Follow the level of the Huron River as it goes through Ann Arbor with the USGS National Water Information System. On March 23, the river is rising, but it's also fluctuating in levels, enough that it's difficult to determine whether current trends would lead you to believe that there is any risk of flooding.
If you were to watch this closely, what would you watch?
The USGS will give you an alert if the level of the river is above or below a certain level.
The first derivative is the rate of change of the water level. You'd want to track that to note trends. If you measured the difference between adjacent water levels, you'd identify spikes, which have been associated with work on the dam in the past; those will give you a metric on the order of rate of change in inches per hour. If you did some smoothing, you'd find trending measured in feet per day.
The second derivative is the rate of the rate of change of the water level; you're looking for that to identify erratic behavior. As a rule of thumb a time series with large movements in both directions (up and down) over a short amount of time is a sign of river disturbance.
A plausible approach would be to compute a smoothed curve, and then alert on deviations from the smoothed curve. You'd love to be able to tell the difference between sudden downpour, steady rain, flash flood, work on the dam, and dam failure.
Another strip chart to line up with this is rainfail (measured in convenient units) and precipitation forecast.
This forecast is from USGS Waterwatch for Michigan. Hidden behind the projected water level is a rainfall forecast for the watershed.
Statewide data, if you want to look for more, from Waterwatch. The black dots are flooding, blue are near flood.
Edward Vielmetti watches water levels on the Huron River. Write to him at firstname.lastname@example.org.