Interpolating 3D Gridded data at specific cordinates

I am working with 3D gridded data with a dimension of (Longitude,Latitude,Height) and size (73x37x41). I want to plot temperature vs longitude at a slice of latitude = 0 degree and Height at 100 km and also temperature vs latitude at a slice of longitude = 0 degrees and height = 100 km.The original data does not provide data at these specific point i.e ( latitude = 0 and height = 100 km and longitude= 0 degree and height = 100 km). I know I have to interpolate my data to plot at these specific point but I am having problem in interpolating.

My data is something like this

[Long,Lat,Height] = ndgrid(0:5:360,-90:5:90,0:15:600);

Temp = rand(73,37,41)*1000;

Answer 1

[Matt J]

    [Long,Lat,Height] = deal(0:5:360,-90:5:90,0:15:600);  %Fake data
    Temp = rand(73,37,41)*1000;
    
    LUT=griddedInterpolant({Long,Lat,Height}, Temp); %interpolation object
    
    TempvLong=LUT({0,Long,100});  %slices
    TempvLat=LUT({Lat,0,100});
    
    figure(1)
    plot(Long(:),TempvLong(:));
    xlabel 'Longitude'; ylabel 'Temperature'

    
    figure(2);
    plot(Lat(:),TempvLat(:));   
    xlabel 'Latitude'; ylabel 'Temperature'

[Mark]

Thanks again @Matt J

[Mark]

Hi Matt, the plots remain same if I try to plot at two different (Height = 100 km and 500 km. Like the plots for Long(:) vs TempvLong=LUT({0,Long,100}); and Long(:) vs TempvLong=LUT({0,Long,500} is same which is not realistic from the data. Can you check why this is happening.

[Matt J]

I don't see it in my test below:

[Long,Lat,Height] = deal(0:5:360,-90:5:90,0:15:600);  %Fake data
Temp = rand(73,37,41)*1000;

LUT=griddedInterpolant({Long,Lat,Height}, Temp); %interpolation object

tiledlayout(1,2)

nexttile
TempvLong=LUT({0,Long,100});  %slices
plot(Long(:),TempvLong(:));
xlabel 'Longitude'; ylabel 'Temperature'

nexttile
TempvLong=LUT({0,Long,500});  %slices
plot(Long(:),TempvLong(:));
xlabel 'Longitude'; ylabel 'Temperature'

[Mark]

Hi @Matt J,

From my actual data the two plots are same at two different heights. I am uploading the link for my data:

Link: shorturl.at/fghNP

My Matlab code is below:

file='data.nc';
Temp = ncread(file1,'Temperature');
Lat = ncread(file1,'Latitude')*(180/pi);% convert rad to degrees
Long = ncread(file1, 'Longitude')*(180/pi);% convert rad to degrees
Alt= ncread(file1,'Altitude');

Temp= double(Temp); %convert from single to double
Long =double(Long);
Lat = double(Lat);
Alt= double(Alt);

Long = Long(:,1,1)';
Lat = Lat(1,:,1);
Alt = Alt(1,1,:);
Alt  = permute(Alt,[1 3 2]);

LUT=griddedInterpolant({Long,Lat,Alt}, Temp); %interpolation object
tiledlayout(1,2)
nexttile
TempvLong1=LUT({0,Long,100});  %slices
plot(Long1(:),TempvLong1(:));
xlabel 'Longitude'; ylabel 'Temperature'
nexttile
TempvLong2=LUT({0,Long,500});  %slices
plot(Long(:),TempvLong2(:));
xlabel 'Longitude'; ylabel 'Temperature'

[Matt J]

Both 100 and 500 are well outside the range of Alt values given, and are in different units, so LUT is just doing meaningless extrapolation.

>> mnmx(Alt)

Maximum entry = 664122.1875

Minimum entry = 96420.9922

NaNs Present = NO

[Mark]

Thanks, @Matt J. I figured out where I was wrong.