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Abstract
The purpose of this paper is two-fold; first, to document and present a limited-area, moist primitive equation model and, second, to give some preliminary results of experiments testing the sensitivity of the model's quantitative precipitation forecasts to the initial horizontal and vertical relative humidity distribution. Three experiments were performed. The first case used a 1.5 km vertical grid and a Gandin humidity analysis based on standard rawinsonde observations. The results indicate that the model has some skill at forecasting precipitation amounts and location in regions of predominately stable rain and in regions of convective rain. However, some glaring defects in both the initialization of the mass-flow fields and the initialization of the moisture field were evident.
The second experiment attempted to enhance the initial moisture field to reflect a narrow band of moisture which was suggested by satellite cloud observations. The inclusion of this moisture band increased the precipitation amounts in the squall-line region which was being fed by the enhanced moisture.
The third experiment in which the low-level vertical grid increment was reduced indicates that in some areas the precipitation amounts are increased by as much as 25% due to increased resolution of the low-level moisture field. This precipitation forecast most nearly agreed with observations.
Abstract
The purpose of this paper is two-fold; first, to document and present a limited-area, moist primitive equation model and, second, to give some preliminary results of experiments testing the sensitivity of the model's quantitative precipitation forecasts to the initial horizontal and vertical relative humidity distribution. Three experiments were performed. The first case used a 1.5 km vertical grid and a Gandin humidity analysis based on standard rawinsonde observations. The results indicate that the model has some skill at forecasting precipitation amounts and location in regions of predominately stable rain and in regions of convective rain. However, some glaring defects in both the initialization of the mass-flow fields and the initialization of the moisture field were evident.
The second experiment attempted to enhance the initial moisture field to reflect a narrow band of moisture which was suggested by satellite cloud observations. The inclusion of this moisture band increased the precipitation amounts in the squall-line region which was being fed by the enhanced moisture.
The third experiment in which the low-level vertical grid increment was reduced indicates that in some areas the precipitation amounts are increased by as much as 25% due to increased resolution of the low-level moisture field. This precipitation forecast most nearly agreed with observations.
Abstract
On 25 April 1975, as part of the National Aeronautics and Space Administration's Atmospheric Variability Experiment IV, frequent upper-air soundings were taken at eastern United States synoptic sounding sites. An intense, long-lived mesoscale convective weather system developed late in the AVE IV period and moved eastward during the remainder of the experiment. With the use of dry and moist numerical simulations, performed with Drexel University's Limited Area and Mesoscale Prediction System (LAMPS), interaction between the widespread, long-lived convective complex and its large-scale environment are examined.
Dissecting the differences between moist and dry simulations reveals that, within the moist numerical simulation, significant up-scale feedbacks occur between the convective system and its large-scale meteorological setting. Pronounced differences in temperature, divergence, vorticity, and height develop between the two simulations. Physical reasons for these differences are discussed. Comparison of the model forecast with analyses of the actual evolution of large-scale features indicates that this type of weather event cannot be properly simulated without inclusion of the effects of the latent-heat driven, mesoscale convective system.
Abstract
On 25 April 1975, as part of the National Aeronautics and Space Administration's Atmospheric Variability Experiment IV, frequent upper-air soundings were taken at eastern United States synoptic sounding sites. An intense, long-lived mesoscale convective weather system developed late in the AVE IV period and moved eastward during the remainder of the experiment. With the use of dry and moist numerical simulations, performed with Drexel University's Limited Area and Mesoscale Prediction System (LAMPS), interaction between the widespread, long-lived convective complex and its large-scale environment are examined.
Dissecting the differences between moist and dry simulations reveals that, within the moist numerical simulation, significant up-scale feedbacks occur between the convective system and its large-scale meteorological setting. Pronounced differences in temperature, divergence, vorticity, and height develop between the two simulations. Physical reasons for these differences are discussed. Comparison of the model forecast with analyses of the actual evolution of large-scale features indicates that this type of weather event cannot be properly simulated without inclusion of the effects of the latent-heat driven, mesoscale convective system.
