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- Author or Editor: RICHARD A. ANTHES x
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Abstract
This paper describes the exciting period of discovery in the 1950s and 1960s in tropical meteorology, and the important role played by Joanne Malkus (Simpson) in her studies of cumulus convection and tropical cyclones. A key concept developed by Joanne, with Herbert Riehl, was that of the “hot tower.” Hot towers were deep tropical cumulonimbus clouds whose cores were undiluted by entrainment and thus carried heat and water vapor from the boundary layer to high in the troposphere. Joanne's observational work led to a major effort by a number of theoreticians and modelers in the 1960s and 1970s to incorporate the effects of the relatively small-scale but energetically important cumulus clouds in numerical models of tropical cyclones.
The important theory of conditional instability of the second kind, or CISK, and its contribution to tropical cyclone theory and modeling, is summarized. The CISK theory envisioned a cooperation between the tropical cyclone–scale circulation and the much smaller-scale convective clouds, including hot towers, that caused tropical cyclones to form and intensify. Although the CISK and hot tower theories were misunderstood and misused by some, they both contributed much to the development of tropical cyclone models and scientific understanding of these violent storms, and their general concepts and importance remain valid today.
Abstract
This paper describes the exciting period of discovery in the 1950s and 1960s in tropical meteorology, and the important role played by Joanne Malkus (Simpson) in her studies of cumulus convection and tropical cyclones. A key concept developed by Joanne, with Herbert Riehl, was that of the “hot tower.” Hot towers were deep tropical cumulonimbus clouds whose cores were undiluted by entrainment and thus carried heat and water vapor from the boundary layer to high in the troposphere. Joanne's observational work led to a major effort by a number of theoreticians and modelers in the 1960s and 1970s to incorporate the effects of the relatively small-scale but energetically important cumulus clouds in numerical models of tropical cyclones.
The important theory of conditional instability of the second kind, or CISK, and its contribution to tropical cyclone theory and modeling, is summarized. The CISK theory envisioned a cooperation between the tropical cyclone–scale circulation and the much smaller-scale convective clouds, including hot towers, that caused tropical cyclones to form and intensify. Although the CISK and hot tower theories were misunderstood and misused by some, they both contributed much to the development of tropical cyclone models and scientific understanding of these violent storms, and their general concepts and importance remain valid today.
Abstract
It is hypothesized that planting bands of vegetation with widths of the order of 50–100 km in semiarid regions could, under favorable large-scale atmospheric conditions, result in increases of convective precipitation. These increases, which could be greater than those associated with the uniform vegetating of large areas, would occur through three major mechanisms. The first would be the modification of the environment to a state more conducive to the formation of moist convection through an increase of low-level moist static energy. This increase would be associated with a decrease in albedo, an increase in net radiation, and an increase in evapotranspiration. The second important mechanism would be the generation of mesoscale (horizontal scale of 20–200 km) circulations associated with the surface inhomogeneities created on this scale by the vegetation. The third mechanism would be the increase of atmospheric water vapor through decreased runoff and increased evaporation.
A number of observational and theoretical studies which have a bearing on the above hypothesis are reviewed. Although individual studies may contain large uncertainties, taken together they provide considerable support for the hypothesis. In these studies, convective rainfall appears to be associated with increases in vegetation and with variations in surface characteristics in many parts of the world on scales ranging from 10 km to large fractions of continents.
A review of recent agricultural research indicates that a variety of plants that thrive in semiarid regions (some under irrigation with saline water) could be suitable for cultivation. Many of these have potential economic value, which could defray or even exceed the cost of the cultivation.
Finally, a preliminary estimate of the preferred horizontal scale of the vegetation bands is made using a linear model. For bands of width less than about 20 km, horizontal mixing limits the vertical penetration of the surface heating perturbation to heights too small to be effective in generating moist convection. For larger scales (widths ∼ 100 km), however, it appears that vertical circulations with order of magnitude 10 cm s−1 that extend to heights of 1 km or more are possible. When combined with increases in low-level moist static energy, circulations of this magnitude and scale appear to be capable of initiating and enhancing moist convection under appropriate atmospheric conditions. Further studies with more realistic models are necessary to obtain a more definitive evaluation of the hypothesis.
