From my previous entry we know that total aerosol scattering is proportional with total aerosol mass at any given period in time. For our purposes t = 1 hour, which is not 'instant' but a relatively short time (the shortest normally reported in routine satellite, temperature, etc observations)
bscat(t) ~ PM2.5(t)
Because these two quantitive are proportional, the re-arrangement means the ratio PM2.5/bscat is a constant:
PM2.5(t)/bscat(t) = C
and the average, too, is constant
<PM2.5(t)/bscat(t)> = <C> = C
The 'average' is an integration over 24 hours; we are summing over twenty four one-hour intervals (if you want, let <bscat> = bscat(24h)). Also we can split the average like so
<PM2.5/bscat> = <PM2.5>/<bscat>
Compare ratios (1-hour and 24-hour) and we find they are of course equal
PM2.5(t)/bscat(t) = <PM2.5>/<bscat>
We now have the setup for a prediction of PM2.5 levels at one-hour time intervals
PM2.5(t) = bscat(t)*<PM2.5>/<bscat>
It's worth considering this formula in detail since each parameter comes from a different source of data.
The bscat(t) and <bscat(24h)> values could be obtained by a nephelometer coupled to a BAM (beta attenuation monitor), or just a BAM. The nephelometer gives us immediate feedback as to the current particle mass in the air, while the BAM gives us integrated one or 24-hour mass totals.
At first glance it seems as though our problem is finished: simply monitor particle mass changes over time from variable bscat(t). But here's the catch: the bscat(t) proportionality with mass holds true only under constant humidity and temperature.
At first glance it seems as though our problem is finished: simply monitor particle mass changes over time from variable bscat(t). But here's the catch: the bscat(t) proportionality with mass holds true only under constant humidity and temperature.
Changing the relative humidity (RH) with time will affect bscat(t) (either increase or decrease it) even if total PM2.5 mass remains constant. At any time during a 24h run bscat is changing because of humidity, temperature, and mass:
bscat = bscat(t, [water], T, m)
or as a function of RH
bscat= bscat(t, RH([water, T], T))
For simplicity we might compare bscat at dry (RH < 40%) and humid conditions. This is defined as the hygroscopic growth factor, f(RH):
f(RH) = bscat(RH > 60%)/bscat(RH < 40%)
This is an empirically-based function. Many studies have measured the scattering of 'dry' particles (often solid) versus 'humid' ones. We will return to this formula. Let's take a step back.
How might bscat depend on changes in humidity? From Hegg (1993):
How might bscat depend on changes in humidity? From Hegg (1993):
It is convenient to consider [changes of particulate scattering] as taking place through three proximate agents: the change in geometry cross section of the individual particles the change in the index of refraction of the particles and the shift of the particle size distribution into (or out of) the size range of more efficient light scattering as the individual particles grow in size.
The above figure indicates there is clearly more scattering for small (but not too small) particles in humid conditions. Total PM2.5 mass in the atmosphere increases with RH, but significantly (and not obviously) most of these particles do not move to a larger size fraction. The water-based weight increases, but not enough to move into the coarse (= PM10 - PM2.5) size range (which is comparatively less dangerous to breathe). The number density of effective light scattering particles remains more or less unchanged. Hence an increase in a bscat signal does not necessarily mean there is more PM2.5 in the air, only a 'heavier' PM2.5 (though water-logged particles are also less dense than dry weight, something else to consider).
Therefore the challenge is to find out whether an increase in the bscat signal is from a water-logged increase or a legitimate boost in aerosol number density. To avoid being fooled we must dissect the bscat signal as a function of RH.
Therefore the challenge is to find out whether an increase in the bscat signal is from a water-logged increase or a legitimate boost in aerosol number density. To avoid being fooled we must dissect the bscat signal as a function of RH.
