Assessment of PM dry deposition on solar energy harvesting systems: Measurement–model comparison

ABSTRACT

Soiling of solar energy systems, or the accumulation of particulate matter on their surface, can cause significant losses in energy conversion efficiency. However, predicting these losses is still not done, as no methods exist. Field measurements of mass accumulation and airborne PM₁₀ were conducted for more than one year at two sites in the Front Range of Colorado with the objective of developing soiling prediction models. For this study, only dry deposition was examined. The two sites, despite having different PM₁₀ concentrations, have indistinguishable average effective deposition velocities of 2 cm/s, although a large spread in the data was noted. These results are similar to results found in other deposition studies. The observed effective deposition velocities indicate that coarse particles are a dominant player in mass accumulation, and sampled airborne size distributions support this hypothesis. Using a model to calculate dry deposition yielded better agreement with deposition than a simple average deposition velocity data fit. This model combined with other research and models can be used for estimating average soiling rates and is most useful over long time scales especially months to years or longer.

Copyright © 2016 American Association for Aerosol Research

EDITOR:

• Jian Wang

1. Background and motivation

The number of solar energy installations is growing rapidly (REN21 2012). This renewable energy has the potential to significantly reduce emissions from energy generation and provide electricity in remote and harsh environments.To improve feasibility assessment for solar energy harvesting, solar energy harvesting models need to more accurately predict energy output. These models are improving; however, soiling is still a process that is not well understood and thus poorly implemented in these models. Soiling, or the loss of energy from dust or particulate matter (PM) deposition on the panels, can reduce energy production significantly. Previous studies have found soiling losses between less than 1% (Hottel and Woertz 1942) and more than 88% (Garg 1974), and soiling rates (loss of energy over time) between 0.1% per day (García et al. 2011) and 5% per day (Sayigh 1978). These large variations in losses can be attributed to location and meteorology, but generalization in the field has not been done.

Several previous studies have related the mass of deposited PM with the loss in solar energy. One study by Hegazy (2001) found a very clear relationship between the mass of deposited particles and the transmission reduction, regardless of angle of deployment (Hegazy 2001), which led to the development of the equation:[1] where Δτ is the transmission loss caused by deposited particles in percent, and ω is the dust deposition density (the mass of dust deposited per square meter) in g/m². This relationship is shown to be valid between 0 and 10 g/m² of accumulated dust, and may apply to more highly soiled samples. More research is needed to ensure that the transmission loss is generalizable to other locations, although a previous study has examined this (Boyle et al. 2015). Using this type of equation could result in much better predictions of energy loses due to soiling, but requires an estimate of the mass of deposited PM.

To understand the fate and transport of atmospheric PM, particularly those that can potentially impact human health, climate, or ecosystem health, researchers have been exploring the deposition process. Previous studies on deposition have found that for dry deposition the mass of PM deposited is related to ambient concentration of PM by the dry deposition velocity[2] where v_d is the deposition velocity, PM is the mass concentration of PM in the ambient air, and m_accumulated is the mass flux of deposited particles (mass per area per time). Deposition velocity is affected by wind speed, surface properties, particle size, and a number of other factors that make it difficult to calculate theoretically; however, it is generally considered a useful tool for understanding deposition (Seinfeld and Pandis 2006).

Previous ambient studies have shown that larger particles, often over 10 µm in aerodynamic diameter, are the dominant contributor to deposited mass (Lin et al. 1994). Field and laboratory experiments have found a wide range of deposition velocities for particles; a snapshot of those studies that focused on larger-size particles is shown in Table 1. Deposition velocities range from 0.17 cm/s (Davidson et al. 1985) to 21 cm/s (Fang et al. 2014). This large range of deposition velocities is a result of varying surface geometry, meteorological conditions, surrounding environment, size of depositing particles, and atmospheric stability.

Table 1. Summary of deposition velocities found in other studies examining coarse particulates.

