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Adam H. Sobel

Abstract

In zonally averaged chemical transport models of the stratosphere, quasi-isentropic mixing is represented by diffusion in latitude. However, it is fairly certain that the real mixing is to some extent nonlocal, so that the diffusive representation is not formally justifiable. This issue is explored from a point of view that combines theory and empiricism. Several models of mixing are described and compared. The most general, including as special cases all of the other models considered, is the integral or “transilient matrix” model. Some known properties of transilient matrices are discussed in a more formal way than has been done previously, and some new results concerning these matrices and associated equations are derived. Simpler models include the familiar diffusion model, a simple model of nonlocal mixing in which tracer concentrations are everywhere relaxed toward the global average, and a “leaky barrier” model in which two regions of nonlocal mixing are separated by a weakly diffusive transport barrier. Solutions to the latter two models, with linear chemistry included to allow nontrivial steady states, are used to derive their “effective diffusivities.” These are then used to test how well a diffusion model can mimic the behavior of the nonlocal mixing models over finite regions of parameter space. The diffusion model proves fairly robust, yielding fairly accurate results in situations where no formal argument indicates that it should. These results provide qualified support, from a purely empirical perspective, for the practice of using the diffusion model to represent stratospheric mixing in zonally averaged models. Several important caveats suggest nonetheless that exploration of more theoretically satisfactory representations is warranted.

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Adam H. Sobel

Abstract

Climatologically, the equatorial western Pacific warm pool region is a local minimum in surface evaporation and a local maximum in precipitation. The moist static energy budget in this situation requires a collocated minimum in radiative cooling of the atmosphere, which is supplied by the greenhouse effect of high clouds associated with the precipitation. However, this diagnostic statement does not explain why the evaporation minimum should coexist with the precipitation maximum. A simple physical model of the Walker circulation is used as the basis for an argument that the surface heat budget and the radiative effects of high clouds are essential to the existence of this feature, while variations in surface wind speed are not, though the latter may play an important role in determining the sea surface temperature.

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Andrew Gettelman
and
Adam H. Sobel

Abstract

This study discusses the direct diagnosis of stratosphere–troposphere exchange. The method introduced by Wei is applied to the Goddard Earth Observation System assimilated dataset. In many respects, the results generally agree with those of other studies using the same method and different datasets. However, sensitivity tests and theoretical considerations indicate that the instantaneous two-way exchange may be significantly exaggerated by the Wei method, because the method is rather sensitive to input data errors such as those that are invariably present in assimilated datasets. The method becomes somewhat better conditioned as the results are more heavily averaged, but this also reduces the method’s ability to diagnose two-way exchange. Additionally, when the flux across various surfaces is averaged over the globe and the entire year, the result implies unrealistically large imbalances in the annually averaged mass budget of the stratosphere. This could be caused by modest biases in the model used to perform the data assimilation. Since pure model simulations have an internal dynamical consistency that is lacking in assimilated datasets, the analysis appears to explain the fairly large discrepancies between the two-way fluxes obtained in studies using models and those obtained in studies using assimilated datasets. It may also explain the discrepancies between the net fluxes obtained by the Wei method and those obtained by other methods.

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Adam H. Sobel
and
R. Alan Plumb

Abstract

Two different approaches are applied to quantify mixing in a shallow water model of the stratosphere. These are modified Lagrangian mean (MLM) theory and a technique referred to as “reverse domain filling with local gradient reversal” (RDF-LGR). The latter is similar to a previously existing technique using contour advection and contour surgery.

It is first proved that in an inviscid shallow water atmosphere subject to mass sources and sinks, if the mass enclosed by a potential vorticity (PV) contour is steady in time, then the integral of the mass source over the area enclosed by the contour must be zero. Next, the MLM and RDF-LGR approaches are used to diagnose the time-averaged transport across PV contours in the model simulations.

The model includes a sixth-order hyperdiffusion on the vorticity field. Except in a thin outer “entrainment zone,” the hyperdiffusion term has only a very weak effect on the MLM mass budget of the polar vortex. In the entrainment zone, the hyperdiffusion term has a significant effect. The RDF-LGR results capture this behavior, providing good quantitative estimates of the hyperdiffusion term, which is equivalent to the degree of radiative disequilibrium at a PV contour. This agreement shows that the main role of the hyperdiffusion is to “mop up” the filaments that are produced by the essentially inviscid large-scale dynamics. All calculations are repeated for two values of the hyperdiffusion coefficient that differ by a factor of 50, with little difference in the results. This suggests that the amount of material entrained from the vortex edge into the surf zone does not depend on the details of the small-scale dissipation, as long as it is sufficiently weak and has some degree of scale selectivity.

