AIR POLLUTION METEOROLOGY
 

In order to perform dispersion calculations which are discussed in the air quality modeling section, it is important for one to understand meteorological aspects of air pollution. In this section basic concepts of meteorology are discussed for solving and understanding air pollution problems. The chapter is divided into four major sections:

    atmospheric thermodynamics

    atmospheric stability

    boundary layer development

    effect of meteorology on plume dispersion.

For in-depth information and some fascinating trivia on atmospheric phenomena go to "http://www.vol.it/UK/EN/SCIENCE/METEOROLOGY/"

The site also includes important links to various weather forecasting and meteorological institutions all over.

The problem of air pollution occurs in the earth's atmosphere. The chemical composition and the physical characteristics of the atmosphere are helpful for interpretation of the pollution cloud. The atmosphere is a mixture of gases. The concentration of each gas varies from trace levels to very high levels. Nitrogen and oxygen are the main constituents. Some constituents such as water vapor vary in space and time.

The earth’s atmosphere can be divided into several layers, depending on the temperature profile. The four major layers are:

    troposphere

    stratosphere

    mesosphere

    thermosphere.

The discussion in this course will be limited to troposphere, and stratosphere.

ATMOSPHERIC THERMODYNAMICS
 

In order to study the atmospheric flows, a parcel of air is defined using the state variables. These variables define the state of an element of the atmosphere. The three important state variables are density, pressure and temperature. For an explanation of atmospheric pressure and experiments you can perform to examine the force exerted by the weight of air, go to "http://kids.mtpe.hq.nasa.gov/air_pressure/index.html"

The units and dimensions for the state variables are given in the following table.

Humidity is the fourth important variable in the study of atmospheric flows which tells us about the amount of water vapor present in a sample of moist air.

Meteorologists also use the term specific volume instead of density. The specific volume is defined as:

Specific Volume, = 1 / Density

Problem 1

Determine the pressure, both absolute and gauge, exerted at the bottom of the column of liquid 1 meter high, with density of 1200 kg / m3

Solution

Pgauge = (density of liquid) X ( acceleration due to gravity) X (height of liquid column)

Pgauge = ( 1200 kg/m³ ) X ( 9.7 m/s² ) X ( 1 N/kg/m/s²)

Pgauge = 11.760 kN/m2

Pgauge = 11.760 kPa
 

Pabsolute = Pgauge + Patmospheric

Pabsolute = 11.760 kPa + 101.3 kPa

Pabsolute = 113.06 kPa

Equation of State

The relationship between the three state variables may be written as:

For a perfect gas,

where,

The specific gas constant for dry air, R d = 0.287 Joules / gm /^oK, and for water vapor, R v = 0.461 Joules / gm /^oK. The specific gas constant for wet air will not be constant quantity but will depend on mixing ratio.

Problem 2

Calculate the density of a gas with a molecular weight of 29 @ 1 atm(absolute) and 80 ^oF. Gas constant, R = 0.7302 ft³atm/lb-mole^oR

Solution

Absolute Temperature = 80 ^oF + 460 = 540 ^oR

Density = P ( molecular weight) / RT

Density = ( 1atm. ) . (29 lb/lb mole) / ( 0.7302 ft³atm/lb-mole^oR). (540 ^oR)

Density = 0.073546 lb/ ft³

Solve this problem online using applet DENS 1.0.

First Law of Thermodynamics

The first law of thermodynamics is based on the law of conservation of total energy of a thermodynamic system which undergoes a change of state. Mathematically one can write it as:

Heat added per unit mass = (Change in internal energy per unit mass) + (work done by a unit mass)

Second Law of thermodynamics

There are several different statements for the second law of thermodynamics in the physics books. In summary, the law can be stated as "no cyclic process exists having the transference of heat from a colder to hotter body as its sole effect".

