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# wgt_runave

Calculates a weighted running average across the rightmost dimension.

## Prototype

```	function wgt_runave (
x       : numeric,
wgt [*] : numeric,
opt  : integer
)

return_val  :  float or double
```

## Arguments

x

An array with one or more dimensions. The fastest varying (i.e. rightmost) dimension will be the dimension on which the weighted running average is performed. Missing values should be indicated by x@_FillValue. If x@_FillValue is not set, then the NCL default (appropriate to the type of x) is assumed.

wgt

A one-dimensional vector containing all the weights. Most commonly, the number of weights is an odd number).

opt

End-point option (opt = 0 is the most common option)

In the following assume the weights add to 1.0 and

N = {last point in the series}
xi = {input series}
xo = {output series}
nwgt = {number of wgts}

```opt < 0 : utilize cyclic conditions
e.g., nave = 2
xo(0) = w(0) * xi(0) + w(1) * xi(1)
xo(N) = w(0) * xi(N) + w(1) * xi(0)
e.g., nwgt = 3
xo(0) = w(0) * xi(N) + w(1) * xi(0) + w(2) * xi(1)
xo(N) = w(0) * xi(N - 1) + w(1) * xi(N) + w(2) * xi(0)
e.g., nwgt = 4
xo(0) = w(0) * xi(N) + w(1) * xi(0) + w(2) * xi(1) + w(3) * xi(2)
xo(N) = w(0) * xi(N - 1) + w(1) * xi(N) + w(2) * xi(1) + w(3) * xi(2)

opt = 0 : set unsmoothed beginning and end pts to x@_FillValue (most common)
e.g., nave = 2
xo(0) = w(0) * xi(0) + w(1) * xi(1)
xo(N) = xi@_FillValue
e.g., nave = 3
xo(0) = xi@_FillValue
xo(1) = w(0) * xi(0) + w(1) * xi(1) + w(2) * xi(2)
xi(N) = xi@_FillValue
e.g., nave = 4
xo(0)     = xi@_FillValue
xo(1)     = w(0) * xi(0) + w(1) * xi(1) + w(2) * xi(2) + w(3) * xi(3)
xo(N - 2) = w(0) * xi(N - 3) + w(1) * xi(N - 2) + w(2) * xi(N - 1) + w(3) * xi(N)
xo(N - 1) = xi@_FillValue
xo(N)     = xi@_FillValue

opt > 0 : utilize reflective (symmetric) conditions
e.g., nave = 2
xo(0) = w(0) * xi(0) + w(1) * xi(1)
xo(N) = w(0) * xi(N) + w(0) * xi(0)
e.g., nwgt = 3
xo(0) = w(0) * xi(1) + w(1) * xi(0) + w(2) * xi(1)
xo(N) = w(0) * xi(N - 1) + w(1) * xi(N) + w(2) * xi(N - 1)
e.g., nwgt = 4
xo(0) = w(0) * xi(1) + w(1) * xi(0) + w(2) * xi(1) + w(3) * xi(2)
xo(N) = w(0) * xi(N - 1) + w(1) * xi(N) + w(2) * xi(0) + w(3) * xi(2)
```

## Return value

Returns an array of the same dimensionality as x with the last dimension smoothed.

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

## Description

This function computes a weighted running average on the rightmost dimension.

The running average is a special case of a filter. The filter is applied to the i-th time of the requested series as follows:

```    F(i) = SUM{w(j) * UF(i - (nwgt / 2) + j)} from j = 0, nwgt - 1
```
where F is the filtered field, UF is the unfiltered field, w(j) is the j-th filter weight, and nwgt is the number of weights.

With the proper choice of weights, this "filter" can also be used to compute time differences and derivatives.

If the number of weights is even, the filter's center falls between series elements; in this case the center is shifted one-half of a time increment towards the latter element.

Use the wgt_runave_Wrap function if metadata retention is desired. The interface is identical.

Use wgt_runave_n if the dimension to do the calculation on is not the rightmost dimension and reordering is not desired. This function can be significantly faster than wgt_runave.

## Examples

Example 1

Let x be dimensioned nlat x mlon x ktimes where nlat = 64, mlon = 128, and ktimes = 1000. Perform a 3 point (1-2-1) average and use opt = 0. Return the nlat x mlon smoothed series to the original x array:

```    x = wgt_runave(x, (/0.25, 0.50, 0.25/), 0)

; Use wgt_runave_Wrap if metadata retention is desired
; x = wgt_runave_Wrap(x, (/0.25, 0.50, 0.25/), 0)
```

Example 2

Let x be dimensioned ntim x nlat x mlon with named dimensions "time," "lat," and "lon." (Assume the "time" dimension contains monthly data.) Use the 11-point Trenberth filter on the monthly data. The Trenberth filter effectively removes fluctuations with periods of less than 8 months but includes all others. At 24 months 80% of the variance is retained. The cited filter is:

Author: K. E. Trenberth
Journal: UCAR/NCAR/MMM Monthly Weather Review, February, 1984.

```    opt = 0
wgt  = (/0.0270, 0.05856, 0.09030, 0.11742, 0.13567, \
0.1421, 0.13567, 0.11742, 0.09030, 0.05856, 0.027/)

; You can use wgt_runave to do the calculation across the time dimension, but it
; requires that you reorder the data so that time is the rightmost dimension.
; To avoid reordering data, use wgt_runave_n.
; Note, however, that y will have time as the leftmost dimension.
y    = wgt_runave_n (x, wgt, opt, 0)

; In the calculation below, y will have time as the rightmost dimension.
;      y    = wgt_runave (x(lat|:, lon|:, time|:), wgt, opt)

; Use wgt_runave_n_Wrap if metadata retention is desired
;      y    = wgt_runave_n_Wrap (x, wgt, opt, 0)

```
If wgt_runave_n is used as described above, then y will be a 3-dimensional array of length ntim x nlat x mlon. If wgt_runave is used, then y will be a 3-dimensional array of length nlat x mlon x ntim.

