Instruments and procedures

I was reading through the paper A review of atmospheric aerosol measurements and found it quite useful, especially since aerosol collection is the core of the SPARTAN project.  It was authored by Peter H. McMurry, a specialist in both theoretical and experimental aerosol science (my kind of guy!). Even better is that he focuses on small aerosols, i.e. PM2.5 and below.

SPARTAN is not about aerosol nucleation theory, which is of course an active field of research but too far off topic from our direct interests: below a few hundred nanometers particles cease to scatter much light or have much mass, hence do not change nephelometer light scattering readouts. Actually I should qualify that: there is one pesky light-scattering gas: NO₂. Nitrogen dioxide is the reason polluted cities look polluted. That brownish colour in the sky is NO₂. At more than a few parts per billion, visible wavelengths get noticeably scattered.

NO2 cross section from here. Note the overlap with the visible spectrum, i.e. above 420 nm, which creates a brownish colour  

Back to instrumentation measurements. Although Dr. McMurry is principally interested in the theory of sulphuric acid nucleation (his definition of small is smaller than ours), his review is extensive. Some highlights:

Size selection methods

Diffusion of particles down the length of a tube is a convenient way to size-sort parties. But only particles below 100 nm can be practically size-sorted by diffusion. Particles are sorted into histogram-like bins from 10-100 nm. Since differences in diffusion are proportional to the square root of the mass then larger particles do not separate well. Sorting heavier aerosols is akin to the problem of sorting 235UF₆ and 238UF₆, i.e. requiring many times more path length. For heavier particles, i.e. 0.1-2.5 um, one would use a multi-stage impactor.

Interesting thing about impactors is that wet particles 'bounce' less than dry ones, so that >75% RH is a good way to capture these particles. Downside is that means we'll need to be extra careful about size correcting these hydroscopic particles.

Ammonium nitrate losses on filters

When it comes to capturing ammonium nitrate, which is volatile, it turns out impactor plates are better than Teflon filters:

Evaporative losses of particulate nitrates have been investigated in laboratory and field experiments with filters and impactors. The laboratory studies involved parallel sampling of ammonium nitrate particles with a Berner impactor and a Teflon filter. Both samplers were followed by nylon filters to collect evaporated nitric acid. Losses from the impactor were 3-7% at 35C and 18% relative humidity, and losses from the filter were 81-95% under the same conditions. This result (that evaporative losses from the filter exceeded those from the impactor) is consistent with theoretical predictions

In other words Teflon is not very good for capturing nitrates. Huge losses, which means total aerosol mass is under predicted, chemical speciation is mis represented and so on.

Here is another great review, but slightly older.

I want to play with one of these H-DTMA instruments (H-DTMA stands for hygroscopic tandem differential mobility analyzer).

Also reading this paper linking hygroscopic aerosol particle growth with organic composition, which is right up my alley. Here's a handy tabulation of aerosol species' properties:

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. 

Linking aerosol scattering to mass

It's time to start hunkering down at plotting some scattering coefficients. There's a lot to describe, and much will be omitted in this post. I'll start with how we plan to predict PM_2.5 mass with time.

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)

b_scat(t) ~ PM_2.5(t)

Because these two quantitive are proportional, the re-arrangement means the ratio PM_2.5/b_scat is a constant:

PM_2.5(t)/b_scat(t) = C

and the average, too, is constant

<PM_2.5(t)/b_scat(t)> = <C> = C

The 'average' is an integration over 24 hours; we are summing over twenty four one-hour intervals (if you want, let <b_scat> = b_scat(24h)). Also we can split the average like so

<PM_2.5/b_scat> = <PM_2.5>/<b_scat>  

Compare ratios (1-hour and 24-hour) and we find they are of course equal

PM_2.5(t)/b_scat(t) = <PM_2.5>/<b_scat> 

We now have the setup for a prediction of PM_2.5 levels at one-hour time intervals

PM_2.5(t) = b_scat(t)*<PM_2.5>/<b_scat> 

It's worth considering this formula in detail since each parameter comes from a different source of data.

