Search Results
CPC’s Probability of Exceedance product ( Barnston et al. 2000 ). The small amount of hindcast data available from most GCM predictions eliminates some ensemble calibration methods from serious consideration. Some calibration methods such as binning procedures ( Anderson 1996 ; Hamill and Colucci 1997 , 1998 ; Eckel and Walters 1998 ) or logistic regression ( Hamill et al. 2004 ) divide the range of the forecast element into a series of categories (bins). The limited data available for seasonal
CPC’s Probability of Exceedance product ( Barnston et al. 2000 ). The small amount of hindcast data available from most GCM predictions eliminates some ensemble calibration methods from serious consideration. Some calibration methods such as binning procedures ( Anderson 1996 ; Hamill and Colucci 1997 , 1998 ; Eckel and Walters 1998 ) or logistic regression ( Hamill et al. 2004 ) divide the range of the forecast element into a series of categories (bins). The limited data available for seasonal
predictor analysis (PPA) are pattern methods specifically tailored for use in linear regression models and, unlike CCA and MCA, are asymmetric in their treatment of the two datasets, identifying one dataset as the predictor and the other as the predictand. RDA selects predictor components that maximize explained variance ( von Storch and Zwiers 1999 ; Wang and Zwiers 2001 ). PPA selects predictor components that maximize the sum of squared correlations ( Thacker 1999 ). Another commonly used pattern
predictor analysis (PPA) are pattern methods specifically tailored for use in linear regression models and, unlike CCA and MCA, are asymmetric in their treatment of the two datasets, identifying one dataset as the predictor and the other as the predictand. RDA selects predictor components that maximize explained variance ( von Storch and Zwiers 1999 ; Wang and Zwiers 2001 ). PPA selects predictor components that maximize the sum of squared correlations ( Thacker 1999 ). Another commonly used pattern
well as its uncertainty, is given by linear regression (LR). The idea of conditional averaging is also found in the constructed analog (CA) method ( Van den Dool 1994 , 2006 ), a statistical forecast method that has been applied in a variety of geophysical problems (e.g., Van den Dool et al. 2003 ; Maurer and Hidalgo 2008 ; Hawkins et al. 2011 ). A prediction y CA is made for a particular value of the predictor x = x 0 by searching through historical data for values of y corresponding
well as its uncertainty, is given by linear regression (LR). The idea of conditional averaging is also found in the constructed analog (CA) method ( Van den Dool 1994 , 2006 ), a statistical forecast method that has been applied in a variety of geophysical problems (e.g., Van den Dool et al. 2003 ; Maurer and Hidalgo 2008 ; Hawkins et al. 2011 ). A prediction y CA is made for a particular value of the predictor x = x 0 by searching through historical data for values of y corresponding
dynamical and statistical approaches. This study presents a novel approach for statistical downscaling or recalibration that derives extremal quantile forecasts of precipitation. In the case of normally distributed response variables (e.g., temperature), only the expectation value and a measure of variance are needed to provide the complete probabilistic behavior of a response variable. The expectation value is estimated by standard linear regression using least squares methods. The variance is derived
dynamical and statistical approaches. This study presents a novel approach for statistical downscaling or recalibration that derives extremal quantile forecasts of precipitation. In the case of normally distributed response variables (e.g., temperature), only the expectation value and a measure of variance are needed to provide the complete probabilistic behavior of a response variable. The expectation value is estimated by standard linear regression using least squares methods. The variance is derived
based on variance inflation, field adjustment, and multiple regression. Other methods have been reviewed by Clemen (1989) . The mere existence of distinct methods for the same problem shows that the technology for combining forecasts is imperfect. These imperfections become clearly evident when the number of model forecasts is not a small fraction of the sample size. Thus, for instance, Robertson et al. (2004) report that as more models are added to the multimodel combination in the Rajagopalan
based on variance inflation, field adjustment, and multiple regression. Other methods have been reviewed by Clemen (1989) . The mere existence of distinct methods for the same problem shows that the technology for combining forecasts is imperfect. These imperfections become clearly evident when the number of model forecasts is not a small fraction of the sample size. Thus, for instance, Robertson et al. (2004) report that as more models are added to the multimodel combination in the Rajagopalan