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Adam H. Sobel
and
Gilles Bellon

Abstract

This paper examines the influence of imposed drying, intended to represent horizontal advection of dry air, on parameterized deep convection interacting with large-scale dynamics in a single-column model framework. Two single-column models, one based on the NASA Goddard Earth Observing System general circulation model version 5 (GEOS5) and the other developed by Bony and Emanuel, are run in weak temperature gradient mode. Drying is imposed by relaxation of the specific humidity field toward zero within a specified vertical layer. The strength of the drying is controlled by specifying either the relaxation time scale or the vertically integrated drying tendency; results are insensitive to which specification is used.

The two models reach very different solutions for the same boundary conditions and model configuration. Even when adjustments to the boundary conditions and model parameters are made to render the precipitation rates similar, large differences in the profiles of relative humidity and large-scale vertical velocity persist. In both models, however, drying in the middle troposphere is more effective, per kg m−2 s−1 (or W m−2) of imposed drying, in suppressing precipitation than is drying in the lower troposphere. Even when compared at equal relaxation time (corresponding to weaker net drying in the middle than lower troposphere), middle-tropospheric drying is comparably effective to lower-tropospheric drying. Upper-tropospheric drying has a relatively small effect on precipitation, although large drying in the upper troposphere cannot be imposed as a steady state because of the lack of moisture there. Consistent with the other model differences, the gross moist stabilities of the two models are quite different and vary somewhat differently as a function of imposed drying, but in both models the gross moist stability increases as the drying is increased when it is less than around 30 W m−2 and located in the middle troposphere. For lower-tropospheric drying, the gross moist stability either decreases with increased drying or increases more slowly than for middle-tropospheric drying.

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Adam H. Sobel
and
Suzana J. Camargo

Abstract

The authors investigate the influence of western North Pacific (WNP) tropical cyclones (TCs) on their large-scale environment by lag regressing various large-scale climate variables [atmospheric temperature, winds, relative vorticity, outgoing longwave radiation (OLR), column water vapor, and sea surface temperature (SST)] on an index of TC activity [accumulated cyclone energy (ACE)] on a weekly time scale. At all leads and lags out to several months, persistent, slowly evolving signals indicative of the El Niño–Southern Oscillation (ENSO) phenomenon are seen in all the variables, reflecting the known seasonal relationship of TCs in the WNP to ENSO. Superimposed on this are more rapidly evolving signals, at leads and lags of one or two weeks, directly associated with the TCs themselves. These include anomalies of positive low-level vorticity, negative OLR, and high column water vapor associated with anomalously positive ACE, found in the region where TCs most commonly form and develop. In the same region, lagging ACE by a week or two and so presumably reflecting the influence of TCs on the local environment, signals are found that might be expected to negatively influence the environment for later cyclogenesis. These signals include an SST reduction in the primary region of TC activity, and a reduction in column water vapor and increase in OLR that may or may not be a result of the SST reduction.

On the same short time scale, an increase in equatorial SST near and east of the date line is seen, presumably associated with equatorial surface westerly anomalies that are also found. This, combined with the correlation between ACE and ENSO indices on the seasonal time scale, suggests the possibility that TCs may play an active role in ENSO dynamics.

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Christopher S. Bretherton
and
Adam H. Sobel

Abstract

The authors investigate the accuracy of the weak temperature gradient (WTG) approximation, in which the divergent flow is computed by an assumed balance between adiabatic cooling and diabatic heating, for a prototype linear problem, the Gill model of a localized tropical heat source in a zonally periodic domain. As in earlier work by Neelin using a realistic, spatially distributed forcing, WTG is found to be a reasonable approximation to the full Gill model even when fairly large values of the thermal damping are used. Use of the local forcing and consideration of the different dispersion relations of free modes in the WTG and full Gill systems helps to clarify differences between the two solutions. WTG does not support an equatorial Kelvin wave. Instead, the Kelvin wave speed can be regarded as infinite in WTG. Hence, WTG becomes highly accurate when the thermal damping is sufficiently weak (0.1 day−1 or less) that an equatorial Kelvin wave can propagate around the globe without substantial loss of amplitude. Free Rossby waves are not equatorially trapped under WTG, and this increases the magnitude of the response far from the equator.

