Ice Effective Radius

[andrewgettelman]

This issue was brought up by David Mitchell:

On Wed, Apr 7, 2021 at 4:04 PM David Mitchell David.Mitchell@dri.edu wrote:

Hi Andrew,

To address referee comments for our ACPD paper we had to replot zonal means for De (effective diameter) as a function of both pressure and temperature, which revealed that the WACCM6 output for De was not following the CALIPSO De constraints in the lower portion of cirrus clouds. So I have been going over the MG2 scheme code and have found a bug that might explain this, but in addition, I noticed something that could be a bug in the standard MG2 scheme. I think you are the point-person for MG2 these days, but I copied Hugh nonetheless. I would like to know your view on whether this is indeed a “bug” or whether I am simply not understanding something.

The code in question starts on p. 59 of the attached doc under “cloud ice effective radius”. There you can see that effi, the effective radius, is calculated in micron units as:

effi(i,k) = 1.5_r8/lami(i,k)*1.e6_r8

This equation is derived from the Slingo (1989, QJRMS) definition of effective radius Re based on an exponential gamma distribution, and is identical to Eq. 45 in Mitchell (2000, JAS). In Mitchell (2002, JAS), it is shown that this equation is equivalent to

Re = (3/4) [IWC/(rhowsA)]

where IWC = ice water content, rhows = density of solid water (i.e., bulk ice) = 0.917 g/cm3, and A = projected area of the ice particle size distribution. Ice density here corresponds to bulk ice since bulk ice is used for refractive index measurements and thus radiative properties. Some lines below the calculation for effi, one finds “! ice effective diameter for david mitchell's optics” and De is given as:

deffi(i,k)=effi(i,k)rhoi/rhows2._r8

(note that [DM1] denotes a comment statement shown at the bottom). This appears to be correcting effi for density differences between cloud ice (having density rhoi = 0.5 g/cm3) and bulk ice, where bulk ice density is implicit for De used in the ice optics scheme. The MG2 deffi calculation makes sense if effi was calculated from a Re definition using rhoi, but effi implicity assumes a density of 0.917 g/cm3 as shown in Mitchell (2002, JAS), as mentioned above. Thus, the ratio rhoi/rhows should be removed from the above calculation of deffi since effi already corresponds to the density of bulk ice.

If this is correct, then deffi is only 54.5% of its true value. It’s interesting that our CALIPSO De retrievals indicate that MG2 Re or effi is roughly a factor of 2 larger than it should be, and the calculation for deffi gives approximately the right range for deffi if the CALIPSO De range for cirrus is correct. So perhaps this bug (if it is a bug) is making the radiation come out reasonable.

There is another part of CAM6 (or WACCM6) called “micro_mg_cam.F90” that also calculates De, apparently a mean grid value, under “! Effective radius and diameter for cloud ice”, shown below:

dei_grid = rei_grid rhoi/rhows 2._r8

Here it is not clear to me where rei_grid comes from, but if it is calculated the same way that effi is calculated above, there may be a bug here as well. Do you know where rei_grid comes from, and do you know of any other components of CAM6 where De and/or Re are calculated?

I would much appreciate your views on this, and whether we should make the corrections suggested above. If we secure DOE/ASR funding, we will definitely redo our simulations and will need to know how to proceed on this.

Thanks for your consideration,

David

[andrewgettelman]

On Fri, Apr 9, 2021 at 11:29 AM Hugh Morrison morrison@ucar.edu wrote:

Hi David,

Thought I'd quick chime in though I'm curious to get Andrew's thoughts (I don't think I coded the "deffi", though don't remember who did..).

That said, I can say that rhoi (500 kg m-3) actually is used to calculate effi. This is because it goes into the calculation of lami, i.e.

lami = (pirhoiN/Q)^(1/3)

It's hard to follow this because in code it's done through pointers and utility functions. So I wouldn't say that effi implicitly assumes a density of solid ice 917 kg m-3. This seems why the factor rhoi/rhows was applied to deffi. Since you say "The MG2 deffi calculation makes sense if effi was calculated from a Re definition using rhoi..." it seems it should then be ok (not a bug).

More generally, I think there are big uncertainties (and probably bias) because the calculation for lami and effi does implicitly assume spherical ice particles, which of course is likely unrealistic in general (though maybe not quite as terrible for the smallest-sized particles). This could explain the fact that "CALIPSO De retrievals indicate that MG2 Re or effi is roughly a factor of 2 larger than it should be", as you say. So overall there is likely some cancellation of errors resulting in reasonable CRF in CAM.

I can't speak to rei_grid (did not code that), so Andrew would have to answer that question..

Best,

Hugh

[andrewgettelman]

Greetings,

Thanks for the reply Hugh.

rei_grid is calculated in micro_mg_cam.F90 (the interface) using the same method as effi (same utility functions), but grid averaged quantities then sorted by cloud fraction.

So I think that follows from what Hugh said: same calculation.

rei_grid is not used again, it's just diagnostic output.

Hope that helps.

Regards,

Andrew

[andrewgettelman]

Dear Hugh and Andrew,

Many thanks for your responses. And thank you Hugh for pointing that out; that lami depends on rhoi via the utilities call. Until I discovered a bug in the code that John and I wrote wrt effective diameter (De), I had not given this section of code (near the end where deffi is calculated from effi) much thought. But now I've put it "under the microscope" so to speak and have a renewed understanding of it which is described in the 2-page Word document attached. I know you are both busy, but I feel it may be worth your time to read it since it could affect CAM6 performance. It is based on the JAS paper I wrote on De, which is also attached. I think Hugh and I agree that a density correction is needed, but the expression of the density correction I came up with differs with the correction now used in the MG2 code. Please share your views on this.

Thanks for your consideration,

David de_eval_mitchell.pdf

[andrewgettelman]

A brief look indicates this proposes a slightly different correction factor for effective radius (0.817 v. 0.545 in the current code). The logic is fine, and we can consider changing this. There is ambiguity in making this change, since we have to go from a spherical assumption in microphysics to a shape recipe in optics for ice which is assumed anyway.

[andrewgettelman]

From David Mitchell:

Thanks for opening this issue on github; seems like a great way to solicit input/feedback. I am still of the view that changing the deffi correction from 0.545 to 0.817 is better.

In addition, most of the sensitivity of radiation to ice particle shape disappears by expressing ice particle size in terms of effective diameter De. Qiang Fu and possibly Greg McFarquhar have written about this, and I have verified this many times. For SW radiation (when using De), the sensitivity to shape shows up through the phase function or asymmetry parameter g in 2-stream models. LW radiation depends on ice particle shape through photon tunneling (also referred to as wave resonance) when the PSD is sufficiently narrow. Tunneling generally accounts for < 20% of the absorption in ice clouds.

[andrewgettelman]

Closing this issue. I think we decided we are okay for now on the ice effective radius