Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

A case study of boundary layer ventilation by convection and coastal processes

It is often assumed that ventilation of the atmospheric boundary layer is weak in the absence of fronts, but is this always true? In this paper we investigate the processes responsible for ventilation of the atmospheric boundary layer during a nonfrontal day that occurred on 9 May 2005 using the UK Met Office Unified Model. Pollution sources are represented by the constant emission of a passive tracer everywhere over land. The ventilation processes observed include shallow convection, turbulent mixing followed by large-scale ascent, a sea breeze circulation and coastal outflow. Vertical distributions of tracer are validated qualitatively with AMPEP (Aircraft Measurement of chemical Processing Export fluxes of Pollutants over the UK) CO aircraft measurements and are shown to agree impressively well. Budget calculations of tracers are performed in order to determine the relative importance of these ventilation processes. Coastal outflow and the sea breeze circulation were found to ventilate 26% of the boundary layer tracer by sunset of which 2% was above 2 km. A combination of coastal outflow, the sea breeze circulation, turbulent mixing and large-scale ascent ventilated 46% of the boundary layer tracer, of which 10% was above 2 km. Finally, coastal outflow, the sea breeze circulation, turbulent mixing, large-scale ascent and shallow convection together ventilated 52% of the tracer into the free troposphere, of which 26% was above 2 km. Hence this study shows that significant ventilation of the boundary layer can occur in the absence of fronts (and thus during high-pressure events). Turbulent mixing and convection processes can double the amount of pollution ventilated from the boundary layer.

Precipitating convection in cold air: virtual potential temperature structure

Simulations of precipitating convection are used to illustrate the importance of the turbulent kinetic energy (TKE) budget in determining the virtual potential-temperature structure of the convecting atmosphere. Two sets of simulations are presented: in one the surface temperature was increased to simulate cold air flowing over a warmer surface and in the second a cooling profile, representing cold-air advection, was imposed. It is shown that the terms in the TKE budgets for both sets of simulations scale in the same way, but that the non-dimensional profiles are different. It is suggested that this is associated with the effects of sublimation of ice. It is shown that the magnitudes of the transport and precipitation terms in the virtual potential temperature budget are determined by the scaling of the TKE budget. Some implications of these results for parametrizations of moist convection are discussed. Copyright © 2007 Royal Meteorological Society

Stratosphere-troposphere transport in a numerical simulation of midlatitude convection

The transport of stratospheric air deep into the troposphere via convection is investigated numerically using the UK Met Office Unified Model. A convective system that formed on 27 June 2004 near southeast England, in the vicinity an upper level potential vorticity anomaly and a lowered tropopause, provides the basis for analysis. Transport is diagnosed using a stratospheric tracer that can either be passed through or withheld from the model’s convective parameterization scheme. Three simulations are performed at increasingly finer resolutions, with horizontal grid lengths of 12, 4, and 1 km. In the 12 and 4 km simulations, tracer is transported deeply into the troposphere by the parameterized convection. In the 1 km simulation, for which the convective parameterization is disengaged, deep transport is still accomplished but with a much smaller magnitude. However, the 1 km simulation resolves stirring along the tropopause that does not exist in the coarser simulations. In all three simulations, the concentration of the deeply transported tracer is small, three orders of magnitude less than that of the shallow transport near the tropopause, most likely because of the efficient dilution of parcels in the lower troposphere.

A stochastic parameterization for deep convection based on equilibrium statistics

A stochastic parameterization scheme for deep convection is described, suitable for use in both climate and NWP models. Theoretical arguments and the results of cloud-resolving models, are discussed in order to motivate the form of the scheme. In the deterministic limit, it tends to a spectrum of entraining/detraining plumes and is similar to other current parameterizations. The stochastic variability describes the local fluctuations about a large-scale equilibrium state. Plumes are drawn at random from a probability distribution function (pdf) that defines the chance of finding a plume of given cloud-base mass flux within each model grid box. The normalization of the pdf is given by the ensemble-mean mass flux, and this is computed with a CAPE closure method. The characteristics of each plume produced are determined using an adaptation of the plume model from the Kain-Fritsch parameterization. Initial tests in the single column version of the Unified Model verify that the scheme is effective in producing the desired distributions of convective variability without adversely affecting the mean state.

A simple model of convection with memory

There are at least three distinct time scales that are relevant for the evolution of atmospheric convection. These are the time scale of the forcing mechanism, the time scale governing the response to a steady forcing, and the time scale of the response to variations in the forcing. The last of these, tmem, is associated with convective life cycles, which provide an element of memory in the system. A highly simplified model of convection is introduced, which allows for investigation of the character of convection as a function of the three time scales. For short tmem, the convective response is strongly tied to the forcing as in conventional equilibrium parameterization. For long tmem, the convection responds only to the slowly evolving component of forcing, and any fluctuations in the forcing are essentially suppressed. At intermediate tmem, convection becomes less predictable: conventional equilibrium closure breaks down and current levels of convection modify the subsequent response.