The b_scat(t) and <b_scat(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 b_scat(t). But here's the catch: the b_scat(t) proportionality with mass holds true only under constant humidity and temperature.

Changing the relative humidity (RH) with time will affect b_scat(t) (either increase or decrease it) even if total PM_2.5 mass remains constant. At any time during a 24h run b_scat is changing because of humidity, temperature, and mass: 

b_scat = b_scat(t, [water], T, m)

or as a function of RH

b_scat= b_scat(t, RH([water, T], T))

For simplicity we might compare b_scat at dry (RH < 40%) and humid conditions. This is defined as the hygroscopic growth factor, f(RH):

f(RH) = b_scat(RH > 60%)/b_scat(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 b_scat 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 PM_2.5 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 - PM_2.5) 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 b_scat signal does not necessarily mean there is more PM_2.5 in the air, only a 'heavier' PM_2.5 (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 b_scat signal is from a water-logged increase or a legitimate boost in aerosol number density.  To avoid being fooled we must dissect the b_scat 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: 

b_ext ≈ 2.2 f_s (RH) [ASO₄]_S + 4.8 f_L (RH) [ASO₄]_L

+ 2.4 f_s (RH) [ANO₃]_S + 5.1 f_L (RH) [ANO₃]_L

+ 2.8 [OM]_S + 6.1 [OM]_L

+ 10 [EC] + [Fine Soil] + 0.6 [CM] + 1.7 f_ss (RH) [Sea Salt]

+ 0.33 [NO₂ (ppb)] + Rayleigh Scattering (site specific)

Here b_ext includes the scattering term b_scat, 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  

 σ_SP [which is our b_scat] = α_ASf(RH)[ASO₄] + α_POM[POM]

where α_AS and α_POM stand for the specific scattering coefficient of [dry] ammonium sulfate and POM in the fine fraction, respectively [where α_AS = 2.66 m²/g, α_POM = 4.19 m²/g].

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 PM_2.5 mass @ RH > 60%)/(calc PM_2.5 mass @ RH = 0%)  

What's nice about this formula is that f(RH) contains the sea salt component f_ss(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 PM_2.5 mass/m³ @ RH > 60%) + [POM]}/{(calc PM_2.5 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 PM_2.5 @ RH > 60%)/[POM] + 1}/{(calc PM_2.5 @ 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

b_ext  ~ [(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):

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

As a reminder (to myself, mostly), the goal of this project is to measure total PM_2.5 mass on short time scales. Since many of these measurements will be done in hot and muggy urban locations we must account for humidity. The scattering coefficient will give us a reasonable mass estimate if we can account for the RH (and temperature) dependence.  Another self-reminder: PM_2.5 mass is best measured using gravity filtration weighing; this yields an actual mass value. But this method only gives -at best- 24h-averaged samplings, and usually spaced every third day or more (for SPARTAN perhaps just once every 10-14 days). In doing this work we might unleash some interesting possibilities...

Aerosol measurements: real and calculated

There are at least four reasons to pay attention to aerosol components. The key components are sulfate ions [SO42-], nitrate ions [NO3-], light-absorbing carbon [LAC], sea salt [SS], organic carbon [OC], and soil content [Soil]. Here they are:

1) Reconstructing light extinction from aerosol measurements. 

To know the extinction coefficient of a particle means predicting its light scattering. The IMPROVE network estimates aerosol Mie scattering of airborne particulates (also some Rayleigh scattering from air and nano-scale particulates). This is calculated via measuring the extinction coefficient b (a conglomerate of extinction values) where

I/I₀ = e^-bL

and L is the (fixed) path length and I/I0 is the fraction of light scattered by the particles. The reference light intensity I₀ requires some assumptions, and setting can vary from one protocol to another. The wavelength used is 545 nm, say for a single-wavelength integrating nephelometer (M903, Radiance Research, Seattle, USA). 450nm, 550, and 700 nm light are used in the TSI 3563.

Scattering as measured by the nephelometer is the sum of all aerosol components and their respective masses:

b = a₁m₁ + a₂m₂ + a₃m₃ +...

