Sampling the atmosphere to analyze contaminants is different from other environmental matrices because measuring the volume of air collected requires a mechanical flow-through device to draw the air and measure its flow rate. The device used must have the capability of concentrating the analytes of interest onto a different substrate because the volumes of air needed are often on the order of hundreds of cubic meters. The use of high-volume air samplers has grown since 1967, when recommended limits of a large number of organic contaminants in air were developed. Equations used for calculating the air flow through the device over time have similarly been developed. However, the complete derivation of those equations has never appeared in the scientific literature. Here a thorough derivation of those equations is provided with definitions of the mechanical systems that are used in the process, along with the method of calibrating and calculating air flow.

Collecting environmental samples of the atmosphere is inherently different from sampling soil, ice, snow, water, or organic matter. With the non-atmospheric matrices, the chemical analytes of interest are specific to a typically small and easily measured volume or mass. The atmosphere is a matrix with a significantly lower density, which raises the question of how to collect and measure the large volume of air where the analytes are found.

The first mention in the scientific literature of high-volume (Hi-Vol) air flow regulation was from a toxicological study by Drinker et al. (1937). In this study, the amount of chlorinated biphenyl released to specific amounts of air had to be known to identify the amount of toxic substance inhaled by the test organism. The air flow was measured by an orifice calibrator that enabled the volume of air to be known over a certain time period. Although the orifice calibrator is mentioned in this report, the calibration system, including the system of equations used for calculating flow, is not identified.

Following the passage of the US Clean Air Act in 1963, a group of US health experts formed a group known as the American Conference of Governmental Industrial Hygienists (ACGIH). In 1966, ACGIH developed recommended no-toxic-effect concentration limits in air of 78 different contaminants, many of them organic compounds (Danielson, 1967). The development of this list led to a requirement of making an air sampler capable of handling large volumes of air because the toxic amounts on the ACGIH list were very low and would be found in low concentrations. Development of Hi-Vol samplers began soon after, with early designs using vacuum systems that generated large flow rates (Jutze and Foster, 1967). After further development, these systems were found to provide reproducible results (Clements et al., 1972) and eventually to be reliable in severe weather (Salamova et al., 2014) and robust over many years when properly maintained (Salamova et al., 2016).

The early development of vacuum-assisted Hi-Vol samplers required a system for measuring the volume of air flow through the sampler. While Hi-Vol manufacturers and the literature now provide equations used for this process, none of them include any derivation of those calculations or discussion about why the variables in the equations are used. The situation is typical of a textbook by Wight (1994), where the basic fluid dynamic principles required for the calculations are outlined, but ultimately the equations are not derived comprehensively. Similarly, the coursework provided by the Air Pollution Training Institute on air sampling (APTI, 1980) presents only the calibration equations along with a multitude of numerical examples, without explaining their origin. Even governmental regulations (40 CFR Appendix B Part 50, US EPA, 2011) and guidelines (US EPA, 1999) focus on the calibration of Hi-Vol samplers but do not derive the procedure in detail. The early literature does not elaborate on the calibration equations. For example, Lynam et al. (1969) investigate different calibration methods for Hi-Vol samplers, showing that significant differences can occur. Similarly, Lee et al. (1972) investigate different methods for measuring suspended particles in air and elaborate in detail on the calibration process of Hi-Vol samplers without deriving any equations. As recently as 2013, ASTM International (2013), in Method D6209-13 for collection of Hi-Vol samples, leave several blanks in sections covering flow control, flow calibration, calibration orifices, and roots meters (Sect. 9.1.2, 9.1.3, 9.1.4 and 9.1.5), all of which are critical to proper calibration. In the calibration section of this method (12.1), there are references to these blanks in Sect. 9.1. Most studies of atmospheric contaminants collected with Hi-Vol samplers assume that the calibration procedure is understood, rarely discuss calibration details, and never include the equations used, this includes Hermanson and Hites (1989), Monosmith and Hermanson (1996), Hermanson et al. (1997, 2003, 2007), Basu et al. (2009), Salamova et al. (2014), and Hites (2018).

The objective here is to derive the calculations required for measurement of
air flow, volume, and calibration of a Hi-Vol air sampler that are missing
from the scientific literature. These calculations are based on principles
of fluid dynamics. The results developed provide the air sampling community
with the missing derivation of equations that are based on the physical
features of a Hi-Vol system. The outcome will improve an air pollution
investigator's understanding of the operational features of Hi-Vol samplers.
Some specialty Hi-Vol samplers, including those for PM

The following presents an educational approach explaining the general
physical equations required to derive the concentration of airborne
particulate-phase and gas-phase contaminants (e.g., pesticides, polychlorinated
biphenyls, polychlorinated dibenzo-

Main components of a typical high-volume air sampler.

