How to calculate averages for a 3D matrix for the same day of data over multiple years in Matlab? - matlab

Question

I am interested in calculating GPH anomalies in Matlab. I have a 3D matrix of lat, lon, and data. Where the data (3rd dimension) is a daily GPH value spaced in one-day increments for 32 years (from Jan. 1st 1979 to Jan. 1st 2011). The matrix is 95x38x11689. How do I compute a daily average across all years for each day of data, when the matrix is 3D?
In other words, how do I compute the average of Jan. 1st dates for all years to compute the climatological mean of all Jan. 1st's from 1979-2010 (where I don't have time information, but a GPH value for each day)? And so forth for each day after. The data also includes leap years. How do I handle that?
Example: Sort, and average all Jan. 1st GPH values for indices 1, 365, 730, etc. And for each day of all years after that in the same manner.

Answer 1

First let's take out all the Feb 29th, because these days are in the middle of the data and not appear in every year, and will bother the averaging:
Feb29=60+365*[1:4:32];
mean_Feb29=mean(GPH(:,:,Feb29),3); % A matrix of 95x38 with the mean of all February 29th
GPH(:,:,Feb29)=[]; % omit Feb 29th from the data
Last_Jan_1=GPH(:,:,end); % for Jan 1st you have additional data set, of year 2011
GPH(:,:,end)=[]; % omit Jan 1st 2011
re_GPH=reshape(GPH,95,38,365,[]);
av_GPH=mean(re_GPH,4);
Now re_GPH is a matrix of 95x38x365, where each slice in 3rd dimension is an average of a day in the year, starting Jan 1st, etc.
If you want the to include the last Jan 1st (Jen 1st 2011), run this line at after the previous code:
av_GPH(:,:,1)=mean(cat(3,av_GPH(:,:,1),Last_Jan_1),3);
For the ease of knowing which slice nubmer corresponds to each date, you can make an array of all the dates in the year:
t1 = datetime(2011,1,1,'format','MMMMd')
t2 = datetime(2011,12,31,'format','MMMMd')
t3=t1:t2;
Now, for example :
t3(156)=
datetime
June5
So av_GPH(:,:,156) is the average of June 5th.
For your comment, if you want to subtract each day from its average:
sub_GPH=GPH-repmat(av_GPH,1,1,32);
And for February 29th, you will need to do that BEFORE you erase them from the data (line 3 up there):
sub_GPH_Feb_29=GPH(:,:,Feb29)-repmat(mean_Feb29,1,1,8);