The best way is to weight your "10 day" data sections. If you are lucky and your 10 days fit perfectly into a 30 day month then you will have 3 sets of 10 days. To weight the data take each section of data (10 days) and divide by total number of days in the month. In your perfect case each 10 day section would multiplied by 1/3 and then each section would be added to give you the average. This would be your simplest case. For more common 10 days that do not fit at the beginning or at the end of the month you would still weight each section of 10 days. For example if you had a month of 31 days and your first section of 10 days of data only included the 1st 4 days of the month then you would take this 1st 10 day section and multiply it by 4/31. The 4 is for the number of days that fit into the beginning of the month and 31 is for the total days of the month. Any 10 day section that does completely fit you would multiply it by 10/31. The last section may only have 7 days at the end of the month. For this 10 day section because only 7 days are part of the month you would multiply 7/10. Then just add all your values to find the average for this 31 day month using 10 day data sections. Here is an example formula : ((1st 10 day section) * (4/31)) + ((2nd 10 day section) * (10/31)) + ((3rd 10 day section) * (10/31)) + ((4th 10 day section) * (7/31)) = month average. This will be different for every month because each 10 day sections will fit differently into each month. To calculate the fit and using the pseudo formula I recommend using Python or some other programming language. Hope this helps.

Dear Istakhar,

to be honest, I would interpolate the 10 day stack using splines/periodic splines to a daily resolution. This is certainly intense computationally but would simplify the way to aggregate the data to true monthly values for the years you investigate. It would even account for leap years.

Here is one example code that I did not try myself but it follows the same idea:

https://www.bike-discount.de/de/kaufen/cube-nuroad-race-fe-black-n-iridium-896299?delivery_country=48&varid=896308&gclid=Cj0KCQjw9fntBRCGARIsAGjFq5FLFGflfciDGX-e6liXTGMxiEMErV00v0PrcVNM4I6TNcllsbmj7IIaAqXgEALw_wcB

Apparently the link was incorrect: here is the right one:

https://www.google.com/amp/s/www.r-bloggers.com/spline-interpolation-of-temporal-resolution-for-satellite-images/amp/