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# Flash flood warning in ungauged basins by use of the flash flood guidance and model‐based runoff thresholds

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## Abstract

This paper investigates the use of the Flash Flood Guidance (FFG) method and a method of model-based threshold runoff computation to improve the accuracy of flash flood forecasts at ungauged locations. The methodology proposed in this paper requires running a lumped hydrological model to derive flood frequencies at the outlet of the ungauged basin under consideration, and then to derive the threshold runoff from these model-based discharges. The study examines the potential of this method to account for the hydrological model's uncertainty and for biases originated by lack of model calibration, which is the typical condition in ungauged basins.

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... Numerous attempts have been made to forecast FF occurrence using modeling approaches for different conditions of complex terrain [10,[14][15][16], urban and rural areas [15,17], ungauged zones [18][19][20] or in the tropics [7,21]. Other studies have taken advantage of the finer resolution of radar rainfall and operated in real or near real time [5,[22][23][24], though several other options exist using satellite-derived precipitation data [25,26]. ...
... Unfortunately, there was no gauged data recorded for the validation in Nam Khat. However, due to the similar conditions of the two watersheds, the model calibration for Nam Kim could be transposed to the ungauged Nam Khat, a method that has been applied in several studies, such as [8,18,20,48]. ...
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Northern Vietnam is a region prone to heavy flash flooding events. These often have devastating effects on the environment, cause economic damage and, in the worst case scenario, cost human lives. As their frequency and severity are likely to increase in the future, procedures have to be established to cope with this threat. As the prediction of potential flash floods represents one crucial element in this circumstance, we will present an approach that combines the two models KINEROS2 and HEC-RAS in order to accurately predict their occurrence. We used a documented event on 23 June 2011 in the Nam Khat and the larger adjacent Nam Kim watershed to calibrate the coupled model approach. Afterward, we evaluated the performance of the coupled models in predicting flow velocity (FV), water levels (WL), discharge (Q) and streamflow power (P) during the 3–5 days following the event, using two different precipitation datasets from the global spectral model (GSM) and the high resolution model (HRM). Our results show that the estimated Q and WL closely matched observed data with a Nash–Sutcliffe simulation efficiency coefficient (NSE) of around 0.93 and a coefficient of determination (R2) at above 0.96. The resulting analyses reveal strong relationships between river geometry and FV, WL and P. Although there were some minor errors in forecast results, the model-predicted Q and WL corresponded well to the gauged data.
... Research on these sudden and devastating floods has increased recently in order to reconstruct hydrological (Camarasa Belmonte and Segura Beltràn, 2001;Gaume et al., 2003Gaume et al., , 2004Gaume et al., , 2009Delrieu et al., 2005;Maréchal et al., 2008) and geomorphologic processes (Piegay and Bravard, 1997;Gutierrez et al., 1998;Merritt and Wohl, 2003) characterising these extreme events. Understanding these processes is extremely important for improving flood-risk management and reducing flash-flood damage (Montz and Gruntfest, 2002;Norbiato et al., 2009). This is especially urgent considering that flood-vulnerable areas are increasingly urbanized and global climate change seems to have increased the occurrence of these extreme events (Goubanova and Li, 2007). ...
... In many areas, however, and especially in small ephemeral mountain streams, that are very common features in the Mediterranean, precise spatial and temporal data on rainfall and river discharge are often fragmentary or absent (De Waele, 2008;Norbiato et al., 2009). Moreover, in carbonate areas, part of the precipitation and resulting superficial flow is rapidly transferred underground, and quantifying this karst aquifer recharge from stream losses is an extremely difficult task (Carter and Driscoll, 2006;Field, 2006;Dogwiler et al., 2007). ...
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... Several indicators have been used to evaluate the susceptibility and severity of flash floods, such as the flashflood potential index (FFPI) (Smith 2003), flashiness (Saharia et al. 2017) and critical rainfall (CR) (Kuo et al. 2018). Of these indexes, CR is the most widely used in the early warning of flash floods (Hapuarachchi et al. 2011;Kong et al. 2020), therefore, its accurate determination is key (Norbiato et al. 2009). Statistical induction based on data-driven methods, and the hydrology and hydraulics method (HHM) which is based on hydrology theory, are commonly used methods to calculate CR . ...
... Therefore, HHM is adopted in the current early warning and forecasting of flash floods. The flash flood guidance (FFG), developed by the American Hydrological Research Center, is widely used in the USA (Norbiato et al. 2009). Based on FFG, many studies have improved CR accuracy from the perspective of hydrological models for simulating rainfall-runoff processes (Seo et al. 2013;Clark et al. 2014). ...
Article
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Flash floods cause great harm to people’s lives and property safety. Rainfall is one of the main causes of flash floods in small watersheds. The uncertainty of rainfall events results in inconsistency between the traditional single rainfall pattern and the actual rainfall process, which poses a great challenge for the early warning and forecasting of flash floods. To carry out the effective flash flood early warning and forecasting, this paper proposes a novel rainfall pattern by coupling total rainfall and peak rainfall intensity based on copula functions, i.e., the rainfall pattern of risk probability combination (RPRPC). On this basis, the Hydrologic Engineering Center-Hydrologic Modeling System (HEC-HMS) hydrological model is used to simulate the rainfall-runoff process, the trial algorithm is used to calculate the critical rainfall (CR), and the optimistic-general-pessimistic (O–G-P) early warning mode considering the decision maker's risk preference is proposed. The small watershed of Xinxian in Henan province, China, is taken as a case study for calculation. The results show that the RPRPC is feasible and closer to the actual rainfall process than the traditional rainfall pattern, Frank copula function is the best for determining the joint distribution function of total rainfall and peak rainfall intensity, and the HEC-HMS model can be applied to small watersheds in hilly areas. Additionally, both RPRPC and antecedent soil moisture condition (ASMC) have influence on CR, and the variation of RPRPC will change the influence of ASMC on CR. Finally, the effectiveness of O–G-P early warning mode is verified.
... Critical rainfall (CR) refers to the minimum magnitude of rainfall at which a flash flood occurs, which is one of the most effective indicators for the early warning of flash floods (Hapuarachchi et al. 2011;Kong et al. 2020). Therefore, the accurate and effective determination of critical rainfall has become an important issue in early warning for flash floods (Norbiato et al. 2009). With the development of hydrometeorological technology, some methods are used to calculate CR. ...
... With the development of hydrometeorological technology, some methods are used to calculate CR. One of the most famous methods is the flash flood guidance (FFG) framework, created by the American Hydrologic Research Center, has made a great contribution to the early warning of flash floods (Norbiato et al. 2009). Based on the FFG, many studies have been worked on hydrological models for the simulation of the rainfall-runoff interaction to improve the accuracy of CR (Seo et al. 2013;Costache 2019). ...
Article
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Flash floods cause great harm to people's lives and property safety. Rainfall is the key factor which induces flash floods, and critical rainfall (CR) is the most widely used indicator in flash flood early warning systems. Due to the randomness of rainfall, the CR has great uncertainty, which causes missed alarms when predicting flash floods. To improve the early warning accuracy for flash floods, a random rainfall pattern (RRP) generation method based on control parameters, including the comprehensive peak position coefficient (CPPC) and comprehensive peak ratio (CPR), is proposed and an early warning model with dynamic correction based on RRP identification is established. The rainfall-runoff process is simulated by the HEC-HMS hydrological model, and the CR threshold space corresponding to the RRP set is calculated based on the trial algorithm. Xinxian, a small watershed located in Henan Province, China, is taken as the case study. The results show that the method for generating the RRP is practical and simple, and it effectively reflects the CR uncertainty caused by the rainfall pattern randomness. All the Nash–Sutcliffe efficiencies are greater than 0.8, which proves that the HEC-HMS model has good application performance in the small watershed. Through sensitivity analysis, (0.5,bmax)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(0.5,b_{max} )$$\end{document}, (r,bmax<0.5)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(r,b_{max} < 0.5)$$\end{document}, and (r,bmax>0.5)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(r,b_{max} > 0.5)$$\end{document} are identified as key, safe, and dangerous rainfall patterns, respectively. The proposed early warning model is effective, which increases the forecast lead time and reduce the omissions rate of flash flood early earning.
