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Abstract
A low-resolution global spectral model truncated at zonal wavenumber 5 and meridional mode 15 is developed to simulate the low-frequency variability of planetary-scale atmospheric motions. The effects of unresolved time and space scales on the slow evolution of the flow are deduced by analyzing their contribution to the tendencies of low-pass-filtered planetary-scale modes in a higher-resolution (R15 truncation) version of the model. This unresolved forcing is parameterized by a quasi-stochastic method formulated on the transform grid of the low-resolution model. The deterministic component of the parameterization consists of a linear regression of the unresolved forcing on the resolved forcing, which represents the autonomous dynamics of the low-resolution model. The regression parameters vary spatially and with the dependent variable. The stochastic component of the parameterization consists of kth-order univariate autoregressive statistical models, AR(k), which simulate the residuals from the linear regression.
Measured against the spatially and temporally filtered flow from the R15 model, the skill exhibited by the low-resolution model without the parameterization, with the deterministic component only, and with the full parameterization using AR(2) and AR(4) models is determined from a set of 30-day simulators. The full parameterization with the AR(4) model demonstrates the greatest skill. For all dependent variables, rms errors are less than their respective saturation values out to 7–11 days. Northern Hemisphere anomaly correlations greater than 0.6 are produced out to 6–8 days, comparable to the low-frequency skill of operational models.
Although this range of skill is not sufficient to cover typical life cycles of persistent anomalies, the low-resolution model is used to investigate the spatial pattern of skill degradation during Atlantic positive persistent anomalies using Monte Carlo simulations. The white-noise component of the AR(k) model provides the dispersion of predictions during the 10-day Monte Carlo runs. The skill degrades most rapidly in regions of enhanced high-frequency transient eddy activity and in regions most sensitive to the stochastic component of the parameterization. Dispersion among the ensemble of predictions is small during the first 4–5 days, indicating that the autoregressive portion of the stochastic model (i.e., excluding the white noise) dominates the loss of skill. Formulating the stochastic model as a multivariate process could conceivably lead to increased skill.
Abstract
A low-resolution global spectral model truncated at zonal wavenumber 5 and meridional mode 15 is developed to simulate the low-frequency variability of planetary-scale atmospheric motions. The effects of unresolved time and space scales on the slow evolution of the flow are deduced by analyzing their contribution to the tendencies of low-pass-filtered planetary-scale modes in a higher-resolution (R15 truncation) version of the model. This unresolved forcing is parameterized by a quasi-stochastic method formulated on the transform grid of the low-resolution model. The deterministic component of the parameterization consists of a linear regression of the unresolved forcing on the resolved forcing, which represents the autonomous dynamics of the low-resolution model. The regression parameters vary spatially and with the dependent variable. The stochastic component of the parameterization consists of kth-order univariate autoregressive statistical models, AR(k), which simulate the residuals from the linear regression.
Measured against the spatially and temporally filtered flow from the R15 model, the skill exhibited by the low-resolution model without the parameterization, with the deterministic component only, and with the full parameterization using AR(2) and AR(4) models is determined from a set of 30-day simulators. The full parameterization with the AR(4) model demonstrates the greatest skill. For all dependent variables, rms errors are less than their respective saturation values out to 7–11 days. Northern Hemisphere anomaly correlations greater than 0.6 are produced out to 6–8 days, comparable to the low-frequency skill of operational models.
Although this range of skill is not sufficient to cover typical life cycles of persistent anomalies, the low-resolution model is used to investigate the spatial pattern of skill degradation during Atlantic positive persistent anomalies using Monte Carlo simulations. The white-noise component of the AR(k) model provides the dispersion of predictions during the 10-day Monte Carlo runs. The skill degrades most rapidly in regions of enhanced high-frequency transient eddy activity and in regions most sensitive to the stochastic component of the parameterization. Dispersion among the ensemble of predictions is small during the first 4–5 days, indicating that the autoregressive portion of the stochastic model (i.e., excluding the white noise) dominates the loss of skill. Formulating the stochastic model as a multivariate process could conceivably lead to increased skill.
