Download - Chapter 5 . Air Pollution Meteorology

Chapter 5. Air Pollution Meteorology

Selami DEMİRAsst. Prof.

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Outline Introduction Solar Radiation Atmospheric Pressure Lapse rate & Potential Temperature Atmospheric Stability Coriolis Force & Gravitational Force Pressure Gradient Force Overall Atmospheric Motion Equations of Motion Wind Speed Profile

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Introduction (1/2)

Air pollutant cycle Emission Transport, diffusion, and transformation Deposition Re-insertion

In large urban areas, there are several concentrated pollutant sources All sources contribute to pollution at any specific site Determined by mainly meteorological conditions Dispersion patterns must be established Need for mathematical models and meteorological input data

for models

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Introduction (2/2)

Three dominant dispersion mechanisms General mean air motion that transport pollutants downwind Turbulent velocity fluctuations that disperse pollutants in all

directions Diffusion due to concentration gradients

This chapter is devoted to meteorological fundamentals for air pollution modelling

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Solar Radiation (1/6)

Solar constant 8.16 J/cm2.min 0.4-0.8 µ visible range, maximum intensity

Ref: http://www.globalwarmingart.com/images/4/4c/Solar_Spectrum.png

http://www.globalwarmingart.com/images/4/4c/Solar_Spectrum.png

http://www.globalwarmingart.com/images/4/4c/Solar_Spectrum.png

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Distribution of solar energy on earth

Ref: OpenLearn Web Site, http://openlearn.open.ac.uk/file.php/1697/t206b1c01f26.jpg

http://openlearn.open.ac.uk/file.php/1697/t206b1c01f26.jpg

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At right angle on June, 21 Tropic of cancer At right angle on December, 21 Tropic of capricorn At right angle on March, 21 and september, 21 Equator

http://upload.wikimedia.org/wikipedia/commons/8/84/Earth-lighting-equinox_EN.png

http://upload.wikimedia.org/wikipedia/commons/8/84/Earth-lighting-equinox_EN.png

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Example: What is the Sun’s angle over Istanbul on June, 21? Note that Istanbul is located on 40° N latitude.

Solution: Sunlight reaches Tropic of Cancer (23° 27′) at right angle on June, 21.

Where θ = Sun’s angle at the given latitudeL2 = Latitude of given region

L1 = Latitude of region where sunlight reaches surface at right angle

1290 LL

'' 277327234090

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Example: What is the Sun’s angle over a city located on 39° N latitude when the sunlight reaches surface at right angle on 21° S latitude?

Solution:

30213990

90 12

LL

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Homework (due 18.04.2008) Make a brief research on Stefan-Boltzman Law and write a one

page report for your research. Comment on what would happen if earth’s inclination were 24°

instead of 23°27′. What determines the seasons? Why some regions of earth get

warmer than other regions. Calculate the sunlight angle over Istanbul

on March, 21 on June, 21 on September, 21 on December, 21

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Atmospheric Pressure (1/4)

Force on earth surface due to the weight of the atmosphere Defined as force exerted per unit surface area Units of measurement Pascal (Pa), atmospheric pressure

unit (apu, atm), newtons per meter-squared (N/m2), water column (m H2O), etc. 1 atm = 101325 Pa 1 atm = 10.33 m H2O 1 atm = 760 mm Hg 1 Pa = 1 N/m2

Atmospheric pressure at sea level is 1 atm

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Consider a stationary air parcel as shown Force balance (assuming no horizontal

pressure gradient)

gdhdP

ghPg

hP

hgPhgAhAgVgmgPA

mgPAAPP

GAPPAPFF

hh

Net

00limlim

0

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Integrating from h = z0 to h = z produces

00 exp

;

00

zzgRTMzPzP

gdhRTM

PdP

gdhRTM

PdPg

RTPM

dhdP

RTPMg

dhdP

A

z

z

A

zP

zP

AA

A

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Homework (due 18.04.2008) Make a research about pressure measurement devices and

prepare a one-page report for your research. Give brief explanations for each type.

Calculate the atmospheric pressure on top of Everest if it is 1013 mb at sea level.