Location	Deposition surface	Orientation	Date	Deposition velocity	Size range	Notes	Source
New York	Greased microscope slides	Placed on ground	1962–1964	5 cm/s	20 µm	Ragweed pollen	Raynor (1974)
New York	Greased microscope slides	Placed on ground	1962–1964	12 cm/s	32–35 µm	Timothy pollen	Raynor (1974)
Champaign, Illinois	Teflon plate	Horizontal and stationary	June 1982	0.17–0.42 cm/s	All	Only sulfate	Davidson et al. (1985)
Champaign, Illinois	Petri dish	Horizontal and stationary	June 1982	0.18–0.61 cm/s	All	Only sulfate	Davidson et al. (1985)
South Chicago	Greased Mylar	Horizontal wind vane	July–Sep. 1986	11.7 cm/s	>1 µm		Noll et al. (1988)
South Chicago	Greased Mylar	Upside-down wind vane	July–Sep. 1986	4.2 cm/s	>1 µm		Noll et al. (1988)
Chicago area	Greased Mylar	Horizontal wind vane	July–Aug. 1991	5.3 cm/s	PM10		Holsen et al. (1993)
Chicago area	Greased Mylar	Horizontal wind vane	July–Aug. 1991	5.7 cm/s	Coarse PM		Holsen et al. (1993)
Around Lake Michigan	Greased Mylar	Horizontal wind vane	Dec. 1993 to Oct. 1995	0.2–12 cm/s	Coarse PM	Metals only	Yi et al. (2001)
Bursa, Turkey	Greased Mylar	Horizontal wind vane	Oct. 2002 to June 2003	2.3–11 cm/s	TSP	Metals only	Tasdemir and Kural (2005)
Taiwan, near an Airport	Greased Mylar	Horizontal wind vane	Sep.–Dec. 2005	2.3–11.7 cm/s	TSP		Fang et al. (2007)
Berlin	Beaker	Horizontal wind vane	Dec. 2007 to July 2009	0.4–1.3 cm/s	PM10	Used Sb as a tracer for PM10	Langner et al. (2011)
Taiwan, near a Harbor	PVC	Horizontal wind vane	June–Nov. 2013	0.95–7.92 cm/s	TSP		Fang et al. (2014)
Taiwan, near an Airport	PVC	Horizontal wind vane	June–Nov. 2013	1.8–21.4 cm/s	TSP		Fang et al. (2014)

Most deposition studies use greased or protected surfaces to prevent particle bounce. However for solar energy applications, where a particle can be resuspended, it is important to only collect particles that remain deposited over a long duration. A handful of studies have considered smooth surfaces, where particle bounce or resuspension is allowed. A study by Goossens considered dust accumulation on several surfaces and found good agreement between the mass accumulated on a glass and metal surface in a wind tunnel (Goossens 2005). The results were also similar to a water surface, which indicates that geometry is more important than the surface composition.

Many models have been developed to predict deposition. Models are typically semi-empirical. The model developed by Zhang et al. (2001) is used in this article and employs a theoretical framework that separates the deposition process into several process steps. Each term that represents a process step is then calculated by a fit from deposition data. This model has seen good agreement with actual deposition in the past (Zhang et al. 2001).

In this work we examine the deposition of particles on glass plates similar to those used as photovoltaic (PV) panel cover plates at two different sites in the Front Range of Colorado when samples were collected for two to five weeks. Additionally, we compare the observed deposition with ambient concentrations and modeled deposition results. The goal of this work is to collect a large dataset for evaluating ambient PM concentrations and dry deposition to improve PV soiling models.

2. Methods

2.1. General approach

Ambient PM and PM deposition samples were collected simultaneously at two different locations in the Front Range of Colorado. Ambient PM was collected using a dichotomous filter sampler such that particles with aerodynamic diameter between 2.5 and 10 µm (PM_10-2.5) are separated from particles with aerodynamic diameter less than 2.5 µm (PM_2.5). Deposition samples were collected on glass substrates similar to those used as covers for PV panels. Additional meteorological data were collected at both sites by other organizations: the Air Pollution Control Division of the Colorado Department of Public Health and the Environment (CDPHE) at the Commerce City site, and the National Oceanic and Atmospheric Administration (NOAA) at the Erie site.

The first sampling location was in Commerce City, Colorado, on the roof of a one-storey elementary school in a mixed industrial and residential area 10 km North of downtown Denver, Colorado. This site had several notable particulate matter sources nearby including an open gravel pit mine, and the intersection of Interstates 25, 76, and 270, and U.S. Highway 36. This site was co-located with a CDPHE PM sampling location (AQS ID: 080010006). The second sampling location was in Erie, Colorado, at the base of the Boulder Atmospheric Observatory tower in a rural and agricultural area 30 km North of downtown Denver. This site was surrounded by active farmland and native grasslands, with one freeway passing 2 km to the east. More information about these two sites was presented previously (Boyle et al. 2015).

