I've got a table with flood event probabilities (recurrence intervals), the associated probability of levee failure given the flood stage corresponding to that event probability, and the monetary consequences that will occur to a utility facility if the levee fails. I need to calculated expected annual damages (i.e. the area under the frequency-damage curve). How does that work with joint probabilities where when multiplied, might no longer be in the same descending order as flood frequency?
I'd also like to show the frequency-damage function on a scatter plot, but the joint probability of flood and levee failure is throwing me off. Normally my X axis would be a log axis corresponding to flood frequencies (1 -> 0), and the y axis would be the damage at a given flood event. However, since I also have the levee failure probability, does my x axis become the joint probability of flood and failure?
See this image for a sketch.
https://imgur.com/a/VCaRR1b
After seeing this article (bottom) about the next Napa quake potentially damaging levees, I had this thought. Sacramento has already been wrecked by floods twice - much more likely than earthquake or fire to ruin your day here - and I wasn't able to find any flood maps. Pointers appreciated.
http://www.sacbee.com/news/local/article4654260.html
