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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
, 7570 – 7585 , doi: 10.1175/JCLI-D-12-00729.1 . Draper , N. R. , and H. Smith , 1981 : Applied Regression Analysis . 2nd ed. John Wiley and Sons, 709 pp . Feldstein , S. B. , 2000 : The timescale, power spectra, and climate noise properties of teleconnection patterns . J. Climate , 13 , 4430 – 4440 , doi: 10.1175/1520-0442(2000)013<4430:TTPSAC>2.0.CO;2 . Graybill , F. A. , 1983 : Matrices with Applications in Statistics . Wadsworth International, 461 pp . Hansen , J. , R. Ruedy
, 7570 – 7585 , doi: 10.1175/JCLI-D-12-00729.1 . Draper , N. R. , and H. Smith , 1981 : Applied Regression Analysis . 2nd ed. John Wiley and Sons, 709 pp . Feldstein , S. B. , 2000 : The timescale, power spectra, and climate noise properties of teleconnection patterns . J. Climate , 13 , 4430 – 4440 , doi: 10.1175/1520-0442(2000)013<4430:TTPSAC>2.0.CO;2 . Graybill , F. A. , 1983 : Matrices with Applications in Statistics . Wadsworth International, 461 pp . Hansen , J. , R. Ruedy
of temperature at several pressure levels within the lower stratosphere. We present a multiple regression analysis of Southern Hemisphere polar temperatures, using the National Centers for Environmental Prediction (NCEP) reanalysis dataset, designed to show the influence of various factors on the seasonal evolution of the polar vortex. We apply the same definition of final warming date as used on the radiosonde temperatures to the NCEP polar data to indicate the extent to which these factors may
of temperature at several pressure levels within the lower stratosphere. We present a multiple regression analysis of Southern Hemisphere polar temperatures, using the National Centers for Environmental Prediction (NCEP) reanalysis dataset, designed to show the influence of various factors on the seasonal evolution of the polar vortex. We apply the same definition of final warming date as used on the radiosonde temperatures to the NCEP polar data to indicate the extent to which these factors may
–2000 is removed from the respective model runs prior to the regression analysis both for GCMs and RCMs. In a typical statistical downscaling setting, the relationship between large-scale predictors and local predictand is established based on the data for the past and current climates and it is then applied to GCM-simulated predictors for the future climate, assuming that the statistical relationship holds in the future. This implies in many applications that the regression relationship is assumed to
–2000 is removed from the respective model runs prior to the regression analysis both for GCMs and RCMs. In a typical statistical downscaling setting, the relationship between large-scale predictors and local predictand is established based on the data for the past and current climates and it is then applied to GCM-simulated predictors for the future climate, assuming that the statistical relationship holds in the future. This implies in many applications that the regression relationship is assumed to
equivalent to testing the hypothesis β ′ = 0 in the model where X and have been switched relative to (1) , and β ′ is an M -dimensional column vector of coefficients, called the projection pattern . Happily, the latter hypothesis test is standard in regression analysis. The test statistic depends on the multiple correlation coefficient R , which is defined as the maximum correlation between X and a linear combination of . The multiple correlation also is equivalent to the canonical
equivalent to testing the hypothesis β ′ = 0 in the model where X and have been switched relative to (1) , and β ′ is an M -dimensional column vector of coefficients, called the projection pattern . Happily, the latter hypothesis test is standard in regression analysis. The test statistic depends on the multiple correlation coefficient R , which is defined as the maximum correlation between X and a linear combination of . The multiple correlation also is equivalent to the canonical
, this study uses a constant finite upwelling time δ [from Eq. (2) ] as opposed to a variable one. Second, the CM2.1 twentieth-century run has climate forcings built in, while the 4000-yr control run keeps climate parameters constant at 1860 values. Third, van Oldenborgh et al. evaluated a single century, while we evaluate multiple centuries, in addition to multidecadal time scales. From our analysis, we can infer that a single-century regression may produce regression coefficients that have very
