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  1. 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. 
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  2. Abstract This study examines the free-tropospheric quasi-equilibrium at different global climate model (GCM) resolutions using the simulation of tropical convection by a cloud-resolving model during the Tropical Western Pacific International Cloud Experiment. The simulated dynamic and thermodynamic fields within the model domain are averaged over subdomains of different sizes equivalent to different GCM resolutions. These coarse-grained fields are then used to compute CAPE and its change with time, and their relationships with simulated convection. Results show that CAPE change with time is controlled predominantly by variations of thermodynamic properties in the planetary boundary layer for all subdomain sizes ranging from 64 to 4 km. Lag correlation analysis shows that CAPE generation by the free-tropospheric dynamical advection (dCAPE ls ) leads convective precipitation but is in phase with convective mass flux at 600 mb and 500 mb vertical velocity for all subdomain sizes. However, the correlation coefficients and regression slopes decrease as the subdomain size decreases for subdomain sizes smaller than 16 km. This is probably due to increased randomness of convection and more scale-dependence of the relationships when the subdomain size reaches the grey zone. By examining the sensitivity of the relationships of convection with dCAPE ls to temporal scales in different subdomain size, it shows that the quasi-equilibrium between dCAPE ls and convection holds well for timescales of 30 min or longer at all subdomain sizes. These results suggest that the free tropospheric quasi-equilibrium assumption may still be useable even for GCM resolutions in the grey zone. 
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  3. Trends in surface air temperature (SAT) are a common metric for global warming. Using observations and observationally driven models, we show that a more comprehensive metric for global warming and weather extremes is the trend in surface equivalent potential temperature (Thetae_sfc) since it also accounts for the increase in atmospheric humidity and latent energy. From 1980 to 2019, while SAT increased by 0.79 ° C , Thetae_sfc increased by 1.48 ° C globally and as much as 4 ° C in the tropics. The increase in water vapor is responsible for the factor of 2 difference between SAT and Thetae_sfc trends. Thetae_sfc increased more uniformly (than SAT) between the midlatitudes of the southern hemisphere and the northern hemisphere, revealing the global nature of the heating added by greenhouse gases (GHGs). Trends in heat extremes and extreme precipitation are correlated strongly with the global/tropical trends in Thetae_sfc. The tropical amplification of Thetae_sfc is as large as the arctic amplification of SAT, accounting for the observed global positive trends in deep convection and a 20% increase in heat extremes. With unchecked GHG emissions, while SAT warming can reach 4.8 ° C by 2100, the global mean Thetae_sfc can increase by as much as 12 ° C , with corresponding increases of 12 ° C (median) to 24 ° C (5% of grid points) in land surface temperature extremes, a 14- to 30-fold increase in frequency of heat extremes, a 40% increase in the energy available for tropical deep convection, and an up to 60% increase in extreme precipitation. 
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