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J. David Neelin, Isaac M. Held, and Kerry H. Cook

Abstract

A mechanism by which feedback between zonal wind perturbations and evaporation can create unstable, low-frequency modes in a simple two-layer model of the tropical troposphere is presented. The modes resemble the 30–50 day oscillation. A series of general circulation model experiments designed to test the effect of suppressing this feedback on low-frequency variability in the model tropics is described. The results suggest that the evaporation-wind feedback can be important to the amplitude of the spectral peak corresponding to the 30–50 day oscillation in the model, but that the existence of the oscillation does not depend on it. The feedback is found to have a much more dramatic effect on low-frequency variability when sea surface temperatures are fixed than when the lower boundary is a zero heat capacity “swamp”.

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Isaac M. Held, Steven W. Lyons, and Sumant Nigam

Abstract

A baroclinic stationary wave model linearized about a zonally symmetric flow is used to interpret the extra-tropical atmospheric response to El Niño produced by a general circulation model. When forced by the anomalous diabatic beating and tendency due to transients, the linear model provides a useful simulation of this response. The direct response to anomalous diabatic heating is found to be small in the extratropics; the dominant term is the response to the anomalous transients, particularly the anomalous upper tropospheric transients in the vorticity equation. These results are complementary to those obtained with a nonlinear barotropic model by Held and Kang, and indicate that the anomalous subtropical convergence which plays a key role in that study is itself primarily forced by the anomalous transients. One can distinguish between two distinct parts of the response of the transients to the tropical heating: the movement of the Pacific storm track associated with the anomalous extratropical wave train, and changes in the penetration of Rossby waves into the tropics resulting from the modified tropical winds.

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Tsung-Lin Hsieh, Stephen T. Garner, and Isaac M. Held

Abstract

Simulations of baroclinic cyclones often cannot resolve moist convection but resort to convective parameterization. An exception is the hypohydrostatic rescaling, which in principle can be used to better represent convection with no increase in computational cost. The rescaling is studied in the context of a quasi-steady, convectively active, baroclinic cyclone. This is a novel framework with advantages due to the unambiguous time-mean structure. The rescaling is evaluated against high-resolution solutions up to a 5-km grid spacing. A theoretical scaling combining convective-scale dynamics and synoptic-scale energy balance is derived and verified by the simulations. It predicts the insensitivity of the large-scale flow to resolution finer than 40 km and to moderate rescaling, and a weak bias in the cyclone intensity under very large rescaling. The theory yields a threshold for the rescaling factor that avoids large-scale biases. Below the threshold, the rescaling can be used to control resolution errors at the convective scale, such as the distribution of extreme precipitation rates.

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Nicholas J. Lutsko, Isaac M. Held, and Pablo Zurita-Gotor

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.

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Samuel F. Potter, Thomas Spengler, and Isaac M. Held

Abstract

The authors discuss reflection of barotropic Rossby waves in an idealized framework with potential applications to tropical–extratropical and interhemispheric interactions. Meridional propagation of Rossby waves has often been studied using the Wentzel–Kramers–Brillouin (WKB) approximation. The WKB approximation neglects reflection. The authors investigate the amount of reflection in simple shear profiles and attempt to evaluate the validity of using the WKB approximation to understand the meridional propagation of Rossby waves. In addition to solving for the reflection coefficient numerically, exact and approximate forms of the reflection coefficient in certain parameter regimes are derived. An application to the observed climatology is discussed in light of the findings.

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Kyle L. Swanson, Paul J. Kushner, and Isaac M. Held

Abstract

Longitudinal variations in the upper-tropospheric time-mean flow strongly modulate the structure and amplitude of upper-tropospheric eddies. This barotropic modulation is studied using simple models of wave propagation through zonally varying basic states that consist of contours separating regions of uniform barotropic potential vorticity. Such basic states represent in a simple manner the potential vorticity distribution in the upper troposphere. Predictions of the effect of basic-state zonal variations on the amplitude and spatial structure of eddies and their associated particle displacements are made using conservation of wave action or, equivalently, the linearized “pseudoenergy” wave activity. The predictions are confirmed using WKB theory and linear numerical calculations. The interaction of finite-amplitude disturbances with the basic flow is also analyzed numerically using nonlinear contour-dynamical simulations. It is found that breaking nonlinear contour waves undergo irreversible amplitude attenuation, scale lengthening, and frequency lowering upon passing through a region of weak basic-state flow.

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Tapio Schneider, Isaac M. Held, and Stephen T. Garner

Abstract

Many aspects of geophysical flows can be described compactly in terms of potential vorticity dynamics. Since potential temperature can fluctuate at boundaries, however, the boundary conditions for potential vorticity dynamics are inhomogeneous, which complicates considerations of potential vorticity dynamics when boundary effects are dynamically significant.

