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- Author or Editor: Xiang-Yu Huang x
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Abstract
A generalized setup is proposed for the poor man’s 4D variational data assimilation system (PMV) of Huang et al. The new scheme is referred to as a generalization of PMV (GPV) and has the same basic idea as that of PMV, that is, to use an adjoint model to improve an optimum interpolation (OI)–based assimilation system. In addition, GPV includes the possibility of using different forecast models in the original OI-based assimilation system and in the variational component of the scheme. This generalization leads to three advantages over the original setup: 1) a wider application of an adjoint model developed for a particular forecast model; 2) an implementation flexibility due to its incremental nature; 3) considerable CPU savings when the variational component is run on low resolutions.
A detailed comparison is made between GPV and PMV. The steps of a practical implementation are also given. A 5-day period characterized by intense cyclone development is chosen for testing different data assimilation schemes. Experiments with GPV using a low-resolution variational component based on different model formulations indicate that the proposed scheme GPV, as its predecessor PMV, also leads to better first guess fields, smaller analysis increments, modified baroclinic structures in the final analyses, and improved forecasts. The differences between the GPV analyses and the original OI-based analyses are mainly in the data-sparse area and are related to baroclinic processes.
Abstract
A generalized setup is proposed for the poor man’s 4D variational data assimilation system (PMV) of Huang et al. The new scheme is referred to as a generalization of PMV (GPV) and has the same basic idea as that of PMV, that is, to use an adjoint model to improve an optimum interpolation (OI)–based assimilation system. In addition, GPV includes the possibility of using different forecast models in the original OI-based assimilation system and in the variational component of the scheme. This generalization leads to three advantages over the original setup: 1) a wider application of an adjoint model developed for a particular forecast model; 2) an implementation flexibility due to its incremental nature; 3) considerable CPU savings when the variational component is run on low resolutions.
A detailed comparison is made between GPV and PMV. The steps of a practical implementation are also given. A 5-day period characterized by intense cyclone development is chosen for testing different data assimilation schemes. Experiments with GPV using a low-resolution variational component based on different model formulations indicate that the proposed scheme GPV, as its predecessor PMV, also leads to better first guess fields, smaller analysis increments, modified baroclinic structures in the final analyses, and improved forecasts. The differences between the GPV analyses and the original OI-based analyses are mainly in the data-sparse area and are related to baroclinic processes.
Abstract
In this paper the standard variational analysis scheme is modified, through a simple transform, to avoid the inversion of the background error covariance matrix. A close inspection of the modified scheme reveals that it is possible to use a filter to replace the multiplication of the covariance matrix. A variational analysis scheme using a filter is then formulated, which does not explicitly involve the covariance matrix. The modified scheme and the filter scheme have the advantage of avoiding the inversion or any usage of the large matrix for analyses using gridpoint representation. To illustrate the use of these schemes, a small-sized and a more realistic analysis problem is considered using real temperature observations. It is found that both the modified scheme and the filter scheme work well. Compared to the standard and modified schemes the storage and computational requirements of the filter scheme can be reduced by several orders of magnitude for realistic atmospheric applications.
Abstract
In this paper the standard variational analysis scheme is modified, through a simple transform, to avoid the inversion of the background error covariance matrix. A close inspection of the modified scheme reveals that it is possible to use a filter to replace the multiplication of the covariance matrix. A variational analysis scheme using a filter is then formulated, which does not explicitly involve the covariance matrix. The modified scheme and the filter scheme have the advantage of avoiding the inversion or any usage of the large matrix for analyses using gridpoint representation. To illustrate the use of these schemes, a small-sized and a more realistic analysis problem is considered using real temperature observations. It is found that both the modified scheme and the filter scheme work well. Compared to the standard and modified schemes the storage and computational requirements of the filter scheme can be reduced by several orders of magnitude for realistic atmospheric applications.
