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Abstract
We consider regimes of low-frequency variability in large-scale atmospheric dynamics. The model used for the study of these regimes is the fully-nonlinear, equivalent-barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography. Twenty-five modes are retained in a spherical harmonics expansion of the streamfunction. Solutions are studied as a function of the nondimensional intensity of the forcing and dissipation.
Multiple stationary solutions are obtained as a result of nonlinear interaction between waves, mean flow and orography. The number of modes retained in the analysis permits these multiple equilibria to appear for realistic values of the forcing. The equilibria exhibit blocked and zonal flow patterns bearing a marked resemblance to synoptically defined zonal and blocked Northern Hemisphere midlatitude flows.
Wave-wave interactions influence strongly the stability properties of the equilibria and the time evolution of nonequilibrium solutions. Time-dependent solutions show persistent sequences which occur in the phase-space vicinity of the zonal and blocked equilibria. Composite flow patterns of the persistent sequences are similar to the equilibria nearby, which permits the unambiguous definition of quasi-stationary flow regimes, zonal and blocked, respectively. The number of episodes of blocked or zonal flow decreases monotonically as their duration increases, in agreement with observations.
The statistics of transitions between the two types of planetary flow regimes are computed from the model's deterministic dynamics. These transitional called breaks in statistical-synoptic long-range forecasting, are shown to be influenced by changes in model parameters. This influence is discussed in terms of the effect of anomalous boundary conditions on large-scale midlatitude atmospheric flow and on its predictability.
Abstract
We consider regimes of low-frequency variability in large-scale atmospheric dynamics. The model used for the study of these regimes is the fully-nonlinear, equivalent-barotropic vorticity equation on the sphere, with simplified forcing, dissipation and topography. Twenty-five modes are retained in a spherical harmonics expansion of the streamfunction. Solutions are studied as a function of the nondimensional intensity of the forcing and dissipation.
Multiple stationary solutions are obtained as a result of nonlinear interaction between waves, mean flow and orography. The number of modes retained in the analysis permits these multiple equilibria to appear for realistic values of the forcing. The equilibria exhibit blocked and zonal flow patterns bearing a marked resemblance to synoptically defined zonal and blocked Northern Hemisphere midlatitude flows.
Wave-wave interactions influence strongly the stability properties of the equilibria and the time evolution of nonequilibrium solutions. Time-dependent solutions show persistent sequences which occur in the phase-space vicinity of the zonal and blocked equilibria. Composite flow patterns of the persistent sequences are similar to the equilibria nearby, which permits the unambiguous definition of quasi-stationary flow regimes, zonal and blocked, respectively. The number of episodes of blocked or zonal flow decreases monotonically as their duration increases, in agreement with observations.
The statistics of transitions between the two types of planetary flow regimes are computed from the model's deterministic dynamics. These transitional called breaks in statistical-synoptic long-range forecasting, are shown to be influenced by changes in model parameters. This influence is discussed in terms of the effect of anomalous boundary conditions on large-scale midlatitude atmospheric flow and on its predictability.
Abstract
Interdecadal climate variability in an idealized coupled ocean–atmosphere–sea-ice model is studied. The ocean component is a fully three-dimensional primitive equation model and the atmospheric component is a two-dimensional (2D) energy balance model of Budyko–Sellers–North type, while sea ice is represented by a 2D thermodynamic model. In a wide range of parameters the model climatology resembles certain aspects of observed climate. Two types of interdecadal variability are found. The first one is characterized by northward-propagating upper-ocean temperature anomalies in the northwestern part of the ocean basin and a westward-propagating, wavelike temperature pattern at depth. The other type has larger-scale temperature anomalies that propagate westward in both the upper and deep ocean, along the sea ice edge. Both types of oscillations have been found previously in similar models that do not include sea ice. Therefore, the oscillation mechanism does not depend on sea-ice feedbacks nor is it modified very much by the inclusion of sea ice. For some parameter values, the interdecadal oscillations are self-sustained, while for others they are damped. Stochastic-forcing experiments show that, in the latter case, significant interdecadal signals can still be identified in the time series of oceanic heat transport. The periods of these signals, however, do not closely match those identified in a stability analysis of the deterministic model when linearized about its steady state. The authors show that linearization around the actual climatology of the stochastically forced integrations provides a better match for some of the modes that were poorly explained when linearizing about the deterministic model's steady state. The main difference between the two basic states is in the distribution of climatological convective depth, which is affected strongly by intermittent atmospheric forcing.
