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WRF v.3.81+ diffuse radiation question-- source code

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This question does not refer specifically to WRF-Solar but regular WRF, but since it's related to radiation I might find a good audience here.

I'm trying to understand the equation that WRF uses to compute the diffuse radiation component of shortwave. Specifically his line in module_ra_sw.

The raw fortran code is:
diffuse_frac = min(1.,1/(max(0.1,2.1-2.8*log(log(SDOWN(kts)/max(SDOWN(kte+1),1.e-3))))))

The code comment says "! Parameterize diffuse fraction of global solar radiation as a function of the ratio between TOA radiation and surface global radiation".

Two questions:
1) Does anyone know where this parameterization comes from? I haven't been able to find a source for this.

2) Can anyone explain the max(SDOWN(kts) term? Is this the "surface global radiation"? I don't fully understand the timesteps either (kte/kts). I think kte is the current model timestep. Maybe kts is the starting timestep(?)

The reason that I'm asking this is that I want to further downscale WRF radiation outputs (SWDOMW) to a finer resolution grid to do offline-land modelling. So I want to re-compute terrain normal shortwave radiation (SWNORM) given the fine resolution topography, and I'd like to use the same method that WRF uses (meaning I need to compute the diffuse frac).

Thanks and I hope that made sense,
I believe this is the reference you are looking for:
Ruiz-Arias, J. A., H. Alsamanra, J. Tovar-Pescador, and D. Pozo-Vázquez, 2010: Proposal of a regressive model for the hourly diffuse solar radiation under all sky conditions. Energy Convers. Manage., 51, 881–893, doi:10.1016/j.enconman.2009.11.024.

Regarding kts and kte, the first one points to the first model vertical level, 1, and the second one to the top vertical level.