Abstract
Before high-resolution numerical models can be of use operationally, they must be restricted to a limited domain, thus necessitating lateral boundary conditions which allow the changes outside the limited domain to influence the results while not contaminating the forecast with spurious boundary-reflected energy. Such a set of time-dependent lateral boundary conditions are presented in this paper. This boundary condition set is investigated using the linear analytic and finite-difference advection equations, the non-linear finite-difference shallow-water equations, and the hydrostatic primitive equations.
The results illustrate how the boundary condition transforms long- and medium-length interior advective and gravity waves into short waves which can then be removed by a low pass filter, thereby giving the appearance that the exiting wave simply passed through the boundary. The results also indicate that large-scale advective and gravity waves enter the forecast domain with little degradation. Thus, from the tests performed, the described boundary condition scheme yields a practical solution for prescribing time-dependent lateral boundaries for a limited-area model.
Abstract
Before high-resolution numerical models can be of use operationally, they must be restricted to a limited domain, thus necessitating lateral boundary conditions which allow the changes outside the limited domain to influence the results while not contaminating the forecast with spurious boundary-reflected energy. Such a set of time-dependent lateral boundary conditions are presented in this paper. This boundary condition set is investigated using the linear analytic and finite-difference advection equations, the non-linear finite-difference shallow-water equations, and the hydrostatic primitive equations.
The results illustrate how the boundary condition transforms long- and medium-length interior advective and gravity waves into short waves which can then be removed by a low pass filter, thereby giving the appearance that the exiting wave simply passed through the boundary. The results also indicate that large-scale advective and gravity waves enter the forecast domain with little degradation. Thus, from the tests performed, the described boundary condition scheme yields a practical solution for prescribing time-dependent lateral boundaries for a limited-area model.
Abstract
A mesoscale primitive equation model is used to create a 36-h simulation of the three-dimensional wind field of an intense maritime extratropical cyclone. The control experiment uses the simulated wind field every 15 min in a trajectory model to calculate back trajectories from various horizontal and vertical positions of interest relative to synoptic features of the storm. The latter trajectories are compared to trajectories that were calculated with the simulated wind data degraded in time to 30 min, 1 h, 3 h, 6 h, and 12 h.
Various error statistics reveal significant deterioration in trajectory accuracy between trajectories calculated with 1- and 3-h data frequencies. Trajectories calculated with 15-min, 30-min, and 1-h data frequencies yielded similar results, while trajectories calculated with data time frequencies 3 h and greater yielded results with unacceptably large errors.
Abstract
A mesoscale primitive equation model is used to create a 36-h simulation of the three-dimensional wind field of an intense maritime extratropical cyclone. The control experiment uses the simulated wind field every 15 min in a trajectory model to calculate back trajectories from various horizontal and vertical positions of interest relative to synoptic features of the storm. The latter trajectories are compared to trajectories that were calculated with the simulated wind data degraded in time to 30 min, 1 h, 3 h, 6 h, and 12 h.
Various error statistics reveal significant deterioration in trajectory accuracy between trajectories calculated with 1- and 3-h data frequencies. Trajectories calculated with 15-min, 30-min, and 1-h data frequencies yielded similar results, while trajectories calculated with data time frequencies 3 h and greater yielded results with unacceptably large errors.
Abstract
In Part I the convective processes important during the release of potential instability were described qualitatively and evaluated quantitatively in a parameterized cumulus model within a primitive equation model. Part II includes a more detailed examination of convective/mesoscale interactions through a basic simulation experiment and tests under different physical conditions and with different computational grids. The cumulus model was documented in Part I and the primitive equation model is documented herein. The example, for which detailed dynamical fields are shown, began with 6 h of convective activity that developed a saturated neutrally buoyant mesoscale updraft which produced the bulk of the precipitation by 12 h into the integration.
The potential instability process is readily understandable and verifiable in general terms by numerical simulation. Increasing moisture bandwidth or large-scale ascent results in a wider precipitation band. Permitting evaporation of convective precipitation above cloud base had surprising little effect on these rain-bands that are about 100 km wide. Decreasing cumulus updraft radius, thereby increasing entrainment effects, delays initial development of the mesoscale circulation and produces a much narrower and more intense circulation later on. Reducing the horizontal grid size from 20 to 10 km results in much narrower rainbands but does little to the area total precipitation. The rate of propagation inward of lateral boundary condition influences shows that rather large areas must be dealt with in mesoscale field projects and numerical weather prediction for phenomena with time scales of several hours.