Specific Heats

The specific heat is defined as the amount of heat needed to change the temperature of unit mass by 1^oK. The specific heat can be computed at the constant volume or at constant pressure. The definitions are:

Specific Heat at Constant Volume

Specific Heat at Constant Pressure

The Carnot's Law provides a relationship between Cp and Cv. For a perfect gas,

C p - C v = R
 

For a perfect diatomic gas ( approximation to dry air), Cp and Cv can be obtained from,

C p = (7/2) . R, and

C v = (5/2) . R
 

For dry air, the value of

C pd = 1.003 Joules / gm / ^oK, and

C vd = 0.717 Joules / gm / ^oK

The ratio of Cp, and Cv is given by = Cp / Cv = 1.4 (for dry air). The value of  for dry air is 1.4. The value of  will be different for different gases.

PROCESSES  IN THE ATMOSPHERE
 

When an air parcel moves from one point to another point in the atmosphere, it can follow several different paths. These are:

    Constant Pressure known as " isobaric " change

    Constant Volume known as " isosteric " change

    Constant Temperature known as " isothermal " change

    Constant Entropy known as " Isentropic " change

    Adiabatic Process i.e. Q= 0 (no heat added or removed from the air parcel)

                 The adiabatic Law is 

STATISTICS OF THE ATMOSPHERE

The vertical variations of parameters such as pressure are studied.

The pressure variation in a "motionless" atmosphere is given by:

where, the left hand side term is the vertical pressure gradient per unit mass, and the right hand side term represents gravitational force per unit mass.

 If the atmosphere is not "motionless", Newton's second law can be used to write the general equation as:

 The hydrostatic equation can be used to derive a relationship between pressure and elevation of the air parcel. The hydrostatic equation and the equation of state can be rewritten as:

 Integration of the equation yields:

 The initial conditions used in the integration are: z = 0, p = 0

Thus the variation of pressure depends on the vertical profile of temperature.

For an isothermal atmosphere, one can integrate the left hand side term of the above equation as:

Where, T_o is the temperature of isothermal atmosphere.

Simple calculation using the equation show that the pressure decreases exponentially with height at a ratio of 12.24 mb per 100 meter.

The lapse rate is the rate of change of temperature with height and is defined as,

The value of  varies throughout the atmosphere.

In order to compare two air parcels at the same temperatures and different pressures, the concept of potential temperature is useful.

The relationship between temperature and pressure can be derived using the first law of thermodynamics as follows:

Consider adiabatic flow

dH = 0

0 = Cp dT - a dp

0 = Cp dT - (RT/p)*dp

Cp dT = (RT/p)*dp

dT/T = (R/Cp)*(dp/p)

d (ln T) = (R/Cp)*d(ln p)

Integrate from ( T, p ) to ( To, po )

Define potential temperature  as the temperature corresponding to the pressure po = 1000 mb,

ATMOSPHERIC STABILITY

Atmospheric stability is defined as the ability of the atmosphere to enhance or to resist atmospheric motions. A simple way to determine the atmospheric stability is to use dry adiabatic lapse rate (_d). The following table shows the conditions for different atmospheric lapse rates.

LAPSE RATE	ATMOSPHERIC STABILITY
> d	Unstable
= d	Neutral
< d	Stable

In the above table, the value of the dry adiabatic lapse rate is -1 ^oC/100 m. The environmental lapse rate is positive in a strongly stable atmosphere while it is negative in an unstable atmosphere.

For more detailed information on Atmospheric Stability, go to the following slide show.

"http://cnr.umn.edu/NRES/courses/fr3103/slides/day10/"

and

"http://www.worc.ac.uk/departs/envman/Staff/Rowland/ums/env/mec/climate/PhysicsBackground/Adibatic2.html"

ATMOSPHERIC STABILITY CLASSIFICATION

  Over the last several decades, a number of classification systems have been proposed to define atmospheric stability. Some of these schemes are explained below.

P- G method is one of the oldest methods to define atmospheric stability. The method requires the measurements of

    Horizontal wind speed,

    Cloud cover,

    Ceiling height and

    Time of observation

The approach is based on original field work. The cloud observations are expensive. The scheme is given in the following table:

---

P-G / NWS Method

This is a variation of P-G method. The only difference between P-G method and this method is that on-site cloud cover observations are replaced by the observation taken at the National Weather Service (NWS) station in that area. The disadvantage of the method is the use of second-hand information for cloud cover. 

