On Steady-State One-Dimensional Models of Cumulus Convection

A critical examination is undertaken of current steady-state one-dimensional cloud models which postulate lateral entrainment. It is found that such models cannot simultaneously predict values of liquid water content and cloud depth which are in agreement with observations. If sufficient entrainment is postulated to get agreement with observations of cloud water content, the model cloud does not grow as high as those observed in the given environment, while entrainment appropriate to the observed height yields liquid water contents that are too high. It is suggested that the success claimed for these models is based on a choice of arbitrary constants which may be valid only for a limited range of atmospheric conditions; in other conditions, predictions from the model may be seriously in error. In addition, since the physical basis of these models is invalid, we have no way of knowing what conditions are most important or how to avoid the necessity of selecting fresh constants by trial and error with each fresh use of the model.