Abstract
It is hypothesized that planting bands of vegetation with widths of the order of 50–100 km in semiarid regions could, under favorable large-scale atmospheric conditions, result in increases of convective precipitation. These increases, which could be greater than those associated with the uniform vegetating of large areas, would occur through three major mechanisms. The first would be the modification of the environment to a state more conducive to the formation of moist convection through an increase of low-level moist static energy. This increase would be associated with a decrease in albedo, an increase in net radiation, and an increase in evapotranspiration. The second important mechanism would be the generation of mesoscale (horizontal scale of 20–200 km) circulations associated with the surface inhomogeneities created on this scale by the vegetation. The third mechanism would be the increase of atmospheric water vapor through decreased runoff and increased evaporation.
A number of observational and theoretical studies which have a bearing on the above hypothesis are reviewed. Although individual studies may contain large uncertainties, taken together they provide considerable support for the hypothesis. In these studies, convective rainfall appears to be associated with increases in vegetation and with variations in surface characteristics in many parts of the world on scales ranging from 10 km to large fractions of continents.
A review of recent agricultural research indicates that a variety of plants that thrive in semiarid regions (some under irrigation with saline water) could be suitable for cultivation. Many of these have potential economic value, which could defray or even exceed the cost of the cultivation.
Finally, a preliminary estimate of the preferred horizontal scale of the vegetation bands is made using a linear model. For bands of width less than about 20 km, horizontal mixing limits the vertical penetration of the surface heating perturbation to heights too small to be effective in generating moist convection. For larger scales (widths ∼ 100 km), however, it appears that vertical circulations with order of magnitude 10 cm s−1 that extend to heights of 1 km or more are possible. When combined with increases in low-level moist static energy, circulations of this magnitude and scale appear to be capable of initiating and enhancing moist convection under appropriate atmospheric conditions. Further studies with more realistic models are necessary to obtain a more definitive evaluation of the hypothesis.
Abstract
This paper investigates the problem of initializing operational hurricane models with several types of real data. Imbalances in real data generate inertia-gravity waves with periods that vary strongly in different regions of the hurricane domain. The energy of these waves is removed by propagation out of the domain, by the horizontal diffusion process, and by the truncation errors associated with the Matsuno time-differencing scheme. Several initialization schemes are tested with a symmetric hurricane model. Random and bias errors superimposed on perfect data produce imbalances that lend to significant errors in short-range forecasts. A general dynamic initialization scheme that is suitable for diabatic, viscous models yields very promising results.
The dynamic initialization technique is utilized in an effort to determine the types of data that will be most useful in initializing operational hurricane models. In general, observations are most useful near the center of the storm at low levels. Temperature and wind observations are about equally effective in reducing initial analysis errors. Specific humidity observations, on the other hand, seem less important. Finally, the sensitivity of the initialization method is tested with observations that include rather large bias errors.
Abstract
This paper investigates the problem of initializing operational hurricane models with several types of real data. Imbalances in real data generate inertia-gravity waves with periods that vary strongly in different regions of the hurricane domain. The energy of these waves is removed by propagation out of the domain, by the horizontal diffusion process, and by the truncation errors associated with the Matsuno time-differencing scheme. Several initialization schemes are tested with a symmetric hurricane model. Random and bias errors superimposed on perfect data produce imbalances that lend to significant errors in short-range forecasts. A general dynamic initialization scheme that is suitable for diabatic, viscous models yields very promising results.
The dynamic initialization technique is utilized in an effort to determine the types of data that will be most useful in initializing operational hurricane models. In general, observations are most useful near the center of the storm at low levels. Temperature and wind observations are about equally effective in reducing initial analysis errors. Specific humidity observations, on the other hand, seem less important. Finally, the sensitivity of the initialization method is tested with observations that include rather large bias errors.
Abstract
A two-dimensional mesoscale model is applied to study the evolution of a strong sea breeze on a stagnant base state. In contrast to previous studies, this paper considers the relationship of the planetary boundary layer (PBL), the thermodynamic structure and the vertical circulation associated with the sea breeze in detail.
The development of the sea breeze circulation is studied quantitatively using the circulation theorem. The circulation in the vertical plane normal to the coast develops as a result of the solenoid term. The vertical diffusion of momentum acts as the most important brake on the developing circulation in agreement with previous theoretical results. The Coriolis term is small until 6 h after the beating cycle. Late in the cycle, however, it reaches a value of 45% that of the solenoid term. Horizontal and vertical advective effects are small.