---

The STAR Method

The instrumentation for monitoring atmospheric stability is relatively expensive and is typically difficult to maintain. The instruments are used in remote locations where trained environmental scientists are not present, and at facilities where personnel are engaged in activities other than the hour by hour monitoring of the weather and/or at plants where it is required by law. The national Climatic Center ( NCC ) in Asheville, North Carolina utilizes a stability computation method which does not require special instruments but, rather, relies solely on the hourly weather observations made by meteorologists at National Weather Service ( NWS ) stations. Unstable conditions occur primarily during periods of strong surface heating and low wind speeds, and stable conditions occur only when the earth's heat is escaping to space ( high negative net radiation ) and winds are light. Also, neutral conditions can occur when it is cloudy and/or windy. The NCC method, then utilizes observations of cloud cover, made hourly by stations weather observer, coupled with the wind speed observed when the sky observation was made.

The data produced from the cloud cover and wind speed observations are referred to as STAR ( for STability ARray ) data. Historical STAR data are extremely useful because they can be obtained quickly from the NCC and they are inexpensive.

Brookhaven National Laboratory (BNL) scheme depends entirely on horizontal wind direction fluctuations. This system will not work if a definite relationship between horizontal fluctuation and vertical fluctuation does not exist at a site.

The classification are as follows:

Type A   : Fluctuations ( peak to peak ) of the horizontal wind direction exceeding 90^o ( Extremely Unstable )

Type B2 : Fluctuations ranging from 40^o - 90^o

Type B1 : Fluctuations similar to A and B2, but confined to 15o and 45^o limits ( Unstable )

Type C   : Fluctuations greater than 15^o distinguished by the unbroken solid core of the trace ( Neutral )

Type D   : The trace approximates a line; short - term fluctuations do not exceed 15^o ( Stable )

Note : Fluctuations are recorded over a 1 hr. period.

The atmospheric stability can be determined using the standard deviation of elevation angle (phi) of the vertical wind direction. Sigma phi is a good indicator of the scale and intensity of the vertical motions of the atmosphere. The disadvantage of the method is that it requires a highly dedicated maintenance program to assure proper calibration of the system.

In this method, sigma phi is indirectly calculated using the standard deviation of the vertical wind speed (sigma omega) and the average horizontal wind speed. This approach reduces the maintenance requirements of the sigma phi method.

The standard deviation of horizontal wind direction is an atmospheric stability classification system recommended by the Nuclear Regulatory Commission. The limits of sigma theta as given in Regulatory Guide 1.23 are given in the following table.

Modified Sigma Theta Method:

Mitchell and Timbre (1979) attempted to modify the NRC sigma theta method (MST) in order to account for lack of insolation during nighttime. The definition for nighttime was: one hour before sunset to one hour after sunrise. According to MST scheme, if stability class based on sigma theta at night is neutral (D) or stable (E,F,G), the stability class is based directly on sigma theta. If it is unstable (A,B,C), the observed wind speed and corresponding stability class are located in the following table and the associated stability class applicable to sigma z is identified. The MST method involves correction factors for plume meander that occur under low wind speed and nighttime conditions.

NRC Temperature Difference Method:

NRC Regulatory Guide 1.23 indicates the use of temperature differences with height for computing standard deviations of the plume. This method relates a set of ranges of temperature lapse rates (^oC/100m) to the Pasquill-Gifford classes.

Sedefian and Bennett (1980) suggested the use of wind speed ratio (U_R) for defining the atmospheric stability. The relationship between stability and U_R is shown below.

Four different atmospheric stability indicators have been examined by Scott-Waslikand & Kumar (1982) for their potential use in a radio nuclide dispersion model at a nuclear power plant.

The schemes are:

    NRC Temperature Difference Method

    NRC Sigma Theta Method

    Modified Sigma Theta (MST) Method

    Wind Speed Ratio Method

The other four schemes were not studied because sufficient meteorological data were unavailable. Inconsistencies were observed between the four schemes for the seven stability classes. The results of this analysis indicate:

The temperature difference and sigma theta methods do not correlate well in the determination of atmospheric stability. However, the two values were within one stability class of each other more than 80% of the time.

