Cumulus Friction Research Articles

A strategy for representing the effects of convective momentum transport in multiscale models: Evaluation using a new superparameterized version of the Weather Research and Forecast model (SP‐WRF)

AbstractThis paper describes a general method for the treatment of convective momentum transport (CMT) in large‐scale dynamical solvers that use a cyclic, two‐dimensional (2‐D) cloud‐resolving model (CRM) as a “superparameterization” of convective‐system‐scale processes. The approach is similar in concept to traditional parameterizations of CMT, but with the distinction that both the scalar transport and diagnostic pressure gradient force are calculated using information provided by the 2‐D CRM. No assumptions are therefore made concerning the role of convection‐induced pressure gradient forces in producing up or down‐gradient CMT. The proposed method is evaluated using a new superparameterized version of the Weather Research and Forecast model (SP‐WRF) that is described herein for the first time. Results show that the net effect of the formulation is to modestly reduce the overall strength of the large‐scale circulation, via “cumulus friction.” This statement holds true for idealized simulations of two types of mesoscale convective systems, a squall line, and a tropical cyclone, in addition to real‐world global simulations of seasonal (1 June to 31 August) climate. In the case of the latter, inclusion of the formulation is found to improve the depiction of key synoptic modes of tropical wave variability, in addition to some aspects of the simulated time‐mean climate. The choice of CRM orientation is also found to importantly affect the simulated time‐mean climate, apparently due to changes in the explicit representation of wide‐spread shallow convective regions.

Kinetic Energy Budget for the Madden–Julian Oscillation in a Multiscale Framework

Abstract A kinetic energy budget for the Madden–Julian oscillation (MJO) is established in a three-scale framework. The three scales are the zonal mean, the MJO scale with wavenumbers 1–4, and the small scale with wavenumbers larger than 4. In the composite budget, the dominant balance at the MJO scale is between conversion from potential energy and work done by the pressure gradient force (PGF). This balance is consistent with the view that the MJO wind perturbations can be viewed as a quasi-linear response to a slowly varying heat source. A large residual in the upper troposphere suggests that much kinetic energy dissipates there by cumulus friction. Kinetic energy exchange between different scales is not a large component of the composite budget. There is a transfer of kinetic energy from the MJO scale to the small scale; that is, this multiscale interaction appears to damp rather than strengthen the MJO. There is some variation in the relative importance of different terms from one event to the next. In particular, conversion from mean kinetic energy can be important in some events. In a few other events, the influence from the extratropics is pronounced.

Convective Momentum Transport in a Simple Multicloud Model for Organized Convection

Abstract Convective momentum transport (CMT) is the process of vertical transport of horizontal momentum by convection onto the environmental flow. The significance of CMT from mesoscale to synoptic- and planetary-scale organized cumulus convection has been established by various theoretical and observational studies. A new strategy mimicking the effect of unresolved mesoscale circulation based on the weak temperature gradient (WTG) approximation with a Gaussian profile to redistribute the heating due to parameterized cumulus convection at the subgrid scale is adopted here to construct a CMT parameterization for general circulation models (GCMs). Two main regimes of CMT are considered: an upscale squall-line regime and a downscale non-squall-line regime. An exponential probability distribution is used to select which of these two effects is active, conditional on the state of the large-scale shear. The shear itself is used as a measure of the persistence of mesoscale organized circulation due to the presence or not of tilted deep convective heating with lagged stratiform anvils. The CMT model is tested in the simple case of the multicloud model of Khouider and Majda, used here as a toy GCM. Numerical simulations are performed here for the simple case without rotation, in a parameter regime where the multicloud model exhibits packets of convectively coupled gravity waves moving in one direction, at 17 m s−1, and planetary-scale wave envelopes moving in the opposite direction, at 4–6 m s−1, reminiscent of the Madden–Julian oscillation (MJO) and the associated embedded synoptic-scale superclusters. The results herein show that the inclusion of CMT intensifies both the synoptic-scale convectively coupled waves and the manifestation of planetary-scale waves in the multicloud model. This provides evidence that the present CMT model captures the essence of the physical mechanism through which kinetic energy is transferred from the subgrid-scale mesoscale circulation to the large-scale/resolved motion. Sensitivity simulations showed that two key parameters for the CMT parameterization are the relative strength of the parameterized stratiform anvils and the dimensional threshold used in the exponential distribution for the cumulus friction and the upscale CMT forcing resulting from organized subgrid mesoscale circulation.

