Atmospheric Stability and Air Quality Measurement Principles of Air Pollution Measurement

Fundamentals of Air Parcel Dynamics and the Dry Adiabatic Lapse Rate

As an imaginary parcel of air (جزئية من الهواء) rises within the Earth's atmosphere, it encounters lower and lower pressure from the surrounding air molecules. Because of this decrease in external pressure, the air parcel expands. This expansion causes a reduction in the temperature of the air parcel. Under ideal conditions, a rising parcel of air cools at a rate of approximately $1\,^∘\text{C}/100\,\text{m}$ or $5.4\,^∘\text{F}/1000\,\text{ft}$ . Conversely, if an air parcel is descending, it warms at the same rate of $1\,^∘\text{C}/100\,\text{m}$ . This specific rate of warming or cooling related to altitude change is theoretically termed the dry adiabatic lapse rate.

In a rising parcel scenario where the air is unsaturated, a parcel starting at ground level (elevation $0\,\text{m}$ ) with a temperature of $10\,^∘\text{C}$ will cool as it ascends. At $100\,\text{m}$ , the temperature reaches $9\,^∘\text{C}$ ; at $200\,\text{m}$ , it reaches $8\,^∘\text{C}$ ; and at $300\,\text{m}$ , it cools to $7\,^∘\text{C}$ . During this process, the surrounding environmental air may have a different temperature profile. For instance, the surrounding air at $0\,\text{m}$ is $10\,^∘\text{C}$ , but at $100\,\text{m}$ it might be $9.8\,^∘\text{C}$ , at $200\,\text{m}$ it might be $9.6\,^∘\text{C}$ , and at $300\,\text{m}$ it might be $9.4\,^∘\text{C}$ . In this specific case, the environmental lapse rate is different from the adiabatic lapse rate, making the rising parcel cooler than its surroundings at higher altitudes.

Classification of Prevailing Lapse Rates and Atmospheric Stability

The actual measurements of temperature change with elevation are known as prevailing lapse rates or environmental lapse rates. These can be categorized into four primary types based on their relationship to the dry adiabatic lapse rate of $1\,^∘\text{C}/100\,\text{m}$ :

Superadiabatic Lapse Rate (Strong Lapse Rate): This occurs when the atmospheric temperature drops by more than $1\,^∘\text{C}/100\,\text{m}$ . This condition leads to unstable atmospheric conditions characterized by a great deal of vertical air movement and turbulence (اضطراب).
Subadiabatic Lapse Rate (Weak Lapse Rate): This is characterized by a temperature drop of less than $1\,^∘\text{C}/100\,\text{m}$ . These conditions represent a stable atmosphere with limited vertical mixing.
Adiabatic Lapse Rate: The condition where the prevailing rate exactly matches the dry adiabatic process ( $1\,^∘\text{C}/100\,\text{m}$ ).
Inversion: This is a special, extreme case of a weak lapse rate where the temperature actually increases with altitude, meaning warmer air sits above colder air. Inversions are considered super stable and significantly inhibit vertical air movement.

Impact of Stability on Pollutants and Vertical Movement

Understanding vertical air movement is critical for managing air quality and ensuring that pollutants do not affect human populations. Stability determines whether a volume of air will resist movement or continue to rise or fall once displaced.

In a superadiabatic (unstable) system, if a parcel of air is displaced, it tends to keep moving in that direction. For example, if a parcel at $500\,\text{m}$ and $20\,^∘\text{C}$ is moved up to $1000\,\text{m}$ , it cools adiabatically to $15\,^∘\text{C}$ . If the surrounding environmental temperature at $1000\,\text{m}$ is $10\,^∘\text{C}$ , the parcel finds itself warmer than the surrounding air. Since warm air rises, it will continue to ascend. If the same parcel is moved downward to ground level ( $0\,\text{m}$ ), its temperature would increase to $25\,^∘\text{C}$ ( $20\,^∘\text{C} + [500\,\text{m} \times 1\,^∘\text{C}/100\,\text{m}]$ ). If the surrounding air at the ground is $30\,^∘\text{C}$ , the parcel is cooler and higher-density than its surroundings, causing it to continue its downward trajectory.