, this study uses a constant finite upwelling time δ [from Eq. (2) ] as opposed to a variable one. Second, the CM2.1 twentieth-century run has climate forcings built in, while the 4000-yr control run keeps climate parameters constant at 1860 values. Third, van Oldenborgh et al. evaluated a single century, while we evaluate multiple centuries, in addition to multidecadal time scales. From our analysis, we can infer that a single-century regression may produce regression coefficients that have very
-masking the combined land and ocean Cowtan and Way data. When carrying out regressions, we exclude grid cells that were marked as NA in any year during the analysis period, to avoid influence from changes in sea ice differing between SST datasets. We also regrid HadISST1 data to match the ECHAM6.3 grid for our amipPiForcing simulation experiments, using with it the HadISST1-based AMIPII sea ice boundary condition dataset. 3. Results a. ECHAM6.3 simulations We first present the ECHAM6.3 amipPiForcing
-masking the combined land and ocean Cowtan and Way data. When carrying out regressions, we exclude grid cells that were marked as NA in any year during the analysis period, to avoid influence from changes in sea ice differing between SST datasets. We also regrid HadISST1 data to match the ECHAM6.3 grid for our amipPiForcing simulation experiments, using with it the HadISST1-based AMIPII sea ice boundary condition dataset. 3. Results a. ECHAM6.3 simulations We first present the ECHAM6.3 amipPiForcing
accumulation reconstruction spanning the period of available core data, here year 1600 and onward. The fundamental goal is to reconstruct the spatial and temporal patterns of net snow accumulation, especially before 1958 when high-resolution regional climate model output remains unavailable. Uncertainty is quantified here using a statistical analysis of residuals from the regressions upon which the reconstruction is based. The time dependence of the net snow accumulation is reassessed for the ice sheet as
accumulation reconstruction spanning the period of available core data, here year 1600 and onward. The fundamental goal is to reconstruct the spatial and temporal patterns of net snow accumulation, especially before 1958 when high-resolution regional climate model output remains unavailable. Uncertainty is quantified here using a statistical analysis of residuals from the regressions upon which the reconstruction is based. The time dependence of the net snow accumulation is reassessed for the ice sheet as
introducing autoregressive error terms. Also, using a better selection procedure for relevant proxies for the nonparametric additive regression model would be of interest, but we note that inference in additive models is not well developed—see, for example, Fan and Jiang (2005) . Our analysis shows that relative to the present group of proxies, two are nonlinear relative to the NH mean temperature. The series are the tree-ring width records Indigirka and Yamal. One possible physical explanation for the
introducing autoregressive error terms. Also, using a better selection procedure for relevant proxies for the nonparametric additive regression model would be of interest, but we note that inference in additive models is not well developed—see, for example, Fan and Jiang (2005) . Our analysis shows that relative to the present group of proxies, two are nonlinear relative to the NH mean temperature. The series are the tree-ring width records Indigirka and Yamal. One possible physical explanation for the
convection (e.g., Lee 2014 ; Baggett and Lee 2017 ). Warming in the Arctic has also been driven by latent energy transport (e.g., Graversen and Burtu 2016 ) and warm air advection (e.g., Messori et al. 2018 ). Thus, the Arctic and the midlatitudes influence and drive variability in each other, with both directions having substantial impacts. Such issues of cause and effect are often probed in observational analyses that primarily use techniques such as compositing or regression/correlation analysis
convection (e.g., Lee 2014 ; Baggett and Lee 2017 ). Warming in the Arctic has also been driven by latent energy transport (e.g., Graversen and Burtu 2016 ) and warm air advection (e.g., Messori et al. 2018 ). Thus, the Arctic and the midlatitudes influence and drive variability in each other, with both directions having substantial impacts. Such issues of cause and effect are often probed in observational analyses that primarily use techniques such as compositing or regression/correlation analysis
