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Abstract
The dynamics of moist orographic flows during the January 1997 floods in northern and central California are investigated using numerical simulations computed with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5). Early in the event (31 December 1996–1 January 1997), the low-level winds offshore of California’s central coast were blocked by the topography of the Santa Lucia Range, and the low-level winds in the Central Valley were blocked by the topography of the central Sierra Nevada Range. In contrast, moisture-laden winds along the northern Coast Ranges and the northern Sierra Nevada flowed over topographic barriers. As the core of humid air migrated to the south over 24 h, the low-level barrier jets weakened as the atmospheric stability decreased, bringing heavy rainfall to the central and southern Sierra Nevada at the end of the event. The heavy precipitation during this event was largely controlled by the interaction of the flow with topography, with little contribution from non–topographically forced dynamical uplift. Latent heating was essential for lowering the effective stability of the flow and allowing the winds to flow over mountainous terrain, particularly in the northern Coast Ranges, and for enhancing the low-level jet and associated moisture transport. The horizontal distribution of static stability played a key role in the event by setting up a complex combination of flow-over and flow-around regimes that enhanced uplift in the northern Sierra Nevada during the period of heaviest rainfall.
Abstract
The dynamics of moist orographic flows during the January 1997 floods in northern and central California are investigated using numerical simulations computed with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5). Early in the event (31 December 1996–1 January 1997), the low-level winds offshore of California’s central coast were blocked by the topography of the Santa Lucia Range, and the low-level winds in the Central Valley were blocked by the topography of the central Sierra Nevada Range. In contrast, moisture-laden winds along the northern Coast Ranges and the northern Sierra Nevada flowed over topographic barriers. As the core of humid air migrated to the south over 24 h, the low-level barrier jets weakened as the atmospheric stability decreased, bringing heavy rainfall to the central and southern Sierra Nevada at the end of the event. The heavy precipitation during this event was largely controlled by the interaction of the flow with topography, with little contribution from non–topographically forced dynamical uplift. Latent heating was essential for lowering the effective stability of the flow and allowing the winds to flow over mountainous terrain, particularly in the northern Coast Ranges, and for enhancing the low-level jet and associated moisture transport. The horizontal distribution of static stability played a key role in the event by setting up a complex combination of flow-over and flow-around regimes that enhanced uplift in the northern Sierra Nevada during the period of heaviest rainfall.
Abstract
The authors present a simple semi-empirical model to explore the hypothesis that the Madden–Julian oscillation can be represented as a moisture mode destabilized by surface flux and cloud–radiative feedbacks. The model is one-dimensional in longitude; the vertical and meridional structure is entirely implicit. The only prognostic variable is column water vapor W. The zonal wind field is an instantaneous diagnostic function of the precipitation field.
The linearized version of the model has only westward-propagating (relative to the mean flow) unstable modes because wind-induced surface latent heat flux anomalies occur to the west of precipitation anomalies. The maximum growth rate occurs at the wavelength at which the correlation between precipitation and surface latent heat flux is maximized. This wavelength lies in the synoptic- to planetary-scale range and is proportional to the horizontal scale associated with the assumed diagnostic wind response to precipitation anomalies.
The nonlinear version of the model has behavior that can be qualitatively different from the linear modes and is strongly influenced by horizontal advection of moisture. The nonlinear solutions are very sensitive to small shifts in the phasing of wind and precipitation. Under some circumstances nonlinear eastward-propagating disturbances emerge on a state of mean background westerlies. These disturbances have a shocklike discontinuous jump in humidity and rainfall at the leading edge; humidity decreases linearly and precipitation decreases exponentially to the west.
Abstract
The authors present a simple semi-empirical model to explore the hypothesis that the Madden–Julian oscillation can be represented as a moisture mode destabilized by surface flux and cloud–radiative feedbacks. The model is one-dimensional in longitude; the vertical and meridional structure is entirely implicit. The only prognostic variable is column water vapor W. The zonal wind field is an instantaneous diagnostic function of the precipitation field.
The linearized version of the model has only westward-propagating (relative to the mean flow) unstable modes because wind-induced surface latent heat flux anomalies occur to the west of precipitation anomalies. The maximum growth rate occurs at the wavelength at which the correlation between precipitation and surface latent heat flux is maximized. This wavelength lies in the synoptic- to planetary-scale range and is proportional to the horizontal scale associated with the assumed diagnostic wind response to precipitation anomalies.
The nonlinear version of the model has behavior that can be qualitatively different from the linear modes and is strongly influenced by horizontal advection of moisture. The nonlinear solutions are very sensitive to small shifts in the phasing of wind and precipitation. Under some circumstances nonlinear eastward-propagating disturbances emerge on a state of mean background westerlies. These disturbances have a shocklike discontinuous jump in humidity and rainfall at the leading edge; humidity decreases linearly and precipitation decreases exponentially to the west.
