[CF-metadata] WRF staggered grids and vertical coordinates

[John Caron]

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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