Generation of a Design Flood-Event Scenario for a Mountain River with Intense Sediment Transport

water

Article Generation of a Design Flood-Event Scenario for a Mountain River with Intense Sediment Transport

Alessio Radice *, Laura Longoni, Monica Papini, Davide Brambilla and Vladislav Ivov Ivanov

Department of Civil and Environmental Engineering, Politecnico di Milano, 20133 Milano, Italy; [email protected] (L.L.); [email protected] (M.P.); [email protected] (D.B.); [email protected] (V.I.I.) * Correspondence: [email protected]; Tel.: +39-2-2399-6251

Academic Editor: Peggy A. Johnson Received: 13 October 2016; Accepted: 12 December 2016; Published: 16 December 2016

Abstract: International directives encourage the incorporation of sediment transport analyses into flood risk assessment, in recognition of the significant role played by sediment in flood hazard. However, examples of risk analysis frameworks incorporating the effect of sediment transport are still not widespread in the literature, resulting in a lack of clear guidelines. This manuscript considers a study site in the Italian Alps and presents a hydro-morphologic model for generation of flood scenarios towards hazard assessment. The analysis is concentrated on a design flood event with 100-year return period, for which an outflowing discharge is computed as a result of the river modeling. However, it is also argued how suitable model input parameter values can be obtained from analyses of river flows in a yearly duration curve. Modeling tools are discussed with respect to their capabilities and limitations. The results of the analysis are site-specific, but the proposed methodology can be exported to other hydro-graphic basins.

Keywords: mountain catchments; flash flood; flood hazard; design flood scenario; sediment transport; river morphology; inundation

1. Introduction In recent years, several studies have demonstrated a major role of sediment in fluvial floods. It has been argued, for example, that stream morphological changes taking place over long periods may significantly change the river response to high flows, e.g., [1–3]. In addition, it has been shown that, sometimes and particularly in mountainous regions, the temporal scales of flow variation and morphological change can be equivalent to each other, resulting in a coupled process, e.g., [4,5]. Thus, a sudden increase of river bed elevation would significantly facilitate stream outflow. Similar arguments have been taken into account by international guidelines. For example, the European Floods Directive [6] mentions that flood risk maps resulting from calamitous scenarios should include information about “areas where floods with a high content of transported sediments and debris floods can occur”. Hydro-morphologic models are effective tools for studying the sediment transport in a river. These models are mostly based on shallow-water equations for one-dimensional and two-dimensional frameworks, with the former (e.g., [7–9]) mostly used for mountain environments. Hazard assessment can be thus performed accounting for the presence and transport of sediment. The results may however suffer from significant uncertainties due to the complexity of the involved processes. Uncertainty analysis can be included by accounting for the variability resulting from different parameterizations of the scenarios, but examples of such approaches are still limited (e.g., [10]). All of the above considerations are particularly relevant for the Italian Alps. This paper addresses the case-study of the Valmalenco catchments, where the main water course is the Mallero River. The site

Water 2016, 8, 597; doi:10.3390/w8120597 www.mdpi.com/journal/water Water 2016, 8, 597 2 of 16 was chosen because several data are available from studies (e.g., [11–14]) performed after a significant flood event of 1987 and, furthermore, the public protection tools presently available to local authorities do not adequately account for an expected effect of sediment on the flood risk (e.g., [15]). The objective of the work is to assess the capabilities and discuss the limitations of hydro-morphologic modeling towards the assessment of hazard levels for the main town situated close to the downstream section of the basin. Therefore, the modeling sequence proposed in this work comprises (i) the short-term hydro-morphologic evolution of the downstream reach of the river consequent to the propagation of a flood wave (the short term is here intended in an engineering sense and is therefore on the order of hours/days) and (ii) the quantification of an expected outflow into the town. The distinctive feature of the present work compared to several others performed by the authors on the same case-study [16–20] is the introduction of a design flood scenario rather than the consideration of a previous flood in a back analysis. The present study meets a local societal thrust and is also relevant in light of the existing literature. Even though some consolidated mathematical/numerical tools are employed for the hydro-morphologic analyses, the novelty of the study lies in the two-way link of (i) a risk-oriented interpretation of the modeling results, that is not present in works where the modeling tools are developed (e.g., [7–9]) and (ii) an appropriate account of sediment in the hazard assessment. For example, [21], presented a similar modeling sequence spanning from water discharge to flood damages, but did not consider the contribution of sediment. The study [10] lacked quantification of a sediment supply into the modeled river reach and considered random values for the sediment volume, albeit acknowledging a crucial need for an appropriate “yield function”. Here the issue of the sediment supply is discussed in light of the earlier results for few case-studies and of new sensitivity analyses. The manuscript is organized as follows: first, the case-study is presented; second, hydro-morphologic evaluations are performed with reference to flows in a yearly duration curve to obtain parameter values to be used in short-term modeling; third, a flood scenario corresponding to a hydrograph with a 100-year return period (henceforth indicated as the ‘design’ scenario) is simulated resulting in the estimation of a flooding hydrograph for the town; fourth, the results are discussed in terms of feasibility and limitations of modeling and of directions for future research, and the main conclusions are summarized.