From Finlayson-Pitts and Pitts' Chemistry of the Upper and Lower Atmosphere, some typical net extinction values are b = 10^-3 m^-1 (for polluted regions) and 10^-7 m^-1 (for remote locations). The equation to obtain b is found here, as part of the IMPROVE background material:

b = 3f(RH)[SO₄] + 3f(RH)[SO₄] + 4f_org(RH)[Organic carbon] + 1[Soil] + 0.6[Coarse mass]  

The pre factor f(RH) is known as the wet to dry scattering ratio f(RH) and accounts for the effects of water content for certain species. It turns out some aerosol constituents scatter more light in wetter conditions. For the IMPROVE network's purposes, which are empirically driven, the change in organic scattering is only weakly dependent on RH, hence they choose to set f_org(RH) as unity. The extinction of nitrates and sulfates, however, cannot be ignored; for these species f(RH) is required. The formula is an empirically derived value, and is also known as the relative humidity adjustment factor:

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

It reminds me of the fugacity fudge factor used for high-pressure gas thermodynamic calculations. The adjustment is small for low-humidity scenarios, but rises rapidly above 95% RH, where f > 7. This means that for the IMPROVE data "errors in reconstructed scattering coefficients (associated with RH measurements) will increase together with RH". This is because, as they put it, "water uptake was responsible for about one third on average of the calculated reconstructed ambient light scattering coefficient."

Recap: For high RH the scattering coefficients are difficult to determine. Data in very wet conditions is often ignored (i.e. not reported in the final tally), as the scattering values are not considered sufficiently reliable. This can lead gaps in data.

Here is the light scattering formula used by Environment Canada's NAPS team:

b_ext ≈ 2.2 f_s (RH) [ASO₄]_S + 4.8 f_L (RH) [ASO₄]_L

+ 2.4 f_s (RH) [ANO₃]_S + 5.1 f_L (RH) [ANO₃]_L

+ 2.8 [OM]_S + 6.1 [OM]_L

+ 10 [EC] + [Fine Soil] + 0.6 [CM] + 1.7 f_ss (RH) [Sea Salt]

+ 0.33 [NO₂ (ppb)] + Rayleigh Scattering (site specific)

I thought it was interesting that NAPS uses a more complex equation despite being a smaller network. Or does that make sense?

After all that work, we need to assume the total scattering is correlated to total mass. Hard to deduce that simple fact based on what I wrote. In case you need some convincing:

   

2) Reconstructing total mass

The IMPROVE network collects particles using three separate filters: Nylon, quartz, and Teflon (also Nucleopore filters made of polycarbonate). Together these yield the PM_2.5 reconstructed fine mass (RCFM), which are summed in the following manner 

RCFM = a[SO₄^-2] + b[NH₄⁺] + c[NO₄^-] + d[POM] + e[LAC] + f[Soil] + g[SS]. 

Or in other words

aerosol components by weight => empirical summation => total aerosol mass

Each of these categories is 'representative' of other species, as many are not measured for practical reasons (too many species, species are below detection limits, etc). Why reconstruct mass this way? Besides having a gross tally with which to compare species' aerosol contribution, the values can be compared to nephelometer measures. It has been said by Sciare et al. that "chemical mass closure experiments are more and more required as they will serve to better constrain the optical properties of aerosols or the formation of cloud condensation nuclei". In other words we cannot rely completely on the simple scattering of aerosols by lasers because these measurements themselves are derived from reconstructed masses. As network arrays grow in number and geographic diversity, the challenges intensify.

3) Predicting change in aerosol size under variable relative humidity (RH)

This section is the key to my project. I want to know aerosols will change in size hourly knowing only the daily (24h) mass/speciations totals in section 2 and the hourly light scattering and RH values reported in section 1. A lot can happen in 24 hours, as Jack Bauer will tell you.

