Quantile Regression Neural Networks Research Articles

Downscaling Extremes—An Intercomparison of Multiple Statistical Methods for Present Climate

Abstract Five statistical downscaling methods [automated regression-based statistical downscaling (ASD), bias correction spatial disaggregation (BCSD), quantile regression neural networks (QRNN), TreeGen (TG), and expanded downscaling (XDS)] are compared with respect to representing climatic extremes. The tests are conducted at six stations from the coastal, mountainous, and taiga region of British Columbia, Canada, whose climatic extremes are measured using the 27 Climate Indices of Extremes (ClimDEX; http://www.climdex.org/climdex/index.action) indices. All methods are calibrated from data prior to 1991, and tested against the two decades from 1991 to 2010. A three-step testing procedure is used to establish a given method as reliable for any given index. The first step analyzes the sensitivity of a method to actual index anomalies by correlating observed and NCEP-downscaled annual index values; then, whether the distribution of an index corresponds to observations is tested. Finally, this latter test is applied to a downscaled climate simulation. This gives a total of 486 single and 162 combined tests. The temperature-related indices pass about twice as many tests as the precipitation indices, and temporally more complex indices that involve consecutive days pass none of the combined tests. With respect to regions, there is some tendency of better performance at the coastal and mountaintop stations. With respect to methods, XDS performed best, on average, with 19% (48%) of passed combined (single) tests, followed by BCSD and QRNN with 10% (45%) and 10% (31%), respectively, ASD with 6% (23%), and TG with 4% (21%) of passed tests. Limitations of the testing approach and possible consequences for the downscaling of extremes in these regions are discussed.

Quantile regression neural networks: Implementation in R and application to precipitation downscaling

The qrnn package for R implements the quantile regression neural network, which is an artificial neural network extension of linear quantile regression. The model formulation follows from previous work on the estimation of censored regression quantiles. The result is a nonparametric, nonlinear model suitable for making probabilistic predictions of mixed discrete-continuous variables like precipitation amounts, wind speeds, or pollutant concentrations, as well as continuous variables. A differentiable approximation to the quantile regression error function is adopted so that gradient-based optimization algorithms can be used to estimate model parameters. Weight penalty and bootstrap aggregation methods are used to avoid overfitting. For convenience, functions for quantile-based probability density, cumulative distribution, and inverse cumulative distribution functions are also provided. Package functions are demonstrated on a simple precipitation downscaling task.