Abstract
Interdecadal climate variability in an idealized coupled ocean–atmosphere–sea-ice model is studied. The ocean component is a fully three-dimensional primitive equation model and the atmospheric component is a two-dimensional (2D) energy balance model of Budyko–Sellers–North type, while sea ice is represented by a 2D thermodynamic model. In a wide range of parameters the model climatology resembles certain aspects of observed climate. Two types of interdecadal variability are found. The first one is characterized by northward-propagating upper-ocean temperature anomalies in the northwestern part of the ocean basin and a westward-propagating, wavelike temperature pattern at depth. The other type has larger-scale temperature anomalies that propagate westward in both the upper and deep ocean, along the sea ice edge. Both types of oscillations have been found previously in similar models that do not include sea ice. Therefore, the oscillation mechanism does not depend on sea-ice feedbacks nor is it modified very much by the inclusion of sea ice. For some parameter values, the interdecadal oscillations are self-sustained, while for others they are damped. Stochastic-forcing experiments show that, in the latter case, significant interdecadal signals can still be identified in the time series of oceanic heat transport. The periods of these signals, however, do not closely match those identified in a stability analysis of the deterministic model when linearized about its steady state. The authors show that linearization around the actual climatology of the stochastically forced integrations provides a better match for some of the modes that were poorly explained when linearizing about the deterministic model's steady state. The main difference between the two basic states is in the distribution of climatological convective depth, which is affected strongly by intermittent atmospheric forcing.
Abstract
An experiment was performed to study the effect of increased model resolution on satellite sounding data impact. Assimilation cycles were carried out with data from 0000 GMT 29 January to 0300 GMT 21 February 1976, using coarse- and fine-resolution versions of the GLAS second-order general circulation model (GCM). For each model resolution, an assimilation cycle was performed using both conventional and experimental data, which included temperature soundings from the NOAA-4 and Nimbus-6 satellites. A second cycle was run using the same data but excluding the satellite-derived temperature soundings.
The objective analyses produced by the assimilation cycles were used as initial states for a series of evenly spaced 72 h numerical weather forecasts. Eleven forecasts with the same resolution in the forecast model as in the data assimilation were performed at 48 h intervals for each assimilation. Additional forecasts were made with the higher resolution forecast model from the lower resolution assimilation cycle and vice versa. Initial state differences were evaluated in terms of the magnitude, location and structure of large-scale differences between meteorological fields. Numerical prediction differences were evaluated by means of objective scores and subjective comparisons.
Objective scores show a substantially larger beneficial impact of the sounding data at 48 and 60 h with the higher resolution version of the model. Subjective evaluation also revealed a larger positive impact of satellite sounding data with the higher resolution model.
This study has two important limitations: it was carried out with two versions of one model, the GLAS GCM, and the number of forecast cases analyzed is small. Within these limitations, our results indicate that model improvement enhances the impact of satellite data.
Abstract
An experiment was performed to study the effect of increased model resolution on satellite sounding data impact. Assimilation cycles were carried out with data from 0000 GMT 29 January to 0300 GMT 21 February 1976, using coarse- and fine-resolution versions of the GLAS second-order general circulation model (GCM). For each model resolution, an assimilation cycle was performed using both conventional and experimental data, which included temperature soundings from the NOAA-4 and Nimbus-6 satellites. A second cycle was run using the same data but excluding the satellite-derived temperature soundings.
The objective analyses produced by the assimilation cycles were used as initial states for a series of evenly spaced 72 h numerical weather forecasts. Eleven forecasts with the same resolution in the forecast model as in the data assimilation were performed at 48 h intervals for each assimilation. Additional forecasts were made with the higher resolution forecast model from the lower resolution assimilation cycle and vice versa. Initial state differences were evaluated in terms of the magnitude, location and structure of large-scale differences between meteorological fields. Numerical prediction differences were evaluated by means of objective scores and subjective comparisons.
