add products for cloud radiative effect

[claresinger]

It would be great to add a little library of available products (or a few different options) for calculating/estimating the radiative properties of the clouds: optical depth, albedo, emissivity, and CRE.

Two different approaches we could start with:

1. Lowe et al 2019

   ∆SWCRE = - eps_s * eps_c * (F0/4) * ∆alpha
   F0 = 1370 * si.W / si.m**2
   alpha = ((1-g) * tau) / (2 + (1-g) * tau)
   g = 0.85
   tau = (3 * LWP) / (2 * rho_w * reff)
   LWP = integral(rho_air(z) * LWC(z), dz)

   where eps_s and eps_c are the fractional coverage of Earth by the aerosol type and average cloud cover for the given aerosol type. Here ∆SWCRE comes from Latham et al 2008 alpha comes from Bohren 1987 g comes from Kravitz et al 2014 and tau comes from Stephens 1978 .

They also give an alternative formulation for ∆alpha = 0.075 * ln(CDNC_1 / CDNC_0) from Schwartz and Slingo 1996.

2. Hoffmann and Feingold 2021

   rCRE = f_c * A_c
   A_c = tau / (gamma + tau)
   gamma = 13.3
   tau = integral(integral(Q_e(r, lambda) * pi * r**2 * n(r,z), dr), dz)
   lambda = 500 * si.nm

   where gamma comes from Glenn et al. 2020, Q_e(r, lambda) comes from Mitchell 2000, and n(r,z) is the activated cloud droplet size distribution as justified by Connolly et al. 2014.

EDIT: Actually after digging through the references, the expressions for albedo(tau) are the same. It seems to be re-derived from the two-stream approximation in many different papers. But Bohren 1987 is a clear reference for it. Hu and Stamnes 1993 provide a detailed calculation and parameterization which justifies the use of g=0.85 for cloud droplets.

[slayoo]

:rocket: albedo (Bohren 1987), cloud depth (Stephens_1978) and related LWP (for parcel env only) added in #1256 kudos @claresinger!

[github-actions[bot]]

Stale issue message

[slayoo]

@claresinger let's note down here what would be the next steps to make the issue understandable. Are emissivity and CRE the next steps?

[claresinger]

There is one formulation currently for shortwave CRE (#1256 ).

So next steps include:

1. Implementing the SWCRE formula used in Hoffmann and Feingold 2021 that involves direct integration over the activated droplet size distribution (see above).
2. Implementing one or more formulae for cloud emissivity and longwave CRE.