How are the fractionation for the accumulation and coarse mode sea spray emissions calculated?

I’m specifically referring to lines 828-835 in SSEMIS, where the baseline number fluxes in each mode are integrated over the entire Dp_min to Dp_max distribution. I’m wondering how these finite integral equations were derived.

The comment in the code says to refer to equations 19 and 20 of “Uma Shankar`s “Integration of Sea-Salt Fluxes” memo”. However, I have not been able to find any documentation online. The equation for calculating the finite integral for each mode looks similar to a cumulative distribution function (see eq 7.46 from Seinfeld and Pandis 1998 for example), but there are differences and I’m wondering where those differences come from.

Any insights would be appreciated! Thanks!

Thank you for the suggestion. I wasn’t able to find specifically what I was looking for in the dissertation, though I may have missed something.

According to @cgnolte, it would be better if the code referenced the following published paper as the method was changed in CMAQ v5.1, as documented in Gantt et al. (2015):

https://www.airqualitymodeling.org/index.php/CMAQv5.1_Sea_Spray_Aerosol_Update

https://gmd.copernicus.org/articles/8/3733/2015/

In making that update, Brett updated the code and translated it to R. See the Theta_code.zip available to download from the google drive. This code calculates the values in the DATA statements for DGNJ, DGNK, SIGJ, SIGK, FNJ, FNK, and VFLUX at the top of SSEMIS.F, which are still used in the current version of CMAQ.

Please let us know if this resolves your issue.

Yes, the Gantt et al. (2015) paper was super useful in explaining several aspects of the code, though not the volume/mass emission fractionation. And thank you for the R code! I’d also been wondering how the standard deviation look-up tables were calculated.

Perhaps I should rephrase my question. In the SSEMIS module, there are look-up tables for the accum and coarse mode number fluxes, and a look-up table for the integrated total volume flux (the FNJ, FNK, and VFLUX @lizadams mentioned). The modal number fluxes are used to calculate the fraction of SSA emission in each mode (lines 828-835 in SSEMIS), and then these fractions are used to separate the integrated total volume flux into modal emissions. Why was this approach used, as opposed to integrating volume flux within each mode directly?

The following response is from @ushankar.

CMAQ’s modal aerosol model predicts both number and volume moments, so we derived the volume emission flux based on the best number emission flux parameterizations we found using the flux formulations of Zhang et al. (2005). Max Zhang derived the mass emission sea salt flux for the sectional aerosol model, which predicts the mass moment of the aerosol, and not number. The source function parameterization of Gong (2003) used in CMAQ extends the Monahan et al. (1986) parameterization to sea salt particle radius at 80% RH (r80) below 1.0 mm (0.03 mm dry radius). The derivations of the number emission fluxes over the applicable size range for each of the two modes based on those source functions are described in this link (June 2005) document. The development of the sea salt emissions module in AERO4 is described in this link to a CMAS Conference poster, along with the relevant references.

Thank you! The June 2005 report is exactly what I was looking for!