Cumulus Heating Research Articles

Some aspects of the characteristics of monsoon disturbances using a combined barotropic-baroclinic model

A standing Rossby wave of wavelength 30‡ longitude with a finite amplitude along the meridional direction is superimposed on the zonal mean component of the monsoon flow and the stability of such a flow is examined by a quasi-geostrophic barotropic, as well as by a quasi-geostrophic combined barotropic and baroclinic model on a beta plane centered at 18‡N latitude. It is found that the growth of synoptic scale disturbance increases with the amplitude of the meridional wind. The barotropic stability analysis at 700 hPa pressure level shows that there is a critical value (Umax = 11 m / s) of the maximum mean zonal wind below which the computed disturbance moves to the west due to the wave-wave superposition. For maximum mean zonal wind greater that 11 m / s, the westerly wind dominates and the disturbance moves to the east. In another analysis the stability of the zonally asymmetric basic flow is studied with a combined barotropic-baroclinic model where cumulus heating is included. The growth rate, intensity, horizontal scale and the westward velocity of computed disturbances reasonably agree with those of observed monsoon disturbances. The fastest growing mode has a horizontal wavelength of 2000 kms and the e-folding time is about 3 days, when the meridional amplitude of the Rossby wave is 4 m / s at 700 hPa pressure level. When cumulus heating is included in the analysis the intensity of geopotential perturbation at 700 hPa disturbance is-304 m2 / s2. Energy calculations show that the kinetic energy of the mean zonal flow is the main source of energy for the perturbation to grow. It is also found that the contribution of the kinetic energy of the basic Rossby wave to the growth of perturbation is more in comparison to the available potential energy.

A Statistical Analysis of the Dependency of Closure Assumptions in Cumulus Parameterization on the Horizontal Resolution

Simulated data from the UCLA cumulus ensemble model are used to investigate the quasi-universal validity of closure assumptions used in existing cumulus parameterizations. A closure assumption is quasi-universally valid if it is sensitive neither to convective cloud regimes nor to horizontal resolutions of large-scale/mesoscale models. The dependency of three types of closure assumptions, as classified by Arakawa and Chen, on the horizontal resolution is addressed in this study. Type I is the constraint on the coupling of the time tendencies of large-scale temperature and water vapor mixing ratio. Type II is the constraint on the coupling of cumulus heating and cumulus drying. Type III is a direct constraint on the intensity of a cumulus ensemble. The macroscopic behavior of simulated cumulus convection is first compared with the observed behavior in view of Type I and Type II closure assumptions using 'quick-look' and canonical correlation analyses. It is found that they are statistically similar to each other. The three types of closure assumptions are further examined with simulated data averaged over selected subdomain sizes ranging from 64 to 512 km. It is found that the dependency of Type I and Type II closure assumptions on the horizontal resolution is very weak and that Type III closure assumption is somewhat dependent upon the horizontal resolution. The influences of convective and mesoscale processes on the closure assumptions are also addressed by comparing the structures of canonical components with the corresponding vertical profiles in the convective and stratiform regions of cumulus ensembles analyzed directly from simulated data. The implication of these results for cumulus parameterization is discussed.

Convective Interaction with Boundary-Layer Dynamics in the Development of a Tropical Intraseasonal System

Abstract Tropical boundary-layer flows interact with the free tropospheric circulation and underlying sea surface temperature, playing a critical role in coupling collective effects of cumulus heating with equatorial dynamics. In this paper a unified theoretical framework is developed in which convective interaction with large-scale circulation includes three mechanisms: convection–wave convergence (CWC) feedback, evaporation–wind (EW) feedback, and convection–frictional convergence (CFC) feedback. We examine the dynamic instability resulting from the convective interaction with circulation, in particular the role of CFC feedback mechanism. CFC feedback results in an unstable mode that has distinctive characteristics from those occurring from CWC feedback or EW feedback in the absence of mean flow. The instability generated by CFC feedback is of low frequency with a typical growth rate on an order of 10−6 s−1. The unstable mode is a multiscale wave packet; a global-scale circulation couples with a large-s...