... Europe has experienced numerous catastrophic flash floods in the last decades with vast social and economic impacts on the affected areas (Hall et al., 2013;Merz et al., 2014). The frequency and the magnitude of the flash flood events have differed between Continental and Mediterranean regions in Europe, with a tendency of the latter to produce more extreme floods (Gaume et al., 2009;Norbiato et al., 2009). ...
... Given the importance of initial soil moisture on flood generation, the use of soil moisture satellite data seems to be a logical way forward to contribute to more reliable flash flood warnings. This can be either done by assimilating soil moisture into hydrological forecasting systems (Parajka et al., 2009(Parajka et al., , 2006Wanders et al., 2014) or by combining flash flood guidance based on rainfall depth-duration thresholds (Norbiato et al., 2009) with satellite estimates of soil moisture. ...
Article
The purpose of this paper is to contribute to the understanding of the importance of the initial soil moisture state for flash flood magnitudes. Four extreme events that occurred in different case study regions were analysed, one winter and one autumn flash flood in the Giofiros and Almirida catchments in Crete, and two summer floods in the Rastenberg catchment in Austria. The hydrological processes were simulated by the spatially distributed flash flood model Kampus. For the Crete cases Kampus model was calibrated against remotely sensed soil moisture while for the Austrian case the model was calibrated against observed runoff. Kampus model was then used to estimate the sensitivity of the stream flow peak to initial soil moisture. The largest of the events analysed (in terms of specific peak discharge) was found to have a sensitivity of less than 0.2% flood peak change per % soil moisture change while the smallest event had a sensitivity of more than 3% flood peak change per % soil moisture change. This suggests that initial soil moisture effects on the flash flood response probably depend on event magnitude rather than on the climate or region. Moreover, the Austrian catchment was found to exhibit a more nonlinear relationship between antecedent soil moisture and the peak discharge than the Cretan catchments which was explained by differences in the soil type.
... This increasing model uncertainty at small scales may obscure the benefits of high-resolution distributed models in flash flood forecasting. A comparative study (Norbiato et al., 2009) was conducted in four Italian catchments, and the results indicated that using model-based thresholds can improve flood warning method using the rainfall threshold in both gauged and ungauged catchments. On the one hand, the distributed model makes hydrological calculations at spatial and temporal scales that are more commensurate with flash flooding; on the other hand, the distributed models perform better than lumped models without calibration (Refsgaard and Knudsen, 1996). ...
Article
Flash flooding is one of the most common natural hazards in China, particularly in mountainous areas, and usually causes heavy damage and casualties. However, the forecasting of flash flooding in mountainous regions remains challenging because of the short response time and limited monitoring capacity. This paper aims to establish a strategy for flash flood warnings in mountainous ungauged catchments across humid, semi-humid and semi-arid regions of China. First, we implement a geomorphology-based hydrological model (GBHM) in four mountainous catchments with drainage areas that ranges from 493 to 1601 km2. The results show that the GBHM can simulate flash floods appropriately in these four study catchments. We propose a method to determine the rainfall threshold for flood warning by using frequency analysis and binary classification based on long-term GBHM simulations that are forced by historical rainfall data to create a practically easy and straightforward approach for flash flood forecasting in ungauged mountainous catchments with drainage areas from tens to hundreds of square kilometers. The results show that the rainfall threshold value decreases significantly with increasing antecedent soil moisture in humid regions, while this value decreases slightly with increasing soil moisture in semi-humid and semi-arid regions. We also find that accumulative rainfall over a certain time span (or rainfall over a long time span) is an appropriate threshold for flash flood warnings in humid regions because the runoff is dominated by excess saturation. However, the rainfall intensity (or rainfall over a short time span) is more suitable in semi-humid and semi-arid regions because excess infiltration dominates the runoff in these regions. We conduct a comprehensive evaluation of the rainfall threshold and find that the proposed method produces reasonably accurate flash flood warnings in the study catchments. An evaluation of the performance at uncalibrated interior points in the four gauged catchments provides results that are indicative of the expected performance at ungauged locations. We also find that insufficient historical data lengths (13 years with a 5-year flood return period in this study) may introduce uncertainty in the estimation of the flood/rainfall threshold because of the small number of flood events that are used in binary classification. A data sample that contains enough flood events (10 events suggested in the present study) that exceed the threshold value is necessary to obtain acceptable results from binary classification.
... Il s'agit d'évaluer la susceptibilité d'un bassin à subir une crue rapide en fonction de la pluie. Pour cela, la méthode FFG détermine le cumul de pluie minimum nécessaire par bassin versant pour causer une crue débordante à l'exutoire du bassin en question (Norbiato, Borga and Dinale 2009 Cette méthode fournit des prévisions d'ensemble de pluies en chaque pixel du réseau hydrographique. Ces données de pluie prévue sont ensuite moyennées à l'échelle des bassins versants, puis comparées à des seuils de sévérité calculés grâce à 20 ans de données de rejeu. ...
Thesis
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Anticiper les inondations constitue un enjeu majeur pour les communes exposées aux crues car c’est sur cette anticipation que repose l’ensemble de la chaîne d’alerte, garante de la sécurité des personnes et des biens. Si un système de suivi du risque de dommages liés aux crues est disponible pour un cinquième du réseau hydrographique français, les petits cours d’eau composant les quatre cinquièmes restants ne font pas partie du dispositif de suivi temps réel du ministère en charge de l’écologie, appelé « Vigicrues ». Or il s’agit également des cours d’eau les plus concernés par le phénomène de crues rapides, pour lesquelles l’anticipation joue un rôle crucial en gestion de crise. Voilà pourquoi début 2017, Vigicrues a été complété par un service automatique d'avertissement des crues appelé Vigicrues Flash. Ce système permet de fournir en temps réel une information sur l’intensité de la crue des cours d’eau pour 10 000 communes françaises.Même si ce nouveau service constitue un réel progrès pour les communes jusqu’alors dépourvues de système d’anticipation, la méthode AIGA qui constitue le cœur de Vigicrues Flash possède certaines limites. L’une d’entre elles, est le fait que la méthode n’avertit que sur le niveau de rareté de la crue, sans tenir compte des enjeux présents. Or, pour générer un avertissement efficace, il est nécessaire de prendre en compte les conséquences potentielles de cette crue. Cette thèse a donc pour but de permettre l’estimation anticipée des dommages liés aux crues rapides, en particulier sur les bassins non jaugés. Pour cela, nous proposons une méthode d’estimation du risque de dommages fondée d’une part sur la qualification de l’intensité de l’aléa crue par la méthode AIGA et d’autre part sur la prise en compte de la vulnérabilité du territoire. Cette dernière a été construite à partir d’une approche bottom-up innovante, directement auprès de gestionnaires du risque. Le croisement de ces deux types d’informations a permis de fournir une première caractérisation du risque de dommages liés aux inondations sous la forme d’un indice de risque dynamique.En adaptant des tests de performances issus de la météorologie, nous avons pu évaluer notre indice par rapport à la méthode AIGA seule. Des informations sur les dommages déjà existantes (les arrêtés « CATNAT » issus de la BD GASPAR) ou spécifiquement collectées (la BD DamaGIS constituée pour cette thèse à partir d’informations présentes notamment sur les réseaux sociaux) constituent nos données de validation. Notre évaluation a porté sur 12 communes dans les Alpes-Maritimes, 69 dans le Gard et 28 dans le Var, et s’est faite de deux manières complémentaires : d’une part une évaluation en continue et exhaustive à partir des arrêtes CATNAT pris pour nos communes sur toute la période 1998-2016 ; et d’autre part une évaluation événementielle, mais à l’échelle infra-communale.Nos résultats montrent que le passage de la caractérisation de l’aléa à celle du risque améliore nettement la pertinence des avertissements émis, surtout à l’échelle infra-communale. Les dommages y sont mieux détectés, avec un taux moindre de fausse alertes. Cette thèse ouvre donc de réelles perspectives d’amélioration de la chaîne de l’alerte actuelle, permettant de mieux organiser la réponse des services de secours et de gestion de crise face à l’annonce de dommages potentiels liés aux crues rapides.
