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Abstract
Topographic effects on radiation, including both topographic shading and slope effects, are included in the Weather Research and Forecasting (WRF) Model, and here they are made compatible with the immersed boundary method (IBM). IBM is an alternative method for representing complex terrain that reduces numerical errors over sloped terrain, thus extending the range of slopes that can be represented in WRF simulations. The implementation of topographic effects on radiation is validated by comparing land surface fluxes, as well as temperature and velocity fields, between idealized WRF simulations both with and without IBM. Following validation, the topographic shading implementation is tested in a semirealistic simulation of flow over Granite Mountain, Utah, where topographic shading is known to affect downslope flow development in the evening. The horizontal grid spacing is 50 m and the vertical grid spacing is approximately 8–27 m near the surface. Such a case would fail to run in WRF with its native terrain-following coordinates because of large local slope values reaching up to 55°. Good agreement is found between modeled surface energy budget components and observations from the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) program at a location on the east slope of Granite Mountain. In addition, the model captures large spatiotemporal inhomogeneities in the surface sensible heat flux that are important for the development of thermally driven flows over complex terrain.
Abstract
Topographic effects on radiation, including both topographic shading and slope effects, are included in the Weather Research and Forecasting (WRF) Model, and here they are made compatible with the immersed boundary method (IBM). IBM is an alternative method for representing complex terrain that reduces numerical errors over sloped terrain, thus extending the range of slopes that can be represented in WRF simulations. The implementation of topographic effects on radiation is validated by comparing land surface fluxes, as well as temperature and velocity fields, between idealized WRF simulations both with and without IBM. Following validation, the topographic shading implementation is tested in a semirealistic simulation of flow over Granite Mountain, Utah, where topographic shading is known to affect downslope flow development in the evening. The horizontal grid spacing is 50 m and the vertical grid spacing is approximately 8–27 m near the surface. Such a case would fail to run in WRF with its native terrain-following coordinates because of large local slope values reaching up to 55°. Good agreement is found between modeled surface energy budget components and observations from the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) program at a location on the east slope of Granite Mountain. In addition, the model captures large spatiotemporal inhomogeneities in the surface sensible heat flux that are important for the development of thermally driven flows over complex terrain.
Abstract
In numerical weather prediction and in reanalysis, robust approaches for observation bias correction are necessary to approach optimal data assimilation. The success of bias correction can be limited by model errors. Here, simultaneous estimation of observation and model biases, and the model state for an analysis, is explored with ensemble data assimilation and a simple model. The approach is based on parameter estimation using an augmented state in an ensemble adjustment Kalman filter. The observation biases are modeled with a linear term added to the forward operator. A bias is introduced in the forcing term of the model, leading to a model with complex errors that can be used in imperfect-model assimilation experiments.
Under a range of model forcing biases and observation biases, accurate observation bias estimation and correction are possible when the model forcing bias is simultaneously estimated and corrected. In the presence of both model error and observation biases, estimating one and ignoring the other harms the assimilation more than not estimating any errors at all, because the biases are not correctly attributed. Neglecting a large model forcing bias while estimating observation biases results in filter divergence; the observation bias parameter absorbs the model forcing bias, and recursively and incorrectly increases the increments. Neglecting observation bias results in suboptimal assimilation, but the model forcing bias parameter estimate remains stable because the model dynamics ensure covariance between the parameter and the model state.
Abstract
In numerical weather prediction and in reanalysis, robust approaches for observation bias correction are necessary to approach optimal data assimilation. The success of bias correction can be limited by model errors. Here, simultaneous estimation of observation and model biases, and the model state for an analysis, is explored with ensemble data assimilation and a simple model. The approach is based on parameter estimation using an augmented state in an ensemble adjustment Kalman filter. The observation biases are modeled with a linear term added to the forward operator. A bias is introduced in the forcing term of the model, leading to a model with complex errors that can be used in imperfect-model assimilation experiments.
Under a range of model forcing biases and observation biases, accurate observation bias estimation and correction are possible when the model forcing bias is simultaneously estimated and corrected. In the presence of both model error and observation biases, estimating one and ignoring the other harms the assimilation more than not estimating any errors at all, because the biases are not correctly attributed. Neglecting a large model forcing bias while estimating observation biases results in filter divergence; the observation bias parameter absorbs the model forcing bias, and recursively and incorrectly increases the increments. Neglecting observation bias results in suboptimal assimilation, but the model forcing bias parameter estimate remains stable because the model dynamics ensure covariance between the parameter and the model state.
Abstract
Ensemble sensitivities have proven a useful alternative to adjoint sensitivities for large-scale dynamics, but their performance in multiscale flows has not been thoroughly examined. When computing sensitivities, the analysis covariance is usually approximated with the corresponding diagonal matrix, leading to a simple univariate regression problem rather than a more general multivariate regression problem. Sensitivity estimates are affected by sampling error arising from a finite ensemble and can lead to an overestimated response to an analysis perturbation. When forecasts depend on many details of an analysis, it is reasonable to expect that the diagonal approximation is too severe. Because spurious covariances are more likely when correlations are weak, computing the sensitivity with a multivariate regression that retains the full analysis covariance may increase the need for sampling error mitigation. The purpose of this work is to clarify the effects of the diagonal approximation, and investigate the need for mitigating spurious covariances arising from sampling error. A two-scale model with realistic spatial covariances is the basis for experimentation. For most problems, an efficient matrix inversion is possible by finding a minimum-norm solution, and employing appropriate matrix factorization. A published hierarchical approach for estimating regression factors for tapering (localizing) covariances is used to measure the effects of sampling error. Compared to univariate regressions in the diagonal approximation, skill in predicting a nonlinear response from the linear sensitivities is superior when localized multivariate sensitivities are used, particularly when fast scales are present, model error is present, and the observing network is sparse.
Abstract
Ensemble sensitivities have proven a useful alternative to adjoint sensitivities for large-scale dynamics, but their performance in multiscale flows has not been thoroughly examined. When computing sensitivities, the analysis covariance is usually approximated with the corresponding diagonal matrix, leading to a simple univariate regression problem rather than a more general multivariate regression problem. Sensitivity estimates are affected by sampling error arising from a finite ensemble and can lead to an overestimated response to an analysis perturbation. When forecasts depend on many details of an analysis, it is reasonable to expect that the diagonal approximation is too severe. Because spurious covariances are more likely when correlations are weak, computing the sensitivity with a multivariate regression that retains the full analysis covariance may increase the need for sampling error mitigation. The purpose of this work is to clarify the effects of the diagonal approximation, and investigate the need for mitigating spurious covariances arising from sampling error. A two-scale model with realistic spatial covariances is the basis for experimentation. For most problems, an efficient matrix inversion is possible by finding a minimum-norm solution, and employing appropriate matrix factorization. A published hierarchical approach for estimating regression factors for tapering (localizing) covariances is used to measure the effects of sampling error. Compared to univariate regressions in the diagonal approximation, skill in predicting a nonlinear response from the linear sensitivities is superior when localized multivariate sensitivities are used, particularly when fast scales are present, model error is present, and the observing network is sparse.
