Abstract

Using Albrecht's model, approximate analytical formulas are found for the dependence of the steady-State mean thermodynamic structure of a partly cloudy convective marine boundary layer on external parameters. Our goals are 1) to understand the physical factors that influence the vertical profiles of mean relative humidity, temperature, and fractional cloudiness within the cloud layer using the model to gain insight into the strato-cumulus-trade cumulus transition in the subtropical trade wind regime, and 2) to understand the sensitivity of the model to tunable internal parameters. The model, a prototype for bulk models of trade cumulus boundary layer, consists of a well-mixed subcloud layer topped by a cumulus layer and a sharp trade inversion. In the simplest formulation discussed here, precipitation is ignored and simple parameterizations for radiative cooling and fractional cloudiness are used.

The analytical approximation agrees well with exact steady-state numerical solutions of Albrecht's model. The cloud-base and trade-inversion heights are not strongly dependent on adjustable parameters within the cloud model and are largely determined by bulk balances of radiative fluxes, surface fluxes, and subsidence in a manner similar to the more empirical model of Betts and Ridgway. The cloud-layer sounding and the cloud fraction are affected by external parameters only through changes in the cloud-base latent heat flux and the cloud thickness. The cloud fraction is quite sensitive to two tunable internal constants in the cloud model that affect rates of cloud entrainment and detrainment, respectively. For most choices of SST and upper-air conditions, these constants can be tuned to produce either a mainly saturated (stratocumulus-like) cloud layer or a trade cumulus-like layer with no environmental saturation. The sensitivity of cloud fraction to SST and mean subsidence is explored for two choices of these constants and the effect of unsteadiness due to downstream changes in external conditions are considered.

Abstract

In Part I, an idealized model of nonprecipitating moist convection in a shallow conditionally unstable layer of viscous and diffusive air between two parallel plates was introduced, and the “linear” instability of an exactly saturated static state maintained by diffusion was investigated. If there are initially many clouds, the “linear” theory predicted that weaker clouds are suppressed by the subsidence warming and drying from the ever-growing stronger clouds, and the average cloud spacing becomes arbitrarily large as time goes on. Each growing cloud is surrounded by compensating subsidence, which decreases away from the cloud with a characteristic decay scale R_s , the subsidence radius, which can be understood from gravity wave arguments.

In Part II, fields of finite amplitude clouds are considered. An asymptotic analysis is performed in which the moist Rayleigh number N_c ² exceeds by only a small amount μ the value N _c0 ² necessary for the onset of convection. This leads to a nonlinear set of “cloud field equations” which predict how the amplitudes and positions of all the clouds evolve in time. These equations predict a minimum stable cloud spacing λ _c ≈ R_s log(μ⁻¹). If the cloud spacing λ < λ _c , slight differences in the strengths of neighboring clouds increase until the weaker clouds are suppressed. Unevenly spaced clouds drift until they become evenly spaced, ultimately resulting in a steady field of identical clouds with uniform spacing λ > λ _c .

Numerical experiments with dry stability N_d = N_c corroborate the conclusions from the cloud field equations when N_c ²/N _c0 ² is less than ten. As N_c ² increases, the numerically determined λ _c . becomes approximately 1.8R_s ≈ 1.8N_d . There is a second threshold spacing λ _t ≈ 1.6N_d <λ _c not predicted by the asymptotic theory, below which a field of identical growing clouds is transient. This leads to two types of cloud field evolution. If N_c ²/N _c0 ² is less than 10, all initial conditions lead to steady uniformly spaced fields of identical clouds. If N_c ²/N _c0 ² is on the order of 10 or larger, a field of clouds initiated by horizontally homogeneous random buoyancy perturbations rapidly grows. While it is growing the subsidence radius around each cloud remains O(1); clouds are quite closely spaced. As the clouds mature, R_s increases rapidly to N_d . The clouds are spaced much closer than λ _t apart, so they all dissipate. If the initial conditions are less random, however, so that a few widely spaced clouds break out first, these clouds inhibit the convection which later grows around them, ultimately become steady and drift toward a uniform spacing. In both cases there is no tendency toward cloud clustering.