Under zero geostrophic wind conditions, the return flow occurs entirely above the PBL. Therefore, neutrally buoyant pollutants emitted at the surface can only enter the return flow through the narrow zone of upward motion at the sea breeze front. Trajectories indicate that considerable recirculation toward the shore of these pollutants as well as pollutants left over in the previous day's mixed layer may occur. For the time and space scale of the sea breeze considered here, Coriolis forces are important in causing significant transports along the coast.
The depth of the circulation and the trajectories are sensitive to the rate of heating over land and the initial static stability. For strong heating in a relatively unstable environment, a significant component to the return circulation exists up to 5 km. For moderate heating in a more stable environment, there is very little return circulation above 3 km.
Abstract
A two-dimensional mesoscale model is applied to study the evolution of a strong sea breeze on a stagnant base state. In contrast to previous studies, this paper considers the relationship of the planetary boundary layer (PBL), the thermodynamic structure and the vertical circulation associated with the sea breeze in detail.
The development of the sea breeze circulation is studied quantitatively using the circulation theorem. The circulation in the vertical plane normal to the coast develops as a result of the solenoid term. The vertical diffusion of momentum acts as the most important brake on the developing circulation in agreement with previous theoretical results. The Coriolis term is small until 6 h after the beating cycle. Late in the cycle, however, it reaches a value of 45% that of the solenoid term. Horizontal and vertical advective effects are small.
Under zero geostrophic wind conditions, the return flow occurs entirely above the PBL. Therefore, neutrally buoyant pollutants emitted at the surface can only enter the return flow through the narrow zone of upward motion at the sea breeze front. Trajectories indicate that considerable recirculation toward the shore of these pollutants as well as pollutants left over in the previous day's mixed layer may occur. For the time and space scale of the sea breeze considered here, Coriolis forces are important in causing significant transports along the coast.
The depth of the circulation and the trajectories are sensitive to the rate of heating over land and the initial static stability. For strong heating in a relatively unstable environment, a significant component to the return circulation exists up to 5 km. For moderate heating in a more stable environment, there is very little return circulation above 3 km.
This paper summarizes recent studies of a variety of atmospheric phenomena in different parts of the world using the Penn State/NCAR mesoscale model. These phenomena include explosive cyclogenesis over the North Pacific and North Atlantic oceans, cyclogenesis over Europe and associated ozone transport during the ALPEX experiment, heavy rainfall and flash flood events over Pennsylvania and China, “Plateau” and “Southwest” vortices over China, severe storms over the United States, mesoscale convective complexes, elevated mixed layers and “lids,” an Australian Southerly Buster, low-level damming of cold air to the east of the United States Appalachian Mountains in winter, urban heat island effects, and regional acid deposition. This paper also reviews Observing System Simulation experiments (OSSEs), several sensitivity studies, the nesting of the mesoscale model in a global climate model for regional climate studies, and some recent real-time forecasting studies conducted by The Pennsylvania State University.
An important result of these and earlier studies is that a general mesoscale model with realistic treatment of surface conditions and physical processes, and initialized with good large-scale conditions is capable of simulating and predicting a large variety of synoptic and mesoscale phenomena in different parts of the world. The model simulations also provide high-resolution, dynamically consistent data sets which are useful in understanding the physical behavior of complex mesoscale systems.
This paper summarizes recent studies of a variety of atmospheric phenomena in different parts of the world using the Penn State/NCAR mesoscale model. These phenomena include explosive cyclogenesis over the North Pacific and North Atlantic oceans, cyclogenesis over Europe and associated ozone transport during the ALPEX experiment, heavy rainfall and flash flood events over Pennsylvania and China, “Plateau” and “Southwest” vortices over China, severe storms over the United States, mesoscale convective complexes, elevated mixed layers and “lids,” an Australian Southerly Buster, low-level damming of cold air to the east of the United States Appalachian Mountains in winter, urban heat island effects, and regional acid deposition. This paper also reviews Observing System Simulation experiments (OSSEs), several sensitivity studies, the nesting of the mesoscale model in a global climate model for regional climate studies, and some recent real-time forecasting studies conducted by The Pennsylvania State University.