Example 3

Let x be dimensioned ntim x klev x nlat x mlon with named dimensions "time," "lev," "lat," and "lon." (Assume the "time" dimension contains twice daily data.) Use the low, medium and high pass 31-point Blackmon filters on the twice daily data. The low-pass filter allows most of the variance from fluctuations of 10 days or more; the medium pass filter allows variance of 2.5 to 6 days; and the high pass filter allows variance 1 to 2 days. The cited filters are:

Author: M. B. Blackmon
Journal: Journal of Atmospheric Science, August, 1976, , pg. 1609.
```    opt   = 0
wlow  = (/-0.0059591606, -0.0074864031, -0.0081766107, -0.0074769889, \
-0.0048789007,  0.0         ,  0.0073407153,  0.0170670479, \
0.0288191067,  0.0419626250,  0.0556356004,  0.0688283154, \
0.0804876892,  0.0896329731,  0.0954676702, \
0.0974726419, \                              ; central wgt
0.0954676702,  0.0896329731,  0.0804876892, \
0.0688283154,  0.0556356004,  0.0419626250,  0.0288191067, \
0.0170670479,  0.0073407153,  0.0         , -0.0048789007, \
-0.0074769889,  -0.0081766107,-0.0074864031, -0.0059591606/)

; Use wgt_runave_n to avoid reordering data:
ylow  = wgt_runave_n(x, wlow, opt, 0)

; Use wgt_runave_n_Wrap if metadata retention is desired
; ylow  = wgt_runave_n_Wrap(x, wlow, opt, 0)

wmed  = (/-0.0030384857, -0.0001341773, -0.0096723016, -0.0191709641, \
-0.0020017146,  0.0304306715,  0.0328072034,  0.0041075557, \
0.0033466748,  0.0419335015,  0.0283041151, -0.0923257264, \
-0.1947701551, -0.1020097578,  0.1433496840, \
0.2776877534, \                              ; central weight
0.1433496840, -0.1020097578, -0.1947701551, \
-0.0923257264,  0.0283041151,  0.0419335015,  0.0033466748, \
0.0041075557,  0.0328072034,  0.0304306715, -0.0020017146, \
-0.0191709641, -0.0096723016, -0.0001341773, -0.0030384857/)

; Use wgt_runave_n to avoid reordering data:
ymed  = wgt_runave_n(x, wmed, opt, 0)

; Use wgt_runave_n_Wrap if metadata retention is desired
; ymed  = wgt_runave_n_Wrap(x, wmed, opt, 0)

whigh = (/0.0036193743,  0.0062672457, -0.0071490567, -0.0089978990, \
0.0125704103,  0.0117924147, -0.0207251125, -0.0144542141, \
0.0333056699,  0.0167834343, -0.0546750050, -0.0185972473, \
0.1009810886,  0.0197489990, -0.3186000638, \
0.4762599236, \                              ; central weight
-0.3186000638,  0.0197489990,  0.1009810886, \
-0.0185972473, -0.0546750050,  0.0167834343,  0.0333056699, \
-0.0144542141, -0.0207251125,  0.0117924147,  0.0125704103, \
-0.0089978990, -0.0071490567,  0.0062672457,  0.0036193743/)

; Use wgt_runave_n to avoid reordering data:
yhigh  = wgt_runave_n(x, whigh, opt, 0)

; Use wgt_runave_n_Wrap if metadata retention is desired
; yhigh  = wgt_runave_n_Wrap(x, whigh, opt, 0)
```
y will be a 4-dimensional array of length ntim x klev x nlat x mlon.

Example 4

Consider the 2x-daily data in example 3. Now use the weights of a slightly broader 2-8 day band pass filter. The cited filter is:

Author: K. E. Trenberth
Journal: Journal of Atmospheric Science, October, 1991, pg. 2162.
```  wgt = (/-0.003, -0.033, -0.037, -0.013, -0.132, -0.188, 0.172, 0.468, \
0.172, -0.188, -0.132, -0.013, -0.037, -0.033, -0.003/)

; Use wgt_runave_n to avoid reordering data.
y    = wgt_runave_n (x, wgt, opt, 0)

; Use wgt_runave_n_Wrap if metadata retention is desired
;      y    = wgt_runave_n_Wrap (x, wgt, opt, 0)

```
y will be a 4-dimensional array of length ntim x klev x nlat x mlon.

Example 5

Let x be dimensioned ntim x klev x nlat x mlon. Perform a 5 point running average using the cyclic option in the longitude direction:

```     opt = -1
wgt  = (/1.0, 3.0, 5.0, 3.0, 1.0/)
wgt  = wgt/sum(wgt)             ; normalize
x    = wgt_runave(x, wgt, opt)

; Use wgt_runave_Wrap if metadata retention is desired
; x    = wgt_runave_Wrap(x, wgt, opt)
```