Estimating extreme river discharges in Europe through a Bayesian network

Abstract

Abstract. Large-scale hydrological modelling of flood hazards requires adequate extreme discharge data. In practise, models based on physics are applied alongside those utilizing only statistical analysis. The former require enormous computational power, while the latter are mostly limited in accuracy and spatial coverage. In this paper we introduce an alternate, statistical approach based on Bayesian networks (BNs), a graphical model for dependent random variables. We use a non-parametric BN to describe the joint distribution of extreme discharges in European rivers and variables representing the geographical characteristics of their catchments. Annual maxima of daily discharges from more than 1800 river gauges (stations with catchment areas ranging from 1.4 to 807 000 km 2 ) were collected, together with information on terrain, land use and local climate. The (conditional) correlations between the variables are modelled through copulas, with the dependency structure defined in the network. The results show that using this method, mean annual maxima and return periods of discharges could be estimated with an accuracy similar to existing studies using physical models for Europe and better than a comparable global statistical model. Performance of the model varies slightly between regions of Europe, but is consistent between different time periods, and remains the same in a split-sample validation. Though discharge prediction under climate change is not the main scope of this paper, the BN was applied to a large domain covering all sizes of rivers in the continent both for present and future climate, as an example. Results show substantial variation in the influence of climate change on river discharges. The model can be used to provide quick estimates of extreme discharges at any location for the purpose of obtaining input information for hydraulic modelling.

Efficient pan-European river flood hazard modelling through a combination of statistical and physical models

“…The analysis presented here was performed over a domain covering most of the European continent, the same as used by Paprotny and Morales Nápoles (2017). This domain excludes most of Russia, the Ukraine and Belarus, as well as some outlying island territories, but adds Cyprus, as it is a member of the European Union.…”

“…This is largely a result of only a modest (on average) increase in river discharge in Europe. As a whole, this corresponds to 5-8 % depending on the scenario, according to the results from Paprotny and Morales Nápoles (2017). However, the significant implications of changes in discharge becomes apparent when taking into account flood protection standards.…”

“…Estimates of annual maxima of river discharges were provided by the Bayesian-network-based (BN) model for three time periods 1971-2000, 2021-2050 and 2071-2100. The BN model was extensively described and validated in Paprotny and Morales Nápoles (2017) and the reader is referred to this paper for details.…”

“…Briefly, the BN model is a statistical method that constructs joint distributions over different random variables (different geographical properties of European catchments in our case) in a parsimonious way (Pearl, 1988). In the model, seven random variables are used to conditionalize annual maxima of river discharges in a non-parametric, continuous BN.…”

“…2). Here, results from one of the high-resolution (0.11 • ) regional models operated within EURO-CORDEX framework was used, produced by the Climate Limited-area Modelling Community utilizing the EC-Earth general circulation model (run by ICHEC) with COSMO_4.8_clm17 regional climate model (Rockel et al, 2008), realization r12i1p1 (see Paprotny and Morales Nápoles, 2017 for details on data sets used in the European BN model). The first one is the historical reference period, used to calibrate and validate the method's performance.…”