Computes the unbiased estimates of the variance of a variable's given dimension(s) at all other dimensions.
Available in version 5.1.1 and later.
function dim_variance_n ( x : numeric, dims [*] : integer ) return_val : float or double
A variable of numeric type and any dimensionality.dims
The dimension(s) of x on which to calculate the variance. Must be consecutive and monotonically increasing.
The output will be double if x is double, and float otherwise.
The output dimensionality will be the same as all but the dims's dimensions of the input variable. The dimension rank of the input variable will be reduced by the rank of dims.
The dim_variance_n function computes the unbiased estimate of the variance of all elements of the dimensions indicated by dims for each index of the remaining dimensions. 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_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.
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_n(q,2) ;==> 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 variance is:
xVarLon= dim_variance_n(x,2) ; ==> xVarLon(ntim,nlat)Generally, users prefer that the returned variable have metadata associated with it. This can be accomplished via the dim_variance_n_Wrap function:
xVarLon = dim_variance_n_Wrap(x,2) ; ==> xVarLon(time,lat)Example 4
Let x be defined as in Example 3: x(time,lat,lon). Compute the temporal sample variance at each latitude/longitude grid point.
xVarTime = dim_variance_n(x,0) ; ==> xVarTime(nlat,nlon)If metadata is desired use
xVarTime = dim_variance_n_Wrap(x,0) ; ==> xVarTime(lat,lon)Example 5
Let x be defined as x(time,lev,lat,lon). Compute the sample variance at each latitude/longitude grid point.
xVar = dim_variance_n(x,(/0,1/)) ; ==> xVar(nlat,nlon)To compute the variance at each time/lev grid point:
xVar = dim_variance_n(x,(/2,3/)) ; ==> xVar(ntim,nlev)