In a subadiabatic (stable) system, vertical movement is dampened. Consider a parcel at $500\,\text{m}$ and $20\,^∘\text{C}$ in a system where the ground is $21\,^∘\text{C}$ and the air at $1000\,\text{m}$ is $19\,^∘\text{C}$ . If the parcel is displaced to $1000\,\text{m}$ , it cools to $15\,^∘\text{C}$ . Finding the surrounding air warmer at $19\,^∘\text{C}$ , the parcel is denser and falls back to its original release point. If moved to the ground, it warms to $25\,^∘\text{C}$ , but because the surrounding ground-level air is cooler at $21\,^∘\text{C}$ , the parcel rises back to its point of origin at $500\,\text{m}$ .

Plume Behavior Conditions based on Enviromental Profiles

The interaction between the environmental lapse rate and the dry adiabatic lapse rate determines the visible shape and behavior of smoke plumes from stacks:

Strong Lapse Condition (Looping): Occurs under superadiabatic conditions where environmental air is cooler than the parcel, leading to high turbulence and an unstable looping plume.
Weak Lapse Condition (Coning): Occurs under subadiabatic conditions where the environmental lapse rate is slightly less than adiabatic, resulting in a conical plume shape.
Inversion Condition (Fanning): Occurs when an inversion exists. The plume spreads horizontally but resists vertical movement, staying in a thin layer.
Inversion Below, Lapse Aloft (Lofting): A favorable condition where pollutants are trapped above an inversion layer, preventing them from reaching the ground.
Lapse Below, Inversion Aloft (Fumigation): A dangerous condition where an inversion layer acts as a cap, forcing pollutants to stay near the ground.
Weak Lapse Below, Inversion Aloft (Trapping): Similar to fumigation, where vertical mixing is severely limited, trapping pollutants in the lower atmosphere.

Categorization and Measurement of Particulate Matter

The Environmental Protection Agency (EPA) classifies particulate matter based on the diameter of the particles:

Ultrafine (رائعة الصر): Diameter range < 0.1\,\mu\text{m}.
Fine (الأرقى): Identified as $PM_{2.5}$ , with a diameter range < 2.5\,\mu\text{m}.
Coarse (الأرقى): Identified as $PM_{10}$ , with a diameter range between $2.5\,\mu\text{m}$ and $10\,\mu\text{m}$ .

Measurement of $PM_{10}$ is historically performed using a high-volume sampler (hi-vol). This device operates similarly to a vacuum cleaner and can force up to $86,000\,\text{ft}^3$ of air through a filter in a $24$ -hour period. It consists of an air inlet, a filter, a blower, a flow controller, and a manometer to calculate flow and pressure. The analysis is gravimetric, meaning the filter is weighed before and after exposure to determine the mass of particulates collected.

Mathematical Calculations for Air Quality

Particulate Concentration (Gravimetric)

The concentration ( $C$ ) is calculated as the mass of particulates divided by the volume of air sampled. In Example 12.2, a clean filter weighs $10.00\,\text{g}$ , and after $24\,\text{hr}$ , it weighs $10.10\,\text{g}$ . The initial and final air flows are $60$ and $40\,\text{cfm}$ ( $\text{ft}^3/\text{min}$ ).

Mass of particulates: $(10.10\,\text{g} - 10.00\,\text{g}) \times 10^6\,\mu\text{g/g} = 0.1 \times 10^6\,\mu\text{g}$ .
Average air flow: $\frac{60 + 40}{2} = 50\,\text{ft}^3/\text{min}$ .
Total volume of air: $(50\,\text{ft}^3/\text{min}) \times (60\,\text{min/hr}) \times (24\,\text{hr}) = 72,000\,\text{ft}^3$ .
Convert volume to $m^3$ : $72,000\,\text{ft}^3 \times (28.3 \times 10^{-3}\,\text{m}^3/\text{ft}^3) = 2038\,\text{m}^3$ .
Concentration: $\frac{0.1 \times 10^6\,\mu\text{g}}{2038\,\text{m}^3} = 49\,\mu\text{g/m}^3$ .

