Reply to "Comment on 'Bias Correction, Quantile Mapping, and Downscaling: Revisiting the Inflation Issue'"

In his comment, G. Burger criticizes the conclusion that inflation of trends by quantile mapping is an adverse effect. He assumes that the argument would be based on the belief that long-term trends and along with them future climate signals are to be large scale. His line of argument reverts to the so-called inflated regression. Here it is shown, by referring to previous critiques of inflation and standard literature in statistical modeling as well as weather forecasting, that inflation is built upon a wrong understanding of explained versus unexplained variability and prediction versus simulation. It is argued that a sound regression-based downscaling can in principle introduce systematic local variability in long-term trends, but inflation systematically deteriorates the representation of trends. Furthermore, it is demonstrated that inflation by construction deteriorates weather forecasts and is not able to correctly simulate small-scale spatiotemporal structure.