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# dim_variance_Wrap

Computes unbiased estimates of the variance of a variable's rightmost dimension at all other dimensions and retains metadata.

## Prototype

```load "\$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl"

function dim_variance_Wrap (
x  : numeric
)

return_val  :  float or double
```

## Arguments

x

A variable of numeric type and any dimensionality.

## Return value

The output will be double if x is double, and float otherwise.

The output dimensionality is the same as the first n-2 dimensions of the input variable. That is, the dimension rank of the input variable will be reduced by one.

## Description

The dim_variance_Wrap function computes the population variance of all elements of the n-1 dimension for each index of the dimensions 0...n-2 and retains metadata. A wrapper function. Missing values are ignored.

Technically, this function calculates an estimate of the sample variance. This means that it divides by [1/(N-1)] where N is the total number of non-missing values.

Use dim_variance_n_Wrap if you want to specify which dimensions to do the calculation across.

## Examples

Example 1

Create a variable q of size (3,5,10) array. Then calculate the sample variance of the rightmost dimension.

```    q   = random_uniform(-20,100,(/3,5,10/))
qVar= dim_variance(q)   ;==>  qVar(3,5)
```
Example 2

Let x be of size (ntim,nlat,mlon) and with named dimensions "time", "lat" and "lon", respectively. Then, for each time and latitude, the the variance is:

```    xVarLon= dim_variance( x )    ; ==> xVarLon(ntim,nlat)
```
Generally, users prefer that the returned variable have metadata associated with it. This can be accomplished via the dim_variance_Wrap function:

```    xVarLon = dim_variance_Wrap( x )    ; ==> xVarLon(time,lat)
```
Example 3

Let x be defined as in Example 2: x(time,lat,lon). Compute the temporal variance at each latitude/longitude grid point. Use NCL's Named Subscripting to reorder the input array such that "time" is the rightmost dimension.

```    xVarTime = dim_variance( x(lat|:, lon|:, time|:) )    ; ==> xVarTime(nlat,nlon)

xVarTime = dim_variance_n( x, 0 )                     ; no reordering needed
```
```    xVarTime = dim_variance_Wrap( x(lat|:, lon|:, time|:) )    ; ==> xVarTime(lat,lon)