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Caren Marzban, Robert Tardif, and Scott Sandgathe

contrast, p values provide information only on the former. 2) Other forecast fields The above analysis is repeated on all forecast quantities F1–F9 in Table 2 . The results are complex and lend themselves to a wide range of interpretations. Table 3 summarizes the most clear and unambiguous findings. The “Influential” model parameters are selected based on both the magnitude and the variability of the effect of the model parameters, assessed qualitatively from the boxplots of the regression

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Michael K. Tippett and Timothy DelSole

is defined to be The matrix is square with positive diagonal entries and is thus invertible. Therefore, the simple LR and CA forecasts are In the language of principal component analysis (PCA), the columns of the matrices and are the empirical orthogonal function (EOFs) and principal components (PCs), respectively, of the anomaly data . The factors of serve to normalize the PCs to have unit variance since the columns of are unit vectors with zero mean. Principal component regression

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P. Friederichs and A. Hense

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

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Bob Glahn

probabilistic guidance forecasts; linear regression applied to forecasting events for that purpose was called regression estimation of event probabilities (REEP) by Bob Miller (1968) . REEP was easy to use, and predictor selection, either forward, backward, or stepwise—whatever the developer preferred—from a large number of potential predictors, typically over 100, was straightforward. Such postprocessing was especially useful because NWP did not at first provide forecasts of the elements desired, such as

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David A. Unger, Huug van den Dool, Edward O’Lenic, and Dan Collins

. Regression relationships a. Simple linear regression Regression has been applied to the output from dynamic numerical prediction models for over 40 yr ( Glahn and Lowry 1972 ; Glahn et al. 2009 ). Regression analysis usually begins with a tentative assumption of a linear relationship between the predictors (in this case the forecasts from a numerical model) and the predictand (observations), with errors represented by the term, ε. For reasons that will become clear later, this will be illustrated by the

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James S. Goerss

invaluable assistance in graphical display and regression analysis and to Jim Gross of NHC and Buck Sampson of NRL Monterey for making possible the implementation of this research on the ATCF. This research was performed on Project A8R2WRP entitled “Quantifying Tropical Cyclone Track Forecast Uncertainty and Improving Extended-range Tropical Cyclone Track Forecasts Using an Ensemble of Dynamical Models,” funded by the National Oceanic and Atmospheric Administration Joint Hurricane Testbed administered by

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Ning Lin, Renzhi Jing, Yuyan Wang, Emmi Yonekura, Jianqing Fan, and Lingzhou Xue

intensification ( Tang and Emanuel 2012 ), we also construct fully nondimensional VI models. The models based on VI, as well as on its component variables, are compared with the models based on previously considered environmental variables. Recent advancement in statistical analysis of complex, large datasets also motivates us to explore new regression methods applied to TC intensity modeling. First, similar to Lee et al. (2015) , we reduce the SHIPS and STIPS models by statistically identifying the most

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Caren Marzban, Xiaochuan Du, Scott Sandgathe, James D. Doyle, Yi Jin, and Nicholas C. Lederer

manner in which MMR allows one to account for spatial correlations ( DelSole and Yang 2011 ). Although other methods exist that take spatial correlations into account when performing inference ( Douglas et al. 2000 ; Elmore et al. 2006 ; Wilks 1997 ), the MMR approach is more natural in the present application because the sensitivity analysis is done within a regression framework already. The terms “multivariate” and “multiple” in MMR refer to several response and predictor variables, respectively

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Chiara Lepore and Michael K. Tippett

° grid over the contiguous United States (CONUS) and to monthly resolution over the period 1979–2016. Report data are analyzed separately for tornadoes rated EF0 (23 458 cases), EF1 (12 799 cases), EF2 (4015 cases), and EF3 (1141 cases). Tornadoes rated EF4 and greater represent less than 1% of the tornadoes in the database and are not included in the analysis here. Following Tippett et al. (2012) , the TEI-EF is developed using environments from the North American Regional Reanalysis ( Mesinger et

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Elizabeth Satterfield, Daniel Hodyss, David D. Kuhl, and Craig H. Bishop

representation due to spectral truncation for 10 equally populated bins based on values of ensemble variances (blue dots). Results are shown for temperature for the month of January. The linear regression is also shown (red line). 4. Analysis of the H–L and Desroziers methods In this section we further explore the predictive relationship between the ensemble variance and the variance associated with representation error, qualitatively illustrated in the previous section. In what follows, we address how well

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