The steady cloud fields predicted by the model are probably never realized in the atmosphere due to other physical processes such as boundary layer forcing or precipitation, which favor small cloud spacings despite the large Rayleigh number. The primary conclusion that one can draw from the model is that compensating motions in the cloud layer are always competing with these other processes, tending to increase the spacing between convective clouds as subsidence-induced warming and drying suppresses the weaker circulations.

Abstract

The fastest growing modes in Emanuel's recent model of inviscid precipitating convection in a saturated atmosphere with no shear have large horizontal wavenumbers, permitting a simple analytical analysis of their phase speed, growth rate, and modal structure as functions of the model parameters. It is found that the fastest growing modes are always localized near the ground, are slightly sloped, and grow almost as fast as if precipitation were to fall instantly to the ground. In any wind profile with weak unidirectional shear, rolls aligned along the shear vector grow fastest.

Abstract

A defining feature of moist convection is latent heating. A simple, mathematically tractable but thermody-namically reasonable Kuo-type model is developed to isolate some important effects of latent heating on the structure and organization of moist convection. Convection in a shallow, unsheared layer of viscous moist air between two rigid horizontal plates is examined. Unlike previous analytical work, a realistic thermodynamic equation is used, based on the assumption that no precipitation falls out of saturated air. This assumption isolates reversible latent heating from the complicating effects of precipitation. The crucial step is to express the buoyancy of moist air as a simple function of adiabatically conserved, linearly mixing properties of the air; this function is different in saturated than in unsaturated air.

In Part I, the new model is used to find analytical solutions for infinitesimal motions in a conditionally unstable, exactly saturated atmosphere. As in previous work, the most unstable circulation is an isolated, cylin-drical, single updraft cloud, surrounded by an infinite expanse of subsiding clear air. In contrast to earlier work, strong downdrafts occur inside the cloud near its edge. In a separate note, it will be shown that all growing circulations of infinitesimal amplitude are station-no “linear” wave-CISK is possible.

The most important prediction is that subsidence decays exponentially away from the cloud in a horizontal distance R_s . A simple approximate formula for R_s in terms of the growth rate, viscosity, and Coriolis parameter is derived and rationalized. The prediction of infinite cloud spacing will be resolved by a theory of finite-amplitude convection developed analytically in Part II and numerically in Part III, which predicts a finite minimum cloud spacing related to R_s and the strength of convection.

Abstract

Integral methods are used to show that in a simple model of nonprecipitating, moist convection, no small-amplitude propagating or oscillatory, two- or three-dimensional convective instabilities can grow from a quiescent basic state. This result holds for an inviscid layer with vertically varying stratification (of either finite or infinite depth) and for a uniformly stratified viscous layer of finite depth. The implications for the theory of wave-CISK are discussed.

Abstract

No abstract available.

Abstract

The authors investigate the hypothesis that horizontal moisture advection is critical to the eastward propagation of the Madden–Julian oscillation (MJO). Consistent diagnostic evidence has been found in recent MJO-permitting global models viewed from the moisture-mode dynamical paradigm. To test this idea in a causal sense, tropical moisture advection by vorticity anomalies is artificially modulated in a superparameterized global model known to produce a realistic MJO signal. Boosting horizontal moisture advection by tropical vorticity anomalies accelerates and amplifies the simulated MJO in tandem with reduced environmental gross moist stability. Limiting rotational horizontal moisture advection shuts the MJO down. These sensitivities are robust in that they are nearly monotonic with respect to the control parameter and emerge despite basic-state sensitivities favoring the opposite response. Speedup confirms what several diagnostic lines of evidence already suggest—that anomalous moisture advection is fundamental to MJO propagation. The rotational component is shown to be especially critical. Amplification further suggests it may play a role in adiabatically maintaining the MJO.