... Hydrographs are routed through the river network by means of the Muskingum-Cunge method [35]. Application of the model requires specification of 14 parameters for the snow routine, the runoff generation module and the runoff propagation module [36]. The calibration procedure for determining the model parameters is detailed in Borga et al. [37]. ...
Article
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The error in satellite precipitation-driven complex terrain flood simulations is characterized in this study for eight different global satellite products and 128 flood events over the Eastern Italian Alps. The flood events are grouped according to two flood types: rain floods and flash floods. The satellite precipitation products and runoff simulations are evaluated based on systematic and random error metrics applied on the matched event pairs and basin-scale event properties (i.e., rainfall and runoff cumulative depth and time series shape). Overall, error characteristics exhibit dependency on the flood type. Generally, timing of the event precipitation mass center and dispersion of the time series derived from satellite precipitation exhibits good agreement with the reference; the cumulative depth is mostly underestimated. The study shows a dampening effect in both systematic and random error components of the satellite-driven hydrograph relative to the satellite-retrieved hyetograph. The systematic error in shape of the time series shows a significant dampening effect. The random error dampening effect is less pronounced for the flash flood events and the rain flood events with a high runoff coefficient. This event-based analysis of the satellite precipitation error propagation in flood modeling sheds light on the application of satellite precipitation in mountain flood hydrology.
... Studies on mountain flash floods have been based on the Flash Flood Guidance (FFG) system of the early American Hydrological Research Center, applied widely in Europe and America (Norbiato et al. 2009). Many scholars outside of China have focused on the rainfall-runoff simulation process within the FFG system to improve and optimize the model for accurate calculation of the precipitation-runoff relationship (Norbiato et al. 2008;Montesarchio et al. 2015). ...
Article
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The sudden occurrence and randomness of heavy rainstorms in hilly areas pose challenges to the identification of early warning indicators for mountain flash flood. This study explores the variation of critical rainfall under different rainfall patterns, mainly considering the effect of differences in the timing of peak rainfall (i.e., early, late or in the middle of the rainfall process). The HEC-HMS model was used to simulate the rainfall-runoff process and determine the early warning indicators under different rainfall patterns through repeated trial calculation. The time-interval characteristic rainfall assessment method was then used to verify the theoretical value of critical rainfall against information from actual flood disasters. The results show that: (1) The timing of peak rainfall within the rainfall event is negatively correlated with the magnitude of the critical rainfall. (2) Critical rainfall is more sensitive to rainfall pattern than to soil moisture content. (3) For the three early warning periods considered, the critical rainfall with the BEF rainfall pattern is about 1.20–1.22 times that with pattern MID, while the critical rainfall with the MID rainfall pattern is about 1.24 times that with BEH. Thus, this paper elucidates the impact of the randomness of rainfall patterns on critical rainfall and provides a valuable reference for the analysis and calculation of early warning indicators of mountain flash flood.
... Among these measures, flash flood early warning (FFEW) has drawn worldwide attention for its high practicality and economic efficiency. Developing countries have built several operational FFEW systems adapted to certain regions with specific input data (Alfieri, Velasco, & Thielen, 2011;Norbiato, Borga, & Dinale, 2009), such as the flash flood guidance system, the HYDRATE project, and Delft-FEWS. However, these systems are difficult to apply outside their calibrated regions without prior knowledge of the selected area, particularly in ungauged basins. ...
Article
Flash floods cause extensive loss of property and human life. Early warning systems present a more efficient approach to flood prevention and mitigation than engineering measures. This article reviews research on flash flood early warnings in China, including long-term prediction methods based on statistical regularity and flood mechanisms, and real-time warning indicators relying on multi-source data and automated systems. Current research shortcomings are discussed, and suggestions for future improvements are proposed. This research can provide public officials with knowledge of flash flood early warnings, influencing policy and protecting people from flash flood disasters.
... The statistical characterization and modeling of rainfall extremes are crucial to support hydrologic, engineering, and climate studies with high societal, economic, and environmental impacts. They are needed to inform hydrologic modeling of floods (Norbiato et al., 2009;Golian et al., 2010;Hapuarachchi et al., 2011;Alfieri et al., 2016), which are one of the most severe natural hazards causing significant losses in terms of both property and fatalities (Ashley and Ashley, 2008;Di Baldassarre et al., 2010;Gochis et al., 2015;Peden et al., 2017). Statistical models of extreme rainfall are critical to design and manage infrastructures (e.g., Madsen et al., 2002;Bonnin et al., 2006;Langousis and Veneziano, 2007;Haddad et al., 2011), which are becoming increasingly interdependent and, then, more vulnerable to extreme events (Rinaldi et al., 2001;Hasan and Foliente, 2015). ...
Article
This study uses daily rainfall records of a dense network of 240 gauges in central Arizona to gain insights on (i) the variability of the seasonal distributions of rainfall extremes; (ii) how the seasonal distributions affect the shape of the annual distribution; and (iii) the presence of spatial patterns and orographic control for these distributions. For this aim, recent methodological advancements in peak-over-threshold analysis and application of the Generalized Pareto Distribution (GPD) were used to assess the suitability of the GPD hypothesis and improve the estimation of its parameters, while limiting the effect of short sample sizes. The distribution of daily rainfall extremes was found to be heavy-tailed (i.e., GPD shape parameter ξ > 0) during the summer season, dominated by convective monsoonal thunderstorms. The exponential distribution (a special case of GPD with ξ = 0) was instead showed to be appropriate for modeling wintertime daily rainfall extremes, mainly caused by cold fronts transported by westerly flow. The annual distribution exhibited a mixed behavior, with lighter upper tails than those found in summer. A hybrid model mixing the two seasonal distributions was demonstrated capable of reproducing the annual distribution. Organized spatial patterns, mainly controlled by elevation, were observed for the GPD scale parameter, while ξ did not show any clear control of location or orography. The quantiles returned by the GPD were found to be very similar to those provided by the National Oceanic and Atmospheric Administration (NOAA) Atlas 14, which used the Generalized Extreme Value (GEV) distribution. Results of this work are useful to improve statistical modeling of daily rainfall extremes at high spatial resolution and provide diagnostic tools for assessing the ability of climate models to simulate extreme events.
... The area selected in North-Eastern Italy includes three main administrative units: Regione Veneto, Provincia Autonoma di Trento, Provincia Autonoma di Bolzano-Southern Tyrol. The area crosses part of the Alps with a climatic gradient from essentially snow-fed catchments at the Northern edge to rainfall fed catchments at the Southern edge of the transect [27]. The regional administrative units coordinated their energy policy, optimizing the joint use of the main renewable energy sources, namely solar and hydropower (see C3-Alps project http//www.c3alps.eu/). ...
Article
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Moving towards energy systems with high variable renewable energy shares requires a good understanding of the impacts of climate change on the energy penetration. To do so, most prior impact studies have considered climate projections available from Global Circulation Models (GCMs). Other studies apply sensitivity analyses on the climate variables that drive the system behavior to inform how much the system changes due to climate change. In the present work, we apply the Decision Scaling approach, a framework merging these two approaches, for analyzing a renewables-only scenario for the electric system of Northern Italy where the main renewable sources are solar and hydropower. Decision Scaling explores the system sensibility to a range of future plausible climate states. GCM projections are considered to estimate probabilities of the future climate states. We focus on the likely future energy mix within the region (25% of solar photovoltaic and 75% of hydropower). We also carry out a sensitivity analysis according to the storage capacity. The results show that run-of-the river power generation from this Alpine area is expected to increase although the average inflow decreases under climate change. They also show that the penetration rate is expected to increase for systems with storage capacity less than one month of average load and inversely for higher storage capacity.
... The rainfall comparison method is a popular tool for warning about flash floods, and this method is commonly used for flash flood forecasting. However, the previous rainfall threshold method has some limitations; recent studies tried to improve warning accuracy by using distributed physical hydrological modeling (Kobold and Brilly, 2006;Reed et al., 2007;Norbiato et al., 2009). Hapuarachchi and Wang (2008) suggested that physically based distributed hydrological models are more appropriate than data-driven models and conceptual hydrological models for flash flood forecasting. ...