Abstract
Cloud water content (CWC) is not treated in most operational objective analyses and initialization schemes. When CWC is used as a prognostic variable in a forecast model, it is necessary to define this variable at the initial time. A commonly used method is to set the initial CWC to zero or use a forecast CWC field from the previous data-assimilation cycle (the first-guess field for the objective analysis) without any modification. The inconsistent treatment of CWC and other fields leads to an imbalance between the first-guess cloud water field and other analyzed fields (winds, temperature humidity, and surface pressure). In this study. the diabatic digital-filtering initialization scheme is used to alleviate this imbalance. It is shown that an intermittent data assimilation system with this initialization scheme can produce a better cloud evolution, a shorter spinup time, and a removal of the initial shock in precipitation.
Abstract
Cloud water content (CWC) is not treated in most operational objective analyses and initialization schemes. When CWC is used as a prognostic variable in a forecast model, it is necessary to define this variable at the initial time. A commonly used method is to set the initial CWC to zero or use a forecast CWC field from the previous data-assimilation cycle (the first-guess field for the objective analysis) without any modification. The inconsistent treatment of CWC and other fields leads to an imbalance between the first-guess cloud water field and other analyzed fields (winds, temperature humidity, and surface pressure). In this study. the diabatic digital-filtering initialization scheme is used to alleviate this imbalance. It is shown that an intermittent data assimilation system with this initialization scheme can produce a better cloud evolution, a shorter spinup time, and a removal of the initial shock in precipitation.
Abstract
In this paper several configurations of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5), which is implemented at Beijing Institute of Urban Meteorology in China, are used to demonstrate the initial noise problem caused either by interpolating global model fields onto an MM5 grid or by using MM5 objective analysis schemes. An implementation of a digital filter initialization (DFI) package to MM5 is then documented. A heavy rain case study and intermittent data assimilation experiments are used to assess the impact of DFI on MM5 forecasts. It is shown that DFI effectively filters out the noise and produces a balanced initial model state. It is also shown that DFI improves the spinup aspects for precipitation, leading to better scores for short-range precipitation forecasts. The issues related to the initialization of variables that are not observed and/or analyzed, in particular those for nonhydrostatic quantities, are discussed.
Abstract
In this paper several configurations of the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5), which is implemented at Beijing Institute of Urban Meteorology in China, are used to demonstrate the initial noise problem caused either by interpolating global model fields onto an MM5 grid or by using MM5 objective analysis schemes. An implementation of a digital filter initialization (DFI) package to MM5 is then documented. A heavy rain case study and intermittent data assimilation experiments are used to assess the impact of DFI on MM5 forecasts. It is shown that DFI effectively filters out the noise and produces a balanced initial model state. It is also shown that DFI improves the spinup aspects for precipitation, leading to better scores for short-range precipitation forecasts. The issues related to the initialization of variables that are not observed and/or analyzed, in particular those for nonhydrostatic quantities, are discussed.
Abstract
An initialization scheme for numerical models containing treatment of cloudiness is presented. The dynamic type of initialization scheme is based on the digital filtering technique, which requires integration of the model backward and forward about the analysis time. As the numerical model contains an advanced condensation-cloud parameterization, the initialization procedure renders initial cloud water and cloud cover fields, yet no cloud observations have been available. The initial cloud fields obtained are in a good agreement with the weather situations as they appear on satellite imagery and in synoptic analyses. The cloud water content is of the same order of magnitude as the one obtained from a 24-h forecast with the model. Improvements are observed in the spinup of the model cloud and of the precipitation rate.
Abstract
An initialization scheme for numerical models containing treatment of cloudiness is presented. The dynamic type of initialization scheme is based on the digital filtering technique, which requires integration of the model backward and forward about the analysis time. As the numerical model contains an advanced condensation-cloud parameterization, the initialization procedure renders initial cloud water and cloud cover fields, yet no cloud observations have been available. The initial cloud fields obtained are in a good agreement with the weather situations as they appear on satellite imagery and in synoptic analyses. The cloud water content is of the same order of magnitude as the one obtained from a 24-h forecast with the model. Improvements are observed in the spinup of the model cloud and of the precipitation rate.