A Numerical Study of a Low-level Jet and Its Accompanying Secondary Circulation in a Mei-Yu System

Abstract A primitive equation numerical model has been used to study the Mei-Yu system that occurred in the middle of May 1987. Although cumulus heating was not included in one of the experiments, all of the major features of a Mei-Yu system other than deep convection are reproduced in that experiment. These features are a cloud band along the coastline in southern China; a weak temperature gradient, a strong moisture gradient, and a strong wind shear across the cloud band; and a supergeostrophic low-level jet (LLJ) with an accompanying secondary circulation. When the moist air coming from the south encounters the migrating high pressure system in the north, it turns to the east-northeast and becomes saturated. The resulting stratiform cloud covers all of southern China and the pressure trough at the 850-hPa level deepens by 1.5 hPa due to the latent heat released. It induces convergent motion in the lower level and generates a direct, cross-frontal secondary circulation that helps keep the low-level wind...

Tropical Intraseasonal Oscillations in a Simple Nonlinear Model

This study examines two possible mechanisms responsible for the selection of the preferred period of the Madden and Julian (40–50 day) oscillation. A global two-level nonlinear model with a positive-only CISK-type cumulus heating parameterization is used to simulate the oscillation, which appears when the SST exceeds a critical value for instability of CISK type. Longitudinal variations of tropical SST are imposed so that a stable and an unstable region coexist. When the cold SST sector is sufficiently stable, the CISK wave propagates efficiently through the stable region in the form of a damped moisture-modified Kelvin wave, and reemerges in the unstable region where its amplitude grows. When the SST in the stable sector is set closer to the instability threshold, the moist Kelvin wave slows down and decays before reentering the unstable region, but the CISK perturbation periodically regenerates over the warm waters in response to a local buildup of instability. This last experiment implies a new mechanism for setting the time scale of the oscillation, alternative to that of simple zonal propagation around the globe. A “discharge-recharge” theory is proposed whereby the 40-day recurrence period in the model is set by the growth and duration times of the convective episode together with the recharge time for the instability. It is shown that the midlatitude baroclinic eddies provide the quasi-stochastic forcing necessary to excite each new intraseasonal episode by organizing a region of subtropical convection, which then grows and expands equatorwards due to the effect of the latent heating. The dynamical picture that emerges from the above results is consistent with observations that suggest a local thermodynamically based time scale for the oscillation, and with case studies indicating that extratropical processes might be responsible for the onset of 40–50-day events.

Monsoon Disturbances, Intraseasonal Oscillations, Teleconnection Patterns, Blocking, and Storm Tracks of the Global Atmosphere during January 1979: Linear Theory

The results of a study are presented that indicate that a wide variety of atmospheric disturbances, including those associated with storm tracks and blocking in both hemispheres, quasi-stationary global teleconnection patterns, and localized monsoon disturbances, as well as intraseasonal oscillations, may be generated through the instability of the three-dimensional global basic state for January 1979 including a wave-CISK cumulus heating parameterization. The analysis has been conducted with a two-level primitive equation eigenvalue model, and the growing disturbances for various specifications of the strengths of the cumulus heating have been analyzed. Within the parameter range studied, inclusion of explicit moisture in the basic state has little effect on the structures of the storm track and onset-of-blocking modes in both hemispheres, but it increases growth rates as expected. It is also responsible for generating a significant amplitude of the tropical shear streamfunction of low-frequency and quasi-stationary teleconnection pattern modes, particularly in the Australian/South Pacific region where a coupling to the Australian monsoon appears to occur. Remarkable localized quasi-stationary monsoon disturbances of fairly small scale are found, which tend to produce either break or active periods of the Australian monsoon depending on their phase. The CISK heating focuses these modes in the Australian region and increases their growth rates. A group of intraseasonal oscillation modes with quite complex structures and periods between about 20 and 60 days is also found. They have eastward-propagating velocity potentials, peaking in the equatorial regions with a zonal wavenumber 1, and possibly 2, envelope wave within which are embedded smaller-scale structures. They have equivalent barotropic streamfunctions in extratropical regions with a baroclinic structure, typical of the first internal mode, in the tropical regions. At certain phases they can produce break or active periods of the Australian monsoon. Both a three-dimensional large-scale basic-state flow and a cumulus heating parameterization appear to be necessary for generating, through instability, intraseasonal oscillation modes with realistic structures.

