Hello all:
I want to revive discussion if possible on how to represent staggered
grids. We need this to get WRF model output into CF. I realize the
previous email was rather rambling, let me see if i can summarize a
concrete proposal:
Add a standard attribute called "stagger", used only by coordinate axes
(we uses "coordinate axis" as a generalization of 1D "coordinate
variable" that can have any number of dimensions).
The stagger attribute associates 2 coordinate axes, indicating that they
represent the same coordinates, but are offset from each other. A
variable can use a staggered coordinate in its coordinates attribute. A
client should use interpolation to translate between staggered and
unstaggered coordinates.
Examples. Note the match (or mismatch) of dimensions between the
variables and their coordinate axes. This is ok because of the "stagger"
attributes.
float x(x);
float x_stag(x_stag);
x_stag:stagger="x";
float y(y);
float y_stag(y_stag);
y_stag:stagger="y";
float lat(t, y, x);
float lon(t, y, x);
float ZNU(t, z);
ZNU:long_name = "eta values on half (mass) levels";
ZNU:positive = "down";
ZNU:standard_name = "terrain-following_eta_coordinate";
ZNU:formula_terms = "pressure_perturbation: P pressure_base: PB";
float ZNW(t, z_stag);
ZNW:long_name = "eta values on full (w) levels";
ZNW:positive = "down";
ZNW:standard_name = "terrain-following_eta_coordinate";
ZNW:formula_terms = "pressure_perturbation: P pressure_base: PB";
// P, PB not on z_stag
float N(t, z, y, x);
N:coordinates = "lat lon ZNU"; // normal case
float U(t, z, y, x_stag);
U:coordinates = "lat lon ZNU"; // lat, lon not on y, x_stag
float V(t, z, y_stag, x);
V:coordinates = "lat lon ZNU"; // lat, lon not on y_stag, x
float W(t, z_stag, y, x);
V:coordinates = "lat lon ZNW"; // normal case
John Caron wrote:
> Further thoughts on WRF staggered and vertical coordinates
>
> Most quantities in the file are on a normal grid, say
> float N(t, z, y, x);
>
> This is a projection, and we do have the 2D lat, lon values:
> float lat(t, y, x);
> float lon(t, y, x);
>
> However there are some quantities on a staggered x coordinate (we'll
> call x_stag), or on a staggered y coordinate (we'll call y_stag).
> Staggrered means that they are offset by half a grid cell, ie these
> are the "edges" of the grids:
>
> float U(z, y, x_stag);
> float V(z, y_stag, x);
>
> The usual thing to do would be to also have lat, lon arrays for these
> 2 cases:
>
> float lat2(t, y, x_stag);
> float lon2(t, y, x_stag);
>
> float lat3(t, y_stag, x);
> float lon3(t, y_stag, x);
>
> (there are none using y-stag, x_stag coordinates, but in principle i
> suppose there could be).
>
>
> Now to add in the vertical coordinates:
>
> The z coordinate is "eta values on half (mass) levels". Here is how
> the WRF experts describe how to transform to pressure:
>
> standard_name = "terrain-following_eta_coordinate"
>
> Definition: (but these are not coordinate definitions)
>
> press(n,k,j,i) = P(n,k,j,i) + PB(n,k,j,i)
> where press is the pressure at model gridpoint (k,j,i) and time (n),
> P is the perturbation pressure and PB the base state pressure
> at gridpoint (k,j,i) and time (n). These pressures are defined at
> non-staggered eta levels, which are defined by ZNU.
>
>
> So we have these fields in the file to satisfy the above definition:
> float P(t, z, y, x);
> float PB(t, z, y, x);
>
> However this will not work for the staggered grids, so we would need:
> float P2(t, z, y, x_stag);
> float PB3(t, z, y, x_stag);
>
> float P3(t, z, y_stag, x);
> float PB3(t, z, y_stag, x);
>
> The z coordinate also comes in a staggered form, we'll call z_stag, so
> we also need
>
> float P4(t, z_stag, y, x);
> float PB4(t, z_stag, y, x);
>
> To summarize, there are staggered coordinates for x, y, and z. In
> principle one could create 8 different grids, in practice it appears
> that only 4 are used.
> This still seems like a mess, and I doubt we really want all these
> variations explicitly added, in the form of 6 extra 4D variables, and
> 4 extra 3D variables.
>
> In actual practice, the advice is to interpolate back to the normal grid:
>
> U and V, together with temp and moisture variables are on non-staggered
> vertical grid (we sometimes call it half-eta levels), and pressure too.
> Only vertical motion, W, and geopotential height fields (PH and PHB) are
> output on staggered vertical grid (we sometimes call these levels
> full-eta
> levels). When we do post-processing using other software, we typically
> average W and PH/PHB to half-eta levels to make all variables colocate
> vertically. This is a simple arithmetic average.
>
> Then there is the horizontal staggering, where U is not colocated with
> V and all other variables. It may be easier to consider averaging U and V
> to the non-staggered horizontal grid, since when one computes
> meteorological
> wind fields (whether it is wind speed, or vectors), the wind components
> need to be colocated. On the other hand, if we'd want to do
> diagnostics, we may
> want to use the U and V on their original staggering. An example maybe
> the
> calculation of divergence or vorticity. So we may have the need to
> provide
> height and pressure on U and V grid. To do that, again we can simply
> average
> the nearby grid values to those at U and V.
>
>
> So one way out is that variables on staggered coordinates can use the
> normal grid coordinates as their coordinate system, by either
> interpolating the variable to the normal grid coordinates, or i
> suppose, interpolate the normal grid coordinates to the staggered
> ones. This is what we might mean by "stagger", that such interpolation
> is reasonable. If its not, then you have to specifiy the coordinate
> systems independently and in all their gorious detail.
>
> So concretely, if the above proposal was implemented, we are allowed
> to use non-staggered lat, lon and Z coordinates for staggered
> variables. The client program would be in charge of the interpolation.
>
> float x(x);
> float x_stag(x_stag);
> x_stag:stagger="x";
> float y(y);
> float y_stag(y_stag);
> y_stag:stagger="y"; float lat(t, y, x);
> float lon(t, y, x);
>
> float ZNU(t, z);
> ZNU:long_name = "eta values on half (mass) levels";
> ZNU:positive = "down";
> ZNU:standard_name = "terrain-following_eta_coordinate";
> ZNU:formula_terms = "pressure_perturbation: P pressure_base: PB";
>
> float ZNW(t, z_stag);
> ZNW:long_name = "eta values on full (w) levels";
> ZNW:positive = "down";
> ZNW:standard_name = "terrain-following_eta_coordinate";
> ZNW:formula_terms = "pressure_perturbation: P pressure_base: PB";
> // P, PB not on z_stag
>
> float N(t, z, y, x);
> N:coordinates = "lat lon ZNU"; // normal case
>
> float U(t, z, y, x_stag);
> U:coordinates = "lat lon ZNU"; // lat, lon not on y, x_stag
>
> float V(t, z, y_stag, x);
> V:coordinates = "lat lon ZNU"; // lat, lon not on y_stag, x
>
> float W(t, z_stag, y, x);
> V:coordinates = "lat lon ZNW";
>
>
>
>
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Received on Tue Dec 09 2003 - 15:10:32 GMT
