Comparison of stationary and nonstationary estimation of return period for sewer design in Antioquia (Colombia)

Abstract

Estimating the probability of occurrence of extreme hydrologic events is a fundamental input in the design of hydraulic infrastructure. The classical approach to this problem has been to fit parametric probability functions to annual maxima streamflow data and use them to calculate the risk of failure. An underlying assumption of this approach is the stationarity of the time series. However, the stationarity of streamflows may not hold due to the effect of land cover change and climate change on rainfall runoff processes on watersheds. This study assesses the effect of considering non-stationarity in the estimation of design peak flows at 33 gauging stations in the state of Antioquia, Colombia. Particularly, the effect of non-stationarity in the mean of Gumbel-distributed peak flows is evaluated. This study focuses on the 5-yr and 10-yr return period annual flood flows, which are customary in the design of type sewerage systems. The results show similar behaviours for both return periods. All gauge stations show an asymptotically tendency in the risk of failure to 100% as the project lifetime tends to 30 years. In general, 71.4% of gauging stations show that the estimated risk of failure is larger when non-stationary conditions are assumed, relative to assuming stationary conditions, and that the magnitude of the difference increases for larger return periods. The rest of gauging stations shows the opposite behaviour. Our results support the use of a probability model that includes non-stationary in the mean, and they suggest that a model that also includes non-stationary in the variance could be important.