| gaussian air dispersion model [message #46529] |
Thu, 24 November 2005 08:48  |
guillaume.drolet.1
Messages: 20
Registered: July 2005
|
Junior Member |
|
|
Hi,
I am using spatial remote sensing data (reflectances over vegetation)
along with field eddy-covariance data, i.e. energy and mass fluxes from
towers to develop better ways of estimating forest productivity.
For a given period, the vegetated area contributing to the fluxes
(footprint) depends on several factors (e.g., wind speed and
direction,surface roughness length, etc.) and can be modeled using a
footprint model.
To extract the data for the pixels contributing to the measured fluxes,
I will use an across-wind integrated footprint model that will give me
the across-wind distance (x-extent) of the footprint (i.e., the minor
axis of an ellipse). Since I have several periods of flux data for
which I need to run the footprint model, I cannot use a
fully-parameterized footprint model that would give me the along- and
cross-wind extents of the footprint. Thus, I need to use a gaussian
dispersion model to estimate the along-wind distance. Knowing both x-
and y- extents, I will be able to create ellipses that will serve as my
'ROIs' to extact reflectance data.
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.
Thanks a lot for your help.
Gui
|
|
|
|
| Re: gaussian air dispersion model [message #46564 is a reply to message #46529] |
Tue, 29 November 2005 06:56  |
guillaume.drolet.1
Messages: 20
Registered: July 2005
|
Junior Member |
|
|
> No worries. I just did a quick search on Google Scholar and came up with
> the following. It's rather old and has an urban focus rather than an
> agricultural one, but it might help...
Thanks Mark. I found the paper you suggested. I'll keep you informed.
|
|
|
|
|
|
| Re: gaussian air dispersion model [message #46566 is a reply to message #46529] |
Mon, 28 November 2005 20:28 |
David Fanning
Messages: 11724
Registered: August 2001
|
Senior Member |
|
|
Mark Hadfield writes:
> Descriptors: atmosphere | boundary layers | meteorology | pollutant
> dispersion; mathematical models | atmospheric conditions |
Don't you have any work to do, Mark?
Cheers,
David
--
David Fanning, Ph.D.
Fanning Software Consulting, Inc.
Coyote's Guide to IDL Programming: http://www.dfanning.com/
|
|
|
|
| Re: gaussian air dispersion model [message #46567 is a reply to message #46529] |
Mon, 28 November 2005 20:00 |
Mark Hadfield
Messages: 783
Registered: May 1995
|
Senior Member |
|
|
guillaume.drolet.1@ulaval.ca wrote:
>> If the distances in question are
>> small you can get away with
>
>
>> sigma-y = sigma-theta * x
>
>
> Are distances between 500 and 1500 m considered small?
Damn, I hoped you weren't going to ask!
I'm reaching way back into my memory banks here. The short answer is
that 500 to 1500 m is probably small enough that the above formula will
be an overestimate, but good enough to get started with. The long answer
is that the distance at which the growth of sigm-y starts to drop away
from the linear formula depends on the correlation time scales of the
cross-wind turbulent fluctuations. You can estimate the Eulerian time
scale from your anemometer. The problem is that what you really want is
the time scale for the fluctuations experienced by a Lagrangian particle
(ie one moving with the wind) and these will generally be longer. There
is a lot of info about this in the literature so you should eventually
be able to come up with reasonable values. Right now I suggest you use
the linear relation.
> Yes. Since the mean wind direction for a 30-minute period comes from
> high frequency measurements (10 Hz), I should be able to get
> sigma-theta.
Good.
> You are right. I definitely need to do some reading and maybe I posted
> in the wrong forum.
No worries. I just did a quick search on Google Scholar and came up with
the following. It's rather old and has an urban focus rather than an
agricultural one, but it might help...
Applied dispersion modelling based on meteorological scaling parameters.
Gryning, S E | Holtslag, A A M | Irwin, J S | Sivertsen, B |
Atmospheric Environment. Vol. 21, no. 1, pp. 79-89. 1987
A method for calculating the dispersion of plumes in the atmospheric
boundary layer is presented. The method is easy to use on a routine
basis. The inputs to the method are fundamental meteorological
parameters, which act as distinct scaling parameters for the turbulence.
The atmospheric boundary layer is divided into a number of regimens. For
each scaling regime the authors suggest models for the dispersion in the
vertical direction. The models directly give the crosswind-integrated
concentrations at the ground, chi sub(y), for non-buoyant releases from
a continuous point source. Generally the vertical concentration profile
is proposed to be other than Gaussian. The lateral concentration profile
is always assumed to be Gaussian, and models for determining the lateral
spread sigma sub(y) are proposed. The method is limited to horizontally
homogeneous conditions and travel distances less than 10 km. The method
is evaluated against independent tracer experiments over land. The over
land. The overall agreement between measurements and predictions is very
good and better than that found with the traditional Gaussian plume model.
Descriptors: atmosphere | boundary layers | meteorology | pollutant
dispersion; mathematical models | atmospheric conditions |
--
Mark Hadfield "Kei puwaha te tai nei, Hoea tahi tatou"
m.hadfield@niwa.co.nz
National Institute for Water and Atmospheric Research (NIWA)
|
|
|
|
| Re: gaussian air dispersion model [message #46568 is a reply to message #46529] |
Mon, 28 November 2005 19:18 |
guillaume.drolet.1
Messages: 20
Registered: July 2005
|
Junior Member |
|
|
> If the distances in question are
> small you can get away with
> sigma-y = sigma-theta * x
Are distances between 500 and 1500 m considered small?
> Do you have any info on sigma-theta?
Yes. Since the mean wind direction for a 30-minute period comes from
high frequency measurements (10 Hz), I should be able to get
sigma-theta.
> You're going to need to do a bit of reading
You are right. I definitely need to do some reading and maybe I posted
in the wrong forum.
|
|
|
|
| Re: gaussian air dispersion model [message #46572 is a reply to message #46529] |
Mon, 28 November 2005 16:04 |
Mark Hadfield
Messages: 783
Registered: May 1995
|
Senior Member |
|
|
guillaume.drolet.1@ulaval.ca wrote:
> [snip]
> 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.
Then you are probably asking these questions in the wrong forum.
But obviously the hard bit is calculating the width parameter to be used
in the Gaussian function. The usual assumption is
sigma-y = sigma-theta * x * f(x)
where x is downwind distance, sigma-theta is standard deviation of wind
direction (in radians) and f(x) is a function that equals 1 at short
distances and then slowly drops away. If the distances in question are
small you can get away with
sigma-y = sigma-theta * x
Do you have any info on sigma-theta?
> 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!
You're going to need to do a bit of reading.
--
Mark Hadfield "Kei puwaha te tai nei, Hoea tahi tatou"
m.hadfield@niwa.co.nz
National Institute for Water and Atmospheric Research (NIWA)
|
|
|
|
comp.lang.idl-pvwave archive
Members
Search
Help
Login
Home