A Study of Two Cases of Comma-Cloud Cyclogenesis Using a Semigeostrophic Model

Abstract The linear stability of two atmospheric flows is examined, with basic-state data taken from environments where comma clouds were observed to form. The basic states each feature a baroclinic zone associated with an upper-level jet, with conditional instability on the north side. The semigeostrophic approximation is used, along with a simple parameterization for cumulus heating, and the eigenvalue problem is solved using a Chebyshev spectral method. The instabilities can be regarded as resulting from the interaction of potential-vorticity anomalies from three sources: advection along isentropic surfaces of the basic-state potential-vorticity (PV) gradient. advection of the surface potential temperature gradient (which is equivalent to a PV gradient in a thin layer at the surface), and potential vorticity generated by release of latent heat. It is found that for the comma clouds the instability is a baroclinic interaction of upper- and lower-level PV anomalies. However, heating is an important sourc...

Cumulus Convection and CISK in Midlatitudes. Part II: Comma-Cloud Formation in Cyclonic Shear Regions

Abstract Observational studies show that polar air stream cyclones form preferentially to the north of the polar front in regions of high vorticity and low static stability, although the baroclinicity may be stronger elsewhere. This phenomenon is investigated by considering a semigeostrophic linear stability analysis of a constant potential vorticity zonal jet in the presence of parameterized cumulus heating in the cold air mass. Three types of unstable modes are found for different amounts of heating. With relatively small heating rates, the usual baroclinic instability occurs, with the disturbance centered on the jet axis. With moderate heating, the fastest growing mode is again a mainly baroclinic system, but with significant amplitude only in the region of heating on the cold-air side of the jet. Finally, for sufficiently large heating rates, a small-scale disturbance, which is driven primarily by diabatic processes, forms in the cold air mass. There is a continuous transition between the three types ...

An Observational Study of the First-Order Vorticity Dynamics in a Tropical Easterly Wave

Abstract GATE Phase III A/B- and B-scale data were analyzed and used to diagnostically test the first-order vorticity equation proposed by Cho et al. The results are given in the form of a composite easterly wave and the analysis shows that the first-order vorticity equation is capable of describing the vorticity dynamics of the composite easterly wave. Cumulus heating produces significant large-scale vertical motion, and it is demonstrated that the effect of cumulus clouds on the large-scale vorticity field is through vortex-tube stretching by cloud-induced vertical motion. The composite analysis of the first-order vorticity equation also shows that the vorticity dynamics of tropical easterly waves are adequately described by a linearized first-order vorticity equation and dominated by the advection of the perturbed vorticity by the relative zonal mean wind, the advection of the zonal mean vorticity by the perturbed wind, and the vortex-tube stretching induced by cumulus activity. It is explained how, du...

A Reexamination of the Genesis of African Waves

Abstract The problem of genesis of easterly African waves is reexamined as a linear eigenvalue instability problem of a supposedly realistic basic zonal shear flow with and without a cumulus heating. Evidence will be presented to show how the growth rate, the propagation speed, and the overall composite structure of the observed tropical easterly waves can he well reproduced in the model in conjunction with a CISK representation of the latent heating. The degree of resemblance between the structure of the model unstable wave and the observed African waves is found to be significantly dependent upon the secondary features of the basic shear flow. This finding is based on a detailed comparison of the results using different structures for the basic flow including the one used by Mass. Much of the kinetic energy of the unstable wave is generated via the barotropic instability process associated with the horizontal shear of the Sahara jet centered at the 650 mb level. But the vertical shear of the zonal flow ...

A numerical study of the parametrization of deep tropical convection

A two-dimensional mesoscale cloud model is used to simulate an ensemble of deep tropical convective clouds using GATE data. Random heating perturbations near the sea surface initiate the development of a population of clouds which grow under the influence of specified large-scale, radiative and surface forcing. Budgets of convective heating and moistening are presented and the model found to be a reasonable representation of the atmosphere. The model is used to investigate the parametrization of cumulus convection in large-scale models. Equations governing the effect of convection upon the large-scale atmosphere are derived in full and compared with approximate forms used by previous workers. These forms are the basis of many parametrization schemes. Simple representations of cumulus heating (Q1), cumulus moistening (Q2), and dynamical transports for use in parametrization schemes in large-scale atmospheric models are studied. The importance of shallow convection in determining the vertical structure of Q2 is recognized. The dependence of convective rainfall upon atmospheric structure and large-scale processes (the closure problem) is investigated. The importance of downdraughts is emphasized and difficulties in the calculation of Q2 identified. Study of parametric forms for cumulus momentum transports indicates that the ‘cumulus friction’ hypothesis is inadequate. It is suggested that present closure schemes are too restrictive.