Abstract
A model of intermediate complexity based on quasi-equilibrium theory—a version of the quasi-equilibrium tropical circulation model with a prognostic atmospheric boundary layer, as well as two free-tropospheric modes in momentum, and one each in moisture and temperature—is used in a zonally symmetric aquaplanet configuration to simulate aspects of the South Asian monsoon and its variability. Key qualitative features of both the mean state and the 30–60-day mode of the intraseasonal variability are simulated satisfactorily. The model has two limit cycles of similar period and structure that can account for this mode. Both feature northward propagation of the tropical convergence zone from 5°S to 25°N with a period of about 50 days. The dynamics of the oscillations are investigated. The system reaches a Hopf bifurcation when the asymmetry of the sea surface temperature (SST) forcing is increased. Beyond the bifurcation, the mean flow is linearly unstable, and the one linearly unstable mode is similar in structure and period to the nonlinear mode. The wind-induced surface heat fluxes are necessary to obtain the instability of the mean monsoon flow, as are the 2 degrees of freedom in the vertical structure of both humidity and wind.
Abstract
A model of intermediate complexity based on quasi-equilibrium theory—a version of the quasi-equilibrium tropical circulation model with a prognostic atmospheric boundary layer, as well as two free-tropospheric modes in momentum, and one each in moisture and temperature—is used in a zonally symmetric aquaplanet configuration to simulate aspects of the South Asian monsoon and its variability. Key qualitative features of both the mean state and the 30–60-day mode of the intraseasonal variability are simulated satisfactorily. The model has two limit cycles of similar period and structure that can account for this mode. Both feature northward propagation of the tropical convergence zone from 5°S to 25°N with a period of about 50 days. The dynamics of the oscillations are investigated. The system reaches a Hopf bifurcation when the asymmetry of the sea surface temperature (SST) forcing is increased. Beyond the bifurcation, the mean flow is linearly unstable, and the one linearly unstable mode is similar in structure and period to the nonlinear mode. The wind-induced surface heat fluxes are necessary to obtain the instability of the mean monsoon flow, as are the 2 degrees of freedom in the vertical structure of both humidity and wind.
Abstract
The authors discuss modifications to a simple linear model of intraseasonal moisture modes. Wind–evaporation feedbacks were shown in an earlier study to induce westward propagation in an eastward mean low-level flow in this model. Here additional processes, which provide effective sources of moist static energy to the disturbances and which also depend on the low-level wind, are considered. Several processes can act as positive sources in perturbation easterlies: zonal advection (if the mean zonal moisture gradient is eastward), modulation of synoptic eddy drying by the MJO-scale wind perturbations, and frictional convergence. If the sum of these is stronger than the wind–evaporation feedback—as observations suggest may be the case, though with considerable uncertainty—the model produces unstable modes that propagate weakly eastward relative to the mean flow. With a small amount of horizontal diffusion or other scale-selective damping, the growth rate is greatest at the largest horizontal scales and decreases monotonically with wavenumber.
Abstract
The authors discuss modifications to a simple linear model of intraseasonal moisture modes. Wind–evaporation feedbacks were shown in an earlier study to induce westward propagation in an eastward mean low-level flow in this model. Here additional processes, which provide effective sources of moist static energy to the disturbances and which also depend on the low-level wind, are considered. Several processes can act as positive sources in perturbation easterlies: zonal advection (if the mean zonal moisture gradient is eastward), modulation of synoptic eddy drying by the MJO-scale wind perturbations, and frictional convergence. If the sum of these is stronger than the wind–evaporation feedback—as observations suggest may be the case, though with considerable uncertainty—the model produces unstable modes that propagate weakly eastward relative to the mean flow. With a small amount of horizontal diffusion or other scale-selective damping, the growth rate is greatest at the largest horizontal scales and decreases monotonically with wavenumber.
Abstract
Climatologically, the equatorial western Pacific warm pool region is a local minimum in surface evaporation and a local maximum in precipitation. The moist static energy budget in this situation requires a collocated minimum in radiative cooling of the atmosphere, which is supplied by the greenhouse effect of high clouds associated with the precipitation. However, this diagnostic statement does not explain why the evaporation minimum should coexist with the precipitation maximum. A simple physical model of the Walker circulation is used as the basis for an argument that the surface heat budget and the radiative effects of high clouds are essential to the existence of this feature, while variations in surface wind speed are not, though the latter may play an important role in determining the sea surface temperature.