2. The Valmalenco Catchments and the Mallero River

2.1. The Hydro-Graphic Basin The river basin considered in this study is located in Northern Italy (Figure1), with an area of around 320 km2 and altitude ranging from 280 to 4050 m a.s.l. Average precipitation is between 1000 and 1500 mm/year, with higher values generally corresponding to higher elevations. From a geological point of view, significant lithological heterogeneity is documented, including various metamorphic and sedimentary rocks. At the highest elevations, outcropping metamorphic and magmatic formations with local debris cover are present. Glacial deposits cover a wide surface of steep slopes at altitudes between 2100 and 2400 m a.s.l., whereas at higher altitude only localized glacial deposits can be found. The lower part of the valley is covered with glacial and colluvial deposits of variable thickness [22]. The soil cover (see Figure1) is mostly associated with debris accumulations and lithoid outcrops deprived of vegetation (37% of the total area), coniferous forests of medium and high density (20%), sparse vegetation (10%), and glaciers and permanent snowfields (8%). Several landslides are present along the upper course of the Torreggio River and a large rock landslide is located near the village of Spriana. The sediment supply in the basin is the result of diverse geomorphic processes, corresponding to different geological and geomorphological characteristics of the areas where they develop. The active phenomena generating sediment supply into the river course have been defined by [14] as basal erosion limited to short reaches of the riverbed, diffuse bank erosion, unstable slopes scattered throughout the WaterWater2016 2016, 8,, 597 8, 597 3 of3 16 of 16

erosion (including the action of runoff water on moraine deposits that are present in the higher entirezones basin of the (whose basin). activity can be increased by thawing), and widespread hillslope erosion (including the actionInhabited of runoff areas water correspond on moraine to 1% deposits of the thattotal are surface present of inthe the watershed. higher zones The most of the populated basin). townInhabited of the areasvalley correspond (Sondrio, with to 1% around of the total22,000 surface inhabitants) of the watershed.is located close The mostto the populated downstream town of thesection. valley (Sondrio, with around 22,000 inhabitants) is located close to the downstream section.

Figure 1. The Mallero catchments in Northern Italy with land cover, major streams, and towns. Figure 1. The Mallero catchments in Northern Italy with land cover, major streams, and towns.

2.2. The River 2.2. The River The 25‐km long Mallero River is the major water stream of the basin (Figure 1). The springs of theThe river 25-km are located long Mallero at an altitude River is of the 1650 major m a.s.l., water while stream the of downstream the basin (Figure section1). of The the springs watershed of the rivercoincides are located with at the an inflow altitude of of the 1650 Mallero m a.s.l., into while the theAdda downstream River that sectionis the main of the water watershed course coincides of the withValtellina the inflow valley. of theThe Malleromost important into the tributaries Adda River are thatthe Lanterna, is the main Torreggio, water course and Antognasco. of the Valtellina The valley.Mallero The is most characterized important by tributaries a highly variable are the Lanterna,slope, the Torreggio,latter ranging and from Antognasco. 4% to 40% The in the Mallero high is characterizedcourse and decreasing by a highly to variableless than slope, 1% in the last latter 2 km ranging before from the confluence 4% to 40% (see in thethe highbed profile course for and decreasingthe last 9.5 to km less in than Figure 1% 2). in theThe lastbed 2 granulometry km before the according confluence to two (see surveys the bed from profile 1989 for and the 1990 last 9.5 [14] km inis Figure presented2). The in bedFigure granulometry 3. For the survey according from 1989, to two longitudinal surveys from variability 1989 and was 1990 given [ 14for] isd10 presented and d50 in(with Figure d3 as. For the the sediment survey size from and 1989, a subscript longitudinal as the variability percentage was in the given granulometric for d10 and distribution).d50 (with d as theComplete sediment granulometric size and a subscript curves were as the given percentage by [14] for in some the granulometriclocations; characteristic distribution). sediment Complete sizes granulometriccould be extracted curves from were these given curves by [and14] fordata some for d10 locations; and d50 were characteristic also included sediment in the plot. sizes The could river be presents the typical variability of a mountain water course, with the median sediment size ranging extracted from these curves and data for d10 and d50 were also included in the plot. The river presents thefrom typical a few variability cm to more of a than mountain 1 m. Sediment water course, sizes with are typically the median larger sediment in the upstream size ranging portion from and a few cmdecrease to more thantowards 1 m. the Sediment river outlet. sizes Two are typically regions with larger the in largest the upstream sediment portion sizes andare recognizable decrease towards at thearound river outlet. 5000 m Two and regions15,000 m, with the former the largest corresponding sediment sizesto the are Cassandre recognizable gorge atin aroundFigure 2. 5000 m and The river flows through Sondrio just downstream of a sharp bend (Figure 4), with a transverse 15,000 m, the former corresponding to the Cassandre gorge in Figure2. section that in this reach is approximately rectangular and has a width of around 40 m. Four bridges The river flows through Sondrio just downstream of a sharp bend (Figure4), with a transverse (also shown in Figure 2) are present in the in‐town reach. The flow duration curve at Sondrio was section that in this reach is approximately rectangular and has a width of around 40 m. Four bridges estimated based on records taken during the 1990s and ranges from a few m3/s to around 150 m3/s, (also shown in Figure2) are present in the in-town reach. The flow duration curve at Sondrio was the 182‐day discharge being around 7 m3/s (Figure 5). estimated based on records taken during the 1990s and ranges from a few m3/s to around 150 m3/s, the 182-day discharge being around 7 m3/s (Figure5).

