# dtrend_n

Estimates and removes the least squares linear trend of the given dimension from all grid points.

## Prototype

function dtrend_n ( y : numeric, return_info [1] : logical, dim [1] : integer ) return_val [dimsizes(y)] : numeric

## Arguments

*y*

A multi-dimensional array or scalar value equal to the data to be detrended. The
dimension from which the trend is calculated is indicated by the *dim* argument.

*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.

## Return value

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, 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:

return_val@slope)return_val@y_intercept)

## Description

Estimates and removes the least squares linear trend of the given dimension from
all grid points.
Missing values are not
allowed, use **dtrend_msg_n** if
missing values exist.
The mean is also removed. Optionally returns the slope (eg, linear trend per unit
time interval) and y-intercept for graphical purposes.

Assumes *y* is equally spaced. If this is not the case, then use
**dtrend_msg_n** even if the data do not contain missing values.

## See Also

**dtrend_quadratic**,
**dtrend_quadratic_msg_n**,
**dtrend_msg_n**,
**dtrend_msg**,
**dtrend**

## Examples

**Example 1**

y is three-dimensional with dimensions lat, lon, and time. The returned array will have the same size. Remember that the mean is also removed.

yDtrend =dtrend_n(y,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_n(y,True,2) ; yDtrend@slope = a one-dimensional array of nlat * nlon elements. ; the units are K/month

Since attributes cannot be returned as two-dimensional arrays, the
user should use **onedtond** to create a two-dimensional array
for plotting purposes:

slope2D =onedtond(yDtrend@slope,(/nlat,nlon/))delete(yDtrend@slope) slope2D = slope2D*120 ; would give [K/decade] yInt2D =onedtond(yDtrend@y_intercept,(/nlat,nlon/))

**Example 3**

Let y be a three-dimensional array with dimensions time, lat, lon. Do the calculation across the time dimension.

yDtrend =dtrend_n(y,False,0) ; yDtrend will be three-dimensional with dimensions time, lat, lon

**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.

zDtrend =dtrend_n(z,True,2) dimz =dimsizes(z) ; retrieve dimension sizes of z 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%