Abstract
Perpetual January data from a simple global two-level model are used to diagnose the forcing of the model's low-frequency (LF), large-scale flow. The forcing is considered within the context of a hypothetical low-order model that resolves only the slowly varying planetary-scale modes. Thus, the forcing is partitioned into “resolved” components consisting of LF, planetary-scale (i.e., autonomous) processes and “unresolved” components that involve high-frequency (HF) transient eddy and LF synoptic-scale effects. Spatial patterns of the net tendencies of low-pass filtered, planetary-scale barotropic streamfunction and vertically averaged temperature are compared with corresponding patterns of resolved and unresolved forcing during the onset, maintenance, and decay stages of composited persistent anomalies.
Growth stages of positive and negative persistent anomalies that are found in both the Atlantic (ATL) and Pacific (PAC) regions are dominated by autonomous processes. For positive anomalies, the net tendencies and resolved forcing patterns resemble large-scale wave trains emanating from the subtropics upstream of the anomaly region. Although only of secondary importance, unresolved forcing contributes positively toward growth just upstream of the ATL anomaly region, but does not contribute substantially in the PAC region. Negative anomaly growth is dominated in both regions by autonomous processes to a greater extent than positive anomaly growth. Unresolved forcing is critical in mechanically maintaining persistent anomalies of both signs, but thermally acts in a destructive sense. Decay stages of all anomalies are dominated by resolved forcing.
The extent to which local signature of barotropic and baroclinic energy sources accompany anomaly onset is examined by constructing these terms in the context of a local kinetic energy budget. Superficially, baroclinic (barotropic) conversion tends to be associated with ATL positive (negative) anomaly onset. However, the kinetic energy source patterns are statistically less significant than, and do not typically resemble, the resolved forcing patterns. This is particularly true for the PAC composite anomalies. Clearly, redistribution terms in the local kinetic energy budget are important. But more important, the representativeness of composites in depicting the dynamics of persistent anomalies is called into question.
An examination of the slowly varying local resolved and unresolved forcing during the life cycles of individual members of the positive anomaly composite shows considerable variability, suggesting that no single mechanism is solely responsible for anomaly development. For example, cases of anomaly growth characterized primarily by unresolved forcing are noted. Also seen are anomaly events that more closely resemble stationary large-scale waves.
Abstract
Perpetual January data from a simple global two-level model are used to diagnose the forcing of the model's low-frequency (LF), large-scale flow. The forcing is considered within the context of a hypothetical low-order model that resolves only the slowly varying planetary-scale modes. Thus, the forcing is partitioned into “resolved” components consisting of LF, planetary-scale (i.e., autonomous) processes and “unresolved” components that involve high-frequency (HF) transient eddy and LF synoptic-scale effects. Spatial patterns of the net tendencies of low-pass filtered, planetary-scale barotropic streamfunction and vertically averaged temperature are compared with corresponding patterns of resolved and unresolved forcing during the onset, maintenance, and decay stages of composited persistent anomalies.
Growth stages of positive and negative persistent anomalies that are found in both the Atlantic (ATL) and Pacific (PAC) regions are dominated by autonomous processes. For positive anomalies, the net tendencies and resolved forcing patterns resemble large-scale wave trains emanating from the subtropics upstream of the anomaly region. Although only of secondary importance, unresolved forcing contributes positively toward growth just upstream of the ATL anomaly region, but does not contribute substantially in the PAC region. Negative anomaly growth is dominated in both regions by autonomous processes to a greater extent than positive anomaly growth. Unresolved forcing is critical in mechanically maintaining persistent anomalies of both signs, but thermally acts in a destructive sense. Decay stages of all anomalies are dominated by resolved forcing.
The extent to which local signature of barotropic and baroclinic energy sources accompany anomaly onset is examined by constructing these terms in the context of a local kinetic energy budget. Superficially, baroclinic (barotropic) conversion tends to be associated with ATL positive (negative) anomaly onset. However, the kinetic energy source patterns are statistically less significant than, and do not typically resemble, the resolved forcing patterns. This is particularly true for the PAC composite anomalies. Clearly, redistribution terms in the local kinetic energy budget are important. But more important, the representativeness of composites in depicting the dynamics of persistent anomalies is called into question.