2.2. Airborne particulate matter

Ambient PM_10–2.5 and PM_2.5 were collected using dichotomous filter samplers located at both field sites; additionally, the combined PM₁₀ is examined in detail here. One of these samplers is shown in the right side of Figure 1. These filter samplers pulled 50 L/min of air through a PM₁₀ inlet. This flow is then passed through a virtual impactor that splits the flow into a 48 L/min PM_2.5 channel, and a 2 L/m PM_10–2.5 channel. Both flows are then split, with half going through a Teflon filter (47 mm, 2 µm pore size, Pall Gelman Teflo) and the other half going through a quartz fiber filter (47 mm, Pall Gelman Tissuequartz). Flow rates through each of the four filters were measured by flow totalizers as well as being controlled by critical orifices downstream. These filter samplers are described in more detail elsewhere (Clements et al. 2014). The filters were changed every 3–10 days, typically 7 days, at the Commerce City site and 3–25 days, typically 14 days, at the Erie site to ensure that there were no flow restrictions caused by pressure drop due to heavily loaded filters. The filter samplers were run continuously between filter changings. Additionally, filters were always changed at the same time as the deposition plates to ensure that the filters were collecting the same ambient PM that the plates were exposed to. The Teflon filters were weighed before and after deployment following the procedures described previously (Dutton et al. 2009). The Teflon filters were allowed to equilibrate in a temperature and relative humidity controlled chamber for 24 h prior to being weighed at least twice on a LabServe model BP210D microbalance with an accuracy of 10 µg. If the difference in masses between the first two weights was more than 30 µg the filter was weighed a third time, and the mass was taken as the average of the closest two masses. Before and after deployment, the filters were stored in pre-cleaned petri dishes (Pall Life Sciences 50mm sterile petri dishes part number 25388-606) in a freezer −18° C ± 7° C. PM₁₀ concentrations were found by[3] where m_{10 − 2.5} and m_2.5 are the masses of the particles in the coarse and fine channels, respectively, and V_{10 − 2.5} and V_2.5 are the volumes of air passed through the coarse and fine channels, respectively. PM_2.5 concentrations are found by[4] The correction factor in the numerator of Equation (4[4] ) is to account for the fine mass that is deposited on the coarse filter due to the nature of the virtual impactor. Analysis of blank samples and controls showed no systematic mass variation, and therefore these masses were not used for correcting the masses calculated by Equations (3[3] ) and (4[4] ). Although both Teflon and quartz filters were collected, only data from the Teflon filters are presented here. The quartz samples were collected for analysis of organic material, while Teflon filters were collected for gravimetric analysis and metals analysis. Chemical analysis, including organic analysis, has not yet been done and is not presented in this work, only gravimetric analysis of filters is presented here.

Figure 1. The experimental setup at the Erie site. On the left is the deposition setup, and on the right is the dichotomous filter sampler.

Airborne particulate samples began being collected in July of 2012 at the Commerce City site and December of 2012 for the Erie site. Sampling continued until May of 2014 at the Commerce City site, and until March of 2014 at the Erie site.

For examining effects of higher time resolution averaging, hourly PM₁₀ measurements were used. These data were collected by the Colorado Department of Public Health and the Environment (CDPHE) at a monitoring site in Welby Colorado (AQS ID: 080013001), approximately 1.5 km northwest of the Commerce City site.

2.3. Deposited PM and effective deposition velocity

PM deposition samples were collected in the same locations as ambient PM concentrations. Glass samples 10 cm x 10 cm were deployed at 0° and 40°, and a field blank was carried with each set of plates to observe contamination from handling, transportation, and storage. A few early samples were deployed at 180° at the Commerce City site, but stopped being deployed after it was found that no appreciable mass accumulation was occurring. The samples were covered by a roof to prevent effects of precipitation. The roof is to allow for only the consideration of dry deposition, and not wet deposition. The roofs were placed 45 cm above the samples to allow for as much natural air flow as possible without getting precipitation on the samples. Samples were deployed for between one and five weeks, with the typical deployment being two weeks at the Commerce City site and four weeks at the Erie site. The deployment is longer at the Erie site to ensure that enough mass has deposited on the plates to be significantly greater than the noise of the measurement. The deposition deployment structure is shown on the left side of Figure 1.

For more than a year of sampling at the Commerce City location deposited PM samples were collected without a roof covering the samples. While in this time period there was never an entire sampling period without rain, there were several with minimal, or rain that occurred very early in the sampling period. All of the samples without a roof collected close to or less than the same amount of mass accumulated on the covered samples (within measurement uncertainty when more mass was collected on the uncovered samples). From this analysis it was determined that the roof was causing a negligible effect on the dry deposition of particulates, and sampling continued with the roof.