Article
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This paper presents quantitative criteria for flash flood warning that can be used to rapidly assess flash flood occurrence based on only rainfall estimates. This study was conducted for 200 small mountainous sub-catchments of the Han River basin in South Korea because South Korea has recently suffered many flash flood events. The quantitative criteria are calculated based on flash flood guidance (FFG), which is defined as the depth of rainfall of a given duration required to cause frequent flooding (1–2-year return period) at the outlet of a small stream basin and is estimated using threshold runoff (TR) and antecedent soil moisture conditions in all sub-basins. The soil moisture conditions were estimated during the flooding season, i.e., July, August and September, over 7 years (2002–2009) using the Sejong University Rainfall Runoff (SURR) model. A ROC (receiver operating characteristic) analysis was used to obtain optimum rainfall values and a generalized precipitation–area (P–A) curve was developed for flash flood warning thresholds. The threshold function was derived as a P–A curve because the precipitation threshold with a short duration is more closely related to basin area than any other variables. For a brief description of the P–A curve, generalized thresholds for flash flood warnings can be suggested for rainfall rates of 42, 32 and 20 mm h⁻¹ in sub-basins with areas of 22–40, 40–100 and > 100 km², respectively. The proposed P–A curve was validated based on observed flash flood events in different sub-basins. Flash flood occurrences were captured for 9 out of 12 events. This result can be used instead of FFG to identify brief flash flood (less than 1 h), and it can provide warning information to decision-makers or citizens that is relatively simple, clear and immediate.
... For the stream flow prediction of ungauged catchments, the presence of well-gauged catchments in proximity is more beneficial than having physically similar catchments [24]. Norbiato et al. found that the model parameters, which transferred directly from gauged to ungauged catchments of the same river system had limitations when computed via FFG [27]. Thus, a more reliable regionalization method was needed. ...
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Flash floods occur in mountainous catchments with short response times, which are among the most devastating natural hazards in China. This paper intends to forecast and provide warnings of flash floods timely and precisely using the flash flood warning system, which is established by a new distributed hydrological model (the China flash flood hydrological model, CNFF-HM). Two ungauged mountainous regions, Shunchang and Zherong, are chosen as the study areas. The CNFF-HM is calibrated in five well-monitored catchments. The parameters for the ungauged regions are estimated by regionalization. River water stage data and reservoir water stage data from Shunchang, and reservoir water stage data from Zherong are used to validate the model. The model performs well and the average Nash-Sutcliffe efficiency (NSE) is above 0.8 for the five catchments. The validation shows the difference in the timing of flood peaks using the two types of water stage data is less than 1 h. The rising and declining trends of the floods correspond to the observed trends over the entire validation process. Furthermore, the flash flood warning system was effectively applied in flash flood event on 28 September 2016 in Zherong. Thus, the CNFF-HM with regionalization is effective in forecasting flash floods for ungauged mountainous regions.
... 2. los cálculos de la FFG, y 3. las condiciones mínimas de la inundación (Norbiato & Dinale, 2009). ...
... This model has been successfully applied in several studies in the greater area of northern Italy (Norbiato, et al., 2009b;. A summary of the modeling framework is provided below, while for a detailed description of the modeling structure, the interested reader is referred to Norbiato, et al. (2008). ...
Thesis
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The overarching goal of the research described in this dissertation is to understand the hydrologic implications of error propagation from satellite precipitation products to hydrologic simulations. The complex interaction between precipitation error and corresponding hydrologic response is examined following a numerical- and an analytical-based method. The application of a hydrologic model forced by various satellite precipitation products is adopted as the numerical-based framework that was used to identify the properties of error propagation with respect to a number of factors (e.g. basin scale, seasonality, severity of rainfall and flow). Results show better consistency between gauges for events occurred over larger scale basins during warm season months that are associated with moderate intensity of rain and flow rate. In addition to the numerical investigation, an analytical framework is developed to decompose the error propagation into space-time components. This essentially allows to assess the relative contribution of the different processes of catchment flood response on error propagation. It is shown that error in timing of flood event is equally attributed to due to error in runoff generation and routing time. Error in hydrograph shape is mainly controlled by the error in the variability of runoff generation time while error in flood volume is predominantly controlled by the error in rainfall volume. Overall, these investigations provide important information for the hydrologic modelers to choose the appropriate precipitation products for the hydrologic-related practice. It also serves as a guidance for the product developers on the designs of more advance retrieval algorithms.
... However, previous studies revealed a poor efficiency of the models when transposed to ungauged catchments (Aubert et al., 2014;Bastola et al., 2008;Lee et al., 2005;Norbiato et al., 2009;Viviroli et al., 2009). The failure of regionalization may be mainly attributable to the equifinality, which makes that several sets of parameters can be accepted for modeling rainfall-runoff relationship; and makes difficult the spatial comparison and the interpretation of those parameters. ...
Thesis
Rainfall-runoff models are essential tools for many hydrological applications, including flood forecasting. The purpose of this thesis was to examine the performances of a distributed event model for reproducing the Mediterranean floods. This model reduces the parametrization of the processes to the flood period, and estimates the saturation of the catchment at the beginning of the event with an external predictor, which is easily observable or available. Such predictor avoids modelling the inter-flood phase and simplifies the parametrization and the calibration of the model. The selected model combines a distributed SCS production function and a Lag and Route transfer function, applied to a discretization of the basin in a grid of regular square meshes.The model was first tested on the Real Collobrier watershed. This Mediterranean basin has been monitored by IRSTEA for more than 50 years and has an exceptional density of rainfall and flow measurements. This favourable environment made it possible to reduce the uncertainties on the rainfall input and to evaluate the actual performances of the model. In such conditions, the floods were correctly simulated by using constant parameters for all the events, but the initial condition of the event-based model. This latter was highly correlated to predictors such as the base flow or the soil water content w2 simulated by the SIM model of Meteo-France. The model was then applied by reducing the density of the rain gauges, showing loss of accuracy of the model and biases in the model parameters for lower densities, which are representative of most of the catchments.The spatial variability of the model parameters was then studied in different Real Collobrier sub-basins. The comparison made it possible to highlight and correct the scale effect concerning one of the parameters of the transfer function. The catchment saturation predictors and the initial condition of the model were still highly correlated, but the relationships differed from some sub-catchments. Finally, the spatial variability of the model parameters was studied for other larger Mediterranean catchments, of which area ranged from some tenth to hundreds of square kilometres. Once more, the model could be efficiently initialized by the base flow and the water content w2, but significant differences were found from a catchment to another. Such differences could be explained by uncertainties affecting as well the rainfall estimation as the selected predictors. However, the relationships between the initial condition of the model and the water content w2 were close together for a given type of catchment.In conclusion, this distributed event model represents an excellent compromise between performance and ease of implementation. The performances are satisfactory for a given catchment or a given type of catchment. The transposition of the model to ungauged catchment is less satisfactory, and other catchment saturation indicators need to be tested, e.g. in situ measurements or satellite measurements of soil moisture.
... Alternatively, data-driven models (Thirumalaiah and Deo, 1998;Jain and Srinivasulu, 2004) require long-term data records not always available everywhere (Hapuarachchi et al., 2011). Finally, simplified approaches (based on rainfall and soil moisture; Ntelekos et al., 2006;Norbiato et al., 2009;Javelle et al., 2010) on runoff (Raynaud et al., 2015), or process-based approaches (Panziera et al., 2016;Antonetti et al., 2019) have been shown to be as accurate as physically based models, particularly when transferred to ungauged river basins (Alfieri et al., 2014). The present paper presents such a simplified methodology which accounts for meteorological and landsurface components together in a flood hazard risk forecast index (FHRFI), by combining information from the main flood-generating land-surface area (such as impervious surfaces, flood plains and wetlands footprints) within the meteorological hazard warning to create a spatial flood hazard index. ...
