Flood frequency analysis of historical flood data under stationary and non-stationary modelling

Abstract

Historical records are an important source of information about extreme and rare floods with a great value to establish a reliable flood return frequency. The use of long historic records for flood frequency analysis brings in the question of flood stationarity, since climatic and land-use conditions can affect the relevance of past flooding as a predictor of future flooding. In this paper, a detailed 400 year flood record from the Tagus River in Aranjuez (Central Spain) was analysed under stationary and non-stationary flood frequency approaches, to assess their implications on hazard studies. Historical flood records in Aranjuez were obtained from documents (Proceedings of the City Council, diaries, chronicles, memoirs, etc.), epigraphic marks, and indirect historical sources and reports. The water levels associated with different floods (derived from descriptions or epigraphic marks) were computed into discharge values using a one-dimensional hydraulic model. Secular variations on flood magnitude and frequency, found to respond to climate and environmental drivers, showed a good correlation between high values of historical flood discharges and a negative mode of the North Atlantic Oscillation index (NAO index). Over the systematic gauge record (1913–2008), an abrupt change on flood magnitude was produced in 1957 due to constructions of three major reservoirs in the Tagus headwaters (Bolarque, Entrepeñas and Buendia) controlling 80% of the watershed surface draining to Aranjuez. Two different models were used for the flood frequency analysis: (a) a stationary model estimating statistical distributions incorporating imprecise and categorical data based on maximum likelihood estimators; (b) a time–varying model based on "generalized additive models for location, scale and shape" (GAMLSS) modelling, that incorporates external covariates related to climate variability (NAO index) and catchment hydrology factors (in this paper a reservoir index; RI). Flood frequency analysis using documentary data (plus gauged record) improved the estimates of the probabilities of rare floods (return intervals of 100 year and higher). Under non-stationary modelling flood occurrence associated with an exceedance probability of 0.01 (i.e. return period of 100 year) has changed over the last 500 year due to decadal and multi-decadal variability of the NAO. Yet, frequency analysis under stationary models was successful on providing an average discharge around which value flood quantiles estimated by non-stationary models fluctuate through time.