Rainfall and irrigation are both volume measurements, so the calculation can be flattened to depth as the area would be the same for both. If you get 1mm of rain it is 1mm deep regardless of the area measurement since your irrigation measurement will be effecting the same area presumably. If you have an indoor watering setup, simply multiplying the rainfall by zero would negate its effect and your irrigation system would be happy. So some sort of Boolean variable for indoor(0)/ outdoor(1) would suffice. Using the weighted averages equation seems the best suited as new data is much more important than old data, or current is more important than forecast. You would end up with something like the following as your final equation:
todayIrrigation – ((yesterdayRain*inOrOut)+yesterdayIrrigation+(todayFallenRain*inOrOut))*.9 + (todayForecastRain*inOrOut)*.1
Using this type of setup uses historical watering cycles to adjust the overall weight of the rainfall. If you have an outdoor zone that needs 1 inch of water based on yesterdays information, and it was watered .5 (50% yesterday) inches yesterday with no rain today, and .25 inches yesterday. The irrigation time would be adjusted by approximately 75%. Another zone using the same data but requiring 2 inches having been watered 1 (50% yesterday) inch, will adjust by about 37.5%. Meaning the same rainfall had half the effect which is correct as the zone is set to water twice as much. At this point all you have to figure out is how much water is needed so you would have the todayIrrigation value to start with.
Weighting and adjusting the data is pretty simple with little to no user input once you have a solid way to figure out your starting point.
Math in a single dimension is sufficient for most of the calculations, since all we are concerned with in the sprinkler world is water depth at a location.
When a sprinkler says it waters 1 inch per hour you can measure this with a pickle jar or a kid pool. Assuming fairly even distribution of the spray pattern, and total coverage of the areas in question, you would have 1 inch of water in both containers after 1 hour.
Using manufacturer and design information or simply measuring output in each zone means you can set all zone to apply the same amount of water then use a weighting method to adjust how much each zone actually gets.
If you know it takes 1 hour to get 1 inch of water, and a zone needs 2 inches, you set the time to 2 hours, or vice versa you know if it is set to 1 hour it will apply 1 inch. I guess what I’m getting at here is by including datalogs in your calculation you can easily adjust for rainfall, or oddball watering times (scheduled 3min ran for 30). As these would negate themselves in the next calculation.