An examination of the slowly varying local resolved and unresolved forcing during the life cycles of individual members of the positive anomaly composite shows considerable variability, suggesting that no single mechanism is solely responsible for anomaly development. For example, cases of anomaly growth characterized primarily by unresolved forcing are noted. Also seen are anomaly events that more closely resemble stationary large-scale waves.
Abstract
The interaction between moisture and baroclinic eddies was examined through eddy life-cycle experiments using a global, primitive equation model. How condensation affects the structural evolution of eddies, their fluxes of heat, moisture, and momentum, and their subsequent interaction with the zonal average state was examined. Initial states corresponded to climatological winter and summer zonal average states. For most experiments the perturbation had a fundamental zonal wavenumber 7, representing an appropriate scale for transient eddies that reach substantial amplitudes in the atmosphere. Additional experiments used fundamental wavenumber 4, 10, or 14.
The wave's vertical motion produced midtropospheric supersaturation whose heating further amplified the vertical motion. Consequently, the largest effects of condensation were associated with vertical transports. Compared to corresponding dry experiments, intensified vertical motions increased the maximum kinetic energy attained by the wave, but they also depleted the eddy available potential energy more rapidly, thus inducing a faster evolution of the life cycle. Even greater condensation occurred near the surface as warm, moist air moving poleward became supersaturated by heat loss into a cooler surface. However, the latent heat thus released was balanced by the heat loss into the surface and so produced no dynamical effect. The hydrological cycle induced by the wave was largely confined to the lower troposphere, but the strongest effects of condensation on eddy dynamics occurred in the upper troposphere, so the condensational heating altered only weakly the intensity of the wave-induced moisture cycle.
Abstract
The interaction between moisture and baroclinic eddies was examined through eddy life-cycle experiments using a global, primitive equation model. How condensation affects the structural evolution of eddies, their fluxes of heat, moisture, and momentum, and their subsequent interaction with the zonal average state was examined. Initial states corresponded to climatological winter and summer zonal average states. For most experiments the perturbation had a fundamental zonal wavenumber 7, representing an appropriate scale for transient eddies that reach substantial amplitudes in the atmosphere. Additional experiments used fundamental wavenumber 4, 10, or 14.
The wave's vertical motion produced midtropospheric supersaturation whose heating further amplified the vertical motion. Consequently, the largest effects of condensation were associated with vertical transports. Compared to corresponding dry experiments, intensified vertical motions increased the maximum kinetic energy attained by the wave, but they also depleted the eddy available potential energy more rapidly, thus inducing a faster evolution of the life cycle. Even greater condensation occurred near the surface as warm, moist air moving poleward became supersaturated by heat loss into a cooler surface. However, the latent heat thus released was balanced by the heat loss into the surface and so produced no dynamical effect. The hydrological cycle induced by the wave was largely confined to the lower troposphere, but the strongest effects of condensation on eddy dynamics occurred in the upper troposphere, so the condensational heating altered only weakly the intensity of the wave-induced moisture cycle.
Abstract
We use a global, primitive equation model to study the evolution of waves growing in a zonal mean state that is initially baroclinically unstable. The waves produce changes in the zonal mean state that we compare with changes predicted by baroclinic adjustment theories We examine mean state adjustment by representative zonal wavenumbers 3, 7 or 12.
In the absence of surface processes, as the wave grows to its maximum amplitude, it reduces the zonal mean state's potential vorticity gradient through the lower troposphere, in accord with adjustment theories. Over the latitudes with largest wave amplitude, changes in the static stability and the zonal wind's vertical shear contribute about equally to the potential vorticity gradient adjustment. However, during the last day of a wave's growth, momentum fluxes strengthen the barotropic component of the zonal wind and the potential vorticity gradient in the middle troposphere, changes that are not anticipated by adjustment theory. The static stability adjustment occurs across the latitudinal band occupied by the growing wave. Further experiments show that the static stability adjustment alone is very effective in reducing the instability of the flow and restricting the maximum amplitude attained by growing waves. Adjustment of the zonal wind's vertical shear is confined to a narrower range of latitude and is partially reversed as the wave decays. Additional experiments indicate that the barotropic governor mechanism of James does not contribute strongly to the mean flow's stabilization in the cases we examine, though it way inhibit secondary growth at latitudes adjacent to the initial disturbance.