Two types of glass plates were used, one a tempered glass and one a low iron glass coated with a transparent conductive oxide; no difference in deposited mass was observed between the two types of plates (Boyle et al. 2015). The tempered glass samples typically weighed around 117 g, and the low iron glass samples typically weighed around 79 g. The plates were thoroughly cleaned, and stored in cleaned glass petri dishes with aluminum foil covers. The same petri dish was used for pre- and post-deployment storage. Nitrile gloves were always worn when handling glass deposition samples to reduce contamination and care was taken not to disturb the exposed surfaces of the plates. After deployment samples were stored in the same freezer as the filters, until they had been post-weighed.

Masses of samples were found by weighing the samples before and after deployment using the same method as the Teflon filters. Mass accumulation was found by subtracting the post masses from the pre masses, correcting for noise in the scale by subtracting the difference in the simultaneously weighed control samples as described in previous work (Boyle et al. 2015). The mass accumulation rate was calculated by[5] where is the rate of mass accumulated per unit surface area, m_accumulated is the mass accumulated on the plate, A_plate is the area of the plate, and Δt is the length of time the plates were deployed. More information on weighing and deposition sample procedure are presented elsewhere (Boyle et al. 2015).

In this work, an effective deposition velocity is calculated. This is found by rearranging Equation (2[2] ), and using the PM₁₀ as a surrogate for total airborne PM,[6] where v_effective is the effective deposition velocity, and appropriate unit conversions are added, so that effective deposition velocity is presented in cm/s in this work. Since we use PM₁₀ to represent all the PM, v_effective is biased high.

Sampling of deposited particulates at the Commerce City site began in August of 2011 and continued to June of 2014. It was nearly a year later that ambient PM samples began being collected at the Commerce City site, and effective deposition velocity calculations did not begin until then. At the Erie site deposited particulate sampling began in November of 2012 and continued until May of 2014. During the vast majority of sampling at the Erie site, both airborne and deposited PM samples were being collected.

2.4. Deposition model

To better understand the utility of deposition theory for estimating solar panel soiling, we used the PM deposition model described by Zhang et al. (2001) to compare to the measured PM deposition rates. This model was chosen because it has been shown to be effective, its ease of application, and because it allows for particle bounce. This model needs ambient PM concentrations including PM size distribution, surface characteristics, and meteorological parameters as inputs. This model uses the original structure developed by Slinn (1982):[7] where v_g is the gravitational settling velocity and R_a and R_s are the aerodynamic resistance and surface resistance, respectively. This is a resistance model of deposition, which examines the processes necessary for deposition and attempts to quantify them individually. The aerodynamic resistance is calculated as[8] where z_R is the height at which deposition is being calculated, taken at 5 m here, z₀ is the roughness length, a value of 1 m was used corresponding to an urban environment, Ψ_H is the stability function, κ is the Von Karman constant, and u_* is the friction velocity. A simplified stability was used based only on wind speed, where wind speed above 5 m/s was considered unstable, between 3 m/s and 5 m/s was considered neutral, and below 3 m/s was considered stable. The corresponding stability functions from Businger et al. (1971) were used. Friction velocity is calculated by[9] where is the wind speed at the reference height, h_r. The wind speed in this work was collected at 10 m.

The surface resistance is calculated by[10] where E_B and E_IM are the collection efficiencies for Brownian diffusion and impaction, respectively, and R₁ is the percentage of particles that stay deposited on the surface. All of these factors have empirical fits from data collected in different experiments. Collection by interception is not included in the model used here due to the smooth surface of the solar collector. E_B is calculated by[11] where Sc is the Schmidt Number, and γ is a parameter based on land use; a value of 0.56 is used here for the urban environment. E_IM is calculated by[12] where St is the Stokes number. This is based on a fit for a smooth collector (Slinn 1982). Finally R₁ is calculated by[13] from Slinn (1982).

Values for PM₁₀ were obtained from the dichotomous filter samplers simultaneously deployed at the sites. Values for temperature and wind speed were obtained from CDPHE at the Commerce City site and NOAA for the Erie site. The data from CDPHE are hourly averaged, and for use in modeling these values are averaged again to correspond to the time that glass coupons were deployed. Data from NOAA are 1-min averaged; these data are again averaged to get one value for the time that corresponding glass coupons were deployed. At the Commerce City site, this data is publicly available at: http://www.colorado.gov/airquality/report. At the Erie site, this data is publicly available at: http://www.esrl.noaa.gov/psd/technology/bao/. In this work we used the fit by Slinn (1982) for the collection efficiency, since the glass coupons represent a smooth surface. For simplicity only deposition samples deployed at 0° were considered in comparisons of modeled and experimental mass accumulation.