Abstract
A digital-filtering initialization scheme, which includes the effects of diabatic processes, has been formulated. This scheme gives a lower noise level in the forecast and a better organized initial pressure-tendency field than for the corresponding adiabatic initialization. The implementation of the scheme is very easy, requiring only the calculation of the filter coefficients and minor adjustments to the model code.
The computational expense of the digital-filtering initialization is directly proportional to the length of the time span over which the filter is applied. By a careful choice of filter weights, based on optimal filter theory, the span of the filter can be reduced by a factor of 2 or 3, with a corresponding increase in efficiency.
Abstract
A digital-filtering initialization scheme, which includes the effects of diabatic processes, has been formulated. This scheme gives a lower noise level in the forecast and a better organized initial pressure-tendency field than for the corresponding adiabatic initialization. The implementation of the scheme is very easy, requiring only the calculation of the filter coefficients and minor adjustments to the model code.
The computational expense of the digital-filtering initialization is directly proportional to the length of the time span over which the filter is applied. By a careful choice of filter weights, based on optimal filter theory, the span of the filter can be reduced by a factor of 2 or 3, with a corresponding increase in efficiency.
Abstract
Spurious high-frequency oscillations occur in forecasts made with the primitive equations if the initial fields of mass and wind are not in an appropriate state of balance with each other. These oscillations are due to gravity-inertia waves of unrealistically large amplitude; the primary purpose of initialization is the removal or reduction of this high-frequency noise by a delicate adjustment of the analyzed data. In this paper a simple method of eliminating spurious oscillations is presented. The method uses a digital filter applied to time series of the model variables generated by short-range forward and backward integrations from the initial time.
The digital filtering technique is applied to initialize data for the High-Resolution Limited-Area Model (HIRLAM). The method is shown to have the three characteristics essential to any satisfactory initialization scheme: (i) high-frequency noise is effectively removed from the forecast; (ii) changes made to the analyzed fields are acceptably small; (iii) the forecast is not degraded by application of the initialization.
The digital filtering initialization (DFI) technique is compared to the standard nonlinear normal-mode initialization (NMI) used with the HIRLAM model. Both methods yield comparable results, though the filtering appears more effective in suppressing noise in the early forecast hours. The computation time required for initialization is about the same for DFI and NMI. The outstanding appeal of the digital filtering technique is its great simplicity in conception and application.
Abstract
Spurious high-frequency oscillations occur in forecasts made with the primitive equations if the initial fields of mass and wind are not in an appropriate state of balance with each other. These oscillations are due to gravity-inertia waves of unrealistically large amplitude; the primary purpose of initialization is the removal or reduction of this high-frequency noise by a delicate adjustment of the analyzed data. In this paper a simple method of eliminating spurious oscillations is presented. The method uses a digital filter applied to time series of the model variables generated by short-range forward and backward integrations from the initial time.
The digital filtering technique is applied to initialize data for the High-Resolution Limited-Area Model (HIRLAM). The method is shown to have the three characteristics essential to any satisfactory initialization scheme: (i) high-frequency noise is effectively removed from the forecast; (ii) changes made to the analyzed fields are acceptably small; (iii) the forecast is not degraded by application of the initialization.
The digital filtering initialization (DFI) technique is compared to the standard nonlinear normal-mode initialization (NMI) used with the HIRLAM model. Both methods yield comparable results, though the filtering appears more effective in suppressing noise in the early forecast hours. The computation time required for initialization is about the same for DFI and NMI. The outstanding appeal of the digital filtering technique is its great simplicity in conception and application.