In its present form, the wind speed ratio method cannot be used for determination of atmospheric stability at the two coastal nuclear power plants that were examined.

Modified sigma theta (MST) is a small improvement over the conventional sigma theta method. However, MST is still not an acceptable substitute for the temperature difference method in the determination of atmospheric stability.

Thermal boundary Layer (TBL) development and maintenance depends on two factors: (i) convectively produced turbulence caused by solar heating of the surface and internal redistribution of heat under the cap of the stable layer, and (ii) mechanically produced turbulence originating from the vertical wind speed shear and the surface roughness. The figure given below shows the various physical processes involved in the TBL growth.

Traditionally, two distinct approaches have been taken to predict the development of the thermal boundary layer: (i) theoretical approach and (ii) experimental studies.

Experimental studies usually involve the determination of temperature profiles with time of day using direct or indirect (remote) sensing techniques. Direct sensing devices such as mini-sondes or thermocouples are used to record temperature variation with height while indirect methods may involve surface-based remote sensors such as acoustic radar to detect the TBL height.

The theoretical approach may be classified into three groups:

Empirical formulae,

Analytical solutions,

Numerical models

One layer models,

Higher order closure models.

The prediction of the boundary layer height (H) as a function of time of day and time of year is based on the solution of the appropriate conservation equations relating both the heat flux and the temperature jump across the inversion layer to the height of the TBL.

A comparison between calculated (using the analytical model) and observed TBL heights is shown in figure below. The TBL heights were obtained from minisonde data using single theodolite or double theodolite.

The TBL heights depends on time of year and time of day. This is evident from the heat flux profiles given in the following figure.

EFFECTS OF METEOROLOGY ON PLUME DISPERSION

Meteorology plays an important role in the dispersion of effluents. Various meteorological factors affect the dispersion of emission into the atmosphere in a variety of ways. One of the most important meteorological variables responsible for high ground level concentrations is the height of thermal boundary layer (or mixing height).

The following figure shows different situations of plume mixing in the atmosphere as a result of the development of the thermal boundary layer during a typical day. The figure shows that at 9 AM convective eddies pull the pollutant to the ground. The spread of the plume is also restricted in vertical due to the thermal boundary height at this time.

 For a small project on Plume Behavior and Dispersion go to

"http://gunsmoke.ecn.purdue.edu/~wenning/project/"

Wind velocity is an important variable in the study of transport of air pollutants from a source. Considerable efforts have been spent to measure wind velocity and to develop equations for computing wind speed. A power law profile is generally used to describe the variation of wind speed with height in the surface boundary layer.

where U₁ is the velocity at z₁ (usually 10 m) and U is the velocity at height z. The values of p are given in the following table.

BEAUFORT SCALE

The scale is helpful in getting an idea on the magnitude of wind speed from real life observations.

WIND ROSE

Wind Rose diagram provides a graphical summary of the frequency distribution of wind direction and wind speed over an extended period of time. The following procedure is followed to develop a wind rose from hourly observations.

Group all winds of a given direction together using the table given below:

Find the number of readings in each directional category and the total number of readings. Then find the percentage that each of the 16 wind directions occurs.

For each wind direction, group the readings into wind speed categories. For example, use ranges of 3 miles/hour , i.e. calm, 1-3 mph, 4-6 mph, 7-10 mph etc.

For each wind direction, find the percentage of readings in each speed range.

On polar coordinate paper, label each of the 16 wind directions

Plot each wind direction percentage from Step II making the length of each line proportional to its corresponding percentage.

For each wind direction line plotted, divide into wind speed categories using the percentages calculated in Step III (2). Put the lowest         speed category (i.e. 1-3 mph) closest to the center of the graph, or,

Put the percentage of calm winds (i.e. 0 mph) in the center circle of the graph.

For each wind direction, find the mean wind speed

Plot each mean wind speed adjacent to the line plotted in Step IV(2) using an appropriate scale.

Click here to see the polar diagram.

