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- Author or Editor: Nicholas J. Lutsko x
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Abstract
An equatorial heat source mimicking the strong diabatic heating above the west Pacific is added to an idealized, dry general circulation model. For small (<0.5 K day−1) heating rates the responses closely match the expectations from linear Matsuno–Gill theory, though the amplitudes of the responses increase sublinearly. This “linear” regime breaks down for larger heating rates and it is found that this is because the stability of the tropical atmosphere increases. At the same time, the equatorial winds increasingly superrotate. This superrotation is driven by stationary eddy momentum fluxes by the waves excited by the heating and is damped by the vertical advection of low-momentum air by the mean flow and, at large heating rates, by the divergence of momentum by transient eddies.
These dynamics are explored in additional experiments in which the equator-to-pole temperature gradient is varied. Very strong superrotation is produced when a large heating rate is applied to a setup with a relatively weak equator-to-pole temperature gradient, though there is no evidence that this is a case of “runaway” superrotation.
Abstract
An equatorial heat source mimicking the strong diabatic heating above the west Pacific is added to an idealized, dry general circulation model. For small (<0.5 K day−1) heating rates the responses closely match the expectations from linear Matsuno–Gill theory, though the amplitudes of the responses increase sublinearly. This “linear” regime breaks down for larger heating rates and it is found that this is because the stability of the tropical atmosphere increases. At the same time, the equatorial winds increasingly superrotate. This superrotation is driven by stationary eddy momentum fluxes by the waves excited by the heating and is damped by the vertical advection of low-momentum air by the mean flow and, at large heating rates, by the divergence of momentum by transient eddies.
These dynamics are explored in additional experiments in which the equator-to-pole temperature gradient is varied. Very strong superrotation is produced when a large heating rate is applied to a setup with a relatively weak equator-to-pole temperature gradient, though there is no evidence that this is a case of “runaway” superrotation.
Abstract
The nonacceleration theorem states that the torque exerted on the atmosphere by orography is exactly balanced by the convergence of momentum by the stationary waves that the orography excites. This balance is tested in simulations with a stationary wave model and with a dry, idealized general circulation model (GCM), in which large-scale orography is placed at the latitude of maximum surface wind speed. For the smallest mountain considered (maximum height H = 0.5 m), the nonacceleration balance is nearly met, but the damping in the stationary wave model induces an offset between the stationary eddy momentum flux (EMF) convergence and the mountain torque, leading to residual mean flow changes. A stationary nonlinearity appears for larger mountains (H ≥ 10 m), driven by preferential deflection of the flow around the poleward flank of the orography, and causes further breakdown of the nonacceleration balance. The nonlinearity grows as H is increased, and is stronger in the GCM than in the stationary wave model, likely due to interactions with transient eddies. The midlatitude jet shifts poleward for H ≤ 2 km and equatorward for larger mountains, reflecting changes in the transient EMFs, which push the jet poleward for smaller mountains and equatorward for larger mountains. The stationary EMFs consistently force the jet poleward. These results add to our understanding of how orography affects the atmosphere’s momentum budget, providing insight into how the nonacceleration theorem breaks down; the roles of stationary nonlinearities and transients; and how orography affects the strength and latitude of eddy-driven jets.
Abstract
The nonacceleration theorem states that the torque exerted on the atmosphere by orography is exactly balanced by the convergence of momentum by the stationary waves that the orography excites. This balance is tested in simulations with a stationary wave model and with a dry, idealized general circulation model (GCM), in which large-scale orography is placed at the latitude of maximum surface wind speed. For the smallest mountain considered (maximum height H = 0.5 m), the nonacceleration balance is nearly met, but the damping in the stationary wave model induces an offset between the stationary eddy momentum flux (EMF) convergence and the mountain torque, leading to residual mean flow changes. A stationary nonlinearity appears for larger mountains (H ≥ 10 m), driven by preferential deflection of the flow around the poleward flank of the orography, and causes further breakdown of the nonacceleration balance. The nonlinearity grows as H is increased, and is stronger in the GCM than in the stationary wave model, likely due to interactions with transient eddies. The midlatitude jet shifts poleward for H ≤ 2 km and equatorward for larger mountains, reflecting changes in the transient EMFs, which push the jet poleward for smaller mountains and equatorward for larger mountains. The stationary EMFs consistently force the jet poleward. These results add to our understanding of how orography affects the atmosphere’s momentum budget, providing insight into how the nonacceleration theorem breaks down; the roles of stationary nonlinearities and transients; and how orography affects the strength and latitude of eddy-driven jets.
