Modelling of Pollutant Transport in the Atmosphere - MANHAZ

MANHAZ position paper on:
Modelling of Pollutant Transport in the Atmosphere
Torben Mikkelsen
July 2003
Atmospheric Physics Division
Wind Energy Department
Risø National Laboratory
Dk-4000 Roskilde, Denmark
I Atmospheric dispersion: Basic
The dispersion of pollutants is intimately related to the state of the
atmosphere. Local scale dispersion is related to the local state of the
atmosphere. The local state of the atmosphere depends in turn on the actual
weather system, the regional scale wind circulation and turbulence, and local
micrometeorological effects. Local micrometeorological effects depend on solar
insolation, topography, surface roughness, surface albedo, local land use and
local long-wave radiative cooling. Local dispersion furthermore depends on the
actual type of release. That is, whether the release is a puff or plume release,
is thermally buoyant or an energetic release, the actual height of the release,
and whether it is influenced by nearby buildings or trees.
Today’s atmospheric dispersion scientists and modellers seek to characterize
air pollution spread in terms of important parameters representing the actual
state of the atmospheric turbulence. Not too long ago this was impossible, and
scientists as late as the 1960s and 1970s instead invented methods for
dispersion parameterisation based on synoptic classification schemes (time of
day, cloud cover, mean wind speed).
This lecture note will first summarize the important features that influence
atmospheric turbulence and thereby atmospheric dispersion. It then describes
the main categories of modern atmospheric dispersion models, and finally
provides details about the key types of dispersion models as they have appeared
in historical order.

Key Factors Influencing Atmospheric Dispersion
Introduction
Local heat flux depends on position with respect to the sun (season, hour of day,
latitude and topography) and the local composition of the atmosphere (clouds).
The temperature depends on the heat transfer and heat capacity
characteristics of the surface (sea, soil, desert, forest, and urban area). The
flows of air masses happen in contact with a surface that has a heterogeneous
aerodynamic roughness, creating small-scale turbulence (see Atmospheric
dispersion: Complex terrain). Each secondary motion leads to smaller eddies,
ultimately transforming the mechanical energy to heat. The result is that at a
given point, winds, and turbulence for that matter, result as the combined
effect due to a series of circulations, with distinct time-scales ranging from
days (general circulation) to seconds (turbulence) (see Figure 1). An additional
complication is the rotation of the earth. A coordinate system, referred to a
fixed point on earth, rotates with the earth during the transport of
the air masses. The weathermen on television show daily movies of satellite
observations of large-scale wind systems and cloud belts that (in the Northern
Hemisphere) are moving counter-clockwise around the low-pressure centres and
clockwise around the high-pressure centres (and the opposite in the Southern
Hemisphere; see Global circulation).
The Structure of the Atmosphere
Approaching the earth from outer space one would first enter the
stratosphere, which extends approximately60 km aloft, then, at about 15 km
height; one would reach the denser troposphere. The lowest (about 1 km) and
usually most turbulent part of the troposphere is called the atmospheric
boundary layer (ABL). The lowest 100 m approximately of the boundary layer is
called the planetary surface layer
(PSL), and is characterized by its more or less constant exchange fluxes of heat
and momentum between the earth’s surface and the atmosphere.
Stratosphere. From about 15 km height and up the air temperature always
increases significantly with height (at a rate of approximately +0.5 K per 100
m). This part of the atmosphere is called the stratosphere (because it is stably
stratified), and is extremely stable with hardly any turbulence.
2

Troposphere. Trapped between the stratosphere and the earth’s surface is
a less stable but denser layer called the troposphere. The troposphere extends
from the earth’s surface up to about 10–15 km above the ground. The
intersection between the stratosphere and the troposphere is called the
tropopause. As commonly experienced during air flights, the part of the
troposphere from 1 to 10 km above ground is usually slightly stably stratified
and therefore contains little or no (small-scale) turbulence. Some 80% of the
earth’s air mass is contained within the troposphere. Nearer the Earth's
surface, however, (say within the lowest 1 km of the atmosphere) the usually
stable stratification of the Troposphere is disturbed by heat and momentum
exchanges exchange with the surface of the Earth. This lowest ~ 1 kilometre of
the Troposphere is called the Atmospheric Boundary Layer (ABL)- and is the
most turbulent, but also most variable part of the atmosphere. It is in this layer
most of our daily activities unfold, and it is here most pollutant are emitted and
dispersed.
Figure 1.
Spatial and temporal characteristics of the atmosphere (after Atkinson, 1995)
3

Atmospheric Boundary Layer (ABL)
The ABL characterizes the part of the atmosphere which is in direct contact
with the Earth's surface, and is therefore often in a highly turbulent state. The
depth and character of the ABL is governed by exchange - via turbulent fluxes -
of: 1) heat, 2) moisture and 3) sheer-stress, all three originating from the air
masses contact with the earth's surface. The vertical extent of these fluxes
depend on the nature of the surface and therefore on the type of surface
(forest, open land, urban, lake, ocean, etc), time of day as well as on the history
of the air.
The depth of the ABL is therefore governed by the energy and scales of the
turbulent eddies which can vary in size from a few tens of meters at night to
one to three kilometres during warm sunny afternoons.
The factor that distinguishes the ABL from the rest of the atmosphere is
turbulence. Turbulence is markedly more efficient at mixing pollutants than is
the generally laminar-like flow of the "free atmosphere" above it.
The main two sources of energy that generates turbulence are "friction" or
"drag" of the air with the ground, and heat. Friction results in so-called shearstress
induced turbulence while heat (given off at day time or taken from the
ground at night time) generates vertical motion in the air through buoyant
forces- warm air rises, cold air descends.
Surface Layer (SL)
The planetary “Surface Layer" (SL) refers to the lowest ~100 meters part of
the ABL previously defined. The Planetary Boundary Layer is the more turbulent
part of the ABL. It is characterized by supporting approximately constant
vertical fluxes of heat and momentum between the Earth's surface and the ABL
above it. The PSL extends, according to its definition of approximately constant
fluxes, vertically from the surface and up to maybe one hundred meters in the
atmosphere.
Most emissions, transports and transformation of pollutants tales place within
the ABL. Its wind and turbulence fields are therefore important for
understanding nature and mechanisms behind the dispersion of pollutants.
4

The importance of the local wind field
The most important meteorological parameter that controls the spreading of
pollutants is the mean wind (speed and its direction). It is the wind speed and
direction that provides the basis for addressing the "WHERE" (does the plume
go) question, and "WHEN" (does the plume arrive) questions.
Of second importance is the degree of mixing (level of turbulence) in the
atmosphere. This quantity provides the basis for answering the "HOW MUCH"
questions.
At any given point on the earth's surface, the local wind speed and its direction
is the combined result of many different processes acting on different "scales":
On the so-called "regional" scale (1000 km and larger) we find the synoptic
weather patterns with their pressure gradients that determine the wind speed
and direction. The location of the Low and High-pressure regions, with
associated weather fronts, and the rotation of the Earth, determines the
regional scale wind speed and direction (Geostrophic balance). As these major
synoptic weather systems move around the globe, the regional winds (in
particular its direction) vary with an average periodicity of about 3-7 days.
Following the release of a potentially hazardous material- whether it is a gas, an
aerosol, or a cloud of fine particles, - it is however the local winds that are
determinant for where the plume is going and where it will be deposited, and
whether it will endanger people and the environment.
Determination of the local wind field, that is its wind speed and its direction, as
it is experienced by the plume or puff of emitted material, is far from easy.
Locally, the wind may vary in a quite complex way with height, with horizontal
position (especially over complex terrain) and with time. Most difficult to handle
are conditions associated with light winds when the plume travels slowly, and
when the vertical mixing is limited (say on cloudless nights) whereby the air
concentration of the material in the plume is relatively high.
On more windy days, however, particular over Northern and Western parts of
Europe, winds are often controlled by so-called "synoptic forcing". This means
that the movements of a plume are controlled by the so-called geostrophic
winds, which again are determined by the pressure gradients of the large-scale
weather features such as depressions and anticyclones.
5

Due to the rotation of the earth, the geostrophic balanced winds tend to
flow parallel (and not across - as one would intuitively think) the isobars (i.e.,
the lines of equal pressure). This happens because on the regional or "synoptic
scale" (i.e., on horizontal scales of the order of ~1000 km or more) there is a
balance on air movement between the pressure gradient force, and the Coriolis
force, the latter being associated with the rotation-rate of the Earth. Other
forces, such as the sheering stress caused by the drag of the ground, and air
channeling through valleys and over passes, will result in strong local wind
deviations from the regional geostrophic wind fields. On the local scale, say out
to distances within 10-20 km from the release point, effects of the underlying
surface with its topographical features also tends to be important for the wind
speed and direction, each tree, house and hill exerts drag on the air, and heat
and moisture profiles of the air becomes important.
The vertical wind profile. The "free" geostrophic wind mentioned above
prevails above the ABL, i.e. above say above ~1 km up in the atmosphere. It
flows parallel to the isobars. Closer to the Earth's surface, that is, within the
strong turbulent ABL, the wind speed is gradually decreasing, due to the
friction with the rough ground surface. Near the surface, houses, trees, hills
and forest perturb the velocity profile.
The local turbulence level depends on the local "atmospheric stability" which in
turn is characterized by 1) the magnitude of the wind speed 2) the surface
roughness, and 3) the vertical temperature profile.
Finally, because of the drag forces that exercises on air that flows near the
Earth's' surface, the wind direction is often turned some 20 degrees counterclockwise
(towards the centre of the low pressure) relative to the direction of
the geostrophic "free" winds that blows parallel to the isobars near the top of
the ABL at ~1 km height. This "veering of the wind direction with height" can
easily be observed on a "cumulus cloudy" day, where the wind direction near the
top of the ABL is marked by the motion of the cumulus clouds, while the near
ground wind direction can be read from a nearby flag, a wind turbine or from a
smoke plume.
6

