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Leo J. Donner

Abstract

A procedure for initializing parameterizations for cumulus convection in numerical weather prediction models is described. The initialization adjust the temperature and humidity fields such that a simplified version of the Kuo cumulus parameterization will yield diagnosed convective precipitation and vertical heating profiles, if a specified velocity field can support them. In an unfavorable velocity field, the initialization will yield the closest approach to diagnosed convective precipitation possible. The initialization minimizes changes in the humidity and temperature fields while satisfying constraints imposed by the cumulus parameterization.

Slight adjustments in the temperature field and relatively larger adjustments in the humidity field can modify the large scale from a state which does not support cumulus convection to a state whose convective heating, as parameterized by the simplified version of the Kuo scheme, agrees to the extent possible for an imposed velocity field. Use of more complicated versions of the Kuo cumulus parameterization with the initialized temperature and humidity profiles yields heating rates agreeing reasonably with diagnosed beating. If used in conjunction with an initialization for the velocity field, cumulus initialization may ameliorate problems associated with spinup of physical processes in numerical weather prediction.

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Leo J. Donner

Abstract

The dependence of the thermal balance of a general circulation model on the parameterization of cumulus convection is investigated. Incorporation of a Kuo-type cumulus parameterization into the NCAR community climate model decreases temperatures in most of the lower and middle tropospheres while increasing temperatures slightly at the tropopause, decreases both relative and specific humidities in large parts of the lower troposphere, and also reduces cloud cover and tropical precipitation. Although the Kuo parameterization represents a vertically integrated heat source, its presence in the general circulation model causes an even larger reduction in heating by the moist adiabatic adjustment, so the total heating associated with cumulus convection is less if the Kuo parameterization is used. The reduction in atmospheric temperatures relative to those at the surface with the Kuo parameterization results in enhanced heating of the lower atmosphere by surface exchange processes. These changes in convective and surface heating dominate changes in the diabatic part of the thermal balance but are moderated by changes in radiative heating associated with reduced cloudiness. Diabatic heating changes are balanced primarily by reduced mean dynamic transport of heat associated with a weakened Hadley circulation.

The dependence of the circulation sensitivity to cumulus parameterization on cloud-convection feedback and the penetrative extent of convection is found to be significant. The penetrative depth of convection is especially important; since penetration by convection depends crucially on the poorly understood entrainment process, some uncertainty plagues estimates of the details of the impact of cumulus convection on the simulated general circulation. Changes in cloudiness associated with the Kuo parameterization alter radiative forcing so as to reduce the sensitivity of the community climate model to the cumulus parameterization.

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Leo J. Donner

Abstract

A formulation for parameterizing cumulus convection, which treats cumulus vertical momentum dynamics and mass fluxes consistently, is presented. This approach predicts the penetrative extent of cumulus updrafts on the basis of their vertical momentum and provides a basis for treating cumulus microphysics using formulations that depend on vertical velocity. Treatments for cumulus microphysics are essential if the water budgets of convective systems are to be evaluated for treating mesoscale stratiform processes associated with convection, which are important for radiative interactions influencing climate.

The water budget (both condensed and vapor) of the cumulus updrafts is used to drive a semi-empirical parameterization for the large-scale effects of the mesoscale circulations associated with deep convection. The parameterization for mesoscale effects invokes mesoscale ascent to redistribute vertically water detrained at the tops of the cumulus updrafts. The local cooling associated with this mesoscale ascent is probably larger than radiative heating of the mesoscale anvil clouds, and the mesoscale ascent may be in part a response to such radiative heating.

The parameterization was applied to two tropical thermodynamic profiles whose diagnosed forcing by convective systems differed significantly. A spectrum of cumulus updrafts was allowed. The deepest of the updrafts penetrated the upper troposphere, while the shallower updrafts penetrated into the region of the mesoscale anvil. The relative numbers of cumulus updrafts of characteristic vertical velocities comprising the parameterized ensemble corresponded well with available observations. However, the large-scale heating produced by the ensemble without mesoscale circulations was concentrated at lower heights than observed or was characterized by excessive peak magnitudes. Also, an unobserved large-scale source of water vapor was produced in the middle troposphere. When the parameterization for mesoscale effects was added, the large-scale thermal and moisture forcing predicted by the parameterization agreed well with observations for both cases.

The significance of mesoscale processes, some of which may depend in part on radiative forcing, suggests that future cumulus parameterization development will need to treat some radiative processes. Further, the long time scale of the mesoscale processes relative to that of the cumulus cells indicates a possible requirement for carrying some characteristics of the convective system in time as cumulus parameterizations are incorporated in large-scale models whose resolutions remain too large to capture explicitly the mesoscale processes.

