Robust handling of extremes in quantile mapping – “Murder your darlings”

Abstract

Quantile mapping is a method often used for the bias adjustment of climate model data toward a reference, i.e. to construct a transformation of the model's distribution to that of the reference. The main moments of the distributions are typically well transformed by quantile mapping, but statistical uncertainty increases towards the extreme tails, making robust transformations challenging. Because of the limited data at the extreme tails, an empirical quantile mapping also needs to make some estimation or fit a parameterised function for data beyond the calibration data range. Here, the MIdAS bias adjustment platform is employed to explore different methods for handling the extreme tail; these approaches are evaluated using an indicator of extreme precipitation – the maximum daily precipitation amount per year. Different methodologies are evaluated for a large ensemble of regional climate model projections over Scandinavia. The sensitivity of the empirical quantile mapping to the tails of the distribution is demonstrated, and it is found that the behaviour is significantly different within and outside of the calibration period, causing severe issues with the temporal consistency of the time series. The sensitivity is identified to be due to differences in the activated features of the bias adjustment within the calibration period (where the empirical transfer function is applied) and outside of that period (where the extrapolation method is likely applied). This means that the bias adjustment method is, in a sense, different between different time periods. Furthermore, finding a robust parameterisation for the tail is not straightforward. We identify a two-step solution that works well for this problem: We refer to the first step as “Murder your darlings”. By excluding data from the tail data in the calibration period, the extrapolation feature is activated for all time periods, even the calibration period. In the second step, applying an outlier-insensitive method for linear regression works well for finding an extrapolation parameterisation for the tail.