For flooding it is a typical estimation from modelling from things like topography maps and known precipitation events. It is all rough estimations without collecting monitoring data, which is what funding for these agencies tend to be used for.

It requires a lot of information to accurately model and predict if any given river valley can handle 1.75 inches in a 3 mile radius in 4 hours, versus 3.25 inches in a 1 mile radius in 2 hours. How much does a 0.2 inch rainfall event in the previous 24 hours impact? What about 1 inch in the same area in 24 hours? (And so on.)

There are models that predict precipitation amounts and river/lake stage (level), yes, but usually it's up to the lead meteorologist to make the call after reviewing those models combined with their experience with the situation. Precip rate is also an output of some forecast models that is considered when issuing an advisory. These models consume huge amounts of data that influence the output prediction in complex, chaotic ways. Better quality data can often produce better forecasts and lead to better decisions but whether or not the specific event would have had a better outcome is harder to answer.

I can't speak for the modeling regarding the amount of rain, but I'm was published in college for watershed analysis and now work in municipal development and review drainage plans.

When use LIDAR to update watershed maps and can estimate the amount of water rise that will occur at a specific location with a specific amount of rainfall. One thing that makes predictions in central Texas is the heavy development and vast difference in development standards.

Some municipalities are very strict, and only allow 15%-25% impervious cover, while others don't care. And with tree coverage it's hard to tell from serials if the ground is sod, mud, gravel, or concrete.

More importantly, many local jurisdictions don't require rainwater detention, and counties typically don't have the resources to inspect stuff installed without their knowledge outdlside of cities, so as development increases runoff into the watershed increases, as there's less pervious cover and what cover remains is more quickly saturated. Also, the grading of land and removal of vegetation leads to less friction, speeding up runoff. If upstream water is flowing faster, then the water rises higher and faster.