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
