I have daily rainfall data for a given site going back about 30 years.

I have a building with an average daily demand for water of $L$ litres and a catchment of $A$ m$^2$ with a runoff coefficient of $c$.

How can I construct a model so that I can determine for a tank size T litres, The mean and variance of the

  1. days per year the tank will be empty
  2. Shortfall of water
  3. days per year the tank will overflow
  4. Amount of water that overflows

I have googled this extensively and found plenty of rules of thumb but noting that uses a probabilistic model.

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    $\begingroup$ I'd be tempted to build a model from the data in order to simulate this to answer these questions. It also facilitates what-if analysis ("What if average rainfall decreased 10% because of climate change?" ... "What if rainfall didn't change on average but became more variable?" ... "What if overflow went into a second, smaller backup tank?") $\endgroup$ – Glen_b Apr 19 '13 at 2:58
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    $\begingroup$ I completely agree with @Glen_b: with your more than 11,000 values, you can precisely characterize almost anything you like concerning the last 30 years. The big unknown is the extent to which the future might or might not behave like the past. I suspect that component of uncertainty dwarfs any other aspect of this problem. If you have a good climatological forecasting model, you might consider exploiting that in your work, using it to create stochastic simulations of future daily rainfall. In all other respects, the calculations would be identical. $\endgroup$ – whuber Apr 19 '13 at 3:34
  • $\begingroup$ I would add that models will need to consider dependence over time; there are both very short-term dependences (if it rained yesterday it's more likely to rain today than if it was dry yesterday, other things being equal) as well as longer term effects (e.g. El Niño/La Niña-type effects dramatically impact rainfall in some parts of the world, sometimes for years at a time). Such dependences, especially the long term ones, may have dramatic effects on some of your items. $\endgroup$ – Glen_b Apr 19 '13 at 3:41
  • $\begingroup$ @Glen_b thanks for your comments. That is what I would like to do. The question I need answering is how do I build the model? I can post some sample data or you can download it from www.bom.gov.au $\endgroup$ – Dale M Apr 29 '13 at 23:49
  • $\begingroup$ I'm not going to do potentially open-ended data analysis for you - not for free, anyway. That could take many, many hours and require close consultation with the client - i.e. you (would you ask your accountant to work on your taxes for free? Questions here are supposed to be "reasonably scoped". "How do I build a model?" is in the 'takes a book to answer' category.). Briefly: typical models that might be considered would include regression models, or time series models, or (more likely) models that contain both. $\endgroup$ – Glen_b Apr 30 '13 at 0:03

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