Figure 2.
Typical vertical wind speed and wind direction profiles as can be observed
from Met-tower data for a) stable, b) neutral, and c) unstable
atmospheric stratification's.
Vertical temperature profile
The vertical temperature profile gradient is the most significant
parameter for distinguishing the atmospheric stability- and thereby the
turbulence levels. In addition, turbulence levels are the most important
factor controlling the diffusion of pollutants.
The Temperature Profile and Atmospheric Stability
Neutral atmospheric stratification. If, on planet Earth, there were no
heating nor no cooling from the ground, the vertical temperature profile
(for well mixed dry air in thermodynamically equilibrium) would get in
equilibrium and exhibit a linear decrease with height, at a rate Γ = -
0.0098 K/m, i.e., the temperature would drop off at about 1 degree
Celsius or Kelvin for each 100 meters as we walk up a mountain. The
equilibrium temperature profile corresponds to a neutrally stratified
atmosphere. When an observed vertical temperature profile actually
corresponds to this adiabatic lapse rate, we say that the air layer has a
neutral atmospheric stability. In this case, a parcel of air (say 1 m 3 ) when
moved adiabatically (without head exchange) from one height to another,
will automatically change its pressure, density and temperature in such a
way that it would remain in thermal equilibrium with its surrounding air.
Consequently, no restoring forces on the parcel will be created in this
case due to pressure, density or temperature differences. The
atmosphere is then neutrally stratified. This means that only shear or
7

gradient driven turbulence will be created in this case (usually near the
surface) - but no heat or buoyancy-driven turbulence is added, nor
destroyed.
Stable atmospheric stratification. Suppose now that an actually
observed temperature gradient is less negative than the corresponding to
the adiabatic lapse rate, say e.g. that the same temperature is observed
at the ground and at + 100 meters height. If we in this environment again
take a small air parcel from near the ground and lift it adiabatically to
the +100 meter level, its temperature will again drop by ~ 1 C because
the pressure and density changes. However, now the parcel temperature
would be one C colder than surrounding air temperature, which remained
constant. At 100 meters, height the air parcel will consequently be colder
and heavier than its surrounding air and the parcel will start to fall down
towards its place of origin- in this case the ground. The actual
temperature profile tends in this case to restore all vertical motions
included those caused by turbulence, and we say that the layer is
"Stable" stratified.
Unstable atmospheric stratification. Consider next the opposite case
where the actual observed temperature gradient is more negative than
the neutral lapse rate Γ, say e.g. we observe a -2 C o per 100 meters
vertical gradient. As our test parcel of air again is lifted adiabatically up
from the ground to 100 meters height, its internal temperature will as
before cool adiabatically by ~1 C o . But the surrounding temperature at
100 meters height is in this case lowered by 2 degrees, so relative to its
surroundings, the adiabatically lifted air parcel is now at + 1 degree C o
relative to its surroundings. The air parcel has become "a hot air balloon"
with a temperature of + 1 C o relative to its surroundings. If we let it
continue to rise it would at 200 meters height experience a +2 C o increase
in temperature relative to its ambient air, supposing that the profile
doesn't change. The atmosphere is said to be "Unstable" because all
vertical motion will tend to be amplified.
Surface Friction (Surface Drag) Another important source of
turbulence is caused by friction (drag). The wind speed on the ground (in
practice at 1 mm height, say) must be zero to fulfil the no-slip condition
of any fluid (in this case air) on a boundary. The resulting strong gradient
in wind speed with height causes "sheer" induced turbulence: the
stronger the wind speed, and the closer to the ground, the stronger is
the generation of shear-induced or mechanically induced turbulence.
8

Notice that this source of turbulence is always positive and independent
of the direction (sign) of the temperature gradient.
Atmospheric stability. Turbulence generated from by temperature
stratification's can sometimes be positive (during unstable daytime
conditions with negative vertical temperature gradients, and sometimes
negative (during night time with positive vertical temperature gradients).
The resulting stability of the ABL is therefore the combined effect of
thermal and friction generated turbulence. At daytime both contributions
add to the turbulence near the ground, while at night time - with low wind
speeds, the thermal "suppression" often "wins" over the creation by
friction.
Measures for Turbulence A simple measure for the level or strength of
turbulence is its level of intensity i, defined as:
2 2 2
i = u + v + w U
′ ′ ′ (1)
That is, the turbulence intensity, i, is defined as the square root of the
sum of the variances of the three velocity components u' (in the
downwind direction), v' (in the crosswind direction) and w' (the vertical
direction), divided by the mean wind speed U .
The mean value (designated by an over-bar) is usually obtained as time
averages over periods ranging from 5 minutes up to 1 hour.
An unstable atmosphere implies a high level of turbulence, with
turbulence intensities ranging between 0.2 and 0.4, whereas a stable
atmosphere, with little or almost zero turbulence at all, is characterized
by intensities in the range 0.05 - 0.01.
Source Types and Source Heights. In addition to wind temperature and
turbulence, also the effluents actual source type and source heights are
important factors, which influences atmospheric dispersion. Air
concentrations highly depend on the effective source height. To first
order, ground level air concentrations depend inversely proportional on
the source height to the second power (see below).
The heat and momentum content of an effluent also add to the effective
source height, and is therefore an equally important factor for
9

dispersion. The buoyancy of the effluent itself can be big importance, if
it’s a cold gas it will fall to the ground (see part II: Atmospheric
Dispersion: Heavy gases) or it can be hot or energetic, in which case we
need to consider plume and momentum rise.
Inversion height. The inversion height and its strength is another very
important parameter to consider for atmosphere dispersion.
Source types may alter between single point sources and line sources over
explosive sources with huge heat and momentum content. The Chernobyl
accident was in its initial phase characterized by a heat and vapor
explosion, followed by a plume release with significant heat content. On
the Ukrainian night of April 26 1986, the burning graphite plume rose
some ~1 km aloft before it blew north-westwards in a strongly stable
stratified atmosphere. It is first today are we about to understand and
model the combined effects of the Chernobyl initial stage release and the
stable stratified atmosphere in connection with local inversion heights
and local wind sheer.
Effluents can also be of continuous type continuous (plumes) or
instantaneous (puffs). In addition, this affects the resulting dispersion
pattern.
Atmospheric Dispersion at different scales
Surface layer scaling The planetary Surface Layer (SL) was earlier
defined as the lowest ~100 meters of the atmosphere. It is
characterized by its approximately constant vertical fluxes of heat and
momentum. The magnitudes of these fluxes can therefore be determined
by measurements near the surface (typically at 10 meters height). It is
only within the PBL, which is within the thin surface layer of the
atmosphere that the surface layer Monin-Obukhov similarity scaling of
dispersion is applicable.
Mesoscale Meso is Greek for " in between" and refers to atmospheric
phenomenon which occurs on horizontal scales large enough that the
hydrostatic approximation (i.e., that the vertical acceleration forces of
the air mass can be neglected compared with the hydrostatic pressure
forces) is a valid assumption (usually it is on scales bigger > 2 km); yet
small enough (

dient winds can approximate the regional wind circulation [Pielke (1984)].
Vertically, the surface layer extends a few hundred meters whereas the
mesoscale extends throughout the entire troposphere.
Mesoscale models utilize grid spacing ranging between a few meters for
modelling of local scale dispersion phenomena and out to 20 km or more in
numerical weather forecast models utilized on the regional scale. The
corresponding time scales ranges from fractions of a second in the nearsurface
layer concentration fluctuations to tens of hours for the meso-γ
scale weather system calculations.
Atmospheric dispersion of a puff progresses with different scaling laws
on the various scales. In the start, within the SL, is expands at first
under influence of the initial source dimension, the heat and momentum
content of the release, by nearby building effects, by down-wind changes
in roughness and surface heatfluxes (in particular by the atmospheric
stability).
Then it undergoes diffusion by transition through various time and
spatially changing boundary layers.
Additional local scale effects include heterogeneous surfaces, hills, and
rolling and steep complex terrain. When a dispersing puff reaches the
Mesoscale ( say when the puff size is comparable to the mixing height
(~2 km) , the expansion will furthermore be influenced by winds
originating from differential heating such as: sea-and land breezes, up
and down slope winds, valley circulation's and orographically induced
winds.
Long Range After a day of travel time or so, most plumes and puffs have
diffused to a lateral extent of the order of ~100 km, that is, they have
diffused horizontally to scales where the atmosphere for all practical
purposes have become two- dimensional.
Turbulence on this scale also takes on a different form known as largescale
enstrophy cascade. The usual local scale plume or puff confined
entity picture soon disappear for two-dimensional turbulence, and the
usual surface and boundary layer parametric descriptions of dispersion is
no longer valid.
11

II Diffusion Theories and associated Atmospheric
Dispersion Models
In the following a short review is given on the diffusion theories and
model categories from which most practical dispersion models used today
are based.
Fixed and moving frames of reference
In this chapter, the word "plume" will be used to designate a continuous
release of pollutant from a point source, while the word "puff" will be
used about an instantaneous released quantity of pollutant. So while the
different segments of pollutants belonging to a plume all have different
travel times since their release from the source point, all pollutants
belonging to a single puff have one, and only one age since their start of
release, namely the puffs travel time t.
Two fundamental different types of atmospheric dispersion must be
discriminated:
1. Fixed frame concentrations
2. Moving frame concentrations
The fixed frame averaged concentration is measured at, or is referred
to, at fixed points (on the ground), while the instantaneous concentration
refers to a moving frame of reference, which follows with the cloud or
puff's centre of mass. For this reason, averaged (whether time averaged
or ensemble-averaged), dispersion is often referred to as " fixed frame"
dispersion or absolute dispersion- while instantaneous dispersion often is
referred to as "moving frame dispersion, or "relative dispersion". The
physical mechanisms behind the two types of dispersion are quite
different: While the averaged mean concentration and its associated
dispersion, process phenomenologically can be described by single and
independent fluid particle's trajectory ensemble statistics; the
instantaneous puff dispersion process involves at least the joint statistics
of two fluid particles or more at the same time.
Much fundamental research and theoretical formation has during the
past century been devoted to model and describe the turbulent diffusion
process within the atmosphere The field has in particular been dominated
12

y Russian and British researchers the Twentieth century. A short review
is given next:
The classical distinctions among diffusion theories as used in the
atmosphere have traditional been (in historical order):
1. diffusion equation methods (stability classes)
2. statistical methods (Random walk models – Kinematic simulation
methods);
3. Lagrangian similarity scaling
Ad. 1 Diffusion equation methods (stability classes)
Anomalous Diffusion The classical approach to describe the atmospheric
diffusion process was based on a generalization of the heat diffusion
process known from solid-state physics, and the molecular diffusion
process known from gas diffusion. In the beginning of last century,
atmospheric physicists such as Prandl referred to the atmospheric
diffusion process as "anomalous" diffusion, because it was much faster
than the hitherto known "nomalous" (molecular) Brownian diffusion.
The Diffusion Equation The classical diffusion equation emerges as a
direct and simple consequence of the conservation of mass principia
(dc/dt =0), that is, the rate (d /dt) of changing the total mass c within a
closed system is zero. In Cartesian coordinates, where the concentration
c is locally distributed, c(xi,t) can change locally as function of both
space coordinates xi (i = 1,2,3), and time t. This conservation principle
implies that the conservation equation now reads, neglecting a small term
due to molecular diffusivity
dc
ct
c
u
dt
dc
= i
dx
∂ + = 0 (2)
i
where ui is the instantaneous, mass advecting wind speed. By here
introducing mean and fluctuations parts
c = c + c′ ; ui = ui + ui′
defined in such a way that the fluctuating parts averages to zero
c′= 0 ;
u′ i = 0
13
(3)
(4)

the diffusion equation results
dc
dt
=
u
i
∂c
= −
dt x
∂
∂
i
' ' euc i j + " sour ces" − " si nks" (5)
Gradient transport: K-closure. Analogous to what is known from
molecular transport, also turbulence transport can be assumed or
modelled proportional to the mean gradient in the concentration field.
This is called first order closure, and implies:
u c K c ∂
′ i ′ =−
(6)
i
dx
That is, the turbulent transport flux u′ i c′
is assumed proportional to
∂ c
diffusivity, Ki , multiplied by the mean gradient .
dx
Analytical solutions to the diffusion equation. In the simplest possible
case with only one dimension (in the z direction in this case), and with a
constant vertical diffusivity (Kz) and constant mean wind speed u = x / t
in the downwind (x) direction, then the solution to the diffusion equation
for mean concentrations becomes the classical Gaussian plume model
equation, namely:
czt (,) =
Q
e
2π
u σ
i
z
i
1 z 2
− ( )
2 σ z
Here, Q is the source strength and σz, the plumes standard deviation,
characterizes the plume size as function of diffusion time t, or
alternatively downwind distance x = ut . The derivative of the standard
deviation squared is related to the diffusivity K through
σ z
2
½ d
dt
(7)
≡ K
(8)
So the plume spread, or more precisely the square of the standard
deviation, can be calculated from the following equation:
14
z

