Statistical methods are commonly used to evaluate natural populations and environmental variables, yet these must recognize temporal trends in population character to be appropriate in an evolving world. New equations presented here define the statistical measures of aggregate historical populations affected by linear changes in population means and standard deviations. These can be used to extract the statistical character of present-day populations, needed to define modern variability and risk, from tables of historical data that are dominated by measurements made when conditions were different. As an example, many factors such as climate change and in-channel structures are causing flood levels to rise, so realistic estimation of future flood levels must take such secular changes into account. The new equations provide estimates of water levels for “100-year” floods in the USA Midwest that are 0.5 to 2 m higher than official calculations that routinely assume population stationarity. These equations also show that flood levels will continue to rise by several centimeters per year. This rate is nearly ten times faster than the rise of sea level, and thus represents one of the fastest and most damaging rates of change that is documented by robust data. Statistical methods are commonly used to evaluate natural populations and environmental variables, yet these must recognize temporal trends in population character to be appropriate in an evolving world. New equations presented here define the statistical measures of aggregate historical populations affected by linear changes in population means and standard deviations. These can be used to extract the statistical character of present-day populations, needed to define modern variability and risk, from tables of historical data that are dominated by measurements made when conditions were different. As an example, many factors such as climate change and in-channel structures are flood level to rise, so realistic estimation of future flood levels must take such secular changes into account. The new equations provide estimates of water levels for “100-year” floods in the USA Midwest that are 0.5 to 2 m higher than official calculations that routinely assume population stationari ty, these equations also show that flood levels will continue to rise by several centimeters per year. This rate is nearly ten times faster than the rise of sea level, and thus represents one of the fastest and most damaging rates of change that is documented by robust data.