Plot contour using matlab and octave

Plot contour using matlab and octave

(example: geostrophic vorticity and vorticity advection)

% Constants

Lx = 6000.e3; % wave length in X (6000 km) Ly = 4000.e3; % wave length in Y (4000 km) k = 2*pi/Lx; % zonal wavenumber [1/m]

l = 2*pi/Ly; % meridional wavenumber [1/m]

...

Define constants

% Define domain size

x1 = (-3000:100:3000)*1.e3; % set domain in x [m]

y1 = (-1000:100:1000)*1.e3; % in y [m]

[x,y] = meshgrid(x1,y1); % make 2D matrix

Set domain

Same as previous lecture

% compute variables (monochromatic wave) phi = 55000 - U*f0*(y);

phi = 55000 - U*f0*(y);

phi = phi + amp*sin(k*x).*cos(l*y);

Ug = U + amp*l*sin(k*x).*sin(l*y)/f0;

Vg = amp*k*cos(k*x).*cos(l*y)/f0;

vor = -amp*(k^2+l^2)* sin(k*x).*cos(l*y)/f0;

vor_x = -amp*(k^2+l^2)*k*cos(k*x).*cos(l*y)/f0;

vor_y = amp*(k^2+l^2)*l*sin(k*x).*sin(l*y)/f0;

vor_adv = -Ug.*vor_x -Vg.*(vor_y+b0);

Compute values

Source: http://folk.ntnu.no/leifh/teaching/tkt4140

Laplacian ( ^∇

²

^{Φ = Φ}

_xx

^{+ Φ}

_yy

)

Source: http://folk.ntnu.no/leifh/teaching/tkt4140

Laplacian ( ^∇

²

^{Φ = Φ}

_xx

^{+ Φ}

_yy

)

Source: http://folk.ntnu.no/leifh/teaching/tkt4140

Laplacian ( ^∇

²

^{Φ = Φ}

_xx

^{+ Φ}

_yy

)

Source: http://folk.ntnu.no/leifh/teaching/tkt4140

Laplacian ( ^∇

²

^{Φ = Φ}

_xx

^{+ Φ}

_yy

)

% compute variables (monochromatic wave) phi = 55000 - U*f0*(y);

phi = 55000 - U*f0*(y);

phi = phi + amp*sin(k*x).*cos(l*y);

Ug = U + amp*l*sin(k*x).*sin(l*y)/f0;

Vg = amp*k*cos(k*x).*cos(l*y)/f0;

% If you like numerical methods --- dx = 100.e3; dy = 100.e3;

Vor = 4*del2(phi, dx, dy)/f0;

[vor_x, vor_y] = gradient(vor, dx, dy) vor_adv = -Ug.*vor_x -Vg.*(vor_y+b0);

Compute values

% Figure2: plot Geopotential and vorticity figure(2)

subplot(2,1,1) % geopotential

[cs,h]=contour(x/1000,y/1000,phi,'linewidth',4);

clabel(cs,h,'LabelSpacing’,400) axis([-3000,3000,-1000,1000]))

xlabel('x (km)’); ylabel('y (km)') title('Geopotential (m^2/s^2)')

Plot contour

% Figure2: plot Geopotential and vorticity figure(2)

subplot(2,1,1) % geopotential ...

subplot(2,1,2) % vorticity and its advection [cs,h]=contourf(x/1000,y/1000,vor_adv,9);

caxis([-1.2e-9, 1.2e-9]), hold on

[cs,h]=contour(x/1000,y/1000,vor,'linewidth',2);

clabel(cs,h,'LabelSpacing',400) axis([-3000,3000,-1000,1000])

title('Vorticity and vorticity advection') xlabel('x (km)'), ylabel('y (km)')

Plot contour

Handel colormap & save figure

% Figure2: plot Geopotential and vorticity figure(2)

subplot(2,1,1) % geopotential ...

subplot(2,1,2) % vorticity advection ...

colorbar('southoutside') colormap('jet')

colorbar

% save graphical current figure (gcf) as PDF saveas(gcf,'geo_vorticity.pdf')