Including organics

In my previous post I had an outline for predicting changes in aerosol scattering, b_ext, versus one hour time intervals.

b_scat = α_ASf(RH){[ASO₄] + [ANO₃]} + α_POM[POM] + others (to be determined)

The key was computing an aerosol hygroscopic growth factor which used the ISORROPIA model and the standard 24h composition measurements (which are taken every third day in situ).

f(RH) = {(calc inorg. mass, wet) + [POM]}/{(calc inorg. mass, dry) + [POM]}

After talking to the developers of the ISORROPIA model I'm tweaking this plan a little. You see originally I was going to ignore the water retention of particulate organic matter (POM) but I will instead heed some advice and include a separate growth factor for organics and inorganic material. First let's reset the above equation to include only inorganics:

f_inorg(RH) = (calc inorg. mass, wet)/(calc inorg. mass, dry)

Then I will use a theoretical calculation for the organic fraction. Starting with the an equation and accompanying theory from this paper,

1/a_w = 1 + kV_s/V_w

where k is the number of soluble moles of organics matter per unit volume dry particle (and k = 0.1), V_s and V_w are the volumes of organic solids and liquid organic-associated water, respectively, and a_w is the water activity of the solution. Assuming all aerosol particles are in equilibrium with humid air, then a_w ~ RH. k can vary from 0.01 to 0.5, however professor Athanasios Nenes recommended to us k = 0.1  for the most up-to-date studies of typical mixed aerosol organics. If k = 0 it means the species is completely insoluble. For a given density p of aerosol-bound organic solids, the organic hygroscopic ratio (water mass/dry mass) becomes 

f_org(RH) = 1+ k/p[RH/(1-RH)]

(density is unit-less, where p_water = 1)


For most values of RH the factor f(RH) is near unity, as expected, but grows rapidly for RH > 0.9. 

Notice the resemblance of f_org(RH) with the empirically-fitted IMPROVE equation:

f(RH) = −0.18614 + 0.99211(1/(1 − RH))  

Enough discussion surrounds hygroscopic growth factors that it's easy to forget their practical use: parametrizing and predicting the water content in aerosols. More water means a greater nephelometer b_ext signal but we don't want to be fooled into thinking there's more PM2.5 dry mass than there truly is. Hence we'll need to relate f(RH) back to actual scattering values.

One serious problem lies in deciding what constitutes a 'dry' aerosol (as a reference point for the denominator in f(RH)). Normally it would be a dry mass anywhere from a theoretical 0% RH value to something below 40%. As long as the particle solidifies (effloresces) it's usually the same mass. But the problem is deciding what to use in day-to-day real-world scattering.

One idea I had was to normalize for (real) relative values of b_ext, divided into 24 1h segments

b_relmeas = b_ext/[24*<b_ext,24h>] 

Then obtain a similar formula for the calculated b_ext,calc

b_relcalc = bcalc/[24*<b_calc,24h>]

where

b_ext,calc = 2.66*f_inorg(RH)*{[ASO₄] + [ANO₃]} + 4.19*f_org(RH)[POM] + C

<b_ext,calc> = 2.66*f_inorg(<RH>)*{[ASO₄] + [ANO₃]} + 4.19*f_org(<RH>)[POM] + C

where C is a constant based on other scattering and absorbing airborne species and the coefficients 2.66 and 4.19 -units of m²/g- are borrowed from Sciare et al's paper. Compare these to the IMPROVE values, which are 3 and 4 m²/g, respectively.

Now to introduce something new from last time: taking the difference in mass values. That is, measuring changes in mass with time subtracting the changes due to RH:

delta M(t) = <M>{b_ext,rel - b_relcalc}

If RH remains constant for the day and PM2.5 mass changes, then only the measured b value should change. But if RH changes and PM2.5 stays constant, both will change hopefully to the same degree and the difference will be zero. In reality both PM2.5 and RH will change, so that's why we need this formula. My hope now is to calibrate these delta M(t) measurements from hourly BAM filters.