Abstract
Climatologically, the equatorial western Pacific warm pool region is a local minimum in surface evaporation and a local maximum in precipitation. The moist static energy budget in this situation requires a collocated minimum in radiative cooling of the atmosphere, which is supplied by the greenhouse effect of high clouds associated with the precipitation. However, this diagnostic statement does not explain why the evaporation minimum should coexist with the precipitation maximum. A simple physical model of the Walker circulation is used as the basis for an argument that the surface heat budget and the radiative effects of high clouds are essential to the existence of this feature, while variations in surface wind speed are not, though the latter may play an important role in determining the sea surface temperature.
Abstract
In zonally averaged chemical transport models of the stratosphere, quasi-isentropic mixing is represented by diffusion in latitude. However, it is fairly certain that the real mixing is to some extent nonlocal, so that the diffusive representation is not formally justifiable. This issue is explored from a point of view that combines theory and empiricism. Several models of mixing are described and compared. The most general, including as special cases all of the other models considered, is the integral or “transilient matrix” model. Some known properties of transilient matrices are discussed in a more formal way than has been done previously, and some new results concerning these matrices and associated equations are derived. Simpler models include the familiar diffusion model, a simple model of nonlocal mixing in which tracer concentrations are everywhere relaxed toward the global average, and a “leaky barrier” model in which two regions of nonlocal mixing are separated by a weakly diffusive transport barrier. Solutions to the latter two models, with linear chemistry included to allow nontrivial steady states, are used to derive their “effective diffusivities.” These are then used to test how well a diffusion model can mimic the behavior of the nonlocal mixing models over finite regions of parameter space. The diffusion model proves fairly robust, yielding fairly accurate results in situations where no formal argument indicates that it should. These results provide qualified support, from a purely empirical perspective, for the practice of using the diffusion model to represent stratospheric mixing in zonally averaged models. Several important caveats suggest nonetheless that exploration of more theoretically satisfactory representations is warranted.
Abstract
In zonally averaged chemical transport models of the stratosphere, quasi-isentropic mixing is represented by diffusion in latitude. However, it is fairly certain that the real mixing is to some extent nonlocal, so that the diffusive representation is not formally justifiable. This issue is explored from a point of view that combines theory and empiricism. Several models of mixing are described and compared. The most general, including as special cases all of the other models considered, is the integral or “transilient matrix” model. Some known properties of transilient matrices are discussed in a more formal way than has been done previously, and some new results concerning these matrices and associated equations are derived. Simpler models include the familiar diffusion model, a simple model of nonlocal mixing in which tracer concentrations are everywhere relaxed toward the global average, and a “leaky barrier” model in which two regions of nonlocal mixing are separated by a weakly diffusive transport barrier. Solutions to the latter two models, with linear chemistry included to allow nontrivial steady states, are used to derive their “effective diffusivities.” These are then used to test how well a diffusion model can mimic the behavior of the nonlocal mixing models over finite regions of parameter space. The diffusion model proves fairly robust, yielding fairly accurate results in situations where no formal argument indicates that it should. These results provide qualified support, from a purely empirical perspective, for the practice of using the diffusion model to represent stratospheric mixing in zonally averaged models. Several important caveats suggest nonetheless that exploration of more theoretically satisfactory representations is warranted.
Abstract
A two-column, nonrotating radiative–convective model is formulated in which the free-tropospheric temperature profiles of the two columns are assumed to be identical and steady and the temperature equation is used diagnostically to calculate the vertical velocities [the weak temperature gradient (WTG) approximation]. These vertical velocities and the continuity equation are then used to calculate the horizontal velocities. No horizontal momentum equation is used. This model differs from other two-column models that have used similar formulations in that here both columns are governed by the same laws rather than different dynamical roles being assigned a priori to the “warm” and “cold” columns. The current formulation has the advantage of generalizing trivially to an arbitrary number of columns, a necessity for developing a 3D model under WTG. The two-column solutions compare reasonably well with a reference two-column model that uses a linear, nonrotating horizontal momentum equation and the same underlying radiative–convective code as the WTG model; the reference model is essentially that used earlier by Nilsson and Emanuel, except modified to have significant viscosity only in a boundary layer near the surface. The two solutions compare best in the limit of large horizontal domain size, behavior opposite to what has been found in models that lack an explicit boundary layer and have viscosity throughout the troposphere. The difference is explained in terms of the circulation driven by boundary layer pressure gradients.
Abstract
A two-column, nonrotating radiative–convective model is formulated in which the free-tropospheric temperature profiles of the two columns are assumed to be identical and steady and the temperature equation is used diagnostically to calculate the vertical velocities [the weak temperature gradient (WTG) approximation]. These vertical velocities and the continuity equation are then used to calculate the horizontal velocities. No horizontal momentum equation is used. This model differs from other two-column models that have used similar formulations in that here both columns are governed by the same laws rather than different dynamical roles being assigned a priori to the “warm” and “cold” columns. The current formulation has the advantage of generalizing trivially to an arbitrary number of columns, a necessity for developing a 3D model under WTG. The two-column solutions compare reasonably well with a reference two-column model that uses a linear, nonrotating horizontal momentum equation and the same underlying radiative–convective code as the WTG model; the reference model is essentially that used earlier by Nilsson and Emanuel, except modified to have significant viscosity only in a boundary layer near the surface. The two solutions compare best in the limit of large horizontal domain size, behavior opposite to what has been found in models that lack an explicit boundary layer and have viscosity throughout the troposphere. The difference is explained in terms of the circulation driven by boundary layer pressure gradients.
