`detrend3`documentation

detrend3performs linear least squares detrending along the third dimension of a matrix.

Syntax

广告= detrend3（a）Ad = detrend3(A,t) Ad = detrend3(...,'omitnan')

Description

广告= detrend3（a）removes the linear trend from the third dimension ofAassuming slices ofAare sampled at constant intervals.

Ad = detrend3(A,t)specifies timestassociated with each slice of A. Timestdo not need to occur at regular intervals in time.

Ad = detrend3(...,'omitnan')applies detrending even in grid cells that containNaNvalues. If many grid cells contains spurious NaNs, you may find that this option is slower than the default.

Example 1: A 3D gridded dataset

This sample dataset has a trend of 3.2 units/timestep everywhere:

t = 50:50:1000; y = 3.2*t + 0.1*randn(size(t));% the trend is 3.2*t (plus some random noise)% Create 5x5 grid w/trend dictated by y:z = expang3（（5），y）;

Here's proof via thetrendtrend function:

trend(Z,t)

ans = 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000 3.2000

Now let's detrend:

Z_detrend = detrend3(Z,t);

And now what's the trend?

趋势(Z_detrend t)

ans = 1.0e-14 * -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212 -0.2212

Just numerical noise (note that it is zero to the level of 1.0e-14).

Example 2: Sea Surface Temperatures

This example calculates an area-averaged sea surface temperature anomaly from a gridded time series, thendetrendsthe gridded sst time series and plots the detrended anomaly time series.

Begin by loading the sample pacific_sst.mat dataset of monthly SSTs. Usecdtareato get the area of each grid cell, and then uselocalto get the 1D time series of area-weighted ssts for all ocean grid cells.

% Load example data:loadpacific_sst% Turn lat,lon arrays into grids:[Lon,Lat] = meshgrid(lon,lat);% Get the area (m^2) of each grid cell:A = cdtarea(Lat,Lon);% area of each grid cell (m^2)% Make a mask of only finite data (to effectively ignore land)mask = all(isfinite(sst),3);% Get 1D time series of area-weighted sst:sst_1 = local(sst,mask,'weight'，一种）;

Now plot the area-weighted sst anomaly using theanomalyfunction. For context, plot the linear trend withpolyplot:

figure anomaly(t,sst_1-mean(sst_1)) axistightdatetick('x','keeplimits') ntitle('sea surface temperature anomaly (not detrended)') holdonpolyplot(t,sst_1-mean(sst_1),1,'k','行宽',3)

Now detrend the entire 3D sst dataset and plot the same area-averaged time series, but this time using the detrended data:

% Detrend the full 3d time series:sst_dt = detrend3(sst);% Get the area-averaged detrended SST time series:sst_dt_1 = local(sst_dt,mask,'weight'，一种）;图异常（t，sst_dt_1-mean（sst_dt_1））轴tightdatetick('x','keeplimits') ntitle('DETRENDED sea surface temperature anomaly') holdonpolyplot(t,sst_dt_1-mean(sst_dt_1),1,'k','行宽',3)

Example 3: The 'omitnan' option

In some cases, your gridded dataset may have spurious NaNs in them. That is the case for the sst dataset we analyzed in the example above. See, for the 802 months of SST data, look at how many values are finite:

figure imagescn(lon,lat,sum(isfinite(sst),3)) cb = colorbar; ylabel(cb,'number of finite data values') caxis([700 802])%设置颜色轴的限制

In the figure above, take a look at Hudson Bay in Canada. You'll notice that not all of the 802 months have valid data there. As many as 100 months of data are missing because it can be hard to get a good SST reading in the winter months when ice screws up the measurement. Still, you may need to remove the long term trend from the available data.

Here's a comparison of detrending the sst dataset without versus with the'omitnan'option. Start by using thetrendfunction, simply to assess the magnitude of the trend:

figure subplot(1,2,1) imagescn(lon,lat,trend(sst,12)) cb = colorbar('location','southoutside'); xlabel(cb,'SST trend \circC/yr') title'trend without omitnan'caxis([-0.04 0.04]) cmocean('balance') subplot(1,2,2) imagescn(lon,lat,trend(sst,12,'omitnan')) cb = colorbar('location','southoutside'); xlabel(cb,'SST trend \circC/yr') title'trend with omitnan'caxis([-0.04 0.04]) cmocean('balance')

In the figure above, note the difference in Hudson Bay, Canada.

现在争取的作品相同。我们将拒绝每个数据集，然后如上所述绘制贬值数据集的趋势：

sst_dt = detrend3(sst); sst_dt_o = detrend3(sst,'omitnan'); figure subplot(1,2,1) imagescn(lon,lat,trend(sst_dt,12)) cb = colorbar('location','southoutside'); xlabel(cb,'SST trend \circC/yr') caxis([-0.000000000000001 0.000000000000001]) cmocean('balance') title'detrended trend without omitnan'subplot(1,2,2) imagescn(lon,lat,trend(sst_dt_o,12,'omitnan')) cb = colorbar('location','southoutside'); xlabel(cb,'SST trend \circC/yr') caxis([-0.000000000000001 0.000000000000001]) cmocean('balance') title'detrended trend with omitnan'

Now the only "trend" that remains in the detrended dataset is numerical noise (Note the 1x10^-15 limits of the color scale.)

Author Info

This function is part of theClimate Data Toolbox for Matlab. The function and supporting documentation were written by Chad A. Greene.

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