Water 2016, 8, 597 4 of 16 Water 2016, 8, 597 4 of 16 Water 2016, 8, 597 4 of 16 Water 2016, 8800, 597 4 of 16 800 800 Start of the 600 computationalStart of the reach 600 computational reach Torre In-town bridges Start of the SantaTorre Maria 600 In-town bridges computational reach Spriana Santa Maria Torre 400 In-town bridges Spriana

elevation (m) elevation Santa Maria 400 Spriana elevation (m) elevation Cassandre gorge 400 Cassandre gorge elevation (m) elevation Bend upstream of the town 200 Bend upstream of the town Cassandre gorge 200 0 2000 4000 6000 8000 10000 0 2000Bend upstream of 4000 the town 6000 8000 10000 200 distance (m) 0 2000 4000distance (m) 6000 8000 10000 Figure 2. Longitudinal profile of the river bed in the last 9.5 km before the confluence, up to the town Figure 2. Longitudinal proﬁle of the river bed indistance the last (m) 9.5 km before the conﬂuence, up to the town ofFigure Torre 2. Santa Longitudinal Maria in profileFigure of1. the river bed in the last 9.5 km before the confluence, up to the town of TorreFigureof Torre Santa 2. SantaLongitudinal Maria Maria in Figure in profile Figure1. of 1. the river bed in the last 9.5 km before the confluence, up to the town of Torre Santa1000 Maria in Figure 1. 1000 1000

100 100 100

10 10 10

sediment size size (mm) sediment 1 sediment size size (mm) sediment 1

sediment size size (mm) sediment 1 d_10 1989 d_50 1989 d_10 [14] d_50 [14] 0.1 d_10 1989 d_50 1989 d_10 [14] d_50 [14] 0.1 0 5000 10000 15000 20000 25000 d_10 1989 d_50 1989 d_10 [14] d_50 [14] 0 5000 10000 15000 20000 25000 0.1 distance (m) 0 5000 10000 15000 20000 25000 distance (m) Figure 3. Sediment size along the river course distanceaccording (m) to a survey by Techint in 1989 and [14], Figure 3. Sediment size along the river course according to a survey by Techint in 1989 and [14], Figured_p 3. indicatingSediment the size size alongcorresponding the river to coursep percent according in the granulometric to a survey distribution. by Techint in 1989 and [14], Figured_p indicating 3. Sediment the size size corresponding along the river to coursep percent according in the granulometric to a survey bydistribution. Techint in 1989 and [14], d_p indicating the size corresponding to p percent in the granulometric distribution. d_p indicating the size corresponding to p percent in the granulometric distribution.

Figure 4. The Mallero River (shaded) crossing the town of Sondrio (map extracted from the Regional TechnicalFigure 4. TheChart Mallero of Lombardia). River (shaded) The course crossing of the the Mallero town of is Sondrio depicted (map in the extracted last 2 km from until the the Regional inflow FigureTechnical 4. The Chart Mallero of Lombardia). River (shaded) The course crossing of thethe Mallerotown of isSondrio depicted (map in theextracted last 2 km from until the the Regional inflow Figureinto 4. theThe Adda. Mallero The River black (shaded) thick lines crossing represent the town four ofin‐ Sondriotown bridges, (map extractednamed Garibaldi, from the Eiffel, Regional TechnicalMarcora,into the andAdda.Chart Railway ofThe Lombardia). blackfrom upstreamthick The lines course to downstream.represent of the Mallero four in is‐ towndepicted bridges, in the lastnamed 2 km Garibaldi, until the inflowEiffel, TechnicalintoMarcora, the Chart Adda.and of Railway Lombardia).The black from thickupstream The lines course to represent downstream. of the Mallero four in is‐town depicted bridges, in the named last 2 Garibaldi, km until theEiffel, inﬂow intoMarcora, the Adda. and The Railway black from thick upstream lines represent to downstream. four in-town bridges, named Garibaldi, Eiffel, Marcora, and Railway from upstream to downstream.

Water 2016, 8, 597 5 of 16 Water 2016, 8, 597 5 of 16

120 /s) 3 80

40 flow rate (m rate flow

0 0 100 200 300 duration (days)

Figure 5. FlowFlow duration duration curve curve at at Sondrio (data from 1992 to 1998 in black, average curve in blue).