σ () t = 2K t + σ () 0
2 2
z z z
where σz(0) is the plume or puffs initial size at time t = 0. Analytical
solutions for the spread can sometimes be found when Kz is given as
known functions of height z or time t. It is seen that the Gaussian plume
model results as solutions to the diffusion equation. The Gaussian plume
model was the model foundation for the Pasquill-Gifford-Turner
atmospheric dispersion parameter system based on stability classes.
The Pasquill stability class dispersion parameter system. PASQUILL,
F. (1961), in collaboration with the American scientists F. Gifford, and B.
Turner, developed the well-known Pasquill-Gifford-Turner (PGT) stability
categories [A, B, C, D, E, F] with corresponding σy (lateral plume size) and
σz (vertical plume size) curves for time averaged (type 1) plume diffusion.
The sigma curves were fitted to plume spread obtained from empirical
plume diffusion data for each stability category.
σy and σz classification schemes. The PGT diffusion scheme and its
associated dispersion parameters have been among the most frequently
applied dispersion schemes all over the World. The PGT categories are
determined from wind speed (at 10 m height above ground) and incoming
insolation (time of day-cloud cover) as governing parameters. A is the
most unstable case, D corresponds to neutral case, and F is the most
stable dispersion class. The PGT stability class method is limited,
however, to conditions (with respect to range and type of land use)
similar to the conditions under which the diffusion experiments were
originally extracted, i.e. diffusion from near-ground releases, and over
terrain with low surface roughness (rural areas).
Today however, the corresponding formula's or nomogrammes (look up
schemes) are progressively being implemented on computers - or, as is in
particular the case for real-time dispersion assessments, are being
replaced by so-called "second-generation" dispersion schemes, based on
micro-meteorological similarity scaling parameters, see e.g. Olesen and
Mikkelsen, (1992).
15
(9)

Insolation Cloud cover
Day: Strong Insolation
Moderate
Slight
Night: Cloud cover ∃4/8
Cloud cover < 4/8
Surface1 Wind speed U [m/s]
< 2 2-3 3-5 5-6
> 6
A
A-B
B
A-B
B
C
Table 1: Definition of the Pasquill stability classes A-F:
F
F
E
F
B
B-C
C
D
E
C
C-D
D
Table.2 The Pasquill stability Classes and their corresponding
turbulence levels, here given in terms of standard deviations as measured
in the horizontal wind direction fluctuations
Pasquil StabilityCategory σθ
A. Extremely unstable conditions 25.0Ε
B. Moderate unstable conditions 20.0 Ε
C. Slightly unstable conditions 15.0 Ε
D. Neutral conditions 10.0Ε
E. Slightly stable 5.0Ε
F. Stable conditions 2.5Ε
1 Usually, surface wind speed is measured at 10 meters height.
16
D
D
C
D
D
D
D

Figure 3
Pasquill stability classification schemes for mean plume standard
deviations. Left: horizontal diffusion, (right) vertical diffusion
coefficients.
Ad 2: Statistical Methods:
Statistical methods for accessing atmospheric diffusion distinguishes 1)
Random walk methods (also called Statistical Simulation methods), and 2)
Kinematic Simulation.
A fundamental statistical description of dispersion based on "single fluid
particles" was presented by Sir G. I. Taylor's theory on "Diffusion by
continuous movements" already in 1921 (Taylor's formula, G. I. Taylor,
1921). Taylor's method can be used for calculation of the crosswind plume
standard deviation σy, based on observed wind statistics at the source
point.
The work of G. I. Taylor demonstrated that it is the Lagrangian rather
than the Eulerian properties of the turbulence that are responsible for
dispersion. Lagrangian statistics means that the turbulent quantities
(velocity) have to be assessed along the moving fluid particle's trajectory
17

(e.g. by following a small neutrally buoyant balloon), while Eulerian
properties imply that e.g. wind statistics that can be obtained from
simpler measurements at a fixed points (e.g. at the release point or from
a Met tower).
Five years later F. L. Richardson (1926) presented results from his
observations on "relative atmospheric diffusion". He showed, on a
distance-neighbor graph, that two-particle's relative separation on
average scaled with the particles instantaneous separation. This
observation later led him to formulate his famous “Diffusivity for
relative dispersion α l 4/3 power law ” , where l is the two particles'
instantaneous separation.
Another British scientist, G. K. Batchelor (1952), related relative
dispersion directly to scaling parameters for the turbulence itself, which
has meanwhile been discovered by Russian scientists (an example of a
turbulence scaling parameter is for instance the Kolmogorov's inertial
subrange dissipation rate ε). In his famous article "Diffusion in the Field
of Homogeneous Turbulence, II. The relative motion of particles" G. K.
Batchelor relates the standard deviation for a puff to the dissipation
rate ε for homogeneous 3-dimensional inertial subrange turbulence (σ 2 y α
εT 3 ).
Ad 3. Lagrangian Similarity Theory (Scaling)
The Lagrangian similarity approach. Similarities scaling of turbulence
means that the vertical profiles of the state quantities (such as
temperature, wind speed, humidity, pollutants etc) are uniquely
determined by the so-called scaling parameters, which are: height z above
the ground, air density ρ, buoyancy parameter g/T, surface shear stress
u*, and the vertical flux of heat H/cpρ. The prerequisites for similarity
scaling to apply is that the turbulence is homogeneous and stationary, and
that the vertical fluxes of momentum - ρu*
2 and heat H/cpρ are constant
independent of height. These assumptions can often be fulfilled in the
Planetary Surface Layer (PSL). The origins of similarity scaling for the
atmospheric surface layer turbulence has roots in early work by Russian
academicians Monin and Obukhov, who formed the similarity based Monin-
Obukhov stability parameter "L", see below.
18

Monin-Obukhov similarity scaling (z/L), applied to mean profiles of wind
speed, temperature and humidity over a homogeneous terrain, were
validated experimentally during the now famous 1968 international Kansas
field experiment (Busch, 1973).
Lagrangian similarity theory as nowadays applied to atmospheric
dispersion origins from the Russian scientist Monin (1959), but was
further crystallized and further elaborated upon by Batchelor (1959,
1964).
The application of "Lagrangian Similarity Scaling" of turbulent
atmospheric dispersion emerged in the 1990'ties within many practical
"new generation" atmospheric dispersion models for regulating industries
in accordance with National Environmental Protection laws. Also
contemporary real-time dispersion modes for emergency management and
decision support nowadays utilize Lagrangian similarity scaling for
detailed dispersion parameterisation in stead of the previous Pasquill-
Gifford-Turner stability classification schemes (A, B, C…F).
As in the case above where similarity theory is used to describe the
turbulent mean profiles in terms of constant scaling parameters,
Lagrangian Similarity Theory applies also to dispersion and assumes that
also the Lagrangian frame properties of dispersing plumes and puffs,
including their key parameters (such as mean height, standard deviation
etc) are governed by the set of scaling parameters that also controls the
mean profiles within the surface layer, in addition to the diffusion time t
itself. Again, scaling parameters are quantities derived from flow
properties and fluxes that are (approximately) constant in a given flow
regime or range of scale. For instance is shear stress velocity u* an
important scaling parameter for a near neutral Surface Layer.
Lagrangian similarity theory applied to particles dispersion in the surface
layer implies that both mean height , and the dispersion of a surface
released puff in neutral stratified atmosphere, "scales" with, or is a
function of (u*, t). The simplest form is (σy, σz) ∝ u* t. British-based P.C.
Chatwin, (1968) was among the first to explore the implications of
Lagrangian similarity scaling in his work on "The dispersion of a puff of
passive contaminant in the constant stress region".
Recently, Danish experimentalists (Mikkelsen et al., 2002) showed that
Lagrangian similarity theory also explains an exponential observed form
19

of the two-particle distance-neighbour function 2 in surface released
smoke plumes they measured during the comprehensive MADONA surface
layer diffusion experiment (Cionco et al, 1999).
Some common and a few new similarity-scaling laws for common
atmospheric turbulence and dispersion subrange follows next:
Example 1. Inertia-subrange "ε":
For 3-dimensional isotropic turbulence, as can be encountered in the ABL
above the surface layer, the only relevant constant scaling parameter for
turbulence is the dissipation rate of kinetic energy ε [m 2 s -3 ].
Consequently, as is evident from dimensional reasons, the corresponding
velocity spectra S(k) (for all three components u, v, w) must take on the
form:
where k is the wave number.
Sk ( ) ∝ ε k
23 / −53
/
20
(10)
An instantaneous released puff will, according to Lagrangian Similarity
theory, expand in this turbulent fields inertia subrange, according to
(Batchelor, 1952):
σ ∝ ε t
2 3
puff
(11)
where σPuff is the standard deviation (root-mean square) of the puff's
particle distribution or simply " size", at diffusion time t.
A "K" diffusivity for the for the puff particles distance-neighbor
function, based on the dissipation parameter ε, was already predicted by
Richardson (1926), as
DN ∝ ε 13 4/ 3
/
K y
2 Distance-neighbor function is a measure of the structure function for the puff particles defined as:
z∞
−∞
)
' ' '
qy ( ) = 〈 cy ( ) cy ( + y) 〉 dy , where < > denotes averaging over all particle pairs in the puff.
(12)

With Richardson's diffusivity KDN in the diffusion equation above, a
corresponding Distance-Neighbor function could already in 1926 be
predicted to be of the form
c h 23
)
/
q ∝ exp − y σ
(13)
This hypothesis has only recently been confirmed experimentally, in the
water tank particle-tracking experiment performed by Ott and Mann
(2000).
Similar scaling arguments can now be used to predict also the puff 's
mean concentration profiles. While the diffusivity KC for the mean
Puff
puff concentration profile, again for dimensional reasons, must be
expected to take on the form (Mikkelsen et al., 2002):
K C Puff
∝
R
S|
13 / 43 /
ε σ
T| ε13 / y 43 / for y ≥ σ
σ Puff
21
u t
∝ *
for y ≤ σ
C Puff ( y )
the corresponding puff mean concentration profile becomes
2/ 3
Gaussian in the centre part cy
σ ≤ 1h,
and of the form exp
−c y σh
in the tails .
cy
σ ≥ 1h
(14)
However, these new predictions for the puffs mean concentration profile
for the inertial subrange still has to be evaluated experimentally.
Example 2. Surface layer scaling "u*” Lagrangian Similarity scaling also
applies to puff dispersion within the atmosphere surface layer (SL). In
the SL close to the ground (z < 100 meters), the proper similarity scaling
parameter for is the approximately constant shear stress velocity scale
u* [m/s]. (Note that the dissipation rate ε [m 2 s -3 ] in the SL is a strong
function of height z and therefore is inappropriate as SL scaling
2 −1
Suv , ( k) ∝ u* k
parameter. Near the ground, where u* is dominant (and constant), the
horizontal turbulent velocity spectra S u,v (k) must for dimensional
reasons, have a subrange of the form (Tchen , 1959, Kadar et al., 1989):
(15)
An instantaneous puff, released from the ground in this layer must
consequently, according to Lagrangian Similarity theory, expand in the

surface layer, that is, at a linear expansion rate, as function of diffusion
time t. This was predicted by P.G. Chatwin already in (1968).
(16)
Also a "K" diffusivity, based on the surface scaling parameter u* , can be
formed for the distance-neighbor function for a surface released puff,
(Mikkelsen, Jørgensen, Nielsen and Ott, 2000):
K u
DN ∝ * y
22
(17)
where y denotes the instantaneous separation of any two-particles in
the puff.
Again by use of the diffusion equation the predicted form of the twoparticle
Distance-Neighbour function for a surface released puffs
becomes
)
q ∝ − y
c u th
exp *
(18)
This exponential and self-similar form for the distance-neighbour
function for surface released puffs has recently been confirmed
experimentally (Mikkelsen et al 2002) from analysis of the MADONA
surface layer smoke plume diffusion experiments (Cionco et al., 1999).
Example 3. Enstrophy cascade subrange "Tc"
As earlier mentioned, two-dimensional enstrophy cascade characterizes
the atmospheres motion at the 1000- 10000 km scale. A single
characteristic time scale Tc [s] can be associated with cascade of eddy
enstrophy (mean squared vorticity). Horizontal turbulent velocity
spectra can both be predicted and measured to have the form (The GAP
experiment; Nastrom and Gage, 1985)
S k 1 T k
uv , c ( ) ∝
2 −3
2 2 −
K ∝ σ / T m s 1
C Puff
c
(19)
Within this global scale atmospheric subrange, puff's can be predicted to
grow according to an eddy diffusivity formed from the parameters:
instantaneous puff size σ and the enstrophy cascade time scale Tc , that
is :
(20)

