Juliette Legrand and Thomas Opitz’s contribution to the Discussion of ‘The First Discussion Meeting on Statistical aspects of climate change’

We congratulate the authors for their carefully constructed spatial model of risk occurrences caused by pluvial flooding. It astutely incorporates meteorological and topographic risk drivers and accounts for other, unknown factors of spatial variability, making it reliable for short-term prediction and long-term projection under climate change. We emphasise that many difficulties identified by the authors arise more generally for various other environmental risks.

Our research group working on wildfires at INRAE faces similar challenges regarding the modelling of their occurrences and sizes (e.g. Koh et al., 2023; Pimont et al., 2021). The problem of a covariate shift in prediction with new data is typical for meteorological covariates simulated by climate models in change scenarios. Prediction often suffers from noisy behaviour of semiparametric predictor components with basis function representation (e.g. splines, as in the discussed paper). Different choices of knots and shapes for basis functions may produce quite different predictions conditional to the tails of the covariate distribution.

Regarding wildfires, useful meteorological covariates are the Fire Weather Index (FWI) and its subindices, which aggregate common weather variables (precipitation, humidity, temperature, wind speed) into biophysical variables providing a rating of fire danger components (e.g. ignition, spread). In the Bayesian setting of the Firelihood model of Pimont et al. (2021), the influence of FWI on counts and burnt areas of wildfires is robustly modelled through a step function (i.e. a zero-degree spline, with around 50 knots) and Gaussian first order random walk prior. Similar to the discussed paper, the spline function is frozen for new (i.e. projected) FWI values beyond the range of historical observations and is extrapolated as a constant. Future projections of FWI often highly exceed its historical maxima (e.g. Varela et al., 2019).

We currently explore avenues towards improved modelling with covariate shifts in the tails of the covariate distribution. A promising idea is to infer an appropriate parametric predictor in the tail region of the covariate, requiring a hybridisation of a semiparametric bulk model with a parametric tail model. Moreover, insights can be gained from the conditional extremes framework (Heffernan & Tawn, 2004) by conditioning the response variable on threshold exceedances of the covariate. While this approach applies to continuous variables, it could be extended to count-valued responses using extreme-value theory for discrete variables (Hitz et al., 2017).

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