Abstract
In Part I the convective processes important during the release of potential instability were described qualitatively and evaluated quantitatively in a parameterized cumulus model within a primitive equation model. Part II includes a more detailed examination of convective/mesoscale interactions through a basic simulation experiment and tests under different physical conditions and with different computational grids. The cumulus model was documented in Part I and the primitive equation model is documented herein. The example, for which detailed dynamical fields are shown, began with 6 h of convective activity that developed a saturated neutrally buoyant mesoscale updraft which produced the bulk of the precipitation by 12 h into the integration.
The potential instability process is readily understandable and verifiable in general terms by numerical simulation. Increasing moisture bandwidth or large-scale ascent results in a wider precipitation band. Permitting evaporation of convective precipitation above cloud base had surprising little effect on these rain-bands that are about 100 km wide. Decreasing cumulus updraft radius, thereby increasing entrainment effects, delays initial development of the mesoscale circulation and produces a much narrower and more intense circulation later on. Reducing the horizontal grid size from 20 to 10 km results in much narrower rainbands but does little to the area total precipitation. The rate of propagation inward of lateral boundary condition influences shows that rather large areas must be dealt with in mesoscale field projects and numerical weather prediction for phenomena with time scales of several hours.
Abstract
The release of potential instability by large-scale lifting and the subsequent interaction of cumulus convection and the hydrostatic mesoscale flow in a most complex scale-interaction process. This process is an essential part of tropical weather but it is also important in extratropical cyclones through the formation of mesoscale rainbands that contribute much of the precipitation. The purpose of this paper is to qualitatively and quantitatively clarify the potential instability release process within a framework that will permit calculation of convective/mesoscale interactions.
The approach is to use an extension of the Lagrangian form of the one-dimensional cumulus model to provide values of convective-scale changes to a hydrostatic primitive equation model. This cumulus sub-routine locates the base of the convection, computes the cumulus plume that will build, accounts for the environmental subsidence, and mixes the subsided environment with the cumulus plume after rainout. These plumes build sequentially when the subroutine is called every 20 min at each column in the hydrostatic model.
The convection model is explained in some detail along with its behavior within the hydrostatic model. The use of this scheme for convective adjustment is contrasted with other schemes; it is emphasized that this scheme is more generally applicable and includes the temporal evolution of mesoscale convective disturbances through consumption of pre-existing potential instability as well as the resupply of warm moist air (fuel).
Examples of convective/mesoscale interaction will he presented in Part II along with examples of the sensitivity of the results to variations in initial conditions and numerical coefficients.
Abstract
The release of potential instability by large-scale lifting and the subsequent interaction of cumulus convection and the hydrostatic mesoscale flow in a most complex scale-interaction process. This process is an essential part of tropical weather but it is also important in extratropical cyclones through the formation of mesoscale rainbands that contribute much of the precipitation. The purpose of this paper is to qualitatively and quantitatively clarify the potential instability release process within a framework that will permit calculation of convective/mesoscale interactions.
The approach is to use an extension of the Lagrangian form of the one-dimensional cumulus model to provide values of convective-scale changes to a hydrostatic primitive equation model. This cumulus sub-routine locates the base of the convection, computes the cumulus plume that will build, accounts for the environmental subsidence, and mixes the subsided environment with the cumulus plume after rainout. These plumes build sequentially when the subroutine is called every 20 min at each column in the hydrostatic model.
The convection model is explained in some detail along with its behavior within the hydrostatic model. The use of this scheme for convective adjustment is contrasted with other schemes; it is emphasized that this scheme is more generally applicable and includes the temporal evolution of mesoscale convective disturbances through consumption of pre-existing potential instability as well as the resupply of warm moist air (fuel).
Examples of convective/mesoscale interaction will he presented in Part II along with examples of the sensitivity of the results to variations in initial conditions and numerical coefficients.