The corresponding predicted puff growth becomes
exponential: σ ∝ exp(
tT).
Large scale cloud size observations (Gifford,
Puff c
, 1988) and numerical weather prediction embedded global multi-particle
model results (Maryon and Buckland, 1995) give experimental and
numerical support to this predicted exponential growth rate for puffs
diffusing within the atmosphere's large scale enstrophy subrange.
Similarity scaling of σ parameters in Gaussian plume models.
Table 3. Definitions of common micro-meteorological scaling
quantities, based on similarity theory. In addition to the definitions given,
ρ is density of standard air (~ 1 kg/ m 3) , cp (~1200 Joule/ Kg) is the airs
specific heat at constant pressure, κ (~0.4) is the Von Karman constant,
g is the gravity ( ~9.8 m/s 2 ), and T is the air temperature (~ 300 K).
SIMILARITY SCALING PARAMETERS
z : Puff height
zi : Boundary layer height
H0 : Surface heat flux [ ≡ ρ cw p 'θ'] u* : Surface sheer stress[ ≡ − uw ' ']
LMO :
3
κT
u*
Monin-Obukhov length [ ≡ − ]
g w′
θ′
w * :
g
Free Convection velocity [ ≡ ( ′
T
′ ) zw i
θ 1 3 ]
The similarity scaling concept is to base the calculations of plume spread
on, in addition to the diffusion time t itself, the physical scaling
parameters that also govern the SL and ABL mean and turbulence
profiles. In addition to the previously mentioned shear stress velocity
scaling parameters u* and the Monin Obukhov stability parameter L, also
the convective velocity scaling parameter [w * g
≡ ( ′ ′ ) ], and the
T
boundary layer height zi becomes important scaling parameters for
diffusion, see Table 3. Physically interpreted, L is the height above
ground where the contribution from mechanically generated turbulence
(by wind sheer) in magnitude equals the contribution (or drain) by
zw i θ 1 3
buoyancy generated (by heat transfer) turbulence.
23

With the introduction of Similarity scaling in dispersion meteorology in
the 1980ties, the former (from about 1960 to the early 1980) stability
class categories (A, B, C, D, E and F) are nowadays being progressively
replaced by the continuous non-dimensional stability parameter: "z/L",
where z is the height above the ground (release height). The well-known
nomogrammes for the dispersion parameters reproduced in Fig. 3a ( for
the lateral diffusion coefficients σy) and Figure 3 b(for the vertical
diffusion coefficient σz) have subsequently being replaced by formulabased,
similarity scaling using the parameters (u*, L, zi, w*), of the form:
σ x, y= σ u, vutFx, y( u* , w* , L, zi, z)
σ = σ utF ( u , w , L, z , z)
z w z * * i
(21)
(22)
As an example, a similarity theory based formula for the plume's vertical
standard deviation during unstable atmosphere from a ground level
release is calculated as (Brandt et al., 1996a, 1996b) ):
Inversion height and the daily stability cycle:
σz 2 = 0.33 w* 2 t 2 + 1.2 u* 2 t 2 (23)
Figure 4. Mixing-height and mixing-layer air pollution during two
consecutive days. The effect of the diurnal mixing height cycle is
affecting the air pollution concentration (shading). (From ApSimon, 1980).
24

The cyclic variation of the stability near the surface also causes a cyclic
variation of the height of the inversion height zi, i.e. the top of the ABL.
Here, at zi there is often observed in the summer time at least a strong
temperature jump or inversion layer, which marks the top of the ABL, and
which pollutants cannot penetrate (because there is no only little
turbulence in the Troposphere above it, cf. the introduction).
Figure 4 (From ApSimon et al., 1980) shows that pollutants released at
night time are diluted by the expansion of the mixing height as the sun
rises. At sunset, some of these pollutants can remain above the mixing
height, where they will travel at high speed without practically any
diffusion, as this layer is stable stratified. The next morning these
pollutants may again be entrained into the mixing layer and thereby
contribute to the pollutant concentration at ground level somewhere else.
Table 4. Typical values for the mixing height as function of Pasquill class
stability.
Stability
Zi [meters]
A
1300
B
900
Table 4 shows the earlier simple scheme for estimation of the mixing
height in terms of Pasquill categories. In today's computerized dispersion
modelling systems, zi is easily accessible in real time from investigation of
the vertical temperature profiles in numerical weather prediction models
used operationally to forecasts of wind, temperature and precipitation
around the clock at many national and international meteorological
services and weather research institutes. Alternatively, zi can be
estimated locally from prognostic mixing height algorithms based on local
surface heat flux and upper air lapse rate measurements (Γupper), see e.g.
(Batchvarova and Gryning , 1991).
25
C
850
D
800
E
400
F
100

III Atmospheric Dispersion Models - Applications:
Modelling atmospheric dispersion is a large scientific, technological and
engineering subject whose results depend on the different space and
time scales in the atmosphere. As evident from the previous discussions
of the many different scales in the atmosphere, dispersion of pollutants
behaves differently on the various scales and is influenced by the initial
source dimension, the heat and momentum content of the release itself,
by nearby buildings, by down-wind changes in surface roughness and
surface heat fluxes (i.e. the atmospheric stability) and by transition through
time and spatially changing layers. Additional effects of the terrain
include heterogeneous surfaces, hills, and even complex terrain.
Atmospheric dispersion is in addition influenced by larger-scale differential
heating (sea-and land breezes, up and down slope valley circulation's)
and orographically induced winds (such as Chinook winds, Santa Anna
winds, Le Mistral, Cirocco winds etc)
For practical applications modelling, modellers often categorize
atmospheric dispersion models according to their type of application.
Dispersion inclusive deposition modelling is usually applied in the following
three main areas:
1. Environmental impact studies
2. Probabilistic Accident Consequence Assessments
3. Real-time (i.e. in real time during an accident) damage assessment
and decision support
The first and most widely used application is "Environmental impact
studies". In this category, dispersion models are used for Government
and regulatory bodies control and assessment on environmental loads
coming from industrial and energy production emissions. The second type
of application is "probabilistic assessment studies" - where, for example,
the annual mean or the monthly peak concentrations over an area are
investigated. The third type of application for is a real-time assessment
model; in which case the actual Pollution State or near future (e.g.
tomorrows) Ozone impact is estimated. This is of interest for the realtime
monitoring of pollution states, decision support concerning accidents,
and for assessing the present or near future state of pollution.
26

Dispersion modelling has also high priority as emergency management
support tools for decision-makers in charge of accident management. The
dispersion models involved need to provide forecasts or real time
predictions so that decision-makers can alert people downstream to go
indoors, and subsequently initiate countermeasures based on the
predictions (e.g. distribute Iodine tablets, relocate etc). In particular in
cases of chemical, biological and radioactive releases, whether they are
accidental or terrorists work, fast and reliable real-time atmospheric
dispersion assessment is an important issue.
Models may vary considerably in type and complexity depending on their
specific goals. The most complex models may take too long to run, or
require too much input data in a real emergency, in which case a simple
but good quality model may be much more practical and still provide the
answers urgently needed by the decision makers exercising emergency
management. It is also a fact that complex models are not always
significantly more accurate than simpler models, - and that no model
produces results of a quality better than the quality of the input data
they require to work. The "bon-mot" amongst modeller’s "Garbage in -
garbage out", reflects this fact. To make sense, the models embedded
"physics" and the quality of the meteorological input data have to match
one other.
Practical Atmospheric Dispersion Models
Except for the simple Gauss plume model already mentioned in section II
(See "Analytical solutions to the diffusion equation"), modelling dispersion
usually involves both a wind (flow) model, and a diffusion (spread) model.
A gallery based on historical order of appearance is presented next. The
gallery also reflects the increase in "Complexity", as models evolve from
the Gaussian plume modes and become increasingly computer-heavy to
operate.
Dispersion Model Gallery:
Gaussian plume and puff models. Starting with the Gaussian plume
models at as the earliest and most simple in this category, Gaussian type
models subsequently spans over the "Segmented Gaussian plume models",
then over simple Lagrangian puff models, then over the more complex
27

Puff model based dispersion models, some of which, although they are
still formulae-based, include advanced features such as "puff-splitting"
to be used in connection with moderate complex terrain.
Wind data to drive the Gaussian plume model can come from a single point
measurement of wind speed and direction and is assumed to apply for the
entire domain (cf. the simple Gaussian plume model). This is only a useful
approximation over flat and homogeneous terrain and during long lasting
stationary conditions.
The first puff models relied on wind fields generated from so-called
"interpolation routines" which were based on two or more observations in
the nearby terrain. The resulting wind fields are "diagnostic" implying
that they "now- cast" the winds based on present (on-line connected)
meteorological sensors.
In addition, in the early eighties, several dispersion modelling groups
made mass-consistent interpolation schemes in which initially guessed or
interpolated winds field was made "divergence-free". Some models of this
type include a vertical stratification relevant for stable flow regime flows
over varying terrain.
Starting in the mid-1980s, practical and fast wind models emerged
suitable for puff advection over heterogeneous terrain. These wind
models are based on linearized versions of the Navier-stokes
conservation equations for mass and momentum in the BL. Linearized wind
and turbulence models nowadays exists for flow over hills, roughness
change, and thermal stratification's such as valley breeze and sea breeze
effects [Astrup et al, 2001, Mikkelsen et al, 2000, Dunkerley 2001]. The
CPU-time required running these linearized models is very modest.
Lagrangian Particle Models. At the next level of complication, the
Lagrangian particle model type is one level up from the puff-model in
complexity. Being particle-type models they typically requires a large
number of particles to build up some statistical significance in the
simulation.
Eulerian Grid Models. Eulerian grid models solve the diffusion equation
including transfer (advection) of pollutants over a large number of grid
points- typically of the order 100 by 100 for each horizontal layer. In
addition, some 10-30 vertical layers are often used to model the vertical
28

structure of the diffusion. In principle, Eulerian grid models are mass
conserving algorithms (by solving the diffusion equation in a 3-d grid) -
but the diffusivity, called Kz is used to parameterise the vertical spread
during different stability categories, or nowadays, as prescribed by
similarity scaling (e.g. Mikkelsen, 1995).
In addition, wind and turbulence equations can be embedded in Eulerian
grid models, of which some are hydrostatic, and others are nonhydrostatic.
The latter is included to accommodate important pressure
features arising from flows over complex terrain at the local scale.
Furthermore, some Eulerian based Mesoscale models (e.g. the US based
RAMS model or the European-German KAMM model) are "Prognostic",
that is, from a given initial state, they are able to make predictions of
the future wind, temperature and thereby also the pollution pattern. To
run such a combined Mesoscale weather and dispersion model, significant
computational and model specific insight is required by the user. Highresolution
Eulerian grid models may locally complement or nest with large
scale weather forecast model outputs as provided by the national or
international numerical forecasting centres, for instance to predict the
evolution of a local sea-breeze evolution.
Most recent and most complex Models Over the last two decades, more
computer heavy dispersion simulation tools have emerged. They principally
solve the atmospheric boundary layer approximated Navier-Stoke fluid
equations for conservation of mass, momentum, and heat, including
constituencies (pollution). However, their uses for practical applications
are limited by their complexity and huge computational requirements. The
methods include:
Large Eddy Simulation LES. LES models solve the full un-truncated
Navier Stokes equations on a Cartesian three-dimensional grid, but rely
on a sub-grid scale parameterisation of the turbulence dissipation. They
are particular suitable for studies of the unstable (convective) BL
diffusion.
Computational Fluid Dynamic CFD. CFD represent fluid dynamical
numerical codes that can solve the mean flow and diffusion field over a
pre-described configuration, e.g. a group of buildings. They are again
based on the full set of Navier-Stokes conservation equations, but rely on
" K-ε closures", that is on generalized K diffusivities.
29

