Trajectory Vertical Motion

In most circumstances the input meteorological data will contain a vertical motion field, usually in pressure units. The trajectory and dispersion model calculations can use these data fields directly. If the vertical motion field is missing, or perhaps some special conditions are required for a simulation, the model has an option to replace these fields with an internally calculated vertical velocity based upon an assumption that the pollutant parcel is transported on some other surface. This is accomplished by computing the velocity (W_η) required to maintain a parcel on the selected η surface:

• W_η = (-∂η/∂t - u ∂η/∂x - v ∂η/∂y) / (∂η/∂z)

1. The effect of changing the vertical motion method can be evaluated by recalculating the backward trajectory from the trajectory error discussion section. Retrieve the CONTROL file traj_back_control.txt which should show the trajectory setup after changing the output file from tdump_back to tdump_data. Save the change, delete the SETUP.CFG if it exists, run the model, and display the results. It should match the previous calculation.


2. Now repeat the process but configuring the simulation using the isobaric option. Make sure to change the output file name to tdump_isob, save and run the model. Repeat this process for each of the vertical motion options, naming the output file suffix with the name of the vertical motion method.


• data - uses the vertical velocity field in the meteorological data file
• isob - isobaric maintains the trajectory on a constant pressure surface
• isen - isentropic maintains the trajectory on surfaces of constant potential temperature
• dens - trajectories stay on constant density surfaces
• sigma - vertical motion is zero and the trajectory stays on the same internal sigma
• divg - the vertical motion is computed by vertical integration of the velocity divergence


3. When the calculations are finished, all trajectories can be superimposed on the same plot by using the + symbol between endpoint file names, or by creating the file traj_files.txt of file names which should be entered into the display menu. Remember to add the forward trajectory tdump_fwrd as the reference trajectory and the trajectory results will show only one other vertical motion method (besides data which should be identical) that is similar to the forward and backward data method.


4. Either examine each endpoints file, or go back and run the display by entering the endpoints file names, such as tdump_isen. This will show that the isentropic trajectory was closest to the one using the meteorological data field. For this display, the theta radio-button was selected to show potential temperature as the vertical plot coordinate, where the temperature varied by only +/- one degree during most of the trajectory. This two degree range still translates into a variation of around 700 m, which can be determined by examining the meteorological profile near the tracer release point.


5. At this point it is not possible to determine a correct answer with absolute certainty because there are no tracer measurements at the off-shore starting location for all these back trajectories. However, the mid-boundary layer data and isentropic trajectories did pass through the middle of the tracer plume.


6. Another way to analyze the situation is to look at a something similar to a weather map. Open the Meteorology / Display Data / Contour Map menu tab and make the following changes to the contour map menu: select the global reanalysis file captex2_gblr.bin because the regional reanalysis covers too small a domain, select the geopotential height HGTS field, for level number 4 which will be the 850 mb surface, set the time offset radio-button to 48 to draw the map at the end of the sampling period near the start time of the back trajectory, set the map center to 40N 80W, and increase the map radius to 25 degrees.


7. The resulting 850 mb heights map shows a high pressure system centered over the eastern U.S. with a divergent region just off the coast. Here the back trajectories easily got caught in different flow regimes, depending upon small differences in height between each method, resulting in very different horizontal trajectories primarily due to large variations of wind direction with height. The flow region to the north of the high pressure system contained most of the tracer.

In general, trajectory calculations should use the meteorological data's vertical velocity fields when available. Each of the computational approaches has its own limitations, isentropic in diabatic conditions (through clouds), isobaric over large terrain variations, the divergence is sensitive to small differences in velocity gradients, and even the data method becomes unreliable when meteorological grid sizes decrease but the data time interval remains unchanged resulting in under-sampling a field that may change direction multiple times between output intervals.