Towards modelling wave height probability distributions of "averaged" and "transient" sea states from first principles

海上的风浪本质上是随机的。尽管工程技术取得了进步，但海洋中不可预测的极端海浪仍然是船舶和近海建筑的严重危险。近年来，发生了多起大型船舶事故，造成人员伤亡和大面积海洋和沿海地区污染。英国作为一个贸易岛国，越来越依赖于不断扩大的航运和离岸活动。生命的损失，供应线或海上能源生产的中断（即使是暂时的）已经变得完全（在道德和经济上）不可接受。为了应对这些挑战，需要对随机海浪有深入的了解，首先，需要了解它们的概率分布对波浪与大气相互作用的依赖性。在气候模式不断变化的情况下，从过去的实验记录中无法获得某一特定地区的“百年一遇的波浪”所需的知识，需要从第一原理推导出一个全面的理论模型。与目前的情况相比，现在已经有了根本的改善。这就是拟议项目的目的。作为常规气象预报的一部分，目前所有的波浪预报和模拟都是基于动力学（哈塞曼）方程的数值积分。由第一性原理导出的方程考虑了风的输入、耗散和不同尺度、不同方向波浪之间的相互作用，描述了风波能谱在时间和空间上的缓慢演化。通过模拟和观测，已经积累了对光谱演化的良好认识。最薄弱的环节是将已获得的能谱知识转化为预测波高的概率分布。现行方法的主要缺点是：(1)它依赖于非常严格的窄谱假设，而从非线性相互作用的角度来看，大多数观测到的谱是广泛的；(2)它没有适当地考虑波的非线性相互作用；(3)它假设过程的平稳性。最近，PI和RCoI找到了一种方法，可以在没有这些限制的情况下，在波浪湍流的既定框架内对概率分布（偏度和峰度）的较高矩进行数值评估。由于这个过程在数值上是昂贵的，我们建议将所有的波谱组合参数化，从而获得简单的概率分布参数化。这将使我们能够从第一原理推导出易于用于各种海况业务预报的概率分布的参数化。现有模型预测的海况或直接测量得到的海况描述了某种程度上的平均（“正常”）海况。由于风的急剧变化，也存在短暂的瞬态，这些瞬态被这种平均方法滤除。我们认为，这些短暂的海况可能导致不成比例的异常高浪。这种短暂的海况从未在此背景下进行过研究。风预报的时间分辨率太低，没有概念和数值工具。对于这个项目至关重要的是，情况已经得到了根本性的改善：风预报的时间分辨率正在显著提高，而PI和RCoI推导了一个能够描述光谱快速演变的广义动力学方程，开发并测试了能够解决这个方程的数值代码。结合作者特别设计的直接数值模拟算法，我们提出了一个明确的路径来检查与大气强迫快速变化有关的瞬态事件波高的概率分布。在此基础上，本项目旨在革新随机风浪和异常风浪预报的建模。

Wind waves in seas are inherently random. Despite the progress of engineering, unpredicted extreme waves in the ocean remain a serious danger for ships and offshore structures. In recent years there was a number of accidents with large ships resulting in loss of life and pollution of large sea and coastal areas. The UK, as an island trading nation, increasingly depends on ever expanding shipping and offshore activities. The loss of life, disruption (even temporary) of supply lines or of offshore energy production have become totally (morally and economically) unacceptable. To address these challenges thorough understanding of random sea waves is needed, first of all, knowledge of the dependence of their probability distribution on wave interaction with atmosphere. In the situation of changing weather patterns the required knowledge of, say, a "100-year wave" for a particular place cannot be obtained from past experimental records, and a comprehensive theoretical model deduced from first principles is needed. Now a radical improvement compared to the present state of affairs has become possible. This is the aim of the proposed project.At present all wave forecasting and modelling, which is a part of routine meteorological forecasting, is based on the numerical integration of the kinetic (Hasselmann) equation. The equation derived from first principles takes into account wind input, dissipation and interaction between waves of different scales and directions and describes the slow evolution of wind wave energy spectra in time and space. There has been accumulated a good understanding of spectra evolution obtained from modelling and observations. The weakest link is in translating the acquired knowledge of energy spectra into predicting probability distributions of wave heights. The major shortcomings of the prevailing approach are: (i) it relies on the very restrictive assumption of narrow spectra, while most of the observed spectra are broad from the viewpoint of nonlinear interactions, (ii) it does not properly take into account wave nonlinear interactions, (iii) it assumes stationarity of the process. Very recently PI and RCoI found a way to evaluate numerically the higher moments of probability distribution (skewness and kurtosis) within the established framework of wave turbulence without these restrictions. Since the procedure is numerically expensive, we propose to parametrize all combinations of wave spectra and thus to obtain simple parametrizations of probability distributions. This will allow us to deduce from first principles a parametrization of probability distributions easy-to-use in operational forecasting for all the variety of sea states.The sea states predicted by the existing models or obtained as a result of direct measurements describe somehow averaged ("normal") sea states. There also exist short-lived transient states caused by sharp changes of wind, which are filtered out by such averaging. We argue that these ephemeral sea states might be responsible for disproportionate share of anomalously high waves. Such transient sea states have never been studied in this context. The time resolution of wind forecasts was far too low, there were no conceptual and numerical tools. Crucially for this project the situation has improved radically: the time resolution of wind forecasts is improving dramatically, while the PI and RCoI derived a generalized kinetic equation able to describe the fast evolution of the spectra, developed and tested the numerical code able to tackle this equation. Combining this with the authors' specially designed direct numerical simulation algorithm, we propose a clear path for examining probability distributions of wave heights of transient events linked to rapid changes of atmospheric forcing.On this basis this project aims to revolutionise modelling of random wind waves and freak wave forecasting.