## Advanced / Special Topics / Puff Split-Merge Issues

When the model is run in 3D particle mode a fixed number of particles are released and followed for the duration of the computational period. A sufficient number of particles need to be released so that at the end of the simulation, after particles have spread out, adjacent concentration grid cells, have enough particles to be able to properly represent the concentration gradients. For very long duration simulations, a large particle number may be required and the computational times may become prohibitive. One compromise is to use one of the hybrid particle-puff combinations. Fewer number of puffs need to be released because as they grow to the size of the meteorological grid, they will split into multiple particles. To avoid the particle-puff number quickly exceed the computational array limits, puffs occupying the same location may be merged. There are several different parameter settings that control the splitting and merging. These are discussed in more detail in this section.

### Basic Namelist Parameters

The namelist parameters KSPL, FRHS, FRVS, FRTS, KRND, FRMR, FRME control the split-merge routines. Normally these should all be left at their default values. Split routines are called at KSPL intervals and merging is always called hourly. Merging is most sensitive to the horizontal parameter FRHS. When going from the default value of 1 to 4 almost all the puffs are merged once FRHS=4. Because merging is called after splitting, most puffs that are merged are already in the same vertical position; hence there is little sensitivity to the vertical parameter FRVS. The time parameter FRTS only matters when there are continuous emissions. KRND controls the interval at which the enhanced merging routines are invoked. Enhanced merging is similar to standard merging except the parameters are 50% larger and selectively applied to those puffs at the lower end of the mass range as defined by FRME. Its default value of 0.10 means that only puffs whose total mass only represents 0.10 of the mass of all puffs will be subjected to enhanced merging.

- KSPL (1) is the interval in hours at which the puff splitting routines are called.
- FRHS (1.0) is the horizontal distance between puffs in sigma units that puffs have to be within each other to be permitted to merge.
- FRVS (0.01) is the vertical distance between puffs in sigma units that puffs have to be within each other to be permitted to merge. This parameter only applies to 3d puff simulations.
- FRTS (0.10) is the fractional difference in the age that puffs have to be within each other to be permitted to merge.
- KRND (6) is the interval in hours at which enhanced puff merging takes place. Enhanced merging is less restrictive (FRHS, FRVS, FRTS are 50% larger) and will degrade the accuracy of the simulation. Puffs can be further apart and still be merged into the same position. Enhanced merging only occurs when the puff number exceeds 25% of MAXPAR.
- FRME (0.10) is the fraction of the total mass that represents a puff mass at which all puffs with a mass less that puff value will only account for FRME of the total mass. These "Low Mass" puffs will be subject to enhanced merging.
- FRMR (0.0) is the fraction of the mass that is permitted to be removed at KRND intervals. The normal situation is to permit no mass loss. However for certain simulations, such as when a pollutant has a high ambient background relative to a typical plume signal, a small removal rate could significantly reduce the number of puffs on the grid with no loss in the accuracy of the simulation.

### Automated Split-Merge Procedures

When the puff-particle number approaches the array limits, further splitting is restricted until the merge procedures have freed up additional array space. Each time splitting shuts down, FRHS is automatically incremented by 0.5 to increase the effectiveness of puff merging, to a maximum value of 3 (FRHMAX in the namelist). Further, when splitting shuts down, those remaining puffs that are eligible to split but cannot due to the split restriction are prevented from increasing in size (both horizontal and vertical) until the split restriction has been removed. Also at the first occurrence of the split restriction, the size to which a puff is permitted to grow before splitting is increased in proportion to the namelist parameter SPLITF. Puff splitting occurs when the size of the puff reaches SPLITF x METEOROLOGY_GRID_SIZE, or concentration grid size, whichever is larger. A termination message to standard output has been added prior to HYSPLIT completion if puff splitting restrictions are in place at the end of the simulation. Such a message would suggest that it might be necessary to rerun the simulation with added array space or different merge parameters.

- FRHMAX (3.0) is the maximum permissible value for FRHS.
- SPLITF (1.0) at the default value of 1.0 is automatically recomputed to be the ratio of the number of concentration grid cells to the maximum number of particles permitted. For values less than one this feature is disabled and splitting occurs as before. For values greater than one, that value is used to determine when a puff splits. The distance adjustment is based upon how many particles are required to cover the concentration grid (assuming 20% in the PBL). If there are insufficient number of particles, then the puffs are allowed to grow larger before they split, providing for smoother patterns.

### Theoretical Considerations

For example, if a global simulation is required using a 1-degree resolution concentration grid, that results in about 65,000 grid points at the surface. Clearly a very long duration simulation that is expected to spread over much of the domain will require a comparable number of puffs as grid cells to provide smooth concentration patterns. If we assume the lowest layer only represents about 10 percent of the volume over which the puffs have been transported and mixed, it is not unrealistic to expect such a simulation to require 10 times as many puffs. An alternate approach, would be to dump the puffs into a global grid model rather than splitting them as they grow to the size of the meteorological grid. Concentrations at any point would then be a sum from the two modeling approaches. This is a variation of a plume-in-grid model.

### Parameter Considerations

Very long duration simulations or simulations using very fine resolution meteorological data, which have an insufficient initial allocation of the puff array space (MAXPAR in the namelist) can result in split shutdown messages or perhaps even emission shutdown messages. If any of these occur, the simulation results should be viewed with caution. The results may be noisy and inaccurate if the emissions (new puffs released) have also been restricted. A simulation with puff split restrictions may be improved by first increasing the array space to a value that still results in acceptable simulation times. If not effective, or the CPU times become too long, the second choice could be to increase the frequency of enhanced merging (perhaps decreasing KRND from 6, to 3, 2, or even 1), and perhaps in combination with decreasing the split interval (increasing KSPLT from 1 to 3, 6, or 12). Although decreasing the split interval will not be effective once splitting has shutdown, it may extend the time at which splitting first shuts down. Enhanced merging has little effect if most of the puffs have the same mass, perhaps because they were released at the same time. It is most effective for continuous emission simulations, where there is a large range in puff mass due to the different number of splits each puff has been subjected. An effective removal method is setting FRMR to a non-zero value. However, this has the effect of purging the simulation of low-mass puffs and would be most appropriate for continuous emissions simulations, where the puffs at longer distances have less importance. Used incorrectly, setting this parameter to a non-zero value can seriously bias the model results. For long-duration continuous emission simulations, it may also be just as effective to stagger the emissions because it would not be necessary to emit puffs every time step for realistic (and accurate) results. This could be accomplished by emitting more mass over a shorter duration and then cycling the emissions. For instance instead of a continuous emission, one could emit 10 times the normal hourly amount over 0.1 hours (6 min) and the repeat the emission cycle (QCYCLE parameter) each hour. The emission cycle could even be staggered over longer times.

### CPU Time Considerations

Long simulations may result in excessive CPU times because puffs will almost certainly be transported to the upper regions of the atmosphere where the winds are strongest which results in very small integration time steps. If computational accuracy in these upper regions is not required, perhaps because the only interest is boundary layer transport, the time step should be set to a fixed value. Given the same number of puffs, the enhanced merging version of the model should run substantially faster than the original version because when puff splitting shuts down and puffs continue to grow, they become quite large and cover many more concentration grid points which must all be sampled. Unrestricted puff splitting or restricting puff growth avoids this computational problem.

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