Hi again:
The WRF people are asking me if i have anything ready. i'm wondering how
to proceed. has anyone had a chance to think about the proposal on
handling staggered coordinates below? if the basic idea is sound, i can
submit some detailed wording that could go into the spec (i assume 1.1 ?)
John Caron wrote:
> 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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>
>
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Received on Fri Jan 23 2004 - 10:30:16 GMT