Article
Hurricane Harvey caused at least 70 confirmed deaths, with estimated losses in the Houston urban area reaching above \$150 billion, making it one of the costliest natural disasters ever in the United States. Here we tested two types of forecast index to provide surface flooding (inundation) warning over the Houston area: a meteorological index based on a global Numerical Weather Prediction System (NWP), and a new combined meteorological and land‐surface index, the Flood Hazard Risk Forecasting Index (FHRFI), where land‐surface is used to condition the meteorological forecast. Both indices use the total precipitation Extreme Forecast Index (EFI) and Shift of Tails (SoT) products from the European Centre for Medium‐range Weather Forecasts (ECMWF) medium‐range ensemble forecasting system (ENS). Forecasts at the medium range (3–14 days ahead) were assessed against 153 observed National Weather Service urban flood reports over the Houston urban area between 26 and August 29, 2017. We show that our method provides skilful forecasts up to 4 days ahead using both approaches. Moreover the FHRFI combined index has a Hit Ratio of up to 74% at 72 hours lead time, with a False Alarm Ratio of only 45%. This amounts to a statistically significant 20% increase in performance compared with the meteorological indices. This first study demonstrates the importance of including land surface information to improve the quality of the flood forecasts over meteorological indices only, and that skilful flood warning in urban areas can be obtained from NWP using the FHRFI.
... Its success is demonstrated by its widespread application (see Gourley et al., 2012). A number of similar methods based on rainfall and soil moisture (e.g., Norbiato et al., 2009;Javelle et al., 2010;Van Steenbergen and Willems, 2013) or on runoff (Raynaud et al., 2014) threshold exceedances have been proposed in recent years. Many of these supported the findings that simplified approaches for flood early warning often provide as accurate results as those of physically based models, particularly when transferred to ungauged river basins. ...
Article
Full-text available
Systems for the early detection of floods over continental and global domains have a key role in providing a quick overview of areas at risk, raise the awareness and prompt higher detail analyses as the events approach. However, the reliability of these systems is prone to spatial inhomogeneity, depending on the quality of the underlying input data and local calibration. This work proposes a simple approach for flood early warning based on ensemble numerical predictions of surface runoff provided by weather forecasting centers. The system is based on a novel indicator, referred to as an extreme runoff index (ERI), which is calculated from the input data through a statistical analysis. It is designed for use in large or poorly gauged domains, as no local knowledge or in situ observations are needed for its setup. Daily runs over 32 months are evaluated against calibrated hydrological simulations for all of Europe. Results show skillful flood early warning capabilities up to a 10-day lead time. A dedicated analysis is performed to investigate the optimal timing of forecasts to maximize the detection of extreme events. A case study for the central European floods of June 2013 is presented and forecasts are compared to the output of a hydro-meteorological ensemble model.
... Die Bedingungen, die in Südtirol zur Auslösung von Murgängen, oberflächlichen Erdrutschen und Sturzfluten (flash flood) führen können, wurden anhand des von der Abteilung Wasser-schutzbauten der Autonomen Provinz Bozen verwalteten Ereigniskatasters ED30 und anhand der mittels Niederschlagsmessern und Radarstationen des Hydrographischen Amts der Autonomen Provinz Bozen ermittelten Daten untersucht. Dadurch wollte man abwägen, ob der Aufbaus eines Warnsystems für nicht instrumentell überwachte Gewässer machbar ist (Norbiato et al. 2009). In einer ersten Phase war es möglich, auf regionaler Ebene eine Beziehung zwischen den Schwellenwerten der Intensität und Dauer des Regens und dem Auftreten der o.g. ...
... Alerts are issued if the observed rainfall data in real-time or rainfall forecast exceed the threshold for a particular duration. This approach requires rainfall data by means of real-time rainfall monitoring or rainfall radar (Norbiato et al., 2009). However, other rainfall threshold methods need the same information. ...
Article
Full-text available
Flash floods are an increasing concern, especially in regions with abrupt topography and small areas where floods are rapid and energy-filled. That is the case of the El Guamo stream basin located in Manizales, Colombia. It has been proposed a duration-independent rainfall threshold for flash floods in this basin, using a hydrodynamic method that links critical water stages to cumulative rainfall. This paper presents a systematic literature review of 19 case studies from 2016 to 2021 to compare and highlight complexities and differences in the methods used in rainfall threshold estimation in both the El Guamo stream basin as in other case studies. The results identified four types of methods: (i) empirical, (ii) hydrological/hydrodynamic, (iii) probabilistic, and (iv) compound. Each method identified the principal indicators and their predictor variables. Each method uses different indicators, such as accumulated rain, accumulated antecedent rainfall, intensity-duration of the rain event, maximum cumulative or cumulative rainfall depth for a specific duration, and critical rainfall within given time periods. Scenario analysis of the predictor variables is a common approach used in rainfall threshold estimation. Some predicting variables found are antecedent moisture conditions, inundation criteria, and synthetic hyetographs. Some case studies include a probabilistic analysis of the predictor variables. This article concludes that indicators and their predicting variables can be adjusted to local flood early warning systems depending on the rainfall threshold method selected. Hydrodynamic models are solid in rainfall threshold estimation. However, it is highly advisable to include uncertainty analysis and new data sources to have more robust rainfall thresholds. Furthermore, probabilistic methods, including uncertainty analysis with utility functions, are a valuable tool to improve decision-making in early warning systems, which can help to refine the rainfall threshold estimation.
... . Therefore, the accurate and effective determination of critical rainfall 38 has become an important issue in early warning for flash floods (Norbiato et al., 2009). In the early 39 stages, a data-driven method is often used to calculate the CR. ...
Preprint
Full-text available
Flash floods cause great harm to people's lives and property safety. Rainfall is the key factor which induces flash floods, and critical rainfall (CR) is the most widely used indicator in flash flood early warning systems. Due to the randomness of rainfall, the CR has great uncertainty, which causes missed alarms when predicting flash floods. To improve the early warning accuracy for flash floods, a random rainfall pattern (RRP) generation method based on control parameters, including the comprehensive peak position coefficient (CPPC) and comprehensive peak ratio (CPR), is proposed and an early warning model with dynamic correction based on RRP identification is established. The rainfall-runoff process is simulated by the HEC-HMS hydrological model, and the CR threshold space corresponding to the RRP set is calculated based on the trial algorithm. Xinxian, a small watershed located in Henan Province, China, is taken as the case study. The results show that the method for generating the RRP is practical and simple, and it effectively reflects the CR uncertainty caused by the rainfall pattern uncertainty. The HEC-HMS model is proved to have good application performance in the Xinxian watershed. Through sensitivity analysis, the effect of the antecedent soil moisture condition, CPPC, and CPR are compared. The proposed early warning model is practical and effective, which increases the forecast lead time.
... Flood forecasting is very important for reducing the risk of flash floods [4,5]. Many studies indicated that precipitation data were one of the essential inputs for hydrological modeling, and about 70-80% of the uncertainties of hydrological simulations were due to the uncertainties in precipitation data [2,[6][7][8]. ...
Article
Full-text available
Satellite remote sensing precipitation is useful for many hydrological and meteorological applications such as rainfall-runoff forecasting. However, most studies have focused on the use of satellite precipitation on daily, monthly, or larger time scales. This study focused on flash flood simulation using satellite precipitation products (IMERG) on an hourly scale in a poorly gauged mountainous catchment in southwestern China. Deep learning (long short-term memory, LSTM) was used, merging satellite precipitation and gauge observations, and the merged precipitation data were used as inputs for flood simulation based on the HEC-HMS model, compared with the gauged precipitation data and original IMERG data. The results showed that the application of original IMERG data used directly in the HEC-HMS hydrological model had much lower accuracy than that of gauged data and merged data. The simulation using the merged precipitation in HEC-HMS exhibited much better performances than gauged data. The mean NSE improved from 0.84 to 0.87 for calibration and 0.80 to 0.84 for verification, while the lower NSE improved from 0.81 to 0.84 for calibration and 0.73 to 0.86 for verification, which showed that accuracy and robustness were both significantly improved. Results of this study indicate the advances of remote sensing precipitation with deep learning for flash flood forecasting in mountainous regions. It is likely that more significant improvements can be made in flash flood forecasting by employing multi-source remote sensing products and deep learning merging methods considering the impact of complex terrain.
... This model has been successfully applied in several studies in the greater area of northern Italy (Norbiato, et al., 2009b;. A summary of the modeling framework is provided below, while for a detailed description of the modeling structure, the interested reader is referred to Norbiato, et al. (2008). ...