2.3. Past Events Several flash flash floods floods occurred in the past: events have have been reported for for 1817, 1834, 1885, 1911, 1927, and 1987. According According to, to, for for example, example, [14], [14], the the majority of of the high-flowhigh‐flow events have been recorded during thethe summer summer and and autumn autumn seasons, seasons, and and thus thus could could be attributedbe attributed to precipitation to precipitation only. only.Events Events of particular of particular intensity intensity have not have been not recorded been duringrecorded spring during and, spring therefore, and, the therefore, contribution the contributionof snowmelt of to thesnowmelt discharge to the of Mallero discharge can of be Mallero considered can negligible.be considered The negligible. existing documentation The existing documentationhighlights that flood highlights hazard that for Sondrio flood hazard is mostly for represented Sondrio byis sedimentmostly represented depositing inby the sediment in-town depositingreach and reducing in the in the‐town section reach conveyance. and reducing A floodthe section in July conveyance. 1987 (for a return A flood period in July of 50–60 1987 years)(for a wasreturn relatively period of well 50–60 documented years) was by relatively some post-event well documented studies (e.g., by [some11–14 post]). The‐event peak studies water (e.g., discharge [11– was14]). 500The m peak3/s, water to be compareddischarge was with 500 an estimatedm3/s, to be value compared of 640 with m3/s an for estimated a return value period of of640 100 m3 years;/s for athe return total period sediment of 100 volume years; mobilized the total sediment throughout volume the catchments mobilized throughout was 3 × 10 6them 3catchments; sediment sourceswas 3 × were106 m mostly3; sediment represented sources by were distributed mostly erosionrepresented (contributing by distributed for ~40%), erosion landslides (contributing along the for Torreggio ~40%), landslidestributary (~30%), along the bank Torreggio erosion (~15%), tributary and (~30%), remobilization bank erosion (~15%), (~15%), frequently and remobilization associated to structure (~15%), frequentlycollapse; the associated sediment to yield structure into the collapse; river 5 the km upstreamsediment yield of the into confluence the river was 5 km 7 × upstream105 m3 (with of the no 5 3 confluencefurther significant was 7 × 10 yield m from (with the no valleyfurther slopes significant downstream yield from of the that valley location); slopes around downstream 2.2 × 10of5 thatm3 5 3 werelocation); deposited around in 2.2 the × 10 in-town m were reach, deposited with aggradationin the in‐town depths reach, upwith to aggradation 5 m that represented depths up ato very 5 m thatsignificant represented fraction a ofvery the significant total bank heightfraction (ranging of the total from bank 5 to 8 height m in the (ranging in-town from reach). 5 to As 8 discussed m in the inby‐town [17], amongreach). others,As discussed the bank-full by [17], discharge among others, in the in-townthe bank reach‐full discharge is around 700in the m3 in/s‐town considering reach is a 3 3 aroundnon-aggraded 700 m bed,/s considering whilst it decreases a non‐aggraded to 150 m 3bed,/s considering whilst it decreases the aggradation to 150 m that/s occurredconsidering during the aggradationthe flood of 1987.that occurred During thisduring event, the however, flood of 1987. the town During was this not event, flooded. however, This was the later town explained was not flooded.considering This that was as later confirmed explained by numerical considering simulations that as confirmed (e.g., [17 ]),by most numerical of the simulations aggradation (e.g., took [17]), place mostduring of the the tail aggradation of the event took where place the during discharge the was tail alreadyof the event much where lower thanthe discharge the peak value.was already much lower than the peak value. 3. Design Flood Scenario Modeling 3. Design Flood Scenario Modeling Historical records demonstrate that the town of Sondrio is prone to flash-floods, whose danger can beHistorical significantly records exacerbated demonstrate by highthat the sediment town of transport Sondrio causing is prone aggradation to flash‐floods, of the whose river danger bed in canthe in-townbe significantly reach. Therefore, exacerbated any by design high scenariosediment developed transport forcausing risk assessment aggradation shall of the account river forbed the in thedescribed in‐town dynamics. reach. Therefore, any design scenario developed for risk assessment shall account for the describedSediment dynamics. may be supplied by different sources, which may contribute to the total yield of the basinSediment (e.g., [23]). may Hillslope be supplied erosion by [ 24different], bank erosionsources, [ 25which], and may concentrated contribute sources to the total [26] are yield the of main the basincontributors. (e.g., [23]). This Hillslope study conceptually erosion [24], considered bank erosion the contribution[25], and concentrated of distributed sources erosion [26] and are scattered,the main contributors.local sediment This sources. study By conceptually contrast, the sedimentconsidered that the could contribution be supplied of by distributed large landslides erosion such and as scattered,the one of Sprianalocal sediment was not takensources. into By account. contrast, Such the a landslide sediment is inthat fact could characterized be supplied by an extremelyby large landslideslarge estimated such volume as the (moreone of than Spriana 20 Mm was3 as reportednot taken by into [27, 28account.]) and its Such collapse a landslide would thus is in lead fact to characterizeda dam-break wave by an rather extremely than a large flash estimated flood (e.g., volume [18]). (more than 20 Mm3 as reported by [27,28]) and itsThe collapse river reach would considered thus lead for to thea dam assessment‐break wave corresponded rather than to a the flash last flood 5 km (e.g., before [18]). the confluence withThe the Addariver (seereach again considered Figures1 forand the2), whereasassessment the in-towncorresponded reach corresponded to the last 5 to km the before last 2 km. the confluenceThe choice towith model the thisAdda reach (see followed again Figures the will 1 toand reduce 2), whereas the effect the of in any‐town sediment reach supplycorresponded condition to the last 2 km. The choice to model this reach followed the will to reduce the effect of any sediment supply condition at the upstream boundary. Previous investigations [16,17] demonstrated that

Water 2016, 8, 597 6 of 16 at the upstream boundary. Previous investigations [16,17] demonstrated that considering the typical duration of an event, the results of hydro-morphologic models were very sensitive to the upstream boundary condition in the upper portion of the modeled reach, but practically insensitive in the in-town reach. In this work, a 100-year return period was considered for the river flood. Using a 100-year return period (or 200-year for larger rivers) is a standard practice in Italy. However, since initial conditions can influence the dynamics of a river reach (see, for example, [29], who also studied the Mallero River), the sediment transport was also preliminarily investigated for flows in the yearly duration curve in order to characterize the river behaviour over a longer term.

4. Hydro-Morphologic Analysis for Flows in the Yearly Duration Curve Several computations were performed for a series of flow rates in the average duration curve (Table1). The objective of these computations was to calculate the critical sediment size, intended as the size of the largest sediment particle that can be transported by the flow at a certain section. A threshold value of the Shields [30] number of 0.05 was assumed as a reference. Local bed shear stresses were determined by clear-water hydraulic computations performed with the assumption of a fixed bed. Figure6 presents a stream-wise evolution of the critical sediment size for a variety of flow rates (only some of those listed in Table1 are depicted for the sake of plot readability), together with an average critical size whose computation took into account the durations corresponding to each value of the discharge and, in turn, of the critical diameter. For interpretative purposes, the continuous variability of the river properties was divided into two homogeneous reaches based on the mean value of the critical size. The two reaches corresponded well with the different slopes in the river reach under consideration (Figure7). A duration curve for the mean critical diameter of each reach could be built accordingly (Figure8). The duration-averaged values of the critical diameters reasonably matched the surveyed sediment sizes (Figure9). This was interpreted as an indication of stability of the river profile for ordinary flows. In turn, it was assumed that using the computed sediment sizes in the river would correspond to a good initial condition for a short-term hydro-morphologic model that shall be described below. Reach-averaged sediment sizes (dashed lines in Figure9) were 50 and 150 mm in the downstream and upstream homogeneous reaches, respectively. An abrupt transition in sediment size was thus introduced at 1.8 km from the end of the river, analogous to the gravel-sand transition described for courses with lower slope (e.g., [31]). Converting a continuous variability into a sharp transition was in part an arbitrary operation. In the following sections, sensitivity analyses will be presented for the chosen location of the transition. The sediment transport capacity of the river was also investigated for these flow conditions, as computed by the Meyer-Peter and Muller formula [32]. The yearly sediment volume transported in the downstream reach is 6 × 105 m3, and the volume for the upstream reach is 3 × 106 m3. Such volumes should be ensured by the sediment productivity of the catchments. Several models are available for estimation of these volumes (see, for review, [33,34]). The study from [20] applied the Erosion Potential Method (described in [20,34]) finding yearly sediment yields on the order of 105, in agreement with present computations, but suggesting a transport-limited and supply-limited behaviour of the downstream and upstream reaches, respectively.