Direct Numerical Simulation DNS. DNS methods symbolize full and untruncated
solutions of the Navier-Stokes equations including particle
tracking on all scales. As the smallest scale of relevance for atmospheric
dispersion is the Kolmogorov microscale (of the order of ~1 mm) it is
evident that DNS methods are not relevant for atmospheric dispersion,
where scales are ranging from meters to thousand of km, cf. Figure1.
Again, neither DNS nor LES type models are suited for direct practical
real-time air pollution control or emergency assessments, but should
rather be considered as research tools.
On-line Numerical Weather Prediction winds for dispersion
Numerical weather forecast data are today available to dispersion
modeller’s for download from the world’s national and international
weather forecast centres.
Limited Area Models (LAM) with an internal grid resolution down to ~10 x
10 km grid resolution, and with internal time steps of the order of
minutes, produce regional scale (e.g. Europe) forecasts with a forecast
length up to + 36 or + 48 hours.
As an example the joint Scandinavian- European corporation project
HIRLAM (for HIgh Resolution Limited Area Model) weather prediction
code operates at several European national Met offices. HIRLAM is a
complete 3-D regional atmospheric forecasting system. Within a vertical
resolved grid containing some thirty levels, and running around the clock
in a 6 hour updated data-assimilation cycle, HIRLAM produces wind,
temperature, humidity and precipitation + 48 hours ahead.
Numerical weather forecasts of local winds and stability are nowadays online
available in Europe for use with local scale atmospheric dispersion
forecasts. For instance are HIRLAM produced local wind and
precipitation forecasts today operationally accessible for local scale
dispersion calculations within two European Emergency management
decision support systems, RODOS and ARGOS (Mikkelsen, 2000).
30

Atmospheric dispersion module for nuclear releases
Prediction and assessment of the atmospheric transport of radionuclides
released from a nuclear accident requires many different disciplines,
including plume rise, windborne transport and turbulent mixing, irradiation
from puffs and plumes, and deposition (both wet and dry), see Figure 5.
Figure 5 In case of a nuclear release is the actual weather (real-time)
and associated atmospheric dispersion of uttermost importance for
actual transfer of radionuclides to the environment. Many disciplines are
involved (From: European Commission - Safeguarding Europe's Citizens).
We end this Chapter with a practical Example of a contemporary Nested
Atmospheric dispersion Module nowadays under development and
dissemination for Practical Emergency Preparedness in Europe. For a
review of the corresponding American approach see e.g. Kramer and
Porch( 1990).
The Met-RODOS Atmospheric Dispersion Module for Real-time
Decision Support
In Europe, an on-line atmospheric dispersion modelling system called Met-
RODOS has recently been developed and serves now as central part of
the joint European decision support system for nuclear emergencies
called RODOS. [Ehrhardt et al., 1997]. The Met-RODOS module
[Mikkelsen, 2000] provides the decision support system with an
31

integrated atmospheric transport module for now- and forecasting of
radioactive airborne spread on all ranges (local, national, and European
scales), and it incorporates local (on-site) weather stations and remote
numerical weather prediction data from national weather services.
The MET-RODOS dispersion module has three sub-systems:
• A Local-Scale Pre-processor LSP,
• A Local-Scale Model Chain LSMC, and
• A Long-Range Model Chain LRMC
A graphical overview of the Met-RODOS atmospheric dispersion module
is shown in Figure 6 (from Mikkelsen et al., 1997). The systems detailed
functionality specifications are described in Mikkelsen et al. (1998).
Real -time
RO DO S
Shared
Memory
Sodar’ s
On-site
Met-
Towers
Off-site
RODOS INTEGRATED DISPERSION MODULES:
ATSTEP RIM PUFF
N
W
P
ON-LINE MET-DATA INTERFACE & STORAGE
PAD SUB’ S
Local Scale
Pre-processor
u*
z/L
Zi
A,B,C
x
x
x
x
I O I
I O
LINCOM provides
Wind & Turbulence grid fields over:
Topograph Roughness
+4
Hr
10Co
o 15Co
20C
Thermal
Long-
Range
Model
Chain
Figure 6. The MET-RODOS real-time atmospheric dispersion forecasting
system with pre-processors and integrated local-scale and long-range
model chains.
32
M
A
T
C
H

LSP is a local scale pre-processing program that maintains the local-scale
system with actual and forecast local scale wind fields and corresponding
micro-meteorological scaling parameters by real-time pre-processing and
use of the local scale wind models.
LSMC is a nested local scale model chain, which contains a suite of
different local scale mean wind and dispersion models, from which casespecific
models are selected depending on the actual topography and
atmospheric stability features in question. It provides ground level air
concentrations (in [Bq/m 3 ]) and concentration of deposited isotopes (in
[Bq/m 2 ]), and ground level gamma dose rates (in Grays per second [Gy/s])
for subsequent use by the RODOS system. When clouds are leaving the
outer bounds of the local scale domain (variable from 20 km to 160 km),
diffusion specific parameters such as cloud size, content and position is
passed on to the long-range model chain LRMC.
LRMC is a system nested long-range model chain, which manages the
dispersion and fallout assessments on national and European scales. Near
surface air concentrations (in [Bq/m 3 ]) and integrated depositions of
isotopes (in [Bq/m 2 ]) are provided as outputs. Input data consists of
numerical weather prediction data from numerical weather prediction,
which provides the long-range dispersion system with the actual and
forecast atmospheric state and motion on meso and synoptic scales. The
MET-RODOS module furthermore contains real-time databases for online
available Met-tower observations and a Numerical Weather
Prediction (NWP) data.
Prognostic Computer-based Decision Support Systems. MET-RODOS is
realised as an integral part of the RODOS operational system. Mode and
time control, data management, user input and graphics control are all
handled via the RODOS Operating Subsystem. As indicated in Figure6, the
MET-RODOS module communicates with the operating system via shared
memory and interacts directly with the RODOS systems integrated realtime
databases. Source terms are provided accident specific from the
RODOS real-time database, while meteorological data are downloaded in
background via on-line networks. The outputs of MET-RODOS module (dose
rates from air and ground deposited material) are archived and displayed
via the RODOS GUIs The type of radio-ecological "End points" the Met-
RODOS system provides is listed in Table 6.
33

Table 5: Typical end-point quantities from the atmospheric dispersion
module in a nuclear emergency decision support system.
Instantaneous Air concentrations [Bq/m 3 ]
Time integrated air concentrations [Bq s/m 3 ]
Ground level deposits [Bq/m 2 ]
Ground level gamma dose rates [Gray/ Hour]
Online meteorological input data from met-towers. Real-time
application of the system requires an on-line connection to quality realtime
measurements of local meteorological quantities (wind, direction,
stability etc). Such data must be available from at least one nearby and
on-line connected Met-tower in the vicinity of the release point (onsite).For
application of the system on distances beyond the local 10 (20)
km) scale, on-line meteorological measurements from within the regional
(100-km scale) such as wind and temperature conditions must also be
provided the MET-RODOS module for “now-casting” of the plume travel
and spread in real time.
Real-time numerical weather prediction data. Forecasting in time
requires that numerical weather prediction data is available to the
system. Such weather forecast data can be downloaded via the Internet
from national or international meteorological forecasting services. For
Europe, Numerical weather prediction (NWP) data have become available
via the Internet in high spatial and temporal resolution (8 –50 km
horizontal grid resolution at three (and in some cases one) hour time
intervals up to typically +72 hours. The Met-RODOS system has been
operated over a two-year test period with on-line NWP data provided by
the Danish Meteorological Institute's DMI-HIRLAM forecast model
(Sass, 1994).
Atmospheric dispersion models in Met-RODOS: The Local Scale Model
Chain (LSMC) is a real-time atmospheric dispersion system for predicting
the spread of airborne materials (primarily radioactive isotopes, but also
bacteria and viruses and chemical substances) in the vicinity of their
release point, i.e. within ~100 km (local and regional scale) from the
source point
34

It consists of nested modules, which may be grouped into two main subsystems:
• the LSP,
• The Risø Meso-scale Puff dispersion model: RIMPUFF.
The pre-processor LSPAD reads on-line meteorological data or numerical
weather prediction data for "now-cast" or "forecast" simulations, then
interpolates/extrapolates these data onto the points of the calculation
grid covering the area of interest, and calculates the fields of derived
parameters needed by the puff dispersion model RIMPUFF. Local landuse
data and local topography, with less than one kilometre resolution is
available to the system from satellite remote sensing, Thykier-Nielsen
and Hasager (2000).
RIMPUFF reads the source data and the data fields of LSP, and performs
the calculations of dispersion, deposition, and, for radioactive isotopes,
gamma-doses. It handles a high number of radioactive isotopes released
simultaneously, including decay and generation of daughter products.
On-line meteorological input data. Real-time application of the model
chain requires an on-line connection to real-time measurements of local
meteorological quantities (wind speed and direction, temperature,
temperature gradient, and rain intensity), or to up to date numerical
weather prediction (NWP) data. With the latter, dispersion forecast can
be made. Data must be available for at least one Met-tower or one NWP
grid node near the release point (on-site). For application of the system
on distances beyond the local (10-20) km scale, on-line meteorological
measurements from within the regional (100 km) scale or a larger number
of NWP points can be used. For test purposes, LSMC was set up to
automatically interface with weather data downloaded from the Danish
Meteorological Institutes high resolution limited area model DMI-
HIRLAM (Sass, 1994).
The Local Scale Pre-processor (LSP). The pre-processor calculates all
necessary mean and turbulence scaling parameters for the dispersion
modes on a high- resolution grid (typically 100 meters x 100 meters) for
subsequent use by the atmospheric dispersion model. In addition to wind
speed, direction and temperature, also turbulence scaling parameters
(friction velocity and Monin-Obukhov length), stability category, mixing
35

