Articles | Volume 19, issue 6
Hydrol. Earth Syst. Sci., 19, 2561–2576, 2015

Special issue: Floods and their changes in historical times – a European...

Hydrol. Earth Syst. Sci., 19, 2561–2576, 2015

Research article 02 Jun 2015

Research article | 02 Jun 2015

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

M. J. Machado1, B. A. Botero2, J. López3, F. Francés4, A. Díez-Herrero5, and G. Benito1 M. J. Machado et al.
  • 1Museo Nacional de Ciencias Naturales, Consejo Superior de Investigaciones Científicas, CSIC, Serrano 115 bis, 28006 Madrid, Spain
  • 2Facultad de Ingenierías, Universidad de Medellín, 65 Medellín, Colombia
  • 3Mexican Institute of Water Technology (IMTA), 62550 Jiutepec, Morelos, Mexico
  • 4Research Institute of Water and Environmental Engineering, Universitat Politècnica de València, 46022 Valencia, Spain
  • 5Geological Hazards Division, Geological Survey of Spain, 28003 Madrid, Spain

Abstract. Historical records are an important source of information on extreme and rare floods and fundamental to establish a reliable flood return frequency. The use of long historical 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 yr flood record from the Tagus River in Aranjuez (central Spain) was analysed under stationary and non-stationary flood frequency approaches, to assess their contribution within 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 in 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 (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, and (b) a time-varying model based on "generalized additive models for location, scale and shape" (GAMLSS) modelling, which 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 records) improved the estimates of the probabilities of rare floods (return intervals of 100 yr and higher). Under non-stationary modelling flood occurrence associated with an exceedance probability of 0.01 (i.e. return period of 100 yr) has changed over the last 500 yr due to decadal and multi-decadal variability of the NAO. Yet, frequency analysis under stationary models was successful in providing an average discharge around which value flood quantiles estimated by non-stationary models fluctuate through time.

Short summary
A flood frequency analysis using a 400-year historical flood record was carried out using a stationary model (based on maximum likelihood estimators) and a non-stationary model that incorporates external covariates (climatic and environmental). The stationary model was successful in providing an average discharge around which value flood quantiles estimated by non-stationary models fluctuate through time.