Article
The overarching goal of the research described in this dissertation is to understand the hydrologic implications of error propagation from satellite precipitation products to hydrologic simulations. The complex interaction between precipitation error and corresponding hydrologic response is examined following a numerical- and an analytical-based method. The application of a hydrologic model forced by various satellite precipitation products is adopted as the numerical-based framework that was used to identify the properties of error propagation with respect to a number of factors (e.g. basin scale, seasonality, severity of rainfall and flow). Results show better consistency between gauges for events occurred over larger scale basins during warm season months that are associated with moderate intensity of rain and flow rate. In addition to the numerical investigation, an analytical framework is developed to decompose the error propagation into space-time components. This essentially allows to assess the relative contribution of the different processes of catchment flood response on error propagation. It is shown that error in timing of flood event is equally attributed to due to error in runoff generation and routing time. Error in hydrograph shape is mainly controlled by the error in the variability of runoff generation time while error in flood volume is predominantly controlled by the error in rainfall volume. Overall, these investigations provide important information for the hydrologic modelers to choose the appropriate precipitation products for the hydrologic-related practice. It also serves as a guidance for the product developers on the designs of more advance retrieval algorithms.
... Currently, several methods are applied in the early warning of flash floods, with rapid development of meteorological-hydrological coupling technology. The Flash Flood Guidance (FFG) system, developed by the American Hydrological Research Center, has been widely used in the USA (Norbiato et al. 2009). FFG is defined as the threshold rainfall over accumulation periods of 1, 3 and 6 h required to initiate flooding on small streams that respond to rainfall within a few hours (Konstantine et al. 2010). ...
Article
Full-text available
Rainfall is one of the main causes of flash floods in mountainous watersheds. The critical rainfall, calculated by the rainfall patterns which represent typical rainfall processes, is an important index for the early warning of flash floods. However, due to the randomness and diversity of the rainfall process, the traditional single rainfall pattern is inconsistent with the actual diversified rainfall process, which brings great challenges to the early warning of flash floods. This paper proposes three characteristic parameters to describe the temporal distribution characteristics of typical rainfall processes. On this basis, the appropriate cumulative distribution functions (CDFs) are chosen to fit the cumulative rainfall-duration curves corresponding to typical rainfall processes, and the probability density functions (PDFs) can be used to represent the characteristic rainfall patterns. The HEC-HMS hydrological model is then used to simulate the rainfall-runoff process, and the critical rainfall corresponding to different characteristic rainfall patterns is calculated with a trial algorithm. The results demonstrate that: (1) the critical rainfall calculated by the designed characteristic rainfall patterns is more accurate than that calculated by the traditional rainfall pattern (TRP), proving that the design method of characteristic rainfall patterns proposed in this paper could increase the accuracy of early warning of flash floods in small watersheds. (2) The effects of the antecedent soil moisture condition (ASMC) and rainfall pattern on the critical rainfall are analyzed, which provides a valuable reference for the analysis and calculation of the critical rainfall of flash floods in small watersheds.
... We can see that 11 events were correctly forecast, 1 event was forecasted as an MA, 14 events were forecasted as FAs, and 11 events had CA. These results led to the evaluation criteria of a POD of 91.7% and an FAR of 56% and an CSI of 42.3%, which is comparable with similar studies [37,38]. Based on this result, for the rain gauge data, the threshold-based forecasting system seems to have reliable performance. ...
Preprint
Full-text available
Convective rainfall can cause dangerous flash floods within less than six hours. Thus, simple approaches are required for issuing quick warnings. The Flash Flood Guidance (FFG) approach pre-calculates rainfall levels (thresholds) potentially causing critical water levels for a specific catchment. Afterwards, only rainfall and soil moisture information is required to issue warnings. This study applied the principle of FFG to the Wernersbach Catchment (Germany) with excellent data coverage using the BROOK90 water budget model. The rainfall thresholds were determined for durations of 1 to 24 hours, by running BROOK90 in “inverse” mode, identifying rainfall values for each duration that led to exceedance of critical discharge (fixed value). After calibrating the model based on its runoff, we ran it in hourly mode with four precipitation types and various levels of initial soil moisture for the period 1996 – 2010. The rainfall threshold curves showed a very high probability of detection (POD) of 91% for the 40 extracted flash flood events in the study period, however, the false alarm rate (FAR) of 56% and the critical success index (CSI) of 42% should be improved in further studies. The approach proved potential as an early flood indicator for head-catchments with limited available information.
... In the system, the model is used as a rainfall-runoff model in order to provide with current and forecasted soil moisture conditions and correlate them with the forecasted rainfall observations and predetermined thresholds to issue warnings. The system is well established (Norbiato et al. 2009) and has been also expanded outside the USA through the global flash flood guidance initiative (Clark et al. 2014;Putra et al. 2021). ...
Article
Full-text available
An evaluation of the Sacramento Soil Moisture Accounting (SAC-SMA) model was conducted to be used in flood event simulations with datasets at a time step up to one hour. The SAC-SMA model is a complex conceptual model which integrates two soil zones, the upper and lower zone, in order to provide current soil moisture conditions and generated streamflow. However, in flood events, where time intervals are small, the generated flood hydrograph is usually the product of only the upper soil layer runoff generation mechanism while the lower zone and baseflow have little impact. In this context, a modified version of the original SAC-SMA model was introduced, where only the upper zone processes are kept in order to reduce the parameter count and the overall model uncertainty involved, and a comparison was made against the original model output. The two models were calibrated and validated for a series of flood events occurred at the Karitaina basin of the Alfeios river, located in southern Greece. The results show that both model versions were able to reproduce the observed runoff with success. The simplified model showed high consistency with the original model in all cases, which is an obvious improvement to the original model, since it provided results of equal quality, while lowering significantly the total parameter count and the computing time. This contributes against the overall model generated uncertainty which is crucial for real-time data processing applications and flood forecasting systems. Highlights • Presentation of the SAC-SMA model concept, variables, parameters and flowchart. • Introduction of a modified – simplified version of the original SAC-SMA model to be used for event-based rainfall runoff applications. • Calibration and validation of the SAC-SMA using fine temporal scale datasets in a mountainous basin in Greece.
... For the event of October 2006 in the Isarco river system, ice-melt was observed. However, its contribution to the runoff was negligible (Norbiato et al., 2009). ...
Chapter
Flash floods are a very hazardous natural process causing major economic damage and fatalities under different climates (Douben, 2006). The potential for flash flood casualties and damage is also increasing in many regions due to the social and economic development increasing pressure on land use. Flash floods are characterised by rapid hydrological response, with discharges attaining the peak within less than one hour to a few hours. The fast time response of flash floods, which causes major concerns in the forecast of these processes and in the management of associated risks, is due to the small size of affected catchments (usually up to a few hundreds of square kilometres), as well as to the activation of rapid runoff processes. Flash floods are common also in alpine regions, where, due to the large availability of loose debris and to steep slopes, their occurrence is often associated to debris flows and shallow landslides on soil-mantled slopes. This results in the simultaneous occurrence of different types of hazards, which require different control measures.
... No matter whether an inverse or positive method is used, TR values are always computed by routing surface runoff using the UH method [1,6,17,19,22]. So deriving the UHs representing the true basin concentration characteristics is a key to calculating the CR estimate matching the minor rainfall value necessary to cause flooding. ...
