NCL Website header
NCL Home > Documentation > Functions > General applied math


Computes the weighted sum of a variable's rightmost dimension at all other dimensions.


	function dim_sum_wgt (
		x       : numeric,  
		w   [*] : numeric,  
		opt [1] : integer   

	return_val  :  float or double



A variable of numeric type and any dimensionality. Missing values are indicated by the _FillValue attribute.


A one dimensional array of weights. The length must be the same as the right dimension of x.


A scalar: (a) opt=0 means compute the weighted sum only if all values are not missing; (b) opt=1 means compute the weighted sum of all non-missing values; (c) opt>1 means to return the sum only if the number of non-missing values is greater-than or equal to opt.

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.


The dim_sum_wgt function computes the weighted sum of all elements of the n-1th (rightmost) dimension for each index of the dimensions 0...n-2.

Basically, the following is done for the rightmost dimension.

    xAvg = SUM [x*w]/SUM[w]
The weighting is strictly positional. EG: If x@_FillValue=1e20, and the rightmost dimension is of size 5 and the values are (/3.7, 1e20, 14.3, 1e20, 7.1 /) with weights (/1,3,5,3,1/) then the result will be
      (3.7*1 + 14.3*5 + 7.1*1) = 82.3

Use dim_sum_wgt_n if you want to specify which dimension to do the weighted sum across.

Use dim_sum_wgt_Wrap if retention of metadata is desired.

See Also

dim_sum_wgt_Wrap , dim_avg_wgt_Wrap , dim_sum, avg, dim_avg, dim_median, dim_stddev, dim_num, dim_product, dim_rmsd, dim_rmvmean, dim_rmvmed, dim_standardize, dim_stat4, dim_stddev, dim_variance


Example 1

Let z(12,nlat,mlon) contain monthly means and with named dimensions "time", "lat" and "lon", respectively. Compute the weighted annual sum (total) at each lat/lon point. Use dimension reordering to make time the rightmost dimension.

Note: in V5.1.1, you will be able to use dim_sum_wgt_n to avoid having to reorder your data.

    wgt = (/0.08493151, 0.076712325, 0.08493151, 0.08219178 \   ; same size as dimension "time"
           ,0.08493151, 0.08219178 , 0.08493151, 0.08493151 \
           ,0.08219178, 0.08493151 , 0.08219178, 0.08493151 /)                             
    pTot = dim_sum_wgt(precip(lat|:,lon|:,time|:), wgt, 0 )    ; ==> pTot(nlat,mlon)
    pTot = dim_sum_wgt_n(precip, wgt, 0, 0)                    ; no reordering needed
Generally, users prefer that the returned variable have metadata associated with it. This can be accomplished via the dim_sum_wgt_Wrap function.

Example 2

Let T(time,lev,lat,lon). Compute the weighted vertical sum total at each time/lat/lon point. Use dimension reordering to make level the rightmost dimension.

    wgt = (/50,50,100,100,100,50,25,10/) ; same size as dimension "lev"

    Tsum = dim_sum_wgt( T(time|:,lat|:,lon|:,lev|:), wgt, 0 )   ; ==> Tsum(time,lat,lon) 
    Tsum = dim_sum_wgt_n( T, wgt, 0, 1 )                        ; no reordering needed