The second physical variable required is the volume of the sampled air

The elapsed sampling time is quantified by using the timer clock mentioned
above. The flow rate is determined using the continuity equation: assuming
steady flow conditions, the flow rate can be calculated with the flow
velocity

The flow velocity is measured with a flow device, such as a venturi nozzle or
an orifice plate, shown in Figs. 2 and 3. These flow devices exhibit a
specific geometry with a given inlet cross section 1 and a constriction 2
shown in Fig. 2. The areas of the cross sections

Note that the hydrostatic pressure is omitted in this case because of the
low density of air and a negligible hydrostatic height difference. The flow
velocity

Venturi nozzle.

To quantify the velocity

Ambient temperature is directly measured with a thermometer, and ambient pressure is measured with a barometer. Substituting density with the ideal gas law, Eqs. (3) and (6) can be summarized to the following.

To underline that Eq. (9) is stating standardized volume flow, the
pressure and temperature variables are presented as normalized,
dimensionless terms, i.e.,

Orifice plate calibrator.

Calibration using a linear correlation with intercept and slope.

Equation (10) presents all variables required to be physically measured and necessary to derive the contaminant concentration: contaminant mass, sampling time, differential pressure at the flow device, ambient temperature, and ambient pressure.

The necessity of calibrating the volume flow rate arises from the fact that
Eq. (10) contains the unknown constant

The aim of the calibration process is to determine the numeric value of the calibration slope and intercept. First, the true flow through the air sampler is determined by using a temporary calibration device, typically with an orifice plate (Fig. 3). The true flow is evaluated at several flow rates (adjusted by regulating the pump voltage or the flow valve in Fig. 1). Second, the true flow rates are correlated to the differential pressure readings with the aforementioned linear approach in Eq. (11). The method is visualized in Fig. 4.

The calibration process will be described for the example of a Tisch Environmental Inc. TE-PUF polyurethane foam high-volume air sampler (Tisch,
2015). This sampling unit uses a venturi nozzle as a flow device and a
Magnehelic^{®} differential pressure gauge. For the calibration,
an orifice calibrator is mounted on the sampler. The calibrator essentially consists of a
cylindrical can with an orifice plate and a pressure tap (Fig. 3). Despite
its simple construction, it is a highly accurate and robust calibration
device (Wight, 1994).

To obtain the flow rate through the orifice calibrator

The slope

With the pressure difference from the U-tube manometer and the orifice slope
and offset, ^{®}) and the slack tube
are taken.

The slope and intercept can be graphically determined by using a linear
trend line and by plotting the results of the calibration measurements in a
graph shown in Fig. 4. The

There are several aspects that can lead to an erroneous calibration, related to operator mistakes and technical issues with the sampler. In both cases, the results obtained from the measurement may be meaningless. One way of identifying a flawed calibration is to operate two Hi-Vol samplers near each other (co-located sampling). This method is similar to analyzing duplicate laboratory samples and is expected to result in similar calibration results. When significant differences between the co-located samplers occur, the calibration procedure and the technical integrity of the samplers should be investigated.

This paper provides a missing piece of information in the literature regarding air sampling in the environment, showing that, by its nature, air sampling is a more complex process than sampling other environmental matrices. We have shown the variables and derivation of the equations used for calculating the air flow rate through a Hi-Vol air sampler and the process used for calibration of that flow rate. This allows investigators to identify the mass of contaminant found in a volume of air, once the analytical work has been completed. This detailed explanation of the process and equations allows a deeper understanding of the required variables and can be used for error estimation purposes.

No data sets were used in this article.

MH devised the idea for the paper, researched the literature, wrote the introduction, and provided feedback on the manuscript. RH developed the theoretical framework, derived the equations, wrote the paper, and prepared the figures.

The authors declare that they have no conflict of interest.

This work was originally prepared as part of the air sampling curriculum for the course “AT-331/831 Arctic Environmental Pollution – Atmospheric Distribution and Processes”, a Masters- and PhD-level course offered at the University Center in Svalbard (UNIS) from 2013 to 2017.

Financial support for Open Access was provided by the Norwegian University of Science and Technology (NTNU).

This paper was edited by Thomas F. Hanisco and reviewed by Kristie Ellickson and one anonymous referee.