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- Author or Editor: Tomislava Vukicevic x
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Abstract
The hypothesis that the short-time evolution of forecast errors originating from initial data uncertainties can be approximated by linear model solutions is investigated using a realistic prognostic model. A tangent linear limited-area model based on a state of the art mesoscale numerical forecast model is developed. The linearization is performed with respect to a temporally and spatially varying basic state. The basic state fields are produced by the nonlinear model using observed data.
The tangent model solutions and the error fields based on the nonlinear integrations are compared. The results demonstrate that the initial error evolution is well represented by the tangent model for periods of 1–1.5 days duration. The linear model solutions based on the time-independent basic state are also good approximations of the real-error evolutions, providing the prognostic fields are not changing rapidly in time.
The application of the linear model for estimating appropriate initial perturbation for the initial error sensitivity study is illustrated using a simple method. Comparison between the nonlinear integrations based on the unstable initial perturbation and an arbitrarily selected initial perturbation shows that the latter initialization can produce misleading results.
Abstract
The hypothesis that the short-time evolution of forecast errors originating from initial data uncertainties can be approximated by linear model solutions is investigated using a realistic prognostic model. A tangent linear limited-area model based on a state of the art mesoscale numerical forecast model is developed. The linearization is performed with respect to a temporally and spatially varying basic state. The basic state fields are produced by the nonlinear model using observed data.
The tangent model solutions and the error fields based on the nonlinear integrations are compared. The results demonstrate that the initial error evolution is well represented by the tangent model for periods of 1–1.5 days duration. The linear model solutions based on the time-independent basic state are also good approximations of the real-error evolutions, providing the prognostic fields are not changing rapidly in time.
The application of the linear model for estimating appropriate initial perturbation for the initial error sensitivity study is illustrated using a simple method. Comparison between the nonlinear integrations based on the unstable initial perturbation and an arbitrarily selected initial perturbation shows that the latter initialization can produce misleading results.
Abstract
The possibility of using forecast errors originating from the finite-time dominant linear modes for the prediction of forecast skill for a primitive equation regional forecast model is studied. This is similar to the method for skill prediction suggested by several other authors using simplified models. Two main problems associated with a sophisticated forecast model not considered in these other studies are investigated. 1) The number of degrees of freedom is typically too large for the evaluation of the spectrum of dominant modes associated with the linear error evolution equation, and 2) many different, physically meaningful, error measures may be used for this model and the dominant linear modes may be sensitive to the selection of the error measure.
It is shown first that the finite-time dominant linear solutions can be computed with sufficient accuracy for the complex forecast model using standard “power” method with a small number of iterations for all error measures considered in this study. The forecast skill is then estimated using the nonlinear forecast errors originating from the initial errors that are defined by these measure-dependent dominant solutions. These results show that the estimated forecast skill is very sensitive to the choice of error measure used for the computation of the finite-time dominant modes.
Abstract
The possibility of using forecast errors originating from the finite-time dominant linear modes for the prediction of forecast skill for a primitive equation regional forecast model is studied. This is similar to the method for skill prediction suggested by several other authors using simplified models. Two main problems associated with a sophisticated forecast model not considered in these other studies are investigated. 1) The number of degrees of freedom is typically too large for the evaluation of the spectrum of dominant modes associated with the linear error evolution equation, and 2) many different, physically meaningful, error measures may be used for this model and the dominant linear modes may be sensitive to the selection of the error measure.
It is shown first that the finite-time dominant linear solutions can be computed with sufficient accuracy for the complex forecast model using standard “power” method with a small number of iterations for all error measures considered in this study. The forecast skill is then estimated using the nonlinear forecast errors originating from the initial errors that are defined by these measure-dependent dominant solutions. These results show that the estimated forecast skill is very sensitive to the choice of error measure used for the computation of the finite-time dominant modes.
Abstract
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Abstract
The influence of one-way interacting lateral bounday conditions upon the predictability of flows in boundeddomains is studied using the barotropic nondivergent model in global and local domains. Past studies haveattempted to reconcile the apparent contradiction between pessimistic forecast of predictability theory and thehigh predictability actually found in regional models. Those investigations have emphasized the rather differentspectra and forcing mechanisms that are not considered in the theoretical estimates. We demonstrate that thepredictability remains high in an unforced, inertially driven local flow characterized by a typical synoptic scalespectrum, and constrained only by lateral boundary specification. We also offer a possible reconciliation ofthese results with the classical theory. It is shown that one-way interacting boundary conditions enhance thepredictability of flow in a local region which, without the boundary constraints, has limited predictabifity. Thedegree of this boundary constraint is dependent on the size of the domain, on the nature of flow in the domainand on the scale structure of the error field. The boundary constraint is particularly strong when a substantialportion of the larger scale flow in the domain is imposed through the boundary condition. In that case, smallscale initial uncertainties have limited interaction with the basic flow field because of scale separation andbecause the largest scales in the domain do not react to internal dynamics.
