Technical Note: The Normal Quantile Transformation and its application in a flood forecasting system

Abstract

The Normal Quantile Transform (NQT) has been used in many hydrological and meteorological applications in order to make the cumulated density function (CDF) of the observed, simulated and forecast river discharge, water level or precipitation data Gaussian. It is also the heart of the meta-Gaussian model for assessing the total predictive uncertainty of the Hydrological Uncertainty Processor (HUP) developed by Krzysztofowicz. In the field of geo-statistics this transformation is better known as Normal-Score transform. In this paper some possible problems caused by small sample sizes for the applicability in flood forecasting systems will be discussed and illustrated by examples. For the practical implementation commands and examples from the freely available and widely used statistical computing language R (R Development Core Team (2011)) will be given (marked in blue) and possible solutions are suggested by combining extreme value analysis and non-parametric regression methods.