Objective scores show a substantially larger beneficial impact of the sounding data at 48 and 60 h with the higher resolution version of the model. Subjective evaluation also revealed a larger positive impact of satellite sounding data with the higher resolution model.
This study has two important limitations: it was carried out with two versions of one model, the GLAS GCM, and the number of forecast cases analyzed is small. Within these limitations, our results indicate that model improvement enhances the impact of satellite data.
Abstract
No abstract available.
Abstract
No abstract available.
Abstract
Methods are derived for the time-continuous four-dimensional assimilation of satellite sounding temperatures. The methods presented include time-continuous versions of direct insertion, successive correction and statistical linear regression. They are applied to temperature sounding data obtained from radiance measurements taken by instruments aboard the polar-orbiting satellites NOAA 4 and Nimbus 6. The data were collected during the U.S. Data System Test in January-March 1976.
A comprehensive series of experiments was performed to study the effects of using various amounts of satellite data and differing methods of assimilation. The experiments included the assimilation of data from the NOAA 4 satellite only, from Nimbus 6 only, and of data from both satellites combined. Other experiments involved variations in the application of our time-continuous statistical assimilation methods and of asynoptic successive correction methods. Intermittent assimilation of the sounding data was also tested, and its results compared with those of time-continuous assimilation.
Atmospheric states determined in the assimilation experiments served as initial states for a sequence of evenly spaced 3-day numerical weather forecasts corresponding to each experiment. The effects of the satellite data were evaluated according to the following criteria: 1) differences between the initial states produced with and without utilization of satellite data, 2) differences between numerical predictions made from these initial states, and. 3) differences in local weather forecasts resulting from the large-scale numerical predictions.
Initial-state differences were evaluated in terms of magnitude and location of large-scale differences between meteorological fields. Numerical prediction differences were evaluated in terms of SI skill scores and rms errors, as well as by synoptic case studies. An automated forecasting model (AFM) based on quasi-geostrophic theory and on subjective forecasting principles was developed to facilitate the objective evaluation of differences produced in local weather forecasts, especially precipitation forecasts.
These studies suggest the following conclusions: 1) satellite-derived temperature data can have a modest, but statistically significant positive impact on numerical weather prediction in the 2-3 day range; 2) the impact is highly sensitive to the quantity of data available, and increases with data quantity; and 3) the method used to assimilate the satellite data can influence appreciably the magnitude of the impact obtained for the same data.
Abstract
Methods are derived for the time-continuous four-dimensional assimilation of satellite sounding temperatures. The methods presented include time-continuous versions of direct insertion, successive correction and statistical linear regression. They are applied to temperature sounding data obtained from radiance measurements taken by instruments aboard the polar-orbiting satellites NOAA 4 and Nimbus 6. The data were collected during the U.S. Data System Test in January-March 1976.
A comprehensive series of experiments was performed to study the effects of using various amounts of satellite data and differing methods of assimilation. The experiments included the assimilation of data from the NOAA 4 satellite only, from Nimbus 6 only, and of data from both satellites combined. Other experiments involved variations in the application of our time-continuous statistical assimilation methods and of asynoptic successive correction methods. Intermittent assimilation of the sounding data was also tested, and its results compared with those of time-continuous assimilation.
Atmospheric states determined in the assimilation experiments served as initial states for a sequence of evenly spaced 3-day numerical weather forecasts corresponding to each experiment. The effects of the satellite data were evaluated according to the following criteria: 1) differences between the initial states produced with and without utilization of satellite data, 2) differences between numerical predictions made from these initial states, and. 3) differences in local weather forecasts resulting from the large-scale numerical predictions.
Initial-state differences were evaluated in terms of magnitude and location of large-scale differences between meteorological fields. Numerical prediction differences were evaluated in terms of SI skill scores and rms errors, as well as by synoptic case studies. An automated forecasting model (AFM) based on quasi-geostrophic theory and on subjective forecasting principles was developed to facilitate the objective evaluation of differences produced in local weather forecasts, especially precipitation forecasts.
