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