To calculate an air parcel trajectory, METEX uses meteorological data for derivation of displacement of the air parcel. The calculation mainly involves spatial and time interpolation to obtain values of meteorological variable at a specific position and time from available data, and involves time integration to estimate the motion of an air parcel. The procedures are outlined as follows:
To calculate trajectories, METEX uses meteorological data provided by NCEP (National Centers for Environmental Prediction).
| Data | |
|---|---|
| Time Resolution | 3 hours |
| Spatial Resolution | 0.5 x 0.5 degree |
| Pressure Level | 1000, 975, 950, 925, 900, 875, 850, 825, 800, 775, 750, 700, 650, 600, 550, 500, 450, 400, 350, 300, 250, 225, 200, 175, 150, 125, 100, 70, 50, 30, 20, 10, 7, 5, 3, 2, 1-hPa |
The kinematic model assumes that an air parcel's trajectory is dominated by u- and v-wind and the vertical pressure velocity.
In spatial interpolation, a variable is first interpolated along the vertical grids to the specified vertical position, which may be represented by geopotential height, pressure, or any hybrid coordinate; and then interpolated laterally to a specified latitude and longitude. The assumption for vertical interpolation is that variables vary linearly with height; and the assumption for laterally interpolation is that variables vary linearly with latitude and longitude.
The isentropic model assumes that the vertical motion of an air parcel is confined on the isentropic surface with uniform potential temperature.
First of all, the initial altitude of an air parcel is converted to the potential temperature at its position by interpolation and by iteratively re-evaluating the potential temperature until the altitude estimated by interpolation on the isentropic surface equals the initial altitude within a given accuracy.
After the initial potential temperature is determined, the isentropic surface is treated as a flat plane in lateral interpolations for u- and v-wind. The flat-plane assumption is valid because the distance between vertical grids is generally much smaller than that between lateral grids.
$$ \boldsymbol{L'}(t+\Delta t) = \boldsymbol{L}(t) + \boldsymbol{Γ}(L,t) \times \Delta t $$
The parcel's position vector \(\boldsymbol{L}(t+\Delta t)\) at time \(t+\Delta t\) is obtained by$$ \boldsymbol{L}(t+\Delta t) = \boldsymbol{L}(t) + 0.5 \times (\boldsymbol{Γ}(L,t)+\boldsymbol{Γ}(L',t+\Delta t)) \times \Delta t $$
where \(\boldsymbol{Γ}(L',t+\Delta t)\) is the velocity vector of the air parcel at time \(t+\Delta t\) located at \(L'\).$$ \Delta t = \frac{\Delta D}{CFL \times \sqrt{u^{2} + v^{2}}} $$
where \(\Delta D\) is the distance between two adjacent lateral grids and \(CFL\) stands for the Courant-Friedrichs-Lewy criterion. METEX uses the value 5 internally for \(CFL = 5\).For more information on the methods and results of the trajectory calculations, please refer to the following paper.