Defining flood risk in a multivariate framework: Application on the
Eleni Maria Michailidi and Baldassare Bacchi
DICATAM, Università degli studi di Brescia, Via Branze 42, 25123 Brescia, Italy
Received: 30 Sep 2016 – Accepted for review: 30 Oct 2016 – Discussion started: 08 Nov 2016
Abstract. One of the most important tasks a hydrologist must face is to estimate the hydrological risk (i.e. probability) of a variable exceeding a certain threshold. This risk is often expressed in terms of a Return Period, T, and refers to the failure of the hydraulic structure which controls this variable. Sometimes the "structure" is simply the river embankmentsthe failure of which means their overtopping by the river. The widely adopted definition of T, in a problem regarding the maxima of hydro-logical variables, is "the average time elapsing between two successive occurrences of an event exceeding a given magnitude of the natural variables".
Conventional approaches for the estimation of T involve a single natural variable (i.e. flood peak, maximum rainfall intensity, etc.) and its frequency analysis.
However, a univariate approach in complex problems ignores the effect of other significant variables leading to different risk levels for each quantity of interest and resulting in an inaccurate estimate of the risk-often wrongfully set equal to the risk of the hydrological event. For example, if one considers the flood inflow in a lake around which establishments are positioned, the variable to be investigated relating to risk assessment is the lake water level. The same water level may occur from very different flood hydrographs, even when the same initial water level and specific spillway characteristics are taken into account. We considered this a result of the interaction of three joint factors: the hydrograph's peak, volume and shape. Consequently, we apply a multivariate distribution framework (using copula functions) in order to find a region where all underlying events are assigned to the same risk- associated here to the maximum water level.
Michailidi, E. M. and Bacchi, B.: Defining flood risk in a multivariate framework: Application on the
Panaro watershed, Hydrol. Earth Syst. Sci. Discuss., doi:10.5194/hess-2016-519, in review, 2016.