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) 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.
- If you are continuing from the last section, change the concentration grid resolution back to 0.005 or otherwise retrieve
cpart_control.txt and cpart_setup.txt.
- 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, save, run the model, and then display the concentration contours (with the color option turned on). The output should still be configured for snapshots every 3 hours which shows a growing circular puff until the end of the simulation at 12 hours after release. If the output were set for three hour averages, would the display still show a circular puff?
- 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 which maintains its circular structure only for the first 6 hours. Although the puff radius is about twice as large (3.0 versus 1.5 σ) as the Top-Hat calculation puff, after 12 hours even after having split to 85 puffs, it still covers much less area than the 3D particle calculation. Puff splitting will be discussed in more detail in the next section. If the center point of either type of puff passes over a sampling location, the integrated concentration at that point will be the same.
- 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 after 6 hours. Although with a slightly more ragged outer perimeter, the puff 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.
- For future reference, save the last configuration to gauss_control.txt and gauss_setup.txt.
- 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. [If your contour intervals do not match the graphic, you will need to select the fixed or user set option]. 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.
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.