Abstract
A process of lee cyclogenesis associated with backsheared baroclinic flow is studied using a fully nonlinear, primitive equation numerical model. A region of low pressure and a narrow baroclinic zone develop to the southwest of the mountain in the model for surface northerly wind with constant backshear. These major features are consistent with theoretical results of other authors. The low-level flow splits around the mountain for low Froude number such as investigated in this study. The splitting process is less pronounced for flow over a lower mountain. The positive pressure deviation has its center displaced northeast with respect to the mountaintop because of the relatively strong ageostrophic advection of cold air. Our numerical simulation indicates that a theory of lee cyclogenesis proposed by Smith is valid, at least in the early stage of cyclogenesis.
The lee cyclogenesis is affected by both the low-level sensible heating and the turning of the wind associated with boundary-layer processes. The development of the low is weakened in the early stage, which is the result of the weakened warm advection associated with the mountain-induced anticyclone. Weak upward motion, instead of strong downward motion, is found near the lee low-pressure region. The upward motion is produced by the mountain acting as an elevated heat source. This upward motion may accelerate and strengthen the cyclogenesis if the low-level flow were saturated and latent heating were to become important.
Abstract
A process of lee cyclogenesis associated with backsheared baroclinic flow is studied using a fully nonlinear, primitive equation numerical model. A region of low pressure and a narrow baroclinic zone develop to the southwest of the mountain in the model for surface northerly wind with constant backshear. These major features are consistent with theoretical results of other authors. The low-level flow splits around the mountain for low Froude number such as investigated in this study. The splitting process is less pronounced for flow over a lower mountain. The positive pressure deviation has its center displaced northeast with respect to the mountaintop because of the relatively strong ageostrophic advection of cold air. Our numerical simulation indicates that a theory of lee cyclogenesis proposed by Smith is valid, at least in the early stage of cyclogenesis.
The lee cyclogenesis is affected by both the low-level sensible heating and the turning of the wind associated with boundary-layer processes. The development of the low is weakened in the early stage, which is the result of the weakened warm advection associated with the mountain-induced anticyclone. Weak upward motion, instead of strong downward motion, is found near the lee low-pressure region. The upward motion is produced by the mountain acting as an elevated heat source. This upward motion may accelerate and strengthen the cyclogenesis if the low-level flow were saturated and latent heating were to become important.
Abstract
Peppler and Smith (1984) discussed truncation errors associated with second-order and fourth-order finite difference approximations used to calculate the geostrophic wind and relative vorticity. They found that these errors were, in general, smaller for longer wavelengths, finer-grid resolution, and fourth-order differencing. Second-order differencing produced fields that were numerically less than their corresponding analytic values and yielded errors which decreased with reduced grid interval. Fourth-order differencing decreased the errors when the grid interval was reduced, but only while the wavelength was ten limes or more greater than the grid interval.
Results presented here indicate that the wind speed and Vorticity errors estimated by the fourth-order scheme decreased when the grid interval was decreased independent of wavelength. Comparison with Peppler and Smith's actual computations showed only one difference: in their finite-(difference equations the coefficients were truncated to the nearest thousandth (for example, 0.083 was used in place of 1/12). On the other hand, we used 1.0/12.0 and allowed the computer's word length to determine the value of the coefficient, thus, preserving greater accuracy.
Abstract
Peppler and Smith (1984) discussed truncation errors associated with second-order and fourth-order finite difference approximations used to calculate the geostrophic wind and relative vorticity. They found that these errors were, in general, smaller for longer wavelengths, finer-grid resolution, and fourth-order differencing. Second-order differencing produced fields that were numerically less than their corresponding analytic values and yielded errors which decreased with reduced grid interval. Fourth-order differencing decreased the errors when the grid interval was reduced, but only while the wavelength was ten limes or more greater than the grid interval.
Results presented here indicate that the wind speed and Vorticity errors estimated by the fourth-order scheme decreased when the grid interval was decreased independent of wavelength. Comparison with Peppler and Smith's actual computations showed only one difference: in their finite-(difference equations the coefficients were truncated to the nearest thousandth (for example, 0.083 was used in place of 1/12). On the other hand, we used 1.0/12.0 and allowed the computer's word length to determine the value of the coefficient, thus, preserving greater accuracy.
