BASIC METEOROLOGICAL PROCESSES

Objectives What is atmospheric thermodynamics? What are the variables of atmospheric thermodynamics? What is lapse rate? Explain the potential temperature. What is atmospheric stability and the various methods that

define atmospheric stability? What is boundary layer development? What are the effects of meteorology on plume dispersion? What is wind velocity profile? What is wind rose diagram and what are the uses of it? Determination of mixing height.

AIR POLLUTION METEOROLOGY Atmospheric thermodynamics

Atmospheric stability

Boundary layer development

Effect of meteorology on plume dispersion

ATMOSPHERE Pollution cloud is interpreted by the chemical

composition and physical characteristics of the atmosphere

Concentration of gases in the atmosphere 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.

Four major layers of earth’s atmosphere are: Troposphere Stratosphere Mesosphere Thermosphere

ATMOSPHERIC THERMODYNAMICS A parcel of air is defined using the state variables Three important state variables are density, pressure

and temperature The units and dimensions for the state variables are

Density(mass/volume)

gm/cm3 ML-3

Pressure (Force/Area) N/m2 ( Pa ) ML-1T-2

Temperature o F, o R, o C, o K T

Humidity is the fourth important variable that gives the amount of water vapor present in a sample of moist air

EQUATION OF STATE Relationship between the three state variables may be

written as: f ( P, ρ ,T) = 0

For a perfect gas: P = ρ .R .T

R is Specific gas constant R for dry air = 0.287 Joules / gm /oK R for water vapor = 0.461 Joules / gm /oK R for wet air is not constant and depend on mixing ratio

Exercise

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-moleoR.

Solution

Absolute Temperature = 80 oF + 460 = 540 oR

Density = P ( molecular weight) / RT Density = ( 1atm. )*(29 lb/lb mole) / ( 0.7302 ft3atm/lb-moleoR)*(540

oR)

Density = 0.073546 lb/ ft3.

Exercise

Determine the pressure, both absolute and gauge, exerted at the bottom of the column of liquid 1 meter high, with density of 1000 kg / m3.

Solution

Step 1 :

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

Step 2 : Pabsolute = Pgauge + Patmospheric

Pabsolute = 111.11 kPa

LAWS OF THERMODYNAMICSFirst Law of Thermodynamics: This law is based on law of conservation of total energy. Heat added per unit mass = (Change in internal energy per unit mass)

+ (Work done by a unit mass) δH = δU+δW

Second Law of Thermodynamics: This 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 HEAT Defined as the amount of heat needed to change the

temperature of unit mass by 1oK.

Specific heat at constant volume

Cv = lim δQ δT→0 δT α = const

Specific heat at constant pressure

Cp = lim δQ δT→0 δT p = const

Relationship between Cv and Cp is given by Carnot’s law:

For perfect gas, Cp – Cv = R For dry air Cp = (7/2)*R (Perfect diatomic gas)

Cv = (5/2)*R (Perfect diatomic gas) Ratio of Cp and Cv for dry air is 1.4

Cpd = 1.003 joules/gm/o K ; Cvd = 0.717 joules/gm/o K

PROCESSES IN THE ATMOSPHERE An air parcel follows several different paths when it

moves from one point to another point in the atmosphere. These are:

Isobaric change – constant pressure Isosteric change – constant volume Isothermal change – constant temperature Isentropic change – constant entropy (E) Adiabatic Process – δQ = 0 (no heat is added or

removed )

The adiabatic law is P. αγ = constant E =

T

Q

STATICS OF THE ATMOSPHERE Vertical variation of the parameters = ?

Hydrostatic Equation: Pressure variation in a "motionless" atmosphere

Pressure variation in an atmosphere:

Relationship between pressure and elevation using gas law:

gz

porg

z

p

1

.

2

21

dt

zd

z

pg

TR

g

z

p

p d

1

STATICS OF THE ATMOSPHERE Integration of the above equation gives

Using the initial condition Z=0, P = P0

The above equation indicates that the variation of pressure depends on vertical profile of temperature.