Table 1. Flow rates in the yearly duration curve used for the analysis of sediment transport.

Flow Rate (m3/s) 108 59 40 23 14 11 8 7 5 3 Duration (Days) 1 5 10 30 60 91 135 182 274 355 Water 2016, 8, 597 7 of 16 WaterWater 2016 2016, 8, ,8 597, 597 7 7of of 16 16 Water 2016, 8, 597 7 of 16 Water 2016, 8, 597 7 of 16 1000 10001000 1000 100 100100 100 10 1010 Q=3 Q=23 Q=40 10 Q=3 Q=23 Q=40

critical diameter (mm) Q=3 Q=23 Q=40

critical diameter (mm) Q=108 mean upstream mean downstream critical diameter (mm) 1 Q=108Q=3Q=108 Q=23meanmean upstream upstream Q=40meanmean downstream downstream

critical diameter (mm) 1 10Q=108 2500mean upstream mean downstream 5000 1 0 2500 5000 0distance 2500 (m) 5000 0distancedistance 2500 (m) (m) 5000 distance (m)

FigureFigure 6. 6.Stream Stream‐wise‐wise variability variability of ofthe the critical critical sediment sediment size size for for a rangea range of offlow flow discharges discharges within within Figure 6. Stream‐wise variability of the critical sediment size for a range3 of flow discharges within theFigure Figureyearly 6. Stream-wise 6.duration Stream ‐curve.wise variability variability Flow rates of of the inthe criticalthe critical legend sediment sediment are expressed size size for for a in rangea mrange/s. of3 of ﬂow flow discharges discharges within within the thethe yearly yearly duration duration curve. curve. Flow Flow rates rates in in the the legend legend are are expressed expressed in in m m3/s./s. yearlythe yearly duration duration curve. curve. Flow Flow rates rates in the in legend the legend are expressedare expressed in m in3 /s.m3/s. 400 400400 400 upstream homogeneous reach upstreamupstream homogeneous homogeneous reach reach downstreamupstream homogeneous homogeneous reach reach 360 downstream homogeneous reach 360 downstreamdownstream homogeneous homogeneous reach 360360

320 elevation (m) 320 elevation (m) 320320 elevation (m) elevation (m)

280 280 2802800 2500 5000 000 2500 2500 5000 5000 5000 distance (m) distancedistance (m)(m) (m)

Figure 7. Homogeneous reaches in the longitudinal profile of the river bed. FigureFigureFigureFigure 7.7. 7. HomogeneousHomogeneous Homogeneous reaches reachesreaches reaches inin in thethe the longitudinallongitudinal longitudinal profile proﬁleprofile profile of of of theof the the the river river river river bed. bed. bed. bed.

500500 500500 forfor upstreamupstream homogeneoushomogeneous reach reach forfor upstream upstream homogeneous homogeneous reach reach forfor downstreamdownstream homogeneoushomogeneous reach reach forfor downstream downstream homogeneous homogeneous reach reach

250250 250250 critical diameter (mm) critical diameter (mm) critical diameter (mm)

critical diameter (mm) 0 0 0 000 100 100 200 200 300 300 0 100 200 300 0 100duration (days) 200 300 durationduration (days) (days) duration (days) Figure 8. Duration curve of the critical diameter (averaged along homogeneous reaches). FigureFigure 8. 8. DurationDuration curve curve of of the the critical critical diameter diameter (averaged (averaged along along homogeneous homogeneous reaches). reaches). FigureFigure 8. 8. Duration Duration curve curve of of the the critical critical diameter diameter (averaged (averaged along along homogeneous homogeneous reaches). reaches). 1000 1000 10001000

100 100 100100 10 10 d_50 1989 d_50 [14] 1010 sediment size (mm) d_50mean 1989 critical diameter upstream d_50mean [14] critical diameter downstream d_50d_50 1989 1989 d_50d_50 [14] [14] sediment size (mm) 1 mean critical diameter upstream mean critical diameter downstream sediment size (mm) sediment size (mm) 1 0meanmean critical critical diameter diameter upstream upstream 2500meanmean critical critical diameter diameter downstream downstream 5000 1 10distance 2500 (m) 5000 00 2500 2500 5000 5000 distancedistance (m) (m) Figure 9. Computed yearly‐averaged critical sedimentdistance size (m) compared with the median sediment size FigureFigurein the 9. 9. consideredComputedComputed reach. yearly yearly-averaged Dashed‐averaged lines critical critical identify sediment sediment the reference size size comparedsizes compared used inwith with the the thefollowing median median computations. sediment sediment size size FigureFigure 9. 9. Computed Computed yearly yearly‐averaged‐averaged critical critical sediment sediment size size compared compared with with the the median median sediment sediment size size inin the the considered considered reach. reach. Dashed Dashed lines lines identify identify the the reference reference sizes sizes used used in in the the following following computations. computations. inin the the considered considered reach. reach. Dashed Dashed lines lines identify identify the the reference reference sizes sizes used used in in the the following following computations. computations.

