I develop and use a low-cost sensor system (the SPSA), but validation of such a system under the circumstances where you use it is also important. The golden standard for validation of PM2.5 measurements in mass concentration (microgram/m3) are gravimetric measurements.
Gravimetric measurements
The principle behind gravimetric measurements is very simple: take the weight of an empty filter, expose that filter to air of your interest, and afterwards again take the weight of the filter. The weight increase is the particle mass. If you know the volume of air from which this mass comes, you can calculate the mass concentration.
While the principle is simple, the execution is less so. Four considerations:
1. Analytical scale
You need an analytical scale that has a precise enough readability and repeatability. If the increase in filter mass is, say, 450 microgram, but your analytical scale only reads up to 0.0001 gram (or 100 microgram), it will tell you either 500 or 400 microgram. Uncertainty resulting from the readability would then be 100/500 = 20%. And, the repeatability (within which range will a scale tell the same with the same weight) is usually less precise.
2. filter sampling Instrument
You need an instrument that can pull air through a filter at a known rate. In other words, a pump (pulling air through a filter), with a logger of the volume of pumped air. Because, apart from the filter weight increase, we need to know the volume of air pulled through the filter.
3. pm2.5 sampling
For PM2.5 sampling, you only want particles with an aerodynamic diameter up to 2.5 micrometer to arrive at the filter. Hence, your sampling instrument will need some preselector based on particle size. This is usually some precise combination of inlet diameter and distance within which the airflow takes a turn. Particles too big cannot follow the turn, and are therefore taken out before the airflow reaches the filter. This, however, does require your instrument to have a constant flowrate. The particle size cutoff is related to the speed of the airflow, so that speed needs to be maintained – otherwise you will get other sized particles than you expected.
4. Sampling time, flowrate and scale
Given the precision of the analytical scale, you need an instrument that has a good flow rate in relation to the average concentrations. Preferably the repeatability of the scale is less than 5% of the expected filter weight. If the repeatability is for example 20 microgram, you would want to have at the very least an expected filter load of 400 microgram. If expected concentrations are on average 20 microgram/m3, and you want a sampling time of 24 hours, then your instrument would need to have a flowrate of at least 0.83 m3/hour.
Instruments in Arba Minch
In my air quality lab, I have a Mettler Toledo AE240 analytical scale, which has a readability of 10 microgram and repeatability of 20 microgram. Furthermore, I have an LVS Leckel with PM2.5 inlet, which has a controlled flowrate of 2.3 m3/hour. This means, that for an outdoor concentration of 10 microgram/m3, with 24 hours of filter loading the filter weight increase would be 10 microgram/m3 * 2.3 m3/hour * 24 hour = 552 microgram. The repeatability of the scale is 20/552 = 3.6%, which is acceptably low. So far, so good. However, now on to more advanced considerations.
Gravimetric measurements, continued
While having the right instrument and analytical scale, there can be other sources of error. Three advanced considerations:
1. Checking the flow
The flow of the LVS is supposed to be 2.3 m3/hour. However, this needs to be checked, and if necessary, calibrated. This leads to the need of another instrument: a flow sensor – which on itself needs to be trusted and/or calibrated of course. The only flow sensor I have is a Kytola hand-held plastic tube, which has a scale in L/min, per five liter.
2. Humidity effect
From the analytical scale, we can trust weight changes beyond 20 microgram. However, changes in room conditions (specifically relative humidity) influence the condensation or evaporation of water onto or from the filter. These changes can result in weight changes beyond 20 microgram. The expensive solution for this is a controlled weighing room, with a stable temperature and relative humidity. This is not available in Arba Minch. The cheaper solution is to always have three empty filters together with the filters of interest. Any changes in empty filter weights must be due to humidity effects. We can correct the weight change in a loaded filter for this. The use of three (or more) filters is to be able to exclude one faulty value.