When the model includes surface friction and heat flux, the waves adjust the zonal mean state less effectively, especially near the surface. Surface heat flux inhibits static stability adjustment, and surface friction inhibits adjustment of the zonal wind's vertical shear. In the absence of surface processes, the adjusted state produced by the wave is quite different from observed mean structures. However, with both surface processes included, the vertical profiles of the adjusted static stability, wind shear and potential vorticity gradient are similar to observed profiles. The model' interaction between the waves and the mean flow corroborates results from previous studies of baroclinic adjustment that used simpler representations of atmospheric dynamics.
Abstract
We use a global, primitive equation model to study the evolution of waves growing in a zonal mean state that is initially baroclinically unstable. The waves produce changes in the zonal mean state that we compare with changes predicted by baroclinic adjustment theories We examine mean state adjustment by representative zonal wavenumbers 3, 7 or 12.
In the absence of surface processes, as the wave grows to its maximum amplitude, it reduces the zonal mean state's potential vorticity gradient through the lower troposphere, in accord with adjustment theories. Over the latitudes with largest wave amplitude, changes in the static stability and the zonal wind's vertical shear contribute about equally to the potential vorticity gradient adjustment. However, during the last day of a wave's growth, momentum fluxes strengthen the barotropic component of the zonal wind and the potential vorticity gradient in the middle troposphere, changes that are not anticipated by adjustment theory. The static stability adjustment occurs across the latitudinal band occupied by the growing wave. Further experiments show that the static stability adjustment alone is very effective in reducing the instability of the flow and restricting the maximum amplitude attained by growing waves. Adjustment of the zonal wind's vertical shear is confined to a narrower range of latitude and is partially reversed as the wave decays. Additional experiments indicate that the barotropic governor mechanism of James does not contribute strongly to the mean flow's stabilization in the cases we examine, though it way inhibit secondary growth at latitudes adjacent to the initial disturbance.
When the model includes surface friction and heat flux, the waves adjust the zonal mean state less effectively, especially near the surface. Surface heat flux inhibits static stability adjustment, and surface friction inhibits adjustment of the zonal wind's vertical shear. In the absence of surface processes, the adjusted state produced by the wave is quite different from observed mean structures. However, with both surface processes included, the vertical profiles of the adjusted static stability, wind shear and potential vorticity gradient are similar to observed profiles. The model' interaction between the waves and the mean flow corroborates results from previous studies of baroclinic adjustment that used simpler representations of atmospheric dynamics.
Abstract
This paper describes the use of a regional-scale air quality model as a diagnostic tool for analyzing problems associated with acid rain. The model, which is hybrid in nature, consists of a puff module and a grid module. The puff module computes the evolution of individual puffs, such as the horizontal and vertical standard deviations of the puff spreads and the location of the center of mass, emitted continuously from each major point source. It also determines the location at which the puff will be released to the grid module and the amount of oxidation and deposition along the trajectory. The grid module then follows the transport, diffusion, and chemical reactions of these aged puffs, as well as emissions from a variety of diffuse sources. Elaborate schemes for both dry and wet deposition have also been incorporated into the model. This model has been exercised for two real-time meteorological scenarios—a dry case and a two-day rainstorm episode in the Northern Great Plains. On the basis of model calculations, atmospheric budgets for SO2 and sulfate over the modeling region have been estimated.
