# Idealized model for equilibrium boundary layer over land.

An idealized equilibrium mixed layer (ML) model is used to explore the coupling between the surface, the ML, and the atmosphere above. It shows that ML depth increases as vegetative resistance to evaporation increases. The surface radiative forcing also increases ML depth; the ML radiative and evaporative cooling processes reduce ML depth. The model largely uncouples mean ML structure from the mean ML fluxes. The upper boundary condition controls ML potential temperature and mixing ratio but does not affect the fluxes; it is the surface radiative forcing and the radiative and evaporative cooling terms within the ML (together with the vegetative resistance Rυ) that control the surface fluxes and evaporative fraction. Furthermore, for a given Rυ, the radiative and evaporative cooling terms in the ML control the surface sensible heat flux, and the surface radiative forcing then controls the surface latent heat flux. The solutions show that, except for extreme high values of vegetative resistance and very dry air above the ML, this idealized equilibrium ML is capped by shallow cumulus clouds, as over the ocean. At the same time as Rυ increases, the ML structure and depth shift from the oceanic limit toward a warmer, drier boundary layer. It is shown that surface evaporation controls equilibrium near-surface relative humidity and not vice versa. The equilibrium solutions also give insight into how the gradient of mean mixing ratio across the Mississippi River basin is linked to changes in surface pressure as well as vegetative resistance to evaporation. The equilibrium model is oversimplified, and the nonlinearities introduced by the diurnal cycle have not been addressed, but nonetheless the solutions are a plausible zero-order fit to daily mean model data for the Missouri and Arkansas–Red River basins and to summer composites from the First International Land-Surface Climatology Project Field Experiment.

**Tim Cronin (MIT) has posted a tested Matlab code for this model** online at: http://mit.edu/~twcronin/www/code/Betts2000_EBLmodel.m

*Thanks Tim: Jan 25, 2013*.

For more details, and further analysis, consult his paper

**Cronin, T. W. (2013)**, A sensitivity theory for the equilibrium boundary layer over land. JAMES, 5, 1–21, doi:10.1002/jame.20048, 2013

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## Full Citation

**Betts, A. K., 2000**: Idealized model for equilibrium boundary layer over land. J. Hydrometeorol., 1, 507-523.

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