Abstract
The influence of one-way interacting lateral bounday conditions upon the predictability of flows in boundeddomains is studied using the barotropic nondivergent model in global and local domains. Past studies haveattempted to reconcile the apparent contradiction between pessimistic forecast of predictability theory and thehigh predictability actually found in regional models. Those investigations have emphasized the rather differentspectra and forcing mechanisms that are not considered in the theoretical estimates. We demonstrate that thepredictability remains high in an unforced, inertially driven local flow characterized by a typical synoptic scalespectrum, and constrained only by lateral boundary specification. We also offer a possible reconciliation ofthese results with the classical theory. It is shown that one-way interacting boundary conditions enhance thepredictability of flow in a local region which, without the boundary constraints, has limited predictabifity. Thedegree of this boundary constraint is dependent on the size of the domain, on the nature of flow in the domainand on the scale structure of the error field. The boundary constraint is particularly strong when a substantialportion of the larger scale flow in the domain is imposed through the boundary condition. In that case, smallscale initial uncertainties have limited interaction with the basic flow field because of scale separation andbecause the largest scales in the domain do not react to internal dynamics.
Abstract
The authors propose a new procedure. designated the adjoint-based genesis diagnostic (AGD) procedure, for studying triggering mechanism and the subsequent genesis of the synoptic phenomena of interest. This procedure makes use of a numerical model sensitivity to initial conditions and the nonlinear evolution of the initial perturbations that are designed using this sensitivity. The model sensitivity is evaluated using the associated adjoint model. This study uses the dry version of the National Center for Atmospheric Research Mesoscale Adjoint Modeling System (MAMS) for the numerical experiments. The authors apply the AGD procedure to two cases of Alpine lee cyclogenesis that were observed during the Alpine Experiment special observation period. The results show that the sensitivity fields that are produced by the adjoint model and the associated initial perturbations are readily related to the probable triggering mechanisms for these cyclones. Additionally, the nonlinear evolution of these initial perturbations points toward the physical processes involved in the lee cyclone formation. The AGD experiments for a weak cyclone case indicate that the MAMS forecast model has an underrepresented topographic forcing due to the sigma vertical coordinate and that this model error can be compensated by adjustments in the initial conditions that are related to the triggering mechanism, which is not associated with the topographic blocking mechanism.
Abstract
The authors propose a new procedure. designated the adjoint-based genesis diagnostic (AGD) procedure, for studying triggering mechanism and the subsequent genesis of the synoptic phenomena of interest. This procedure makes use of a numerical model sensitivity to initial conditions and the nonlinear evolution of the initial perturbations that are designed using this sensitivity. The model sensitivity is evaluated using the associated adjoint model. This study uses the dry version of the National Center for Atmospheric Research Mesoscale Adjoint Modeling System (MAMS) for the numerical experiments. The authors apply the AGD procedure to two cases of Alpine lee cyclogenesis that were observed during the Alpine Experiment special observation period. The results show that the sensitivity fields that are produced by the adjoint model and the associated initial perturbations are readily related to the probable triggering mechanisms for these cyclones. Additionally, the nonlinear evolution of these initial perturbations points toward the physical processes involved in the lee cyclone formation. The AGD experiments for a weak cyclone case indicate that the MAMS forecast model has an underrepresented topographic forcing due to the sigma vertical coordinate and that this model error can be compensated by adjustments in the initial conditions that are related to the triggering mechanism, which is not associated with the topographic blocking mechanism.
