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pattern_cor

Compute centered or uncentered pattern correlation.

Available in version 6.0.0 and later.

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 pattern_cor (
		x       : numeric,  
		y       : numeric,  
		w       : numeric,  
		opt [1] : integer   
	)

Arguments

An array of two-to-four dimensions. The two rightmost dimensions are expected to be the spatial dimensions, e.g.: (...,lat,lon)

An array the same size and shape as x.

A scalar (w[1]) or one- (w[*]) or two- (w[*][*]) dimensional array containing the weights. If no weighting is desired set w=1.0 (a scalar value). If w[*] then it must be the same sizes as the second rightmost dimension. e.g.: 'lat'. If w[*][*] then the sizes of the two rightmost dimensions of x and w must conform.

opt

opt=0 means compute the centered pattern correlation; opt=1 means compute the uncentered pattern correlation.

Return value

The results could be a scalar if x and y are two-dimensional; if x and y are (ntim,nlat,mlon), a one-dimensional array of length ntim will be returned; if x and y are (ntim,klev,nlat,mlon), a two-dimensional array of size (/ntim,klev/) will be returned.

If either x or y are all missing (_FillValue), then the returned quantity will be set to _FillValue.

Description

The pattern correlation is the Pearson product-moment coefficient of linear correlation between two variables that are respectively the values of the same variables at corresponding locations on two different maps. The two different maps can be for different times, for different levels in the vertical direction, for forecast and observed values, etc. The anomaly correlation is a special case of pattern correlation.

Pattern correlations can be computed directly (uncentered) or by computing anomalies from a central mean (centered). For diagnostic studies (eg, Taylor Diagrams) the centered pattern correlation is most commonly used. However, as discussed in the "IPCC Third Assessment Report - Climate Change 2001", the centered pattern correlation should not be used for climate change attribution.

     Pattern correlation statistics come in two types - centred and uncentred 
     (see Appendix 12.3). The centred (uncentred) statistic measures the similarity 
     of two patterns after (without) removal of the global mean.
     :
     :
     Centred correlations alone are not sufficient for the attribution of climate change."

Note: If all of either x or y are missing (ie, all equal_FillValue) then the _FillValue associated with x or y will be returned.

Pattern correlation The Pearson product-moment coefficient of linear correlation between two variables that are respectively the values of the same variables at corresponding locations on two different maps. The two different maps can be for different times, for different levels in the vertical direction, for forecast and observed values, etc. Occasionally referred to as map correlation. See anomaly correlation, a special case of pattern correlation.

Examples

The following require that contributed.ncl be loaded prior to invoking the function.

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

Example 1

Consider x(lat,lon) and y(lat,lon) and (say) gaussian weights, gw(lat). Assorted pattern correlations are computed via

           ra = pattern_cor(x, y, 1.0, 0)    ; no weighting, centered
           rb = pattern_cor(x, y, 1.0, 1)    ; no weighting, uncentered
           rc = pattern_cor(x, y,gw, 0)      ; gaussian weighting, centered
           rd = pattern_cor(x, y,gw, 1)      ; gaussian weighting, uncentered

           clat = cos(0.01745329*lat)        ; cos(lat) weight
           re = pattern_cor(x, y,clat, 0)    ; cos(lat) weighting, centered
           rf = pattern_cor(x, y,clat, 1)    ; cos(lat) weighting, uncentered

Example 2

Consider x(time,lat,lon) and y(time,lat,lon) and weights, w(lat). Assorted pattern correlations are computed via

           rc = pattern_cor(x, y,w, 0)      ; weighting, centered; rc(time)
           rd = pattern_cor(x, y,w, 1)      ; weighting, uncentered; rd(time)

Example 3

Consider x(time,lev,lat,lon) and y(time,lev,lat,lon) and weights, w(lat). Assorted pattern correlations are computed via

           rc = pattern_cor(x, y,w, 0)      ; weighting, centered; rc(time,lev)
           rd = pattern_cor(x, y,w, 1)      ; weighting, uncentered; rd(time,lev)

Example 4

Consider x(time,lev,lat,lon) and y(time,lev,lat,lon) and weights, w(lat,lon). Assorted pattern correlations are computed via