Abstract
This paper describes the use of a regional-scale air quality model as a diagnostic tool for analyzing problems associated with acid rain. The model, which is hybrid in nature, consists of a puff module and a grid module. The puff module computes the evolution of individual puffs, such as the horizontal and vertical standard deviations of the puff spreads and the location of the center of mass, emitted continuously from each major point source. It also determines the location at which the puff will be released to the grid module and the amount of oxidation and deposition along the trajectory. The grid module then follows the transport, diffusion, and chemical reactions of these aged puffs, as well as emissions from a variety of diffuse sources. Elaborate schemes for both dry and wet deposition have also been incorporated into the model. This model has been exercised for two real-time meteorological scenarios—a dry case and a two-day rainstorm episode in the Northern Great Plains. On the basis of model calculations, atmospheric budgets for SO2 and sulfate over the modeling region have been estimated.
Abstract
The nonlinear development of baroclinically unstable waves in the presence of surface friction and heat flux is studied, using a global primitive equation model. The experiments use zonal wavenumber 3.7 or 12 and a variety of initial conditions, mostly representative of observed initial states. Other initial states consist of solidbody rotation with vertical shear of the zonal wind. In addition to comparisons of inviscid and dissipative experiments, the effect of linear and nonlinear drag formulations is compared. Starting from a small-amplitude perturbation in the temperature field, a modal structure emerges and grows exponentially for a few days. Unstable waves assume a structure that reduces frictional energy IOU when surface drag is present, but they still retain a normal mode character during a period of rapid growth. As the wave grows in amplitude, the ratio of upper-level to low-level eddy kinetic energy increases substantially in the presence of nonlinear surface drag. In the absence of surface drag or in the presence of linear drag the waves experience less structural change. Surface processes reduce the maximum amplitude achieved by the wave and damp the slowly growing wavenumber-3 and shallow wavenumber-12 disturbances more effectively than the rapidly growing, deep wavenumber 7.In the mature wave, surface momentum drag and heat flux suppress eddy velocity and temperature fields near the surface, causing the meridional heat flux to peak at about 800 mb rather than near the surface as itdoes when surface fluxes are excluded. When surface fluxes are present, the structures of mature waves resemble observations more closely than when the fluxes are absent. When initial conditions are similar to those used by Simmons and Hoskins, the Eliassen-Palm flux produced by the mature wave tends to converge in the upper troposphere, primarily as the result of the vertical gradient in poleward heat flux. However, the convergence is sensitive to initial conditions and is spread more broadly through the troposphere for other configurations of the initial state.
Abstract
The nonlinear development of baroclinically unstable waves in the presence of surface friction and heat flux is studied, using a global primitive equation model. The experiments use zonal wavenumber 3.7 or 12 and a variety of initial conditions, mostly representative of observed initial states. Other initial states consist of solidbody rotation with vertical shear of the zonal wind. In addition to comparisons of inviscid and dissipative experiments, the effect of linear and nonlinear drag formulations is compared. Starting from a small-amplitude perturbation in the temperature field, a modal structure emerges and grows exponentially for a few days. Unstable waves assume a structure that reduces frictional energy IOU when surface drag is present, but they still retain a normal mode character during a period of rapid growth. As the wave grows in amplitude, the ratio of upper-level to low-level eddy kinetic energy increases substantially in the presence of nonlinear surface drag. In the absence of surface drag or in the presence of linear drag the waves experience less structural change. Surface processes reduce the maximum amplitude achieved by the wave and damp the slowly growing wavenumber-3 and shallow wavenumber-12 disturbances more effectively than the rapidly growing, deep wavenumber 7.In the mature wave, surface momentum drag and heat flux suppress eddy velocity and temperature fields near the surface, causing the meridional heat flux to peak at about 800 mb rather than near the surface as itdoes when surface fluxes are excluded. When surface fluxes are present, the structures of mature waves resemble observations more closely than when the fluxes are absent. When initial conditions are similar to those used by Simmons and Hoskins, the Eliassen-Palm flux produced by the mature wave tends to converge in the upper troposphere, primarily as the result of the vertical gradient in poleward heat flux. However, the convergence is sensitive to initial conditions and is spread more broadly through the troposphere for other configurations of the initial state.