Abstract

By comparing regional model simulations with the observations collected at the southern Great Plains (SGP) site and the tropical western Pacific (TWP) Nauru site of the Atmospheric Radiation Measurement (ARM) project, this paper evaluates the overall performance of a recently developed shallow cumulus parameterization scheme under different meteorological conditions. The scheme is incorporated into the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5). The simulations indicate that the shallow cumulus scheme can accurately simulate both marine shallow cumuli and the observed diurnal cycle of continental shallow cumuli. Both subgrid cloud properties and the resolved thermodynamic structures and the surface energy budget are well simulated by the model.

Using the simulations performed in this study, the authors also investigate the impact of shallow cumuli on the boundary layer structure. The simulations indicate that maritime shallow convection moistens and cools the cloud layer but dries and slightly heats the subcloud layer. This effect also occurs over land, where it is weaker in the mean but has a pronounced diurnal cycle. Although continental shallow cumuli barely affect the surface energy budget, their maritime counterpart can have a significant impact on the surface evaporation. This study also compares the impacts of continental shallow convection on the boundary layer in winter versus summer at the SGP site, and addresses the effects of shallow cumuli on the middle troposphere and their interaction with stratiform clouds.

Abstract

The impact of physical parameterizations on simulations of cloud-topped marine boundary layers is investigated using the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5). Three-month MM5 simulations of the northeast and southeast Pacific during June–August 1987 are boundary forced with time- varying ECMWF analyses. Runs with four planetary boundary layer (PBL) parameterizations already implemented in MM5 are compared with runs using new parameterizations of boundary layer turbulence and shallow cumulus convection (ShCu) described in a companion paper. Numerous modifications to the MM5 that allow it to be used as a regional climate model are described.

The simulated 3-month mean shortwave cloud radiative forcing (SWCF) and vertical structure of cloud-topped boundary layers in the northeast Pacific are sensitive to the PBL/shallow convection schemes. All four current MM5 PBL schemes [the Blackadar, Medium-Range Forecast (MRF), Burk–Thompson, and Gayno–Seaman schemes] produce overly shallow boundary layers with excessive SWCF throughout this region, especially in the transition from stratocumulus to trade cumulus where their SWCF errors range from 130 (Gayno–Seaman) to 200 W m⁻² (MRF). These errors likely reflect inadequate vertical mixing by parameterized turbulence and shallow convection. The only shallow convection scheme available for MM5, the Grell scheme, was almost totally inactive in this region, so no shallow convection scheme was used for the above simulations. The Grenier– Bretherton () scheme, which entrains more aggressively above stratocumulus-capped convective layers, has much better regional SWCF and vertical structure. Without shallow cumulus convection, the scheme still produces excessive cloud in the transition regions; the main impact of the ShCu parameterization is to remove this bias. With all schemes, the near-surface air has a cool, dry bias, and surface turbulent fluxes are somewhat larger than observed.

Sensitivity studies show that the SWCF is sensitive to a halving of the cloud droplet concentration, to plausible uncertainties in parameterized penetrative mixing at cumulus cloud tops and in stratocumulus entrainment, and (in the coastal zone) to horizontal resolution. Southeast Pacific simulations show that the GB01+ShCu scheme can also accurately represent another subtropical boundary layer cloud regime.

Abstract

Wave-CISK and evaporation-wind feedback modes, also known as WISHE (wind-induced surface heat exchange) modes, are investigated using a two-dimensional (x−p), hydrostatic, nonrotational model linearized about a basic state in radiative-convective equilibrium with no vertical shear. Cumulus convection is parameterized using version 1.22 of the Emanuel convective parameterization scheme, a mass flux scheme that includes the effects of evaporatively driven unsaturated downdrafts. It is found that the only unstable modes are long-wavelength WISHE modes. All wave–CISK modes are damped, though the longest-wavelength modes have nearly neutral growth rates. It is demonstrated that the presence of evaporatively driven unsaturated downdrafts plays a major role in damping both short-wave WISHE and wave-CISK modes in the model. The model favors approximately the same horizontal scale as observed for the Madden–Julian oscillation (40–60 day wave), but the phase speed is too large by a factor of ∼4–5. A general analytical two-dimensional model designed to work with any convective parameterization is used to show that the unusually high phase speeds are most likely a result of a time lag in the vertical transport of water vapor by the Emanuel convective parameterization.