Deep Learning and Bayesian Time Series Analysis for Probabilistic Weather Forecasting

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.