A Three-Dimensional Anelastic Model Based on the Vorticity Equation

Abstract A three-dimensional anelastic model has been developed using the vorticity equation, in which the pressure gradient force is eliminated. The prognostic variables of the model dynamics are the horizontal components of vorticity at all heights and the vertical component of vorticity and the horizontally uniform part of the horizontal velocity at a selected height. To implement the anelastic approximation, vertical velocity is diagnostically determined from the predicted horizontal components of vorticity by solving an elliptic equation. This procedure replaces solving the elliptic equation for pressure in anelastic models based on the momentum equation. Discretization of the advection terms uses an upstream-weighted partially third-order scheme. When time is continuous, the solution of this scheme is quadratically bounded. As an application of the model, interactions between convection and its environment with vertical shear are studied without and with model physics from the viewpoint of vorticity dynamics, that is, the deceleration/acceleration process of the basic flow in particular. The authors point out that the process is purely three-dimensional, especially when the convection is relatively localized, involving the twisting terms and the horizontal as well as vertical transports of vorticity. Finally, it is emphasized that parameterization of cumulus friction is a resolution-dependent problem of vorticity dynamics associated with cumulus convection.

Equilibrium mechanism analysis on the physical processes of IAP3.0

Based on the detection of the dynamic and thermodynamic functions of the physical processes in IAP3.0, the equilibrium mechanisms of the temperature, moisture and wind are analyzed. The negative feedback between the longwave radiation and temperature is verified. The cooling regulation of net radiation on temperature is mostly balanced by the heating of precipitation; the leading actions on temperature of other processes such as vertical diffusion, shallow cumulus convection and friction are merely available for lower air. The moisture consumption of precipitation is compensated on the whole by the provision of shallow cumulus convection, which sustains the moisture conservation to a high degree. The wind field is directly regulated by the momentum redistribution of cumulus, the dry adiabatic convection and vertical diffusion. Yet, the prominent influences of these processes are generally confined to the lower level. The east wind at low latitudes and the west wind at high latitudes are both weakened by the regulations and furthermore, by virtue of the transportation of mean meridional circulation, such a variation exactly maintains the angular momentum conservation.

The global response to tropical heating in the Madden–Julian oscillation during the northern winter

AbstractA life cycle of the Madden–Julian oscillation (MJO) was constructed, based on 21 years of outgoing long‐wave radiation data. Regression maps of NCEP–NCAR reanalysis data for the northern winter show statistically significant upper‐tropospheric equatorial wave patterns linked to the tropical convection anomalies, and extratropical wave patterns over the North Pacific, North America, the Atlantic, the Southern Ocean and South America. To assess the cause of the circulation anomalies, a global primitive‐equation model was initialized with the observed three‐dimensional (3D) winter climatological mean flow and forced with a time‐dependent heat source derived from the observed MJO anomalies. A model MJO cycle was constructed from the global response to the heating, and both the tropical and extratropical circulation anomalies generally matched the observations well. The equatorial wave patterns are established in a few days, while it takes approximately two weeks for the extratropical patterns to appear. The model response is robust and insensitive to realistic changes in damping and basic state. The model tropical anomalies are consistent with a forced equatorial Rossby–Kelvin wave response to the tropical MJO heating, although it is shifted westward by approximately 20° longitude relative to observations. This may be due to a lack of damping processes (cumulus friction) in the regions of convective heating. Once this shift is accounted for, the extratropical response is consistent with theories of Rossby wave forcing and dispersion on the climatological flow, and the pattern correlation between the observed and modelled extratropical flow is up to 0.85. The observed tropical and extratropical wave patterns account for a significant fraction of the intraseasonal circulation variance, and this reproducibility as a response to tropical MJO convection has implications for global medium‐range weather prediction. Copyright © 2004 Royal Meteorological Society