An important result of these and earlier studies is that a general mesoscale model with realistic treatment of surface conditions and physical processes, and initialized with good large-scale conditions is capable of simulating and predicting a large variety of synoptic and mesoscale phenomena in different parts of the world. The model simulations also provide high-resolution, dynamically consistent data sets which are useful in understanding the physical behavior of complex mesoscale systems.
Abstract
This review describes recent development in operational and research limited-area numerical weather prediction models in middle latitudes. The current skill of limited-area models is summarized through the use of conventional measures of verification such as S 1 scores, root-mean-square errors and correlations between forecast and observed changes. Additional measures of verification, which measure the skill or realism of regional models in reproducing atmospheric structure on those scales, are discussed. Use of a uniform set of verification measures such as those discussed here would facilitate model comparisons and assessment of the impact of changes in model components on short-range (0–48 h) forecasts.
Three major components of regional models are discussed. These include numerical aspects (e.g., the grid structure, boundary conditions and the approximations to the analytic differential equations), physical aspects (modeling surface and boundary layer processes, condensation and evaporation, and radiation) and the analysis and initialization procedure. The paper emphasizes the impact of these components on the forecast rather than the details of each component.
The main conclusion of the paper is that further increases in the overall skill of operational regional forecasts are likely to occur through improvements in all the components of limited-area models. Improvements in various components developed and tested in research models are currently being incorporated in several operational models, and some modest but significant improvements in regional forecast skill are likely over the next five years.
Abstract
This review describes recent development in operational and research limited-area numerical weather prediction models in middle latitudes. The current skill of limited-area models is summarized through the use of conventional measures of verification such as S 1 scores, root-mean-square errors and correlations between forecast and observed changes. Additional measures of verification, which measure the skill or realism of regional models in reproducing atmospheric structure on those scales, are discussed. Use of a uniform set of verification measures such as those discussed here would facilitate model comparisons and assessment of the impact of changes in model components on short-range (0–48 h) forecasts.
Three major components of regional models are discussed. These include numerical aspects (e.g., the grid structure, boundary conditions and the approximations to the analytic differential equations), physical aspects (modeling surface and boundary layer processes, condensation and evaporation, and radiation) and the analysis and initialization procedure. The paper emphasizes the impact of these components on the forecast rather than the details of each component.
The main conclusion of the paper is that further increases in the overall skill of operational regional forecasts are likely to occur through improvements in all the components of limited-area models. Improvements in various components developed and tested in research models are currently being incorporated in several operational models, and some modest but significant improvements in regional forecast skill are likely over the next five years.
Abstract
A diagnostic axisymmetric model in isentropic coordinates is developed to study the effect of differential heating on the dynamics and energetics of the steady-state tropical cyclone. From the thermal forcing specified by various heating distributions, slowly varying solutions for the mass and momentum fields are obtained by an iterative technique.
The theory of available potential energy for open systems is utilized to study the energy budget for the hurricane. In the slowly varying state, the gain of available potential energy by diabatic heating and lateral boundary processes balances the conversion of potential to kinetic energy that, in turn, offsets frictional dissipation. For a domain of radius 500 km, the boundary flux of available potential energy is about 40 percent of the generation by diabatic heating. For a domain of radius 1000 km, however, the boundary flux is about 15 percent of the generation.
Horizontal and vertical mixing are studied through the use of constant exchange coefficients. As the horizontal mixing decreases, the maximum surface wind increases and moves closer to the center.
Several horizontal and two vertical distributions of latent heating are investigated. The maximum surface wind is dependent primarily on heating within 100 km. The transverse (radial) circulation is closely related to the heat release beyond 100 km. In experiments in which the vertical variation of heating is pseudoadiabatic, the temperature and outflow structures are unrealistic. A vertical distribution that releases a higher proportion of heat in the upper troposphere yields results that are more representative of the hurricane.
Abstract
A diagnostic axisymmetric model in isentropic coordinates is developed to study the effect of differential heating on the dynamics and energetics of the steady-state tropical cyclone. From the thermal forcing specified by various heating distributions, slowly varying solutions for the mass and momentum fields are obtained by an iterative technique.
