Description

This PR adds two tuning parameters, one to tune the surface layer parameterization during stable, and one to tune it during unstable conditions. The default values correspond to the original formulation. These two parameters have an effect only over water surfaces when the land/sea/ice mask takes a value of 0 and when tune_ocean_surface_layer=True. Otherwise, the standard parameterization is used and the tuning parameters have no effect.

For consistency, these same modified profiles are also used in the PBL schemes satmedmfvdiff, satmedmfvdiffq, and moninedmf.

The design of these tuning coefficient is as follows:

• Stable regime: The original formulation is a linear function of stability. The slope of this empirical fit corresponds to the inverse of the critical Richardson number and is per default set to 5 for both momentum and scalars. Based on measurement campaigns this slope - named alpha_stable in the code - may take on a value in the range of about [4-10] (see Hogstrom (1988) and Long (1986)). A larger value implies a smaller critical Richardson number, thus less turbulent drag. The tuning parameter sets the slope for both momentum and scalars to maintain a Prandtl number of one.
• Unstable regime: The original formulation of the dimensionless gradient of momentum follows a (1-alpha*Zeta)**-0.25 law, whereby alpha is 16 following Dyer (1974) and Hicks (1976). The formulation for the gradient for scalars is the square root of it. Note that a numerical approximation is implemented (see Eqs. 2.37 and 2.64 in Long (1990)) that is baed on alpha=16. If tune_ocean_surface_layer=True, the gradient for momentum is computed on the unapproximated form (see Eq. 2.19 in Long (1990) (with fixed signs)) which differs slightly from the approximation even for alpha=16 of instabilities are very large. Per design, the Prandtl number, ratio of gradient of heat to momentum, is one for neutral conditions and drops down to around 0.4 for largely unstable conditions. Various measurement campaigns came up with different values for alpha (see Hogstrom, 1988) and the range roughly spans [10, 30]. Note that the Prandtl number is largely determined by the different exponents used in the momentum versus heat gradients, rather than by the value of alpha used in each. On top of this, other empirical formulations use separate values for alpha for momentum and heat. For this reason, the tuning variable added here only affects the alpha used in the dimensionless gradient of momentum.

References:
-Dyer, 1974: A review of flux-profile relations. Bound. Layer Meteor., 7, 363-372.
-Hicks, 1976: Wind profile relationships from the Wangara experiment. QJRMS, 102, 535-551.
-Hogstrom, 1988: Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation. Boundary-Layer Meteorol., 42, 55-78.
-Long, 1986: An economical and compatible scheme for parameterizing the stable surface layer in the medium range forecast model. Office note 321, NOAA.
-Long, 1990: Derivation and suggested method of the application of simplified relations for the surface fluxes in the medium-range forecast model: Unstable case. Office note 356, NOAA.

How Has This Been Tested?
No.

Checklist:

Please check all whether they apply or not

• My code follows the style guidelines of this project
• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• My changes generate no new warnings
• Any dependent changes have been merged and published in downstream modules