NOTES AND CORRESPONDENCE Convective Eddy Momentum Tendencies in Long Cloud-Resolving Model Simulations

Abstract Domain-average momentum budgets are examined in several multiday cloud-resolving model simulations of deep tropical convection in realistic shears. The convective eddy momentum tendency F, neglected in many global circulation models, looks broadly similar in two- and three-dimensional simulations. It has a large component in quadrature with the mean wind profile, tending to cause momentum profile features to descend. This component opposes, and exceeds in magnitude, the corresponding large-scale vertical advective tendency, which would tend to make features ascend in convecting regions. The portion of F in phase with the mean wind is isolated by vertically integrating F · u, yielding a kinetic energy tendency that is overwhelmingly negative. The variation of this energy damping with shear flow kinetic energy and convection intensity (measured by rain rate) gives a “cumulus friction” coefficient around −40% to −80% per centimeter of rain in 3D runs. Large scatter reflects the effects of varying co...

Transitions from Hadley to Rossby Flows in Internally Forced Rotating Spherical Systems

The possibility of global-scale transitions between the Hadley and Rossby atmospheric regimes is investiated using a simple three-dimensional rotating spherical model without a boundary layer structure, bottom topography, or cumulus friction, and the expected occurrence of the Hadley to Rossby transition is demonstrated. It is shown that a transition from Hadley flow to wavenumber-5 Rossby flow is preferred, in agreement with standard baroclinic instability results. This result gives a reasonable Rossby wave bifurcation from the Hadley solution. For the cases examined, it was found that the upper symmetric Hadley regime does not exist and that the Hadley to Rossby transition depends on the values of the eddy viscosities.

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.

On the derivation of the divergent flow from the rotational flow: The χ problem

AbstractThe vertical component of the vorticity equation in pressure coordinates involves only the divergent and rotational components of the horizontal motion. Taking the dominant rotational component as specified, the equation may be considered as an equation for the velocity potential, χ, of the divergent motion. Solving this χ problem yields a divergence pattern which is dynamically consistent with the generally much better observed rotational flow (provided, of course, that the vorticity dynamics is represented correctly). A simple way of doing this is described, and applied to seasonally averaged and instantaneous winds analysed at the European Centre for Medium Range Weather Forecasts (ECMWF). In view of the delicate nature of the vorticity balance, a comparison of δ, the horizontal divergence obtained in this manner, with D, derived directly from the analysed winds, provides a stringent test for the data assimilation system.For seasonal averages, D̃ based on an inviscid vorticity equation in the upper troposphere is generally found to agree well with D, even in the deep tropics. However, some features achieve a more interesting and believable structure than in the analyses. Allowing for a vorticity sink in regions of strong organized convection changes this estimate of δ only slightly, well within the range of observational uncertainty, and not always in the sense of improving the agreement with D. It is therefore possible that on the large scale, ‘cumulus friction’ is only important in areas of strong convection, and if so, is not large enough to be determined unambiguously from existing data sets.Solution of the χ problem at a particular initial time requires an additional piece of information, the vorticity tendency, which could be obtained operationally using a suitable backward time‐differencing scheme. This contrasts with the use of the usual balance procedures, which require a knowledge of the less readily accessible diabatic heating rate.

The Walker Circulation with Observed Zonal Winds, a Mean Hadley Cell, and Cumulus Friction

Abstract The term Walker Circulation is used to refer to the zonal overturning across the equatorial Pacific driven by enhanced convection over the Indonesian region. In this work, an attempt is made to simulate the Walker Circulation using a linear model that includes a cumulus friction parameterization. The work of Geisler is extended by including a realistic mean zonal wind field obtained from the FGGE dataset and a prescribed mean Hadley cell that is computed from an analytical streamfunction. The model is forced by a stationary tropical heat source. The sensitivity of the model circulation to changes in the basic state is examined. Model results show that the inclusion of a nonzero mean zonal wind field tends to enhance the extratropical response in the winter hemisphere. Including a cumulus friction parameterization tends to damp the zonal wind response near the heating center and also lower the level of zero zonal wind in the model Walker Circulation. Including a mean Hadley cell in the basic state...

