Probabilistic modelling and simulation of big spatio-temporal climate data for quantifying future changes of compound events

The analysis of climate change impacts involves the utilisation of climate model output. Quite often, quantities of interest are compound events rather than “raw variables” such as temperature. Questions such as "what is the probability that temperature will exceed a high threshold for five consecutive days and how will this change in the future?" are quite common. Statistical (probabilistic) modelling of climate model output can be used to answer such questions by stochastically simulating the raw variables and then quantifying the compound events as a “by-product”. This is particularly useful since any compound event can be investigated using the same approach – since the raw variables are the ones being modelled.

Such approaches however do not always scale well with big data sets and are often too complicated to even interpret appropriately. Here we present a way of analysing such data, using the (well-established) idea of a ‘moving window’ in conjunction with penalised smoothing splines and Generalised Additive Models (GAMs). The probabilistic nature of the resulting predictions provides a way of extrapolating beyond the range of the original data to robustly quantify the likelihood of rare events and their future changes. The approach is implemented in the Bayesian framework which results in full quantification of the associated uncertainty in using this method, e.g. increased uncertainty for extreme events way outside the range of the original data.

The method is both scalable and paralleliseable and we present it in quantifying changes in regional climate model output. Due to the simplicity of the components that make up the approach, it can be argued that it is highly interpretable as well as robust to the choice of variables – we demonstrate this using temperature as well as humidity and precipitation, variables which are known to have very different statistical behaviour. We also demonstrate how the approach can be extended to capture the behaviour of more that one variable and use it to quantify the changes in compound hazard events such as the frequency of “warm-dry” days.