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Lapse Rate & Potential Temperature (1/5)

Adiabatic no heat exchange with surroundings

Consider an air parcel moving upward so rapidly that it experiences no heat exchange with surrounding atmosphere

Enthalpy change:where

H1 = initial enthalpy of air parcelH2 = final enthalpy of air parcel

U1 = initial internal energyU2 = final internal energy

V1 = initial volume

V2 = final volume

12 HHH

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Enthalpy change is a function of only temperature when pressure is constant

Substituting differential pressure as follows:

Since the process is adiabatic, no heat exchange occurs


By enthalpy’s definition

In infinitesimal expression

Internal energy substitution

By internal energy definition

pVUH

pVUpVUH

12

pdVVdpdUpVddUdH

pdVVdpWQddH

VdpdQpdVVdppdVdQdH

dTCVdpdQdH p

dTCgVdhdQ p

mC

CgV

dhdT

dTCgVdh

p

p

10098.0

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This approximation assumed there is no phase change in the air parcel called Dry Adiabatic Lapse Rate (DALR)

If any phase change takes place during the motion, the temperature change will be far more different from DALR Called Saturated (Wet) Adiabatic Lapse Rate (SALR, WALR) Variable, must be calculated for each case Also significant in some cases; this course does not focus on it

For standardization purposes, Standard Lapse Rate (SLR), also known as Normal Lapse Rate (NLR), has been defined On average, in middle latitude, temperature changes from 1°C

to -56.7°C SLR = -0.66°C/100 m

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Lapse rate measurements are taken by a device called Radiosonde Results of measurements are plotted to obtain Environmental

Lapse Rate (ELR) ELR is real atmospheric lapse rate Another significant concept is Potential Temperature

Defined as possible ground level temperature of an air parcel at a given altitude

HDALRTTp * whereθ = Tp = potential temperature of air parcelT = Temperature of air parcelH = Height of air parcel from groundDALR = Dry adiabatic lapse rate

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Homework (due 18.04.2008) Calculate potential temperature for given data

Calculate the atmospheric temperature at 800 m from the ground if the atmosphere shows adiabatic characteristic and the ground level temperature is 12°C.

Height, m Temperature, °C

350 8

750 2

1200 14

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Atmospheric Stability (1/8)

If ELR < DALR Then Superadiabatic meaning unstable

ElseIf ELR = DALR Then Neutral

ElseIf DALR < ELR < 0 Then Subadiabatic meaning stable (weakly stable)

ElseIf DALR < 0 < ELR Then Inversion meaning strongly stable

EndIf

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Superadiabatic

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Neutral

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Subadiabatic

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Inversion

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If dθ/dz < 0 Then Superadiabatic

ElseIf dθ/dz = 0 Then Neutral

ElseIf dθ/dz > 0 Then Subadiabatic

EndIf

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Example: Calculate vertical temperature gradient and comment on atmospheric stability condition if the atmospheric temperature at 835 m is 12 °C when the ground temperature is 25 °C.

Solution:

The atmosphere is said to be unstable since ELR < DALR m

CmC

mC

zTT

dzdTELR groundaloft

10056.10156.0

08352512

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Homework (due 25.04.2008) Following measurements are taken over Istanbul at different

times. Determine atmospheric stability condition for each case.

Briefly explain stable air, unstable air, neutral air and inversion. Make a brief research about the role of atmospheric stability in

dispersion of pollutants in the atmosphere and prepare a-one-page report for your research.

What is conditional stability? Explain.

Height, m

Temperature, °C

Case 1 Case 2 Case 3 Case 4

0 14 22 17 4

1000 8 8 7 6

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Coriolis Force

“The Coriolis effect is an apparent deflection of moving objects from a straight path when they are viewed from a rotating frame of reference. Coriolis effect is caused by the Coriolis force, which appears in the equation of motion of an object in a rotating frame of reference.” (Wikipedia Web Site, http://en.wikipedia.org/wiki/Coriolis_Force)

xvm

Ff

xvmF

Corioliscoriolis

Coriolis

2

2

http://en.wikipedia.org/wiki/Coriolis_Force

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Gravitational Force (1/3)