Gas Concentration Conversion

Gaseous concentrations are expressed as parts per million ( $ppm$ ) or micrograms per cubic meter ( $\mu\text{g/m}^3$ ). The conversion formula at $1\,\text{atm}$ and $25\,^∘\text{C}$ is: $\mu\text{g/m}^3 = \frac{MW \times 1000}{24.5} \times ppm$ Where $MW$ is the molecular weight of the gas. At $0\,^∘\text{C}$ , the constant changes to $22.4$ .

Example 12.3: Calculations for Carbon Monoxide ( $CO$ , $MW = 28\,\text{g/mol}$ ) at $10\%$ volume.

Since $1\% = 10,000\,ppm$ , then $10\% = 100,000\,ppm$ .
Concentration: $\frac{28 \times 1000}{24.5} \times 100,000 = 114 \times 10^6\,\mu\text{g/m}^3$ .

Large-Scale Case Study: 1952 London Fog

During a 2-week episode, $25,000\,\text{metric tons}$ of coal with $4\%$ sulfur ( $S$ ) content were burned per week. The mixing depth (inversion cap) was $150\,\text{m}$ over an area of $1200\,\text{km}^2$ . Calculating the expected $SO_2$ concentration:

$SO_2$ emitted per week (using $MW_S = 32\,\text{g/mol}$ , $MW_{SO_2} = 64\,\text{g/mol}$ ): $(25,000\,\text{tons}) \times (0.04\,S) \times (64/32) = 2000\,\text{metric tons/wk}$ .
Total mass for 2 weeks ( $A$ ): $2 × 2000 = 4000\,\text{metric tons}$ .
Volume of mixing layer: $150\,\text{m} \times 1200\,\text{km}^2 \times 10^6\,\text{m}^2/\text{km}^2 = 180,000 \times 10^6\,\text{m}^3$ .
Concentration: $\frac{4000\,\text{metric tons} \times 10^6\,\text{g/ton} \times 10^6\,\mu\text{g/g}}{180,000 \times 10^6\,\text{m}^3} = 22,000\,\mu\text{g/m}^3$ .

Questions & Discussion

Question 1: What is the relationship between Carbon Monoxide ( $CO$ ) and Carboxyhemoglobin ( $COHb$ )? Response: Exposure to $CO$ causes impairment in time-interval discrimination even at $2.5\%$ $COHb$ levels. In crowded city streets where $CO$ can reach $10\,\mu\text{g/m}^3$ , the approximate relationship after prolonged exposure is $COHb(\%) = 0.5 + (0.16) \times (10) \times (CO\, \mu\text{g/m}^3)$ . A traffic cop working a full day would be subject to levels dictated by this ratio.

Question 2: How much $CO$ and $HC$ would a 1974 car emit in a year if driven $1000\,\text{mi/month}$ , and how lethal would it be in a garage? Response: Standards for 1974 were $3.4\,\text{g/mi}$ for $HC$ and $30\,\text{g/mi}$ for $CO$ . At $12,000\,\text{mi/year}$ , total emissions are $12,000 \times 3.4 = 40,800\,\text{g}$ of $HC$ and $12,000 \times 30 = 360,000\,\text{g}$ of $CO$ . In a double-car garage ( $20 \times 25 \times 7\,\text{ft}$ ), lethal concentrations of $CO$ would be reached rapidly based on the mass-to-volume ratio ( $C = \text{Mass}/\text{Volume}$ ).

Question 3: Calculate particulate concentration if a hi-vol clean filter weighs $18.0\,\text{g}$ and the dirty filter weighs $18.6\,\text{g}$ with initial/final flows of $70$ and $40\,\text{ft}^3/\text{min}$ . Response: Mass $= 0.6\,g$ . Average flow $= 55\,\text{ft}^3/\text{min}$ . Total volume over $24\,\text{hr}$ is $55 \times 60 \times 24 = 79,200\,ft^3$ . Converting this to $m^3$ and dividing the mass by the volume yields the concentration.

Question 4: Convert the primary ambient air quality standard for $NO_2$ ( $100\,\mu\text{g/m}^3$ ) into $ppm$ . Response: Using the formula $ppm = \frac{\mu\text{g/m}^3 \times 24.5}{MW \times 1000}$ , one would insert the molecular weight of $NO_2$ ( $MW \approx 46\,g/mol$ ) to find the standard in $ppm$ at $25\,^∘\text{C}$ and $1\,\text{atm}$ .