Abstract
A dry atmospheric general circulation model is forced with large-scale, Gaussian orography in an attempt to isolate a regime in which the model responds linearly to orographic forcing and then to study the departures from linearity as the orography is increased in amplitude. In contrast to previous results, which emphasized the meridional propagation of orographically forced stationary waves, using the standard Held–Suarez (H–S) control climate, it is found that the linear regime is characterized by a meridionally trapped, zonally propagating wave. Meridionally trapped waves of this kind have been seen in other contexts, where they have been termed “circumglobal waves.” As the height of the orography is increased, the circumglobal wave coexists with a meridionally propagating wave and for large-enough heights the meridionally propagating wave dominates the response. A barotropic model on a sphere reproduces this trapped wave in the linear regime and also reproduces the transition to meridional propagation with increasing amplitude. However, mean-flow modification by the stationary waves is very different in the two models, making it difficult to argue that the transitions have the same causes. When adding asymmetry across the equator to the H–S control climate and placing the orography in the cooler hemisphere, it becomes harder to generate trapped waves in the GCM and the trapping becomes sensitive to the shape of the orography. The barotropic model overestimates the trapping in this case. These results suggest that an improved understanding of the role of circumglobal waves will be needed to understand the stationary wave field and its sensitivity to the changes in the zonal-mean climate.
Abstract
A dry atmospheric general circulation model is forced with large-scale, Gaussian orography in an attempt to isolate a regime in which the model responds linearly to orographic forcing and then to study the departures from linearity as the orography is increased in amplitude. In contrast to previous results, which emphasized the meridional propagation of orographically forced stationary waves, using the standard Held–Suarez (H–S) control climate, it is found that the linear regime is characterized by a meridionally trapped, zonally propagating wave. Meridionally trapped waves of this kind have been seen in other contexts, where they have been termed “circumglobal waves.” As the height of the orography is increased, the circumglobal wave coexists with a meridionally propagating wave and for large-enough heights the meridionally propagating wave dominates the response. A barotropic model on a sphere reproduces this trapped wave in the linear regime and also reproduces the transition to meridional propagation with increasing amplitude. However, mean-flow modification by the stationary waves is very different in the two models, making it difficult to argue that the transitions have the same causes. When adding asymmetry across the equator to the H–S control climate and placing the orography in the cooler hemisphere, it becomes harder to generate trapped waves in the GCM and the trapping becomes sensitive to the shape of the orography. The barotropic model overestimates the trapping in this case. These results suggest that an improved understanding of the role of circumglobal waves will be needed to understand the stationary wave field and its sensitivity to the changes in the zonal-mean climate.
Abstract
Annular modes are the leading mode of variability in extratropical atmospheres, and a key source of predictability at midlatitudes. Previous studies of annular modes have primarily used dry atmospheric models, so that moisture’s role in annular mode dynamics is still unclear. In this study, a moist two-layer quasigeostrophic channel model is used to study the effects of moisture on annular mode persistence. Using a channel model allows moisture’s direct effects to be studied, rather than changes in persistence due to geometric effects associated with shifts in jet latitude on the sphere. Simulations are performed in which the strength of latent heat release is varied to investigate how annular mode persistence responds as precipitation becomes a leading term in the thermodynamic budget. At short lags (<20 model days, ≈4 Earth days), moisture increases annular mode persistence, reflecting weaker eddy activity that is less effective at disrupting zonal-mean wind anomalies. Comparisons to dry simulations with weaker mean flows demonstrate that moisture is particularly effective at damping high-frequency eddies, further enhancing short-lag persistence. At long lags (>20 model days), moisture weakly increases persistence, though it decreases the amplitudes of low-frequency annular mode anomalies. In the most realistic simulation, the greater short-lag persistence increases the e-folding time of the zonal index by 21 model days (≈4 Earth days). Moisture also causes a transition to propagating variability, though this does not seem to affect the leading mode’s persistence.