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Adam H. Sobel
and
Christopher S. Bretherton

Abstract

This study addresses the origin of the synoptic-scale disturbances that occur in the tropical western North Pacific ocean (WP) region in Northern Hemisphere summer. These have been called “easterly waves” and“tropical depression–type” (TD) disturbances. This analysis uses the National Center for Environmental Prediction–National Center for Atmospheric Research reanalysis dataset. By performing a regression analysis on several terms in the vorticity equation at 850 hPa, it is shown that the TD disturbances propagate approximately as barotropic Rossby waves at 850 hPa. Given this, ray-tracing calculations and the wave activity diagnostic introduced by Plumb are used to show that wave accumulation is a promising candidate for the initial development mechanism of the TD disturbances. The expected local “growth rate” from this mechanism is simply the convergence of the group velocity, which reaches values corresponding to a growth timescale of 3 days. This convergence is dominated by, but somewhat larger than, the convergence in the time-mean flow. The wave accumulation mechanism can operate either on waves coming from outside the WP region or on those generated in situ; in particular, mature tropical cyclones are probably a climatologically important source of waves. While the results presented here provide no direct information on the nature of the feedbacks between diabatic processes and large-scale wave dynamics, they do indicate that no linear instability mechanism involving any diabatic process need be invoked to explain the initial development of TD disturbances. It is possible, rather, that diabatic processes do not provide a positive feedback until the disturbances reach finite amplitude, whether at the stage of true tropical cyclogenesis or some prior intermediate stage.

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Eric D. Maloney
and
Adam H. Sobel

Abstract

Idealized experiments are conducted using a GCM coupled to a 20-m slab ocean model to examine the short-term response to an initial localized positive equatorial SST anomaly, or “hot spot.” A hot spot is imposed upon an aquaplanet with globally uniform 28°C SST, insolation, and trace gas concentrations designed to mimic tropical warm pool conditions. No boundary condition or external parameter other than the Coriolis parameter varies with latitude. A 15-member ensemble is initiated using random atmospheric initial conditions. A 2°C equatorial warm anomaly is switched on, along with ocean coupling (day 0).

Enhanced deep convection rapidly develops near the hot spot, forcing an anomalous large-scale circulation that resembles the linear response of a dry atmosphere to a localized heating, as in the Gill model. Enhanced convection, the anomalous large-scale circulation, and enhanced wind speed peak in amplitude at about day 15. Enhanced latent heat fluxes driven primarily by an increase in vector mean wind damp the anomalous heat content of the ocean near the hot spot before day 20. Between day 20 and day 50, suppressed latent heat fluxes due to suppressed synoptic eddy variance cause a warming of the remote Tropics in regions of anomalous low-level easterly flow. This wind-driven evaporative atmosphere–ocean exchange results in a 60–70-day oscillation in tropical mean oceanic heat content, accompanied by a compensating out-of-phase oscillation in vertically integrated atmospheric moist static energy. Beyond day 70 of the simulation, positive SST anomalies are found across much of the tropical belt. These slowly decay toward the 28°C background state.

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Shuguang Wang
and
Adam H. Sobel

Abstract

A set of idealized cloud-permitting simulations is performed to explore the influence of small islands on precipitating convection as a function of large-scale wind speed. The islands are situated in a long narrow ocean domain that is in radiative–convective equilibrium (RCE) as a whole, constraining the domain-average precipitation. The island occupies a small part of the domain, so that significant precipitation variations over the island can occur, compensated by smaller variations over the larger surrounding oceanic area.

While the prevailing wind speeds vary over flat islands, three distinct flow regimes occur. Rainfall is greatly enhanced, and a local symmetric circulation is formed in the time mean around the island, when the prevailing large-scale wind speed is small. The rainfall enhancement over the island is much reduced when the wind speed is increased to a moderate value. This difference is characterized by a change in the mechanisms by which convection is forced. A thermally forced sea breeze due to surface heating dominates when the large-scale wind is weak. Mechanically forced convection, on the other hand, is favored when the large-scale wind is moderately strong, and horizontal advection of temperature reduces the land–sea thermal contrast that drives the sea breeze. Further increases of the prevailing wind speed lead to strong asymmetry between the windward and leeward sides of the island, owing to gravity waves that result from the land–sea contrast in surface roughness as well as upward deflection of the horizontal flow by elevated diurnal heating. Small-amplitude topography (up to 800-m elevation is considered) has a quantitative impact but does not qualitatively alter the flow regimes or their dependence on wind speed.

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