Air Pollution (2) · Air Pollution (2) CVEN 301 Introduction to Environmental Engineering Fall 2012. Dr. Qi Ying. Department of Civil Engineering. Air pollution meteorology – ...

Air Pollution (2)

CVEN 301 Introduction to Environmental EngineeringFall 2012

Dr. Qi Ying

Department of Civil Engineering

Air pollution meteorology –Stability of the Atmosphere

Horizontal and Vertical Motion of air near the surface

Horizontal motion –usually driven by pressure gradient

Vertical motion –usually driven bybuoyancy force

The vertical airtemperature structuregreatly affects thethe vertical motion.

http://upload.wikimedia.org/wikipedia/en/5/54/LAKE_BREEZE.gif

Stability Concept

Stable – Resistance to small perturbation. Spontaneously restore to the original state

Unstable – Small perturbation of the system leads to positive feedback that further move the system away from the original state

stable

unstable

neutral

Dry Adiabatic Lapse Rate (Γ)

Consider an dry air parcel that is forced to move up or down from its original position.

This process can be approximated as a adiabatic process (no heat transfer between the parcel and the environment)

Using thermal dynamics, we can derive that temperature change of the air parcel with respect to height is ~ 9.8K/1000m (5.4F per 1000 ft)

9.8 /p

dT gK km

dz c

cp: heat capacity of air under constant pressure (J/kg.K)g: gravitation acceleration constant (m/s2)

Actual (Environmental) Temperature Profile

Land, wind, sun all influence the actual temperature profile in the atmosphere - the measured temperature profile is only rarely exactly at the adiabatic lapse rate

Stable Atmosphere

Parcel temperature < ambient temperature sink back to original position

Parcel temperature > ambient temperaturefloat back to original position

Dry air parcel originally at this location

- Dry adiabatic lapse rate = - 9.8 K/km(5.4F per 1000ft)

Heig

ht

above s

urf

ace (

km

)

Ambient temperature profile

Unstable Atmosphere

- Dry adiabatic lapse rate = - 9.8 K/km

Dry air parcel originally at this location

Parcel temperature > ambient temperature Will continue rise

Parcel temperature < ambient temperature Will continue sink

Heig

ht

above s

urf

ace (

km

)

Temperature Profiles and Atmospheric Stability Classes

unstable

stable

inversion

isothermal

Temperature

Heig

ht

neutral

A temperature inversioncan very effectively “trap”pollutants and lead to poor air quality

Mixing under Unstable Condition

Mixing will cause a redistribution of temperature and lead to a neutral temperature profile

Temperature

Heig

ht

Unstable temperature

Neutral temperature, dT/dz = -9.8K/km

Formation of Surface Inversion due to Radiative Cooling

Longwave radiation from the surface cools the surface.

The air just above the surface cools down first, followed by the layers of air above it

This cooling of air gradually creating a temperature inversion near surface.

Formation of Upper-level Inversion

Night hours

Temperature

Heig

ht

10pm

Before sunset

6pm

3am6am

Temperature

Heig

ht

5pmnoon

8am6am

Upper level inversion layer

Day hours

Formation of surface inversion Destruction of surface inversion

Night time surface inversion

Mixing height

Dry adiabatic laps rate

Effect of Upper inversion

The plume seems hit a “lid”

Plume from a stack

http://en.wikipedia.org/wiki/Image:Sha1993_smog_wkpd.jpg

GAUSSIAN DISPERSION MODELING

Plume from Stacks

Tasks

Predict pollutant concentration downwind of a plume from a stack under different atmospheric stability conditions

Determine the maximum ground level pollutant concentrations from the plume

Estimate pollutant concentration downwind of a freeway section

Estimate exposure to pollutant due to an accidental release

Instantaneous and Time-averaged Plume

At any given time, the plume looks rather turbulent and does not have a well defined shape

However, under steady wind condition and averaged over sufficient time, the plume shows well defined shape

Plume photographs (a) instantaneous 1/50s exposure, (b) 5-min time exposure (Slade, 1968) – Walton J.C. (2008)

Pollutant Concentration Profile

Gaussian Distribution of Pollutant Concentration

Time-averaged pollutant concentration follows Gaussian distribution:

2

2

1( ) exp

22

: Plume spread

yC y

0

Distance away from the center

Polluta

nt

Concentr

ation

Gaussian Plume

Under proper assumptions, the time-averaged, steady-state pollutant concentration in a plume vertical cross section (A-A) can be described by a two-variable Gaussian distribution function:

A-A cross section

A

A

x

yz

y

z

2 2

2 2

2 2

2 2

1 1( , , ) exp exp

2 22 2

exp exp2 2 2

y zy z

y z y z

E y zC x y z

U S SS S

E y z

S S U S S

C(x,y,z) = pollutant concentration at (x,y,z) (kg/m3)E = pollutant emission rate (kg/s)U = wind speed at plume center line (m/s)Sy = horizontal plume spread parameter (m)Sz = vertical plume spread parameter (m)

Y direction Gaussian Dist.

