EXACTLY!!!
I'm not a fan of just having a monthly averaged value...and to extend on this not a big fan of just looking at the averaged 500 pattern for the month either. You aren't going to capture any transition periods and it's the transition periods where a weather event is likely to occur.
This is precisely I would love to use the daily data and construct a weekly/bi-weekly index but that will never happen. Unless I just do it simply and take 7 and 14-days worth of values, add them, then divide by the period (7 or 14 days) but that isn't going to be accurate...I don't think.
then with these values can further analyze height anomalies, etc.