Plotting Eddy Kinetic Energy

Hi I have problem with plotting eddy kinetic energy (EKE)

I have a data of sea surface height (variable name: adt) with matrix [n m k]. n is latitude, m is longitude and k is time.

I want to plot EKE with equation below

here is my initial code

regionName = 'SouthIndian' % change as you need to ..

eval(['load ' regionName]); %to evaluate the data

[n, m, k] = size(b.adt); %n =lat, m= lon, k = absolute topohraphy

adt_mean = squeeze(mean(shiftdim(b.adt,2)));

g=(9.8).^2;

f=2.*(coriolisf(b.lat)).^2;

dhx=(diff(adt_mean)./diff(b.lat)).^2;

dhy=(diff(shiftdim(adt_mean,1))./diff(b.lon)).^2;

eke=g/f*(dhx+dhy);

But it doesnt working. Plese help or any suggestion about it.

[Desak Made Pera Rosita Dewi]

matlab said the matrix size do not match

[Amilton Roberto Muhosse]

I DO NOT UNDERSTAND WHAT IS ABSOLUTE P=TOPOGRAPHY

Answer 1

[Nipun]

Hi Desak,

I understand that you want to calculate and plot the Eddy Kinetic Energy (EKE) from sea surface height (adt) data. Based on the shared information about the code, I can confirm that the root cause of the problem is dimension handling and related calculation.

Here is the recommended version for the expected output:

regionName = 'SouthIndian'; % change as needed
eval(['load ' regionName]); % load the data

% Extract dimensions
[n, m, k] = size(b.adt); % n = lat, m = lon, k = time

% Compute the mean absolute dynamic topography (adt) over time
adt_mean = mean(b.adt, 3);

% Constants
g = (9.8)^2;

% Compute Coriolis parameter squared (f^2)
f = 2 * (coriolisf(b.lat)).^2;

% Calculate spatial derivatives
[lat_grid, lon_grid] = meshgrid(b.lat, b.lon);
dhx = (diff(adt_mean, 1, 1) ./ diff(lat_grid, 1, 1)).^2; % Gradient in lat direction
dhy = (diff(adt_mean, 1, 2) ./ diff(lon_grid, 1, 2)).^2; % Gradient in lon direction

% Extend the matrices to original size by padding with zeros
dhx = padarray(dhx, [1, 0], 'post');
dhy = padarray(dhy, [0, 1], 'post');

% Compute EKE
eke = g ./ f .* (dhx + dhy);

% Plotting EKE
figure;
imagesc(b.lon, b.lat, eke');
set(gca, 'YDir', 'normal');
colorbar;
title('Eddy Kinetic Energy (EKE)');
xlabel('Longitude');
ylabel('Latitude');

For more information on the functions used, refer to the following MathWorks documentation:

1. "coriolisf" : https://www.mathworks.com/matlabcentral/fileexchange/47338-coriolisf
2. "padarray" : https://www.mathworks.com/help/images/ref/padarray.html
3. "meshgrid" : https://www.mathworks.com/help/matlab/ref/meshgrid.html

Hope this helps.

Regards,

Nipun