Robust handling of extremes in quantile mapping – "Murder your darlings"

Abstract. Quantile mapping is a method often used for 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, also an empirical quantile mapping needs to make some estimation or fit a parameterized function for data beyond the calibration data range. The MIdAS bias adjustment platform is here employed to explore different methods for handling the extreme tail, which are evaluated using an indicator for 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 for the tails of the distribution is demonstrated, and it is found that the behaviour is significantly different within and without the calibration period, causing severe issues with the temporal consistency of the timeseries. 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 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. Currently MIdAS uses separate calibrations for each day of the year, as opposed to e.g. for each calendar month, further aggravates this issue. Further, finding a robust parametrisation for the tail is not straightforward. We identify a two-step solution which works well for this problem: (i) "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, and (ii) applying an outlier insensitive method for linear regression works well for finding an extrapolation parametrisation for the tail.