Table of Contents - The Atmospheric Studies Group at TRC

Section 7: Prognostic Meteorological Interfaces
MM5 defines U and V wind components on dot points, and all other variables on cross points. In the
vertical direction, MM5 uses sigma coordinate (Figure 7-2), where sigma is calculated using Equation 7-1
where P is pressure, and P top is the pressure at model top. P* is the pressure difference between the
= (P - PTop
)/P*
(7-1)
surface and the model top. All variables are defined at half sigma levels, except vertical velocity (W),
which is defined on full sigma levels. Table 7-4 lists defined horizontal and vertical locations for MM5
variables used by CALMM5.
CALMET uses a non-staggered horizontal coordinate system (see Figure 7-3) and a terrain-following
vertical coordinate system. In horizontal, all variables are defined at the center of each grid cell.
Therefore the staggered MM5 variables have to be interpolated to one of its two set grid locations, either
dot points or cross points. Horizontal wind is the most important in air pollution modeling, which is
defined at MM5 dot points. To keep it unaffected, all MM5 variables defined at MM5 cross points are
interpolated to dot points using Equation 7-2 for internal grids
xd( i,
j)
[ xc(
i 1,
j 1)
xc(
i,
j 1)
xc(
i 1,
j)
xc(
i,
j)]/
4.0
(7-2)
where x d is the value at a dot points, and x c is the value at four surrounding cross points. For a dot point
along the model boundary, only the two cross points next to it are used. The interpolation in Equation 7-2
is based on actual horizontal spatial distance in meters, not on latitude and longitude degrees. The X and
Y, or I and J, in MM5 horizontal coordinate system are confusing. MM5 uses X (or I) as its south-north
coordinate, and Y (or J) as its west-east coordinate, which is opposite to the conventional use of X and Y.
To eliminate this confusion, the output from CALMM5 uses conventional X and Y definition, that is, X
(or I) represents the west-east direction, and Y (or J) the south-north direction.
In the vertical direction, MM5 vertical velocities (present in MM5 Version 3 and only in non-hydrostatic
runs in MM5 Version 2) are computed at full sigma levels while all other variables are defined at half
sigma levels (see Figure 7-2). CAMM5 interpolates the vertical velocities at full sigma levels to half
sigma levels first using Equation 7-3
w ( k)
[ w(
k)
w(
k 1)]/
2.0
(7-3)
where k is vertical level index starting from the model top. Since the vertical velocity in MM5 is defined
at cross point, the vertical velocities from Equation 7-3 are further interpolated to dot points using
Equation 7-2.
7-5