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that measures the discrepancies of the atmospheric state from a background (i.e., a model forecast) as well as from observations. The control variables can be the prognostic model variables or any diagnostic variables derived from them. Three pairs of control variables for momentum are typically used in variational DA systems: streamfunction and velocity potential ( ψχ ), eastward and northward velocity components ( UV ), and vorticity and divergence ( ζδ ). Historically, the ψχ and ζδ momentum
that measures the discrepancies of the atmospheric state from a background (i.e., a model forecast) as well as from observations. The control variables can be the prognostic model variables or any diagnostic variables derived from them. Three pairs of control variables for momentum are typically used in variational DA systems: streamfunction and velocity potential ( ψχ ), eastward and northward velocity components ( UV ), and vorticity and divergence ( ζδ ). Historically, the ψχ and ζδ momentum
represented by a blend of homogeneous and isotropic covariances and 4D flow-dependent covariances derived from a global ensemble Kalman filter (EnKF). In this paper we report on the implementation of the same 4DEnVar scheme in the Regional Deterministic Prediction System (RDPS), a forecasting system based on a limited-area version of the Global Environmental Multiscale (GEM) model ( Côté et al. 1998 ) covering North America ( Fig. 1 ) with an approximate 10-km horizontal grid spacing. The previous RDPS
represented by a blend of homogeneous and isotropic covariances and 4D flow-dependent covariances derived from a global ensemble Kalman filter (EnKF). In this paper we report on the implementation of the same 4DEnVar scheme in the Regional Deterministic Prediction System (RDPS), a forecasting system based on a limited-area version of the Global Environmental Multiscale (GEM) model ( Côté et al. 1998 ) covering North America ( Fig. 1 ) with an approximate 10-km horizontal grid spacing. The previous RDPS
1. Introduction For more than a decade, numerous operational numerical weather prediction (NWP) centers have had significant improvements in analysis and forecast accuracy by adopting the four-dimensional variational data assimilation (4DVar) approach (e.g., Rabier et al. 2000 ; Rabier 2005 ; Rawlins et al. 2007 ; Gauthier et al. 2007 ). In parallel with these developments, a significant research and development effort has led to the successful application of the ensemble Kalman filter
1. Introduction For more than a decade, numerous operational numerical weather prediction (NWP) centers have had significant improvements in analysis and forecast accuracy by adopting the four-dimensional variational data assimilation (4DVar) approach (e.g., Rabier et al. 2000 ; Rabier 2005 ; Rawlins et al. 2007 ; Gauthier et al. 2007 ). In parallel with these developments, a significant research and development effort has led to the successful application of the ensemble Kalman filter
1. Introduction Atmospheric motion vectors (AMVs) are proxies for the local horizontal wind, and are derived from sequential multispectral satellite images by tracking the motion of targets that include cirrus clouds, gradients in water vapor, and lower-tropospheric cumulus clouds ( Velden et al. 1997 ). AMV data are assimilated routinely into operational global numerical weather prediction (NWP) systems, and have been found to improve forecasts of tropical cyclone (TC) tracks (e.g., Goerss
1. Introduction Atmospheric motion vectors (AMVs) are proxies for the local horizontal wind, and are derived from sequential multispectral satellite images by tracking the motion of targets that include cirrus clouds, gradients in water vapor, and lower-tropospheric cumulus clouds ( Velden et al. 1997 ). AMV data are assimilated routinely into operational global numerical weather prediction (NWP) systems, and have been found to improve forecasts of tropical cyclone (TC) tracks (e.g., Goerss
1. Introduction The ensemble Kalman filter (EnKF) is a popular method for doing data assimilation (DA) in the geosciences. This study is concerned with the treatment of model noise in the EnKF forecast step. a. Relevance and scope While uncertainty quantification is an important end product of any estimation procedure, it is paramount in DA because of the sequentiality and the need to correctly weight the observations at the next time step. The two main sources of uncertainty in a forecast are
1. Introduction The ensemble Kalman filter (EnKF) is a popular method for doing data assimilation (DA) in the geosciences. This study is concerned with the treatment of model noise in the EnKF forecast step. a. Relevance and scope While uncertainty quantification is an important end product of any estimation procedure, it is paramount in DA because of the sequentiality and the need to correctly weight the observations at the next time step. The two main sources of uncertainty in a forecast are
