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- Author or Editor: Jeng-Ming Chen x
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Abstract
When a turbulence closure model is used for cloud simulations, the effect of turbulence-scale saturation must be taken into account in determining the turbulent buoyancy flux. Sommeria and Deardorff derived statistical relations through which the fractional saturation or cloudiness and the mean liquid water specific humidity can be calculated from the moments of conservative thermodynamic quantities, such as total water specific humidity and liquid water potential temperature. In deriving these relations, however, they had to rely on assumptions that were only empirically justified.
Mellor showed, by a direct integration of the probability density function, that the assumptions which Sommeria and Deardorff used were not necessary for deriving those relations. But Mellor's direct integration method had to be carried out for each different relation, and can not be generalized to other derivations.
In the present paper, the same relations are derived from theorems on Gaussian distributions by introducing a new quantity, qx , which converts the original two-parameter turbulence-scale saturation parameterization problem to a single-parameter problem. A systematic solution method is established based on these theorems. Quantities involving liquid water specific humidity can be obtained through this parameterization from those conservative variables for which predictive equations are available and for which Gaussian distributions are presumed.
Abstract
When a turbulence closure model is used for cloud simulations, the effect of turbulence-scale saturation must be taken into account in determining the turbulent buoyancy flux. Sommeria and Deardorff derived statistical relations through which the fractional saturation or cloudiness and the mean liquid water specific humidity can be calculated from the moments of conservative thermodynamic quantities, such as total water specific humidity and liquid water potential temperature. In deriving these relations, however, they had to rely on assumptions that were only empirically justified.
Mellor showed, by a direct integration of the probability density function, that the assumptions which Sommeria and Deardorff used were not necessary for deriving those relations. But Mellor's direct integration method had to be carried out for each different relation, and can not be generalized to other derivations.
In the present paper, the same relations are derived from theorems on Gaussian distributions by introducing a new quantity, qx , which converts the original two-parameter turbulence-scale saturation parameterization problem to a single-parameter problem. A systematic solution method is established based on these theorems. Quantities involving liquid water specific humidity can be obtained through this parameterization from those conservative variables for which predictive equations are available and for which Gaussian distributions are presumed.
Abstract
This study attempts to isolate the dynamic and microphysical effects of seeding. A two-dimensional, time-dependent cloud model has been used to simulate silver iodide (AgI) seeding of convective clouds. Two major dynamic effects (latent heat of fusion and condensate loading) are separated through a sequence of differential processes to examine their individual effect. A High Plains sounding is used for the tests.
The effects of condensate loading and latent heat of fusion are due to natural processes as well as to cloud seeding. Separate discussions and comparisons are made of both processes. Condensate loading has the greater influence on cloud development.
A method of differencing the results from different cases is used to illustrate the overall seeding effects and to isolate those portions of the latent heat of fusion and loading effects which are due solely to ice-phase cloud seeding. The results indicate significant fusion and loading effects due to seeding, but at 10 min or so after the seeding. Glaciation via accretional freezing of the cloud water is accomplished at this time. Direct seeding glaciation of this vigorous cloud within a minute or so of seeding time is not accomplished.
The model results show a natural cloud system that consists of three cloud cycles during the period of integration (covering a real-time period of about one hour). The first cloud cycle is produced by a model thermal and humidity perturbation, the two second-cycle clouds are set off by the acceleration stage of the first cloud, and the third-cycle clouds are initiated by downdraft outflow induced by falling precipitation in the boundary layer. Major cloud growth and precipitation formation are caused by interactions of the second-cycle clouds with the first cloud.
The seeded cloud system, although identical to the unseeded system until seeding is simulated (at 19 min of simulated real-time), forms precipitation earlier than the unseeded system and produces four cloud cycles during the 60 min of simulated real-time. The first-cycle cloud is more vigorous than its unseeded counterpart, but the earlier formed precipitation interacts destructively with the two second-cycle clouds, denying their liquid water contents to the later growth stages of the first-cycle cloud. The third- and fourth-cycle clouds are produced by precipitation-induced downdraft outflow, but are weak and produce little precipitation.
Those cases with the loading effect turned off develop much more rapidly than those with the latent heat of fusion effect turned off. Compared with a “normal” run (i.e., all effects turned on), peak values of domain-averaged kinetic energy increase by nearly 100% with the loading effect off and decrease by 40% with the latent heat of fusion effect turned off. Of course, loading is always present in a cloud—latent heat of fusion may or may not depend on the development of the cells. The premature sweepout of the second-cycle cloud liquid by first-cycle precipitation from above, before the cloud liquid has a chance to freeze, thus decreases the intensity of storm development.