These studies suggest the following conclusions: 1) satellite-derived temperature data can have a modest, but statistically significant positive impact on numerical weather prediction in the 2-3 day range; 2) the impact is highly sensitive to the quantity of data available, and increases with data quantity; and 3) the method used to assimilate the satellite data can influence appreciably the magnitude of the impact obtained for the same data.
Abstract
Multiple flow regimes are reexamined in a global, three-level, quasigeostrophic (QG3) model with realistic topography in spherical geometry. This QG3 model, using a T21 triangular truncation in the horizontal, has a fairly realistic climatology for Northern Hemisphere winter and exhibits multiple regimes that resemble those found in atmospheric observations. Four regimes are robust to changes in the classification method, k-means versus mixture modeling, and its parameters. These regimes correspond roughly to opposite phases of the Arctic Oscillation (AO) and the North Atlantic Oscillation (NAO), respectively.
The Markov chain representation of regime transitions is refined here by finding the preferred transition paths in a three-dimensional (3D) subspace of the model's phase space. Preferred transitions occur from the positive phase of the NAO (NAO+) to that of the AO (AO+), from AO+ to NAO−, and from NAO− to NAO+, but not directly between opposite phases of the AO. The angular probability density function (PDF) of the regime exits that correspond to these preferred transitions have one or, sometimes, two fairly sharp maxima. These angular PDF maxima are, in most cases, not aligned with the line segments between regime centroids in phase space and might point to heteroclinic or homoclinic connections between unstable equilibria in the model's phase space. Preferred transitions paths are also determined for a stochastically forced Lorenz system to help explain this striking feature of the QG3 model.
The episodic description of the model's low-frequency variability via the Markov chain of multiple regimes is complemented by an oscillatory description. Multichannel singular-spectrum analysis is applied to the trajectory in the same 3D subspace. Two statistically significant oscillations are found and have periods of 19 and 37 days, respectively. Both oscillations have four composites that include NAO+, AO+, and NAO−, in this order. The fourth composite occurs between AO+ and NAO−; it resembles the Pacific–North American pattern, which is not captured by the model's episodic description. The two oscillations have similar spatial patterns, and are weakly phased locked. They have certain features in common with the westward-propagating Branstator–Kushnir wave, as well as with the standing oscillation that arises from the oscillatory topographic instability of Ghil and associates.
Abstract
Multiple flow regimes are reexamined in a global, three-level, quasigeostrophic (QG3) model with realistic topography in spherical geometry. This QG3 model, using a T21 triangular truncation in the horizontal, has a fairly realistic climatology for Northern Hemisphere winter and exhibits multiple regimes that resemble those found in atmospheric observations. Four regimes are robust to changes in the classification method, k-means versus mixture modeling, and its parameters. These regimes correspond roughly to opposite phases of the Arctic Oscillation (AO) and the North Atlantic Oscillation (NAO), respectively.
The Markov chain representation of regime transitions is refined here by finding the preferred transition paths in a three-dimensional (3D) subspace of the model's phase space. Preferred transitions occur from the positive phase of the NAO (NAO+) to that of the AO (AO+), from AO+ to NAO−, and from NAO− to NAO+, but not directly between opposite phases of the AO. The angular probability density function (PDF) of the regime exits that correspond to these preferred transitions have one or, sometimes, two fairly sharp maxima. These angular PDF maxima are, in most cases, not aligned with the line segments between regime centroids in phase space and might point to heteroclinic or homoclinic connections between unstable equilibria in the model's phase space. Preferred transitions paths are also determined for a stochastically forced Lorenz system to help explain this striking feature of the QG3 model.
The episodic description of the model's low-frequency variability via the Markov chain of multiple regimes is complemented by an oscillatory description. Multichannel singular-spectrum analysis is applied to the trajectory in the same 3D subspace. Two statistically significant oscillations are found and have periods of 19 and 37 days, respectively. Both oscillations have four composites that include NAO+, AO+, and NAO−, in this order. The fourth composite occurs between AO+ and NAO−; it resembles the Pacific–North American pattern, which is not captured by the model's episodic description. The two oscillations have similar spatial patterns, and are weakly phased locked. They have certain features in common with the westward-propagating Branstator–Kushnir wave, as well as with the standing oscillation that arises from the oscillatory topographic instability of Ghil and associates.
