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state is evaluated in isolation. Splitting assumes that the processes are either evaluated based on the same state and, hence, do not see the impact of other processes on that state, or they are evaluated sequentially ( Donahue and Caldwell 2018 ). Both approaches are inaccurate reflections of reality. While splitting is useful and often unavoidable, it can lead to undesirable features in the numerical solutions. For example, process splitting can impact the model performance when processes compete
state is evaluated in isolation. Splitting assumes that the processes are either evaluated based on the same state and, hence, do not see the impact of other processes on that state, or they are evaluated sequentially ( Donahue and Caldwell 2018 ). Both approaches are inaccurate reflections of reality. While splitting is useful and often unavoidable, it can lead to undesirable features in the numerical solutions. For example, process splitting can impact the model performance when processes compete
require that forecast and observed events match at the grid scale for a forecast to be considered perfect, have not always corroborated subjective evaluations favoring convection-allowing models over convection-parameterizing models (e.g., Mass et al. 2002 ; Weisman et al. 2008 ). Thus, in an attempt to reconcile disparities between objective metrics and subjective evaluations, several spatial verification methods have been developed that can broadly be categorized into “neighborhood,” scale
require that forecast and observed events match at the grid scale for a forecast to be considered perfect, have not always corroborated subjective evaluations favoring convection-allowing models over convection-parameterizing models (e.g., Mass et al. 2002 ; Weisman et al. 2008 ). Thus, in an attempt to reconcile disparities between objective metrics and subjective evaluations, several spatial verification methods have been developed that can broadly be categorized into “neighborhood,” scale
-area models (LAMs), which is the focus of the current review. 1 The first LAM application of the EnKF was found in Snyder and Zhang (2003) and Zhang et al. (2004) , where synthetic radar data was assimilated into a cloud model. Those two studies demonstrated that the EnKF analysis can faithfully approximate the truth in terms of both dynamic and thermodynamic variables of a supercell storm ( Fig. 1 ). Fig . 1. The performance of a convective-scale EnKF in assimilating radar radial velocity for
-area models (LAMs), which is the focus of the current review. 1 The first LAM application of the EnKF was found in Snyder and Zhang (2003) and Zhang et al. (2004) , where synthetic radar data was assimilated into a cloud model. Those two studies demonstrated that the EnKF analysis can faithfully approximate the truth in terms of both dynamic and thermodynamic variables of a supercell storm ( Fig. 1 ). Fig . 1. The performance of a convective-scale EnKF in assimilating radar radial velocity for
-implicit semi-Lagrangian global modelof the shallow-water primitive equations. Its performance at comparable resolution matched that of theircorresponding 1988 model based on a spectral discretization, and this performance was achieved withoutrecourse to any divergence damping. By evaluating the product term (of the geopotentialperturbation and divergence) in the continuity equation using quantities at time t rather than at time t+/xt/2, but still evaluating it at the trajectory midpoint,Higgins and
-implicit semi-Lagrangian global modelof the shallow-water primitive equations. Its performance at comparable resolution matched that of theircorresponding 1988 model based on a spectral discretization, and this performance was achieved withoutrecourse to any divergence damping. By evaluating the product term (of the geopotentialperturbation and divergence) in the continuity equation using quantities at time t rather than at time t+/xt/2, but still evaluating it at the trajectory midpoint,Higgins and
extratropical regions are reviewed, despitethe fact that models of similar scale are showingpromise in the tropics as well (Krishnamurti et al.,1979; Harrison and Fiorino, 1982; Fiorino et al.,1982).2. Quantitative measures of forecast skill and realism of simulations Before reviewing the components of regional models, it is worthwhile to review methods of judging theaccuracy and skill of models, not only to be able tocompare the relative performance of different modelsbut also to evaluate the impact
extratropical regions are reviewed, despitethe fact that models of similar scale are showingpromise in the tropics as well (Krishnamurti et al.,1979; Harrison and Fiorino, 1982; Fiorino et al.,1982).2. Quantitative measures of forecast skill and realism of simulations Before reviewing the components of regional models, it is worthwhile to review methods of judging theaccuracy and skill of models, not only to be able tocompare the relative performance of different modelsbut also to evaluate the impact