Abstract
Assimilation of cloud-affected infrared radiances from the Geostationary Operational Environmental Satellite-8 (GOES-8) is performed using a four-dimensional variational data assimilation (4DVAR) system designated as the Regional Atmospheric Modeling Data Assimilation System (RAMDAS). A cloud mask is introduced in order to limit the assimilation to points that have the same type of cloud in the model and observations, increasing the linearity of the minimization problem. A series of experiments is performed to determine the sensitivity of the assimilation to factors such as the maximum-allowed residual in the assimilation, the magnitude of the background error decorrelation length for water variables, the length of the assimilation window, and the inclusion of other data such as ground-based data including data from the Atmospheric Emitted Radiance Interferometer (AERI), a microwave radiometer, radiosonde, and cloud radar. In addition, visible and near-infrared satellite data are included in a separate experiment. The assimilation results are validated using independent ground-based data. The introduction of the cloud mask where large residuals are allowed has the greatest positive impact on the assimilation. Extending the length of the assimilation window in conjunction with the use of the cloud mask results in a better-conditioned minimization, as well as a smoother response of the model state to the assimilation.
Abstract
Assimilation of cloud-affected infrared radiances from the Geostationary Operational Environmental Satellite-8 (GOES-8) is performed using a four-dimensional variational data assimilation (4DVAR) system designated as the Regional Atmospheric Modeling Data Assimilation System (RAMDAS). A cloud mask is introduced in order to limit the assimilation to points that have the same type of cloud in the model and observations, increasing the linearity of the minimization problem. A series of experiments is performed to determine the sensitivity of the assimilation to factors such as the maximum-allowed residual in the assimilation, the magnitude of the background error decorrelation length for water variables, the length of the assimilation window, and the inclusion of other data such as ground-based data including data from the Atmospheric Emitted Radiance Interferometer (AERI), a microwave radiometer, radiosonde, and cloud radar. In addition, visible and near-infrared satellite data are included in a separate experiment. The assimilation results are validated using independent ground-based data. The introduction of the cloud mask where large residuals are allowed has the greatest positive impact on the assimilation. Extending the length of the assimilation window in conjunction with the use of the cloud mask results in a better-conditioned minimization, as well as a smoother response of the model state to the assimilation.
Abstract
An adjoint of the Pennsylvania State University-National Center for Atmospheric Research (PSU-NCAR) Mesoscale Model has been developed for use in sensitivity analysis following Cacuci. Sensitivity analysis is defined as the determination of the potential impact on some quantitative measure of a forecast aspect due to arbitrary perturbations of the model dynamic fields at earlier times. Input to the adjoint operator is the gradient of the forecast-aspect measure with respect to the model fields at the verification time, and output is the corresponding gradients defined at earlier times. The adjoint is exactly determined from a tangent linear model, which is itself an approximation to the dry nonlinear model. This approximation is shown to be accurate even when evaluated with regard to the moist nonlinear model for periods up to 36 h, although this accuracy is necessarily case and perturbation dependent. The mathematics describing the scheme are applied to the model in its spatially and temporally discrete form, which greatly simplifies the scheme's presentation. Examples of adjoint fields for three forecast aspects and two synoptic cases are shown, and their meanings and implications are discussed. They are valuable for determinations of forecast dependencies on data, predictability, and the relationships between consecutive synoptic conditions. The uses of the adjoint model therefore have much greater scope than only variational analysis and parameter filling.
Abstract
An adjoint of the Pennsylvania State University-National Center for Atmospheric Research (PSU-NCAR) Mesoscale Model has been developed for use in sensitivity analysis following Cacuci. Sensitivity analysis is defined as the determination of the potential impact on some quantitative measure of a forecast aspect due to arbitrary perturbations of the model dynamic fields at earlier times. Input to the adjoint operator is the gradient of the forecast-aspect measure with respect to the model fields at the verification time, and output is the corresponding gradients defined at earlier times. The adjoint is exactly determined from a tangent linear model, which is itself an approximation to the dry nonlinear model. This approximation is shown to be accurate even when evaluated with regard to the moist nonlinear model for periods up to 36 h, although this accuracy is necessarily case and perturbation dependent. The mathematics describing the scheme are applied to the model in its spatially and temporally discrete form, which greatly simplifies the scheme's presentation. Examples of adjoint fields for three forecast aspects and two synoptic cases are shown, and their meanings and implications are discussed. They are valuable for determinations of forecast dependencies on data, predictability, and the relationships between consecutive synoptic conditions. The uses of the adjoint model therefore have much greater scope than only variational analysis and parameter filling.