A numerical study of the parametrization of deep tropical convection

AbstractA two‐dimensional mesoscale cloud model is used to simulate an ensemble of deep tropical convective clouds using GATE data. Random heating perturbations near the sea surface initiate the development of a population of clouds which grow under the influence of specified large‐scale, radiative and surface forcing. Budgets of convective heating and moistening are presented and the model found to be a reasonable representation of the atmosphere.The model is used to investigate the parametrization of cumulus convection in large‐scale models. Equations governing the effect of convection upon the large‐scale atmosphere are derived in full and compared with approximate forms used by previous workers. These forms are the basis of many parametrization schemes. Simple representations of cumulus heating (Q1), cumulus moistening (Q2), and dynamical transports for use in parametrization schemes in large‐scale atmospheric models are studied. The importance of shallow convection in determining the vertical structure of Q2 is recognized. The dependence of convective rainfall upon atmospheric structure and large‐scale processes (the closure problem) is investigated.The importance of downdraughts is emphasized and difficulties in the calculation of Q2 identified. Study of parametric forms for cumulus momentum transports indicates that the ‘cumulus friction’ hypothesis is inadequate. It is suggested that present closure schemes are too restrictive.

Cumulus Initialization in a Global Model for Numerical Weather Prediction

Abstract A procedure for adjusting temperature and humidity analyses used as initial conditions for numerical weather prediction models so that diagnosed distributions of cumulus convection exist during the initial stages of the forecast is applied in a global atmospheric model. This cumulus initialization procedure is designed to ameliorate the problem of numerical weather prediction spinup, the departure of diabatic forcing from diagnosis and observation, which is characteristic of the early portions of integrations in numerical weather prediction. Formally, cumulus initialization consists of a minimization of the adjustments to the original analyses of temperature and humidity, subject to nonlinear constraints imposed by the cumulus parameterization in the numerical weather prediction model, if cumulus heating is taken as known by diagnostic methods as an initial condition. Experiments with a global model exhibiting severe spinup when initialized with an analysis subject only to diabatic normal-mode in...

Northward propagation of the 30–50 day mode in the Indian monsoon region

A highly simplified zonally symmetric system of equations is used to understand the basic mechanism of the northward movement of the 30–50 day oscillation in the Indian monsoon region. Zonally symmetric perturbations are used on the July mean basic flow in the Indian region. A two-level model is employed. A simple parametrization of cumulus heating is included. An expression is derived for the northward phase speed. A right order of magnitude for the phase speed is obtained. The northward movement appears to be controlled by the basic zonal wind profile and cumulus heating.

Cumulus Heating and CISK in the Extratropical Atmosphere. Part I: Polar Lows and Comma Clouds

Abstract The effects of cumulus heating and the possibility of CISK in extratropical latitudes are explored by combining the Eady model of baroclinic instability with wave-CISK. For perturbations about a state of rest, there is no intrinsic time scale, however the equations can be solved for geopotential tendency. It was found that CISK disturbances could not grow unless the heating exceeded a threshold value. This value is reduced when the boundary layer moisture content is increased, the static stability decreased, or the heating distributed lower in the troposphere. Perturbations about a baroclinic basic state, for small heating rates resemble a baroclinic wave with heating acting mainly to reduce the effective static stability, resulting in faster growth and shorter wavelengths. However, as the heating is increased, the instability gradually takes on the characteristics of the pure CISK disturbance. The transition level shows the same dependencies on model parameters as for the threshold in the CISK c...

