Effects of variance adjustment techniques and time-invariant transfer functions on heat wave duration indices and other metrics derived from downscaled time-series. Study case: Montreal, Canada

Statistical downscaling techniques are often used to generate finer-scale projections of climate variables affected by local-scale processes not resolved by coarse resolution numerical models like global climate models (GCMs). Statistical downscaling models rely on several assumptions in order to produce finer-/local-scale projections of the variable of interest; one of these assumptions is the time-invariance of the relationships between predictors (e.g. coarse resolution GCM output) and the local-scale predictands (e.g. gridded observation-based time-series or weather station observations). However, in the absence of future observations, statistical downscaling studies use historical data to evaluate their models and assume that these historical simulation skills will be retained in the future. In addition, regression-based downscaling models fail to reproduce the observed variance, and hence their projections need to be adjusted accordingly. Two approaches are usually employed to perform this adjustment: randomization and variance inflation. Here, we study the effect of the stationarity assumption when downscaling daily maximum temperatures and using the downscaled information to estimate historical and future metrics like return periods and heat waves durations over Montreal, Canada; and the effect of the two variance adjustment techniques on the historical and future time-series. To do so, we used regional climate model (RCM) output from the Canadian RCM 4.2, as proxies of historical and future local climates, and daily maximum temperatures obtained from the Canadian GCM 3.1. The results show that the root-mean-squared errors between the pseudo-observations and the statistically downscaled time-series (historical and future) varied over time, with higher errors in the future period; and the effects of randomization and variance inflation on the tails of the statistically downscaled time-series.