Abstract. Recent literature shows several examples of simplified approaches that perform flood hazard (FH) assessment and mapping across large geographical areas on the basis of fast-computing geomorphic descriptors. These approaches may consider a single index (univariate) or use a set of indices simultaneously (multivariate). What is the potential and accuracy of multivariate approaches relative to univariate ones? Can we effectively use these methods for extrapolation purposes, i.e., FH assessment outside the region used for setting up the model? Our study addresses these open problems by considering two separate issues: (1) mapping flood-prone areas and (2) predicting the expected water depth for a given inundation scenario. We blend seven geomorphic descriptors through decision tree models trained on target FH maps, referring to a large study area (∼ 105 km2). We discuss the potential of multivariate approaches relative to the performance of a selected univariate model and on the basis of multiple extrapolation experiments, where models are tested outside their training region. Our results show that multivariate approaches may (a) significantly enhance flood-prone area delineation (accuracy: 92 %) relative to univariate ones (accuracy: 84 %), (b) provide accurate predictions of expected inundation depths (determination coefficient ∼ 0.7), and (c) produce encouraging results in extrapolation.

<p>Due to the limited length of locally available sequences of precipitation extremes, point rainfall depth associated with given duration and return period is usually estimated through regional frequency analysis. Several statistical regionalization methods proposed in the literature enable one to exploit sequences of precipitation extremes observed at homogeneous pooling groups of sites, that supposedly share the same frequency regime of rainfall extremes with the site of interest. Homogeneous sites can be identified by looking at specific climatic descriptors; for instance, some reliable authors successfully utilize Mean Annual Precipitation (MAP) as the sole proxy for locally characterizing the frequency regime of sub-daily rainfall extremes, and for grouping sequences of rainfall extremes records. We aim at advancing this traditional approach (1) by relaxing the hypothesis of the existence of a homogeneous pooling group of sites characterized by a unique regional parent distribution and (2) by incorporating additional morphological and climatic information in the regional model. We rely on more than 2350 Annual Maximum Series of rainfall depth for different time-aggregation intervals between 1 and 24 hours, observed since 1928 to 2011 in a vast study area in Northern Italy.  We refer to MAP as well as to additional morphologic descriptors (e.g.  minimum distance to Tyrrhenian (Adriatic) Sea, mean elevation and slope around the station, etc.).</p><p>We train a probabilistic neural network that models the frequency regime of observed annual maxima of rainfall depth resorting to a Generalized Extreme Value (GEV) distribution, whose parameters are data-driven functions of the local values of the selected descriptors and duration. Then, several cross-validation experiments are performed to assess the accuracy of the developed regional model relative to a simpler regional GEV model, whose parameters are functions of MAP and time-aggregation intervals.</p><p>Our analyses address several research problems: (a) identifying the most descriptive morphological proxies to combine with MAP for representing the frequency regime of sub-daily rainfall extremes in the study area, (b) highlighting limitations and potential of data-driven multivariate regional models of the frequency regime of rainfall extremes, (c) the advantages of a multivariate approach relative to a regionalization scheme based on MAP alone.</p>

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<p><span xml:lang="EN-US" data-contrast="auto"><span>Every year flood events cause worldwide vast economic losses, as well as heavy social and environmental impacts, which have been steadily increasing for the last five decades due to the complex interaction between climate change and anthropogenic pressure (</span></span><span xml:lang="EN-US" data-contrast="auto"><span>i.e.</span></span><span xml:lang="EN-US" data-contrast="auto"><span> land-use and land-cover modifications). As a result, the body of literature on flood risk assessment is constantly and rapidly expanding, aiming at developing faster, computationally lighter and more efficient methods relative to the traditional and resource</span></span><span xml:lang="EN-US" data-contrast="auto"><span>-</span></span><span xml:lang="EN-US" data-contrast="auto"><span>intensive hydrodynamic numerical models. Recent and reliable fast-processing techniques for flood hazard assessment and mapping consider binary geomorphic classifiers retrieved from the analysis of Digital Elevation Models (DEMs). These procedures (termed herein “DEM-based methods”) produce binary maps distinguishing between floodable and non-floodable areas based on the comparison between the local value of the considered geomorphic classifier and a threshold, which in turn is calibrated against existing flood hazard maps. Previous studies have shown the reliability of DEM-based methods using a single binary classifier, they also highlighted that different classifiers are associated with different performance, depending on the geomorphological, climatic and hydrological characteristics of the study area. The present study maps flood-prone areas and predicts water depth associated with a given non-exceedance probability by combining several geomorphic classifiers and terrain features through regression trees and random forests. We focus on Northern Italy (c.a. 100000 km</span></span><sup><span xml:lang="EN-US" data-contrast="auto"><span>2</span></span></sup><span xml:lang="EN-US" data-contrast="auto"><span>, including Po, Adige, Brenta, Bacchiglione and Reno watersheds), and we consider the recently compiled MERIT (Multi-Error Removed Improved-Terrain) DEM, with 3sec-resolution (~90m at the Equator). We select the flood hazard maps provided by (</span></span><span xml:lang="EN-US" data-contrast="auto"><span>i</span></span><span xml:lang="EN-US" data-contrast="auto"><span>) the Italian Institute for Environmental Protection and Research (ISPRA), and (ii) the Joint Research Centre (JRC) of the European Commission as reference maps. Our findings (a) confirm the usefulness of machine learning techniques for improving univariate DEM-based flood hazard mapping, (b) enable a discussion on potential and limitations of the approach and (c) suggest promising pathways for further exploring DEM-based approaches for predicting a likely water depth distribution with flood-prone areas.</span></span><span> </span></p>

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