## Impact of Flood Control Systems on the Probability Distribution of Floods

Detention dams are one of the most effective practices for flood mitigation. Therefore, the impact of these structures on the basin hydrological response is critical for flood management and the design of flood control structures. With the aim to provide a mathematical framework to interpret the effect of flow control systems on river basin dynamics, the functional relationship between inflows and outflows is investigated and derived in a closed-form. This allowed the definition of a theoretically derived probability distribution of the peak outflows from in-line detention basins. The model has been derived assuming a rectangular hydrograph shape with a fixed duration, and a random flood peak. In the present study, the undisturbed flood distribution is assumed to be Gumbel distributed, but the proposed mathematical formulation can be extended to any other flood-peak probability distribution. A sensitivity analysis of parameters highlighted the influence of detention basin capacity and rainfall event duration on flood mitigation on the probability distribution of the peak outflows. The mathematical framework has been tested using for comparison a Monte Carlo simulation where most of the simplified assumptions used to describe the dam behaviours are removed. This allowed to demonstrate that the proposed formulation is reliable for small river basins characterized by an impulsive response. The new approach for the quantification of flood peaks in river basins characterised by the presence of artificial detention basins can be used to improve existing flood mitigation practices, support the design of flood control systems and flood risk analyses.

How to cite: Manfreda, S., D. Miglino, and C. Albertini, Impact of Flood Control Systems on the Probability Distribution of FloodsHydrology and Earth System Sciences, https://doi.org/10.5194/hess-2021-47, in review, 2021. [pdf]

## PROCESSI STOCASTICI IN IDROLOGIA

TEMA 1: PROCESSI STOCASTICI IN IDROLOGIA – STOCHASTIC PROCESSES IN HYDROLOGY
L’approccio statistico rappresenta uno dei principali strumenti di analisi per lo studio dei fenomeni naturali. Eventi estremi e processi di base sono stati analizzati e caratterizzati utilizzando diversi metodi statistici quali: teoria dei valori estremi, distribuzioni di probabilità teoricamente derivate, processi di Poisson, e equazioni differenziali stocastiche. Questi metodi sono stati utilizzati per fornire strumenti di calcolo in diversi ambiti delle costruzioni idrauliche, dell’idrologia e dell’ecoidrologia. Tra questi è opportuno menzionare i modelli per la caratterizzazione spazio-temporale del contenuto idrico del suolo, le distribuzioni derivate per la stima delle piene e dell’erosione localizzata, ed i modelli interpretativi sulla organizzazione spaziale della vegetazione.

## The Theoretically Derived Probability Distribution of Scour

Based on recent contributions regarding the treatment of unsteady hydraulic conditions in the state-of-the-art scour literature, theoretically derived probability distribution of bridge scour is introduced. The model has been derived assuming a rectangular hydrograph shape with a given duration, and a random flood peak, following a Gumbel distribution. A model extension for a more complex flood event has also been presented, assuming a synthetic exponential hydrograph shape. The mathematical formulation can be extended to any flood-peak probability distribution. The aim of the paper is to move forward the current approaches adopted for the bridge design, by coupling hydrological, hydraulic, and erosional models, in a mathematical closed form. An example of the application of the proposed distribution has been included with the aim to provide a guidance for the parameters estimation.

How to cite: Manfreda S., O. Link, A. Pizarro, The Theoretically Derived Probability Distribution of Scour, Water, 10, 1520, 2018. [pdf]

## Comparison of different methods describing the peak runoff contributing areas during floods

In the last few years, the scientific community has developed several hydrological models aimed at the simulation of hydrological processes acting at the basin scale. In this context, the portion of peak runoff contributing areas represents a critical variable for a correct estimate of surface runoff. Such areas are strongly influenced by the saturated portion of a river basin (influenced by antecedent conditions) but may also evolve during a specific rainfall event. In the recent years, we have developed 2 theoretically derived probability distributions that attempt to interpret these 2 processes adopting daily runoff and flood ‐ peak time series. The probability density functions (PDFs) obtained by these 2 schematisations were compared for humid river basins in southern Italy. Results highlighted that the PDFs of the peak runoff contributing areas can be interpreted by a gamma distribution and that the PDF of the relative saturated area provides a good interpretation of such process that can be used for flood prediction.

