This thesis discusses the transports of sensible heat and water vapour by ordinary convection in a field of non-precipitating cumulus clouds.
The stratification and time development of the convective boundary layer during dry and moist convection are investigated theoretically. A model is proposed which distinguishes for budget purposes 3 layers: the sub-cloud layer, and an upper and lower part of the cumulus layer. The model relates the cumulus convection to the surface boundary conditions, the ‘free’ atmosphere above the cumulus layer, and the large scale vertical motion.
The significant aspects of the thesis are as follows:
(1) Formulae for the dilution of clouds by their environment show the essential irreversibility of the vertical transports in non-precipitating cumulus convection, One significant consequence is that the convection destabilizes the layer it occupies.
(2) A new conservative variable, (θL), related to potential temperature and liquid water mixing ratio, greatly simplifies the understanding of cloud parcel thermodynamics and cloud heat transports. With this variable dry and wet convection become closely analogous.
(3) A mass transport model is used to clarify the mechanism of modification of the mean atmosphere by the convection.
(4) A model for the sub-cloud layer predicts from the surface fluxes and the large scale vertical motion the convective mass flux into the cumulus layer (a measure of the amount of active cloud).
(5) A lapse-rate model is developed by relating the mechanics and thermodynamics of a typical cloud to the mean stratification, so as to predict the lapse rate characteristic of the cumulus layer.
(6) The control of cloud-base variations and large-scale vertical motion on cumulus convection is made quantitative. For example rise of cloud-base and large-scale subsidence are found to have some closely similar quantitative effects: both tend to suppress clouds.
My PhD work on “Cumulus Convection”, introduced or extended many important concepts: a mixed layer model for dry convection and the sub-cloud layer; the liquid water potential temperature; and mass, enthalpy and water transport models for shallow convective BLs. This work was largely conceptual, but it would be fair to say that it was inspired by my spending the summer of 1969 as a graduate student in Venezuela with Herbert Riehl and the VIMHEX-1969 experiment. I launched and tracked pilot balloons with a theodolite, and filmed cloud development with a 16mm time-lapse camera.
Every morning Riehl held a forecast discussion, but every day I saw that afternoon convective storms over land in the tropics were not predictable - until they developed or appeared on the radar! I was inspired on my return to create conceptual models for the developing cumulus boundary layer.
This work was published in part as Betts, A. K., 1973: Non-Precipitating Convection and Its Parameterization. Quart. J. Roy. Meteor. Soc., 99, 178-196.
Abstract: This paper discusses the thermodynamic transports of heat, liquid water and (briefly) water vapour by non-precipitating cumulus convection. It is shown that because of the irreversible mixing between cloud and environment, there is a downward transport of enthalpy in the cumulus layer. A lapse-rate adjustment model relates stratification to the life-cycle of a model cloud parcel. A sub-cloud layer model specifies the lower boundary of the lapse-rate model, and the convective transports through cloud-base. Budget equations together with the lapse-rate model, and its time dependent boundary conditions, predict the time development of the cumulus layer, and show the dependence on large-scale mean vertical motion, cloud-base variations, and the surface sensible heat flux.
Betts, A. K. (1970): Cumulus Convection. Ph.D. Thesis, University of London, 151 pp. Available from https://alanbetts.com/research/paper/cumulus-convection/#abstract