2.5. Airborne PM size distributions

Airborne size distribution information was collected at the Commerce City site following the collection of deposition samples. A TSI Aerodynamic Particle Sizer (APS) Spectrometer (Model 3321) was deployed for a several-week period in the Spring of 2015 beginning 30th April and continuing through 21st May. During this time the weather was especially rainy, with nearly daily rain showers. Because of the consistent rain, the data are likely skewed slightly from typical size distributions in the area. Data were not collected for several days during this time period due to computer failure. Over this time, a total of 902 size distribution measurements were taken. Each sample was a 20-s averaged size distribution. Size distributions were collected and saved every 15 min while the system was operational. This instrument samples particle sizes from 0.5 µm to 20 µm in diameter by observing the time of flight of particles in an accelerating airflow. A lab calibration check of the instrument showed an uncertainty of 0.1 µm in particle diameter.

The median shape of these size distributions, as well as the size distributions individually, were used in modeling of particle deposition. When this was done, the size distribution was scaled to match ambient concentrations based on the corresponding PM₁₀ measurement.

3. Results and discussion

3.1. Deposition

Mass accumulation rate (or deposition) values were collected over more than two years at the Commerce City site and more than one year at the the Erie site. The time series of these values is show in in Figure 2. Figure 2 differentiates the two sites as well as the 0°, 40°, 180°, and field blanks. From this figure, we can see that the Commerce City site (abbreviated CC) in general has higher mass accumulation rates. Additionally, the 0° plates show higher mass accumulation rates than the 40° plates. The 180° plates are nearly indistinguishable from the field blanks indicating that the main method of deposition is gravitational settling and not diffusion. This is reasonable as the majority of mass is in larger sizes of particles that deposit almost exclusively by gravitational settling. Small particles, which are preferentially removed via diffusion, may be depositing on the 180° plates but do not have appreciable mass even with significantly longer deployment times (up to two months).

Figure 2. Plot of mass accumulation on the glass deposition plates. The samples are grouped by location and orientation to highlight the differences that location and angle of deployment have on mass accumulation. Note that only mass accumulations above zero are shown here, many blank and 180° samples have negative mass accumulation and are not presented in this figure.

Summary statistics for mass accumulation rates are shown in Table 2. The highest values were seen in Commerce City where deposition values between 0.01 and 0.12 g/m²/day were observed for horizontally deployed plates, and between 0.01 and 0.08 g/m²/day for the 40° plates. Lower mass accumulation rates were seen at the Erie site where deposition values between 0.005 and 0.06 g/m²/day for 0° plates and 0.005 and 0.02 g/m²/day for 40° plates were observed. These are similar to results found by Holsen et al. (1993) outside Chicago, and lower than those seen by Fang et al. (2007) in Taiwan. This is a likely indication of the respective concentrations of airborne particulates, since these two studies saw similar values for deposition velocity (see Table 1).

Table 2. Summary of mass accumulation data collected in this study.

		Mass accumulation rate		Effective deposition velocity
Location	Position	Number of samples	Mean (± STD) mg/m^2/day	Number of samples	Mean (± STD) cm/s
Commerce	0°	174	43.2 (17.8)	134	2.14 (1.03)
City	40°	66	44.3 (15.8)	48	2.42 (1.13)
Erie	0°	40	20.0 (11.6)	33	2.12 (1.05)
	40°	10	13.0 (5.6)	10	1.40 (0.58)

3.2. Effective deposition velocity

Deposition theory indicates that ambient PM concentrations and deposition are related by deposition velocity, Equation (2[2] ). Comparing PM₁₀ concentrations with deposition rates yields Figure 3. Despite the wide spread in the data seen in Figure 3, the range of deposition velocities that were observed between the two sites were comparable. At the Commerce City site the range of effective deposition velocity values was 0.52–5.7 cm/s (174 samples) with a mean of 2.14 cm/s, and at the Erie site the range of effective deposition velocity values is 0.61–4.0 cm/s (40 samples) with a mean of 2.12 cm/s. The results for effective deposition velocity are summarized in Table 2. While the range of effective deposition velocities at the Commerce City site was slightly larger, the mean effective deposition velocity at both sites were not statistically significantly different (p = 0.92). Additionally, the variances of the two distributions are not statistically significantly different (p = 0.86). There were many more samples collected at the Commerce City site because sampling started earlier at that location and there were two deposition setups in Commerce City to assess measurement uncertainty (Boyle et al. 2015), thus doubling the number of samples collected. Additionally, the higher PM concentration allows samples to be collected more often.