Abstract
This study attempts to isolate the dynamic and microphysical effects of seeding. A two-dimensional, time-dependent cloud model has been used to simulate silver iodide (AgI) seeding of convective clouds. Two major dynamic effects (latent heat of fusion and condensate loading) are separated through a sequence of differential processes to examine their individual effect. A High Plains sounding is used for the tests.
The effects of condensate loading and latent heat of fusion are due to natural processes as well as to cloud seeding. Separate discussions and comparisons are made of both processes. Condensate loading has the greater influence on cloud development.
A method of differencing the results from different cases is used to illustrate the overall seeding effects and to isolate those portions of the latent heat of fusion and loading effects which are due solely to ice-phase cloud seeding. The results indicate significant fusion and loading effects due to seeding, but at 10 min or so after the seeding. Glaciation via accretional freezing of the cloud water is accomplished at this time. Direct seeding glaciation of this vigorous cloud within a minute or so of seeding time is not accomplished.
The model results show a natural cloud system that consists of three cloud cycles during the period of integration (covering a real-time period of about one hour). The first cloud cycle is produced by a model thermal and humidity perturbation, the two second-cycle clouds are set off by the acceleration stage of the first cloud, and the third-cycle clouds are initiated by downdraft outflow induced by falling precipitation in the boundary layer. Major cloud growth and precipitation formation are caused by interactions of the second-cycle clouds with the first cloud.
The seeded cloud system, although identical to the unseeded system until seeding is simulated (at 19 min of simulated real-time), forms precipitation earlier than the unseeded system and produces four cloud cycles during the 60 min of simulated real-time. The first-cycle cloud is more vigorous than its unseeded counterpart, but the earlier formed precipitation interacts destructively with the two second-cycle clouds, denying their liquid water contents to the later growth stages of the first-cycle cloud. The third- and fourth-cycle clouds are produced by precipitation-induced downdraft outflow, but are weak and produce little precipitation.
Those cases with the loading effect turned off develop much more rapidly than those with the latent heat of fusion effect turned off. Compared with a “normal” run (i.e., all effects turned on), peak values of domain-averaged kinetic energy increase by nearly 100% with the loading effect off and decrease by 40% with the latent heat of fusion effect turned off. Of course, loading is always present in a cloud—latent heat of fusion may or may not depend on the development of the cells. The premature sweepout of the second-cycle cloud liquid by first-cycle precipitation from above, before the cloud liquid has a chance to freeze, thus decreases the intensity of storm development.
Abstract
Application of an empirical orthogonal function (EOF) analysis to a data matrix that contains two or more variable fields has been referred to as extended EOF (EEOF) analysis. Coherence between individual features contained within one EEOF has been implied to represent interrelationships between the fields (in the case of a combination of different variables) or propagating features (in the case of the same field at different times). However, caution must be exercised in the interpretation of interrelationships within one EEOF because the derivation of the EEOFs is based on the optimization of the variance of every EEOF as an entity and may not indicate correlations among substructures within one EEOF. These types of problems associated with interpretation of EEOF analyses are highlighted through an analytic example and application to a dataset with known statistical properties.
Although other multivariate analysis techniques such as singular value decomposition and canonical correlation analysis are being used with more frequency, it is important to highlight potential difficulties associated with the EEOF technique that has been an integral analysis tool in meteorological research.
Abstract
Application of an empirical orthogonal function (EOF) analysis to a data matrix that contains two or more variable fields has been referred to as extended EOF (EEOF) analysis. Coherence between individual features contained within one EEOF has been implied to represent interrelationships between the fields (in the case of a combination of different variables) or propagating features (in the case of the same field at different times). However, caution must be exercised in the interpretation of interrelationships within one EEOF because the derivation of the EEOFs is based on the optimization of the variance of every EEOF as an entity and may not indicate correlations among substructures within one EEOF. These types of problems associated with interpretation of EEOF analyses are highlighted through an analytic example and application to a dataset with known statistical properties.
Although other multivariate analysis techniques such as singular value decomposition and canonical correlation analysis are being used with more frequency, it is important to highlight potential difficulties associated with the EEOF technique that has been an integral analysis tool in meteorological research.
Abstract
In Part I a multiple-set canonical correlation analysis (MCCA) was proposed to generalize the conventional two-set canonical correlation analysis. The MCCA seeks the optimal correlation among more than two data fields through a diagonalization of the product or the squared product of the correlation matrices between selected (desired) field pairs. In this study a specific case is used to empirically test the sensitivities of the MCCA technique. The case study uses an MCCA application of the 850-hPa meridional wind data over the tropical western Pacific to study tropical synoptic wave disturbances during summer. Successive 12-h meridional winds are used as the different data fields. The result shows that the method is stable with respect to sampling changes when the data contain significant signals of physical phenomenon and not stable when the data are random. The study also confirms the use of the largest residual correlation, or the largest cross-component correlation, as a preliminary significance test for the technique.
