The Weak Temperature Gradient Approximation and Balanced Tropical Moisture Waves*

Sobel, Adam H.; Nilsson, Johan; Polvani, Lorenzo M.

doi:10.1175/1520-0469(2001)058<3650:twtgaa>2.0.co;2

Cited by 575 publications

(665 citation statements)

References 56 publications

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“…This is referred to as the weak temperature gradient (WTG) approximation (Sobel et al 2001). In the case of slow rotations, the WTG approximation becomes valid globally, and the free-tropospheric temperatures are nearly constant at low pressure levels (only shown along the equator in Fig.…”

Section: Atmospheric Profile Over the Nightsidementioning

confidence: 99%

The role of sea-ice albedo in the climate of slowly rotating aquaplanets

2017

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We investigate the influence of the rotation period (Prot) on the mean climate of an aquaplanet, with a focus on the role of sea-ice albedo. We perform aquaplanet simulations with the atmospheric general circulation model ECHAM6 for various rotation periods from one Earth-day to 365 Earth-days in which case the planet is synchronously rotating. The global-mean surface temperature decreases with increasing Prot and sea ice expands equatorwards. The cooling of the mean climate with increasing Prot is caused partly by the high surface albedo of sea ice on the dayside and partly by the high albedo of the deep convective clouds over the substellar region. The cooling caused by these deep convective clouds is weak for non-synchronous rotations compared to synchronous rotation. Sensitivity simulations with the sea-ice model switched off show that the global-mean surface temperature is up to 27 K higher than in our main simulations with sea ice and thus highlight the large influence of sea ice on the climate. We present the first estimates of the influence of the rotation period on the transition of an Earth-like climate to global glaciation. Our results suggest that global glaciation of planets with synchronous rotation occurs at substantially lower incoming solar irradiation than for planets with slow but non-synchronous rotation

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Section: Atmospheric Profile Over the Nightsidementioning

confidence: 99%

The role of sea-ice albedo in the climate of slowly rotating aquaplanets

2017

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“…Remarkably, the resulting patterns of precipitation and divergence were approximately the same as those that occurred in the full model. Bretherton dubbed this approximation the 'weak temperature gradient' (WTG) approximation (Sobel et al, 2001), and Sobel and Bretherton (2000) showed that it represents reasonably well the net effect of the rest of the model on any tropical grid column.…”

Section: Introductionmentioning

confidence: 99%

Testing a cumulus parametrization with a cumulus ensemble model in weak‐temperature‐gradient mode

Raymond

2007

Quart J Royal Meteoro Soc

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This paper prototypes a method for calibrating a cumulus parametrization against a cumulus ensemble model. The key to this technique is to run the cumulus model and the parametrization in identical 'test cells' that provide forcing typical of that seen over tropical oceans. In particular, the mean temperature profile is relaxed to a reference profile that is assumed to be characteristic of the environment of the convection. This is done by calculating the mean vertical velocity needed to balance heating due to convection, latent-heat release, and radiation with adiabatic cooling. This 'weak-temperature-gradient' vertical-velocity profile is then used to advect moisture vertically and, via mass continuity, through the sides of the test cell, entraining reference-profile air as needed.As an example, a toy cumulus parametrization used previously is altered to reproduce the dependence of rainfall rate on surface wind speed shown by the cumulus ensemble model. This alteration greatly changes the behaviour of simulated large-scale disturbances in an aquaplanet equatorial beta-plane model. In particular, increasing the slope of the curve of rainfall rate against wind speed results in the development of much greater synoptic-scale variance.

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“…Related analyses using the present approach are work in progress. With (36), (37), we have a set of equations characterized by a single small parameter, ε. The limit ε → 0 is singular as is evident from the degeneration of the momentum equation (36) 1 in this limit.…”

Section: Distinguished Limit and Multiple Scales Ansatzmentioning

confidence: 99%

“…5, top left) develop on characteristic scales of 100 m to 10 km, both horizontally and vertically, and on time scales of up to 20 min. These are also the scales used in nondimensionalizing the governing equations in (36). Therefore, the special case of our solution ansatz in (38) with expansion functions…”

Section: Mesoscale Anelastic and Buoyancy-controlled Modelsmentioning

confidence: 99%

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Multiple spatial scales in engineering and atmospheric low Mach number flows

Klein

2005

ESAIM: M2AN

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Abstract. The first part of this paper reviews the single time scale/multiple length scale low Mach number asymptotic analysis by Klein (1995Klein ( , 2004. This theory explicitly reveals the interaction of small scale, quasi-incompressible variable density flows with long wave linear acoustic modes through baroclinic vorticity generation and asymptotic accumulation of large scale energy fluxes. The theory is motivated by examples from thermoacoustics and combustion. In an almost obvious way specializations of this theory to a single spatial scale reproduce automatically the zero Mach number variable density flow equations for the small scales, and the linear acoustic equations with spatially varying speed of sound for the large scales. Following the same line of thought we show how a large number of wellknown simplified equations of theoretical meteorology can be derived in a unified fashion directly from the three-dimensional compressible flow equations through systematic (low Mach number) asymptotics. Atmospheric flows are, however, characterized by several singular perturbation parameters that appear in addition to the Mach number, and that are defined independently of any particular length or time scale associated with some specific flow phenomenon. These are the ratio of the centripetal acceleration due to the earth's rotation vs. the acceleration of gravity, and the ratio of the sound speed vs. the rotational velocity of points on the equator. To systematically incorporate these parameters in an asymptotic approach, we couple them with the square root of the Mach number in a particular distinguished so that we are left with a single small asymptotic expansion parameter, ε. Of course, more familiar parameters, such as the Rossby and Froude numbers may then be expressed in terms of ε as well. Next we consider a very general asymptotic ansatz involving multiple horizontal and vertical as well as multiple time scales. Various restrictions of the general ansatz to only one horizontal, one vertical, and one time scale lead directly to the family of simplified model equations mentioned above. Of course, the main purpose of the general multiple scales ansatz is to provide the means to derive true multiscale models which describe interactions between the various phenomena described by the members of the simplified model family. In this context we will summarize a recent systematic development of multiscale models for the tropics (with Majda).Mathematics Subject Classification. 34E13, 76B99, 76Q05, 86A10.

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The Weak Temperature Gradient Approximation and Balanced Tropical Moisture Waves*

Cited by 575 publications

References 56 publications

The role of sea-ice albedo in the climate of slowly rotating aquaplanets

The role of sea-ice albedo in the climate of slowly rotating aquaplanets

Testing a cumulus parametrization with a cumulus ensemble model in weak‐temperature‐gradient mode

Multiple spatial scales in engineering and atmospheric low Mach number flows

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