Error in interpolating: Actual data does not match with interpolated data

Hi,

I am trying to interpolate my gridded data of dimension (longitude x latitude x altitude) at specific latitude and altitude which are not included in the dataset. To check my code and verify if my interpolated data is correct, I tried to interpolate at the point (Lat = 15 Degree & Alt = 100 km) which is included in the original data. By surpise, the plots for interpolated data and original data didnt match. I am not sure what I am doing wrong so requesting if you could help me out.

Below is my matlab code (attached) and link for my data:

Link for my data: https://drive.google.com/drive/folders/195GxDtuUIGRxqMSVsWPZpWeapJ9s2kEc?usp=share_link

%% read data
file1='data_nc\data_10x10\data.nc'; %76x94x54
Temp1_4d = ncread(file1,'Temperature');
Temp1_4d =Temp1_4d(3:38,3:20,:);
Lat1_4d = ncread(file1,'Latitude')*(180/pi);
Lat1_4d = Lat1_4d(3:38,3:20,:);
Long1_4d = ncread(file1, 'Longitude')*(180/pi);
Long1_4d =Long1_4d(3:38,3:20,:);
Alt1_4d = ncread(file1,'Altitude');
Alt1_4d = Alt1_4d(3:38,3:20,:);

Temp1_4d = double(Temp1_4d);% converts single data to double
Temp1a_4d = Temp1_4d(19:36,:,:);Temp1b_4d =Temp1_4d(1:18,:,:);Temp1c_4d = [Temp1a_4d;Temp1b_4d];
Long1_4d =double(Long1_4d);Long1_4d = wrapTo180(Long1_4d);
Long1a_4d = Long1_4d(19:36,:,:);Long1b_4d = Long1_4d(1:18,:,:);Long1c_4d = [Long1a_4d;Long1b_4d];
Lat1_4d = double(Lat1_4d);
Lat1a_4d = Lat1_4d(19:36,:,:);Lat1b_4d = Lat1_4d(1:18,:,:);Lat1c_4d = [Lat1a_4d;Lat1b_4d];
Alt1_4d = double(Alt1_4d);
Alt1a_4d = Alt1_4d(19:36,:,:);Alt1b_4d = Alt1_4d(1:18,:,:);Alt1c_4d = [Alt1a_4d;Alt1b_4d];

Long1 = Long1c_4d(:,1,1); %reads vector of Long
Lat1 = Lat1c_4d(1,:,1); %reads vector of Long
Alt1 = Alt1c_4d(1,1,:);%reads vector of Alt
Alt1   = permute(Alt1,[1 3 2]);


%% interpolate
LUT1=griddedInterpolant({Long1,Lat1,Alt1}, Temp1_4d); %interpolation object 2

TempvLong1=LUT1({Long1,15,100000});  %slices

TempvLong1b=LUT1({Long1,15,100000});  %slices


%%Plot
tiledlayout(1,1)
    
nexttile
hold on;

plot(Long1(:),TempvLong1(:),'-hexagram','Color','k','MarkerSize',2,'MarkerEdgeColor','k','MarkerFaceColor','k');
plot(Long1c_4d(:,11,3),Temp1c_4d(:,11,3),'-hexagram','Color','b','MarkerSize',2,'MarkerEdgeColor','b','MarkerFaceColor','b');
xlabel 'Longitude'; 
ylabel 'Temperature'
title 'Lat = 15^o & Alt = 100 km';
%legend ('72x54 cells (5 long x 3.33 lat)','72x90 cells (5 long x 2 lat)','72x180 cells (5 long x 1 lat)','120x90 cells (3 long x 2 lat)');
%legend('location','north','box','on','FontSize',7);
legend('location','north','box','on','FontSize',7);
legend('interpolated data', 'origina data');
xlim([-180 180]);
ax = gca;
set(ax,'Box','on');
ax.XTick = -180:60:180;
hold off;
    

[Matt J]

It would be best just to attach LUT1 in a .mat file, so we can examine everything directly.

[Mark]

Thanks, @Matt J. I have now attached the .mat file.

[Matt J]

I don't think so. I see no .mat file attached. Just a .m file with a copy of your already posted code.

[Mark]

Hi @Matt J My bad, it is attached here.

[Star Strider]

It should be possible to upload the .nc file directly to here. If not, use the zip function to create a .zip file from it and then upload the .zip file. It is not convenient to download files from external sites.

The ‘code_mark.m’ file is a .mat file with the same information as ‘LUT1.mat’ and not a code file.

It will likely be necessary to use the intrplat and intrplon functions instead of the others to do the coordinate interpolation. It may then may be possible to use griddata or scatteredInterpolant to interpolate the altitude data. I don’t have the Mapping Toolbox, so I have no experience with this sort of interpolation.

[Mark]

Hi @Star Strider, thanks for your suggestion. Just uploaded the zip file of data.

[Mark]

Hi @Matt J, did you see my LUT1 data file in .mat format. If not then can you help me get to save LUT in a right format please.

Answer 1

[Matt J]

load inputData

i=11; j=3; %query points (Lat and Alt)


%% interpolate
LUT1=griddedInterpolant(Long1c_4d,Lat1c_4d,Alt1c_4d, Temp1c_4d); %interpolation object 

[Long1,Lat1,Alt1]=deal(LUT1.GridVectors{:}); %1D versions of the coordinates

TempvLong1=LUT1({Long1,Lat1(i),Alt1(j)});  %slices



%%Plot
tiledlayout(1,1)
    
nexttile
hold on;

plot(Long1(:),TempvLong1(:),'-hexagram','Color','k','MarkerSize',2,'MarkerEdgeColor','k','MarkerFaceColor','k');
plot(Long1c_4d(:,i,j),Temp1c_4d(:,i,j),'o','Color','r','MarkerSize',8,'MarkerEdgeColor','r');
xlabel 'Longitude'; 
ylabel 'Temperature'
title(sprintf('Lat = %.2f^o & Alt = %.2f km',Lat1(i),Alt1(j)/1000));
legend('location','northeast','box','on','FontSize',12);
legend('interpolated data', 'original data');
xlim([-180 180]);
ax = gca;
set(ax,'Box','on');
ax.XTick = -180:60:180;
hold off;

[Mark]

Many thanks @Matt J