Deep Learning and Bayesian Time Series Analysis for Probabilistic Weather Forecasting

背景：天气预报是最复杂和方法要求最高的挑战之一，特别是在基于深度学习算法的数值应用中。这通常涉及每天处理来自多个预测模型和集合的数TB流数据。由于涉及各种数据处理链，因此为不同的天气变量（如温度、降水、云、能见度或风）生成定期更新的概率预报非常重要。虽然传统的预测主要依赖于大气物理学，但由于有希望的实验结果，新的数据驱动方法越来越受欢迎。由于气象界最近才开始认识到数学数据分析的优势，因此需要更多的科学工作来进一步改进复杂分析的方法框架。从方法论的角度来看，拟议的项目为贝叶斯分析，时间序列和机器学习的新技术的发展提供了很大的空间。该项目与EPSRC的数学科学主题密切相关，主要优先领域是统计与应用概率、运筹学、人工智能技术和数值分析。目标：该项目将开发先进的统计方法，以有效地处理数值天气预报中的大数据集，从而使用观测或模拟数据校准概率预报。这个博士项目的研究兴趣有两个方面：i）首先，探索序贯蒙特卡罗（SMC）和贝叶斯多变量时间序列建模，通过偏差校正可以减少随时间变化的模型误差增长的影响。潜在地，这可以通过自适应卡尔曼和/或粒子滤波器来实现，该滤波器在每个时间段的联合概率分布的递归集合中更新估计的天气参数。ii）其次，通过调查用于顺序数据流的长短期记忆递归神经网络（LSTM）的不同架构来进行单站点和多站点天气预测。包括堆叠版本的单变量和多变量天气预报，同时也估计相关的时间和时空噪声相关structues.Methodology：贝叶斯时间序列分析：从贝叶斯概率建模的观点，技术已经导致了新版本的自适应卡尔曼滤波器的出现近似的测量分布（例如每小时的温度）和估计的非线性系统状态。另一个密切相关的贝叶斯估计方法是粒子滤波（PF）。深度学习在天气预报中的应用：深度学习程序在天气界受到越来越多的关注，许多研究人员已经使用人工神经网络（ANN）来处理大数据集，并通过考虑先前记录的数据模式来预测未来的输出。最值得注意的是，长短期记忆（LSTM）神经网络似乎很有前途，因为它们能够处理整个数据序列，同时记住以前看到的数据的一部分。此外，Ernst已经积累了在不同环境下处理天气数据的丰富经验，这帮助我理解了这种非线性（混沌）数据的特点，包括它们的数学形式化和统计建模。最重要的是，Ernst在R，SAS，Python方面的计算技能得到了通过R markdown，Latex和Applyter notebook报告研究结果的专业知识的补充。总的来说，他的背景不仅与他通过与Saptarshi Das博士和气象局合作者讨论共同开发的这个雄心勃勃的研究项目密切相关。

Background:Weather forecasting is one of the most complex and methodologically demanding challenges, particularly, in numerical applications of deep learning-based algorithms. This typically involves handling several terabytes of streaming data per day from multiple forecast models and ensembles. With various data processing chains involved, it is of great importance to generate regularly updated probabilistic forecasts for different weather variables such as: temperature, precipitation, clouds, visibility or wind. While traditional forecasts have primarily relied on atmospheric physics, new data-driven approaches enjoy increased popularity due to promising experimental results. As the weather community has only recently started to recognise the advantages of mathematically grounded data analytics, more scientific work is required to further improve the methodological framework for sophisticated analysis. From a methodological standpoint, the proposed project offers great scope for the development of novel techniques in Bayesian Analysis, Time Series and Machine Learning. In relation to the Mathematical Sciences theme of EPSRC, this project is in close agreement with key priority areas, most distinctively Statistics and Applied Probability, Operational Research, Artificial Intelligence Technologies and Numerical Analysis.Aims:This project will develop advanced statistical methods to efficiently process big datasets in numerical weather prediction to calibrate the probabilistic forecasts using observational or simulated data. The research interests within this PhD project are two-fold.i) Firstly, to explore Sequential Monte Carlo (SMC) and Bayesian multivariate time series modelling that can reduce the impact of time-dependent model error growth through bias correction. Potentially this could be achieved by means of adaptive Kalman and/or Particle Filters, that update the estimated weather parameters in a recursive set of joint probability distributions for each timeframe.ii) Secondly, to carry out single and multi-site weather predictions by investigating different architectures of Long Short-Term Memory Recurrent Neural Networks (LSTMs) for sequential data flows. Including stacked versions for univariate and multivariate weather forecast while also estimating the associated temporal and Spatio-temporal noise correlation structures.Methodology:Bayesian Time Series Analysis:From a Bayesian probabilistic modelling viewpoint, techniques have resulted in the advent of new versions of adaptive Kalman Filters for approximating the distribution of measurements (for example hourly temperature) and estimating the nonlinear system state. Another closely related Bayesian estimation method is Particle Filtering (PF). Here Monte Carlo (MC) simulation based on sequential importance sampling (SIS) is applied.Deep Learning for Weather Forecasting:Deep-Learning procedures are receiving increasing attention within the weather community, Many researchers have used Artificial Neural Network (ANN) to process a big data set and to predict future outputs by taking into account the previously recorded data pattern. Most notably Long Short-Term Memory (LSTMs) Neural Networks appear promising due to their ability in being able to process entire sequences of data while memorizing some proportion of previously seen data.Additionally, Ernst have already gathered extensive experience in working with weather data in different settings which helped me to understand the peculiarities of such nonlinear (chaotic) data including their mathematical formalization and statistical modelling. On top of that, Ernst's computing skills in R, SAS, Python are supplemented by expertise in reporting research findings via R markdown, Latex and Jupyter notebook. Overall, his background not only strongly aligns to deliver this ambitious research project which he has co-developed by discussing with Dr Saptarshi Das and the Met Office collaborators.