Abstract
In Part I a multiple-set canonical correlation analysis (MCCA) was proposed to generalize the conventional two-set canonical correlation analysis. The MCCA seeks the optimal correlation among more than two data fields through a diagonalization of the product or the squared product of the correlation matrices between selected (desired) field pairs. In this study a specific case is used to empirically test the sensitivities of the MCCA technique. The case study uses an MCCA application of the 850-hPa meridional wind data over the tropical western Pacific to study tropical synoptic wave disturbances during summer. Successive 12-h meridional winds are used as the different data fields. The result shows that the method is stable with respect to sampling changes when the data contain significant signals of physical phenomenon and not stable when the data are random. The study also confirms the use of the largest residual correlation, or the largest cross-component correlation, as a preliminary significance test for the technique.
Abstract
A multiple-set canonical correlation analysis (MCCA), which can be used to study atmospheric motions by analyzing the relationships among more than two sets of data fields, is proposed. By using the product or squared product of correlation matrices as the optimization criterion, this method generalizes the two-set canonical correlation analysis (CCA) and reduces the complications associated with the supermatrix approaches previously proposed in statistical textbooks. The final optimization equations can be greatly simplified to involve weighting functions of one field at a time. Furthermore, excluding or emphasizing correlations between special field pairs based on physical considerations can be easily implemented.
The method is identical to a supermatrix approach based on maximizing the product of canonical correlation coefficients when the individual canonical correlation matrices are perfectly diagonal. This would be true for idealized data that contain only orthogonal motion systems so that all datasets are perfectly correlated. In such a case, all supermatrix methods will also converge to the same solution. In real cases, cross-component correlations will occur, and their largest values, called largest residual correlations (LRCs), are a crude measure of the validity of the approximation. When LRCs are small compared to the corresponding canonical correlation coefficients, the results are reliable. Otherwise, solutions of different methods diverge and are all doubtful.
A statistical textbook example illustrates that solutions obtained are comparable to those from the supermatrix methods, and the relative LRCs are about 20%. A meteorological application example shows that, compared to the two-set CCA, the proposed MCCA gives a more powerful concentration of variance in the leading modes and higher canonical correlation coefficients. The resultant relative LRCs are small throughout all leading modes, apparently because meteorological data contain highly correlated variations.
The proposed technique nay also be applied to the singular-value decomposition analysis to allow a multiple-set singular-value decomposition analysis to be used on mart than two sets of data fields.
Abstract
A multiple-set canonical correlation analysis (MCCA), which can be used to study atmospheric motions by analyzing the relationships among more than two sets of data fields, is proposed. By using the product or squared product of correlation matrices as the optimization criterion, this method generalizes the two-set canonical correlation analysis (CCA) and reduces the complications associated with the supermatrix approaches previously proposed in statistical textbooks. The final optimization equations can be greatly simplified to involve weighting functions of one field at a time. Furthermore, excluding or emphasizing correlations between special field pairs based on physical considerations can be easily implemented.
The method is identical to a supermatrix approach based on maximizing the product of canonical correlation coefficients when the individual canonical correlation matrices are perfectly diagonal. This would be true for idealized data that contain only orthogonal motion systems so that all datasets are perfectly correlated. In such a case, all supermatrix methods will also converge to the same solution. In real cases, cross-component correlations will occur, and their largest values, called largest residual correlations (LRCs), are a crude measure of the validity of the approximation. When LRCs are small compared to the corresponding canonical correlation coefficients, the results are reliable. Otherwise, solutions of different methods diverge and are all doubtful.
A statistical textbook example illustrates that solutions obtained are comparable to those from the supermatrix methods, and the relative LRCs are about 20%. A meteorological application example shows that, compared to the two-set CCA, the proposed MCCA gives a more powerful concentration of variance in the leading modes and higher canonical correlation coefficients. The resultant relative LRCs are small throughout all leading modes, apparently because meteorological data contain highly correlated variations.
The proposed technique nay also be applied to the singular-value decomposition analysis to allow a multiple-set singular-value decomposition analysis to be used on mart than two sets of data fields.