Abstract
The authors investigate the accuracy of the weak temperature gradient (WTG) approximation, in which the divergent flow is computed by an assumed balance between adiabatic cooling and diabatic heating, for a prototype linear problem, the Gill model of a localized tropical heat source in a zonally periodic domain. As in earlier work by Neelin using a realistic, spatially distributed forcing, WTG is found to be a reasonable approximation to the full Gill model even when fairly large values of the thermal damping are used. Use of the local forcing and consideration of the different dispersion relations of free modes in the WTG and full Gill systems helps to clarify differences between the two solutions. WTG does not support an equatorial Kelvin wave. Instead, the Kelvin wave speed can be regarded as infinite in WTG. Hence, WTG becomes highly accurate when the thermal damping is sufficiently weak (0.1 day−1 or less) that an equatorial Kelvin wave can propagate around the globe without substantial loss of amplitude. Free Rossby waves are not equatorially trapped under WTG, and this increases the magnitude of the response far from the equator.
Abstract
The authors investigate the accuracy of the weak temperature gradient (WTG) approximation, in which the divergent flow is computed by an assumed balance between adiabatic cooling and diabatic heating, for a prototype linear problem, the Gill model of a localized tropical heat source in a zonally periodic domain. As in earlier work by Neelin using a realistic, spatially distributed forcing, WTG is found to be a reasonable approximation to the full Gill model even when fairly large values of the thermal damping are used. Use of the local forcing and consideration of the different dispersion relations of free modes in the WTG and full Gill systems helps to clarify differences between the two solutions. WTG does not support an equatorial Kelvin wave. Instead, the Kelvin wave speed can be regarded as infinite in WTG. Hence, WTG becomes highly accurate when the thermal damping is sufficiently weak (0.1 day−1 or less) that an equatorial Kelvin wave can propagate around the globe without substantial loss of amplitude. Free Rossby waves are not equatorially trapped under WTG, and this increases the magnitude of the response far from the equator.
Abstract
It is well known that vertical wind shear can organize deep convective systems and greatly extend their lifetimes. Much less is known about the influence of shear on the bulk properties of tropical convection in statistical equilibrium. To address the latter question, the authors present a series of cloud-resolving simulations on a doubly periodic domain with parameterized large-scale dynamics based on the weak temperature gradient (WTG) approximation. The horizontal-mean horizontal wind is relaxed strongly in these simulations toward a simple unidirectional linear vertical shear profile in the troposphere. The strength and depth of the shear layer are varied as control parameters. Surface enthalpy fluxes are prescribed.
The results fall in two distinct regimes. For weak wind shear, time-averaged rainfall decreases with shear and convection remains disorganized. For larger wind shear, rainfall increases with shear, as convection becomes organized into linear mesoscale systems. This nonmonotonic dependence of rainfall on shear is observed when the imposed surface fluxes are moderate. For larger surface fluxes, convection in the unsheared basic state is already strongly organized, but increasing wind shear still leads to increasing rainfall. In addition to surface rainfall, the impacts of shear on the parameterized large-scale vertical velocity, convective mass fluxes, cloud fraction, and momentum transport are also discussed.
Abstract
It is well known that vertical wind shear can organize deep convective systems and greatly extend their lifetimes. Much less is known about the influence of shear on the bulk properties of tropical convection in statistical equilibrium. To address the latter question, the authors present a series of cloud-resolving simulations on a doubly periodic domain with parameterized large-scale dynamics based on the weak temperature gradient (WTG) approximation. The horizontal-mean horizontal wind is relaxed strongly in these simulations toward a simple unidirectional linear vertical shear profile in the troposphere. The strength and depth of the shear layer are varied as control parameters. Surface enthalpy fluxes are prescribed.
The results fall in two distinct regimes. For weak wind shear, time-averaged rainfall decreases with shear and convection remains disorganized. For larger wind shear, rainfall increases with shear, as convection becomes organized into linear mesoscale systems. This nonmonotonic dependence of rainfall on shear is observed when the imposed surface fluxes are moderate. For larger surface fluxes, convection in the unsheared basic state is already strongly organized, but increasing wind shear still leads to increasing rainfall. In addition to surface rainfall, the impacts of shear on the parameterized large-scale vertical velocity, convective mass fluxes, cloud fraction, and momentum transport are also discussed.