height is generated for each 10-min time step. Local scale wind and
turbulence fields are generated from the LSP-embedded LINCOM model.
Linearized mean and turbulence wind models LINCOM
Detailed modelling of the wind and turbulence fields on the local scale is
important for prediction of the trajectory-directions and the time of
arrival of radioactive clouds traversing hilly terrain and heterogeneous
surfaces (e.g. over land-water-land interfaces).
LINCOM is a fast diagnostic mean wind model based on linearized Navier-
Stokes equations for mass and momentum conservation, using a first
order spectral turbulent diffusion closure. Local scale grid files
consisting of mean wind and turbulence (u*) fields are In LINCOM
modelled with respect to: local topography (Troen and de Baas, 1986], 2)
the surface aerodynamic roughness [Astrup et a1, 1997], and 3) the
vertical thermal stratification of the atmosphere [Moreno et al 1994], 4)
local sea breeze effects [Dunkerley et al., 2001]. Figure 7 shows LINCOM
generated fields of wind speed and turbulence over Northern Zealand,
Denmark.
Figure 7: Met-RODOS Pre-processor generated fields over Northern
Zealand - Denmark, on a 0.5 km * 0.5 km grid. left: Roughness distribution
(z0); mid: LINCOM-z0 mean wind field (U); right: LINCOM-z0 generated
turbulence wind field (u*).
Pasquill-Gifford Stability, Similarity Scaling and Mixing Height.
Within LSMC, the stability parameters are calculated at each grid node
according to the local velocity and turbulence levels, combined with the
temperature gradient at the nearest measurement station or numerical
weather prediction (NWP) node point. Due to the large discrepancies
between temperature gradients over land and over water, stability over
36

land uses the nearest land-based Met-station or NWP point, and over
water, the nearest water-based station is used.
Mixing height determination. In LSP, the friction velocity and Monin-
Obukhov length are calculated following the descriptions given by van
Ulden and Holtslag (1985), and the mixing height is taken as the maximum
of the mechanical mixing height according to the model of Nieuwstadt,
1980 and the convective mixing height (Batchvarova and Gryning, 1991)
Alternatively, if high quality NPW data are available, inversion height zi is
determined from a critical bulk Richardson number (Sørensen et al. 1996.)
The puff dispersion model RIMPUFF. RIMPUFF, the systems local scale
puff diffusion model [Mikkelsen et al.(1984); Mikkelsen et al. (1997);
Mikkelsen et al. (1998)], provides a detailed real-time simulation of the
actual atmospheric dispersion scenario by accounting for local changes in
dispersion characteristics in both time and space. RIMPUFF is based on
Lagrangian tracking of a number of dispersing puffs, where each puff
represents an instantaneous released amount of isotopes, the
concentration profile of which is approximated with a Gaussian profile.
RIMPUFF has puff-splitting features such as "pentafurcation" (horizontal
split of a puff into five minor puffs) and "trifurcation" (vertical split of a
puff into three minor puffs) for improving its dispersion modelling with
horizontal wind shear and shear effects over inversion layers, but also
for dispersion over terrain causing channelling. The advection and growth
of each puff uses typically time steps of ~ 10 second and are calculated
with the local wind and turbulence fields as provided by LSP. All diffusion
and deposition calculation within RIMPUFF is formula-based
(parameterised). For the puffs dispersion parameters σy and σz, three
different parameterization options are included, depending on the release
type:
1. Karlsruhe-Jülich plume parameters: Release height and distance
dependent 1-hour averaged plume sigma's.
2. Risø instantaneous instant puff-diffusion sigma's (no averaging).
3. Similarity-theory scaled plume-sigma's (averaging time 10 minutes to 1
hour).
In RIMPUFF, dry deposition accounts for deposition of different
chemical forms of the dispersed material, e.g. iodine vapour (elementary
iodide) and iodine aerosols. Deposition velocities furthermore depend on
land use.
37

Figure8:
Deposition footprint
simulation by RIMPUFF of a
depositing 137 Cs plumes from a
simulated accident at the
Ignalina NPP; Lithuanian.
Figure 8 shows a RIMPUFF calculated footprint of deposited
radioactivity from a 137 Cs plume from the Ignalina NPP. During the plume
passage, the deposition rate varies according to the local surface
characteristics (land, water, forest, urban, etc.).
Figure 9
Simulations of
continuous plume
dispersion from the
Met-tower at the
Risø National
Laboratory,
Roskilde, Denmark,
during a period with
strong vertical winddirectional
shear.
Solid curves:
accounting for wind
shear (by RIMPUFF
model features
shear rise and
trifurcation), dotted curves: ignoring the wind shear effects.
38

Another example, showing the effect of strong vertical directional shear,
is shown in Fig. 9. The consequence for emergency response strategy may
be dramatic!
Urban Dispersion:
Figure 10. Urban Dispersion scenario from a hypothetical release of
Anthrax in the stairways to the metro at Kgs. Nytorv, Copenhagen.
Urban Dispersion. An example of local dispersion within an urban area
(Central Copenhagen in this case), is shown in Figure 10. The calculation
has been performed with the British UDM Urban dispersion model (Hall
et al., 2002). UDM can be nested with RIMPUFF so that UDM calculates
the initial urban dispersion influenced by the buildings, while RIMPUFF
takes over at longer distances.
39

IV Atmospheric Dispersion: Release of Heavy gases
Morten Nielsen, Risø, has produced the text in Chapter IV
Dispersion models for industrial safety
Manufacturers, distributing agents, and public authorities need to
formulate safety policies for toxic and flammable gases. This involves a
wide range of aspects: intrinsic process safety, equipment, alarm
systems, handling procedures, personnel training, spatial planning, and the
likelihood and consequences of possible accidents. Gas dispersion is an
important task in the consequence analysis and in the context of
industrial accidents the source buoyancy and momentum may alter the
flow and turbulence fields significantly. This calls for special dispersion
models.
Source terms. Some gases used in industry are simply denser than air,
for example chlorine, which has a molecular weight 2.45 times that of air.
The temperature deficit may also contribute significantly to the density
effect. To understand this, we shall review the typical source conditions.
It is convenient to store gas in a compressed state in pressurised or
refrigerated containers. An accidental spill of liquefied gas from a
refrigerated container will typically form a pool on the ground. If the
atmospheric boiling-point temperature of the compound is lower than the
ambient air temperature, the pool will boil as long as the heat transfer
from the ground is sufficient. The evaporation rate will depend on the
available heat, the ventilating airflow above the pool, and the surface
area. Obvious mitigation methods are to cover the pool by foam or try to
limit horizontal spreading. It is generally a bad idea to pour water on the
pool, since this will contribute with additional heat for evaporation - in
particular if the chemical reacts with water. The evaporation rate will be
most intense in the initial stage of the accident, since the heat supply
weakens as the ground is cooled. A multi-component pool has a timedependent
composition, since the most volatile component tends to
evaporate first. A leakage from a pressure-liquefied tank will usually
produce a two-phase jet, with liquid aerosols so tiny that they deposit
only if the jet hits a nearby obstruction. The heat requirement for
aerosol evaporation will keep the two-phase cloud cold for a longer time
than a single-phase cloud. The combined effect of temperature deficit
and latent heat of evaporation is characterised by source enthalpy.
40

Density calculations. Numerical dispersion models for non-isothermal gas
clouds usually rely on a thermodynamic sub-model, based on the
assumption of homogeneous thermal equilibrium. This steady-state
approximation claims that liquid aerosols and the gaseous phase are of
equal temperature and sets the gas partial pressure in balance with the
vapour pressure of the condensed material. The thermodynamic state is
determined by an enthalpy budget, and the thermodynamic model is used
to find the mixture temperature, the degree of condensation, and the
density for a given mixing ratio. Rapid chemical reactions are treated in a
similar way. The homogeneous equilibrium assumption allows the model
developer to separate all this from the dispersion calculation, and it
provides sufficiently accurate density predictions when the aerosol
droplets are small. This is usually the situation in an emission from a
pressurised tank, where the liquid often becomes quite superheated by
the pressure relief. The flash-boiling emission efficiently entrains air and
most liquefied gas evaporates within a short distance. The water content
of the entrained air will condense, and these almost pure water aerosols
will persist to the downwind distance where the cloud reaches its dewpoint
temperature.
Relative density difference, ∆ρ/ρ air
1
0.1
0.01
M * approximation
H 2 O aerosols
Immiscible aerosols
Hygroscopic aerosols
Fladis 9 (Ammonia)
T air =16 °C and R.H.=86%
0.1 1.0 10.0 100.0
Mixture Concentration, c [mole%]
Figure 11: Density difference of a two-phase mixture of ammonia and
humid air as a function of concentration as predicted by four
models, see text for discussion.
41

Figure 11 shows relative excess density ∆ρ ρ air as a function of mixing
concentration c calculated by four models of different complexities. Each
model assumes adiabatic mixing, i.e. it neglects possible heat transfer
from the ground. The chosen atmospheric conditions match the most
humid case in a set of field experiments with liquefied ammonia (Nielsen
et al, 1987). Ammonia is a hygroscopic substance (i.e. readily reacting with
air humidity) and the thick solid curve, calculated by Wheatley´s (1987)
model, is the most accurate one. This solution may be divided into three
domains: dry mixing, nearly pure water aerosols and nearly pure ammonia.
The moisture affects the aerosol formation in two ways: the relative
humidity determines the limit of transition between dry and wet mixing,
while the absolute humidity (depending on air temperature) determines
the magnitude of the deviation from dry mixing. The immiscible aerosol
model (dashed line) does surprisingly well with just a slight over
prediction of the density in the domain of almost pure water aerosols.
Most heavy gas sources produce an initial dilution, and the domain of
almost pure ammonia is unimportant for heavy-gas dispersion. The
relatively simple pure water condensation model (thin line) is therefore
adequate for most heavy-gas calculations. The straight dotted line,
∆ρρair ≈ c ∆M∗M
air , is based on the effective molecular weight,
air
M∗ = M−∆H0c c p Tairh, which approximates the dilute limit of pure gasphase
mixtures (Nielsen & Ott, 1999). M is the contaminant molar weight
[kg mole -1 air
], cp and
T air are the heat capacity [J (kg K) -1 ] and absolute
temperature [K] of the entrained air, and the enthalpy difference [J kg -1 ]
between source and ambient conditions, ∆H 0 , is assumed constant. The
simple M∗ approximately describes the domain of dry mixing quite well,
but has a deviation of up to 78% in the domain of almost pure water
aerosols. The test scenario is however a demanding one, partly because of
the high relative humidity and partly because of the large heat of
evaporation and low molecular weight of ammonia. The M∗ approximation
will be more successful for other release conditions and it is a useful
concept when comparing the results of wind-tunnel test with those from
large-scale releases of liquefied gasses.
Cloud Dynamics. The combined forces of gravity and the ambient wind
drive heavy gas dynamics. The negative buoyancy makes the cloud spread
horizontally and gives it a tendency to move downhill in sloping terrain.
The density stratification between the cloud and the air above reduces
the turbulent kinetic energy level and vertical mixing. Thus, a heavy-gas
42

