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

海上的风浪天生就是随机的。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对船舶和近海结构物构成严重威胁。近年来，发生了多起大型船舶事故，造成人员伤亡和大片海域和沿海地区的污染。英国作为一个岛屿贸易国，越来越依赖不断扩大的航运和离岸活动。生命损失、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，需要彻底了解随机海浪，首先要了解其概率分布与海浪与大气相互作用的关系。在天气模式变化的情况下，不能从过去的实验记录中获得所需的关于某一特定地点的“百年一遇”的知识，需要从第一原理推导出一个全面的理论模型。现在，与目前的情况相比，根本的改善已经成为可能。目前，作为常规气象预报的一部分，所有的海浪预报和模拟都是基于动力(Hasselmann)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、耗散以及不同尺度和方向的海浪之间的相互作用，描述了风浪能谱在时间和空间上的缓慢演化。通过模拟和观测，人们已经对光谱演化有了很好的了解。最薄弱的环节是将所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：(I)它依赖于非常有限的窄谱假设，而从非线性相互作用的观点来看，大多数观测到的谱是宽的；(Ii)它没有适当地考虑波的非线性相互作用；(Iii)它假定过程是平稳的。最近，Pi和RCoI发现了一种方法，可以在没有这些限制的已建立的波浪湍流框架内对概率分布的高阶矩(偏度和峰度)进行数值评估。由于这一过程在数值上是昂贵的，我们建议将波谱的所有组合参数化，从而获得概率分布的简单参数化。这将允许我们从第一原理推导出一种易于用于各种海态的业务预报的概率分布的参数化。由现有模型预测的海态或通过直接测量获得的海态描述了某种程度上的平均(正常)海态。也存在由风的急剧变化引起的短暂的暂态，这些暂态被这样的平均过滤掉。我们认为，这些短暂的海况可能是异常高海浪的不成比例的原因。在这种背景下，从来没有人研究过这种瞬变的海况。风预报的时间分辨率太低，没有概念和数值工具。对于这个项目来说，至关重要的是，情况已经得到了根本的改善：风预报的时间分辨率正在显著提高，而PI和RCoI导出了能够描述谱快速演变的广义动力学方程，开发并测试了能够处理该方程的数值代码。结合作者专门设计的直接数值模拟算法，我们提出了一条检验与大气作用力快速变化相关的瞬变事件波高概率分布的明确路径。在此基础上，本项目旨在改革随机风浪模拟和异常海浪预报。

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.