Abstract
The objective of this study is to examine the performance of the adiabatic digital filtering initialization scheme of Lynch and Huang, the diabatic digital filtering initialization scheme of Huang and Lynch, and the diabatic nonlinear normal-mode initialization scheme of Cederskov in a complete data assimilation system. In particular, the authors wish to examine the handling of observations and the changes that the initialization makes to the analysis in an intermittent data assimilation cycle. As a reference the authors use the adiabatic nonlinear normal-mode initialization of Machenhauer, formulated according to Bijlsma and Hafkenscheid, which is the current operational initialization scheme at the, Danish Meteorological Institute.
The initialization schemes tested are found to produce a well-balanced model state that is at least as good as that produced by the reference scheme. Furthermore, the changes to the analysis made by the different initialization schemes are similar and the observations are therefore treated similarly with the different schemes. It is thus found that the introduction of a new initialization procedure has no detrimental effect on the data assimilation cycle. On the contrary, the two diabatic schemes reduce the noise level considerably compared to the adiabatic ones albeit at an increased computational cost. Considering the advantages of a diabatic scheme, in particular the future possibility of including cloud properties in the initialization procedure (Huang and Sundqvist), the use of a diabatic scheme seems well justified. The noise reduction is perhaps not the most important aspect as all schemes behave identically in the handling of observations. Instead, the possibility of including satellite-derived cloudiness and precipitation data in the analysis and initialization cycle is a much move important aspect. From this point of view the digital filter has a clear advantage over the normal-mode initialization scheme as all dependent variables of the model are initialized.
Abstract
The objective of this study is to examine the performance of the adiabatic digital filtering initialization scheme of Lynch and Huang, the diabatic digital filtering initialization scheme of Huang and Lynch, and the diabatic nonlinear normal-mode initialization scheme of Cederskov in a complete data assimilation system. In particular, the authors wish to examine the handling of observations and the changes that the initialization makes to the analysis in an intermittent data assimilation cycle. As a reference the authors use the adiabatic nonlinear normal-mode initialization of Machenhauer, formulated according to Bijlsma and Hafkenscheid, which is the current operational initialization scheme at the, Danish Meteorological Institute.
The initialization schemes tested are found to produce a well-balanced model state that is at least as good as that produced by the reference scheme. Furthermore, the changes to the analysis made by the different initialization schemes are similar and the observations are therefore treated similarly with the different schemes. It is thus found that the introduction of a new initialization procedure has no detrimental effect on the data assimilation cycle. On the contrary, the two diabatic schemes reduce the noise level considerably compared to the adiabatic ones albeit at an increased computational cost. Considering the advantages of a diabatic scheme, in particular the future possibility of including cloud properties in the initialization procedure (Huang and Sundqvist), the use of a diabatic scheme seems well justified. The noise reduction is perhaps not the most important aspect as all schemes behave identically in the handling of observations. Instead, the possibility of including satellite-derived cloudiness and precipitation data in the analysis and initialization cycle is a much move important aspect. From this point of view the digital filter has a clear advantage over the normal-mode initialization scheme as all dependent variables of the model are initialized.
Abstract
This study compares the performance of an ensemble Kalman filter (EnKF) with both the three-dimensional and four-dimensional variational data assimilation (3DVar and 4DVar) methods of the Weather Research and Forecasting (WRF) model over the contiguous United States in a warm-season month (June) of 2003. The data assimilated every 6 h include conventional sounding and surface observations as well as data from wind profilers, ships and aircraft, and the cloud-tracked winds from satellites. The performances of these methods are evaluated through verifying the 12- to 72-h forecasts initialized twice daily from the analysis of each method against the standard sounding observations. It is found that 4DVar has consistently smaller error than that of 3DVar for winds and temperature at all forecast lead times except at 60 and 72 h when their forecast errors become comparable in amplitude, while the two schemes have similar performance in moisture at all lead times. The forecast error of the EnKF is comparable to that of the 4DVar at 12–36-h lead times, both of which are substantially smaller than that of the 3DVar, despite the fact that 3DVar fits the sounding observations much more closely at the analysis time. The advantage of the EnKF becomes even more evident at 48–72-h lead times; the 72-h forecast error of the EnKF is comparable in magnitude to the 48-h error of 3DVar/4DVar.