Water 2016, 8, 597 8 of 16 Water 2016, 8, 597 8 of 16

5. Hydro-MorphologicHydro‐Morphologic Analysis for Peak Flow The propagationpropagation of of the the ﬂood flood wave wave and and the the resulting resulting morphologic morphologic evolution evolution of the of river the river bed were bed modeledwere modeled using using the one-dimensional the one‐dimensional Saint-Venant Saint‐Venant equations equations (stating (stating the conservation the conservation of mass of mass and momentumand momentum for the for ﬂow) the andflow) the and Exner the equation Exner equation (stating the(stating conservation the conservation of mass for of the mass sediment). for the Thesediment). numerical The solver numerical used solver was implemented used was implemented in the Basement in the software Basement [35 ]software provided [35] by provided ETH Zurich. by TheETH model Zurich. assumes The model immediate assumes adaptation immediate of theadaptation sediment of transport the sediment rate to transport the local rate hydro-dynamic to the local conditions.hydro‐dynamic The conditions. bed-load solid The dischargebed‐load wassolid computed discharge using was computed the equation using by Meyer-Peterthe equation and by MullerMeyer‐Peter [32] which, and Muller according [32] towhich, [5], is according suitable for to bed[5], slopesis suitable lower for than bed 5%slopes (the lower slope valuesthan 5% in (the the Malleroslope values reach in used the Mallero for the computations reach used for respect the computations such a limitation). respect Thesuch sediment a limitation). transport The sediment formula bytransport [36] was formula also used by [36] for comparison. was also used for comparison. The geometric model included 57 crosscross sectionssections (see(see FigureFigure7 7).). The The spacing spacing between between neighboring neighboring sections ranged ranged between between 31 31 and and 116 116 m, m, apart apart from from four four instances instances of 154, of 154, 169, 169, 177, 177,and and256 m. 256 The m. Thetemporal temporal step of step the of computation the computation was dominated was dominated by the shortest by the shortest spacing, spacing, as it was as computed it was computed based on baseda Courant on a number Courant of number 0.9. of 0.9.

5.1. Model Parameterization/Validation The model was used to simulatesimulate the floodflood eventevent ofof 1987,1987, for whichwhich [[12,14]12,14] providedprovided datadata representingrepresenting thethe post-eventpost‐event profileprofile ofof thethe bedbed elevation.elevation. These data were used as benchmarks forfor thethe simulation. InIn this this way, way, an an attempt attempt was was made made to overcome to overcome the lack the of fieldlack validationof field validation that is frequently that is afrequently shortcoming a shortcoming in similar studies in similar (e.g., studies [37,38 ]).(e.g., [37,38]). The modelmodel input input parameters parameters were were (i) a(i) flow a flow hydrograph; hydrograph; (ii) the (ii) bed the roughness; bed roughness; (iii) the sediment (iii) the sizesediment and (iv) size a sedimentand (iv) a supply sediment at the supply upstream at the computational upstream computational boundary. The boundary. flow hydrograph The flow providedhydrograph by provided [14] among by others [14] among was used others (Figure was used10), with (Figure a duration 10), with of a 60 duration h and a of peak 60 h discharge and a peak of 495discharge m3/s. of The 495 sediment m3/s. The sizes sediment obtained sizes from obtained the computations from the computations for flows in for the flows duration in the curve duration were implemented,curve were implemented, thus 50 mm thus in the 50 downstreammm in the downstream reach and 150 reach mm and in 150 the upstreammm in the reach upstream (Figure reach9). Corresponding(Figure 9). Corresponding roughness coefficients roughness were coefficients computed were as 26/computedd1/6 (with as d26/asd the1/6 (with sediment d as size the expressedsediment insize m) expressed and were in equal m) and to were 36 and equal 43 s/m to 361/3 and, respectively. 43 s/m1/3, respectively. An equilibrium An equilibrium condition forcondition sediment for transportsediment transport was used was at the used upstream at the upstream boundary. boundary. This is indeed This is a indeed condition a condition of frequent of frequent use in similar use in studiessimilar (e.g.,studies [39 (e.g.,,40]). [39,40]).

800 1987

/s) 600 design 3

400

flow rate (m rate flow 200

0 0 204060 time (hours)

Figure 10. Flow hydrographs for the 1987 ﬂoodflood event and the designdesign event.event.

The resultresult of aof hydro-morphologic a hydro‐morphologic model canmodel be sensitivecan be to sensitive the values to used the for values parameterization. used for Resultsparameterization. for the Mallero Results river for werethe Mallero presented river by were [17] in presented terms of aby sensitivity [17] in terms analysis of a of sensitivity the back simulationanalysis of ofthe the back 1987 simulation event to the of the sediment 1987 event size, forto the which sediment values size, from for 1 to which 10 cm values were used.from In1 to that 10 study,cm were a limited used. In sensitivity that study, was a limited found sensitivity that was attributed was found to that an equal-mobility was attributed condition to an equal associated‐mobility withcondition high associated bed shear stresseswith high that bed are shear typical stresses of high that ﬂows. are typical Such aof condition high flows. also Such favors a condition the use also of a singlefavors sedimentthe use of size a single mimicking sediment a granulometric size mimicking distribution. a granulometric Furthermore, distribution. the studies Furthermore, of [16,17 ,37the] demonstratedstudies of [16,17,37] (in the demonstrated former case, for (in the the same former river case, considered for the here)same thatriver aggradation considered patterns here) that in aggradation patterns in a downstream portion of a computational reach were almost independent of the sediment supply, provided that the duration of the modeled event was short. This piece of