Abstract
Observational studies have revealed some coherent extratropical patterns associated with the tropical Madden–Julian (MJ) wave. This study is an attempt to clarify and constrain the interpretation of these patterns by investigating tropical–extratropical interactions on intraseasonal time scales in a global spectral model (GSM). Forcing representative of northern winter is used. A simple heating-only cumulus parameterization scheme is included to generate the MJ wave. The wave period in the model falls within the 30–60 day range observed and has a structure consistent with observations.
Various statistical techniques including compositing, empirical orthogonal function (EOF) analysis, and singular value decomposition (SVD) have been used to identify those extratropical patterns associated with the tropical MJ wave.
Under zonally symmetric external conditions (no topography) the MJ wave maintains a highly regular amplitude and phase speed. Nevertheless, there is no statistically significant coherent variability between the tropics and extratropics—no matter how much one field lags the other, and despite the frequent appearance of upper-level equatorial waveguides. Significance is determined by a Monte Carlo data scrambling method.
When topography is included, the MJ wave has a more variable amplitude in both space and time. All the statistical analyses reveal consistent planetary-scale extratropical patterns associated with different phases of the tropical wave. EOF and SVD analyses indicate that the MJ wave can explain about 10% of the variance in the extratropical 250-mb height field on intraseasonal time scales. Monte Carlo significance testing indicates that about 5% can be attributed to physical processes and 5% to chance.
The signal of tropical–extratropical interaction in the mountain case can be exposed more clearly by reducing the radiative driving by half and by using a specified propagating heat source as a proxy MJ wave. In this case up to 40% of the extratropical variance can be explained by the tropical wave, while the principal patterns of interaction remain similar to those obtained with strong driving.
The authors conclude that topography is essential to the propagation of a coherent MJ signal into the extratropics, while topography tends to disrupt the MJ wave in the tropics. The MJ wave (and its associated extratropical patterns) must be maintained in the presence of topography by wave activity penetrating the tropics from higher latitudes. A sufficiently high level of eddy activity in the extratropics is necessary for this to occur.
Abstract
Observational studies have revealed some coherent extratropical patterns associated with the tropical Madden–Julian (MJ) wave. This study is an attempt to clarify and constrain the interpretation of these patterns by investigating tropical–extratropical interactions on intraseasonal time scales in a global spectral model (GSM). Forcing representative of northern winter is used. A simple heating-only cumulus parameterization scheme is included to generate the MJ wave. The wave period in the model falls within the 30–60 day range observed and has a structure consistent with observations.
Various statistical techniques including compositing, empirical orthogonal function (EOF) analysis, and singular value decomposition (SVD) have been used to identify those extratropical patterns associated with the tropical MJ wave.
Under zonally symmetric external conditions (no topography) the MJ wave maintains a highly regular amplitude and phase speed. Nevertheless, there is no statistically significant coherent variability between the tropics and extratropics—no matter how much one field lags the other, and despite the frequent appearance of upper-level equatorial waveguides. Significance is determined by a Monte Carlo data scrambling method.
When topography is included, the MJ wave has a more variable amplitude in both space and time. All the statistical analyses reveal consistent planetary-scale extratropical patterns associated with different phases of the tropical wave. EOF and SVD analyses indicate that the MJ wave can explain about 10% of the variance in the extratropical 250-mb height field on intraseasonal time scales. Monte Carlo significance testing indicates that about 5% can be attributed to physical processes and 5% to chance.
The signal of tropical–extratropical interaction in the mountain case can be exposed more clearly by reducing the radiative driving by half and by using a specified propagating heat source as a proxy MJ wave. In this case up to 40% of the extratropical variance can be explained by the tropical wave, while the principal patterns of interaction remain similar to those obtained with strong driving.
The authors conclude that topography is essential to the propagation of a coherent MJ signal into the extratropics, while topography tends to disrupt the MJ wave in the tropics. The MJ wave (and its associated extratropical patterns) must be maintained in the presence of topography by wave activity penetrating the tropics from higher latitudes. A sufficiently high level of eddy activity in the extratropics is necessary for this to occur.