cloud is expected to cover a larger surface with higher gas concentration
than a cloud of neutral buoyancy.
Heavy gas dispersion may be predicted by three-dimensional numerical
flow models with a k-ε turbulence closure (e.g. Pereira & Chen, 1996).
These models parameterise the turbulent mixing by concentration
gradients and an isotropic diffusion coefficients, predicted by the local
turbulent kinetic energy, local stratification and distances to solid
boundaries. In heavy-gas applications the k-ε models must update the
turbulence field during the time integration, since the turbulence
depends on the developing gas field. At present the typical grid is a
relatively coarse mesh of 30×30×30 cells and often arranged with an
irregular spacing that enhances the resolution near the source and near
the ground.
An alternative and computationally cheaper method is to parameterise
the mixing process by an entrainment function. Following this approach,
the heavy fluid and the ambient fluid are considered to be two distinct
volumes, the mixing zone is idealised to an interface. Horizontal spreading
may then be predicted by two-dimensional layer-integrated flow
equations (e.g. Hankin & Britter 1999).
The most popular models in risk assessment are of the box model type,
which requires less computation as it simplifies the gas field to a single
control volume, whose time development is predicted by ordinary
differential equations (e.g. Witlox 1994).
The driving potential for the horizontal spreading is the excess pressure
resulting from the density difference between the cloud and ambient air.
b g , where g is
The front velocity [m s -2 ] in calm air is ufgh 105 . ρ ρair gravity [m s -2 ] and h is the cloud height [m] (Brighton et al. 1985). In box
models, the mixing in the turbulent wake of the spreading front is
interpreted as `edge entrainment´ and parameterised by the mixing rate
016 . u (Simpson & Britter, 1979) multiplied by the cloud perimeter and
f
ue f
height. The mixing through the cloud top is formulated as the
entrainment velocity ue
multiplied by the top area. One parameterisation
out of several alternatives is ue e 25 . 333 . Rie
d i
velocity scale e u 01
. w
3 3
* *
13
b g with the turbulence
defined by the friction velocity, u , and the
heat-convection velocity scale, w * , typical for the conditions inside the
gas cloud (Nielsen, 1998). Jensen (1981) proposed an analogy with the
43
*

uair
uair
.
ue
u(t)
.
.
uf
Fd
f
ue
ue
x(t)
uair
uf ue ue
f
uef
u
.
ue
ue
uf
f
Figure 12: Various box-models for heavy gas dispersion: a) Model for
instantaneous releases, b) Model for a jet or plume with ground contact,
c) ’Ballistic’ model for a free jet, d) Model for an instantaneous releases
on sloping ground.
atmospheric surface layer and used Monin-Obukhov theory to estimate
the turbulent velocity scales u * and w * . The in-plume Monin-Obukhov
length was estimated by the cloud height, advection speed, and
temperature deficit relative to the surface. The dimensionless number in
the denominator of the entrainment function is a bulk Richardson number,
Rie gh e
ρ ρ air , which represents the internal cloud stability. There is no
clear consensus on entrainment functions – probably because of the lack
of adequate turbulence measurements in the field. Box model developers
have been forced to calibrate coefficients in their entrainment functions
by the resulting gas field. Comparison of entrainment functions is further
complicated by the fact that individual model definitions of Richardson
numbers and cloud height vary.
Figure 12 shows a collection of heavy-gas box models of variable
geometry. The first model, designed for instantaneous gas releases,
considers the entire cloud as its control volume and adopts the cloud
radius, mass and enthalpy as the main variables in the integration.
44
.

Auxiliary parameters like concentration, temperature, density, volume,
height, turbulence, and heat flux from the ground are derived from the
main variables. The front velocity and the mass and enthalpy balances
provide differential equations for the time development. The cloud
velocity is either set equal to the ambient wind velocity or determined by
a momentum balance. The second part of the figure shows a model of a
jet or plume with ground contact. Here, the plume width is the relevant
horizontal dimension and the cloud mass and enthalpy described as fluxes
through the plume cross section instead of the integral values. The
differential equations and the auxiliary parameters are very similar to
those of the box model for instantaneous release. There are many
publicly available heavy gas models of this type, e.g. HEGADAS (Witlox,
1994), DEGADIS (Spicer and Havens, 1986), SLAM (Ermak, 1990), and
DRIFT (Webber et al., 1992). The third part of the figure shows a free
jet whose trajectory is influenced by gravity in a `ballistic’ manner,
which also includes the drag force of the ambient flow and the momentum
of the entrained air (e.g. Ooms and Duijm, 1983). The entrainment rate in
this model is different from that for the model of clouds with ground
contact; it mainly depends on the velocity shear between the jet and the
surrounding air. The fourth part of the figure shows a model for
instantaneous releases in sloping terrain. The top is flat and horizontal,
which is the steady state solution of a layer-integrated two-dimensional
model (Webber et al, 1993). The sharp profiles of the various box models
are unrealistic and the predicted fields are often smoothed by empirical
similarity profiles before presentation to the model users.
Heat transfer from the ground. The heat transfer from the ground to
a cold gas cloud affects the dispersion in two ways: It modifies the cloud
density and produces additional turbulence. The resulting density effect
is linked to the dispersion process as illustrated in Figure 13.
A box model calculates these curves, and in order to avoid the complexity
of two-phase density calculations the diluting air has no humidity. The
release conditions are listed in Table 6. The heat transfer is most
significant when the cloud has a large temperature deficit, i.e. close to
the source where gas concentrations are relative high. In the reference
case (fat solid line) the accumulated heating changes the cloud buoyancy.
This is compared to the cases of no ground heating (thin straight line),
enhanced mixing near the source (doted line), a higher wind speed
(dashed line) and enhanced entrainment rate (dashed-dotted line). Each
of these factors moderates the heating effect.
45

Relative density difference, ∆ρ/ρ air
1
0.1
0.01
0.001
1: No heat transfer
2: Extra source dilution
3: Increased wind speed
4: Enhanced entrainment
Reference case
0.1 1.0 10.0
Mixture Concentration, c [mole%]
Figure 13: Predicted Heat-Flux Effect on the Density Difference of a
Propane Plume as a Function of Concentration. Release conditions are
given in Table 1.
Table 6: Release conditions for test cases in Figure 13.
Reference
case
Compariso
n cases
Release rate
Wind speed
Surface roughness
Air temperature
Air pressure
Air humidity
1: No heat transfer
2: Extra source dilution
3: Increased wind speed
4: Enhanced entrainment
46
&m= 3 kg s -1 C3H8(l)
u10= 2 m s -1
z0= 0.01 m
Tair = 288 K
pair = 100 kNm -2
R.H.= 0%
ϕ 0
3initial dilution
u10 = 4 m/s
ue doubled

Variable atmospheric wind conditions make the integral heat balances
quite difficult, and as an alternative, Nielsen and Ott (1999) preferred to
test whether local cloud enthalpies were in accordance with the
assumption of adiabatic mixing, ∆H = c ⋅ ∆H0
. The cloud enthalpies were
calculated by adjacent measurements of temperature and concentration,
using the homogeneous-equilibrium assumption and Wheatley's (1987)
aerosol model to evaluate the degree of aerosol condensation. The
analysis found reductions in excess cloud buoyancy in the range 38-
59%, which is almost as significant as suggested in Figure 3. The heattransfer
effect was found to depend on the distance from the source and
seemed to depend on the efficiency of the near-source mixing.
Obviously the ground will not sustain heat transfer forever. Nielsen and
Ott (1999) analysed in-soil heat flux measurements from the Desert
Tortoise liquefied ammonia experiments (Goldwire et al 1985) and
concluded that the surface heat flux at 100-m distance decreased to
62% of its initial value.
That’s all folks…
Acknowledgements:
The author acknowledges contributions to this article from colleagues
Morten Nielsen, Poul Astrup, Søren Thykier-Nielsen and Fay Dunkerley.
47

References
Atmosheric dispersion, Chapter I- III
ApSimon, H. M., A. Goddard and J. Wrigley (1980): Estimating the
possible transfrontier consequences of accidental releases: the MESOS
Model for long range atmospheric dispersal. In: Seminar on Radioactive
Releases and Their Dispersion in the Atmosphere Following a Hypothetical
Reactor Accident. Risø, 22-25 April 1980. Edited by F. van Hoeck and P.
Recht. Vol. 2. (Commission of the European Communities, Luxembourg,
1980) pp 819-866.
Astrup P., N.O. Jensen and T. Mikkelsen (1997): A fast model for mean
and turbulent winds characteristics over terrain with mixed surface
roughness. Radiat. Prot. Dosim. (1997) Vol. 73, pp. 257-260
Batchelor, G.K. (1952): Diffusion in the Field of Homogeneous Turbulence,
II. The relative motion of particles, Proc. Camb, Phil. Soc., Vol. 48, p 345.
Batchelor, G.K (1959) Note on the diffusion from sources in a turbulent
boundary layer (Unpublished)
Batchelor, G.K. (1964) Diffusion from sources in a turbulent boundary
layer, Archiv Mechanik i Stosowanej, Vol 3, p 661.
Batchvarova E. and S.-E. Gryning (1991): Applied Model for the Growth of
the Daytime Mixed Layer. Boundary-Layer Meteorology. Vol 56, pp. 261--
274.
Brandt, J.; Mikkelsen, T.; Thykier-Nielsen, S.; Zlatev, Z.( 1996a): The
Danish RIMPUFF and Eulerian accidental release model (the dream). 21.
General assembly of the European Geophysical Society, The Hague (NL),
6-10 May 1996. Ann. Geophys. Suppl. 2 (1996) 14, C486
Brandt, J.; Mikkelsen, T.; Thykier-Nielsen, S.; Zlatev, Z.,( 1996b): The
Danish Rimpuff and Eulerian Accident release model (The DREAM). Phys.
Chem. Earth (1996) Vol. 21, pp 441-444.
48

Busch, N.E., On the Mechanics of Atmospheric Turbulence. In: Workshop
on Micrometeorology. Edited by D.A. Hangen. (American Meteorological
Society, Boston, 1973), pp 1-65.
Chatwin, P.C. (1968) The dispersion of a puff of passive contaminant in
the constant stress region, Quart. J. R. Met. Soc., Vol. 94, pp 350-360
Cionco, R.M.; aufm Kampe, W.; Biltoft, C.; Byers, J.H.; Collins, C.G.; Higgs,
T.J.; Hin, A.R.T.; Johansson, P.E.; Jones, C.D.; Jørgensen, H.E.; Kimber,
J.F.; Mikkelsen, T.; Nyren, K.; Ride, D.J.; Robson, R.; Santabarbara, J.M.;
Streicher, J.; Thykier-Nielsen, S.; Raden H. van; Weber, H., An overview
of MADONA: A multinational field study of high-resolution meteorology
and diffusion over complex terrain. Bull. Am. Meteorol. Soc. (1999) Vol.
80, pp 5-19.
Dunkerley, F.N.; Mikkelsen, T.; Griffiths, I.H., A simple model for
predicting the local mean wind field near a coastline. EGS 2001, 26.
General assembly, Nice (FR), 25-30 Mar 2001.
Ehrhardt, J.; Brown, J.; French, S.; Kelly, G.N.; Mikkelsen, T.; Müller, H.,
RODOS: Decision-making support for offside emergency management
after nuclear accidents. Kerntechnik (1997) 62, 122-128
Gifford, F. (1988). A simple theory for the description of cloud spreading
at ranges from 1-2000 km. In: Air Pollution Modelling and Its Application
VI. Proceedings of the 16. NATO/CCMS International Technical Meeting.
Lindau, 6-10 Apr 1987. Dop, H. van (ed.), (Plenum Press, New York, 1988)
(NATO Challenges of Modern Society, 11) p. 569-577.
Hall, D.J., A.M. Spanton , I.H. Griffiths, M. Hargarve and S. Walker
(2002): The Urban Dispersion Model (UDM): Version 2.2 Technical
Documentation; DSTL/TR04774; 2 September, 2002.
Kadar B. A, Yaglom, A.M. and Zubkovskii, S. L. (1989) Spatial correlation
functions of surface-layer atmospheric turbulence in neutral
stratification. Boundary-Layer Meteorology, Vol. 47, 233-249.
Kramer, M.L. & W. M. Porch (Eds.) 1990: Meteorological aspects of
Emergency Response, American Meteorological Society. 119 pp.
49

