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？我们能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雨的程度（或不下雨！）。降雨对现代生活的许多其他方面都有不那么明显的影响--例如，它会影响无线电通信，因此通信工程师在设计新技术时需要考虑降雨量。在规划未来时，仅仅依靠过去的观测是不明智的，因为天气永远不会每天都完全相同：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。水文学家可以利用这些模拟数据来检验他们的计划和设计。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。这样的模式应该产生具有正确结构的模拟降雨序列。不过，这是什么意思，或如何量度，往往并不清楚，因为降雨过程在时间和空间上通常是有复杂的组织的;这种组织的某些特征对控制某次降雨事件的影响非常重要，而其他特征则可能不那么重要。在这种情况下，拟议的研究旨在开发的方法，总结在观测到的降雨场的复杂结构，并将这些摘要应用于降雨模型，目前正在开发的国家应用在英国。考虑的摘要是基于缩放的想法，即降雨过程的结构在一个空间或时间尺度可以在另一个相关。将考虑两个特定类别的汇总测量：1。空间平均降雨率过程的谱多尺度分析。这是一种将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，一个100平方公里区域的每小时平均降雨量序列与一个10，000平方公里区域的每小时平均降雨量序列通常看起来非常不同;光谱多尺度描述了两个序列属性之间的关系。2.不同空间尺度下干湿期的标度特性。例如，在大的空间尺度上，干旱期可能比小区域的干旱期短，因为大区域的某个地方比小区域的某个地方更可能下雨。SARR与降雨率超过给定阈值的面积分数（在聚集区）之间的关系。以前的大量工作表明，在热带地区观测到的降雨量在一系列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天气雷达站和雨量计的数据，确定这些关系是否更普遍。如果是这样的话，这将开辟令人兴奋的可能性-例如，其结果可以用于从更粗尺度的观测中重新创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重现，这些模型目前正在由研究人员开发，供英国全国应用。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的可能性，使用的措施，可以说是比目前使用的更相关。

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.