1. Introduction Regression patterns are useful diagnostics of multivariate variability associated with a prespecified time series. For instance, patterns of trend coefficients often are used to quantify the spatial structure of climate change (see Trenberth et al. 2007 ), and the relation between El Niño and seasonal climate has been investigated using regression patterns at least since Walker (1923) . However, a major limitation of regression patterns is the absence of a rigorous
1. Introduction Regression patterns are useful diagnostics of multivariate variability associated with a prespecified time series. For instance, patterns of trend coefficients often are used to quantify the spatial structure of climate change (see Trenberth et al. 2007 ), and the relation between El Niño and seasonal climate has been investigated using regression patterns at least since Walker (1923) . However, a major limitation of regression patterns is the absence of a rigorous
mitigate overfitting, including truncated singular value decomposition (SVD) analysis, ridge regression, and constrained least squares ( Yun et al. 2003 ; van den Dool and Rukhovets 1994 ; DelSole 2007 ). These procedures often are applied on a point-by-point basis. Recently, it has been recognized that seemingly different approaches to multimodel forecasting are actually special cases of a single Bayesian methodology, each distinguished by different prior assumptions on the model weights ( DelSole
mitigate overfitting, including truncated singular value decomposition (SVD) analysis, ridge regression, and constrained least squares ( Yun et al. 2003 ; van den Dool and Rukhovets 1994 ; DelSole 2007 ). These procedures often are applied on a point-by-point basis. Recently, it has been recognized that seemingly different approaches to multimodel forecasting are actually special cases of a single Bayesian methodology, each distinguished by different prior assumptions on the model weights ( DelSole
1. Introduction Linear regression has long played an important role in weather and climate forecasting, both in empirical prediction models and statistical postprocessing of physics-based prediction model output (e.g., Glahn and Lowry 1972 ; Penland and Magorian 1993 ). Here we focus on the use of regression to correct and calibrate climate forecasts, although our findings are generally applicable to all regression-based forecasts. A regression between past model output and observations
1. Introduction Linear regression has long played an important role in weather and climate forecasting, both in empirical prediction models and statistical postprocessing of physics-based prediction model output (e.g., Glahn and Lowry 1972 ; Penland and Magorian 1993 ). Here we focus on the use of regression to correct and calibrate climate forecasts, although our findings are generally applicable to all regression-based forecasts. A regression between past model output and observations
Wallace 1981 ; Hoskins and Karoly 1981 ; Simmons et al. 1983 ). The spatial structure of the midlatitude response to tropical SST perturbations is a robust property in atmospheric general circulation models ( Geisler et al. 1985 ; Yang and DelSole 2012 ). Seasonal weather could be predicted to some extent if its relation with SST perturbations could be identified. A common, but problematic, approach to identifying such relations is to compute a regression map between the quantity being predicted
Wallace 1981 ; Hoskins and Karoly 1981 ; Simmons et al. 1983 ). The spatial structure of the midlatitude response to tropical SST perturbations is a robust property in atmospheric general circulation models ( Geisler et al. 1985 ; Yang and DelSole 2012 ). Seasonal weather could be predicted to some extent if its relation with SST perturbations could be identified. A common, but problematic, approach to identifying such relations is to compute a regression map between the quantity being predicted
of the predictive distribution. In analog forecasting, cases similar to the present forecast situation are searched for in long historical archives and applied as forecast ( van den Dool 1989 ; Hamill and Whitaker 2006 ). Methods based on regression trees have recently also received increasing attention due to their flexibility and ease of use; for example, Taillardat et al. (2016) use quantile regression forest, a slight modification of random forest. A very different strategy is to make
of the predictive distribution. In analog forecasting, cases similar to the present forecast situation are searched for in long historical archives and applied as forecast ( van den Dool 1989 ; Hamill and Whitaker 2006 ). Methods based on regression trees have recently also received increasing attention due to their flexibility and ease of use; for example, Taillardat et al. (2016) use quantile regression forest, a slight modification of random forest. A very different strategy is to make