Figure 3. Comparison of ambient PM₁₀ and mass accumulation for the two sites in this study. A trend line shows a similar relationship between the two sites, which are statistically not differentiable.

The range in deposition velocities was also compared for the various deployment angles (0°, 40°, 180°, and field blanks). A box and whiskers plot of these data are shown in Figure 4. The median deposition velocity for both 180° samples and the field blanks is near zero, supporting the previous results that significant deposition is not being caused by diffusion of small particles. The large spread in the effective deposition velocity values particularly for the 180° plates may be caused by compounding of uncertainty in PM concentrations as these samples were deployed longer, and the similar uncertainty in mass as the field blanks. The 0° and 40° samples have very similar deposition velocities, despite the 40° samples having been tilted. This may be due to particles depositing by impaction during wind events, or may be a result of the uncertainties in mass accumulation and PM₁₀ concentrations.

Figure 4. A comparison of the deposition velocities for plates deployed at different angles. The data from both sites are combined in this box and whiskers plot.

These values for effective deposition velocity were similar to values previously observed, particularly for those studies that focus on larger particles (see Table 1). The range of effective deposition velocities seen in this work spans more than an order of magnitude, which makes generalization difficult; however, the similarity between the two sites in this study, and other studies, has some positive implications. If the similarity in deposition velocities to smooth horizontal surfaces is minimally effected by airborne particle distributions, meteorology, and surrounding environment, than a first-order estimate of mass accumulation on PV panels may be relatively easy, and accomplished with only knowledge of the relationship with PM₁₀ concentrations.

When exploring the linear relationship between mass accumulation on the surface and airborne PM₁₀ concentrations, PM₁₀ concentrations accounted for 9% of the variability in mass accumulation. More of the variability can be accounted for by adding additional variables to this linear model, including temperature and wind speed. When using all three of these variables, 26% of the variability can be accounted for. Neither PM_2.5 nor relative humidity were significant predictors of mass accumulation. Adding temperature and wind speed does improve the predictions of mass accumulation; however, this model has been built and tuned to the data collected here. Section 3.4 provides a better estimate of mass accumulation with these same variables without tuning to this specific dataset.

One reason that PM₁₀ may be a poor predictor of mass accumulation is that particles larger than 10 µm in aerodynamic diameter can deposit but are not counted in the PM₁₀ measurement. PM₁₀ can be a poor predictor of total airborne particulates. This is likely one of the driving factors in the variability of the effective deposition velocity and the spread in Figure 3.

3.3. Airborne PM size distributions

Several days of size distribution data are shown in Figure 5. The frequent rainstorms are easily observable as the concentrations of coarse particles decrease drastically. There are also periods without rain, where we can see the quick rise in particle concentrations. The particle concentrations are not very stable, with the size distributions varying widely over even relatively short time scales (hour to hour for example) especially with the effects of precipitation. The median size distribution and interquartile range data show a clear single mode distribution in coarse particulates, see Figure 6.

Figure 5. Size distributions collected for five days at the Commerce City site in May 2015. Frequent rainstorms are easily noted by the significantly lower PM concentrations. The APS used in this study samples particles up to 20 µm in aerodynamic diameter.

Figure 6. Variability in the size distributions collected in Spring of 2015 at the Commerce City site. The histogram is the median size distribution, and the two dotted lines represent where the 25th and 75th quartile distributions would be.

Figure 5 shows that the size distribution can be highly variable with time and that using a single size distribution may not accurately represent the true conditions over long (in this case multi-week) time scales. Precipitation especially can affect the shape of the size distribution. The peak in coarse PM occurs around 14 µm, although the variability in this is quite high. Figure 6 shows the median normalized size distribution and the middle 25–75% quartiles. Size distributions were normalized so that the total mass in each size distribution was equal to one (the mass in each bin divided by the total mass in that sample). The median and quartiles are for each size bin individually across all of the samples and do not represent specific normalized size distributions, but represent how much of the airborne mass is typically in each of these bins. The lack of larger particles in the lower quartile is likely caused by the persistent precipitation that scavenged the larger particles, and may not be typical for the Front Range area. Figure 6 also indicates that there are likely larger particles that were not sampled by the APS, as seen by the shape of the distribution.