recently, Supertyphoon Haiyan in 2013. Owing to the enormous societal impact of hurricanes, it is of great importance to accurately predict the track and intensity of these storms many hours in advance. In addition, as suggested by Landsea (1993) and Elsberry (2005) , hurricane damage increases exponentially with low-level wind speed. Therefore, accurate forecasting of a hurricane’s structure near its landfall is of great significance for effectively warning the public and reducing economic damage
recently, Supertyphoon Haiyan in 2013. Owing to the enormous societal impact of hurricanes, it is of great importance to accurately predict the track and intensity of these storms many hours in advance. In addition, as suggested by Landsea (1993) and Elsberry (2005) , hurricane damage increases exponentially with low-level wind speed. Therefore, accurate forecasting of a hurricane’s structure near its landfall is of great significance for effectively warning the public and reducing economic damage
1. Introduction For more than a decade four-dimensional variational data assimilation (4DVar) has been used by most of the main global numerical weather prediction (NWP) centers ( Rabier 2005 ); the Met Office implemented 4DVar in 2004 ( Rawlins et al. 2007 ). A weakness of the basic 4DVar method is the use of a fixed “climatological” model of the error covariance in the background forecast, which does not describe the flow-dependent errors of the day as well as ensemble Kalman filter methods
1. Introduction For more than a decade four-dimensional variational data assimilation (4DVar) has been used by most of the main global numerical weather prediction (NWP) centers ( Rabier 2005 ); the Met Office implemented 4DVar in 2004 ( Rawlins et al. 2007 ). A weakness of the basic 4DVar method is the use of a fixed “climatological” model of the error covariance in the background forecast, which does not describe the flow-dependent errors of the day as well as ensemble Kalman filter methods
1. Introduction Assessment of the impact of observations on reducing ocean model forecast error from data assimilation is a fundamental aspect of any ocean analysis and forecasting system. The purpose of assimilation is to reduce the model initial condition error. Improved initial conditions should lead to an improved forecast. However, it is likely that not all observations assimilated have equal value in reducing forecasting error. Estimation of which observations are best and the
1. Introduction Assessment of the impact of observations on reducing ocean model forecast error from data assimilation is a fundamental aspect of any ocean analysis and forecasting system. The purpose of assimilation is to reduce the model initial condition error. Improved initial conditions should lead to an improved forecast. However, it is likely that not all observations assimilated have equal value in reducing forecasting error. Estimation of which observations are best and the
. Formulation of a 3DVAR using STCS (STCS-3DVAR) 1) A formulation of a background-error covariance model using STCS To construct a 3DVAR system based on STCS, we designed a background-error covariance model making use of STCS. Suppose that the forecast model is a hydrostatic model, and that the ns background-error samples δ on the CSGEA are given as the differences of the forecasts at the same time issued from different times, or the ensemble deviations from the mean of an ensemble forecast as follows
. Formulation of a 3DVAR using STCS (STCS-3DVAR) 1) A formulation of a background-error covariance model using STCS To construct a 3DVAR system based on STCS, we designed a background-error covariance model making use of STCS. Suppose that the forecast model is a hydrostatic model, and that the ns background-error samples δ on the CSGEA are given as the differences of the forecasts at the same time issued from different times, or the ensemble deviations from the mean of an ensemble forecast as follows
1. Introduction Forecast errors from numerical weather prediction (NWP) models arise in part from imperfect initial conditions, as a result of the lack of sufficient observations as well as their suboptimal use. Different data assimilation systems (DASs) have been developed since the objective analysis of meteorological fields was introduced in the midtwentieth century; for example, Cressman (1959) developed the empirical successive corrections method and Gandin (1963) introduced optimal
1. Introduction Forecast errors from numerical weather prediction (NWP) models arise in part from imperfect initial conditions, as a result of the lack of sufficient observations as well as their suboptimal use. Different data assimilation systems (DASs) have been developed since the objective analysis of meteorological fields was introduced in the midtwentieth century; for example, Cressman (1959) developed the empirical successive corrections method and Gandin (1963) introduced optimal