The effect of mechanical stirring on horizontal convection

An important experimental result, as yet poorly understood, is that mechanical stirring can significantly enhance the strength of horizontal convection. A contentious issue is whether this necessarily implies that the mechanical stirring replaces the buoyancy forcing as the main source of energy driving the observed overturning circulation, as has been suggested for the Atlantic meridional overturning circulation (AMOC). In this paper, rigorous energetics considerations and idealized numerical experiments reveal that the rate at which the surface buoyancy forcing supplies energy to the fluid, as measured by the production rate of available potential energy G(APE), does not solely depend upon the buoyancy forcing, as is often implicitly assumed, but also upon the vertical stratification, such that the deeper the thermocline depth, the larger G(APE). This suggests that mechanical stirring enhances horizontal convection because it causes more energy to be extracted from the buoyancy forcing. It does so by enhancing turbulent mixing, which allows surface heating to reach greater depths, which increases the thermocline depth and hence G(APE). This paper therefore proposes a new hypothesis, namely that mechanically stirred horizontal convection and the AMOC are best described as mechanically controlled heat engines.

How well do high resolution models reproduce tropical convection?

Cascade is a multi-institution project studying the temporal and spatial organization of tropical convective systems. While cloud resolving numerical models can reproduce the observed diurnal cycle of such systems they are sensitive to the chosen resolution. As part of this effort, we are comparing results from the Met. Office Unified Model to data from the Global Earth Radiation Budget satellite instrument over the African Monsoon Interdisciplinary Analyses region of North Africa. We use a variety of mathematical techniques to study the outgoing radiation and the evolution of properties such as the cloud size distribution. The effectiveness of various model resolutions is tested with a view to determining the optimum balance between resolution and the need to reproduce the observations.

The chlorine isotope composition of Earth's mantle

Chlorine stable isotope compositions ( delta Cl-37) of 22 mid- ocean ridge basalts ( MORBs) correlate with Cl content. The high-delta Cl-37, Cl- rich basalts are highly contaminated by Cl- rich materials ( seawater, brines, or altered rocks). The low-delta(37) Cl, Cl- poor basalts approach the composition of uncontaminated, mantle- derived magmas. Thus, most or all oceanic lavas are contaminated to some extent during their emplacement. MORB- source mantle has delta(37) Cl <= -1.6 per mil (%), which is significantly lower than that of surface reservoirs (similar to 0 parts per thousand not equal). This isotopic difference between the surface and deep Earth results from net Cl isotopic fractionation ( associated with removal of Cl from the mantle and its return by subduction over Earth history) and/ or the addition ( to external reservoirs) of a late volatile supply that is Cl-37- enriched.

Atmosphere feedbacks during ENSO in a coupled GCM with a modified atmospheric convection scheme

The too diverse representation of ENSO in a coupled GCM limits one’s ability to describe future change of its properties. Several studies pointed to the key role of atmosphere feedbacks in contributing to this diversity. These feedbacks are analyzed here in two simulations of a coupled GCM that differ only by the parameterization of deep atmospheric convection and the associated clouds. Using the Kerry–Emanuel (KE) scheme in the L’Institut Pierre-Simon Laplace Coupled Model, version 4 (IPSL CM4; KE simulation), ENSO has about the right amplitude, whereas it is almost suppressed when using the Tiedke (TI) scheme. Quantifying both the dynamical Bjerknes feedback and the heat flux feedback in KE, TI, and the corresponding Atmospheric Model Intercomparison Project (AMIP) atmosphere-only simulations, it is shown that the suppression of ENSO in TI is due to a doubling of the damping via heat flux feedback. Because the Bjerknes positive feedback is weak in both simulations, the KE simulation exhibits the right ENSO amplitude owing to an error compensation between a too weak heat flux feedback and a too weak Bjerknes feedback. In TI, the heat flux feedback strength is closer to estimates from observations and reanalysis, leading to ENSO suppression. The shortwave heat flux and, to a lesser extent, the latent heat flux feedbacks are the dominant contributors to the change between TI and KE. The shortwave heat flux feedback differences are traced back to a modified distribution of the large-scale regimes of deep convection (negative feedback) and subsidence (positive feedback) in the east Pacific. These are further associated with the model systematic errors. It is argued that a systematic and detailed evaluation of atmosphere feedbacks during ENSO is a necessary step to fully understand its simulation in coupled GCMs.

The diurnal cycle of convection and atmospheric tides in an aquaplanet

The diurnal cycle of tropical convection and its relationship to the atmospheric tides is investigated using an aquaplanet GCM. The diurnal and semidiurnal harmonics of precipitation are both found to contribute significantly to the total diurnal variability of precipitation in the model, which is broadly consistent with observations of the diurnal cycle of convection over the open ocean. The semidiurnal tide is found to be the dominant forcing for the semidiurnal harmonic of precipitation. In contrast the diurnal tide plays only a small role in forcing the diurnal harmonic of precipitation, which is dominated by the variations in shortwave and longwave heating. In both the diurnal and semidiurnal harmonics, the feedback onto the convection by the humidity tendencies due to the convection is found to be important in determining the phase of the harmonics. Further experiments show that the diurnal cycle of precipitation is sensitive to the choice of closure in the convection scheme. While the surface pressure signal of the simulated atmospheric tides in the model agree well with both theory and observations in their magnitude and phase, sensitivity experiments suggest that the role of the stratospheric ozone in forcing the semidiurnal tide is much reduced compared to theoretical predictions. Furthermore, the influence of the cloud radiative effects seems small. It is suggested that the radiative heating profile in the troposphere, associated primarily with the water vapor distribution, is more important than previously thought for driving the semidiurnal tide. However, this result may be sensitive to the vertical resolution and extent of the model.