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Leo J. Donner and Philip J. Rasch

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 initialization show that cumulus initialization can recover initial horizontal and vertical distributions of latent heat release (produced synthetically by spinning up the same global model through an independent integration using an earlier analysis to provide initial conditions) quite successfully. This recovery depends on the simultaneous initialization of the divergence, temperature, and humidity fields. The magnitudes of the adjustments in the temperature and humidity fields produced by cumulus initialization are smaller than the changes in those fields produced by the global model itself as it is integrated forward from an analysis without cumulus initialization through spinup. The cumulus initialization procedure can be modified to allow for uncertainties in the diagnosis of initial heating rates. Despite the successfully initial recovery of cumulus heating, further adjustment occurs as the global model is integrated forward from a cumulus-initialized analysis; this adjustment is characterized by an overshoot in the intensity of both latent heat release and divergence. A severe imbalance between globally averaged precipitation and evaporation that occurred without cumulus initialization is considerably ameliorated in integrations with cumulus initialization.

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Andrew J. Heymsfield and Leo J. Donner

Abstract

The optical properties of ice clouds are a primary issue for climate and climate change. Evaluating these optical properties in three-dimensional models for studying climate will require a method to calculate the ice water content of such clouds. A procedure is developed to parameterize ice water content as a function of large-scale meteorological characteristics for use in circulation models in which the ice water content is not calculated by means of a three-dimensional prognostic equation for condensed water. The technique identifies large-scale flows in which ice clouds exist and calculates their ice water content by reconstructing the trajectory associated with cloud formation. As the cloud forms, its ice content changes both by deposition of ice from water vapor and by ice removal by sedimentation. The sedimentation process is found to modify significantly the ice water content expected from deposition alone. Ice water contents predicted by the parameterization are compared with aircraft observations collected in the middle latitudes and the tropics, and show reasonable agreement over four orders-of-magnitude of ice water content. A parameterization for the sublimation of ice crystals settling into ice-subsaturated environments is also presented.

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Eric M. Wilcox and Leo J. Donner

Abstract

The frequency distributions of surface rain rate are evaluated in the Tropical Rainfall Measuring Mission (TRMM) and Special Sensor Microwave/Imager (SSM/I) satellite observations and the NOAA/GFDL global atmosphere model version 2 (AM2). Instantaneous satellite rain-rate observations averaged over the 2.5° latitude × 2° longitude model grid are shown to be representative of the half-hour rain rate from single time steps simulated by the model. Rain-rate events exceeding 10 mm h−1 are observed by satellites in most regions, with 1 mm h−1 events occurring more than two orders of magnitude more frequently than 10 mm h−1 events. A model simulation using the relaxed Arakawa–Schubert (RAS) formulation of cumulus convection exhibits a strong bias toward many more light rain events compared to the observations and far too few heavy rain events. A simulation using an alternative convection scheme, which includes an explicit representation of mesoscale circulations and an alternative formulation of the closure, exhibits, among other differences, an order of magnitude more tropical rain events above the 5 mm h−1 rate compared to the RAS simulation. This simulation demonstrates that global atmospheric models can be made to produce heavy rain events, in some cases even exceeding the observed frequency of such events. Additional simulations reveal that the frequency distribution of the surface rain rate in the GCM is shaped by a variety of components within the convection parameterization, including the closure, convective triggers, the spectrum of convective and mesoscale clouds, and other parameters whose physical basis is currently only understood to a limited extent. Furthermore, these components interact nonlinearly such that the sensitivity of the rain-rate distribution to the formulation of one component may depend on the formulation of the others. Two simulations using different convection parameterizations are performed using perturbed sea surface temperatures as a surrogate for greenhouse gas–forced climate warming. Changes in the frequency of rain events greater than 2 mm h−1 associated with changing the convection scheme in the model are greater than the changes in the frequency of heavy rain events associated with a 2-K warming using either model. Thus, uncertainty persists with respect to simulating intensity distributions for precipitation and projecting their future changes. Improving the representation of the frequency distribution of rain rates will rely on refinements in the formulation of cumulus closure and the other components of convection schemes, and greater certainty in predictions of future changes in both total rainfall and in rain-rate distributions will require additional refinements in those parameterizations that determine the cloud and water vapor feedbacks.

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Leo J. Donner and Hsiao-Lan Kuo

Abstract

The stationary wave components of the planetary-scale circulation are maintained by topographic forcing and by latent and sensible heat transfers and radiation. These waves have a potential vorticity balance mainly due to vertically differential thermal advection, advection of planetary vorticity, heating, and topographic convergence or divergence. To elucidate the role of solar and longwave transfers in maintaining stationary planetary waves, the potential vorticity equation appropriate to these disturbances in the middle latitudes of the Northern Hemisphere during winter is solved with realistic radiation physics included in the heating term.

