A Dynamical System Approach to Mixed Layer Models with Interactive Surface Fluxes

A mixed layer approach is performed to study the response of convective boundary layers to changing surface conditions. Following the method outlined in van Driel and Jonker (JAS 68, 2011) we can analytically derive the internal time-scales of the dynamical boundary layer system (PBL depth, and mixed layer values of temperature and humidity), and hence determine and understand the response to transient conditions in terms of delay and amplitude. The analysis is conducted for different boundary conditions: 1) fixed (i.e. prescribed) surface fluxes for temperature and humidity, 2) interactive fluxes where the fluxes depend on the mixed layer values of temperature and humidity via a transfer velocity, 3) fluxes following from a land-surface energy balance (using the Penman-Monteith equations, see e.g. van Heerwarden et al 2009, QJRMS 135). It turns out that even in the third, rather complicated, situation, one can analytically derive the three internal time-scales of the dynamical system, which allows one to quantify the relation between the response of the boundary layer and the particular surface properties, solar irradiation and the free-tropospheric conditions. This information provides important insight into the response characteristics of mixed layers to changing conditions, such as governed by the diurnal cycle, but also faster variations due to solar blocking by clouds. The analytical predictions are tested by numerical integration of the mixed layer equations, as well as by a series of Large Eddy Simulations.