Water 2016, 8, 597 9 of 16

aWater downstream 2016, 8, 597 portion of a computational reach were almost independent of the sediment supply,9 of 16 provided that the duration of the modeled event was short. This piece of information was used to chooseinformation the extent was used of the to computational choose the extent domain, of the as alreadycomputational mentioned domain, in Section as already3. Additional mentioned issues in ofSection the location 3. Additional of a transition issues forof the sediment location size of and a transition of the transport for sediment formula size used and in theof the computation transport willformula be addressed used in the in thecomputation following. will be addressed in the following. TheThe resultresult ofof thethe hydro-morphologichydro‐morphologic modelmodel forfor thethe fullfull computationalcomputational reachreach isis presentedpresented inin FigureFigure 1111.. TheThe temporaltemporal evolutionevolution of thethe aggradationaggradation processprocess showedshowed aa dispersivedispersive behaviourbehaviour ofof thethe sediment,sediment, as alsoalso foundfound inin severalseveral otherother studiesstudies (e.g.,(e.g., [[41,42]),41,42]), withwith thethe solidsolid materialmaterial accumulatingaccumulating inin thethe intermediateintermediate portionportion of thethe reach,reach, wherewhere initialinitial slopesslopes werewere lower.lower. AsAs seen,seen, thethe riverriver sectionssections areare quitequite highhigh forfor distancesdistances largerlarger thanthan 25002500 m.m. Therefore, inin thethe following,following, attentionattention willwill bebe focusedfocused onon the last 2.5 2.5 km km that that moreover moreover correspond correspond to to the the in‐ in-towntown reach reach where where population population and and property property are areexposed exposed to the to the flood flood hazard. hazard. Results Results for for the the in in-town‐town reach reach are are depicted depicted in in Figure 12 includingincluding additionaladditional sensitivitysensitivity analysesanalyses toto thosethose presentedpresented byby [[16,17].16,17]. NeitherNeither thethe sedimentsediment transporttransport formulaformula nornor thethe locationlocation of of a a transition transition for for sediment sediment size size significantly significantly influenced influenced the the river river profile profile computed computed at theat the end end of theof the event. event. The The comparison comparison between between the modelingthe modeling results results and and the post-event the post‐event surveys surveys is also is includedalso included in Figure in Figure 12. The 12. field The data field were data reproduced were reproduced well in well the upstream in the upstream portion ofportion the in-town of the reach,in‐town whilst reach, the whilst computed the computed bed elevations bed elevations were significantly were significantly lower than lower the than surveyed the surveyed ones in ones the downstreamin the downstream portion. portion. This could This could be due be to due the to fact the that fact thethat survey the survey was notwas performed not performed just just after after the floodthe flood and additionaland additional morphologic morphologic processes processes could could have takenhave place.taken Sinceplace. the Since flood the happened flood happened almost 30almost years 30 ago, years it was ago, very it was difficult very difficult to find information to find information in that respect. in that However,respect. However, the agreement the agreement between thebetween model the and model the survey and the in survey the upstream in the portionupstream was portion considered was considered more important more thanimportant the agreement than the inagreement the downstream in the downstream portion as the portion former as wasthe former the place was where the place the outflow where wouldthe outflow take placewould in take the designplace in scenario the design (see scenario the following (see the section). following section).

440 Left bank Right bank

420 In-town bridges Bed, initial

400 Bed, final

380

360

elevation (m) elevation 340

320

300

280 0 1000 2000 3000 4000 5000 distance (m) Figure 11. Result of the numerical model of the 1987 flood event comparing the river profile at the Figure 11. Result of the numerical model of the 1987 ﬂood event comparing the river proﬁle at the beginning and at the end of the simulation. beginning and at the end of the simulation.

Water 2016, 8, 597 10 of 16 Water 2016, 8, 597 10 of 16

320 Left bank Right bank In-town bridges Bed, initial Bed, post-event [12] Bed, post-event [14] Bed, final Water elev., max 310 Bed, final - S-J Bed, final - 2.5km

300 elevation (m) elevation

290

280 0 5001000150020002500 distance (m)