A series of experiments with the model isolates the roles of the various optically active constituents in maintaining the stationary planetary waves. Clouds and the net radiative heating tend to amplify stationary planetary wavenumber 1 by increasing the forcing asymmetry, but destructive interference between radiative beating and other diabatic processes and topography causes the net radiative heating to dampen stationary planetary wavenumber 2. In the presence of clouds, water vapor and, to a lesser extent, carbon dioxide, damp the waves by reducing cloud-generated forcing asymmetries, particularly at zonal wavenumber 1.Ozone asymmetries have a minor role because they produce a heating asymmetry in the stratosphere where the zonally-averaged state limits the forcing. Radiative forcing comprises a significant source of diabatic forcing at wavenumber 1, while surface exchange processes are very important at wavenumber 2. The topographic component of the waves was smaller than the thermal component in these calculations.

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Leo J. Donner, Charles J. Seman, and Richard S. Hemler

Abstract

Deep convection and its associated mesoscale circulations are modeled using a three-dimensional elastic model with bulk microphysics and interactive radiation for a composite easterly wave from the Global Atmospheric Research Program Atlantic Tropical Experiment. The energy and moisture budgets, large-scale heat sources and moisture sinks, microphysics, and radiation are examined.

The modeled cloud system undergoes a life cycle dominated by deep convection in its early stages, followed by an upper-tropospheric mesoscale circulation. The large-scale heat sources and moisture sinks associated with the convective system agree broadly with diagnoses from field observations. The modeled upper-tropospheric moisture exceeds observed values. Strong radiative cooling at the top of the mesoscale circulation can produce overturning there. Qualitative features of observed changes in large-scale convective available potential energy and convective inhibition are found in the model integrations, although quantitative magnitudes can differ, especially for convective inhibition.

Radiation exerts a strong influence on the microphysical properties of the cloud system. The three-dimensional integrations exhibit considerably less sporadic temporal behavior than corresponding two-dimensional integrations. While the third dimension is less important over timescales longer than the duration of a phase of an easterly wave in the lower and middle troposphere, it enables stronger interactions between radiation and dynamics in the upper-tropospheric mesoscale circulation over a substantial fraction of the life cycle of the convective system.

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Vaughan T. J. Phillips, Leo J. Donner, and Stephen T. Garner

Abstract

A novel type of limited double-moment scheme for bulk microphysics is presented here for cloud-system-resolving models (CSRMs). It predicts the average size of cloud droplets and crystals, which is important for representing the radiative impact of clouds on the climate system. In this new scheme, there are interactive components for ice nuclei (IN) and cloud condensation nuclei (CCN). For cloud ice, the processes of primary ice nucleation, Hallett–Mossop (HM) multiplication of ice particles (secondary ice production), and homogeneous freezing of aerosols and droplets provide the source of ice number. The preferential evaporation of smaller droplets during homogeneous freezing of cloud liquid is represented for the first time. Primary and secondary (i.e., in cloud) droplet nucleation are also represented, by predicting the supersaturation as a function of the vertical velocity and local properties of cloud liquid. A linearized scheme predicts the supersaturation, explicitly predicting rates of condensation and vapor deposition onto liquid (cloud liquid, rain) and ice (cloud ice, snow, graupel) species. The predicted supersaturation becomes the input for most nucleation processes, including homogeneous aerosol freezing and secondary droplet activation.

Comparison of the scheme with available aircraft and satellite data is performed for two cases of deep convection over the tropical western Pacific Ocean. Sensitivity tests are performed with respect to a range of nucleation processes. The HM process of ice particle multiplication has an important impact on the domain-wide ice concentration in the lower half of the mixed-phase region, especially when a lack of upper-level cirrus suppresses homogeneous freezing. Homogeneous freezing of droplets and, especially, aerosols is found to be the key control on number and sizes of cloud particles in the simulated cloud ensemble. Preferential evaporation of smaller droplets during homogeneous freezing produces a major impact on ice concentrations aloft. Aerosols originating from the remote free troposphere become activated in deep convective updrafts and produce most of the supercooled cloud droplets that freeze homogeneously aloft. Homogeneous aerosol freezing is found to occur only in widespread regions of weak ascent while homogeneous droplet freezing is restricted to deep convective updrafts. This means that homogeneous aerosol freezing can produce many more crystals than homogeneous droplet freezing, if conditions in the upper troposphere are favorable.

These competing mechanisms of homogeneous freezing determine the overall response of the ice concentration to environmental CCN concentrations in the simulated cloud ensemble. The corresponding sensitivity with respect to environmental IN concentrations is much lower. Nevertheless, when extremely high concentrations of IN are applied, that are typical for plumes of desert dust, the supercooled cloud liquid is completely eliminated in the upper half of the mixed phase region. This shuts down the process of homogeneous droplet freezing.

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Leo J. Donner, Hsaio-Lan Kuo, and Eric J. Pitcher

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 between cumuli and the large-scale flow. Cumulus convection influences the general circulation both directly through heating and moistening and also indirectly by inducing changes in the mean meridonal circulation. Such cumulus convection does not appear to alter substantially the heat balance which maintains the time-mean, zonally-averaged temperature field, and the changes which do occur in the temperature balance are predominantly dynamic.

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