空氣品質模式(air quality model)
空氣品質模式(air quality model)是空氣品質管
理系統中重要的工具，所謂空氣品質模式乃利用數
學或定量的方式，計算或模擬污染物由排放源釋出
之後在大氣中傳送、擴散、轉換所形成的濃度場之
時空分佈。
空氣品質模式雖然希望能反應出真正的大氣過
程，但模式畢竟不是真實的情況，即使是最完善的
模式也只能代表真實情況的簡化。有時，因為我們
對物理、化學現象或機制，並不完全了解，所以，
推導出來的模式不免有所缺失，因此模式在使用前
，必先了解其依據的原理、假設、限制、適用時機
...等，以選擇最為合適的模式。
模式使用的時機
• 新污染源設立之許可（環境影響評估、設置許可
等）
• 污染防制策略之擬定（如減量計畫)
• 總量管制（如污染泡策略）
• 污染防制策略施行之結果評估
• 監測站設置
• 長期空氣品質之評估（如國土規畫等）
• 緊急意外事件的應變措施
• 短期空氣品質預報及應變（如空氣預警系統及緊
急應變系統）。
高斯煙流模式(Gaussian Plume Model)
• 高斯煙流模式為最廣泛使用的空氣品質模式，一閉合的解
析公式(analytical closed-form)，最早由Sutton所發展
用以推求連續排放的點源下風處非時變(Steady-State)狀
態下之濃度分佈
• 此一模式之基本假設為
– 非時變狀態，亦即所有之變數和參數在同一時段（一
般定為1小時）之內為一定值。
– 氣象條件在整個面為相同（風速、風向不隨平面點而
改變）。
– 在垂直及側風方向濃度分佈為高斯分佈，其濃度分佈
之標準偏差 為經驗值。
– 在下風方向，其擴散可以忽略，同時，假設y<<x（狹
窄煙流）。
高斯模式的優缺點
• 高斯模式之優點為：
– 容易使用，可作長期評估。
– 已有豐富的使用經驗，一般而言，與實驗之結果相當吻合。
– 具有良好的概念。
– 具有極大的彈性，容易加以修改以適合不同的情況。
• 缺點為：
– 無法考慮風速、風向在不同時間或地點改變的情形，因此不適合於
長距離傳送使用。(通常用於幾十公里內)
– 為steady模式，無法考慮瞬間排放或意外情況釋出時擴散的情形。
– 無法考慮垂直風切的效應。
– 因為狹窄煙流假設，所以無法考慮靜風或幾乎靜風的情況。
– 無法考慮非線性的化學反應。
– 並不適合用於不均勻的地形(不均勻風場、等煙流高度不合理,…)
。
Gaussian distribution curve
This figure shows a plume emitted from a stack of height hs, , that has leveled out at
a height he . The coordinate system, which is used for all calculations, has the origin
at the ground directly under the source. The x-axis is pointed directly downwind and
the y-axis is perpendicular to the average direction of the wind. The source for the
diffusion calculations is considered to be a point at height he above the origin. For a
ground-level source, the source is at the ground. The average concentration profile is
assumed to be described by a Gaussian or normal-shaped curve in both the vertical
and horizontal directions.
不考慮地面和高空反射
The concentration in the plume is given by
  y2 
  ( z  he ) 2 
C ( x, y, z, he ) 
exp 2  exp

2
2 y z u
2

2

 y 
z


Q
The first exponential term gives the Gaussian distribution in
the horizontal or crosswind direction. The second exponential
gives the vertical concentration distribution for a source
located at a height he . Q is the mass emission of the
particular air pollutant and u is the average wind speed at a
height hs. It is assumed that Q is conserved in the downwind
direction.
Figure 3 shows the vertical
distribution of pollutants
predicted by Equation 1 for
the real source at height he.
As can easily be seen, this
formula predicts that a small
fraction of the pollutants
emitted by the source will be
below ground. In reality, most
of all of the pollutants that
reach the ground will be
reflected back upward. To
correct this shortcoming, a
fictious image source at a
distance he below the ground
is mathematically added to
the real source term.
考慮地面反射,但不考慮高空反射
Considering the real and image sources, the concentrations can be
calculated by:
  y 2 
  ( z  he ) 2 
  ( z  he ) 2  