For iso-thermal atmosphere

Therefore, pressure decreases exponentially with height at a ratio of 12.24 mb per 100m.

zT

R

g

p

po

do

.exp 1

z

do

dzTR

g

p

p

0

1.ln

Lapse Rate: Lapse rate is the rate of change of temperature with

height Lapse rate is defined as Γ = -δT δz Value of Γ varies throughout the atmosphere

Potential Temperature: Concept of potential temperature is useful in comparing two air

parcels at same temperatures and different pressures.

CONCEPT OF POTENTIAL TEMPERATURE

θ

ATMOSPHERE STABILITY The ability of the atmosphere to enhance or to resist

atmospheric motions

Influences the vertical movement of air.

If the air parcels tend to sink back to their initial level after the lifting exerted on them stops, the atmosphere is stable.

If the air parcels tend to rise vertically on their own, even when the lifting exerted on them stops, the atmosphere is unstable.

If the air parcels tend to remain where they are after lifting stops, the atmosphere is neutral.

ATMOSPHERIC STABILITY The stability depends on the ratio of suppression to

generation of turbulence

The stability at any given time will depend upon static stability ( related to change in temperature with height ), thermal turbulence ( caused by solar heating ), and mechanical turbulence (a function of wind speed and surface roughness).

ATMOSPHERIC STABILITY Atmospheric stability can be determined using adiabatic

lapse rate.

Γ > Γd Unstable

Γ = Γd Neutral

Γ < Γd Stable

Γ is environmental lapse rate Γd is dry adiabatic lapse rate (10c/100m) and dT/dZ = -10c /100 m

ATMOSPHERIC STABILITY CLASSIFICATION Schemes to define atmospheric stability are:

P- G Method P-G / NWS Method The STAR Method BNL Scheme Sigma Phi Method Sigma Omega Method Modified Sigma Theta Method NRC Temperature Difference Method Wind Speed ratio (UR) Method Radiation Index Method AERMOD Method (Stable and Convective cases)

PASQUILL-GIFFORD STABILITY CATEGORIES

Surface WindSpeed (m/s)

Daytime InsolationNighttime cloud

cover

StrongModerat

eSlight

Thinly overcast or

4/8 low cloud3/8

< 2 A  A - B B - -

2 - 3 A - B B C E F

3 - 5 B B - C C D E

5 - 6 C C - D D D D

> 6 C D D D D

Source: Met Monitoring Guide – Table 6.3

SIGMA THETA STABILITY CLASSIFICATION

CATEGORY PASQUILL CLASS SIGMA THETA (ST)

EXTREME UNSTABLE A ST>=22.5

MODERATE UNSTABLE B 22.5>ST>=17.5

SLIGHTLY UNSTABLE C 17.5>ST>=12.5

NEUTRAL D 12.5>ST>=7.5

SLIGHTLY STABLE E 7.5>ST>= 3.8

MODERATE STABLE F 3.8>ST>=2.1

EXTREMELY STABLE G2.1>ST

Source: Atmospheric Stability – Methods & Measurements (NUMUG - Oct 2003)

TEMPERATURE DIFFERENCE (∆T)

Source: Regulatory guide; office of nuclear regulatory research- Table 1

TURBULENCE Fluctuations in wind flow which have a frequency of

more than 2 cycles/ hr

Types of Turbulence Mechanical Turbulence Convective Turbulence Clear Air Turbulence Wake Turbulence

LOCAL CLIMATOLOGICAL DATA - TOLEDO

WEATHER CONDITIONS OF TOLEDO

Weather Station Home, Professional, and Live

Weather Balloon Pressure, Temperature, Wind Speed, Wind Direction, &

Humidity

Use of Towers Velocity, Temperature, & Turbulence

LOCAL CLIMATOLOGICAL DATA - TOLEDO

Greatest snowfall – 73.1” (1997-1998) Least snowfall – 6.0” (1889-1890) Average number of days with a tenth of an inch or more

snowfall – 27 days

Annual 38.3”

December 9.1”

January 9.8”

February 8.0”

March 6.3”

SnowfallAnnual 49.6°F

January 25.7°F

July 73.2°F

Temperature

Annual 31.62”

January 2.18”

June 3.45”