The force exerted by the earth on an object in earth’s attraction range

Caused by attraction forces between two masses

m1 being the mass of earth (M) and m2 is that of an object near earth surface

321

rrmmFA

FA = attraction forceγ = 6.668*10-11 Nm2/kg2

m1,m2 = objects’ massesr = distance bw masses

kgNf

rrM

mFf

rrMmF

G

GGG

81.9

33

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Example: Determine the acceleration of an object near the Erath’s surface due to gravitational attraction force

Solution:

2

3

242

211

3

sec85.9

11000*6360*

11000*6360

10*9736.5*10*668.6

mf

kmmkm

kmmkm

kgkgNm

rrMf

G

G

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Homework (due 25.04.2008) Determine the acceleration of an object near the Martian surface

due to gravitational attraction force Determine the acceleration of an object near the Moon’s surface

due to gravitational attraction force

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Pressure Gradient Force

Consider an air parcel accelerating in a horizontal direction

In three dimensional representation,

xPf

xP

VPA

mPA

mF

f

PAF

APPPAFF

X

X

X

X

P

PP

P

Net

1

zPf

yPf

Z

Y

P

P

1

1

PfP

1

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Overall Atmospheric Motion (1/7)

Consider an air parsel accelerating around the Earth Overall acceleration

fxdtfd

dtfdNote

ar

rMPa

aaaa

rotatingfixed

fNet

fGPGNet

:

13

rxxVxdtVd

dtVda

rotatingfixedfixedNet

2

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Neglecting vertical terms and re-arranging, we get

SinfxP

fv

yP

fu

jxP

fi

yP

fV

2

1

1

11

u = velocity of atmospheric motion in east-west direction

v = velocity of atmospheric motion in north-south direction

Ω = rotational speed of earth = 7.29*10-5 r/s

Φ = latitude on which the motion occurs

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Example: Briefly explain the mechanisms that forced radioactive pollutants towards Turkey’s coasts after Chernobyl. Tell about the meteorological conditions then. Show the pressure centers and wind patterns on the day of accident and two day after the accident on a brief map. Consider the aspects of geostrophic winds.

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Solution

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Example: Isobars are shown in the figure below, for 40° latitude in the Northern Hemisphere, at an altitude of 5600 meters. Determine the geostrophic wind speed in km/hour

Temperature at 5600 m : -28°C Coriolis force: 2 Ω V sin β Ω= 7.3 x 10-5 radians/s; β= Latitude degrees ; V= geostrophic

wind speed 1 mb = 100 N/m3

180 km

500 mb

504 mb

N

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Example:Suppose a nuclear accident occurs at a place of 3,000 km west of Istanbul. Radioactive pollutants are pumped above the planetary boundary layer (PBL) with the power of explosion. On the day of nuclear accident, the radiosonde data taken at different places of Europe shows that atmospheric pressure is decreasing towards north at a rate of 0.0015 N/m3 and this pattern is valid for the whole Europe. Will the radioactivity affect Istanbul? If yes, when? Note that Istanbul is located on 40° northern latitude and world’s angular speed of rotation is 7.3 * 10-5 radians/sec. You may assume the density of air at the level where geostrophic wind equations apply as 0.70 kg/m3.

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Solution

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Equations of Motion (1/3)

Eularian Approach The observer stays stationary and observes the change in the

value of a function f (concentration, atmospheric parameters, etc.)

The coordinate system (reference frame) is stationary The objective is moving

Lagregian Approach The observer moves with the moving objective and observes

the change in the value of a function f The coordinate system is moving with the objective at the same

speed and direction

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Lagregian Approach (cont’d)

wzfv

yfu

xf

tf

dtdf

dtdy

zf

dtdy

yf

dtdy

xf

tf

dtdf

fVdttfdf

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Examples will be given later…

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Wind Speed Profile (1/2)

Due to friction near surface, wind speed increases with height exponentially

Wind speed is measured by a device called anemometer 10 m should be chosen for anemometer height

pzmuzu

10

10 Stability Class P

A 0.15

B 0.15

C 0.20

D 0.25

E 0.40

F 0.60

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Wind Speed Profile (2/2)

Homework (due 25.08.2008) Calculate wind speeds for Class B stability at 20, 30, 50, 100,

200, and 500 m if it is 1.2 m/sec. Plot the results. Comment on how the wind speed would change with altitude if

the stability class were Class E.

Download - Chapter 5 . Air Pollution Meteorology

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