Z direction Gaussian Dist.

SySz

(0,0)

Plume center line

More about Sy and Sz

Called “plume spread parameter”

Function of downwind distance (x)

The further downwind, the greater the spread parameter values

Function of atmospheric stability

The more unstable the larger the parameter values

Sz usually smaller than Sy

Vertical Cross Section of a Gaussian Plume

Rela

tive c

oncentr

ation

2 2

0 2 2( , , ) ~ exp exp

2 2y z

y zC x y z

S S

Sy=100 mSz=30 m

Top View (Cross Center Line) of Gaussian Plume

Distance downwind

A

A

A-A

2

2( , ,0) exp

2 2y z y

E yC x y

S S U S

Consider Stack Height

A simple coordinate transformation yields

22

2 2( , , ) exp exp

2 2 2y z y z

z HE yC x y z

S S U S S

x

y

z

U

H

(0,0,H)

z

z-H

Ground Effect

In our previous derivation, it is assumed that pollutant dispersion is not limit by the existence of ground surface.

In reality, the ground can either “absorb” the pollutants or “reflect” the pollutants

Pollutant reflecting from ground

x

y

z

U

H

(0,0,H)

Pollutant hit ground and reflects

Pollutant reflecting from ground

x

y

z

U

H

(0,0,H)

Pollutant from “imaginary” source

(0,0,-H)The ground reflecting effectcan be accounted for usingan imaginary source

Imaginary source

Equation for Reflecting Ground

x

y

z

H

(0,0,H)

(0,0,-H)

Real source:

Imaginary source:

22

2 2( , , ) exp exp

2 2 2y z y z

z HE yC x y z

S S U S S

22

2 2( , , ) exp exp

2 2 2y z y z

z HE yC x y z

S S U S S

Combine both:

2 22

2 2 2( , , ) exp exp exp

2 2 2 2y z y z z

z H z HE yC x y z

S S U S S S

Ground surface concentration

The surface concentration can be derived by setting z=0 in the equation:

2 22

2 2 2

2 2

2 2

0 0( , ,0) exp exp exp

2 2 2 2

exp exp2 2

y z y z z

y z y z

H HE yC x y

S S U S S S

E y H

S S U S S

The Pasquill Stability Classes

Stability class Definition Stability class Definition

A very unstable D neutral

B unstable E slightly stable

C slightly unstable F stable

Meteorological Conditions Define the Pasquill Stability Classes

Surface wind speedDaytime incoming solar

radiationNighttime cloud

cover

m/s mi/h Strong Moderate Slight > 50% < 50%

< 2 < 5 A A – B B E F

2 – 3 5 – 7 A – B B C E F

3 – 5 7 – 11 B B – C C D E

5 – 6 11 – 13 C C – D D D D

> 6 > 13 C D D D D

Note: Class D applies to heavily overcast skies, at any wind speed day or night

Determine Solar Radiation Strength

As a rule of thumb

Strong: Solar intensity > 700 W/m2

Moderate: Solar intensity > 350 W/m2

Slight: Solar intensity > 100 W/m2

Solar intensity < 100 W/m2 but still day hours neutral

Sy, Sz Charts

Sy

Equations to Estimate Sy and Sz

Sy = a*x0.894 Sz = c*xd + f

a, c, d, f are parameters. They are functions of stability classes and distance downwind (x). NOTE: x should be in units of km.

x<1km x>1km

Stability a c d f c d f

A 213 440.8 1.941 9.27 459.7 2.094 -9.6

B 156 106.6 1.149 3.3 108.2 1.098 2

C 104 61 0.911 0 61 0.911 0

D 68 33.2 0.725 -1.7 44.5 0.516 -13

E 50.5 22.8 0.678 -1.3 55.4 0.305 -34

F 34 14.35 0.74 -0.35 62.6 0.18 -48.6