Abstract
Annular modes are the leading mode of variability in extratropical atmospheres, and a key source of predictability at midlatitudes. Previous studies of annular modes have primarily used dry atmospheric models, so that moisture’s role in annular mode dynamics is still unclear. In this study, a moist two-layer quasigeostrophic channel model is used to study the effects of moisture on annular mode persistence. Using a channel model allows moisture’s direct effects to be studied, rather than changes in persistence due to geometric effects associated with shifts in jet latitude on the sphere. Simulations are performed in which the strength of latent heat release is varied to investigate how annular mode persistence responds as precipitation becomes a leading term in the thermodynamic budget. At short lags (<20 model days, ≈4 Earth days), moisture increases annular mode persistence, reflecting weaker eddy activity that is less effective at disrupting zonal-mean wind anomalies. Comparisons to dry simulations with weaker mean flows demonstrate that moisture is particularly effective at damping high-frequency eddies, further enhancing short-lag persistence. At long lags (>20 model days), moisture weakly increases persistence, though it decreases the amplitudes of low-frequency annular mode anomalies. In the most realistic simulation, the greater short-lag persistence increases the e-folding time of the zonal index by 21 model days (≈4 Earth days). Moisture also causes a transition to propagating variability, though this does not seem to affect the leading mode’s persistence.
Abstract
Although Earth’s troposphere does not superrotate in the annual mean, for most of the year—from October to May—the winds of the tropical upper troposphere are westerly. We investigate this seasonal superrotation using reanalysis data and a single-layer model for the winds of the tropical upper troposphere. We characterize the temporal and spatial structures of the tropospheric superrotation, and quantify the relationships between the superrotation and the leading modes of tropical interannual variability. We also find that the strength of the superrotation has remained roughly constant over the past few decades, despite the winds of the tropical upper troposphere decelerating (becoming more easterly) in other months. We analyze the monthly zonal-mean zonal momentum budget and use numerical simulations with an axisymmetric, single-layer model of the tropical upper troposphere to study the underlying dynamics of the seasonal superrotation. Momentum flux convergence by stationary eddies accelerates the superrotation, while cross-equatorial easterly momentum transport associated with the Hadley circulation decelerates the superrotation. The seasonal modulations of these two competing factors shape the superrotation. The single-layer model is able to qualitatively reproduce the seasonal progression of the winds in the tropical upper troposphere, and highlights the northward displacement of the intertropical convergence zone in the annual mean as a key factor responsible for the annual cycle of the tropical winds.
Abstract
Although Earth’s troposphere does not superrotate in the annual mean, for most of the year—from October to May—the winds of the tropical upper troposphere are westerly. We investigate this seasonal superrotation using reanalysis data and a single-layer model for the winds of the tropical upper troposphere. We characterize the temporal and spatial structures of the tropospheric superrotation, and quantify the relationships between the superrotation and the leading modes of tropical interannual variability. We also find that the strength of the superrotation has remained roughly constant over the past few decades, despite the winds of the tropical upper troposphere decelerating (becoming more easterly) in other months. We analyze the monthly zonal-mean zonal momentum budget and use numerical simulations with an axisymmetric, single-layer model of the tropical upper troposphere to study the underlying dynamics of the seasonal superrotation. Momentum flux convergence by stationary eddies accelerates the superrotation, while cross-equatorial easterly momentum transport associated with the Hadley circulation decelerates the superrotation. The seasonal modulations of these two competing factors shape the superrotation. The single-layer model is able to qualitatively reproduce the seasonal progression of the winds in the tropical upper troposphere, and highlights the northward displacement of the intertropical convergence zone in the annual mean as a key factor responsible for the annual cycle of the tropical winds.