C ( x, y, z, he ) 
exp
exp

exp






2
2
2
2 y z u
 2 y  
 2 z

 2 z



Q
At the ground, the total concentration is exactly twice that
predicted by Equation 1 for just the real source term. At higher
altitudes, the total concentrations asymptotically approach the
concentration due to the real source term. Since the primary
emphasis is predicting ground level concentrations, this can be
simplified for the case z equal to zero.
 y2 
  he2 
C ( x, y,0) 
exp 2  exp 2 
 y z u
 2 y 
 2 z 
Q
考慮地面反射,但不考慮高空反射
The ground level concentrations at plume center line (y=0)
can be obtained by:
  he2 
C ( x,0,0) 
exp
2 
 y z u
2

z 

Q
Maximum Ground-Level Concentration
The maximum ground-level concentration due to an elevated
point source in the absence of an elevated inversion is found
by differentiating the above equation, setting it equal to zero,
and solving for the maximum. With an assumption that the
ratio  z /  y is constant, the maximum concentration anywhere
downwind is
C max
2Q

euhe2
z


 y




This maximum occurs a distance xmax downwind where xmax is
given implicitly by the relation:
 z ( xmax ) 
he
2
考慮地面反射
和高空反射
If there is an elevated
inversion that effectively
limits the vertical extent
of the plume. Equation 3
will under predict the
concentrations. Figure 6
shows a plume emitted
beneath a stable inversion
with its base at height L.
考慮地面反射和高空反射
A generalized equation for Gaussian diffusion model which
considers ground level and inversion reflections can be
expressed as
Q
C ( x, y, z; H )  Fy Fz
u
where Fy is the concentration distribution in the crosswind
direction which is
Fy 

exp  y 2 /(2 y2 )
 y 2

and Fz is the vertical concentration distribution which can
be computed as
g1  g 2  g 3
Fz 
 z 2
where
  (z  H )2 
g1  exp