Abstract
This study compares the performance of an ensemble Kalman filter (EnKF) with both the three-dimensional and four-dimensional variational data assimilation (3DVar and 4DVar) methods of the Weather Research and Forecasting (WRF) model over the contiguous United States in a warm-season month (June) of 2003. The data assimilated every 6 h include conventional sounding and surface observations as well as data from wind profilers, ships and aircraft, and the cloud-tracked winds from satellites. The performances of these methods are evaluated through verifying the 12- to 72-h forecasts initialized twice daily from the analysis of each method against the standard sounding observations. It is found that 4DVar has consistently smaller error than that of 3DVar for winds and temperature at all forecast lead times except at 60 and 72 h when their forecast errors become comparable in amplitude, while the two schemes have similar performance in moisture at all lead times. The forecast error of the EnKF is comparable to that of the 4DVar at 12–36-h lead times, both of which are substantially smaller than that of the 3DVar, despite the fact that 3DVar fits the sounding observations much more closely at the analysis time. The advantage of the EnKF becomes even more evident at 48–72-h lead times; the 72-h forecast error of the EnKF is comparable in magnitude to the 48-h error of 3DVar/4DVar.
Abstract
The major goal of this two-part study is to assimilate radar data into the high-resolution Advanced Research Weather Research and Forecasting Model (ARW-WRF) for the improvement of short-term quantitative precipitation forecasting (QPF) using a four-dimensional variational data assimilation (4D-Var) technique. In Part I the development of a radar data assimilation scheme within the WRF 4D-Var system (WRF 4D-Var) and the preliminary testing of the scheme are described. In Part II the performance of the enhanced WRF 4D-Var system is examined by comparing it with the three-dimensional variational data assimilation system (WRF 3D-Var) for a convective system over the U.S. Great Plains. The WRF 4D-Var radar data assimilation system has been developed with the existing framework of an incremental formulation. The new development for radar data assimilation includes the tangent-linear and adjoint models of a Kessler warm-rain microphysics scheme and the new control variables of cloud water, rainwater, and vertical velocity and their error statistics. An ensemble forecast with 80 members is used to produce background error covariance. The preliminary testing presented in this paper includes single-observation experiments as well as real data assimilation experiments on a squall line with assimilation windows of 5, 15, and 30 min. The results indicate that the system is able to obtain anisotropic multivariate analyses at the convective scale and improve precipitation forecasts. The results also suggest that the incremental approach with successive basic-state updates works well at the convection-permitting scale for radar data assimilation with the selected assimilation windows.
Abstract
The major goal of this two-part study is to assimilate radar data into the high-resolution Advanced Research Weather Research and Forecasting Model (ARW-WRF) for the improvement of short-term quantitative precipitation forecasting (QPF) using a four-dimensional variational data assimilation (4D-Var) technique. In Part I the development of a radar data assimilation scheme within the WRF 4D-Var system (WRF 4D-Var) and the preliminary testing of the scheme are described. In Part II the performance of the enhanced WRF 4D-Var system is examined by comparing it with the three-dimensional variational data assimilation system (WRF 3D-Var) for a convective system over the U.S. Great Plains. The WRF 4D-Var radar data assimilation system has been developed with the existing framework of an incremental formulation. The new development for radar data assimilation includes the tangent-linear and adjoint models of a Kessler warm-rain microphysics scheme and the new control variables of cloud water, rainwater, and vertical velocity and their error statistics. An ensemble forecast with 80 members is used to produce background error covariance. The preliminary testing presented in this paper includes single-observation experiments as well as real data assimilation experiments on a squall line with assimilation windows of 5, 15, and 30 min. The results indicate that the system is able to obtain anisotropic multivariate analyses at the convective scale and improve precipitation forecasts. The results also suggest that the incremental approach with successive basic-state updates works well at the convection-permitting scale for radar data assimilation with the selected assimilation windows.
