For pretty much this entire decade I've always wanted to explore constructing weekly or even bi-weekly values for such indices like the NAO, AO, PNA (virtually whatever here is access to daily values too). However, I am not entirely sure how to go about such a project. I've read the methodologies used in constructing the monthly values and despite finishing school and going through all that math I (embarrassingly) suck at math...like awful. I've always wanted to do this, however, b/c I think having just a monthly averaged value doesn't accurately tell the story...unless the oscillation was in a particularly phase with consistent strength for an extended period. But at the end of the day, I feel like it's those transition periods which hold significant weight on pattern evolution/storms and having an index broken down into smaller time scales might accurately capture these periods more.
I understand at the end of the day height anomalies and the placement of anomalies far outweigh the value of an indexed value, however, with this said I do believe there is a great deal of importance with having a value. For one, I think it can assist in research purposes. You can skim through values and sort of generate some thoughts/ideas and then explore charts/graphics.
I thought perhaps may you could just take 7-days worth of data, sum them up, and divide by 7...but obviously it wouldn't be that easy. I tried a test of taking monthly values for a month, summing them, and dividing by the number of days in the month but this did not yield the same value as the monthly reading.
I guess what I'm looking for is for some input/guidance from those who are far more advanced and knowledgeable with math then i am. (I've even considered going back and re-taking math classes from Algebra to Differential equations and approaching them differently...although I used to be really good with algebra).
Thanks for any input/assistance! I also really love this place and have been doing a ton of reading the past few months on here...excellent source of knowledge and information here.