Draw a wind rose showing both directional frequencies and wind speed frequencies from 3 hourly observations for a one week period for Toledo airport given in the following table.

The observations were taken in December 1982 and are obtained from Local Climatological Data sheet for Toledo.

Note:

WIND DIRECTION:	DIRECTIONS ARE THOSE FROM WHICH THE WIND BLOWS, INDICATED IN TENS OF DEGREES FROM TRUE NORTH: I.E., 09 FOR EAST, 18 FOR SOUTH, 27 FOR WEST. AN ENTRY OF 00 INDICATES CALM.
MPH = KNOTS x 1.151

DETERMINATION OF MAXIMUM MIXING HEIGHT

The following steps can be used to determine the maximum mixing height for a day from a temperature profile:

Plot the temperature profile, if needed.

Plot the maximum surface temperature for the day on the graph for morning temperature profile.

Draw a dry adiabatic line (-1^oC/100m) from the point of maximum surface temperature to the point where it interests the morning temperature profile.

Read the corresponding height above ground at the point of intersection obtained in step 2. This is the maximum mixing height for the day.

Problem: Find the maximum mixing height for the day shown in the figure given below. The maximum surface temperature for the day was 22^oC.

METEOROLOGICAL DATA

Air pollution studies require data on wind speed, wind direction, mixing height, atmospheric stability and other meteorological variables. In the US, the data are available from NOAA (http://www.fsl.noaa.gov/) and the USEPA (www.epa.gov).

QUESTIONS

1. What term is used by meteorologists to describe the temperature change in the atmosphere that occurs with increasing height?

2. What is the lapse rate that is the dividing line between stable and unstable atmospheric conditions?

3. What type plume from an elevated source produces highest ground level concentration of pollutant?

4. What type graphical display is used to estimate the stability of the atmosphere?

5. Describe the inversion condition and how it may effect air pollution from a tall stack.

6. What are the three general methods that can be used to maximize the dilution capacity of the atmosphere?

7. What are the three most important meteorological variables to be measured for air pollution work?

1. The ground level wind velocity at 10 m elevation is 5.2 m/sec in a city. What would you estimate the velocity to be at 125m elevation in moderately stable atmosphere.

2. If a parcel, initially at -27 ^oC at some level in the atmosphere, is heated dry adiabatically in descending to the 1000 mb pressure level to +15 ^oC , what is the parcel's potential temperature.

3. Calculate the potential temperature for the following cases:
 

4. The wind speed is 1m/s at a height of 10m. Estimate the wind speed at heights of (a) 83m, and (b) 183m for the six stability conditions used in air quality models for a rural area.

5. Plot the temperature variation for a day during this year (or last year). You can use information from weather service.

6. What is the atmospheric stability for the standard deviation of horizontal wind direction: (a) 35^o, (b) 15^o, (c) 20^o, (d) 10^o, (e) 5^o and (f) 1^o.

7. During a field program carried by a utility in Ohio, the atmospheric lapse rate on July 29, 1990 was found constant up to 1200 m. The pressure (Po) is 1067 mbar and the temperature (To) is 21 ^oC at ground level . A radiosonde measurement indicates that at some elevation z the pressure and temperature are 890 mbar and 9.5 ^oC respectively. Determine:

• the atmospheric temperature gradient dT/dz in degree Kelvin per meter
• the elevation of the observation.

9. During a dispersion study the lapse rate was constant at 1.3^oC per 100 m. If the atmosphere is assumes to behave as a perfect gas, at what altitude was the pressure one-fifth the sea level. The sea level temperature and pressure were 18^oC and 1 atm respectively.

10. Determine whether the atmosphere is unstable, neutral or stable for the following case.
 

Initial Temperature	30.2 oC
Final Temperature	- 58.5 oC
Initial Height	221 m
Final Height	23214 m

11. Calculate the maximum mixing height from the following early morning temperature data given below:
 

Height (m)	0	250	350	450	550	650
Temperature (oC)	9.5	12.2	15.1	15.6	16.2	16.5

The maximum surface temperature for the day was 15^oC.

References:

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