Abstract
A severe extratropical cyclcone was initiated from a low-level medium-scale cyclone over the ocean northeast of Taiwan during the initial phase of the AMTEX '75. The analyses of Soliz and Fein were used to examine the time evolution and the three-dimensional structure of the medium-scale cyclone associated with this AMTEX cyclone.
During the initial period of this system's development there was no evidence that forcing by an approaching synoptic-scale system was involved. The distribution of zonal wind did not suggest the existence of barotropically or baroclinically unstable conditions in the lower troposphere.
The analysis shows that several processes were important in the initiation and development of this system. Heat flux from the Kuroshio current rapidly destabilized the lower layer of the polar air mass. Mild lifting due to warm advection led to latent heat release and the formation of the 850 mb short wave and surface pressure trough. Further release of latent heat within the region of the low-level disturbance resulted in the development of the medium-scale cyclone. The vertical coupling of the cyclone and the incoming upper-level synoptic system led to the development of the severe extratropical cyclone.
Abstract
A severe extratropical cyclcone was initiated from a low-level medium-scale cyclone over the ocean northeast of Taiwan during the initial phase of the AMTEX '75. The analyses of Soliz and Fein were used to examine the time evolution and the three-dimensional structure of the medium-scale cyclone associated with this AMTEX cyclone.
During the initial period of this system's development there was no evidence that forcing by an approaching synoptic-scale system was involved. The distribution of zonal wind did not suggest the existence of barotropically or baroclinically unstable conditions in the lower troposphere.
The analysis shows that several processes were important in the initiation and development of this system. Heat flux from the Kuroshio current rapidly destabilized the lower layer of the polar air mass. Mild lifting due to warm advection led to latent heat release and the formation of the 850 mb short wave and surface pressure trough. Further release of latent heat within the region of the low-level disturbance resulted in the development of the medium-scale cyclone. The vertical coupling of the cyclone and the incoming upper-level synoptic system led to the development of the severe extratropical cyclone.
Abstract
The structure of upper level and surface frontal zones associated with a cyclone developing over the central United States on 21–22 February 1971, as predicted by a limited-area, moist, primitive equation model with horizontal and vertical grid spacing on the order of 100 and 1.5 km, respectively, Is qualitatively examined and discussed. A comparison of crow-section analyses of the frontal zones, constructed from rawinsondo observations and from model output data, reveals that the horizontal and vertical scales of the observed fronts are ∼100 and ∼1 km, while those for the model-predicted fronts are ∼200–400 and ∼1–2 km. The discrepancy in scale can be explained by the coarse model resolution, which essentially renders be frontal zones subgrid-scale phenomena. Despite the model's lack of fidelity in reproduce the observed details in frontal structure, point calculations with Miller' equation appear reasonable in view of those results obtained in previous synoptic investigations. Vertical tilting dominates the frontolysis predicted in the upper level frontal exit region, and the stretching deformation term provides a strong frontogenetical contribution in the surface frontal zone.
Abstract
The structure of upper level and surface frontal zones associated with a cyclone developing over the central United States on 21–22 February 1971, as predicted by a limited-area, moist, primitive equation model with horizontal and vertical grid spacing on the order of 100 and 1.5 km, respectively, Is qualitatively examined and discussed. A comparison of crow-section analyses of the frontal zones, constructed from rawinsondo observations and from model output data, reveals that the horizontal and vertical scales of the observed fronts are ∼100 and ∼1 km, while those for the model-predicted fronts are ∼200–400 and ∼1–2 km. The discrepancy in scale can be explained by the coarse model resolution, which essentially renders be frontal zones subgrid-scale phenomena. Despite the model's lack of fidelity in reproduce the observed details in frontal structure, point calculations with Miller' equation appear reasonable in view of those results obtained in previous synoptic investigations. Vertical tilting dominates the frontolysis predicted in the upper level frontal exit region, and the stretching deformation term provides a strong frontogenetical contribution in the surface frontal zone.