Article
Full-text available
To obtain critical rainfall (CR) estimates similar to the rainfall value that causes minor basin outlet flooding, and to reduce the flash flood warning missed/false alarm rate, the effect of unit hydrographs (UHs) and rainfall hyetographs on computed threshold rainfall (TR) values was investigated. The Tanjia River basin which is a headwater subbasin of the Greater Huai River basin in China was selected as study basin. Xin’anjiang Model, with subbasins as computation units, was constructed, and time-variant distributed unit hydrographs (TVUHs) were used to route the channel network concentration. Calibrated Xin’anjiang Model was employed to derive the TVUHs and to obtain the maximum critical rainfall duration (Dmax) of the study basin. Initial soil moisture condition was represented by the antecedent precipitation index (Pa). Rainfall hyetographs characterized by linearly increasing, linearly decreasing, and uniform hyetographs were used. Different combinations of the three hyetographs and UHs including TVUHs and time-invariant unit hydrographs (TIVUHs) were utilized as input to the calibrated Xin’anjiang Model to compute the relationships between TR and Pa (TR-Pa curves) by using trial and error methodology. The computed TR-Pa curves reveal that, for given Pa and UH, the TR corresponding to linearly increasing hyetograph is the minimum one. So, the linearly increasing hyetograph is the optimum hyetograph type for estimating CR. In the linearly increasing hyetograph context, a comparison was performed between TR-Pa curves computed from different UHs. The results show that TR values for different TIVUHs are significantly different and the TR-Pa curve gradient of TVUHs is lower than that of TIVUHs. It is observed that CR corresponds to the combination of linearly increasing hyetograph and TVUHs. The relationship between CR and Pa (CR-Pa curves) and that between CR and duration (D) (CR-D curves) were computed. Warnings for 12 historical flood events were performed. Warning results show that the success rate was 91.67% and that the critical success index (CSI) was 0.91. It is concluded that the combination of linearly increasing hyetograph and TVUHs can provide the CR estimate similar to the minimum rainfall value necessary to cause flash flooding. 1. Introduction Flooding is the worst weather-related hazard, causing loss of life and excessive property damage [1–3]. In general, flash floods are characterized by their rapid onset, leaving very limited effective response opportunities [3–5]. Flood damage mitigation is provided through a variety of structural and nonstructural methods. A significant nonstructural method is the operation of flood warning systems [1]. Currently, three criteria are used for an expected flooding determination: critical discharge, critical runoff, and critical rainfall (CR). Critical rainfall criterion is used by most flood warning systems [3, 6–9]. Given an initial soil moisture condition and a rainfall duration (D), different hyetographs show the diverse areal rainfall volumes over the study basin necessary to cause minor basin outlet flooding which is defined as threshold rainfall (TR), and the minimum of these TR values is referred to as CR. That is to say, TR is a function of initial soil moisture condition, rainfall duration, and the form of rainfall hyetograph, but CR is a function of only initial soil moisture condition and rainfall duration. By comparing real-time observed or predicted rainfall volume of a given duration to the CR value, the CR-based flood warning systems decide whether to issue a warning. For early warning, the consequences of under- or overestimating the CR value are extremely different. Adopting a CR value higher than the rainfall volume that actually produces flood damage leads to missing such events and failure to issue an alarm. Underestimating the CR may instead determine the issue of false alarms [10]. For flood warning systems development, it is important to obtain as accurate as possible CR estimates. The most significant way to reduce missed/false alarm rate is to have the CR estimates be comparable to the minimum rainfall value necessary to cause flooding. The false warning costs are commonly not only much lower than the avoidable flood loss, but also cannot match up to indirect and/or intangible flood damages such as serious injury or loss of life [11, 12]. So considering that an error will always be present, it is better to underpredict rather than overpredict the CR estimate for safety reasons [10]. Currently, there are three CR value computation methods: inverse, positive, and empirical. The Flash Flood Guidance (FFG) system [6] is representative of an inverse method. The computational process of FFG is divided into three steps. First, the critical discharge value is estimated. In the second step, threshold runoff estimates for various rainfall durations are obtained based on critical discharge and unit hydrograph (UH) peak, which belongs to runoff concentration computation of hydrology. In the third step, the FFGs are obtained based on threshold runoff values where the rainfall vs. runoff curves as a function of soil moisture conditions are needed [13], which belongs to runoff generation computation of hydrology. A significant disadvantage of FFG is that uniform rainfall over rainfall duration is presumed [14]. The empirical methods are based on historical rainfall and streamflow data [15]. Miao et al. [15] proposed an empirical method to determine TR value by using a linear binary classification based on long-term historical rainfall and flood data. Enough flood event data are necessary to derive the binary classification. So this method cannot be implemented in ungauged basins. The positive methods based on a watershed hydrological model estimate the TR values from critical discharge by trial and error [16, 17]. The hydrological responses of different cumulative rainfall values, for fixed duration, initial soil moisture condition, and hyetograph type, are simulated by calibrated watershed hydrological model. The cumulative rainfall value generating the critical discharge is taken as the TR estimate. The computation process of the positive method has an explicit hydrology theoretical basis, so the disadvantages inherent in the inverse method may be overcome. In this study, the calibrated Xin’anjiang Model with its subbasins being used as computation units [18] is employed to compute TR and CR values. Montesarchio et al. [3] estimated TR values for the Mignone River cross section using an entropy-based decision approach and a simulation approach based on radar data and rain gauge data. Results show that the TR values computed using various methods are obviously different and that, for the fixed watershed hydrological model, the type of rainfall data source used for model calibration significantly affects the TR estimates. According to hydrological rainfall-runoff formation theory, for a fixed computing method, the TR estimate is generally a function of initial soil moisture condition, rainfall duration, and hyetograph. The effect of initial soil moisture conditions has been taken into account in the vast majority of current methods [6, 7, 16, 17, 19, 20]. In [6], the rainfall vs. runoff curves were taken as a function of initial soil moisture content to take into account the effect of initial soil moisture conditions on TR estimates. In [3, 7, 16], initial soil moisture conditions were classified into antecedent moisture classes AMC I, AMC II, and AMC III, representing dry soil, moderately saturated soil, and wet soil, according to the total amount of accumulative rain. In [17], the initial soil moisture conditions were taken into account by imposing an initial discharge value of the watershed hydrological model, and the effect of different initial conditions is analyzed by varying the initial discharge in the model simulations. In [19], a probability distributed moisture model was used to estimate the soil moisture content as the initial soil moisture condition of a rainfall-runoff model employed to compute TR values. In [20], both AMC and antecedent precipitation index (API) were utilized to estimate the initial soil conditions. Given an initial soil moisture condition, for the same rainfall volume, the hydrographs and peak discharge rates may be significantly different when different rainfall hyetographs are adopted [16, 17, 21]. Consequently, for the same initial soil moisture conditions, various hyetograph types result in different TR values [16, 17]. In [17, 21], three synthetic hyetograph types characterized by linearly increasing intensity, decreasing intensity, and linearly increasing-decreasing intensity were employed to investigate the effect of rainfall hyetograph type on the hydrograph at given rainfall volume. In [16], four standards hyetographs including step hyetograph, triangular increasing rate hyetograph, triangular decreasing rate hyetograph, and isosceles triangular hyetograph were used to analyze the effect of rain type on TR estimates. If the hyetograph type corresponding to the minimum rainfall necessary to cause flooding is found, it can be used to directly compute CR value. So determining the hyetograph type corresponding to the minimum rainfall to cause flooding is one objective of this work. No matter whether an inverse or positive method is used, TR values are always computed by routing surface runoff using the UH method [1, 6, 17, 19, 22]. So deriving the UHs representing the true basin concentration characteristics is a key to calculating the CR estimate matching the minor rainfall value necessary to cause flooding. For more than 75 years since the inception of UH theory was presented by Sherman, it is still one of the most widely used methods for flood prediction and warning system development in gauged basins with observed rainfall and runoff data, but this data-driven traditional approach limits the UH derivation only to gauged watersheds. Synthetic UHs may only be used in basins whose hydrographs have a single peak [23–25]. Geomorphologic UHs, regardless of time-invariant (TIVUH) [26–31] or time-variant (TVUH) [32, 33], do not take the dynamic factor (flow velocity) spatial distribution into account. Distributed UHs based on a spatially distributed velocity field can adequately take the nonuniformity of basin characteristics into account [34–36]. Formulas defined as a function of rainfall intensity are adopted to compute spatially distributed velocity fields so as to derive TVUHs [18, 37, 38] that can solve to a certain extent the nonlinear problem of runoff concentration. For a fixed runoff generation computing method, different rainfall-runoff transformation methods may lead to different TR estimates. By doing this work, investigating the effect of UHs on TR estimates and suggesting a reasonable UH used in computing CR value is another study objective. In this study, three rainfall hyetograph types (linearly increasing, linearly