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wgt_runave_leftdim

Calculate a weighted running average over the leftmost dimension (usually, "time") and return in the original order with metadata.

Prototype

load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl"  ; This library is automatically loaded
                                                             ; from NCL V6.2.0 onward.
                                                             ; No need for user to explicitly load.

	function wgt_runave_leftdim (
		x    : numeric,  
		wgt  : numeric,  
		opt  : integer   
	)

	return_val  :  float or double

Arguments

x

An array with one or more dimensions, nominally, (time), (time,lat,lon), etc.

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 leftmost 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 is a utility function that (a) reorders the input array, x; (b) uses wgt_runave_Wrap to apply the weights; and (c) return to the original dimension order.

This function computes a weighted running average on the leftmost dimension and retains metadata.

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 - 1)} 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.

This function is identical to the built-in function wgt_runave, except it retains metadata.

See Also

wgt_runave, wgt_runave_Wrap, wgt_areaave_Wrap, wgt_areaave, wgt_areaave2, wgt_arearmse, wgt_arearmse2, wgt_areasum2, wgt_volave, wgt_volave_ccm, wgt_volrmse, wgt_volrmse_ccm

Examples

Example 1

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/)
    y    = wgt_runave_leftdim (x, wgt, opt)
y will be a 3-dimensional array of length of the same size, shape and metadata.

Example 2

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 weight
               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/)
    ylow  = wgt_runave_leftdim(x, wlow, opt)

    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/)
    ymed  = wgt_runave_leftdim (x, wmed, opt)

    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/)
    yhigh = wgt_runave_leftdim(x, whigh, opt)
y will be the same size and shape as x but the leftmost dimensions will be filtered.

Example 3

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/)
             
  y   = wgt_runave_leftdim(x, wgt, opt)
y will be the same size and shape as x, but the leftmost dimensions will be smoothed.