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# wgt_volrmse_ccm

Calculates a weighted volume root-mean-square-difference between two variables from the CCM.

## Prototype

```	function wgt_volrmse_ccm (
q        : numeric,
r        : numeric,
wgtq     : numeric,
wgtr     : numeric,
wgty [*] : numeric,
wgtx [*] : numeric,
opt      : integer
)

return_val  :  float or double
```

## Arguments

q

An array of 3 or more dimensions containing the data to be averaged. The rightmost dimensions should correspond to "level" (lev), "latitude" (lat), and "longitude" (lon) when dealing with quantities on a sphere ([...,],lev,lat,lon), and "z", "y", and "x" otherwise ([...,],z,y,x).

r

An array of 3 or more dimensions containing the data to be averaged. The rightmost dimensions should correspond to "level" (lev), "latitude" (lat), and "longitude" (lon) when dealing with quantities on a sphere ([...,],lev,lat,lon), and "z", "y", and "x" otherwise ([...,],z,y,x).

wgtq

An array dimensioned the same size as q and r. For the atmospheric component of the CCM, these will contain the "delta-pressures" as computed by NCL's dpres_hybrid_ccm function.

wgtr

An array dimensioned the same size a q and r. For the atmospheric component of the CCM, these will contain the "delta-pressures" as computed by NCL's dpres_hybrid_ccm function.

wgty

A scalar (typically 1.0) or 1-dimensional array of size "lat" (y) containing the weights. A scalar value of 1.0 means no weighting.

wgtx

A scalar (typically 1.0) or 1-dimensional array of size "lon" (x) containing the weights. A scalar value of 1.0 means no weighting.

opt

If opt = 0, the area average is calculated using available non-missing data. If opt = 1, then if any point in q is missing, the area average is not computed. In this case, it will be set to the missing value, which is indicated by q@_FillValue, or the default missing value if q@_FillValue is not set.

## Return value

Returns a scalar if q is a two-dimensional array. Otherwise, the output dimensionality is the same as the leftmost dimensions of the input q.

The return type is floating point if the input is floating point, and double if the input is of type double.

## Description

This function computes the volume root-mean-square-difference [rmse] between two variables using weights.

## Examples

Example 1

Assume q, r, wgtq and wgtr are global arrays dimensioned time x lev x lat x lon, with dimension sizes ktime = 120, nlev = 28, nlat = 64, mlon = 128. Further assume wgty(nlat) is a 1D array containing gaussian or cosine weights and that no special weighting is applied in the longitude (x) direction. Then:

```  wgty  = f->gwt     ; same for both "q" and "r"
wgtx  = 1.0        ; no special weighting
p0    = f->P0

; get "q" info
hyai  = f->hyai
hyai  = f->hyai
ps    = f->PS
q     = f->Q
wgtq  = dpres_hybrid_ccm(ps, p0, hyai, hybi)

; get "r" info
hyai  = g->hyai
hyai  = g->hyai
ps    = g->PS
r     = g->R
wgtr  = dpres_hybrid_ccm(ps, p0, hyai, hybi)

glRmse = wgt_volrmse_ccm(q, r, wgtq, wgtr, wgty, 1.0, 0)   ; glRmse(ktime)
delete (wgtr)
delete (wgtq)
```
will calculate the volume (global) rmse for each time. glRmse will be a 1D array with dimension (ktime = 120). If a missing value is encountered at any of the two rightmost dimensions it is ignored (equivalent to a weight of 0.0) and the average is calculated using available non-missing data (opt = 0).

Example 2

```  nhRmse = wgt_volrmse_ccm(q(:, :, 33:nlat - 1, :), r(:, :, 33:nlat - 1, :), \
wgtq(:, :, 33:nlat - 1, :), wgtr(:, :, 33:nlat - 1, :), \
wgty(33:nlat - 1), 1.0, 1)
```
will calculate the volume (northern hemisphere) rmse for each time. Standard subscripting is used to subset the input global array. nhRmse will be a 1D array with dimensions (ktime = 120). If a missing value is encountered at any of the two rightmost dimensions then the result will be set to _FillValue (opt = 1).

Example 3

Same as above, but q, r, wgtq, wgtr and wgty must have named dimensions and coordinate variables.

```  shRmse =  wgt_volrmse_ccm(q(:, 5:7, {lat | -90:0}, :), r(:, 5:7, {lat | -90:0}, :), \
wgtq(:, 5:7, {lat | -90:0}, :), wgtr(:, 5:7, {lat | -90:0}, :), \
wgty({lat | -90:0}), 1.0, 0)
```
will calculate the volume (southern hemisphere) rmse for each time using levels 5, 6, 7. Coordinate subscripting and standard subscripting are used to subset the input global array. shRmse will have dimension length ktime.