3. Loaded filter effect
When the filter is loaded, its weight might change over time. Possibly, PM2.5 components react away, or others increase. This would imply it matters how soon after sampling you take the weight. And if this indeed matters, then a sampling campaign with seven filters and afterwards weighing these would see an influence from whether a filter happened to be first or last.
Measurements with students
Together with third-year Water Supply and Environmental Engineering students, I have used the LVS and analytical scale over the past month for validation of the SPSA.
So far, across 28 weighing moments, 194 times filters (empty or filled) were weighed. 15 filters were loaded; eight in a lab and seven outside. Let’s dive into the three sources of error, with help of the past month’s measurements.
Evaluating the advanced considerations
1. instrument flow
I have checked the flow of the LVS five times, and each time the Kytola flow sensor seems to show a reading somewhat under the 35 L/min mark (say: 34 L/min). This would imply a flowrate of 34 * 60 / 1000 = 2.04 m3/hour, instead of the required 2.3 m3/hour. I do not yet want to calibrate the flow of the LVS before I get confirmation from another flow sensor. While waiting for this, let us calculate the implications. There are two implications of a wrong flow: the volume is different, and the particle size cutoff is different.
1.1 Volume implications of a wrong flowrate
While sampling for 24 hours, if I have collected a filter weight increase of 900 microgram, this would imply a mass concentration of 900 / (2.3 * 24) = 16.3 microgram/m3 with the normal flowrate. If, however, the flowrate was 2.04 m3/hour instead, the concentration would be in fact 900 / (2.04 * 24) = 18.4 microgram/m3.
At the one hand important to know, but at the other hand not too problematic: as long as I keep the data, I can correct it as soon as I am confident of the correct flow. If the flowrate is indeed 2.04 / 2.3 = 89% of what it should be, then the concentration inversely proportional increases with 1 / 89% = 113%. In other words: I need to get to know the correct flowrate for final results, but by having measured potentially with a wrong flow rate, I have not made the data useless.
1.2 Cutoff implications of a wrong flowrate
The size cutoff, however, might be more problematic. I am using this instrument to validate the PM2.5 measurements of the low-cost sensor system. The LVS is designed to have a cutoff at 2.5 micrometer if the flowrate is 2.3 m3/hour. If the flowrate is lower, the speed of the air is lower, and it becomes easier for bigger particles to make the turn. In other words, we might be measuring PM>2.5 instead of PM2.5.
We can calculate this. The expected cutoff is a function of the inlet diameter, the flowrate (Q), and some other physical parameters and constants. All else equal, the expected cutoff is a function of √(1/Q). If the flowrate is 88% of what is expected (2.04 instead of 2.3 m3/hour), the expected cutoff increases with √(1/0.88) = 107%. An original cutoff of 2.5 micrometer at 2.3 m3/hour would imply a cutoff at 2.5 * 1.07 = 2.67 micrometer at 2.04 m3/hour. I do not expect that the mass concentration of PM2.67 significantly differs from PM2.5. Hence, I conclude that the possible incorrect flow rate is not a problem with respect to the cutoff.
2. Humidity effect
2.1 Is there a humidity effect?
Possibly, conditions in the weighing room affect the filter weight, by increasing or decreasing the condensed water on the filter. To control for this, three blank filters with any field filter are used: at the before- and after-weighing of the field filter, the blank filters are weighed as well. Any change in weight of the blank filters can only be from a change in weighing room conditions, and the field filter weight change should be corrected for this.
Below figure shows filter weights of empty filters weighed multiple times over the past two months – normalized by subtracting the lowest weight per filter. As we can see, variations per filter across different weighing moments can be up to 360 microgram. This means that, for the same filter, with the same scale and in the same room, still the weight changed significantly. It makes sense that we correct for this effect.
