# cdtcurl documentation

cdtcurl calculates the z component of curl for gridded vectors on an ellipsoidal Earth.

See also: cdtgradient, cdtdivergence and ekman.

## Syntax

Cz = cdtcurl(lat,lon,U,V)

## Description

Cz = cdtcurl(lat,lon,U,V) uses cdtdim to estimate the dimensions of each grid cell in the lat,lon grid, then computes the curl of the gridded vectors U,V.

## Example

Load this sample of 10-meter winds u and v. Note that when we load the wind data, we're just taking the mean winds for this example.

filename = 'ERA_Interim_2017.nc';
u = mean(ncread(filename,'u10'),3);
v = mean(ncread(filename,'v10'),3);
lat = double(ncread(filename,'latitude'));
lon = double(ncread(filename,'longitude'));
[Lat,Lon] = meshgrid(lat,lon);


The raw data are on a grid that goes from 0 to 360 longitude. I'd rather put the prime meridian in the middle of the map, so let's recenter the grids. This step isn't necessary, but it's a preference:

[Lat,Lon,u,v] = recenter(Lat,Lon,u,v);


Here are the winds on a global map:

figure
earthimage
hold on

q = quiversc(Lon,Lat,u,v,'density',75);

legend(q,'wind speed')


To illustrate the use of the cdtcurl function, we can recreate Figure S11.03a of the Sixth Edition of Talley et al.'s book, Descriptive Physical Oceanography.

Start by using the windstress function to convert the 10 meter wind speed vectors to wind stress in N/m^2:

[Taux,Tauy] = windstress(u,v);


Now use cdtcurl to get the global wind stress curl:

C = cdtcurl(Lat,Lon,Taux,Tauy);


Use island to mask out the grid cells corresponding to land, and following Talley et al., multiply southern hemisphere curls by negative 1:

% Mask out land:
land = island(Lat,Lon);
C(land) = NaN;
Taux(land) = NaN;
Tauy(land) = NaN;

% Multiply southern hemisphere curl by negative 1:
C = C.*sign(Lat);


Now we're ready to recreate Talley et al.'s map relating wind stress to wind stress curl:

figure
pcolor(Lon,Lat,C)
shading flat
hold on

% Overlay continents:
borders('countries','facecolor',rgb('gray'),'edgecolor','none');

% Overlay wind stress vectors:
quiversc(Lon,Lat,Taux,Tauy,'k','density',100)

% Jet is never a good idea, but we'll do it to mimic the published figure:
colormap(jet(20))

% Set the color axis limits and make a colorbar:
caxis([-2 2]*1e-7)
cb = colorbar('location','southoutside');
xlabel(cb,'wind stress curl x sign(lat) (\times10^{-7} N/m^3)')

% Set map extents:
axis([10 150 -60 30])

% Format tick labels as degrees:
xtickformat('degrees')
ytickformat('degrees')


In case you're curious, here's the same figure with a more appropriate, divergent colormap from cmocean (Thyng et al., 2016)

cmocean bal


## Author Info

This function is part of the Climate Data Toolbox for Matlab. The function and supporting documentation were written by Chad A. Greene of the University of Texas at Austin.