How Flashy Are Six US Rivers? The Richards–Baker Index, 1952–2025, Trends, and Why the Gaussian Formula for Flashiness Overstates It by a Factor of Two to Ten

The Richards–Baker flashiness index is the sum of absolute day-to-day changes in flow divided by the sum of flows. I compute it for 74 complete water years (1952–2025) at six USGS gauges. Mean annual values range from 0.0533 for the snowmelt-dominated Fish River in Maine to 0.3416 for the Rapidan River in Virginia and 0.3454 for the Guadalupe River in Texas. Two gauges show a trend significant at 5% in a Mann–Kendall test: the Fish River has become flashier (Kendall tau 0.186, p 0.019, Sen slope 0.0009 per decade) and the Guadalupe less flashy (tau -0.186, p 0.019, Sen slope -0.0269 per decade); with six tests, these results are not strong evidence of change. For a stationary Gaussian series the expected absolute daily change is 2 sigma sqrt((1-rho)/pi), which gives the approximation RB = 2 CV sqrt((1-rho)/pi); I verify the formula by simulation (0.5050 against 0.5046). Applied to real flows, the approximation overstates the index by factors of 1.9 to 9.7, because daily flows are strongly skewed (coefficients of variation 0.92 to 4.90): a few large floods inflate the standard deviation far more than they add to day-to-day changes. I also confirm numerically that the area under the flow-duration curve equals the mean flow.