Abstract
The fluctuation–dissipation theorem (FDT) provides a means of calculating the response of a dynamical system to a small force by constructing a linear operator that depends only on data from the internal variability of the unperturbed system. Here the FDT is used to estimate the response of a two-layer quasigeostrophic model to two zonally symmetric torques, both barotropic, with the same sign of the forcing in the two layers, and baroclinic, with opposite sign forcing in the two layers. The supercriticality of the model is also varied to test how the FDT fares, as this parameter is varied. To perform the FDT calculations the data are decomposed onto empirical orthogonal functions (EOFs) and only those EOFs that are well resolved are retained in the FDT calculations. In the barotropic case good qualitative estimates are obtained for all values of the supercriticality, though the FDT consistently overestimates the response, perhaps because of significant non-Gaussian behavior present in the model. Nevertheless, this adds to the evidence that the annular-mode time scale plays an important role in determining the response of the midlatitudes to small perturbations. The baroclinic case is more challenging for the FDT. However, by constructing different bases with which to calculate the EOFs, it is shown that the issue in this case is that the baroclinic variability is poorly sampled, not that the FDT fails. The strategies developed in order to generate these estimates may be applicable to situations in which the FDT is applied to larger systems.
Abstract
The fluctuation–dissipation theorem (FDT) provides a means of calculating the response of a dynamical system to a small force by constructing a linear operator that depends only on data from the internal variability of the unperturbed system. Here the FDT is used to estimate the response of a two-layer quasigeostrophic model to two zonally symmetric torques, both barotropic, with the same sign of the forcing in the two layers, and baroclinic, with opposite sign forcing in the two layers. The supercriticality of the model is also varied to test how the FDT fares, as this parameter is varied. To perform the FDT calculations the data are decomposed onto empirical orthogonal functions (EOFs) and only those EOFs that are well resolved are retained in the FDT calculations. In the barotropic case good qualitative estimates are obtained for all values of the supercriticality, though the FDT consistently overestimates the response, perhaps because of significant non-Gaussian behavior present in the model. Nevertheless, this adds to the evidence that the annular-mode time scale plays an important role in determining the response of the midlatitudes to small perturbations. The baroclinic case is more challenging for the FDT. However, by constructing different bases with which to calculate the EOFs, it is shown that the issue in this case is that the baroclinic variability is poorly sampled, not that the FDT fails. The strategies developed in order to generate these estimates may be applicable to situations in which the FDT is applied to larger systems.
Abstract
Climate models and observations robustly agree that Earth’s clear-sky longwave feedback has a value of about −2 W m−2 K−1, suggesting that this feedback can be estimated from first principles. In this study, we derive an analytic model for Earth’s clear-sky longwave feedback. Our approach uses a novel spectral decomposition that splits the feedback into four components: a surface Planck feedback and three atmospheric feedbacks from CO2, H2O, and the H2O continuum. We obtain analytic expressions for each of these terms, and the model can also be framed in terms of Simpson’s law and deviations therefrom. We validate the model by comparing it against line-by-line radiative transfer calculations across a wide range of climates. Additionally, the model qualitatively matches the spatial feedback maps of a comprehensive climate model. For present-day Earth, our analysis shows that the clear-sky longwave feedback is dominated by the surface in the global mean and in the dry subtropics; meanwhile, atmospheric feedbacks from CO2 and H2O become important in the inner tropics. Together, these results show that a spectral view of Earth’s clear-sky longwave feedback elucidates not only its global-mean magnitude, but also its spatial pattern and its state dependence across past and future climates.
Significance Statement
The climate feedback determines how much our planet warms due to changes in radiative forcing. For more than 50 years scientists have been predicting this feedback using complex numerical models. Except for cloud effects the numerical models largely agree, lending confidence to global warming predictions, but nobody has yet derived the feedback from simpler considerations. We show that Earth’s clear-sky longwave feedback can be estimated using only pen and paper. Our results confirm that numerical climate models get the right number for the right reasons, and allow us to explain regional and state variations of Earth’s climate feedback. These variations are difficult to understand solely from numerical models but are crucial for past and future climates.