To use these size distribution data in modeling deposition, the median size distribution was used as time-averaged size distribution of the particles, and the median size distribution was shown to match deposition results better than the mean size distribution. This was shown by running a comparison between deposition calculated every hour and every two weeks. Hourly averaged meteorological data were combined with bootstrapped size distributions to calculate a theoretical deposition for every hour over two weeks. This hourly deposition was summed and compared with the deposition calculated using two-week averaged meteorological data, combined with mean and median size distributions. Using this method with several years of meteorological data, the median size distribution was shown to better predict the hourly summed size deposition results than the mean size distribution. The PM₁₀ concentration that was collected with the dichotomous filter sampler was used as a scalar to multiply the normalized size distribution to get an average size distribution for the period of deployment of the plates.

3.4. Comparison between observations and model

Figure 7b shows the comparison between actual mass accumulation and modeled mass deposition, using the model developed by Zhang and collaborators (see Section 2.4) and using the median size distribution collected with the APS. These data have an R² value of 0.32, and smaller spread than the PM₁₀ versus mass accumulation plot (Figure 3) (p = 0.46). This indicates that this model does a better job of estimating mass accumulation than employing a single effective deposition velocity. The model does a good job of getting the right order of magnitude fit to the data and a regression of the data forced through the origin gives a slope of 1. Although the model makes a good first-order approximation of deposition, there is still noticeable spread in the data of 0.018 g/m²/day.

Figure 7. Comparison of mass accumulation and modeled mass deposition for the Commerce City site. Particulate concentrations were collected from the dichotomous filter sampler, and meteorological data averaged over the glass coupon deployment from data available from the CDPHE. Plot (a) shows the model using size bins corresponding to the APS size bins, and plot (b) shows results using a simple 2-bin model with the PM_10–2.5 and PM_2.5 collected from the dichotomous filter sampler.

Figure 7a shows the results of the same model as above but instead of using 52 size bins corresponding to the size bins of the APS, the model uses only two size bins one for PM_2.5 and one for PM_10–2.5. This model does almost as well as the model with 52 size bins (R² = 0.31), with less information. Not only is this likely the better model tested in this study, but also it shows that the same accuracy can be achieved with relatively rudimentary ambient size distribution information, as with a more specific size distribution. Both PM₁₀ and PM_2.5 data are widely available in the US through the Environmental Protection Agency, and this model could easily be applied with this level of accuracy in many locations across the US.

Figure 7 shows similar magnitudes for results of both the 2-bin and 52-bin models, despite the 52-bin model including particles between 10 and 20 µm in diameter that are not included in the 2-bin model. This is most likely due to both models using the same mass of particles, just distributed between the bins differently. The 52-bin model has larger particles, but the total particle mass is still the same, so the model finds less deposition of the smaller particles. Additionally, the 2-bin model uses simultaneously collected PM_2.5 and PM₁₀, so that more or fewer smaller particles may be represented in the model—compared with the 52-bin model that has one constant size distribution.

Previous research has found that long time-averages for deposition significantly reduce the accuracy of model results and the relationship between ambient PM and deposition (Noll and Fang 1989). In an attempt to understand if this is a driver for the spread between modeled and predicted results, a theoretical study was conducted. Real hourly PM₁₀, temperature, and wind speed data from the CDPHE were used to model deposition every hour over two week increments. Additionally, the size distributions collected with the APS were bootstraped for these hourly calculations, choosing one size distribution at random for every hour. Then the median size distribution from the bootstrap population and the averaged PM₁₀, temperature, and wind speed data were used to calculate total deposition over the two week period and the deposition results were compared. The spread in the results was 0.005 g/m²/day. As such, high time averaging was not able to fully explain the differences observed between modeled and observed deposition results in this experiment.

Another possible explanation for the spread is in the measurement uncertainty in calculating mass accumulation, caused by uncertainty in mass, time, and area measurements. This uncertainty has previously been shown to be on the order of 0.01 g/m²/day (Boyle et al. 2015).

