationships can be reproduced by rainfall models that are currently being developed by the investigators for national application in the UK. Currently, the performance of such models is usually assessed using conventional statistical summaries. The proposed research allows the possibility of carrying out much more detailed performance assessment, using measures that are arguably more relevant than those currently in use.