How to calculate circular mean every 8 cells?

Hi all,

I have a dataset with wind directions at 3-hourly time steps and I would like to calculate daily average wind directions. I am, however, stuck. I got this (with dir = the wind direction in degrees, 0 to 360):

dir = accumarray(ceil((1:numel(dir))/8)',dir(:),[],@mean);

This, however, does not take into account the circular nature of the values. How can I do this?

I attach a small sample of the data (year - month - day - hour - wind direction):

2020	4	1	0	77.0016556593828
2020	4	1	3	61.6846224380681
2020	4	1	6	31.4624383596130
2020	4	1	9	35.1994739111645
2020	4	1	12	56.7123189304487
2020	4	1	15	337.212660715222
2020	4	1	18	332.720394142200
2020	4	1	21	359.309990882483
2020	4	2	0	1.81332665386765
2020	4	2	3	316.084846935155
2020	4	2	6	297.362308097189
2020	4	2	9	286.447414863766
2020	4	2	12	253.377128455776
2020	4	2	15	272.755841963236
2020	4	2	18	283.300130880562
2020	4	2	21	305.805458428448
2020	4	3	0	303.435585960465
2020	4	3	3	305.408085546923
2020	4	3	6	314.945219141016
2020	4	3	9	301.363197206495
2020	4	3	12	297.344102342364
2020	4	3	15	294.845524112617
2020	4	3	18	301.544742721005
2020	4	3	21	320.320593041074

Answer 1

[Star Strider]

One option would be to ‘decompose’ the angles into their ‘x’ and ‘y’ components, calculate the means of those, and then use atan2 to return the result —

D =    [2020	4	1	0	77.0016556593828
        2020	4	1	3	61.6846224380681
        2020	4	1	6	31.4624383596130
        2020	4	1	9	35.1994739111645
        2020	4	1	12	56.7123189304487
        2020	4	1	15	337.212660715222
        2020	4	1	18	332.720394142200
        2020	4	1	21	359.309990882483
        2020	4	2	0	1.81332665386765
        2020	4	2	3	316.084846935155
        2020	4	2	6	297.362308097189
        2020	4	2	9	286.447414863766
        2020	4	2	12	253.377128455776
        2020	4	2	15	272.755841963236
        2020	4	2	18	283.300130880562
        2020	4	2	21	305.805458428448
        2020	4	3	0	303.435585960465
        2020	4	3	3	305.408085546923
        2020	4	3	6	314.945219141016
        2020	4	3	9	301.363197206495
        2020	4	3	12	297.344102342364
        2020	4	3	15	294.845524112617
        2020	4	3	18	301.544742721005
        2020	4	3	21	320.320593041074];

dir = D(:,5);
meandir = @(a) atan2d(mean(sind(a)),mean(cosd(a)));
dir = accumarray(ceil((1:numel(dir))/8)',dir(:),[],meandir)

dir = 3×1

27.0977 -64.0652 -55.1192

dir = wrapTo360(dir)                                        % Mapping Toolbox Function

dir = 3×1

27.0977 295.9348 304.8808

.