Editing IPCC:AR6/WGI/Chapter-10 (section)

==== 10.3.1.3 Statistical Approaches to Generate Regional Climate Projections ====

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An alternative or addition to dynamical downscaling is the use of statistical approaches to generate regional projections. In AR5 these methods were collectively referred to as statistical downscaling, but their performance assessment has received little attention. A major conclusion was that a wide range of different methods exist and a general assessment of their performance is difficult ( [[#Flato--2014|Flato et al., 2014]] ). Since AR5, several initiatives have been launched to improve the understanding of statistical approaches such as VALUE (Validating and Integrating Downscaling Methods for Climate Change Research, now merged into the EURO-CORDEX activities; [[#Maraun--2015|Maraun et al., 2015]] ), STaRMIP (Statistical Regionalization Models Intercomparisons and Hydrological Impacts Project; [[#Vaittinada%20Ayar--2016|Vaittinada Ayar et al., 2016]] ) and BADJAM (Bias ADJustment of climate scenarios for Agricultural Model applications; [[#Galmarini--2019|Galmarini et al., 2019]] ). The performance of different implementations of these approaches will be assessed in [[#10.3.3.7|Section 10.3.3.7]] .

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===== 10.3.1.3.1 Perfect prognosis =====

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Perfect-prognosis models are statistical models calibrated between observation-based large-scale predictors (e.g., from reanalysis) and observed local-scale predictands ( [[#Maraun--2018b|Maraun and Widmann, 2018b]] ). Regional climate projections are then generated by replacing the quasi-observed predictors by those from climate model (typically global model) projections. Predictor patterns that are common to observations and climate model data can be defined by common empirical orthogonal functions ( [[#Benestad--2011|Benestad, 2011]] ). The perfect prognosis approach can either be used to generate daily (or even sub-daily) time series, or local weather statistics (e.g., [[#Benestad--2018|Benestad et al., 2018]] ).

Regression-like models ( [[#Maraun--2018b|Maraun and Widmann, 2018b]] ) rely on a transfer function linking an observed local statistic (such as the temperature at a given day) to some set of large-scale predictors. Recent developments include stochastic regression models to explicitly simulate local variability ( [[#San-Martín--2017|San-Martín et al., 2017]] ; those explicitly modelling temporal dependence are assessed in [[#10.3.1.3.4|Section 10.3.1.3.4]] ). The use of machine learning techniques has been reinvigorated, including genetic programming to construct a data-driven model structure ( [[#Zerenner--2016|Zerenner et al., 2016]] ) and deep and convolutional neural networks ( [[#Reichstein--2019|Reichstein et al., 2019]] ; [[#Baño-Medina--2020|Baño-Medina et al., 2020]] ).

Analogue methods ( [[#Martin--1996|Martin et al., 1996]] ; [[#Maraun--2018b|Maraun and Widmann, 2018b]] ) compare a simulated large-scale atmospheric field with an archive of observations and select, using some distance metric, the closest observed field in the archive. The downscaled atmospheric field is then chosen as the local atmospheric field observed on the instant the analogue occurred. New analogue methods have been developed to simulate unobserved values including a rescaling of the analogue ( [[#Pierce--2014|Pierce et al., 2014]] ) or by combining analogues and regression models ( [[#Chardon--2018|Chardon et al., 2018]] ).

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===== 10.3.1.3.2 Bias adjustment =====

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Bias adjustment is a statistical post-processing technique used to pragmatically reduce the mismatch between the statistics of climate model output and observations. The approach estimates the bias or relative error between a chosen simulated statistical property (such as the long-term mean or specific quantiles of the climatological distribution) and that observed over a calibration period; the simulated statistic is then adjusted taking into account the simulated deviation. Bias adjustment methods are regularly applied on a spatial scale similar to that of the simulation being adjusted, but they are often used as a simple statistical downscaling method by calibrating them between coarse resolution (e.g., global) model output and finer observations ( [[#Maraun--2018b|Maraun and Widmann, 2018b]] ).

