Interpolating data to get values at specific depth

Dear experts, please help. I was searching and trying for anentire day and I couldn't figure it out by my own.

I have X, Y, Z, data.

X is longitude, Y is latitude, Z is depth, and data is temperature for example.

X and Y are 2D matrices (224x164). Z and data are 3D matrices (224x164x37).

The depth is unevenly spaced, for exemple, 1.0, 2.3, 5.6, 8.3 and so on, but I need the values of temperature exactly at 5m for example.

What I need is to get the data values at a specif depth all over the domain to plot a colored 2D map.

Please, could someone help me on how is such interpolation?

P.S. I know how to plot, I did it by plotting the surface Z(:,:,1), but as I mentioned, I need other depth layer.

Thank you so much in advance!

Answer 1

[Torsten]

Make X and Y also 224x164x37 (just by repeating the planar profile 37 times) and use interp3 to interpolate to the depth of your choice.

Then make your contourf or surf plot.

[Luís Henrique Bordin]

Thank you for your reply, Torsten!

I created a new matrix (dptU) for depth (224,164,37), in which the depth dimension increases by 100 from 0 to 3600.

From Vq = interp3(X,Y,Z,data,xq,yq,zq) I tried:

Vq = interp3(lon, lat, depth, temp, lon, lat, dptU);

I didn't know what to put as xq and yq, so I repeated it since it has to stay the same, I just want to change de values among depths.

All the variables has the same size(224,164,37), but I got the error "Input grid is not a valid MESHGRID".

Please, do you know why and what I should do to solve it?

Thank you very much!

[Torsten]

Do your X and Y matrices define a valid MESHGRID for longitude and latitude, i.e. something like

x = 5:10;
y = 30:40;
[X,Y] = meshgrid(x,y);

ans = 1×2

11 6

ans = 1×2

11 6

plot(X,Y,'ob')

Or are (X(i,j),Y(i,j)) 1<=i<=224, 1<=j<=164 are just 224*164 wildly spread points in the X-Y-plane ?

[Luís Henrique Bordin]

The grid is unevenly spaced, so they are wildly spread points in the X-Y-plane.

[Torsten]

I guess your data will be well-behaved.

This code only takes the temperature data at the point (X(i,j),Y(i,j)) over the 37 heights and makes a 1d-interpolation to the required height (0.5 m) for all these points. I don't know if the results get better if you include temperatures in neighbouring points, but the interpolation will become more complicated. You will most probably have to use "ScatteredInterpolant".

X = rand(224,164);               % random X-coordinates
Y = rand(224,164);               % random Y-coordinates
Z = 10*rand(224,164,37);         % random heights at points (X,Y)
data = 20 + rand(224,164,37)*20; % random temperatures at points (X,Y,Z)
h = 5;                           % interpolation level
for i = 1:224
    for j = 1:164
        [z,idx] = sort(squeeze(Z(i,j,:)));
        d = squeeze(data(i,j,idx));
        temp_5(i,j) =  interp1(z,d,h);
    end
end
surf(X,Y,temp_5)

[Luís Henrique Bordin]

Now it worked perfectly. Thank you very much, Torsten! Best!

Answer 2

[William Rose]

@Luís Henrique Bordin,

x=(0:10); y=(0:11)'; z=[1.0, 2.3, 5.6, 8.3]; % vectors x,y,z
[X,Y]=meshgrid(x,y);
%Make data() with desired dimensions, same at each depth 
data=repmat(sin(2*pi*y/11)*cos(2*pi*x/10),[1,1,length(z)]); 
% Make data different at different depths
for k=1:length(z), data(:,:,k)=data(:,:,k)+z(k)^2/10; end
% check that the array sizes are as desired
fprintf('Size X, Y, Z= %dx%d, %dx%d, %dx%dx%d.\n',size(X),size(Y),size(data))

Size X, Y, Z= 12x11, 12x11, 12x11x4.

% Plot data(x,y,z=5.6), as a test
surf(X,Y,data(:,:,3)); 
grid on; xlabel('X'); ylabel('Y'), zlabel('Data'); title('Data(:,:,z=5.6)')

data5=zeros(size(X)); % allocate array for data interpolated to z=5
for i=1:length(y), for j=1:length(x)
        data5(i,j)=interp1(z,squeeze(data(i,j,:)),5);
end, end
% Plot data(x,y,z=5)
surf(X,Y,data5); 
grid on; xlabel('X'); ylabel('Y'), zlabel('Data'); 
title('Data, Interpolated to z=5')

OK