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- Author or Editor: Claude Fischer x
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Abstract
The concept of a singular mode underlies optimal linear amplification theories. This concept is studied in the frame of the two-dimensional, quasigeostrophic Eady problem with uniform potential vorticity. Analytical solutions are produced for the relevant physical norms. Exact relations are also derived for the amplifications, which give the lower and upper bounds to any linear development. Results show significant differences in the structure of the singular modes, as well as in the associated amplifications, when the horizontal wavenumber is varied or the inner product is changed. It is found that the singular modes can depart significantly from the normal modes, though the dynamics of the problem are very simple. Comparisons with previous works are also performed. Finally, the derived equations are used to present the linear evolution of error growth within the Eady problem, as predicted by a Kalman filter. Considerations on the spectral space error covariance matrix are made, and a particular case of error dynamics in the 2D physical space is shown. The derivation of the general algebraic solutions is included in the .
Abstract
The concept of a singular mode underlies optimal linear amplification theories. This concept is studied in the frame of the two-dimensional, quasigeostrophic Eady problem with uniform potential vorticity. Analytical solutions are produced for the relevant physical norms. Exact relations are also derived for the amplifications, which give the lower and upper bounds to any linear development. Results show significant differences in the structure of the singular modes, as well as in the associated amplifications, when the horizontal wavenumber is varied or the inner product is changed. It is found that the singular modes can depart significantly from the normal modes, though the dynamics of the problem are very simple. Comparisons with previous works are also performed. Finally, the derived equations are used to present the linear evolution of error growth within the Eady problem, as predicted by a Kalman filter. Considerations on the spectral space error covariance matrix are made, and a particular case of error dynamics in the 2D physical space is shown. The derivation of the general algebraic solutions is included in the .
Abstract
This paper deals with the characteristics and effects of digital filter initialization, as implemented in the operational three-dimensional variational data assimilation (3DVAR) system of the Aire Limitée Adaptation Dynamique Développement International (ALADIN)-France regional weather forecast model.
First, a series of findings on the properties of the initialization of the model are discussed. Examples of initial spinup linked with inertia–gravity wave occurrence are shown, and the major sources for their generation are listed. These experimental results are compared with past and present experiences concerning the use and need for digital filter initialization. Furthermore, the impacts of switching to an incremental formulation of the filter in data assimilation mode are demonstrated. Second, the effects of the filter formulation on the results of an observation impact study are illustrated. The latter consists of implementing screen-level, 10-m horizontal wind information into the ALADIN 3DVAR analysis. There can, indeed, be some delicate interference between observation impact evaluation and the effects of filtering, at least on short-term forecasts.
The paper is concluded with some general considerations on the experimental evaluation of spinup and the link between the assimilation system design and model state filtering.
Abstract
This paper deals with the characteristics and effects of digital filter initialization, as implemented in the operational three-dimensional variational data assimilation (3DVAR) system of the Aire Limitée Adaptation Dynamique Développement International (ALADIN)-France regional weather forecast model.
First, a series of findings on the properties of the initialization of the model are discussed. Examples of initial spinup linked with inertia–gravity wave occurrence are shown, and the major sources for their generation are listed. These experimental results are compared with past and present experiences concerning the use and need for digital filter initialization. Furthermore, the impacts of switching to an incremental formulation of the filter in data assimilation mode are demonstrated. Second, the effects of the filter formulation on the results of an observation impact study are illustrated. The latter consists of implementing screen-level, 10-m horizontal wind information into the ALADIN 3DVAR analysis. There can, indeed, be some delicate interference between observation impact evaluation and the effects of filtering, at least on short-term forecasts.
The paper is concluded with some general considerations on the experimental evaluation of spinup and the link between the assimilation system design and model state filtering.
Abstract
Both upper-air and surface frontogenesis have often been depicted as processes whose dynamics could he reduced to 2D balanced problems in which “self-sharpening” configurations could be highlighted.
This paper reports on a 3D adiabatic simulation of a baroclinic wave life cycle. Great care has been devoted to the vertical resolution, allowing for a good description of both surface and upper-air frontogenesis. The authors introduce a kinematic diagnostic (Q′ vector) that permits the identification of frontogenetic areas in such complex 3D flows where classical, low-Rossby number balance conditions can be violated. Relations and specificity with respect to frontogenetic forcing diagnostics are discussed. First, Q′ is used for surface frontogenesis, where it describes well the actual frontal activity, including the complex warm-frontal seclusion process. Upper-air frontogenesis is also investigated, both in terms of this kinematic diagnostic or in terms of potential vorticity displacements on isentropic surfaces. Both types of diagnostics clearly distinguish between dynamics of the entrance zone of the northerly jet—where 2D concepts may usefully be applied—and those of the strongly curved zone near the trough axis. Classical cyclogenetic terms (stretching and tilting) as well as the separation of ageostrophic circulations in terms of natural components of the wind also lead to a clear dynamical separation.
The cold front is shown to extend from the surface far into the troposphere. This is shown to be related to a singular property of the 3D flow. Parcels undergoing frontogenegis in the northwesterly upper-air flow are advected on top of those that were forced at the surface cold front in a southwesterly flow. The occurrence of a feedback proem between these upper-air frontogenesis processes and the surface ones is then investigated. Stepwise vertical profiles of horizontal diffusion are used to force local frontolysis. The resulting upper-air frontolysis, despite its local efficiency, does not have any remote effect on the surface front, whose frontolysis in turn has no effect on the upper-air front. The feedback process is thus not occurring in our simulation.