We start with a the full IMPROVE-derived formula for the light extinction coefficient. In theory this accounts for every major gas/aerosol component that would scatter or absorb light:
bext ≈ 2.2 fs (RH) [ASO4]S + 4.8 fL (RH) [ASO4]L
+ 2.4 fs (RH) [ANO3]S + 5.1 fL (RH) [ANO3]L
+ 2.8 [OM]S + 6.1 [OM]L
+ 10 [EC] + [Fine Soil] + 0.6 [CM] + 1.7 fss (RH) [Sea Salt]
+ 0.33 [NO2 (ppb)] + Rayleigh Scattering (site specific)
Here bext includes the scattering term bscat, among others (i.e. absorption from EC & coarse mass, and Rayleigh gas scattering). The S and L subscripts refer to solid and liquid aerosol components, respectively. You can see the term f(RH) has been used; it accounts for both increase in particle size due to swelling and change in refractive index. Because most of these particles remain in the PM2.5 size fraction, concentrations of species [X] do not themselves alter with RH. We have the formula, but we'll need to simplify it a little. Our two paths to reduction come in the form of 1) ignoring trace species 2) grouping hygroscopic species together.
For instance Sciare et al make the following assumptions:
We will consider here only ammonium sulfate and POM as the main chemical components of aerosols in the fine size fraction, since nitrate, potassium, sea salt and dust aerosols only account for 0.4, 2.4, 1.2% and 3.3% of the total mass respectively. Based on these assumptions
σSP [which is our bscat] = αASf(RH)[ASO4] + αPOM[POM]
where αAS and αPOM stand for the specific scattering coefficient of [dry] ammonium sulfate and POM in the fine fraction, respectively [where αAS = 2.66 m2/g, αPOM = 4.19 m2/g].
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They used an empirical equation for f(RH):
f(RH) = −0.18614 + 0.99211(1/(1 − RH))
which stays close to unity until above 80%, then rises quickly. As you can see, using this method Sciare's scattering values are comparable to the nephelometer's. This is because, as they state, most of an aerosol consists of (liquid) ammonium sulfate and organics; aerosol sulfate composition in the United States is 40-60% by weight while POM is 40-75%. Fortunately a species' concentration is roughly proportional to scattering.
But we'd like to do better than use an empirical f(RH) (or at least try something different): We want to create our own computationally tailored version of f(RH) that takes advantage of known, but variable, aerosol composition. At out disposal is the aerosol modelling tool ISORROPIA II that can predict just how water logged an aerosol ought to be given a reported RH, temperature, and ion concentration (ions NH4, Ca, Na, K, Mg, anions Cl, NO3, SO4). Here is what I'm thinking:
f(RH) = (calc PM2.5 mass @ RH > 60%)/(calc PM2.5 mass @ RH = 0%)
What's nice about this formula is that f(RH) contains the sea salt component fss(RH) (important for coastal areas). What's not so nice is that organics are ignored, which is a huge component to PM2.5 aerosols. Hence we'll need to re-include them to create a semi-empirical formula. To revise,
f(RH)' = {(calc PM2.5 mass/m3 @ RH > 60%) + [POM]}/{(calc PM2.5 mass/m3 @ RH = 0%) + [POM]}
Dividing through by POM creates a unit less ratio of POM to inorganic components (if that turns out to be useful, I don't yet know)
f(RH)' = {(calc PM2.5 @ RH > 60%)/[POM] + 1}/{(calc PM2.5 @ RH = 0%)/[POM] + 1}
(Aside: Another other issue is accounting for the change in the particles refractive index, m, due to dilution. In theory I'd calculate m as a function of individual particle's ASO4, NaCl, and ANO3 concentrations (which become more dilute with RH, unlike total ion concentration per cubic meter), then apply the relation
bext ~ [(m2 - 1)/(m2 + 2)]2
For now I will just ignore it. End of aside).
I will then use this calculated f(RH) in a formula like the following (an expanded version of Sciare's):
bscat = αASf(RH){[ASO4] + [ANO3]} + αPOM[POM] + others (to be determined)
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