MATLAB: How to produce bin averaged (or summed) latitude and longitude grids

grid bin latitude longitude bin averaged grid matrix

I have a set of data with each row representing a series of observations taken at a particular point. Each column represents a different observation as well as information regarding where and when the data was collected (year, month, latitude (column 3), longitude (column 4), rainfall1, error1, rainfall2, and error2). The data needs to be gridded so that the data is over 2.5 degrees latitude 2.5 degrees longitude bin-averaged (or summed up) grids. How would I go about doing this? Here are some additional info from the dataset documentation: latitude (-88.75 –> 88.75), longitude (eastward from 1.25 E).

Thank you.

Best Answer

minlat = -90;     %adjust these if needed. They determine where the boxes start
minlong = 0;
gridspacing = 2.5;
latidx = 1 + floor((Latitudes - minlat) ./ gridspacing);
longidx = 1 + floor((Longitudes - minlong) ./ gridspacing);

Now to count the number of entries per grid space:

accumarray( [latidx(:), longidx(:)], 1)

If you want to sum data items within a particular grid cell, replace the "1" with a column vector of the data items.

If you want averaging of the items within a particular grid cell, taking into account only the elements in that grid cell (not dividing by total number of all elements), then

accumarray( [latidx(:), longidx(:)], Observation_column, [], @mean)

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MATLAB: Produce bin averaged latitude and longitude grids

Assuming that longitudes are in the range [0,360[ and latitudes in the range ]-90,90[, here is part of a solution that you could fine tune. I assume that your data set is stored in numeric array data.

First, build longitude and latitude bin IDs, and an array of bin IDs matching lon/lat of columns 4/5 of your data set:

 lon_binID =  1 + floor( data(:,4) ./ 5 ) ;
 lat_binID = 37 + floor( data(:,5) ./ 2.5 ) ;
 binID     = [lon_binID, lat_binID] ;
 nBin      = 72 ;                                  % # of bins per lon/lat.

For extensive data, compute the sum per bin as follows. Assume that column 3 is e.g. a mass of something..

 sum_bin = accumarray( binID, data(:,3), [nBin, nBin] ) ;

Here sum_bin is a 72x72 array of sum per bin. It is slightly more complicated for intensive data, as in theory we would need a count of binned values to compute the mean (by division of sums by counts). Thankfully, ACCUMARRAY allows us to specify the accumulation function (default = @sum). Assume that column 2 of data is the temperature..

mean_bin = accumarray( binID, data(:,2), [nBin, nBin], @mean ) ;

What changed here is that we passed a handle for function MEAN to ACCUMARRAY. The @ operator returns a handle on/for the function which follows; it's a way to pass functions to other functions.

Note that ACCUMARRAY can be quite slow when used with a user defined accumulation function, or sometimes a count per bins is really needed. Here is a trick to get it: accumulating a vector of ones..

 onesVector = ones( size(data,1), 1 ) ;
 count_bin  = accumarray( binID, onesVector, [nBin, nBin] ) ;

It would be easy to compute the mean temperature from there if we had to..

sum_bin  = accumarray( binID, data(:,2), [nBin, nBin] ) ;
mean_bin = sum_bin ./ count_bin ;

Hope it helps!

MATLAB: How to make pcolor plot from three vector

You can calculate the bin averages pretty quickly using discretize and accumarray:

Some sample data:

npt = 10000;
A = [rand(npt,1)*180-90 rand(npt,1)*360-180 rand(npt,1)];

5-degree bins:

latbin = -90:5:90;
lonbin = -180:5:180;
nlat = length(latbin);
nlon = length(lonbin);

Use discretize to figure out which latitude and longitude bin each point falls into, then convert the row/column indices into a single array index.

ilat = discretize(A(:,1), latbin);
ilon = discretize(A(:,2), lonbin);
idx = sub2ind([nlat nlon], ilat, ilon);

Use accumarray to average the values assigned to each index, then reshape to a grid:

altg = accumarray(idx, A(:,3), [nlat*nlon 1], @(x) mean(x), NaN);
altg = reshape(altg, nlat, nlon);

Finally, plot:

pcolor(lonbin, latbin, altg);

Best Answer

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MATLAB: Produce bin averaged latitude and longitude grids

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