## Uncertainty along trajectory endpoint

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je.petit
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Joined: April 13th, 2016, 10:41 am
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### Uncertainty along trajectory endpoint

Hi all,

For the purpose of a particular study (trajectory analysis by eg PSCF), I was wondering if I could implement uncertainty to the backtrajectory's endpoints coordinates. I figured that this uncertainty should increase with time so that it could account a little bit for dispersion.
So, for each endpoint, I have made a resample of 1000 points, with a 2-D Gaussian noise centered at the endpoint's coordinate, and where the width of the cumulative probability function increases with time (around 0.025 x i, where i is time). An output of this approach is enclosed hereinbelow.

So my question is: do you guys feel that this can make some sense ?

Best,
J-E
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ariel.stein
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### Re: Uncertainty along trajectory endpoint

Conceptually it makes sense. However, your 2-D Gaussian noise should reflect the state of the atmosphere. Ideally, you should use the standard deviation of the horizontal wind speed as a measure for the with of your Gaussian distribution. HYSPLIT explicitly calculates the standard deviations in the concentration calculation.
je.petit
Posts: 14
Joined: April 13th, 2016, 10:41 am
Registered HYSPLIT User: Yes

### Re: Uncertainty along trajectory endpoint

Dear Ariel,

Thanks for your answer. It is rather comforting that this makes sense. Few more questions though: should this noise be function of time AND wind speed standard deviation, or could it be only function of ws stdev ?
Because, in the case of receptor modelling, the further back in time we're going, the higher the uncertainty should be, right? this is just a raw assumption, I don't know if it applies to HYSPLIT...

Then, the concentration mode in HYSPLIT is dedicated to plume investigations, could it be applied to backtrajectory analysis (eg PSCF, CWT) ? If no, is there any way to include in the backtrajectory file the value of ws stdev at each endpoint ? This because I am outsourcing the PSCF calculation with ZeFir (an Igor package that I have developped, https://sites.google.com/site/zefirproject/home ), taking traj files as they are.

J-E
ariel.stein
Posts: 659
Joined: November 7th, 2012, 3:14 pm
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### Re: Uncertainty along trajectory endpoint

This "noise" function or dispersion/turbulent component is a function of time and ws stdev. The uncertainty, as you mentioned in your comment, increases as you go further back in time.
In principle, the concentration mode is just a group of trajectories that have a turbulent component included in their calculation. That is why, as time passes, each lagrangian particle gets further apart from each other creating a plume shaped concentration. So, the short answer is yes, you could apply back trajectory analysis to the lagrangian particles, the problem is that we have not developed the tools to do those calculations. To do this analysis you will need to know the position of each particle at different times which you can get by generating a PARDUMP file. See below for more information:

Here you can find more information about the format of the Particle Dump File:

The concentration configuration menu provides an option to write a model initialization file, which by default is always
named "PARDUMP" (for particle dump). This file can be written at regular intervals during the simulation, a
convenient way to restart a simulation in case of unexpected failure. To restart the model using the PARDUMP file it is
only necessary for the file to be present in the root working directory. If the internal time stamp of the file matches the
start time of the simulation, the model will initialize the particle count from the file before emitting new particles
according to the emission scenario defined in the control file. The format of the PARDUMP file is given below:
Record #1
INT*4 Number of particles
INT*4 Number of pollutants
INT*4 Time of particle dump (YEAR, MONTH, DAY, HOUR, MINUTES)
Record #2 - Loop to record: Number of particles
REAL*4 Particle pollutant mass (times the number of pollutants)
REAL*4 Particle LATITUDE, LONGITUDE, HEIGHT, SIGMA-U,SIGMA-V, SIGMA-X
INT*4 Particle AGE, DISTRIBUTION, POLLUTANT, METEO-GRID,SORT-INDEX
The "Particle" tab of the "Special File Display" menu brings up a Windows based viewer that shows the particle
positions over a map background. The display can be zoomed and otherwise adjusted using the left and right mouse
buttons in conjunction with the shift and cntl keys. Help is provided on the screen with the left and right side comments
corresponding to the respective mouse button. The particle viewer can also be used to overlay satellite images on the
particle positions. More information on this is provided "FTP Satellite Data" help menu. The particle position file may
be converted to a binary concentration file through the command line utility program par2conc.