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Empirical-Statistical Downscaling: Nonlinear Statistical Downscaling

Empirical-statistical downscaling (ESD) models use statistical relationships to infer local climate information from large-scale climate information produced by global climate models (GCMs), as an alternative to the dynamical downscaling provided by regional climate models (RCMs). Among various statistical downscaling approaches, the nonlinear methods are mainly used to construct downscaling models for local variables that strongly deviate from linearity and normality, such as daily precipitation. These approaches are also appropriate to handle downscaling of extreme rainfall.
 There are nonlinear downscaling techniques of various complexities. The simplest one is represented by the analog method that originated in the late 1960s from the need to obtain local details of short-term weather forecasting for various variables (air temperature, precipitation, wind, etc.). Its first application as a statistical downscaling approach in climate science was carried out in the late 1990s. More sophisticated statistical downscaling models have been developed based on a wide range of nonlinear functions. Among them, the artificial neural network (ANN) was the first nonlinear regression–type method used as a statistical downscaling technique in climate science in the late 1990s. The ANN was inspired by the human brain, and it was used early in artificial intelligence and robotics. The impressive development of machine learning algorithms that can automatically extract information from a vast amount of data, usually through nonlinear multivariate models, contributed to improvements of ANN downscaling models and the development of other new, machine learning-based downscaling models to overcome some ANN drawbacks, such as support vector machine and random forest techniques. The mixed models combining various machine learning downscaling approaches maximize the downscaling skill in local climate change applications, especially for extreme rainfall indices.
 Other nonlinear statistical downscaling approaches refer to conditional weather generators, combining a standard weather generator (WG) with a separate statistical downscaling model by conditioning the WG parameters on large-scale predictors via a nonlinear approach. The most popular ways to condition the WG parameters are the weather-type approach and generalized linear models.
 This article discusses various aspects of nonlinear statistical downscaling approaches, their strengths and weaknesses, as well as comparison with linear statistical downscaling models. A proper validation of the nonlinear statistical downscaling models is an important issue, allowing selection of an appropriate model to obtain credible information on local climate change. Selection of large-scale predictors, the model’s ability to reproduce historical trends, extreme events, and the uncertainty related to future downscaled changes are important issues to be addressed.
 A better estimation of the uncertainty related to downscaled climate change projections can be achieved by using ensembles of more GCMs as drivers, including their ability to simulate the input in downscaling models. Comparison between more future statistical downscaled climate change signals and those derived from dynamical downscaling driven by the same global model, including a complex validation of the RCMs, gives a measure of the reliability of downscaled regional climate changes.