A formulation of potential vorticity dynamics is presented that encompasses boundary effects. It is shown that, for arbitrary flows, the generalization of the potential vorticity concept to a sum of the conventional interior potential vorticity and a singular surface potential vorticity allows one to replace the inhomogeneous boundary conditions for potential vorticity dynamics by simpler homogeneous boundary conditions (of constant potential temperature). Functional forms of the surface potential vorticity are derived from field equations in which the potential vorticity and a potential vorticity flux appear as sources of flow quantities in the same way in which an electric charge and an electric current appear as sources of fields in electrodynamics. For the generalized potential vorticity of flows that need be neither balanced nor hydrostatic and that can be influenced by diabatic processes and friction, a conservation law holds that is similar to the conservation law for the conventional interior potential vorticity. The conservation law for generalized potential vorticity contains, in the quasigeostrophic limit, the well-known dual relationship between fluctuations of potential temperature at boundaries and fluctuations of potential vorticity in the interior of quasigeostrophic flows. A nongeostrophic effect described by the conservation law is the induction of generalized potential vorticity by baroclinicity at boundaries, an effect that plays a role, for example, in mesoscale flows past topographic obstacles. Based on the generalized potential vorticity concept, a theory is outlined of how a wake with lee vortices can form in weakly dissipative flows past a mountain. Theoretical considerations and an analysis of a simulation show that a wake with lee vortices can form by separation of a generalized potential vorticity sheet from the mountain surface, similar to the separation of a friction-induced vorticity sheet from an obstacle, except that the generalized potential vorticity sheet can be induced by baroclinicity at the surface.

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Ming Zhao, Isaac M. Held, and Gabriel A. Vecchi

Abstract

Retrospective predictions of seasonal hurricane activity in the Atlantic and east Pacific are generated using an atmospheric model with 50-km horizontal resolution by simply persisting sea surface temperature (SST) anomalies from June through the hurricane season. Using an ensemble of 5 realizations for each year between 1982 and 2008, the correlations of the model mean predictions with observations of basin-wide hurricane frequency are 0.69 in the North Atlantic and 0.58 in the east Pacific. In the North Atlantic, a significant part of the degradation in skill as compared to a model forced with observed SSTs during the hurricane season (correlation of 0.78) can be explained by the change from June through the hurricane season in one parameter, the difference between the SST in the main development region and the tropical mean SST. In fact, simple linear regression models with this one predictor perform nearly as well as the full dynamical model for basin-wide hurricane frequency in both the east Pacific and the North Atlantic. The implication is that the quality of seasonal forecasts based on a coupled atmosphere–ocean model will depend in large part on the model’s ability to predict the evolution of this difference between main development region SST and tropical mean SST.

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Isaac M. Held, David I. Linder, and Max J. Suarez

Abstract

The sensitivity of a two-level primitive equation atmospheric model to solar constant perturbations is examined in the presence of surface albedo feedback. The model is simplified to the point that a large number of numerical experiments can be performed and statistically steady states defined with relative case. Exceptionally sensitive equilibrium states are found that are unrelated to the large and small ice-cap instabilities obtained in the simplest diffusive energy balance models. Similar results are produced in a two-level diffusive model closely patterned after the dynamic model, and in a more highly idealized one-level model, by choosing a diffusivity with pronounced meridional structure resembling that of the effective diffusivity of the dynamic model. Sensitive states occur in the diffusive models when the albedo gradient enters the region equatorward of 60° in which the effective heat diffusivity of the atmosphere increases with increasing latitude.

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Sumant Nigam, Isaac M. Held, and Steven W. Lyons

Abstract

The validity of linear stationary wave theory in accounting for the zonal asymmetries of the winter-averaged tropospheric circulation obtained in a general circulation model (GCM) is ascertained. The steady linear primitive equation model used towards this end has the same vertical and zonal resolution as the spectral GCM, but is finite-differenced in the meridional direction. It is linearized about a zonally symmetric basic state and forced by topography and 3-dimensional diabatic heating and transient flux convergence fields, all of which are taken from the GCM. As in Part I, (in which we studied a GCM with a flat lower boundary) we obtained the best correspondence, between the GCM and the linear solutions when strong Rayleigh friction is included in the linear model not only near the surface, but in the interior of the tropical troposphere as well.

There is sufficient quantitative correspondence between the GCM and the linear solution to justify decomposing the linear simulation into parts forced by different processes, although in some regions, such as over North America, the simulation is unsatisfactory. Different fields give different impressions as to the relative importance of orography, heating, and transients. The eddy zonal velocity field in the upper troposphere shows the orographic and thermal plus transient contributions to he nearly equal in amplitude, whereas the eddy meridional velocity field, dominated by shorter zonal scales, shows the orographic contribution to be decisively dominant. Although there is no systematic phase relationship between these two contributions, they are roughly in phase over the cast Asian coast, where each of them is largest. They also contribute roughly equal amounts to the low level Siberian high.

Other findings are that (i) the 300 mb extratropical response to tropical forcing reaches 50 gpm over Alaska (given our frictional parameterization), which is smaller than the response to local thermal forcing, (ii) the responses to sensible heating and lower tropospheric thermal transients are strongly anticorrelated, and (iii) the circulation in the vicinity of the Andes in the GCM is not attributable to direct mechanical forcing by the mountains.

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