2
2

z


  (z  H )2 
g 2  exp

2
2

z


   ( z  H  2mL) 2 
  ( z  H  2mL) 2  
g 3   exp
  exp

2
2
2 z
2 z

m  





m 0

考慮地面和高空反射
If L is much greater then he, it will have little effect close to the
source. Equation 3 can be used for estimating ground-level
concentrations. When the plume grows such that it "touches" the
inversion, which is assumed to occur when σz=0.47L, the
concentration profile is assumed to be uniform in the vertical
due to turbulence in the well-mixed layer. In that case, the
concentration is given by
C ( x, y , z ) 
 y2 
exp 2 
2  y Lu
 2 y 
Q
Required input data for Gaussian Plume model
• x, y : determined from source location and
wind direction
• U (m/s) : interpolated from surface
observation to stack height by Power’s law
• Q (g/s) : source strength
• σy、σz (m): turbulent typing and diffusion
curves
• he (m): plume rise
• L (m): mixing height
The Pasquill-Gifford dispersion curves for the various Pasquill
stability classes
Pasquill stability classification
The Brookheaven National
Laboratory (BNL) scheme
Tennessee Valley
Authority (TVA)
scheme
Source: Arya
Briggs’ plume diffusion curves for open country
Maximum ground level
concentration
normalized by mean
wind speed and source
strength
and
distance to the
maximum g.l.c
as functions of
stability class and
effect stack height
Diffusion in complex terrain
Plume rise
Effective stack height
Rise due to vertical momentum
Buoyancy flux
Gradual plume rise in neutral conditions :
two-thirds law
Final plume rise (neutral or unstable condition)
Final plume rise (stable)
Mixing Height (混合層高度)
• Arya (1999): The top of the PBL is usually defined as
the level where the PBL turbulence disappears or
becomes insignificant. … The PBL depth is also called
the mixing depth or height.
• Mixing height determine the volume available for
pollutant dispersion.
• The mixing height cannot be observed directly by
standard measurements, so that it must be
parameterized or indirectly estimated from profile
measurements or simulation.
Radiosonde 無線電探空
A radiosonde is a unit for use in weather
balloons that measures various
atmospheric parameters, including
temperature, relative humidity, pressure,
and wind speed. This information is
transmitted back to a surface receiver.
A rawinsonde is a radiosonde that is
designed to only measure wind speed
and direction.
Weather balloons are launched around
the world for observations used to
diagnose current conditions. About 800
locations around the globe do routine
releases, twice daily, usually at 0000 UTC
and 1200 UTC.
Left: Rawinsonde weather balloon just after
launch. Notice a parachute in the center of the
string and a small instrument box at the end.
Source: http://en.wikipedia.org/wiki/Weather_balloon
Interpreting Rawinsondes –
Estimating Mixing Heights
Holtzworth Method: Starting at the forecasted maximum temperature, follow
the dry adiabat (dashed line) until it crosses the morning sounding. This is the
estimated peak mixing height for the day.
2,000 m
2,000 m
T
T
1,500 m
1,000 m
Estimated
mixing height
1,500 m
Estimated peak
mixing height
Dry adiabat
500 m
1,000 m
Dry adiabat
500 m
Increasing temperature
Forecasted max. temp.
Forecasted max. temp.
Determine the hourly mixing height
某天某地上午八時探空測得的高空中溫度剖面如下圖所示：
(i)請問A到B，B到C，C到D的大氣穩定度為何。
(ii)某一煙囪煙流的有效高度為180公尺,請問此煙流擴散的
形狀如何？
(iii)假設下午兩點地面溫度為32℃，請估計當時的混合層高
度。
2000
1800
1600
1400
1200
1000
800
600
400
200
0
20
22
24
26
28
30
32
(i)有一500MW的電廠，使用含硫量2%的煤，煤的
LHV=30000KJ/Kg ，如果能源轉換效率為0.38 ，則每
天煤使用量為多少公噸？
(ii)此一電廠裝有排煙脫硫設備，可去除90%的SO2，
此一電廠每秒排放SO2多少公克？
(iii) 如果廢氣由一煙囪排出，煙囪高度為60m，且假設
煙流上升高度為140m，煙囪出口處風速為3m/s，假設大
氣穩定度為中性穩定(D級)，此一煙囪在5km下風處(煙
流中心)的地面SO2濃度的增量為多少μg/m3?
(iv)如果當時大氣壓力為1atm ，溫度為25 ℃ ，則地
面SO2濃度的增量為多少ppm?
Stability and Diurnal Temperature
6 AM
Warm
Cool
Cool Surface
Temperature
9 AM
Warming
Warm
Temperature
Sunset
Height
3 PM
Height
Height
Cool
Warming
Temperature
12 NOON
Maximum
Warming
Temperature
Height
Warm layer
Height
Height
12 AM
Temperature
Cooling
Temperature
Stability, Inversions, and Mixing
Mixing height:
The vertical extent to which pollutants emitted at the surface
mix
Weak inversion: Pollutants mix into large volume resulting in low pollution
levels
Height
Temperature soundings
Weak Inversion
Inversion Breaks
CBL
NBL
Midnight
NBL
Sunrise
Sunset
Inland
CBL = Convective Boundary Layer
= Surface-based mixing depth
NBL = Nocturnal Boundary Layer
= Surface-based vertical mixing
44
Stability, Inversions, and Mixing
Strong inversion: Pollutants mix into smaller volume resulting in higher
pollution levels
Height
Inversion Holds
Strong Inversion
CBL
RL
Trapped Air
NBL
Midnight
NBL
Sunrise
Sunset
Inland
RL
= Residual Layer
CBL = Convective Boundary Layer
= Surface-based mixing depth
= Surface-based vertical mixing
NBL = Nocturnal Boundary Layer
45
From: Arya, 1999, Air pollution meteorology and dispersion