Precipitation

National Weather Map US Forecast

National Air Quality Ozone

Climate Temperature

NATIONAL WEATHER MAP

H – High Pressure AreaL – Low Pressure Area

•A high pressure area forecasts clear skies. •A low pressure area forecasts cloudiness and precipitation

BOUNDARY LAYER DEVELOPMENT

BOUNDARY LAYER DEVELOPMENT Thermal boundary Layer (TBL) development depends on

two factors: Convectively produced turbulence Mechanically produced turbulence

Development of TBL can be predicted by two distinct approaches:

Theoretical approach Experimental studies

BOUNDARY LAYER DEVELOPMENT Theoretical approach may be classified into three

groups: Empirical formulae Analytical solutions Numerical models

One layer models Higher order closure models

TBL USING ANALYTICAL SOLUTION

Time

Time

Time

Time

EFFECTS OF METEOROLOGY ON PLUME DISPERSION

EFFECTS OF METEOROLOGY ON PLUME DISPERSION Dispersion of emission into atmosphere depends on

various meteorological factors.

Height of thermal boundary layer is one of the important factors responsible for high ground level concentrations

At 9 AM pollutants are pulled to the ground by convective eddies

Spread of plume is restricted in vertical due to thermal boundary height at this time

WIND VELOCITY A power law profile is used to describe the variation of

wind speed with height in the surface boundary layer

U = U1 (Z/Z1)p

Where, U1 is the velocity at Z1 (usually 10 m)

U is the velocity at height Z.

The values of p are given in the following table.Stability Class Rural p Urban p

Very Unstable 0.07 0.15

Neutral 0.15 0.25

Very Stable 0.55 0.30

BEAUFORT SCALE This scale is helpful in getting an idea on the magnitude

of wind speed from real life observations

Atmosphericcondition Wind speed Comments

Calm < 1mph Smoke rises vertically

Light breeze 5 mph Wind felt on face

Gentle breeze 10 mph Leaves in constant motion

Strong 25 mph Large branches in motion

Violent storm 60 mph Wide spread damage

WIND ROSE DIAGRAM (WRD)

Wind Direction (%)Wind Speed (mph)

WIND ROSE DIAGRAM (WRD) WRD provides the graphical summary of the

frequency distribution of wind direction and wind speed over a period of time

Steps to develop a wind rose diagram from hourly observations are:

Analysis for wind direction Determination of frequency of wind in a given wind

direction Analysis for mean wind speed Preparation of polar diagram

Calculations for Wind Rose

% Frequency = Number of observations * 100/Total Number

of Observations

Direction: N, NNE, ------------------------,NNW, Calm

Wind speed: Calm, 1-3, 4-6, 7-10, -----------

DETERMINATION OF MAXIMUM MIXING HEIGHT Steps to determine the maximum mixing height for a

day are: Plot the temperature profile, if needed Plot the maximum surface temperature for the day

on the graph for morning temperature profile Draw dry adiabatic line from a point of maximum

surface temperature to a point where it intersects the morning temperature profile

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

DETERMINATION OF MAXIMUM MIXING HEIGHT

POWER PLANT PLUMES IN MICHIGAN

Monroe Power Plant

POWER PLANT PLUMES IN MICHIGAN

Trenton Channel

POWER PLANT PLUMES IN MICHIGAN

Belle River Power Plant

River Rouge Power Plant

Photo credit:  Kimberly M. Coburn

PROBLEMS

During an air pollution experiment the lapse rate was a constant at 1.1 °C per 100 m. If the atmosphere is assumed to behave as a perfect gas and the sea level temperature and pressure were 16 °C and 1 atm, at what altitude was the pressure one-third the sea level?

SOLUTION Step1:

Step 2:Calculate Temperature

Step 3:Substitute for temperature

Step 4:Integrate between P = 1 and P = 0.333, and between z = 0,

and z = z.

Z = 7817.13m

REFERENCES Met Monitoring Guide:

http://www.webmet.com/met_monitoring/toc.html Regulatory Guide – office of nuclear regulatory research:

http://www.nrc.gov/reading-rm/doc-collections/reg-guides/power-reactors/active/01-023/01-023r1.pdf NOAA-National Climate Data Center