The cumulus-capped boundary layer. II: Interface fluxes

This paper considers the relationship between the mean temperature and humidity profiles and the fluxes of heat and moisture at cloud base and the base of the inversion in the cumulus-capped boundary layer. The relationships derived are based on an approximate form of the scalar-flux budget and the scaling properties of the turbulent kinetic energy (TKE) budget. The scalar-flux budget gives a relationship between the change in the virtual potential temperature across either the cloud base transition zone or the inversion and the flux at the base of the layer. The scaling properties of the TKE budget lead to a relationship between the heat and moisture fluxes and the mean subsaturation through the liquid-water flux. The 'jump relation' for the virtual potential temperature at cloud base shows the close connection between the cumulus mass flux in the cumulus-capped boundary layer and the entrainment velocity in the dry-convective boundary layer. Gravity waves are shown to be an important feature of the inversion.

The cumulus-capped boundary layer. I: Modelling transports in the cloud layer

Scalar-flux budgets have been obtained from large-eddy simulations (LESs) of the cumulus-capped boundary layer. Parametrizations of the terms in the budgets are discussed, and two parametrizations for the transport term in the cloud layer are proposed. It is shown that these lead to two models for scalar transports by shallow cumulus convection. One is equivalent to the subsidence detrainment form of convective tendencies obtained from mass-flux parametrizations of cumulus convection. The second is a flux-gradient relationship that is similar in form to the non-local parametrizations of turbulent transports in the dry-convective boundary layer. Using the fluxes of liquid-water potential temperature and total water content from the LES, it is shown that both models are reasonable diagnostic relations between fluxes and the vertical gradients of the mean fields. The LESs used in this study are for steady-state convection and it is possible to treat the fluxes of conserved thermodynamic variables as independent, and ignore the effects of condensation. It is argued that a parametrization of cumulus transports in a model of the cumulus-capped boundary layer should also include an explicit representation of condensation. A simple parametrization of the liquid-water flux in terms of conserved variables is also derived.

Comments on “An ensemble cumulus convection parameterization with explicit cloud treatment”

Wagner and Graf (2010) derive a population evolution equation for an ensemble of convective plumes, an analogue with the Lotka–Volterra equation, from the energy equations for convective plumes provided by Arakawa and Schubert (1974). Although their proposal is interesting, as the present note shows, there are some problems with their derivation.

A new modelling framework for statistical cumulus dynamics

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits.

Ice formation and development in aged, wintertime cumulus over the UK: observations and modelling

In situ high resolution aircraft measurements of cloud microphysical properties were made in coordination with ground based remote sensing observations of a line of small cumulus clouds, using Radar and Lidar, as part of the Aerosol Properties, PRocesses And InfluenceS on the Earth's climate (APPRAISE) project. A narrow but extensive line (~100 km long) of shallow convective clouds over the southern UK was studied. Cloud top temperatures were observed to be higher than −8 °C, but the clouds were seen to consist of supercooled droplets and varying concentrations of ice particles. No ice particles were observed to be falling into the cloud tops from above. Current parameterisations of ice nuclei (IN) numbers predict too few particles will be active as ice nuclei to account for ice particle concentrations at the observed, near cloud top, temperatures (−7.5 °C). The role of mineral dust particles, consistent with concentrations observed near the surface, acting as high temperature IN is considered important in this case. It was found that very high concentrations of ice particles (up to 100 L−1) could be produced by secondary ice particle production providing the observed small amount of primary ice (about 0.01 L−1) was present to initiate it. This emphasises the need to understand primary ice formation in slightly supercooled clouds. It is shown using simple calculations that the Hallett-Mossop process (HM) is the likely source of the secondary ice. Model simulations of the case study were performed with the Aerosol Cloud and Precipitation Interactions Model (ACPIM). These parcel model investigations confirmed the HM process to be a very important mechanism for producing the observed high ice concentrations. A key step in generating the high concentrations was the process of collision and coalescence of rain drops, which once formed fell rapidly through the cloud, collecting ice particles which caused them to freeze and form instant large riming particles. The broadening of the droplet size-distribution by collision-coalescence was, therefore, a vital step in this process as this was required to generate the large number of ice crystals observed in the time available. Simulations were also performed with the WRF (Weather, Research and Forecasting) model. The results showed that while HM does act to increase the mass and number concentration of ice particles in these model simulations it was not found to be critical for the formation of precipitation. However, the WRF simulations produced a cloud top that was too cold and this, combined with the assumption of continual replenishing of ice nuclei removed by ice crystal formation, resulted in too many ice crystals forming by primary nucleation compared to the observations and parcel modelling.

Does convective aggregation need to be represented in cumulus parameterizations?