Abstract
Both upper-air and surface frontogenesis have often been depicted as processes whose dynamics could he reduced to 2D balanced problems in which “self-sharpening” configurations could be highlighted.
This paper reports on a 3D adiabatic simulation of a baroclinic wave life cycle. Great care has been devoted to the vertical resolution, allowing for a good description of both surface and upper-air frontogenesis. The authors introduce a kinematic diagnostic (Q′ vector) that permits the identification of frontogenetic areas in such complex 3D flows where classical, low-Rossby number balance conditions can be violated. Relations and specificity with respect to frontogenetic forcing diagnostics are discussed. First, Q′ is used for surface frontogenesis, where it describes well the actual frontal activity, including the complex warm-frontal seclusion process. Upper-air frontogenesis is also investigated, both in terms of this kinematic diagnostic or in terms of potential vorticity displacements on isentropic surfaces. Both types of diagnostics clearly distinguish between dynamics of the entrance zone of the northerly jet—where 2D concepts may usefully be applied—and those of the strongly curved zone near the trough axis. Classical cyclogenetic terms (stretching and tilting) as well as the separation of ageostrophic circulations in terms of natural components of the wind also lead to a clear dynamical separation.
The cold front is shown to extend from the surface far into the troposphere. This is shown to be related to a singular property of the 3D flow. Parcels undergoing frontogenegis in the northwesterly upper-air flow are advected on top of those that were forced at the surface cold front in a southwesterly flow. The occurrence of a feedback proem between these upper-air frontogenesis processes and the surface ones is then investigated. Stepwise vertical profiles of horizontal diffusion are used to force local frontolysis. The resulting upper-air frontolysis, despite its local efficiency, does not have any remote effect on the surface front, whose frontolysis in turn has no effect on the upper-air front. The feedback process is thus not occurring in our simulation.
Abstract
This paper provides an experimental framework designed to assess the performance and the evolution of the diabatic Aire Limitée Adaptation Dynamique Développement International (ALADIN) adjoint model at 10-km grid size. Numerical experiments are carried out with the goal of evaluating the adjoint model solutions and the benefit of employing a complex linearized physical parameterization package in the gradient computation. Sensitivity studies with respect to initial conditions at high resolution on real meteorological events are performed. Numerical results obtained in the gradient computations show that, at high resolution, a strong nonlinear flow over complex orography might be a potential source of numerical instability in the absence of a robust dissipative physics employed in the adjoint model. Also, the scheme of the linearized large-scale precipitation is a source of noise in precipitating areas. The results on one particular case suggest that on the one hand the adjoint model is able to capture the dynamically sensitive area, but on the other hand the subsequent sensitivity forecast is more sensitive to the sign and the amplitude of the initial state perturbation rather than the structure of the gradient field.
Abstract
This paper provides an experimental framework designed to assess the performance and the evolution of the diabatic Aire Limitée Adaptation Dynamique Développement International (ALADIN) adjoint model at 10-km grid size. Numerical experiments are carried out with the goal of evaluating the adjoint model solutions and the benefit of employing a complex linearized physical parameterization package in the gradient computation. Sensitivity studies with respect to initial conditions at high resolution on real meteorological events are performed. Numerical results obtained in the gradient computations show that, at high resolution, a strong nonlinear flow over complex orography might be a potential source of numerical instability in the absence of a robust dissipative physics employed in the adjoint model. Also, the scheme of the linearized large-scale precipitation is a source of noise in precipitating areas. The results on one particular case suggest that on the one hand the adjoint model is able to capture the dynamically sensitive area, but on the other hand the subsequent sensitivity forecast is more sensitive to the sign and the amplitude of the initial state perturbation rather than the structure of the gradient field.
Abstract
This note presents recent results on the properties of background error covariances computed using the National Meteorological Center (now known as the National Centers for Environmental Prediction) method and applied to a mesoscale limited-area model. The error covariances are computed over a winter period for the Moroccan version of the ALADIN forecast system. The overall results compare well with previous outputs obtained with the same forecast model but on a typical midlatitude domain (viz., ALADIN-France). Thus, the climatological error statistics can be used with an equivalent efficiency in the frame of a 3DVAR analysis system over a wide range of low-latitude and midlatitude limited-area domains. Furthermore, the error statistics between the true forecast fields and the coupling fields for the same domain are compared. The coupling fields are provided by interpolation from the global ARPÈGE model. The comparison gives insight into the range of scales over which ALADIN is building its own dynamics and errors. In particular, the study shows at what scale the limited-area model dynamics depart from the global model–forced solution.
Abstract
This note presents recent results on the properties of background error covariances computed using the National Meteorological Center (now known as the National Centers for Environmental Prediction) method and applied to a mesoscale limited-area model. The error covariances are computed over a winter period for the Moroccan version of the ALADIN forecast system. The overall results compare well with previous outputs obtained with the same forecast model but on a typical midlatitude domain (viz., ALADIN-France). Thus, the climatological error statistics can be used with an equivalent efficiency in the frame of a 3DVAR analysis system over a wide range of low-latitude and midlatitude limited-area domains. Furthermore, the error statistics between the true forecast fields and the coupling fields for the same domain are compared. The coupling fields are provided by interpolation from the global ARPÈGE model. The comparison gives insight into the range of scales over which ALADIN is building its own dynamics and errors. In particular, the study shows at what scale the limited-area model dynamics depart from the global model–forced solution.