Abstract
This paper constructs and analyzes a reduced nonlinear stochastic model of extratropical low-frequency variability. To do so, it applies multilevel quadratic regression to the output of a long simulation of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography; the model's phase space has a dimension of O(104).
The reduced model has 45 variables and captures well the non-Gaussian features of the QG3 model's probability density function (PDF). In particular, the reduced model's PDF shares with the QG3 model its four anomalously persistent flow patterns, which correspond to opposite phases of the Arctic Oscillation and the North Atlantic Oscillation, as well as the Markov chain of transitions between these regimes. In addition, multichannel singular spectrum analysis identifies intraseasonal oscillations with a period of 35–37 days and of 20 days in the data generated by both the QG3 model and its low-dimensional analog.
An analytical and numerical study of the reduced model starts with the fixed points and oscillatory eigenmodes of the model's deterministic part and uses systematically an increasing noise parameter to connect these with the behavior of the full, stochastically forced model version. The results of this study point to the origin of the QG3 model's multiple regimes and intraseasonal oscillations and identify the connections between the two types of behavior.
Abstract
This paper constructs and analyzes a reduced nonlinear stochastic model of extratropical low-frequency variability. To do so, it applies multilevel quadratic regression to the output of a long simulation of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography; the model's phase space has a dimension of O(104).
The reduced model has 45 variables and captures well the non-Gaussian features of the QG3 model's probability density function (PDF). In particular, the reduced model's PDF shares with the QG3 model its four anomalously persistent flow patterns, which correspond to opposite phases of the Arctic Oscillation and the North Atlantic Oscillation, as well as the Markov chain of transitions between these regimes. In addition, multichannel singular spectrum analysis identifies intraseasonal oscillations with a period of 35–37 days and of 20 days in the data generated by both the QG3 model and its low-dimensional analog.
An analytical and numerical study of the reduced model starts with the fixed points and oscillatory eigenmodes of the model's deterministic part and uses systematically an increasing noise parameter to connect these with the behavior of the full, stochastically forced model version. The results of this study point to the origin of the QG3 model's multiple regimes and intraseasonal oscillations and identify the connections between the two types of behavior.
Abstract
A potential vorticity model in a β-channel is used to analyze the resonant response of equivalent-barotropic flow to topography in the presence of a forced zonal jet with arbitrary meridional structure. The nonlinear dynamics near different resonances is studied considering both wave-wave and wave-zonal flow interactions. It is shown that Hopf bifurcations from stationary to periodic flows are possible due to the nonlinear instability of nonzonal, topographically forced flow. Low-frequency, finite-amplitude oscillations arise due to a combination of two factors: (i) nonlinear wave-wave interactions, which tend to reduce the Rossby wave frequency; and (ii) wave-zonal flow interactions, which reflect the importance of wave momentum transport in shifting the westerly jet and of the topographic form drag. The physical mechanism of atmospherically realistic Hopf bifurcations depends crucially on the meridional profile of the mean zonal flow giving rise to a dipole-shaped resonance. The bifurcation phenomena studied here might give some insight into the inherent dynamics of intraseasonal oscillations in the Northern Hemisphere extratropics.
Abstract
A potential vorticity model in a β-channel is used to analyze the resonant response of equivalent-barotropic flow to topography in the presence of a forced zonal jet with arbitrary meridional structure. The nonlinear dynamics near different resonances is studied considering both wave-wave and wave-zonal flow interactions. It is shown that Hopf bifurcations from stationary to periodic flows are possible due to the nonlinear instability of nonzonal, topographically forced flow. Low-frequency, finite-amplitude oscillations arise due to a combination of two factors: (i) nonlinear wave-wave interactions, which tend to reduce the Rossby wave frequency; and (ii) wave-zonal flow interactions, which reflect the importance of wave momentum transport in shifting the westerly jet and of the topographic form drag. The physical mechanism of atmospherically realistic Hopf bifurcations depends crucially on the meridional profile of the mean zonal flow giving rise to a dipole-shaped resonance. The bifurcation phenomena studied here might give some insight into the inherent dynamics of intraseasonal oscillations in the Northern Hemisphere extratropics.