Maryon R.H. and A.T. Buckland (1995) Tropospheric dispersion: The first
ten days after a puff release. Q. J. R. Meteorol. Soc. Vol 121B , pp 1799-
1834.
Mikkelsen, T.; Larsen, S.E.; Thykier-Nielsen, S., Description of the Risø
Puff Diffusion Model. Nucl. Technol. 67 (1984) 56-65.
Mikkelsen, T. (1995): Modelling Diffusion and Dispersion of Pollutants. In:
Diffusion and Transport of Pollutants in Atmospheric Mesoscale Flow
Fields. Eds. A. Gyr and F-S. Rys, Kluwer Academic Publishers, ERCOFTAC
SERIES, 1995.
Mikkelsen, T.; Thykier-Nielsen, S.; Astrup, P.; Santabárbara, J.M.;
Sørensen, J.H.; Rasmussen, A.; Robertson, L.; Ullerstig, A.; Deme, S.;
Martens, R.; Bartzis, J.G.; Päsler-Sauer, J., MET-RODOS: A
comprehensive atmospheric dispersion module. Radiat. Prot. Dosim. (1997)
73, 45-56.
Mikkelsen, T.; Thykier-Nielsen, S.; Astrup, P.; Santabárbara, J.M.;
Havskov Sørensen, J.; Rasmussen, A.; Deme, S.; Martens, R., An
operational real-time model chain for flow- and forecasting of radioactive
atmospheric releases on the local scale. In: Air pollution modelling and its
application 12. 22. NATO/CCMS international technical meeting,
Clermont-Ferrand (FR), 2-6 Jun 1997. Gryning, S. -E.; Chaumerliac, N.
(eds.), (Plenum Press, New York, 1998) (NATO Challenges of Modern
Society, 22) pp. 501-508.]
Mikkelsen, T. (2000) Meteorology and atmospheric dispersion. In:
Ehrhardt, J.; Weis, A. (Eds.) RODOS: Decision support system for offsite
nuclear emergency management in Europe. Final project report. EUR-
19144 (2000) p. 57-88.
Mikkelsen, T., Meteorology and atmospheric dispersion. In: Ehrhardt, J.;
Weis, A. (eds.), RODOS: Decision support system for off-site nuclear
emergency management in Europe. Final project report. EUR-19144
(2000) p. 57-88
Mikkelsen, T., H. E. Jørgensen, M. Nielsen and S. Ott (2002): Similarity
Scaling of Surface-released Smoke Plumes. Boundary-Layer Meteorology
105: 483–505, 2002.
50

Monin A.S. (1959) Smoke propagation in the surface layer of the
atmosphere, Atmospheric Diffusion and Air Pollution, ed. F. N. Frenkiel
and P.A. Sheppard, Advances in Geophysics, 6, 331pp, Academic Press.
Moreno, J., A.M. Sempreviva, T. Mikkelsen, G. Lai and R. Kamada (1994). A
spectral diagnostic model for wind flow simulation: extension to thermal
forcing. In proceedings of the Second International Conference on Air
Pollution, 27-29 September 1994, Barcelona, Spain. (Eds.) J.M. Baldasano,
C.A. Brebbia, H. Power and P. Senate, Computational Mechanics
Publications, Southhamton, U.K., Vol II, pp 51-58.
Nagstrom, G. D. and K.S. Gage (1985): A climatology of atmospheric wavenumber
spectra of wind and temperature observed by a commercial
aircraft. J. Atmos. Sci. Vol. 42. p 950.
Nieuwstadt, F.T.M. (1981): The Steady-State Height and Resistance Laws
of the Nocturnal Boundary Layer: Theory compared with Cabauw
Observations. Boundary-Layer Meteorology. Vol. 20, pp. 3-17.
Olesen, H.R. and Mikkelsen, T. (Eds.) 1992: Proceedings of the workshop
"Objectives for Next Generation of Practical short-range Atmospheric
Dispersion Models", Risø, Denmark, May 6-8 Danish Centre for Atmospheric
Research (DCAR), P.O.BOX 358, DK-4000 Roskilde. 262 pp.
Ott, S., Mann, J. (2000) An experimental investigation of the relative
diffusion of particle pairs in three-dimensional turbulent flow. J. Fluid
Mech. 422 , 207-223
Pasquill, F. (1961) The Estimation of the Dispersion of Windborne
Material. Meteorol. Mag., 90 (1063), pp33-49.
Pielke, R. A. 1984 Mesoscale Meteorological Modelling, Academic Press.
Richardson, F. L. (1926): Atmospheric diffusion shown on a distanceneighbour
graph, Proc. Roy. Soc. Soc., A, Vol. 97, p 354.
Sass, B.H. (1994): The DMI Operational HIRLAM Forecasting System,
Version 2.3. Danish Meteorological Institute. DMI Technical Report 94-8.
51

Smagorinsky, J. (1981) Epilogue: a perspective of dynamical meteorology.
In Dynamical meteorology. An Introductory selection. Ed. B.W. Atkinson,
Methuen, 205-219.
Sørensen J.H., A. Rasmussen and H. Svensmark (1996): Forecast of
Atmospheric Boundary-Layer Height Utilised for ETEX Real-time
Dispersion Modelling. Physics and Chemistry of the Earth. Vol. 21, pp.
435--439.
Taylor, G. I. (1921) Diffusion by continuous movements. Proc. London
Math. Soc., Ser.2, Vol. 20, p 196.
Tchen, C.M. (1959) Diffusion of Particles in Turbulent Flow. In : Frenkiel,
F.N.; Sheppard, P.A. (Eds.). Atmospheric diffusion and air pollution.
Academic Press. 1959. 488 pp
Thykier-Nielsen, S.; Hasager, C.B., Satellite maps of land cover used in a
real-time air pollution deposition model. Scenarios for Ignalina nuclear
power plant, Lithuania. EGS 2000, 25. General assembly: Millennium
conference on earth, planetary and solar systems sciences, Nice (FR), 25-
29 Apr 2000. Geophys. Res. Abstr.
Troen, I. and de Baas, A. F. (1986): A spectral diagnostic model for wind
flow simulation in complex terrain. In: Proceedings of the European Wind
Energy Association Conference & Exhibition, pp.37-41, Rome, 1986.
van Ulden, A.P. and A.A.M. Holtslag (1985): Estimation of Atmospheric
Boundary Layer Parameters for Diffusion Applications. Journal of Climate
and Applied Meteorology. Vol. 24, pp. 1196-1207.
References, cont.: Heavy gases (Chapter IV).
Brighton, P.W.M., Prince, A..J. and Webber, D. M. (1985) Determination of
cloud area and path from visual and concentration records, J. Hazard.
Mater. 11 ,155-178.
Ermak, D. L., (1990) User's Manuals for SLAB: An Atmospheric Dispersion
Model for Denser-Than-Air Releases, UCRL-MA-105607, Lawrence
Livermore National Laboratory, Ca., 144p.
52

Goldwire, H. C., McRae, T. G., Johnson, G. W., Hipple, D. L., Koopman, R. P. ,
McClure, J. W., Morris, L. K. and Cederwall, R. T. (1985) Desert Tortoise
series data report - 1983 Pressurized ammonia spills, UCID-20562, US
Lawrence Livermore National Laboratory, 244 pp.
Hankin, R. K. S. and Britter, R. E. (1999) TWODEE: the Helath and Safety
Laboratory's shallow water layer model for heavy gas dispersion. Part 1:
Mathematical basis and physical assumptions, J. Hazard. Mater. A66 ,
211-226,
Jensen, N. O., (1981), Entrainment through the top of a heavy gas cloud,
In C. de Wispelaere,: Air Pollution Modeling and its Application- I, Plenum
Press, New York, 477-487.
Nielsen, M., Ott, S., Jørgensen, H. E., Bengtsson, R., Nyrén, K., Winter, S.,
Ride, D. and Jones, C. (1997) Field experiments with dispersion of
pressure liquefied ammonia, J. Hazard. Mater. 56 ,59-105.
Nielsen, M. (1998) Dense gas dispersion in the atmosphere, Risø-R-
1030(EN), Risø National Laboratory, 276 pp.
Nielsen, M. and Ott, S. (1999) Heat transfer in large-scale heavy-gas
dispersion, J. Hazard. Mater. A67, 41-58.
Ooms, G. and Duijm, N. J. (1983) Dispersion of a stack plume heavier than
air, In: Ooms, G. and Tennekes, H. (Eds.) Atmospheric Dispersion of
Heavy Gas and Small Particles, Springer Verlag, 1-23.
Pereira, J. C. F. and Chen, X.-Q. (1996) Numerical calculation of unsteady
heavy gas dispersion, J. Hazard. Mater. 46, 253-272.
Simpson, J. E. and Britter, R. E. (1979) The dynamics of a head of a
gravity current advancing over a horizontal surface, J. Fluid Mech. 94,
447-495.
Spicer, T. O. and Havens, J. A. (1986) Development of a Heavier-Than-Air
Dispersion Model for the US Coast Guard Hazard Assessment Computer
System, in S. Hartwig (ed.), Heavy Gas and Risk Assessment - III,
Battelle Institute e. V., Frankfurt am Main, Germany, pp. 73-121.
53

Webber, D. M., Jones, S. J., Tickle, G. A. and Wren, T. (1992) A Model of
a Dispersion Dense Gas Cloud, and the Computer Implementation II.
Steady Continuous Releases, SRD-R587, UK Atomic Energy Authority,
Safety and Reliability Directorate, 101 p.
Webber, D. M., Jones, S. J. and Martin, D. (1993) A model of the motion
of a heavy gas cloud released on a uniform slope, J. Hazard. Mater. 33,
101-122.
Wheatley, C. J. (1987) Discharge of liquid ammonia to moist atmospheres
- survey of experimental data and model for estimating initial conditions
for dispersion calculations, SRD/HSE-R410, UK Athomic Energy
Authority, 41 pp.
Witlox, H. W. M. (1994) The HEGADAS model for ground-level heavy-gas
dispersion, Atm. Env. 28, 2917-2932.
54

Table of Content
Modelling of Pollutant Transport in the Atmosphere .......................................1
I Atmospheric dispersion: Basic ............................................................................1
Key Factors Influencing Atmospheric Dispersion .........................................2
Introduction........................................................................................................2
The Structure of the Atmosphere ...............................................................2
The importance of the local wind field ........................................................5
The Temperature Profile and Atmospheric Stability...............................7
Atmospheric Dispersion at different scales.............................................10
II Diffusion Theories and associated Atmospheric Dispersion Models ....12
Fixed and moving frames of reference......................................................12
III Atmospheric Dispersion Models - Applications: .......................................26
Practical Atmospheric Dispersion Models .....................................................27
Dispersion Model Gallery:..............................................................................27
On-line Numerical Weather Prediction winds for dispersion ...............30
Atmospheric dispersion module for nuclear releases.............................31
The Met-RODOS Atmospheric Dispersion Module for Real-time
Decision Support..............................................................................................31
Urban Dispersion: ............................................................................................39
IV Atmospheric Dispersion: Release of Heavy gases .....................................40
Dispersion models for industrial safety.....................................................40
References ................................................................................................................48
Atmosheric dispersion, Chapter I- III......................................................48
References, cont.: Heavy gases (Chapter IV). ........................................52
55