Degrees of Freedom in PCA

Question

Suppose we are doing PCA over a historic time series of temperatures. The feature for the PCA to be explained is the time when the temperature was observed every hour. Let’s say for the sake of analysis, we broke the series into temporally mutually exclusive subsets(i.e. for the first subset, time is less than 12 pm and vice versa). So now we perform independent PCA on each of these two subsets with A and B components explaining the first part and second part respectively and then merge the two subsets, we see that it is performing better than the PCA done on the same curve as a whole with max(A,B) components and performing worse than the PCA done on the whole curve with A+B components. What can be said about the degree of freedoms in each case? Intuitively, I feel that the degrees of freedom should lie somewhere between A+B and max(A,B) but I don’t have a way to quantify it. Has someone gone through something similar? Thank you!