The uncertainty caused by lower time resolution and measurement uncertainty accounts for roughly two-thirds of the difference between modeled and observed deposition. The remainder of the unexplained variance likely originates from model ”inaccuracies” or inability of the model to fully capture real world deposition processes, meteorological variable uncertainties that are not examined here, and size distribution uncertainties. Another likely source of uncertainty in this approach is not accounting for particulates larger than 10 or 20 µm in aerodynamic diameter. These larger particles are in the atmosphere and depositing, but are not being included in the measurements of airborne particulates or the calculations of deposition. Previous experiments on solar energy systems have seen a peak in deposited size distributions around 20 µm (Roth and Anaya 1980; Biryukov 1996; Cabanillas and Munguía 2011), indicating that these larger particles are present and significant.

A sensitivity analysis of the model was conducted, examining the sensitivity to temperature, wind speed, PM₁₀, and particle size (increasing or decreasing the size of each particle by the given percentage). For each parameter, the other parameters were kept constant while the parameter of interest was increased and decreased by 5 and 10% for all the samples in the dataset. The numerical output from this sensitivity analysis is shown in Table 3. The model was found to be most sensitive to PM₁₀, with any change in the input of PM concentration giving an equal percent change in the output. All the other parameters were less sensitive. Temperature and particle size had similar sensitivities, with every percent change in the input in these parameters causing a 0.2% change in the modeled mass accumulation with wide variability across the input parameter space noted. Finally, wind speed was the most variably sensitive parameter with every percent increase in wind speed causing a 0.06% increase in mass accumulation and every percent decrease in wind speed causing a 0.3% decrease in mass accumulation, and wide spread in this relationship was again noted across the input parameter space.

Table 3. Summary of deposition model sensitivities given as the average percentage change in mass of particle dry deposition. Mean values for the range of input found in this experiment as well as the range of values observed are presented.

	Increase 10%	Increase 5%	Decrease 5%	Decrease 10%
	Mean (Range) %	Mean (Range) %	Mean (Range) %	Mean (Range) %
Wind speed	0.8 (−3.8 to 4.8)	0.2 (−2.6 to 2.7)	−1.3 (−3.3 to 2.0)	−3.0 (−7.2 to 4.7)
Temperature	1.7 (−3.0 to 5.7)	1.0 (−1.4 to 2.9)	−1.1 (−2.9 to 1.1)	−2.4 (−5.7 to 1.8)
Particle size	1.60 (−1.9 to 6.0)	0.80 (−1.2 to 3.1)	−0.90 (−3.5 to 1.7)	−2.10 (−7.4 to 3.9)
PM10	10 (10 to 10)	5 (5 to 5)	−5 (−5 to −5)	−10 (−10 to −10)

4. Conclusions

An average effective deposition velocity of 2 cm/s was observed at both sites in this study but an order of magnitude spread is observed in effective deposition velocity over the entire sampling campaign. A more complex model did a better job of predicting mass deposition but required temperature, wind speed, and size distribution data. All methods showed significant spread in the deposition results when compared with experimental deposition; however, these results represent a significant step forward in modeling soiling losses for solar energy. Because soiling happens over long time scales (months to years), an average effective deposition velocity is useful even if there is high variability on shorter time scales. For solar energy harvesting modeling, short-term variability is driven by clouds and temperature, which dominate any effects that might be seen from soiling. However, monthly and yearly output of a system can be greatly affected by soiling, and being able to predict these losses can significantly improve estimates of how much energy a PV system will produce over its lifetime, which dictates the payback period. The accuracy in predicting deposition achieved in this study is likely not useful for understanding short-term fate of airborne species, or high precision calculations of deposition.

Being able to predict mass accumulation on PV panels, or other solar energy harvesting devices, could improve prediction of energy loss due to soiling when paired with other study results and models. Here results are presented that indicate that mass deposition is related to ambient concentrations, even over periods of time greater than a week. This means that using readily available PM₁₀ data, and easily implemented deposition models, even as simple as a constant effective deposition velocity, soiling losses could begin to be predicted at sites anywhere in the country or the world. Both the simple and more complex model are sensitive to PM₁₀ concentration inputs, and high-quality data for this parameter are necessary for accurately predicting mass accumulation. The more complex model was less sensitive to wind speed, temperature, and particle sizes indicating that lower quality data (from more distant stations, or with higher uncertainty) may be used in these parameters.

Acknowledgments

The authors thank the Air Pollution Control Division of the Colorado Department of Public Health and the Environment for generously sharing data, especially Bradley Rink for his continued help with data from CDPHE. Additionally, the authors thank the Physical Sciences Division of the National Oceanic and Atmospheric Administration for sharing data collected at the BAO Tower, and Daniel Wolfe and Bruce Bartram for their support with sampling and instrument monitoring at the BAO Tower.

Funding

This material is based upon the work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE 1144083.