Spatio-temporal variability in observed and simulated rainfall fields

我们如何确保每个人都有足够的安全饮用水？我们可以做些什么来保护我们的城镇免受洪水的侵袭？最终，这些问题的答案取决于下多少雨（或不下雨！）降雨以不太明显的方式影响现代生活的许多其他方面——例如，它影响无线电通信，因此通信工程师在设计新技术时需要考虑降雨。在规划未来时，仅仅依靠过去的观测是不明智的，因为天气从不可能每天都完全相同：未来肯定与过去不同（即使不考虑地球气候的变化）。因此，能够使用计算机模拟允许随机变化的伪降雨数据是有用的。水文学家可以使用这些模拟数据来测试他们的计划和设计。模拟降雨数据的一种方法是将其视为空间和时间上的随机过程，并为该过程建立概率模型。这样的模型应该能产生具有正确结构的模拟降雨序列。然而，人们并不总是清楚这是什么意思，或者如何衡量它。这是因为，通常，降雨过程在时间和空间上都是以一种复杂的方式组织的；该组织的某些特征对控制特定降雨事件的影响非常重要，而其他特征则可能不那么重要。在此背景下，提出的研究旨在开发总结观测到的降雨场的复杂结构的方法，并将这些总结应用于目前正在开发的用于英国国家应用的降雨模型。所考虑的摘要是基于尺度思想，即一个空间或时间尺度上的降雨过程结构可以与另一个空间或时间尺度上的降雨过程结构相关联。将考虑两类特别的简要措施：空间平均降雨率（SARR）过程的多尺度谱。这是一种将在不同空间区域观测到的降雨序列的特性联系起来的方法。例如，100平方公里地区的每小时平均降雨量序列通常与10,000平方公里地区的每小时降雨量序列非常不同；谱多尺度描述了两个序列性质之间的关系。2. 不同空间尺度上干湿期的标度特性例如，在大空间尺度上，干旱期可能比小区域短，因为在大区域的某个地方比在小区域更有可能下雨。SARR与降雨率超过给定阈值的面积（在聚集区域）的比例之间的关系。以前的许多工作已经表明，在热带地区观测到的降雨在不同的空间尺度上存在着非常稳定的关系。拟议研究的目的之一是通过分析英国气象雷达站和雨量计的数据来确定这些关系是否更普遍。如果是这样，这将开启令人兴奋的可能性——例如，研究结果可用于从更粗尺度的观测中重建精细空间或时间尺度的降雨数据。拟议工作的另一个方面是确定这些关系是否可以通过降雨模型再现，这些模型目前正在由研究人员开发，用于英国的国家应用。目前，通常使用传统的统计摘要来评估这些模型的性能。拟议的研究允许进行更详细的业绩评估，使用比目前使用的措施更相关的措施。

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.