2.2 Can we correct for the humidity effect?
There were 28 weighing moments. Per combination of two moments, we can establish a likely humidity effect, if there were three or more the same blank filters weighed at both moments. We take the weight difference per filter between moment 2 and moment 1, then remove the most extreme differences, and use the average of the remaining differences as correction for any weight comparison between these two moments. The range between these remaining differences (highest – lowest value) tells us something about how stable this humidity effect is across filters.
For example: at moments 1 and 2, three the same blank filters were weighed. At moment 1, weights were respectively 152880, 153320 and 152550 microgram. At moment 2, weights were respectively 152930, 153290 and 152530 microgram. Weight differences were respectively 50, -30 and -20. The most extreme difference is 50 (it differs the most from the average difference). After removal of this value, an average correction of -25, with a range of 10 microgram, is calculated.
There were in total 231 pairs of weighing moments with three or more of the same blank filters. Below figure shows the range between remaining differences.
Of the 231 pairs, only 15 (6%) have a range higher than 20 microgram amongst them. Overall, the range across weight differences for pairs of weighing moments is much smaller than the range of filter weights across weighing moments. In 94% of the cases, multiple filters confirm the required correction within a range of 20 microgram from each other. And 20 microgram of difference can simply be due to variations of the analytical scale, since that is its repeatability. In other words: it makes sense to correct for the humidity effect, since several filters confirm it.
3. Loaded filter effect
3.1 Is there a loaded filter effect?
Possibly, there is a change in the weight of a loaded filter over time. If this is the case, then for loaded filters across different weighing moments, the range in differences should be more extreme than that for empty filters.
There were in total 26 pairs of weighing moments with three or more of the same loaded filters. Below figure shows the range between remaining differences.
Of the 26 pairs, 11 (42%) have a range higher than 20 microgram amongst them. In other words: the differences across weighing moments for loaded filters have a larger spread than the differences for empty filters – for which only 6% of the differences within the same paired weighing moments were more than 20 microgram apart. So, indeed, it seems that the filter weight of a loaded filter changes more than can be explained by the humidity effect only. It is possible that the humidity effect is different for loaded filters, or that the PM2.5 load increases or decreases over time.
3.2 Is there a trend in the loaded filter effect?
Let us try to see whether there is a trend in the weight change of loaded filters over time. For that, we take a couple of steps: (1) we calculate for each loaded filter, for every moment of weighing, the likely PM2.5 load based on the weight difference with when the filter was empty. (2) We correct each of these PM2.5 loads based on the most likely humidity correction. For example, if we took the empty weight of filter x at moment 1, and the loaded weight at moment 5, we correct the weight difference for the difference of filters that were empty at both moments 1 and 5. (3) We compare the loads with the time difference between the moment of loaded weighing and end of sampling.
Below figure shows the weight of twelve loaded filters that had at least three loaded weighing moments. Instead of showing absolute weights, I subtracted the first weight of a filter from all weights of that filter. divided weights by the first weight of the respective filter. In other words, the figure shows the difference over time relative to the first weight measurement.
Looking to all filters, there is no clear trend of decay or increase. Some filters show decrease at some point, while others show an increase. Except for filter 11, all changes are within 60 microgram difference. Filter 11 was one of the most heavily loaded filters. Relative to the filter weight, differences are between 0.94 and 1.06, or +- 6%. It seems, at this point, that we mostly can conclude that the variation in filter weight for loaded filters is bigger, but that there is no clear trend or likely correction with respect to hours after sampling.
Conclusions on gravimetry
What I conclude, so far, on the use of gravimetry in Arba Minch:
- I will look for another type of flow sensor, to get confirmation on the flow of the LVS. A possible error in the flow, however, does not mean that we cannot use samples taken so far.
- Missing a controlled weighing room, correcting for room conditions and a humidity effect is important. Several pairings of empty filter weighing moments confirm that a stable (within reliability of the analytical scale) correction for this is possible.
- The moment of weighing a loaded filter, and the time period between end of sampling and weighing, might matter. Current evidence does not give a clear trend and possible correction. For now, we must see this as a +-6% uncertainty.
