Calculate Air Trajectory
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For large number of trajectory calculations, it is recommended to use the batch trajectory calculation service. Dataset source: NCEP Climate Forecast System. This serice uses the data with time resolution of 3 hours and spatial resolution of 0.5x0.5 degree on pressure levels of 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, and 1 hPa. We would appreciate that you cite the data source and inform zeng @ nies.go.jp about your use of METEX in publications. |
Notes on Trajectory Calculation
METEX uses the Petterssen method to calculate a parcel's move from position L(t) to L(t+Δt) by first estimating
L'(t+Δt) = L(t) + Γ(L,t)*Δt
where Γ(L,t) is the velocity vector; and then by
L(t+Δt) = L(t) + 0.5*Δt*(Γ(L,t)+Γ(L',t+Δt))
To achieve both good accuracy and fast computing, METEX adopted FLEXTRA's method of using flexible time steps in integration. The time step is determined according to the horizontal wind velocity by
Δt = ΔD/(CFL*sqrt(u*u + v*v))
where ΔD is the distance between two adjacent lateral grids and CFL stands for the Courant-Friedrichs-Lewy criterion.
Discrete meteorological data are interpolated in space and time for the calculation. The spatial interpolation depends on model assumptions.
Kinematic Model
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.
Isentropic Model
The isentropic model assumes that the vertical motion of an air parcel is confined on the isentropic surface of 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 are generally much smaller than that between lateral grids.
Interpolation of variable.