. (2) . The forward operator performs the mapping from model space to observation space. Finally, a forecast model is needed to transport the new estimate to the next analysis time as in Eq. (3) : In a pure Monte Carlo implementation, the i th member of an -member analysis ensemble is obtained by evaluating Eq. (1) using a randomly perturbed vector of observations and using a member of a corresponding ensemble of background estimates: Similarly, to obtain a member of the background
. (2) . The forward operator performs the mapping from model space to observation space. Finally, a forecast model is needed to transport the new estimate to the next analysis time as in Eq. (3) : In a pure Monte Carlo implementation, the i th member of an -member analysis ensemble is obtained by evaluating Eq. (1) using a randomly perturbed vector of observations and using a member of a corresponding ensemble of background estimates: Similarly, to obtain a member of the background
dimension of ψ and γ is the volume of a unit sphere in R n . Pham (2001) proposes to sample new particles from a Gaussian density centered around particles with multiple identical copies, found from probabilistic resampling. Applications to the Lorenz 63 model show that some 200 particles are needed for good performance. As an extreme case Xiong et al. (2006) , probably unaware of the work by Pham (2001) , draw their new particles from a Gaussian posterior density with mean and covariance found
dimension of ψ and γ is the volume of a unit sphere in R n . Pham (2001) proposes to sample new particles from a Gaussian density centered around particles with multiple identical copies, found from probabilistic resampling. Applications to the Lorenz 63 model show that some 200 particles are needed for good performance. As an extreme case Xiong et al. (2006) , probably unaware of the work by Pham (2001) , draw their new particles from a Gaussian posterior density with mean and covariance found
. 1980; Grell et al. 1991 ) provide a means of evaluating from real data the instantaneous heating andmoistening profiles and rainfall rates produced by cumulus parameterizations. Such tests are limited, becausethey do not measure time evolution. This particularlyholds for the hybrid approach, in which several hoursof integration are required for evaluation. New~rtheless,semiprognostic tests provide a necessary step in tlaeevaluation of a cumulus parameterization. Cumulus ensemble models, which
. 1980; Grell et al. 1991 ) provide a means of evaluating from real data the instantaneous heating andmoistening profiles and rainfall rates produced by cumulus parameterizations. Such tests are limited, becausethey do not measure time evolution. This particularlyholds for the hybrid approach, in which several hoursof integration are required for evaluation. New~rtheless,semiprognostic tests provide a necessary step in tlaeevaluation of a cumulus parameterization. Cumulus ensemble models, which
), and an open wave at 500 hPa ( Demirci et al. 2007 ) were unable to reliably distinguish between recurving TCs that did and did not become extratropical, independent of their posttransition evolution. Similar findings for the scalar frontogenesis and open wave metrics were obtained by Wang et al. (2012) . Jones et al. (2003) advocated for an evaluation of the utility of potential vorticity (PV) toward diagnosing ET in both numerical models and observations. In conducting such an evaluation
), and an open wave at 500 hPa ( Demirci et al. 2007 ) were unable to reliably distinguish between recurving TCs that did and did not become extratropical, independent of their posttransition evolution. Similar findings for the scalar frontogenesis and open wave metrics were obtained by Wang et al. (2012) . Jones et al. (2003) advocated for an evaluation of the utility of potential vorticity (PV) toward diagnosing ET in both numerical models and observations. In conducting such an evaluation
shift associated with an advancing cold front. Understanding the reasons for such wind shifts in these situations has the potential to improve forecast performance. I restrict attention in this paper to prefrontal features associated with surface-based cold fronts for five reasons. First, the conceptual model of surface cold fronts emphasizes the simultaneous occurrence of the temperature drop, wind shift, and pressure minimum. If structures differ from this conceptual model, then learning more
shift associated with an advancing cold front. Understanding the reasons for such wind shifts in these situations has the potential to improve forecast performance. I restrict attention in this paper to prefrontal features associated with surface-based cold fronts for five reasons. First, the conceptual model of surface cold fronts emphasizes the simultaneous occurrence of the temperature drop, wind shift, and pressure minimum. If structures differ from this conceptual model, then learning more
