| Re: gaussian air dispersion model [message #46503] |
Sun, 27 November 2005 17:27  |
Mark Hadfield
Messages: 783
Registered: May 1995
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Senior Member |
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guillaume.drolet.1@ulaval.ca wrote:
> Hi Mark,
>
> The following comes from N. Kljun. She developed the footprint model:
>
> "...you'll get the along-wind extent, but it's a crosswind-integrated
> model (no y-information).
> the full model gives you the y-information, but is not easy to be
> applied and it will be extremely time-consuming to run it for that many
> cases as you will have to.
> it'll be easier to estimate the y-extent using a simple gaussian
> dispersion function."
>
> I'm sorry, I made a mistake in my first post: I need to estimate the
> 'across-wind' extent (y-extent), and NOT the 'along-wind' (x-extent),
> which will be given by the model.
So are you going to estimate the cross-wind-integrated ground level
concentration with the footprint model and the across-wind variation in
concentration with a gaussian function? In which case you will need an
estimate of across-wind width vs downwind distance (sigmay as a function
of x). How are you going to estimate that?
> For this simple model, the following inputs are needed:
>
> zm = Measurement height [m]
> znot = Roughness length [m]
> h = Boundary layer height [m]
> sigmaw = sigmaw [m s-1]
> ustar = u* [m s-1]
> r = Percentage to be included [%]
>
> Some inputs are available from flux towers measurements
> (zm,sigmaw,ustar) while others are estimates (znot,h). The outputs are:
>
> xmax: location of maximum influence for the location
> xr :distance from receptor which include r% of the area contributing
> to the measured flux.
By "this simple model" you mean the footprint model, right?
> Is that enough information? For more details on the model, see:
> http://footprint.kljun.net
I've looked at the URL, but not read the paper. It sounds like the
footprint model is a simple set of formulae. Do you plan to implement
this in IDL? Shouldn't be too hard.
So where do you want help?
--
Mark Hadfield "Kei puwaha te tai nei, Hoea tahi tatou"
m.hadfield@niwa.co.nz
National Institute for Water and Atmospheric Research (NIWA)
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| Re: gaussian air dispersion model [message #46514 is a reply to message #46503] |
Fri, 25 November 2005 09:28  |
guillaume.drolet.1
Messages: 20
Registered: July 2005
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Junior Member |
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Hi Mark,
The following comes from N. Kljun. She developed the footprint model:
"...you'll get the along-wind extent, but it's a crosswind-integrated
model (no y-information).
the full model gives you the y-information, but is not easy to be
applied and it will be extremely time-consuming to run it for that many
cases as you will have to.
it'll be easier to estimate the y-extent using a simple gaussian
dispersion function."
I'm sorry, I made a mistake in my first post: I need to estimate the
'across-wind' extent (y-extent), and NOT the 'along-wind' (x-extent),
which will be given by the model.
For this simple model, the following inputs are needed:
zm = Measurement height [m]
znot = Roughness length [m]
h = Boundary layer height [m]
sigmaw = sigmaw [m s-1]
ustar = u* [m s-1]
r = Percentage to be included [%]
Some inputs are available from flux towers measurements
(zm,sigmaw,ustar) while others are estimates (znot,h). The outputs are:
xmax: location of maximum influence for the location
xr :distance from receptor which include r% of the area contributing
to the measured flux.
Is that enough information? For more details on the model, see:
http://footprint.kljun.net
Thanks again.
Gui
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| Re: gaussian air dispersion model [message #46524 is a reply to message #46514] |
Thu, 24 November 2005 15:34 |
Mark Hadfield
Messages: 783
Registered: May 1995
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Senior Member |
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Kenneth P. Bowman wrote:
> In article <1132850938.403782.225280@o13g2000cwo.googlegroups.com>,
> guillaume.drolet.1@ulaval.ca wrote:
>
>
>> Since I do almost all my work with IDL, I am looking for IDL ways of
>> estimating along-wind distances of the footprints using a gaussian
>> dispersion model (functions, procedures, etc.). I don't have a strong
>> background in physics so I need some solutions I will understand. My
>> background is mostly in forest sciences and remote sensing and I do a
>> lot of programming.
>
>
> This sounds like a pretty big problem.
Maybe. In a previous life I worked in pollution dispersion etc and am
familiar with Gaussian dispersion models. In their simplest form they
are semi-analytical expressions for concentration as a function of
spatial coordinates (x, y, z). They model a plume as having a Gaussian
profile in cross-wind (conventionally y, or is it x? I forget) and
vertical (z) directions. They normally achieve their simplicity by
neglecting plume growth in the alongwind direction (x) and also shear. I
say *semi* analytical because the basic Gaussian plume expression is
analytical and not very complicated, but it involves parameters sigma-y
and sigma-z that are functions of downwind distance, and those functions
might be implemented as piecewise polynomial expressions of look-up
tables or (in my day) graphs on paper.
Tell us more, Guillaume, about which bits you need help with. Your basic
Gaussian plume model can be implented as a function of x, y and z and
containing just one line of code. This will contain references to your
sigma-y and sigma-z, which will be implemented as functions of x, using
whatever method you consider best. Calculating the ground-level
concentration is then straightforward and then you might want to contour
it to establish the horizontal extent of the footprint? That last bit
requires a bit of IDL-specific knowledge, but it can be done.
--
Mark Hadfield "Kei puwaha te tai nei, Hoea tahi tatou"
m.hadfield@niwa.co.nz
National Institute for Water and Atmospheric Research (NIWA)
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| Re: gaussian air dispersion model [message #46588 is a reply to message #46503] |
Mon, 28 November 2005 09:00 |
guillaume.drolet.1
Messages: 20
Registered: July 2005
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Junior Member |
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> So are you going to estimate the cross-wind-integrated ground level
> concentration with the footprint model and the across-wind variation in
> concentration with a gaussian function?
For my purpose, I am not interested in concentrations. What I need are
the dimensions (major and minor axes of an ellipse) contributing to the
measured fluxes.
The footprint model will give me one dimension: the distance of the
footprint in the mean wind direction, for a given measurement period
and a given percentage (r) to be included. This distance will be the
major-axis of the ellipse. The length of the ellipse's minor-axis (i.e.
across-wind width) will be missing and this is what I want to estimate
with a gaussian function. How I will do that, honestly, I don't know???
This is where I need help.
> By "this simple model" you mean the footprint model, right?
Yes, this is what I meant.
> I've looked at the URL, but not read the paper. It sounds like the
> footprint model is a simple set of formulae. Do you plan to implement
> this in IDL? Shouldn't be too hard.
I don't plan to implement it in IDL. I've been given it implemented in
Matlab. I will use this implementation to get the 'along-wind' distance
(i.e. referred to as 'xr' in the footprint model, see previous post).
> So where do you want help?
As I said before, I need a way to estimate the 'across-wind width',
knowing the 'along-wind extent' and other variables measured by the
tower sensors (e.g., mean wind direction (x,y,z), etc.). I don't have a
clue how I'm gonna find this but one thing is sure, I'm gonna need help!
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