How will I do this in practice? Knowing the components of aerosols combined with ab initio thermodynamics (via ISORROPIA II and/or AIM) will tell us how much water is retained in an aerosol at a given relative humidity, called a reverse problem (reverse-engineering an aerosol)

{aerosol components by weight} + {RH, T} => computational calc => total aerosol mass 

We then re-insert this value into the program to obtain new masses using variable RH and temperature T values. This is solving the forward problem, i.e. finding a new aerosol weight with known gas+aerosol conditions (as opposed to knowing only the aerosol conditions alone)

starting aerosol mass + {new RH, new T} => computational calc => new aerosol mass 

 As the hierarchy goes, a computationally reported aerosol mass ranks slightly below reconstructed mass: Both rely on empirical estimates but computational methods require more assumptions and ignore more data (less attention paid to organics  in the computational methods). So why do it this way? A lot of work goes into reconstructing aerosol mass using (see previous section), but there's no guarantee the specific water content was correctly accounted for: The upside is that an hourly resolution is now available. More critically, the SPARTA network may only provide weekly, or even just 21 day sampling periods. Hence computational estimates might be a way to interpolate aerosol values. Not sure yet if that's the best way to go about it. I'm thinking of collecting PM2.5 data from around the world to calibrate initial estimates. There's always the chance that a 100% purely empirical approach is a better avenue. It's my job to find this out.

4) Health impacts

Health impacts is the ultimate reason many are interested in sub 2.5 micron sized aerosols. But we don't have enough worldwide dispersed data sets. Notably it has been stated in a recent global aerosol health assessment that  

surface measurement data (for PM and even more so for ozone) are still far too sparse in most of the high concentration regions for direct use in exposure assessment throughout the world. 

To estimate the health impacts of aerosols, we need their total mass: adverse health effects (reparatory and cardiac) are related best to total mass. Knowing aerosol components helps to distinguish acceptable PM2.5 from 'bad' PM2.5. Most PM2.5 is bad since things like dust and salt don't usually get that small. But ignoring these differences in composition could lead to erroneous health advisories. Knowing details of each aerosol type is important, especially since most of the ground networks now are located only in Europe and North America. That leaves a lot of earth left to cover.  

Some fresh aerosol info

Aerosols are to atmospheric scientists what living cells are to biologists. Both are impossibly complex, variable in time, space, size, and composition. Neither can be solved numerically. Aerosols are, however, not alive. They can be better approximated by computers, but many mysteries of their inner workings remain hidden.

I'm currently looking into how aerosols change diameter with time. Specifically how they change during the diurnal cycle. That is, humidity changes with time, naturally, and can be rather unpredictable if we're speaking about rain storms and sudden weather events. Humidity levels constantly change, and not always in a simple pattern. I came across this collection of Canadian weather stats.

The cycling is not simple. But this is not a problem because RH values are merely input parameters, whatever they may be. Given the RH numbers, we then use these values to predict aerosol diameter. The diameter of aerosols matters since this may affect whether or not they are trapped in a PM2.5 filter.

Here is a website that models aerosol thermodynamics, called E-AIM (Extended Inorganic Aerosol Model), which provides a simple input/output scheme for aerosols. The calculations are of course complex. I'll post more on the calculations when I understand them better.

PM2.5 monitoring network

Continuing my exploration into aerosol studies I now explore the American IMPROVE initiative. IMPROVE stands for Interagency Monitoring of Protected Visual Environments. Their website defines the program as

a cooperative measurement effort between the U. S. Environmental Protection Agency (EPA), federal land management agencies, and state agencies. The network is designed to

1. Establish current visibility and aerosol conditions in 156 mandatory Class I areas (CIAs)  

2. Identify chemical species and emission sources responsible for existing anthropogenic
visibility impairment 

3. Document long-term trends for assessing progress towards the national visibility goal  

4. With the enactment of the Regional Haze Rule, provide regional haze monitoring
representing all visibility-protected federal CIAs where practical. 

They link to a cool feature VIEWS, which displays aerosol data for every type of particulate composition in the country. Below is IMPROVE aerosol PM2.5 levels from NYC from 2004-2010

As you can see there's a lot more 'dirty' aerosols in a big city than, say, Rocky Mountain, Colorado:

Sophisticated stuff. I really like how full-disclosure these websites are. Excel files, readable plots, publications galore. There is little to hide. Here's the geography of the IMPROVE network: