Computes the unbiased estimates of the variance of a variable's rightmost dimension.
function dim_variance ( x : numeric ) return_val : float or double
A variable of numeric type and any dimensionality.
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_variance function computes the unbiased estimate of the variance of all elements of the n-1 dimension for each index of the dimensions 0...n-2. 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 if you want to specify which dimension(s) to calculate the variance.
Use dim_variance_Wrap if retention of metadata is desired.
The following calculates the population and sample variance of 5 values. For illustration, a step-by-step calculation of the variance is done. The variances returned by NCL's three built-in variance functions are included. All return the sample variance.
f = (/ 7, 9, -2, -8, 2/) favg = avg(f) ; average fdev = f-favg ; deviations fdev2 = fdev^2 ; deviations squared nf = dimsizes(f) ; N pvar = sum(fdev2)/nf ; population variance svar = sum(fdev2)/(nf-1) ; sample variance var1 = variance(f) var2 = dim_variance(f) var3 = dim_variance_n(f,0) print("pvar="+pvar+" svar="+svar+" var1="+var1+" var2="+var2+" var3="+var3) === output: pvar=37.84 svar=47.3 var1=47.3 var2=47.3 var3=47.3
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 3
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 4
Let x be defined as in Example 3: 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.
Note: in V5.1.1, you will be able to use dim_variance_n to avoid having to reorder your data.
xVarTime = dim_variance( x(lat|:, lon|:, time|:) ) ; ==> xVarTime(nlat,nlon) xVarTime = dim_variance_n(x, 0) ; no reordering neededIf metadata is desired use:
xVarTime = dim_variance_Wrap( x(lat|:, lon|:, time|:) ) ; ==> xVarTime(lat,lon) xVarTime = dim_variance_n_Wrap(x,0) ; no reordering needed