# BASIC METEOROLOGICAL PROCESSES

Mechanics

Oct 27, 2013 (4 years and 8 months ago)

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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.

A
IR

P
OLLUTION

M
ETEOROLOGY

Atmospheric thermodynamics

Atmospheric stability

Boundary layer development

Effect of meteorology on plume dispersion

A
TMOSPHERE

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

A
TMOSPHERIC

T
HERMODYNAMICS

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/cm
3

ML
-
3

Pressure (Force/Area)

N/m
2
( P
a
)

ML
-
1
T
-
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

E
QUATION

OF

S
TATE

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 /
o
K

R for water vapor = 0.461 Joules / gm /
o
K

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
o
F. Gas constant, R = 0.7302 ft
3
atm/lb
-
mole
o
R.

Solution

Absolute Temperature = 80
o
F + 460 = 540
o
R

Density = P ( molecular weight) / RT

Density = ( 1atm. )*(29 lb/lb mole) / ( 0.7302 ft
3
atm/lb
-
mole
o
R)*(540
o
R)

Density = 0.073546 lb/ ft
3
.

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

L
AWS

OF

T
HERMODYNAMICS

First 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"

S
PECIFIC

H
EAT

Defined as the amount of heat needed to change the
temperature of unit mass by 1
o
K.

Specific heat at constant volume

C
v
= lim
δQ

δT

0 δT
α = const

Specific heat at constant pressure

C
p
= lim
δQ

δT

0 δT
p = const

Relationship between C
v
and C
p
is given by Carnot’s law:

For perfect gas, C
p

C
v
= R

For dry air C
p

= (7/2)*R (Perfect diatomic gas)

C
v
= (5/2)*R (Perfect diatomic gas)

Ratio of C
p

and C
v

for dry air is 1.4

C
pd

= 1.003 joules/gm/
o

K ;
C
vd

= 0.717 joules/gm/
o

K

P
ROCESSES

IN

THE

A
TMOSPHERE

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)

δQ = 0

removed )

The adiabatic law is P. α
γ
= constant

E =

S
TATICS

OF

THE

A
TMOSPHERE

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:

S
TATICS

OF

THE

A
TMOSPHERE

Integration of the above equation gives

Using the initial condition Z=0, P = P
0

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.

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.

C
ONCEPT

OF

P
OTENTIAL

T
EMPERATURE

θ

A
TMOSPHERE

S
TABILITY

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
.

A
TMOSPHERIC

S
TABILITY

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).

A
TMOSPHERIC

S
TABILITY

Atmospheric stability can be determined using adiabatic
lapse rate.

Γ >
Γ
d

Unstable

Γ = Γ
d

Neutral

Γ <
Γ
d

Stable

Γ is environmental lapse rate

Γ
d

is dry adiabatic lapse rate (1
0
c/100m) and
dT
/
dZ

=
-
1
0
c /100 m

A
TMOSPHERIC

S
TABILITY

C
LASSIFICATION

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 (U
R
) Method

AERMOD Method (Stable and Convective cases)

P
ASQUILL
-
GIFFORD

S
TABILITY

C
ATEGORIES

Surface Wind

Speed (m/s
)

Daytime Insolation

Nighttime cloud
cover

Strong

Moderate

Slight

Thinly
overcast or 4/8
low cloud

3/8

< 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

S
IGMA

T
HETA

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

G

2.1>ST

Source: Atmospheric Stability

Methods & Measurements (NUMUG
-

Oct 2003)

T
EMPERATURE

D
IFFERENCE

(∆T)

Source: Regulatory guide; office of nuclear regulatory research
-

Table 1

T
URBULENCE

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

L
OCAL

CLIMATOLOGICAL
DATA

-

T
OLEDO

W
EATHER

CONDITIONS

OF

TOLEDO

Weather Station

Home, Professional, and Live

Weather Balloon

Pressure, Temperature, Wind Speed, Wind Direction, &
Humidity

Use of Towers

Velocity, Temperature, & Turbulence

L
OCAL

CLIMATOLOGICAL
DATA

-

T
OLEDO

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”

D散emb敲

9.1”

January

9.8”

䙥Fruary

8.0”

䵡r捨

6.3”

Snowfall

Annual

49.6
°
F

January

25.7
°
F

July

73.2
°
F

Temperature

Annual

31.62”

䩡nuary

2.18”

䩵ne

3.45”

Precipitation

National Weather Map

US Forecast

National Air Quality

Ozone

Climate

Temperature

N
ATIONAL

W
EATHER

M
AP

H

High Pressure Area

L

Low Pressure Area

A high pressure area forecasts clear skies.

A low pressure area forecasts cloudiness and precipitation

B
OUNDARY

L
AYER

D
EVELOPMENT

B
OUNDARY

L
AYER

D
EVELOPMENT

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

B
OUNDARY

L
AYER

D
EVELOPMENT

Theoretical approach may be classified into three
groups:

Empirical formulae

Analytical solutions

Numerical models

One layer models

Higher order closure models

TBL
USING

A
NALYTICAL

S
OLUTION

Time

Time

Time

Time

E
FFECTS

OF

M
ETEOROLOGY

ON

P
LUME

D
ISPERSION

E
FFECTS

OF

M
ETEOROLOGY

ON

P
LUME

D
ISPERSION

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

W
IND

V
ELOCITY

A power law profile is used to describe the variation of
wind speed with height in the surface boundary layer

U = U
1
(Z/Z
1
)
p

Where,

U
1

is the velocity at Z
1

(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

B
EAUFORT

S
CALE

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

Atmospheric

condition

Wind speed

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

W
IND

R
OSE

D
IAGRAM

(WRD)

Wind Direction (%)

Wind Speed (mph)

W
IND

R
OSE

D
IAGRAM

(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,
-----------

D
ETERMINATION

OF

M
AXIMUM

M
IXING

H
EIGHT

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

D
ETERMINATION

OF

M
AXIMUM

M
IXING

H
EIGHT

P
OWER

PLANT

P
LUMES

IN

M
ICHIGAN

Monroe Power Plant

P
OWER

PLANT

P
LUMES

IN

M
ICHIGAN

Trenton Channel

P
OWER

PLANT

P
LUMES

IN

M
ICHIGAN

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?

S
OLUTION

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

R
EFERENCES

Met Monitoring Guide:
http://www.webmet.com/met_monitoring/toc.html

Regulatory Guide

office of nuclear regulatory research:

-
rm/doc
-
collections/reg
-
guides/power
-
reactors/active/01
-
023/01
-
023r1.pdf

NOAA
-
National Climate Data Center