Abstract
A simple statistical-synoptic technique for tropical cyclone (TC) track forecasting to 72 h in the western North Pacific is derived. This technique applies to the standard (S) pattern/dominant ridge region (S/DR) and poleward/poleward-oriented (P/PO) combinations, which are the two most common and represent about 73% of all situations. Only eight predictors that involve present and past 12-h and 24-h positions, intensity, and date are used. The track predictions are simple to calculate and understand; are available in near–real time each 6 h; apply at all intensities, as compared to the complex global or regional dynamical model predictions that are only available each 12 h at about 3–4 h after synoptic time; are not calculated for weak TCs; and tend to have accurate predictions only for tropical storm stage and above. The statistical-synoptic technique for S/DR cases has an improvement (skill) relative to the operational climatology and persistence (WPCLPR) technique of 12% after 12 h and 24% after 72 h if the TC remains in the S/DR pattern/region for the entire 72 h. The statistical-synoptic technique for P/PO cases have an improvement relative to WPCLPR of 11% after 12 h and about 13% for 72-h forecasts if the TC remains in P/PO for the entire 72 h.
Assuming a perfect knowledge of the S/DR to P/PO and P/PO to S/DR transitions, a simple blending of a composite post-transition track with the statistical-synoptic technique is tested. For the 72-h forecasts initiated 12 h before the S/DR to P/PO transition, the statistical-synoptic track error is about 290 n mi (537 km) compared to 410 n mi (759 km) for WPCLPR. For corresponding P/PO to S/DR transition, the statistical-synoptic technique 72-h error is 215 n mi (398 km) compared to about 485 n mi (898 km) for WPCLPR.
Abstract
A simple statistical-synoptic technique for tropical cyclone (TC) track forecasting to 72 h in the western North Pacific is derived. This technique applies to the standard (S) pattern/dominant ridge region (S/DR) and poleward/poleward-oriented (P/PO) combinations, which are the two most common and represent about 73% of all situations. Only eight predictors that involve present and past 12-h and 24-h positions, intensity, and date are used. The track predictions are simple to calculate and understand; are available in near–real time each 6 h; apply at all intensities, as compared to the complex global or regional dynamical model predictions that are only available each 12 h at about 3–4 h after synoptic time; are not calculated for weak TCs; and tend to have accurate predictions only for tropical storm stage and above. The statistical-synoptic technique for S/DR cases has an improvement (skill) relative to the operational climatology and persistence (WPCLPR) technique of 12% after 12 h and 24% after 72 h if the TC remains in the S/DR pattern/region for the entire 72 h. The statistical-synoptic technique for P/PO cases have an improvement relative to WPCLPR of 11% after 12 h and about 13% for 72-h forecasts if the TC remains in P/PO for the entire 72 h.
Assuming a perfect knowledge of the S/DR to P/PO and P/PO to S/DR transitions, a simple blending of a composite post-transition track with the statistical-synoptic technique is tested. For the 72-h forecasts initiated 12 h before the S/DR to P/PO transition, the statistical-synoptic track error is about 290 n mi (537 km) compared to 410 n mi (759 km) for WPCLPR. For corresponding P/PO to S/DR transition, the statistical-synoptic technique 72-h error is 215 n mi (398 km) compared to about 485 n mi (898 km) for WPCLPR.
Abstract
The Central Weather Bureau (CWB) in Taipei, Republic of China has entered the era of operational numerical weather prediction with the complete online operations of a Global Forecast System (GFS) and the Limited-Area Forecast Systems (LAFS). A brief description of the Regional Forecast System (RFS) and the Mesoscale Forecast System (MFS) of the LAFS are presented in this paper. The RFS has a horizontal resolution of 90 km, depends on the GFS for boundary values, and produces forecast up to 48 h over the eastern parts of Asia and the northwestern Pacific Ocean. The MFS has a resolution of 45 km, uses RFS analysis and forecast as initial and boundary conditions, and produces 24-h forecasts for Taiwan and its immediate vicinity. Model configurations, numerics, physical parameterizations, performance statistics, and two significant weather cases of the two forecast systems are discussed. Future improvements and new plans will also be given.
Abstract
The Central Weather Bureau (CWB) in Taipei, Republic of China has entered the era of operational numerical weather prediction with the complete online operations of a Global Forecast System (GFS) and the Limited-Area Forecast Systems (LAFS). A brief description of the Regional Forecast System (RFS) and the Mesoscale Forecast System (MFS) of the LAFS are presented in this paper. The RFS has a horizontal resolution of 90 km, depends on the GFS for boundary values, and produces forecast up to 48 h over the eastern parts of Asia and the northwestern Pacific Ocean. The MFS has a resolution of 45 km, uses RFS analysis and forecast as initial and boundary conditions, and produces 24-h forecasts for Taiwan and its immediate vicinity. Model configurations, numerics, physical parameterizations, performance statistics, and two significant weather cases of the two forecast systems are discussed. Future improvements and new plans will also be given.
