Backward Calculation from a Sampler

In the previous section we computed the dilution factor from the source to various sampling locations and then used the measured concentration value to estimate the emission rate. In situations where the source location is not known, a frequently employed option is to compute the dilution factor from the sampler to all possible source locations. If there are multiple samplers it may be possible to combine the information from each sampler to estimate the source location as well as the release rate. Some of these issues will be explored in subsequent sections. Here we will determine if the "backward dispersion" calculation from the sampler gives the same dilution factor as the forward calculation from the source.

1. Start with the same configuration as in the previous section where we were comparing results to the 3-hr sampling data. Open the Setup Run / Pollutant Emission menu and simplify the emissions even further, set the rate to 1.0 unit for 1 hour. Then open the concentration grid menu and change the averaging time from 03 hours to 01 hour and the start of the sampling back to 83 09 25 17. Save the changes and run the model.


2. When the run has completed, open the Utility / Grid to Station menu and pick a site, such as 316, which we already know is within the calculated and measured plume. Set the location to 41.30 -82.22. Also to keep enough significant digits in the fixed format output, increase the multiplier from 1.0E+12 to 1.0E+15. This last step is necesssary because we reduced the emission rate from its actual value 67000.0 to a unit value. The resulting hourly output file at station 316 shows a value of 275 near the center time (0500-0600) of the plume passage.


3. To configure the reverse calculation, open the setup run menu and set the start time to 26 06 and the run duration to 13 hours; set the back radio-button to change the sign to negative. Open the starting location menu and change the starting location to the position of sampler 316 (41.30 -82.22). Then open the concentration grid menu and reverse the sampling start and stop times. Set the start time of sampling to 26 06 and the stop time to 25 17. Save the changes and run the simulation.


4. When the run completes, open the Grid to Station menu and set the sampling site to the original release location 39.90 -84.22. The resulting time series at the source location shows a value of 240 between 1800-1700, the same transport time as the original calculation to 0500-0600. There is about a 12% difference in the calculated dilution factors between the two approaches.

The results shown here indicate that the dilution factors between the forward and backward calculations are similar, they are not identical. Some of these issues were explored in previous sections, for instance when a particle intersects the ground the transport calculation is no longer reversible. Also the particle dispersion calculation depends upon the turbulence the previous time step:

• U'(t+Δt) = R(Δt) U'(t) + ...