decreasing, and uniform) and two UH types (TIVUHs and TVUHs) are used to investigate the effects of hyetographs and UHs on TR/CR estimates and warning results. The objectives are (1) to explain, for fixed duration and initial conditions, that rainfall hyetographs and UHs significantly affect the TR estimates; (2) to suggest that the rainfall hyetograph type leading to minimum TR estimate and the UH resulting in optimal simulation results should be adopted to compute CR estimates; and (3) to propose a method for CR computation. Determining TR and CR value is a hydrological problem. The uncertainties of TR and CR estimates related principally to the method (including runoff generation and runoff concentration), parameters, data sources (including rainfall and discharge), and adopted rainfall hyetograph types [3, 16, 17, 21]. In this work, the method based on watershed hydrological model was used. For the fixed study watershed and data sources (observed data), in order to obtain the CR estimate approximate as far as possible with the minimum rainfall value necessary to cause flooding, the appropriate model (Xin’anjiang Model and UHs) and opportunely calibrated parameters were employed. For nonlinear types, no matter increasing or decreasing, the forms of rainfall hyetograph are innumerable. In this study, the linearly change hyetograph types were used. In fact, the rainfall hyetograph corresponding to the minimum rainfall value causing flooding is nonlinear. This paper consists of six sections: Section 2 introduces the methods used in the study including the watershed hydrological model structure, TR and CR computation methods, and warning system assessment method. Section 3 describes the study basin and model calibration. Section 4 introduces the computation process and results of CR. In Section 5, the application of CR values in warnings historical flood event is performed. Finally, some conclusions are presented in Section 6. 2. Methods 2.1. Watershed Hydrological Model 2.1.1. Structure of Model The Xin’anjiang Model is employed in this study and the basin is divided into a series of subbasins as computation units. Runoff generation and flow concentration computations are performed within the subbasins and the runoff from each subbasin is routed to the main basin outlet. The total hydrograph at the main basin outlet is equal to the sum of all subbasin hydrographs. 2.1.2. Rainfall Computation Component The Kriging interpolation method is used to derive rainfall depth of all cells within subbasins from that of rainfall gauges. Mean areal rainfall values of each subbasin are computed by arithmetic mean method using rainfall depth for all cells within the subbasin. 2.1.3. Runoff Generation Computation Component A tension water storage capacity curve, also named a parabolic curve, is used to represent the nonuniform distribution of tension water storage capacity and to compute the runoff value. The computational equations are as follows:where PE is the rainfall value, mm; R is the runoff value, mm; W is the mean areal tension water storage, mm; WM is the mean areal tension water storage capacity, mm; WMM is the maximum tension water storage capacity of the watershed, mm; and b is the tension water capacity distribution curve exponent (parabolic curve). A free water storage capacity curve is used to represent the nonuniform distribution of free water storage capacity over runoff-producing areas and to separate runoff R into surface flow, interflow, and groundwater. Computational equations are as follows:where PE is the rainfall value (equal to excess rainfall R in the runoff-producing area), mm; RS, RI, and RG are surface flow, interflow, and groundwater, respectively, mm; S is the equivalent free water storage over the runoff-producing area, mm; SM is the area mean free water storage capacity (maximum possible deficit of free water storage), mm; EX is the free water storage capacity curve exponent (parabolic curve); SMM is the maximum watershed free water storage capacity, mm; FR is runoff-producing area; KI is the outflow coefficient of free water storage to interflow; and KG is the outflow coefficient of free water storage to groundwater. Estimating initial soil moisture conditions is necessary for runoff generation computation. In this study, the antecedent precipitation index (Pa), used in the past as a moisture content indicator, is used and calculated at the beginning of every storm event as follows:where Pa,i is the antecedent precipitation index, mm; is daily rainfall, mm; i is day of estimate; and k is depletion constant (in this study, k = 0.83 [39]). Because the tension water storage capacity curve is a parabolic type, the relationship between Pa and W is as follows: 2.1.4. Concentration Computation Components (1). Hillside concentration. The surface flow passing directly into the channel systems is treated as TRS, and the interflow RI and groundwater RG are routed through linear reservoirs into channel systems as TRI and TRG. The computational equations are as follows:where TRS, TRI, and TRG are inflow into channel systems of surface flow, interflow, and groundwater, respectively, m³/s; TTR is the total inflow, m³/s; U is the transformation coefficient transforming runoff depth to discharge rate, , where F is the drainage area, km², and is computational time interval, h; CI is the recession constant of interflow storage; CG is the recession constant of groundwater storage. (2). Channel network concentration. The channel network routing within a subbasin is represented by convolution of TTR(t) with a dimensionless UH as follows:where Q(t) is the subbasin outlet discharge rate, m³/s; UH is the ordinate of dimensionless unit hydrograph; and N is the number of dimensionless UH time intervals. The method presented by Kong et al. [18] is used to derive the TVUHs of each subbasin. Given a velocity within a cell of DEM, the travel time through the cell is computed as follows:where τk is the travel time within cell k, s; L is cell size, m; and Vk is the velocity within cell k, m/s. The travel time of a cell to subbasin outlet is computed as follows:where Tj is the travel time of cell j to the subbasin outlet, s; m is the number of cells along the drainage network to subbasin outlet; τk is the travel time within cell k, s. Based on the travel time of all cells to the subbasin outlet, the S-hydrograph of dimensionless UH can be obtained as follows:where St is the ordinate value of S-hydrograph at time t; F is the subbasin area, km²; Aj is the area of cell j, km²; and n is the number of cells whose T being less than or equal to t. The ordinate of dimensionless UH is computed as follows:where Δt is computational time interval, h. It can be seen that the key to obtain UH is deriving the velocity of each cell. The fundamental equation form used to compute velocity is as follows:where k is a coefficient based on the flow type; Sorrell et al. [40] provide values of k for several flow types; and S is the flow path slope. To take the effect of excess rainfall intensity on velocity into account, equation (17) is modified as follows:where i is the excess rainfall intensity, mm/h; i0 is the excess rainfall intensity corresponding to the coefficient k, determined by calibration; and c is a parameter, on the basis of literature [37, 38], with 0.4 being adopted. Equation (18) can not only take into account the effect of excess rainfall intensity on velocity, but also can employ the values of k provided by Sorrell et al. [40]. By using equation (18), the time-variant spatially distributed velocity fields and TVUHs of different rainfall duration in a rainfall event are derived. 2.1.5. Channel Routing Method The dynamic Muskingum method presented by Tewolde et al. 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For a given D (taken as an integer multiple of Δt), Pa, and a combination of hyetograph type and UH, computation steps of TR value are as follows: (1) D is divided into n time intervals; (2) according to the hyetograph, the proportion of each time interval rainfall to total rainfall of D (P) is determined; (3) trial and error: for a given P, running hydrological model to derive discharge hydrograph and comparing peak rate and critical discharge value. The P making the computed peak rate equal or close to critical discharge value is taken as the TR value. 2.2.2. CR Computation CR is related only to D and Pa. For a given Pa and D combination, the minimum of all TR values is taken as the CR value. The relationship between CR and Pa of different D and the relationship between CR and D of different Pa are obtained, being the basis of flash flood warning. 2.3. Representation of Warning Results The contingency table (Table 1) shows four possible results for a single flash flood warning, X denotes an event occurred and warning was issued (hits), Y denotes an event occurred but warning was not issued (missed events), Z denotes an event did not occur but warning was issued (false alarms), and W denotes an event did not occur and warning was not issued. Observations Forecasts Warning No warning Event X Y Nonevent Z W
... At gauged locations in which a reliable rating curve is available bank full water level values can be used as the Thresh-R [27]. For ungauged sites, Thresh-R values can be estimated from the flow frequency analysis of simulation datasets [28]. ...
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A hierarchical scheme for the systematic testing of hydrological simulation models is proposed which ties the nature of the test to the difficulty of the modelling task. The testing is referred to as operational, since its aim is merely to assess the performance of a model in situations as close as possible to those in which it is supposed to be used in practice; in other words, to assess its operational adequacy. The measure of the quality of performance is the degree of agreement of the simulation result with observation. Hence, the power of the tests being proposed is rather modest, and even a fully successful result can be seen only as a necessary, rather than a sufficient, condition for model adequacy vis-à-vis the specific modelling objective. The scheme contains no new and original ideas; it is merely an attempt to present an organized methodology based on standard techniques, a methodology that can be viewed as a generalization of the routine split-sample test. Its main aim is to accommodate the possibility of testing model transposability, both of the simple geographical kind and of more complex kinds, such as transposability between different types of land use, climate, and other types of environmental changes.
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The principles governing the application of the conceptual model technique to river flow forecasting are discussed. The necessity for a systematic approach to the development and testing of the model is explained and some preliminary ideas suggested.
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