The theory of available potential energy for open systems is utilized to study the energy budget for the hurricane. In the slowly varying state, the gain of available potential energy by diabatic heating and lateral boundary processes balances the conversion of potential to kinetic energy that, in turn, offsets frictional dissipation. For a domain of radius 500 km, the boundary flux of available potential energy is about 40 percent of the generation by diabatic heating. For a domain of radius 1000 km, however, the boundary flux is about 15 percent of the generation.
Horizontal and vertical mixing are studied through the use of constant exchange coefficients. As the horizontal mixing decreases, the maximum surface wind increases and moves closer to the center.
Several horizontal and two vertical distributions of latent heating are investigated. The maximum surface wind is dependent primarily on heating within 100 km. The transverse (radial) circulation is closely related to the heat release beyond 100 km. In experiments in which the vertical variation of heating is pseudoadiabatic, the temperature and outflow structures are unrealistic. A vertical distribution that releases a higher proportion of heat in the upper troposphere yields results that are more representative of the hurricane.
Abstract
Additional experiments with the slowly varying axisymmetric hurricane model described by Anthes are presented. Variable horizontal eddy viscosity coefficients are utilized to study circulations that result from an increased heating function and a heating function with a double maximum along the radial direction. Infrared radiative cooling is modeled for the clear tropical atmosphere following Sasamori. A representative cooling rate is used to study the effect of cooling in the hurricane environment on the dynamics and energetics of the slowly varying tropical cyclone.
Abstract
Additional experiments with the slowly varying axisymmetric hurricane model described by Anthes are presented. Variable horizontal eddy viscosity coefficients are utilized to study circulations that result from an increased heating function and a heating function with a double maximum along the radial direction. Infrared radiative cooling is modeled for the clear tropical atmosphere following Sasamori. A representative cooling rate is used to study the effect of cooling in the hurricane environment on the dynamics and energetics of the slowly varying tropical cyclone.
Abstract
Steady-state solutions to the complete axisymmetric Navier-Stokes equations are obtained by an iterative technique for an intense pressure-gradient force representative of the tropical cyclone. Solutions for the horizontal and vertical components of motion are compared for various horizontal and vertical mixing coefficients, drag coefficients, and Coriolis parameters. A multilevel model is used, and the results are compared with those from a simple one-level model.
Abstract
Steady-state solutions to the complete axisymmetric Navier-Stokes equations are obtained by an iterative technique for an intense pressure-gradient force representative of the tropical cyclone. Solutions for the horizontal and vertical components of motion are compared for various horizontal and vertical mixing coefficients, drag coefficients, and Coriolis parameters. A multilevel model is used, and the results are compared with those from a simple one-level model.
Abstract
A two-dimensional horizontal variable grid is derived that has maximum resolution at the center and minimum resolution near the boundaries of the grid. By using the analytic transformation that defines the variable grid, the equations of motion for a free-surface model are transformed in terms of new independent space variables in a computational domain with constant resolution. Numerical experiments utilize the variable grid to (1) increase the domain size with a fixed resolution at the center and (2) increase the resolution at the center with a fixed domain size.
Several finite-difference analogs and three time-integration schemes are tested. For a given domain size and number of grid points, several variable grid experiments show superior results in the mass and momentum fields compared to constant grid results. Most variable grid experiments, however, show a small (less than 1 percent) increase in total energy after 2000 time steps due apparently to the presence of additional nonlinear terms in the forecast equations.
The results show that, although care must be taken with the nonlinear terms, the variable grid may be effectively used in certain physical problems to economically gain resolution at the center of the domain.
Abstract
A two-dimensional horizontal variable grid is derived that has maximum resolution at the center and minimum resolution near the boundaries of the grid. By using the analytic transformation that defines the variable grid, the equations of motion for a free-surface model are transformed in terms of new independent space variables in a computational domain with constant resolution. Numerical experiments utilize the variable grid to (1) increase the domain size with a fixed resolution at the center and (2) increase the resolution at the center with a fixed domain size.
Several finite-difference analogs and three time-integration schemes are tested. For a given domain size and number of grid points, several variable grid experiments show superior results in the mass and momentum fields compared to constant grid results. Most variable grid experiments, however, show a small (less than 1 percent) increase in total energy after 2000 time steps due apparently to the presence of additional nonlinear terms in the forecast equations.
The results show that, although care must be taken with the nonlinear terms, the variable grid may be effectively used in certain physical problems to economically gain resolution at the center of the domain.