How to cite: Gioia, A., S. Manfreda, V. Iacobellis, M. Fiorentino, Comparison of different methods describing the peak runoff contributing areas during floodsHydrological Processes, 31(11), 2041-2049 (doi: 10.1002/hyp.11169), 2017.  [pdf]

## Performance of a Theoretical Model for the Description of Water Balance and Runoff Dynamics in Southern Italy

In the present paper, an analytical work for the description of the soil water balance and runoff production was adopted over a significant number of river basins belonging to a humid region of Southern Italy. The model is based on a stochastic differential equation, where the spatial heterogeneity of a basin is incorporated by a parabolic function describing the distribution of soil water storage capacity at the basin scale. The model provides an analytical description of the probability density function (PDF) of relative saturation of a basin as well as the PDF of daily runoff production. The proposed model includes five parameters that depend on climatic and soil characteristics. In particular, two parameters describe the rainfall process (α and λ), two characterize the distribution of soil water storage capacity (wmax and b), and the last is the soil water loss coefficient (V). Application of the model allowed the regionalization of model parameters based on physically consistent characteristics of the river basins. In particular, it was found that the soil water loss coefficient is strongly controlled by the fraction of forest cover of the river basin, while the parameter b, controlling the shape of the distribution of soil water storage capacity, is influenced by the basin topography.

How to cite: Gioia, A., S. Manfreda, V. Iacobellis, M. Fiorentino, Performance of a theoretical model for the description of the water balance and runoff dynamics in Southern ItalyJournal of Hydrologic Engineering, 19(6), 1113-1123, (doi: 10.1061/(ASCE)HE.1943-5584.0000879), 2014. [pdf]

## Inﬂuence of inﬁltration and soil storage capacity on the skewness of the annual maximum ﬂood peaks in a theoretically derived distribution

Understanding the spatial variability of key parameters of ﬂood probability distributions represents a strategy to provide insights on hydrologic similarity and building probabilistic models able to reduce the uncertainty in ﬂood prediction in ungauged basins. In this work, we exploited the theoretically derived distribution of ﬂoods model TCIF (Two Component Iacobellis and Fiorentino model; Gioia et al., 2008), based on two different threshold mechanisms associated to ordinary and extraordinary events. The model is based on the hypotheses that ordinary ﬂoods are generally due to rainfall events exceeding a constant inﬁltration rate in a small source area, while the so-called outlier events responsible for the high skewness of ﬂood distributions are triggered when severe rainfalls exceed a storage threshold over a large portion of the basin. Within this scheme, a sensitivity analysis was performed with respect to climatic and geomorphologic parameters in order to analyze the effects on the skewness coefﬁcient and provide insights in catchment classiﬁcation and process conceptualization. The analysis was conducted to investigate the inﬂuence on ﬂood distribution of physical factors such as rainfall intensity, basin area, and particular focus on soil behavior.

How to cite: Gioia, A., V. Iacobellis, S. Manfreda, and M. Fiorentino, Influence of infiltration and soil storage capacity on the skewness of the annual maximum flood peaks in a theoretically derived distributionHydrology and Earth System Sciences, 16, 937-951, (doi:10.5194/hess-16-937-2012), 2012. [pdf]

## Inﬂuence of soil parameters on the skewness coe ﬃ cient of the annual maximum ﬂood peaks

Understanding the spatial variability of key parameters of ﬂood probability distributions represents a strategy to provide insights on hydrologic similarity and building probabilistic models able to reduce the uncertainty in ﬂood prediction in ungauged basins. In this work, we exploited the theoretically derived distribution of ﬂoods TCIF (Gioia et al., 2008), based on two diﬀerent threshold mechanisms associated respectively to ordinary and extraordinary events. The model is based on the hypotheses that ordinary ﬂoods are generally due to rainfall events exceeding a threshold inﬁltration rate in a small source area, while the so-called outlier events, responsible of the high skewness of ﬂood distributions, are triggered when severe rainfalls exceed a storage threshold over a large portion of the basin. Within this scheme, a sensitivity analysis was performed in order to analyze the eﬀects of climatic and geomorphologic parameters on the skewness coeﬃcient. In particular, the analysis was conducted investigating the inﬂuence on ﬂood distribution of physical factors such as rainfall intensity, soil inﬁltration capacity, and basin area, in order to provide insights in catchment classiﬁcation and process conceptualization.

