Estimates and removes the least squares linear trend of the dim-th dimension from all grid points (missing values allowed).
function dtrend_msg_n ( x [*] : numeric, y : numeric, remove_mean  : logical, return_info  : logical, dim  : integer ) return_val [dimsizes(y)] : numeric
One-dimensional array containing the coordinate of the dim-th dimension of y. [eg: time].y
A multi-dimensional array or scalar value equal to the data to be detrended. The dimension from which the trend is calculated needs to be the dim-th dimension. This is usually time.remove_mean
A logical scalar indicating whether or not the mean is removed from return_val. True = remove mean, False = do not remove mean.return_info
A logical scalar controlling whether attributes corresponding to the y-intercept and slope are attached to return_val. True = attributes returned. False = no attributes returned.dim
A scalar integer indicating which dimension of y to do the calculation on. Dimension numbering starts at 0.
An array of the same size as y. Double if y is double, float otherwise.
Two attributes (slope and y_intercept) may be attached to return_val if return_info = True. These attributes will be one-dimensional arrays if y is one-dimensional. If y is multi-dimensional, the attributes will be the same size as y minus the dim-th dimension but in the form of a one-dimensional array. e.g. if y is 45 x 34 and dim is 1, then the attributes will be a one-dimensional array of size 45*34. This occurs because attributes cannot be multi-dimensional. Double if return_val is double, float otherwise.
You access the attributes through the @ operator:
Estimates and removes the least squares linear trend of the dim-th dimension from all grid points. The mean is optionally removed. Missing values are allowed. Optionally returns the slope (i.e., linear trend per unit time interval) and y-intercept for graphical purposes.
Let x be one-dimensional with dimension time and y be three-dimensional with dimensions lat,lon, and time. The return_val will be three-dimensional with dimensions lat,lon, time. The mean is removed.
yDtrend = dtrend_msg_n (x,y,True,False,2)Example 2
Same as example 1 but with the optional attributes. Let y be temperatures in units of K and the time dimension have units of months.
yDtrend = dtrend_msg_n (x,y,True,True,2) ; yDtrend@slope is a one-dimensional array of size nlat x nlon elements.
Since attributes cannot be returned as two-dimensional arrays, the user should use onedtond to create a two-dimensional array for plotting purposes:
yDtrend = dtrend_msg_n (x,y,False,True,2) slope2D = onedtond(yDtrend@slope, (/nlat,mlon/) ) delete (yDtrend@slope) slope2D = slope2D*120 ; would give [K/decade] yInt2D = onedtond(yDtrend@y_intercept, (/nlat,mlon/) ) delete (yDtrend@y_intercept)Example 3
Let y be a three-dimensional array with dimensions time, lat, lon.
yDtrend = dtrend_msg_n(y&time,y,True,False,0) ; yDtrend will be three-dimensional with dimensions lat, lon, time.Example 4
This example shows how to calculate the significance of trends by evaluating the incomplete beta function using betainc. Let z be a three-dimensional array with dimensions named lat, lon, time.
dimz = dimsizes(z) ; retrieve dimension sizes of z zDtrend = dtrend_msg_n(ispan(0,dimz(2)-1,1),z,True,True,2) tval = new((/dimz(0),dimz(1)/),"float") ; preallocate tval as a float array and df = new((/dimz(0),dimz(1)/),"integer") ; df as an integer array for use in regcoef rc = regcoef(ispan(0,dimz(2)-1,1),z,tval,df) ; regress z against a straight line to ; return the tval and degrees of freedom df = equiv_sample_size(z,0.05,0) ; If your data may be significantly autocorrelated ; it is best to take that into account, and one can ; do that by using equiv_sample_size. Note that ; in this example df (output from regcoef) is ; overwritten with the output from equiv_sample_size. ; If your data is not significantly autocorrelated one ; can skip using equiv_sample_size. df = df-2 ; regcoef/equiv_sample_size return N, need N-2 beta_b = new((/dimz(0),dimz(1)/),"float") ; preallocate space for beta_b beta_b = 0.5 ; set entire beta_b array to 0.5, the suggested value of beta_b ; according to betainc documentation z_signif = (1.-betainc(df/(df+tval^2), df/2.0, beta_b))*100. ; significance of trends ; expressed from 0 to 100%