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Convective parameterization is the long-lasting bottleneck of global climate modelling and one of the most difficult problems in atmospheric sciences. Uncertainty in convective parameterization is the leading cause of the widespread climate sensitivity in IPCC global warming projections. This paper reviews the observations and parameterizations of atmospheric convection with emphasis on the cloud structure, bulk effects, and closure assumption. The representative state-of-the-art convection schemes are presented, including the ECMWF convection scheme, the Grell scheme used in NCEP model and WRF model, the Zhang-MacFarlane scheme used in NCAR and DOE models, and parameterizations of shallow moist convection. The observed convection has self-suppression mechanisms caused by entrainment in convective updrafts, surface cold pool generated by unsaturated convective downdrafts, and warm and dry lower troposphere created by mesoscale downdrafts. The post-convection environment is often characterized by “diamond sounding” suggesting an over-stabilization rather than barely returning to neutral state. Then the pre-convection environment is characterized by slow moistening of lower troposphere triggered by surface moisture convergence and other mechanisms. The over-stabilization and slow moistening make the convection events episodic and decouple the middle/upper troposphere from the boundary layer, making the state-type quasi-equilibrium hypothesis invalid. Right now, unsaturated convective downdrafts and especially mesoscale downdrafts are missing in most convection schemes, while some schemes are using undiluted convective updrafts, all of which favour easily turned-on convection linked to double-ITCZ (inter-tropical convergence zone), overly weak MJO (Madden-Julian Oscillation) and precocious diurnal precipitation maximum. We propose a new strategy for convection scheme development using reanalysis-driven model experiments such as the assimilation runs in weather prediction centres and the decadal prediction runs in climate modelling centres, aided by satellite simulators evaluating key characteristics such as the lifecycle of convective cloud-top distribution and stratiform precipitation fraction. 

The surface wind structure and vertical turbulent transport processes in the eyewall of hurricane Isabel (2003) are investigated using six large-eddy simulations (LESs) with different horizontal grid spacing and three-dimensional (3D) sub-grid scale (SGS) turbulent mixing models and a convection permitting simulation that uses a coarser grid spacing and one-dimensional vertical turbulent mixing scheme. The mean radius-height distribution of storm tangential wind and radial flow, vertical velocity structure, and turbulent kinetic energy and momentum fluxes in the boundary layer generated by LESs are consistent with those derived from historical dropsonde composites, Doppler radar, and aircraft measurements. Unlike the convection permitting simulation that produces storm wind fields lacking small-scale disturbances, all LESs are able to produce sub-kilometer and kilometer scale eddy circulations in the eyewall. The inter-LES differences generally reduce with the decrease of model grid spacing. At 100-m horizontal grid spacing, the vertical momentum fluxes induced by the model-resolved eddies and the associated eddy exchange coefficients in the eyewall simulated by the LESs with different 3D SGS mixing schemes are fairly consistent. Although with uncertainties, the decomposition in terms of eddy scales suggests that sub-kilometer eddies are mainly responsible for the vertical turbulent transport within the boundary layer (~1 km depth following the conventional definition) whereas eddies greater than 1 km become the dominant contributors to the vertical momentum transport above the boundary layer in the eyewall. The strong dependence of vertical turbulent transport on eddy scales suggests that the vertical turbulent mixing parameterization in mesoscale simulations of tropical cyclones is ultimately a scale-sensitive problem. 

In a tropical cyclone (TC), turbulence not only exists in the planetary boundary layer (PBL) but also can be generated above the PBL by the cloud processes in the eyewall and rainbands. It is found that the Hurricane Analysis and Forecast System (HAFS), a new multi-scale operational model for TC prediction, fails to capture the intense turbulent mixing in eyewall and rainband clouds due to a poor estimation of static stability in clouds. The problem is fixed by including the effects of multi-phase water in the stability calculation. Simulations of 21 TCs and tropical storms in the North Atlantic basin of 2016–2019 hurricane seasons totaling 118 forecast cycles show that the stability correction substantially improves HAFS's skill in predicting storm track and intensity. Analyses of HAFS's simulations of Hurricane Michael (2018) show that the positive tendency of vortex's tangential wind resulting from the radially inward transport of absolute vorticity dominates the eddy correlation tendencies induced by the model-resolved asymmetric eddies and serves as a main mechanism for the rapid intensification of Michael. The sub-grid scale (SGS) turbulent transport above the PBL in the eyewall plays a pivotal role in initiating a positive feedback among the eyewall convection, mean secondary overturning circulation, vortex acceleration via the inward transport of absolute vorticity, surface evaporation, and radial convergence of moisture in the PBL. Without the SGS transport above the PBL, the model-resolved vertical transport alone may not be sufficient in initiating the positive feedback underlying the rapid intensification of TCs. 

This paper reviews the evolution of planetary boundary layer (PBL) parameterization schemes that have been used in the operational version of the Hurricane Weather Research and Forecasting (HWRF) model since 2011. Idealized simulations are then used to evaluate the effects of different PBL schemes on hurricane structure and intensity. The original Global Forecast System (GFS) PBL scheme in the 2011 version of HWRF produces the weakest storm, while a modified GFS scheme using a wind-speed dependent parameterization of vertical eddy diffusivity (Km) produces the strongest storm. The subsequent version of the hybrid eddy diffusivity and mass flux scheme (EDMF) used in HWRF also produces a strong storm, similar to the version using the wind-speed dependent Km. Both the intensity change rate and maximum intensity of the simulated storms vary with different PBL schemes, mainly due to differences in the parameterization of Km. The smaller the Km in the PBL scheme, the faster a storm tends to intensify. Differences in hurricane PBL height, convergence, inflow angle, warm-core structure, distribution of deep convection, and agradient force in these simulations are also examined. Compared to dropsonde and Doppler radar composites, improvements in the kinematic structure are found in simulations using the wind-speed dependent Km and modified EDMF schemes relative to those with earlier versions of the PBL schemes in HWRF. However, the upper boundary layer in all simulations is much cooler and drier than that in dropsonde observations. This model deficiency needs to be considered and corrected in future model physics upgrades.