Abstract
Symmetric inertial instability (SII) is studied here as a mechanism for stratospheric and tropospheric phenomena in the equatorial regions. We investigate the linear and nonlinear dynamics of SII in a two-layer, zonally symmetric model on an equatorial beta plane, in the presence of a basic flow with horizontal and vertical shear, with and without dissipative effects.
Linear symmetric instabilities are, in accordance with previously published results, purely exponential, that is, nonoscillatory. Nonlinear SII, studied here for the first time on a planetary scale, can produce finite-amplitude oscillatory behavior, periodic or chaotic. The period of oscillations in the inviscid case depends on the initial data. In the presence of dissipative effects, all solutions tend to a limit cycle or to a strange attractor. The dominant period in this case, over a wide range of parameters and whether vertical shear is present or not, is in the intraseasonal, 20–30-day range. It appears therefore that nonlinear SII might be a contributing mechanism to low-frequency oscillations in the tropical atmosphere.
Abstract
Symmetric inertial instability (SII) is studied here as a mechanism for stratospheric and tropospheric phenomena in the equatorial regions. We investigate the linear and nonlinear dynamics of SII in a two-layer, zonally symmetric model on an equatorial beta plane, in the presence of a basic flow with horizontal and vertical shear, with and without dissipative effects.
Linear symmetric instabilities are, in accordance with previously published results, purely exponential, that is, nonoscillatory. Nonlinear SII, studied here for the first time on a planetary scale, can produce finite-amplitude oscillatory behavior, periodic or chaotic. The period of oscillations in the inviscid case depends on the initial data. In the presence of dissipative effects, all solutions tend to a limit cycle or to a strange attractor. The dominant period in this case, over a wide range of parameters and whether vertical shear is present or not, is in the intraseasonal, 20–30-day range. It appears therefore that nonlinear SII might be a contributing mechanism to low-frequency oscillations in the tropical atmosphere.
Abstract
A study of stable periodic solutions to a simple nonlinear model of the ocean-atmosphere-ice system is presented. The model has two dependent variables: ocean-atmosphere temperature and latitudinal extent of the ice cover. No explicit dependence on latitude is considered in the model. Hence all variables depend only on time and the model consists of a coupled set of nonlinear ordinary differential equations.
The globally averaged ocean-atmosphere temperature in the model is governed by the radiation balance (Budyko, 1969; Sellers, 1969). The reflectivity to incoming solar radiation, i.e., the planetary albedo, includes separate contributions from sea ice and from continental ice sheets. The major physical mechanisms active in the model are 1) albedo-temperature feedback, 2) continental ice-sheet dynamics (Weert-man, 1964, 1976) and 3) precipitation-rate variations.
The model has three equilibrium solutions, two of which are linearly unstable, while one is linearly stable. For some choices of parameters, the stability picture changes and sustained, finite-amplitude oscillations obtain around the previously stable equilibrium solution. The physical interpretation of these oscillations points to the possibility of internal mechanisms playing a role in glaciation cycles.
Abstract
A study of stable periodic solutions to a simple nonlinear model of the ocean-atmosphere-ice system is presented. The model has two dependent variables: ocean-atmosphere temperature and latitudinal extent of the ice cover. No explicit dependence on latitude is considered in the model. Hence all variables depend only on time and the model consists of a coupled set of nonlinear ordinary differential equations.
The globally averaged ocean-atmosphere temperature in the model is governed by the radiation balance (Budyko, 1969; Sellers, 1969). The reflectivity to incoming solar radiation, i.e., the planetary albedo, includes separate contributions from sea ice and from continental ice sheets. The major physical mechanisms active in the model are 1) albedo-temperature feedback, 2) continental ice-sheet dynamics (Weert-man, 1964, 1976) and 3) precipitation-rate variations.
The model has three equilibrium solutions, two of which are linearly unstable, while one is linearly stable. For some choices of parameters, the stability picture changes and sustained, finite-amplitude oscillations obtain around the previously stable equilibrium solution. The physical interpretation of these oscillations points to the possibility of internal mechanisms playing a role in glaciation cycles.