Tropical deep convection exhibits a variety of levels of aggregation over a wide range of scales. Based on a multisatellite analysis, the present study shows at mesoscale that different levels of aggregation are statistically associated with differing large-scale atmospheric states, despite similar convective intensity and large-scale forcings. The more aggregated the convection, the dryer and less cloudy the atmosphere, the stronger the outgoing longwave radiation, and the lower the planetary albedo. This suggests that mesoscale convective aggregation has the potential to affect couplings between moisture and convection and between convection, radiation, and large-scale ascent. In so doing, aggregation may play a role in phenomena such as “hot spots” or the Madden-Julian Oscillation. These findings support the need for the representation of mesoscale organization in cumulus parameterizations; most parameterizations used in current climate models lack any such representation. The ability of a cloud system-resolving model to reproduce observed relationships suggests that such models may be useful to guide attempts at parameterizations of convective aggregation.

Statistical properties of cloud lifecycles in cloud-resolving models

A new technique is described for the analysis of cloud-resolving model simulations, which allows one to investigate the statistics of the lifecycles of cumulus clouds. Clouds are tracked from timestep-to-timestep within the model run. This allows for a very simple method of tracking, but one which is both comprehensive and robust. An approach for handling cloud splits and mergers is described which allows clouds with simple and complicated time histories to be compared within a single framework. This is found to be important for the analysis of an idealized simulation of radiative-convective equilibrium, in which the moist, buoyant, updrafts (i.e., the convective cores) were tracked. Around half of all such cores were subject to splits and mergers during their lifecycles. For cores without any such events, the average lifetime is 30min, but events can lengthen the typical lifetime considerably.

A review of the theoretical basis for bulk mass flux convective parameterization

Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function (the dilute CAPE), the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterization that use the non-entraining parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

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

A 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

Mesoscale simulations of organized convection: importance of convective equilibrium

The validity of convective parametrization breaks down at the resolution of mesoscale models, and the success of parametrized versus explicit treatments of convection is likely to depend on the large-scale environment. In this paper we examine the hypothesis that a key feature determining the sensitivity to the environment is whether the forcing of convection is sufficiently homogeneous and slowly varying that the convection can be considered to be in equilibrium. Two case studies of mesoscale convective systems over the UK, one where equilibrium conditions are expected and one where equilibrium is unlikely, are simulated using a mesoscale forecasting model. The time evolution of area-average convective available potential energy and the time evolution and magnitude of the timescale of convective adjustment are consistent with the hypothesis of equilibrium for case 1 and non-equilibrium for case 2. For each case, three experiments are performed with different partitionings between parametrized and explicit convection: fully parametrized convection, fully explicit convection and a simulation with significant amounts of both. In the equilibrium case, bulk properties of the convection such as area-integrated rain rates are insensitive to the treatment of convection. However, the detailed structure of the precipitation field changes; the simulation with parametrized convection behaves well and produces a smooth field that follows the forcing region, and the simulation with explicit convection has a small number of localized intense regions of precipitation that track with the mid-levelflow. For the non-equilibrium case, bulk properties of the convection such as area-integrated rain rates are sensitive to the treatment of convection. The simulation with explicit convection behaves similarly to the equilibrium case with a few localized precipitation regions. In contrast, the cumulus parametrization fails dramatically and develops intense propagating bows of precipitation that were not observed. The simulations with both parametrized and explicit convection follow the pattern seen in the other experiments, with a transition over the duration of the run from parametrized to explicit precipitation. The impact of convection on the large-scaleflow, as measured by upper-level wind and potential-vorticity perturbations, is very sensitive to the partitioning of convection for both cases. © Royal Meteorological Society, 2006. Contributions by P. A. Clark and M. E. B. Gray are Crown Copyright.

Variation in the ovarian reserve Is linked to alterations in intrafollicular estradiol production and ovarian biomarkers of follicular differentiation and oocyte quality in cattle

The mechanisms whereby the high variation in numbers of morphologically healthy oocytes and follicles in ovaries (ovarian reserve) may have an impact onovarian function, oocyte quality, and fertility are poorly understood. The objective was to determine whether previously validated biomarkers for follicular differentiation and function, as well as oocyte quality differed between cattle with low versus a high antral follicle count (AFC). Ovaries were removed (n = 5 per group) near the beginning of the nonovulatory follicular wave, before follicles could be identified via ultrasonography as being dominant, from heifers with high versus a low AFC. The F1, F2, and F3 follicles were dissected and diameters determined. Follicular fluid and thecal, granulosal, and cumulus cells and the oocyte were isolated and subjected to biomarker analyses. Although the size and numerous biomarkers of differentiation, such as mRNAs for the gonadotropin receptors, were similar, intrafollicular concentrations of estradiol and the abundance of mRNAs for CYP19A1 in granulosal cells and ESR1, ESR2, and CTSB in cumulus cells were greater, whereas mRNAs for AMH in granulosal cells and TBC1D1 in thecal cells were lower for animals with low versus a high AFC during follicle waves. Hence, variation in the ovarian reserve may have an impact on follicular function and oocyte quality via alterations in intrafollicular estradiol production and expression of key genes involved in follicle-stimulating hormone action (AMH) and estradiol (CYP19A1) production by granulosal cells, function and survival of thecal cells (TBC1D1), responsiveness of cumulus cells to estradiol (ESR1, ESR2), and cumulus cell determinants of oocyte quality (CTSB).