Abstract
Climate models and observations robustly agree that Earth’s clear-sky longwave feedback has a value of about −2 W m−2 K−1, suggesting that this feedback can be estimated from first principles. In this study, we derive an analytic model for Earth’s clear-sky longwave feedback. Our approach uses a novel spectral decomposition that splits the feedback into four components: a surface Planck feedback and three atmospheric feedbacks from CO2, H2O, and the H2O continuum. We obtain analytic expressions for each of these terms, and the model can also be framed in terms of Simpson’s law and deviations therefrom. We validate the model by comparing it against line-by-line radiative transfer calculations across a wide range of climates. Additionally, the model qualitatively matches the spatial feedback maps of a comprehensive climate model. For present-day Earth, our analysis shows that the clear-sky longwave feedback is dominated by the surface in the global mean and in the dry subtropics; meanwhile, atmospheric feedbacks from CO2 and H2O become important in the inner tropics. Together, these results show that a spectral view of Earth’s clear-sky longwave feedback elucidates not only its global-mean magnitude, but also its spatial pattern and its state dependence across past and future climates.
Significance Statement
The climate feedback determines how much our planet warms due to changes in radiative forcing. For more than 50 years scientists have been predicting this feedback using complex numerical models. Except for cloud effects the numerical models largely agree, lending confidence to global warming predictions, but nobody has yet derived the feedback from simpler considerations. We show that Earth’s clear-sky longwave feedback can be estimated using only pen and paper. Our results confirm that numerical climate models get the right number for the right reasons, and allow us to explain regional and state variations of Earth’s climate feedback. These variations are difficult to understand solely from numerical models but are crucial for past and future climates.
Abstract
In Earth’s atmosphere eddy momentum fluxes (EMFs) are largest in the upper troposphere, but EMFs in the lower troposphere, although modest in amplitude, have an intriguing structure. To document this structure, the EMFs in the lower tropospheres of a two-layer quasigeostrophic model, a primitive equation model, and the Southern Hemisphere of a reanalysis dataset are investigated. The lower-tropospheric EMFs are very similar in the cores of the jets in both models and the reanalysis data, with EMF divergence (opposing the upper-tropospheric convergence) due to relatively long waves with slow eastward phase speeds and EMF divergence (as in the upper troposphere) due to shorter waves with faster eastward phase speeds.
As the two-layer model is able to capture the EMF divergence by long waves, a qualitative picture of the underlying dynamics is proposed that relies on the negative potential vorticity gradient in the lower layer of the model. Eddies excited by baroclinic instability mix efficiently through a wide region in the lower layer, centered on the latitude of maximum westerlies and encompassing the lower-layer critical latitudes. Near these critical latitudes, the mixing is enhanced, resulting in increased EMF convergence, with compensating EMF divergence in the center of the jet. The EMF convergence at faster phase speeds is due to deep eddies that propagate on the upper-tropospheric potential vorticity gradient.
Abstract
In Earth’s atmosphere eddy momentum fluxes (EMFs) are largest in the upper troposphere, but EMFs in the lower troposphere, although modest in amplitude, have an intriguing structure. To document this structure, the EMFs in the lower tropospheres of a two-layer quasigeostrophic model, a primitive equation model, and the Southern Hemisphere of a reanalysis dataset are investigated. The lower-tropospheric EMFs are very similar in the cores of the jets in both models and the reanalysis data, with EMF divergence (opposing the upper-tropospheric convergence) due to relatively long waves with slow eastward phase speeds and EMF divergence (as in the upper troposphere) due to shorter waves with faster eastward phase speeds.
As the two-layer model is able to capture the EMF divergence by long waves, a qualitative picture of the underlying dynamics is proposed that relies on the negative potential vorticity gradient in the lower layer of the model. Eddies excited by baroclinic instability mix efficiently through a wide region in the lower layer, centered on the latitude of maximum westerlies and encompassing the lower-layer critical latitudes. Near these critical latitudes, the mixing is enhanced, resulting in increased EMF convergence, with compensating EMF divergence in the center of the jet. The EMF convergence at faster phase speeds is due to deep eddies that propagate on the upper-tropospheric potential vorticity gradient.
