Interpolation data to achieve gridded latitude and longitude when I have 360 month

Hey all,

I have a table that has four columns (longitude, latitude, date, and observed_value). In my table latitude and longitude values represent 95 unique locations that are scattered randomly. Each one for 360 months; I mean I have 360 observed_value data for each unique location from like 1/1/1989, 2/1/1989, 3/1989, ... 12/1/2018. I want to convert this scattered data to gridded data by interpolation. I want to have data for longitude = 44.25:.5:63.75 and latitude: 24.25:.5:39.75 for each month. So, in the end, I will have so many locations rather than 95 (for example 11000) that have observed_data for these 360 months.

I have been thought about it for 2 days I really search for everything but I don't know how can I do this. I want to ask you please help me with the issue. If it is important, after that I want to make 1 x n cell which each array in it is a table for these gridded data locations for each month.

If you have any additional questions or require further clarification, please, do not hesitate to tell me.

I attached my table, any advice is highly appreciated, Thank you.

Answer 1

[Jacob Wood]

Behzad,

I believe the scatteredInterpolant() function is ideal for this case. This solution below is certainly not the fastest, but hopefully it is clear in how it achieves your goal.

dates = unique(mytable.date); %pick out the unique dates in the table
[new_lats,new_lons] = ndgrid(24.25:.5:39.75,44.25:.5:63.75); %make the grid for our new lats/lons

output_array = cell(1,numel(dates)); %make the output array we can store the newly interpolated data in

for ii = 1:numel(dates) %go through each month
    
    %use logical indexing to select only the data for the relevant month
    idx = mytable.date == dates(ii);
    lats = mytable.lat(idx);
    lons = mytable.lon(idx);
    vals = mytable.observed_value(idx);
    
    F = scatteredInterpolant(lats,lons,vals); %make interpolator object from unstructured data
    new_vals = F(new_lats,new_lons); %apply interpolator at each new lat/lon 
    
    output_array{ii} = new_vals; %save the gridded data into a cell for this month
end

[BN]

Dear Jacob,

I'm very thankful to you for helping me with the question, really appreciate it. It's awesome. This code creates a 1x360 cell that each array represents a month. It's very nice. do you know it is possible to have all 360 months for each location as an array or not? I mean is this possible to use this output_array to achieve such a cell? 40 x 32 cell like this picture below.

40 longitude and 32 latitude so 40 x 32 = 1280 cell array and each array includes data for one location from 1/1/1989 to 12/1/2018, like this picture:

is this possible?

Thank you again

Best Regards????

[Jacob Wood]

Behzad,

It sure is! The cell array can be kind of a bugger to work with, so it is probably easier if we use a numerical array first and then collapse the dimensions as necessary. Note the changes to how we are implementing output_array:

output_array = NaN([size(new_lats) numel(dates)]);

for ii = 1:numel(dates)
    
    idx = mytable.date == dates(ii);
    lats = mytable.lat(idx);
    lons = mytable.lon(idx);
    vals = mytable.observed_value(idx);
    
    F = scatteredInterpolant(lats,lons,vals);
    new_vals = F(new_lats,new_lons);
    
    output_array(:,:,ii) = new_vals;
end

Here we have a 32x40x360 array, which you can index into with typical Matlab indexing. For example, to look at the first 12 months of the most Southwest location:

output_array(1,1,1:12)

If the cell array you described above is more suitable for your needs you can collapse the 3rd dimension using num2cell():

num2cell(output_array,3)

And finally, to get rid of those pesky floating dimensions you can use squeeze:

output_cell_array = cellfun(@squeeze,num2cell(output_array,3),'UniformOutput',false);

[BN]

Dear Jacob,

I am so very thankful for your time. You fix my problem, I very much appreciate your help ?????.

Best Regards