The Effect of Cumulus Momentum Mixing on the Development of a Symmetric Model Hurricane

The effect of the vertical transport of horizontal momentum by cumulus clouds on the development of a symmetric model hurricane is investigated. This is accomplished by using Sundqvist's symmetric hurricane model with parameterized cumulus friction. The scheme used to include cumulus friction in the model is essentially the same as that given by Stevens and Lindzen in 1978 and Lindzen in 1981. The results of two sets of numerical integrations are presented. In one, the initial wind and moisture distributions were derived from atmospheric observations in Atlantic intensifying cyclones as composited by McBride. In the other, the initial vortex was specified as that which corresponds to the linearly most unstable mode in Mak's 1980 linear analysis of the effect of cumulus friction on hurricane formation. Given each initial wind, temperature and moisture distribution, numerical integrations were performed with and without cumulus friction present in the model. With cumulus friction included, the growth rates of the initial disturbances and their final intensities are smaller than those obtained in the absence of cumulus friction. The Atlantic intensifying cyclone with cumulus friction reaches storm strength, whereas without cumulus friction it develops into a hurricane. In the second pair of numerical integrations with the initial vortex specified as described above, the model develops hurricanes with and without cumulus frictions, but the rate of intensification and final strength of the vortex are significantly smaller when cumulus friction is included. The damping effect of cumulus friction is attributed to the fact that the angular momentum transported from the lower into the upper troposphere by cumulus mixing is not fully replenished in the lower troposphere by the cumulus induced secondary (radial) circulation. This contrasts with the effect of the inward eddy flux of momentum, reported on previously, which was found to enhance the intensification of hurricanes. The crucial difference between the two mechanisms, both of which induce secondary radial circulations due to a vertical differential in cyclonic torque, appears to be the net increase of momentum in the vortex due to inward eddy flux of momentum, which is not present in the case of cumulus friction. The latter mechanism simply redistributes the momentum vertically, actually reducing the strength of both the low-level cyclone and the upper-level anticyclone.

The Bulk Effects of Cumulus Momentum Transports in Tropical Cyclones

Abstract The net influence of subgrid scale processes on the tangential momentum field in tropical cyclones is calculated as a residual of the grid-scale momentum budget for eight rawinsonde composite data sets. Results show that developing cyclones of the northwest Pacific and northwest Atlantic have similar residual profiles in the vertical: positive cyclonic acceleration at upper and lower levels and negative cyclonic acceleration at between levels. Stronger systems have a greater magnitude of the subgrid scale effect. These results are believed to represent primarily the cumulus momentum transport (defined as cumulus friction). A simple single cloud model is developed to diagnose vertical momentum rearrangement through mass recycling. Model results agree well with the residual calculations from the composites. The total convective effect (TCE) on the tangential momentum includes the vertical transport by all the upward and downward motions which can be decomposed into the mean vertical motion and the ...

The Significance of Thermodynamic Forcing by Cumulus Convection in a General Circulation Model

Abstract To assess the effects of cumulus convection on the general circulation of the atmosphere, a medium-resolution, spectral general circulation model was integrated twice for 40 simulated days from identical initial conditions, with and without a version of a cumulus parameterization scheme developed by Kuo. The cumulus parameterization scheme allows cumuli to interact with the large-scale flow by condensation and cumulus flux convergences of entropy and moisture; cumulus friction is not included. Cumulus convection warms the upper troposphere and slightly cools the lower tropical troposphere; additional cooling occurs in the lower troposphere of the winter-hemisphere baroclinic zone. Cumulus convection also dries the lower troposphere, especially in the tropics and summer hemisphere, and weakens the Hadley cells. The zonal wind field responds geostrophically to cumulus-induced temperature changes. Condensation and cumulus vertical-flux convergence are both important in determining the interaction be...

