Particle Growth using Puffs

In the previous section we needed to follow many thousands of particle trajectories to get a reasonably realistic simulation. Another option is, instead of following each individual particle that makes up the pollutant cloud, we follow the mean trajectory of the cloud and model the growth of horizontal (and optionally the vertical too) particle distribution; a single number to represent the particle distribution about the centroid point. There are two distribution options, the Top-Hat where the concentration is zero outside and a constant average value inside and the Gaussian option, which follows a normal distribution over a range of 3 σ.

1. To configure the two-dimensional Top-Hat puff simulation, open the Advanced / Configuration Setup / Concentration / Particle-Puff Release Mode (menu #3), and select the Top-Hat-Horizontal Particle-vertical radio-button, then save. Also open menu #4, and change the particle release number back to 1, and save, run the model, and then display the concentration contours. The output should still be configured for snapshots every 3 hours which shows a growing circular puff. Note that after 12 hours the puff does not cover as much domain as the 3D particle simulation.


2. Go back to menu #3 and this time select the Gaussian-horizontal particle-vertical puff option. Save the change, rerun the model, and display the new result. Although the puff radius is about twice as large (3.0 versus 1.5 σ) as the top-hat calculation puff, it is still covers much less area than the 3D particle calculation. If the center point of either type of puff passes over a sampling location, the integrated concentration at that point will be the same.


3. You've probably noticed that these calculations have been taking quite some time considering that we are only following a single particle trajectory. The reason is that as the puff grows, at each integration time step, all the grid points covered by the puff radius accumulate mass. At hour +12, the Gaussian puff had a diameter of about 100 km and with a grid resolution of 0.005 (0.5 km), there would be about 15,000 grid points within the puff. Go to the Concentration / Setup Run / Grids menu and change the concentration grid resolution from 0.005 back to its original value of 0.05. Save, rerun the model, and display the result. Although with a slightly more ragged outer perimeter, the puff at the last time period (+12 h) still shows the same circular pattern. However, this time the calculation was much faster because 100 times fewer concentration grid cells were involved in the integration.


4. The remaining issue is why the single puff calculation was still insufficient to describe the more complex 3D particle calculation. In the previous section, the particle display showed particles transported at different levels, the higher levels having faster transport speeds. One puff can only describe the horizontal particle distribution at that level. Each level must have its own puff. Go the the Advanced / Configuration Setup / Concentration / Release Number Limits (#4) and change the Particles Released per Cycle from 1 to 100. Save, rerun the model, and display the new result. After 12 hours the concentration pattern is much more complex and very similar to the previous 10,000 3D particle calculation. Although these 100 Gaussian puffs were released the same time at a height of 10 m they quickly mixed to different levels. This is the advantage of one of the unique features of HYSPLIT, a hybrid calculation, where the horizontal dispersion is modeled through the puff approach, while vertical mixing is treated in the particle mode. Growing vertical puffs would have to be split up very frequently to properly simulate the boundary layer wind shear.


5. The puff splitting process also occurs in the horizontal when the puff grows larger that the meteorological grid size. To more clearly see this effect, go back to the 1 particle release calculation (configuration menu #4), but in the main setup menu, run the calculation for a duration of 48 hours instead of 12 hours. The simulation at 48 hours shows the effect of the horizontal splitting, particularly evident by the circular puffs near the edge of the main pollutant cloud.


6. The exact splitting times can be determined from the diagnostic message file. Press the Advanced / View MESSAGES menu tab to open the listing MESSAGE file. The lines starting with NOTICE main: give the simulation hour, the time in minutes, the number of particles/puffs, and the total mass of all the particles on the computational domain. The first split occurs between hours 14 to 15, when the calculation goes from 1 to 5 puffs. Note the total mass stays the same, at 1.0 unit, now distributed over 5 puffs. At the end of the calculation, we are following 161 puffs. Note that puff merging also occurs when previously split puffs are in the same location. So there is no simple formula to compute the puff number growth rate.


7. The results after 48 hours look somewhat discontinuous, puff calculations suffer the same limitations as the 3D particle calculation, there still needs to be a sufficient number to describe the complexity of the pattern, just fewer puffs are required for the same calculation. The use of snapshot concentrations is also not very realistic. For instance, if the 48 calculation is rerun, but computing 12 h averaged concentrations, the resulting pattern is much smoother.

The modeling of the change in the particle distribution with time rather than modeling individual turbulent particle trajectories can be a satisfactory alternative in computing air concentration patterns. The default HYSPLIT option is to compute 3D particle transport and dispersion. It is up to the user to recognize the limitations and if more particles or a different modeling approach are required. In the next section, we will explore the equations that are the basis for the particle and puff calculations.