Typical implementations of bias adjustment are (i) additive adjustments, where the model data is adjusted by adding a constant, (ii) rescaling, where the model data is adjusted by a factor, and (iii) more flexible quantile mapping approaches that adjust different ranges of a distribution individually. Hempel et al. (2013), [[#Pierce--2015|Pierce et al. (2015)]] , [[#Switanek--2017|Switanek et al. (2017)]] , and [[#Lange--2019|Lange (2019)]] developed variants of quantile mapping that preserve trends in the mean or even further distributional statistics. Multivariate bias adjustment extends univariate methods, which adjust statistics of individual variables separately, to joint adjustment of multiple variables simultaneously. Implementations remove biases in (i) specific measures of multivariate dependence, like correlation structure, via linear transformations ( [[#Bárdossy--2012|Bárdossy and Pegram, 2012]] ; [[#Cannon--2016|Cannon, 2016]] ), or, more flexibly, (ii) the full multivariate distribution via non-linear transformations ( [[#Vrac--2015|Vrac and Friederichs, 2015]] ; [[#Dekens--2017|Dekens et al., 2017]] ; [[#Cannon--2018|Cannon, 2018]] ; [[#Vrac--2018|Vrac, 2018]] ; [[#Robin--2019|Robin et al., 2019]] ). Other research strands focus on the explicit separation of bias adjustment and downscaling ( [[#10.3.1.3.5|Section 10.3.1.3.5]] ), or the integration of process understanding ( [[#Maraun--2017|Maraun et al., 2017]] ), such as by conditioning the adjustment on the occurrence of relevant phenomena ( [[#Addor--2016|Addor et al., 2016]] ; [[#Verfaillie--2017|Verfaillie et al., 2017]] ; [[#Manzanas--2019|Manzanas and Gutiérrez, 2019]] ). Some authors suggest to mitigate the influence of large-scale temperature or circulation biases by performing a bias adjustment of the driving fields prior to dynamical downscaling ( [[#Colette--2012|Colette et al., 2012]] ; [[#Hernández-Díaz--2013|Hernández-Díaz et al., 2013]] , 2019). Issues that may arise when using bias adjustment are discussed in Cross-Chapter Box 10.2.

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===== 10.3.1.3.3 Delta-change approaches =====

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In the delta change approach, selected observations are modified according to corresponding changes derived from dynamical model simulations. Traditionally, only long-term means have been adjusted, but recently approaches to modify temporal dependence ( [[#Webber--2018|Webber et al., 2018]] ) have been developed, as well as quantile mapping approaches that individually adjust quantiles of the observed distribution ( [[#Willems--2011|Willems and Vrac, 2011]] ). By construction, the approach cannot modify the spatial and temporal dependence structure of the input observations ( [[#Maraun--2016|Maraun, 2016]] ).

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===== 10.3.1.3.4 Weather generators =====

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Weather generators are statistical models that simulate weather time series of arbitrary length. They are calibrated to represent observed weather statistics, in particular daily or even sub-daily variability. One variant of these models are advanced stochastic perfect-prognosis methods, conditioned on large-scale atmospheric predictors on a daily basis, for instance multisite generalized linear models ( [[#Chandler--2020|Chandler, 2020]] ). Another widely used variant is change-factor weather generators: the weather generator parameters are calibrated against present and future climate model simulations, and the climate change signals are then applied to the parameters calibrated to observations. Recent research has mainly focussed on multi-site Richardson type (Markov-chain) weather generators ( [[#Keller--2015|Keller et al., 2015]] ; [[#Dubrovsky--2019|Dubrovsky et al., 2019]] ), some explicitly modelling extremes and their spatial dependence ( [[#Evin--2018|Evin et al., 2018]] ).

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===== 10.3.1.3.5 Hybrid approaches and emulators =====

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A wide variety of approaches has been proposed to combine the advantages of different statistical approaches. For instance, to overcome the scale mismatch between climate model output and observations, bias adjustment has been combined with stochastic downscaling ( [[#Volosciuk--2017|Volosciuk et al., 2017]] ; [[#Lange--2019|Lange, 2019]] ) or rescaled analogues ( [[#Pierce--2014|Pierce et al., 2014]] ). Other approaches known as emulators have been developed to emulate an RCM using a statistical model and also applied to a range of driving global models ( [[#Déqué--2012|Déqué et al., 2012]] ; [[#Haas--2012|Haas and Pinto, 2012]] ; [[#Walton--2015|Walton et al., 2015]] , 2017; [[#Beusch--2020|Beusch et al., 2020]] ; [[#Erlandsen--2020|Erlandsen et al., 2020]] ).

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