Abstract
Recently, optimistic reports have appeared indicating that mesoscale circulations are more predictable than synoptic scale circulations. These have been based on studies using limited-area meso-α-scale forecast models. Warnings have also appeared suggesting that these results are party artifacts of the experimental and model designs, particularly strong diffusion and an “error sweeping effect” of lateral boundaries. We demonstrate that an additionally important effect of the lateral boundaries is to restrict the scales at which errors can grow: if the domain is sufficiently large, forecast differences grow with time, but only at large scales. Our results show a strong sensitivity to synoptic situation and selection of an initial perturbation. Experiments with and without topography reveal that predictability is enhanced due to systematic topographic forcing. Detailed scale analysis of forecast differences and comparison with global model results indicate that the predictability using limited-area mesoscale models is not fundamentally different from that using global synoptic scale models.
Abstract
Recently, optimistic reports have appeared indicating that mesoscale circulations are more predictable than synoptic scale circulations. These have been based on studies using limited-area meso-α-scale forecast models. Warnings have also appeared suggesting that these results are party artifacts of the experimental and model designs, particularly strong diffusion and an “error sweeping effect” of lateral boundaries. We demonstrate that an additionally important effect of the lateral boundaries is to restrict the scales at which errors can grow: if the domain is sufficiently large, forecast differences grow with time, but only at large scales. Our results show a strong sensitivity to synoptic situation and selection of an initial perturbation. Experiments with and without topography reveal that predictability is enhanced due to systematic topographic forcing. Detailed scale analysis of forecast differences and comparison with global model results indicate that the predictability using limited-area mesoscale models is not fundamentally different from that using global synoptic scale models.
Abstract
In the current study, a technique that offers a way to evaluate ensemble forecast uncertainties produced either by initial conditions or different model versions, or both, is presented. The technique consists of first diagnosing the performance of the forecast ensemble and then optimizing the ensemble forecast using results of the diagnosis. The technique is based on the explicit evaluation of probabilities that are associated with the Gaussian stochastic representation of the weather analysis and forecast. It combines an ensemble technique for evaluating the analysis error covariance and the standard Monte Carlo approach for computing samples from a known Gaussian distribution. The technique was demonstrated in a tutorial manner on two relatively simple examples to illustrate the impact of ensemble characteristics including ensemble size, various observation strategies, and configurations including different model versions and varying initial conditions. In addition, the authors assessed improvements in the consensus forecasts gained by optimal weighting of the ensemble members based on time-varying, prior-probabilistic skill measures. The results with different observation configurations indicate that, as observations become denser, there is a need for larger-sized ensembles and/or more accuracy among individual members for the ensemble forecast to exhibit prediction skill. The main conclusions relative to ensembles built up with different physics configurations were, first, that almost all members typically exhibited some skill at some point in the model run, suggesting that all should be retained to acquire the best consensus forecast; and, second, that the normalized probability metric can be used to determine what sets of weights or physics configurations are performing best. A comparison of forecasts derived from a simple ensemble mean to forecasts from a mean developed from variably weighting the ensemble members based on prior performance by the probabilistic measure showed that the latter had substantially reduced mean absolute error. The study also indicates that a weighting scheme that utilized more prior cycles showed additional reduction in forecast error.
Abstract
In the current study, a technique that offers a way to evaluate ensemble forecast uncertainties produced either by initial conditions or different model versions, or both, is presented. The technique consists of first diagnosing the performance of the forecast ensemble and then optimizing the ensemble forecast using results of the diagnosis. The technique is based on the explicit evaluation of probabilities that are associated with the Gaussian stochastic representation of the weather analysis and forecast. It combines an ensemble technique for evaluating the analysis error covariance and the standard Monte Carlo approach for computing samples from a known Gaussian distribution. The technique was demonstrated in a tutorial manner on two relatively simple examples to illustrate the impact of ensemble characteristics including ensemble size, various observation strategies, and configurations including different model versions and varying initial conditions. In addition, the authors assessed improvements in the consensus forecasts gained by optimal weighting of the ensemble members based on time-varying, prior-probabilistic skill measures. The results with different observation configurations indicate that, as observations become denser, there is a need for larger-sized ensembles and/or more accuracy among individual members for the ensemble forecast to exhibit prediction skill. The main conclusions relative to ensembles built up with different physics configurations were, first, that almost all members typically exhibited some skill at some point in the model run, suggesting that all should be retained to acquire the best consensus forecast; and, second, that the normalized probability metric can be used to determine what sets of weights or physics configurations are performing best. A comparison of forecasts derived from a simple ensemble mean to forecasts from a mean developed from variably weighting the ensemble members based on prior performance by the probabilistic measure showed that the latter had substantially reduced mean absolute error. The study also indicates that a weighting scheme that utilized more prior cycles showed additional reduction in forecast error.
