How to interpret WRF variables

Grid

Grids in WRF are logically rectilinear. Variables for WRF cell indexed (i,j,k) can be located at one of 4 possible points. You can tell where by looking at the WRF registry or the attributes of NetCDF files, which WRF uses as I/O format. You can also tell by the fact that staggered variables have the staggered dimension larger by one, since there needs to be variable at the last boundary face.

• at the center of the cell - theta points, not staggered
• at the center of the left face - U point, staggered in X
• at the center of the front face - V point, staggered in Y
• at the center of the bottom face - W point, staggered in Z

Scalar variables (such as thermodynamical variables, hence the theta: temperature, pressure,...) generally live at theta-points. One exception is the geopotential, which lives at W-points. The documentation and comments of the code talk about theta-height (mid-level of the cell) and W-height (bottom of the cell).

The orientation of the axes in the real world, such as "east-west", in the order of increasing index, such as i, can be found from the registry, or, preferably, at runtime as attributes in the NetCDF files.

Arrays in files and in memory

Files are (by default) in NetCDF format. The values associated with the cell (i,j,k) at time step n are stored in the files as the array entry U(i,j,k,n), e.t.c. The value of the time at the step n is stored in character array Times(:,n).

All arrays are described in the Registry, which is a collection of text files in WRFV3/Registry. The variable names in memory and in files are sometimes different. While arrays in files are indexed as (i,j,k), arrays in memory are indexed as (i,k,j). Of course, there is no 4th index for the time step in arrays in memory.

Wind

Components of the wind velocity vector U, V, W live at the corresponding points, hence the point names. These are in the geometrically horizontal and vertical directions. On flat ground, W on the first level k=1 is zero. However, when the ground has nonzero slope, the vertical velocity components W is generally not zero, because the normal vector to the ground is not vertical.

Because the components of the wind velocity vector are on different staggered grids, and visualization software usually expects all three components of the velocity vector based at the same point, they need to be interpolated to theta-points (cell centers) for display:

U_THETA(i,j,k) = 0.5*(U(i,j,k) + U(i+1,j,k))

V_THETA(i,j,k) = 0.5*(V(i,j,k) + V(i,j+1,k))

W_THETA(i,j,k) = 0.5*(W(i,j,k) + W(i,j,k+1))

Location

The longitude and latitude of the theta and U nodes are given by arrays XLONG and XLAT, which are set at initialization and then do not change. However the elevation has to be computed from the flow solution as geopotential height by

ELEVATION_W = (PHB + PH)/9.81"'

where PHB + PH is the geopotential. PHB is constant, set at initialization, and PH, called perturbation geopotential, starts as zero and varies with time.

PH and PHB live at the W-points, thus the geopotential height at the lowest level is the same as terrain height

HGT(i,j) = PHB(i,j,1)/9.81

up to rounding error.

To find the elevation of the cell theta-points (the cell midplane), you need to interpolate the elevation of the top and the bottom:

ELEVATION_THETA(i,j,k) =0.5*(PHB(i,j,k) + PH(i,j,k) + PHB(i,j,k+1) + PH(i,j,k+1))/9.81

See also

• WRF output fields from the WRF-ARW user's guide
• Grid: A Description of the Advanced Research WRF Version 3 (June 2008) Fig 7.3 page 59
• WRF Coding Conventions
• WRF Registry and Examples
• WRF v2 Software Tools and Documentation
• Description of WRF Registry

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