# How do I plot a hodograph?

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Russ on 25 Nov 2012
Commented: Nathan Anderson on 10 Mar 2018
I can't seem to find a function in Matlab that allows me to plot a hodograph. Any ideas?
Ashim on 17 Jul 2014
Did you find a solution to plot a hodgraph. I seem to find a solution to plot the points but since i am not a Matlab expert. I cannot find a way to connect the points within the hodograph...I am positing a minimal example here
Ws = 15.*rand(10,1);
Wd = 360.*rand(10,1);
H = (20:20:200)';
Wd = double(Wd);
Ws = double(Ws);
Wd = Wd.*(pi/180);
[WdX, WsY] = pol2cart(Wd, Ws);
polar(WdX, WsY,':b*');
It would be great if you would write the solution you came to. I am unable to think of something to connect the points within the polar plot

bym on 25 Nov 2012
do
compass
or
feather
work?
Ashim on 22 Oct 2014
I do have an answer to connect the points here is the simple Hodograph example. However, i am not sure if the wind direction is correctly displayed. I am sure i am doing something wrong there. Any suggestions to make the wind directions correct??
if true
%code
Ws = [6.4;6.7;7.4;7.4;7.7;7.9;8.5;8.9;9.1;9.5];
Wd = [185;186;183;186;186.5;187;191;192;197;193];
H = [40;52;60;80;100;108;140;160;180;200];
Wd = Wd.*(pi/180);
Ws = Ws;
[U, V] = pol2cart(Wd, Ws);
polar(U, V,'ob');
text(U, V, num2str(H));
%WdXi = flipud((min(WdX):0.1:max(WdX))');
%WsYi = interp1(WdX, WsY, WdXi,'spline' );
%hold on;
%polar(WdXi, WsYi);
t = 1:numel(Ws);
ts = 1:1/numel(Ws):numel(Ws);
xs = pchip(t,U,ts);
ys = pchip(t, V, ts);
hold on;
polar(xs, ys,'r');
end

Nathan Anderson on 10 Mar 2018
Edited: Nathan Anderson on 10 Mar 2018
A few subtle changes are required. First, decide on coordinates. Do you want to plot using mathematical conventions (counterclockwise from East), or meteorological (clockwise from North)? Also note that in meteorology, degrees are the direction the wind is blowing FROM. See http://colaweb.gmu.edu/dev/clim301/lectures/wind/wind-uv
On a hodograph, the wind is blowing from the origin to the position on the hodograph, so a 180 degree rotation is required. I'm assuming we chose meteorological winds (so Wd = 185 is from the SSW to NNE), but are confined to the limitations of the polar plot (math direction), which we'll flip later.
Ws = [6.4;6.7;7.4;7.4;7.7;7.9;8.5;8.9;9.1;9.5];
Wd = [185;186;183;186;186.5;187;191;192;197;193];
Wd = Wd-180; % Wind dir on hodograph will be opposite the usual MET convention (blowing from, not to)
H = [40;52;60;80;100;108;140;160;180;200];
Wd = Wd.*(pi/180);
[U, V] = pol2cart(Wd, Ws);
polar(Wd,Ws,'ob'); % Don't use U/V here...they are cartesian.
text(U, V, num2str(H)); % Use U/V here...for text placement.
t = 1:numel(Ws);
ts = 1:1/numel(Ws):numel(Ws);
xs = pchip(t,U,ts);
ys = pchip(t,V,ts);
hold on;
[th,r] = cart2pol(xs,ys); % Need to convert back to polar, here!
polar(th, r,'r');
view([90 -90]) % Correct the view angle, so we see directions as clockwise from North. I'm sure other ways exist, but this was a fudge to get around the fact that "polar" is not too good with met directions.
Enjoy.
Nathan Anderson on 10 Mar 2018
Who are we kidding? We need more helicity.
Ws = [10;15;15;18;20;25;30;30;30;30];
Wd = [90;130;150;170;190;200;210;230;250;270];