Kelvin Wave-CISK: A Possible Mechanism for the 30–50 Day Oscillations

Abstract Two categories of theories have been proposed to explain the observed tropical intraseasonal oscillations whose main periodicity is between 30–50 days: (i) those based on eastward propagating Kelvin waves maintained by cumulus heating; and (ii) those based on interactions with stationary oscillations of the basic state. Recent numerical modeling studies have simulated certain important aspects of the oscillation particularly the slower propagation speed as compared with the normal Kelvin waves. Motivated by these results which lend support to the first category, a linear theoretical analysis of the equatorial β-plane wave-CISK was carried out with a focus on the Kelvin modes. Our results show that two types of CISK modes may arise from an interaction of vertical modes. For heating with a maximum in the lower troposphere, the instability is due to the lowest internal mode which gives a stationary, east-west symmetrical structure. When heating is maximum in the midtroposphere, eastward propagating ...

A Simple Model of the 40-50 Day Oscillation

Abstract The effects of a positive-only cumulus heating parameterization on equatorially trapped waves are investigated using both nonlinear and linear single vertical mode models. In the linear model the cumulus heating is shown to slow down the equatorial waves. In particular the eastward moving Kelvin wave is readily slowed from the free phase speed (45 m s−1) to the intrinsic speed associated with the observed 40–50 day oscillation (<10 m s−1). Slow eastward propagating Kelvin waves only occur for stable cumulus heating (stable meaning that adiabatic cooling is able to compensate for the cumulus heating). However these linear moist waves decay rapidly and are thus an unlikely explanation of the observed oscillation. The observed meridional wind perturbation is also unexplained by this mechanism. For unstable cumulus heating, growing linear CISK waves develop but remain stationary. Thus no satisfactory explanation of the 40–50 day oscillation is possible with this single vertical mode linear model. For...

Numerical Simulations of the Atmospheric Response to a Sea Surface Temperature Anomaly over the Equatorial Eastern Pacific Ocean

Abstract The atmospheric response to a sea surface temperature anomaly over the equatorial eastern Pacific Ocean (SSTA) is investigated using the UCLA General Circulation Model. The SSTA used is an idealization of that compiled by Rasmusson and Carpenter for the mature phase of El Nino. Two simulations over seasons, one without and the other with the SSTA, are performed and their results are compared for the Northern Hemisphere winter season. In the tropics the SSTA enhances precipitation over the central and eastern equatorial Pacific, while it decreases precipitation over the adjacent regions. The anomalous precipitation is predominantly balanced by the anomalous moisture flux convergence, which has comparable magnitude in the planetary boundary layer (PBL), and in the free atmosphere with quite different geographical distribution. This suggests that the anomalous precipitation, and hence the anomalous tropical cumulus heating, cannot be related exclusively to either flow anomalies in the PBL or in the ...

Diurnally Forced Tropical Tropospheric Circulation over South America

The impact of diurnally varying thermal forcing on the tropical circulation is studied with a linearized shallow water model on an equatorial beta plane. The mass and flow fields are interpreted as an internal mode with equivalent depth of the order of 250 m. This is the preferred vertical mode excited by typical cumulus heating profiles in the tropics. The diurnal forcing with the horizontal scale of the Amazon source partitions approximately 40% of the input energy to slow modes. The fast modes are trapped by the critical latitudes contributing significantly to oscillations in the divergence field, which emanate out of the source region. The divergence field at the source is approximately in phase with the forcing; the vorticity field lags the forcing by approximately 10 hours. A comparison of the model results with the 500 mb level vertical motion, derived from the National Meteorological Center analysis, shows a similar pattern of propagating oscillations. It is suggested that the diurnally forced convection over the tropical sector of South America controls the timing of heavy precipitation over the adjoining regions.

Baroclinic Instability with Cumulus Heating

Abstract We have investigated baroclinic instability with cumulus heating using a vertically discrete, linearized, quasi-geostrophic model on a β-plane. Two formulations of cumulus heating were used. The first formulation (η-model) rests on the assumption that heating at all levels is proportional to the vertical p-velocity at the top of the lowest model layer. The second formulation (AS-model) follows the cumulus parameterization proposed by Arakawa and Schubert. We present results for basic states with a constant temperature lapse rate and zonal flows linear in pressure. With both formulations, we found the Green modes for easterly shears destabilized by cumulus heating. We discuss the mechanism of this destabilization along with the vertical structure and energetics of the perturbations. We extended the analyses for basic zonal flows similar to those observed during the Indian summer monsoon season, with the AS-model. The wavelength, phase speed, growth rate and vertical structure corresponding to a pe...