A study of the sensitivity of the winter mean meridional circulation to sources of heat and momentum

The time and zonally averaged momentum and thermodynamic equations on a spherical earth are combined to formulate an equation for the mean meridional circulation based on the quasi-static assumption discussed in Eliassen (Astrophys. Nor. 1951, 19–60). The forcing terms and coefficients in the equation are taken from previously published zonally and seasonally averaged data, which include the net radiative heating, condensation heating, boundary layer friction and sensible heating, tropical cumulus friction, the mean zonal wind and large-scale eddy transports of momentum and heat in winter. The computed meridional circulation in the Northern Hemisphere compares well to the observations with a three-cell structure of Hadley, Ferrel and polar circulations. To estimate the relative importance in maintaining the meridional circulation a series of solutions is computed by removing one of the individual sources at a time and the solutions are compared to the standard solution. It is found that the Hadley cell maintains the intensity level at only one-third of the standard solution if the condensation heating is absent. Although there is virtually no source in the tropics due to eddy momentum and heat transports, the mid-latitude eddy transport affects the Hadley circulation significantly, suggesting that the cooling due to eddy heat transport in the subtropics is an important component balancing the adiabatic heating in the downward branch of the Hadley cell. The individual effects of radiation, surface sensible heating and surface friction are all comparable, but the contributions in the balance of meridional circulation is, on the global average, not more than one-third of the condensation and resultant eddy effect, although the effects are different for the individual Hadley, Ferrel and polar circulations. DOI: 10.1111/j.2153-3490.1981.tb01756.x

A Linear Model of the Walker Circulation

Abstract In this paper we present results of a model study of the Walker Circulation defined as the steady response of a stratified atmosphere to an isolated equatorial heat source. The model equations are linearized with respect to a basic state of no motion and constant static stability. Cumulus friction provides the momentum damping. In the absence of cumulus friction, the center of the overturning in the equatorial plane is near 500 mb. With the addition of cumulus friction in an amount consistent with a zonally averaged precipitation of 2 m year−1, the center is lowered to 600 mb. Cumulus friction in this amount also seems to provide reasonable amplitudes in the response. It is found that the branch of the overturning in the equatorial plane east of the heating is weaker than and has a larger longitudinal scale than the branch west of the heating. This asymmetry becomes more pronounced with a narrowing of the longitudinal width of the heat source. The mass flux in meridional overturnings is found to ...

Comments on “Cumulus Friction: Estimated Influence on the Tropical Mean Meridional Circulation”

Comments on “Cumulus Friction: Estimated Influence on the Tropical Mean Meridional Circulation”

“Cumulus Friction”: Estimated Influence on the Tropical Mean Meridional Circulation

A simple diagnostic study is performed in order to examine the influence of parameterized westerly momentum exchange by cumulus convection on the observed Hadley circulation. Observed precipitation and 200 mb winds are used to diagnose the mean 100–200 mb tropical cumulus friction using the parameterization proposed by Schneider and Lindzen (1976). By using seasonal data on a latitude-longitude grid, we estimate not only the annual (standing) zonally symmetric cumulus friction but the seasonal (transient) and zonally asymmetric contributions as well. In general, the standing zonally symmetric contribution dominates the total cumulus friction, but other components are significant at certain latitudes. The meridional mass flux induced by cumulus friction is estimated through the use of an approximate u-momentum equation. The diagnosed meridional mass transports are about an order of magnitude smaller than those which are observed by direct measurements. Therefore it appears unlikely that cumulus friction plays a dominant role in maintaining the tropical mean meridional circulation.

The Effect of Cumulus Friction on the Simulation of the January Hadley Circulation by the GLAS Model of the General Circulation

A method of parameterizing the vertical mixing of horizontal momentum by cumulus convection was added to the GLAS model of the general circulation of the tropics. Addition of the cumulus friction term strengthened the winter Hadley circulation and smoothed the mean meridional wind field, with a slight increase in the eddy kinetic energy. The results showed that the intensity of the meridional circulation is regulated by the atmosphere's angular momentum budget, changes in the zonally-averaged Coriolis force correlate with the new cumulus friction term, and the intensification of Hadley circulation is a response of the mean meridional flow field to the downward cumulus field of relative angular momentum in the winter hemisphere.