How to cite: Gioia, A., V. Iacobellis, S. Manfreda, and M. Fiorentino, Inﬂuence of soil parameters on the skewness coeﬃcient of the annual maximum ﬂood peaks, Hydrology and Earth System Sciences Discussions, 8, Pages 5559–5604 (doi: 10.5194/hessd-8-5559-2011), 2011. [pdf]

## Flood quantiles estimation based on theoretically derived distributions: regional analysis in Southern Italy

A regional probabilistic model for the estimation of medium-high return period ﬂood quantiles is presented. The model is based on the use of theoretically derived probability distributions of annual maximum ﬂood peaks (DDF). The general model is called TCIF (Two-Component IF model) and encompasses two different threshold mechanisms associated with ordinary and extraordinary events, respectively. Based on at-site calibration of this model for 33 gauged sites in Southern Italy, a regional analysis is performed obtaining satisfactory results for the estimation of ﬂood quantiles for return periods of technical interest, thus suggesting the use of the proposed methodology for the application to ungauged basins. The model is validated by using a jack-knife cross-validation technique taking all river basins into consideration.

How to cite: Iacobellis, V., A. Gioia, S. Manfreda, M. Fiorentino, Flood quantiles estimation based on theoretically derived distributions: regional analysis in Southern ItalyNatural Hazards and Earth System Sciences, 11, 673-695, (doi:10.5194/nhess-11-673-2011), 2011. [pdf]

## Regional analysis of runoff thresholds behaviour in Southern Italy based on theoretically derived distributions

The analysis of runoff thresholds and, more in general, the identiﬁcation of main mechanisms of runoff generation controlling the ﬂood frequency distribution is investigated, by means of theoretically derived ﬂood frequency distributions, in the framework of regional analysis. Two nested theoretically-derived distributions are ﬁtted to annual maximum ﬂood series recorded in several basins of Southern Italy. Results are exploited in order to investigate heterogeneities and homogeneities and to obtain useful information for improving the available methods for regional analysis of ﬂood frequency.

How to cite: Fiorentino, M., A. Gioia, V. Iacobellis, and S. Manfreda, Regional analysis of runoff thresholds behaviour in Southern Italy based on theoretically derived distributionsAdvances in Geosciences, 26, 139-144, (doi:10.5194/adgeo-26-139-2011), 2011. [pdf]

## Confronto fra i tempi di ritorno di piogge e portate di rilevante entità

Nel presente lavoro, viene analizzato il comportamento dei bacini idrografici durante eventi di piena per approfondire le dinamiche afflussi/deflussi. Le analisi sono condotte mediante simulazione idrologica in continuo utilizzando il modello DREAM accoppiato al modello IRP per la generazione di serie sintetiche di precipitazione. Tale approccio consente di portare in debita considerazione l’eterogeneità spaziale delle caratteristiche geomorfologiche, tessiturali dei suoli e della vegetazione, permettendo di estendere lo studio delle piene a periodi di ritorno alti prescindendo dall’estrapolazione di relazioni basate su brevi periodi di osservazione. Le caratteristiche delle distribuzioni di probabilità delle piene ed alcuni dei principali fenomeni che le influenzano sono analizzate sfruttando centinaia di eventi sintetici generati mediante il DREAM in due casi di studio con condizioni climatiche differenti.

How to cite: Fiorentino, M., A. Gioia, S. Manfreda, V. Iacobellis, Confronto di differenti metodologie per la determinazione dell’area contribuente al picco di piena, Tecniche per la Difesa dall’Inquinamento, Editoriale Bios, 2018.