Figure 12. Comparison between the numerical simulation of the 1987 flood flood event and field field data for the bed elevation at the end of thethe event,event, includingincluding sensitivitysensitivity analyses for thethe transporttransport formulaformula (S-J(S‐J == equationequation by by [ 36[36])]) and and for for the the location location of a of transition a transition in sediment in sediment size (moved size (moved from 1.8 from to 2.5 1.8 km). to 2.5 km). 5.2. Design Flood Event 5.2. Design Flood Event A discharge hydrograph corresponding to a return period of 100 years was computed by [14] usingA a discharge Nash model. hydrograph The hydrograph corresponding had ato duration a return ofperiod 60 h of and 100 a peakyears dischargewas computed of 640 by m [14]3/s (Figureusing a Nash10). It model. is acknowledged The hydrograph here that had thea duration estimation of 60 of h a and flood a peak hydrograph discharge for of a 640 relatively m3/s (Figure high return10). It is period acknowledged may be not here fully that supported the estimation by the length of a flood of available hydrograph rainfall for records a relatively (that were high limited return toperiod several may years). be not However, fully supported in the absence by the of length different of evaluations,available rainfall the available records hydrograph(that were limited was used to hereseveral as anyears). upstream However, boundary in the condition absence of for different the hydro-morphologic evaluations, the available model. Other hydrograph parameters was of used the modelhere as (sediment an upstream sizes, boundary roughness condition coefficients, for the and hydro upstream‐morphologic sediment model. supply) Other were parameters the same as of those the previouslymodel (sediment used for sizes, the simulationroughness ofcoefficients, the 1987 flood. and upstream sediment supply) were the same as thoseThe previously result obtained used for from the simulation the hydro-morphologic of the 1987 flood. modeling of the design scenario is depicted in FigureThe result 13. The obtained reliability from of the this hydro result‐morphologic was tested by modeling a series of the analyses design where scenario the is sensitivity depicted ofin theFigure final 13. bed The profile reliability to different of this parametersresult was tested was demonstrated. by a series of Consideredanalyses where items the were sensitivity the sediment of the size,final thebed locationprofile to of different a transition parameters in sediment was size, demonstrated. the sediment Considered supply at items the upstream were the boundary,sediment andsize, the the sediment location of transport a transition equation. in sediment Results size, are depictedthe sediment in Figures supply 14 at–17 the. The upstream only parameter boundary, with and a markedthe sediment influence transport on the equation. results was Results the sediment are depicted size, in that Figures was however14–17. The determined only parameter based with on the a analysismarked ofinfluence the flows on in the the results duration was curve the sediment (Section4 ).size, The that stability was ofhowever the presented determined results based is therefore on the consideredanalysis of satisfactory.the flows in the duration curve (Section 4). The stability of the presented results is therefore considered satisfactory.

Water 2016, 8, 597 11 of 16 Water 2016, 8, 597 11 of 16 Water 2016, 8, 597 1111 of of16 16

320 320 Left bank Right bank LeftLeft bankbank RightRight bank bank Bed, initial In-town bridges Bed,Bed, initialinitial In-townIn-town bridges bridges

Bed,Bed, finalfinal WaterWater elev., elev., max max 310

300 elevation (m) elevation (m) elevation (m)

290

280 00 500 500 1000 1000 1500 1500 2000 2000 2500 2500

distancedistance (m) (m)

Figure 13. 13. ResultsResults (thalweg(thalweg and and free free surface surface profiles) proﬁles)profiles) for for the thethe simulation simulationsimulation of ofof the thethe design designdesign event. event.event.

320 320 LeftLeft bankbank RightRight bank bank Bed,Left bankinitial In-townRight bank bridges Bed, initial In-townIn-town bridgesbridges 310 Bed,Bed, finalfinal Bed,Bed, final final - -10-50 10-50 310 Bed,Bed, finalfinal - 100-300 Bed, final - 10-50 Bed, final - 100-300 300 300 elevation (m) elevation

elevation (m) elevation 290 elevation (m) elevation 290

280 280 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 distancedistance (m) (m) distance (m) Figure 14. Model of the design flood scenario: sensitivity to the sediment size (sizes for the FigureFigure 14.14.Model Model of theof the design design ﬂood flood scenario: scenario: sensitivity sensitivity to the sediment to the sediment size (sizes forsize the (sizes downstream for the downstream and upstream homogeneous reaches indicated in mm in the legend), considering that anddownstream upstream and homogeneous upstream homogeneous reaches indicated reaches in mm indicatedindicated in the legend), inin mm consideringinin the legend),legend), that considering the benchmark that the benchmark model is for 50–150 mm. modelthe benchmark is for 50–150 model mm. isis for 50–150 mm. 320 320 Left bank Right bank Left bank Right bank Bed,Left bankinitial In-townRight bank bridges 310 Bed, initial In-townIn-town bridgesbridges 310 Bed, final Bed, final - 2.5km Bed, final Bed, final - 2.5km 300 300

elevation (m) elevation 290 elevation (m) elevation elevation (m) elevation 290 280 280 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 distance (m) distance (m) Figure 15. Model of the design flood scenario: sensitivity to the location chosen for a transition in Figure 15. Model of the design flood scenario: sensitivity to the location chosen for a transition in Figuresediment 15.15. size Model (moved of the from designdesign 1.8 to ﬂoodflood 2.5 km). scenario:scenario: sensitivity to the location chosen for a transitiontransition inin sediment size (moved from 1.8 to 2.5 km). sedimentsediment sizesize (moved(moved fromfrom 1.81.8 toto 2.52.5 km).km).

Water 2016, 8, 597 12 of 16 Water 2016, 8, 597 12 of 16 Water 2016, 8, 597 12 of 16 Water 2016, 8, 597 12 of 16 320 320 Left bank Right bank 320 Left bank Right bank Bed,Bed,Left initialbank initial In-townRightIn-town bank bridges bridges 310 310 Bed,Bed, final finalinitial Bed,In-townBed, final final bridges - -no no supply supply 310 Bed,Bed, final final -- supply=Ysupply=Y Bed, final - no supply Bed, final - supply=Y 300300 300 elevation (m) elevation elevation (m) elevation 290290 elevation (m) elevation 290

280280 28000 500 500 1000 1000 1500 1500 2000 2000 2500 2500 0 500 1000 1500 2000 2500 distance (m) distance (m) distance (m) Figure 16. Model of the design flood scenario: sensitivity to the sediment supply at the upstream FigureFigure 16. 16.Model Model of of the the design design ﬂood flood scenario: scenario: sensitivitysensitivity to the sediment supply supply at at the the upstream upstream Figure 16. Model of the design flood scenario: sensitivity to the sediment supply5 at3 the upstream boundaryboundary (equilibrium (equilibrium conditions conditions forfor the benchmark model, model, no no supply, supply, Y Y= 2= ×2 10× 10 m5 5m). 3).3 boundaryboundary (equilibrium (equilibrium conditions conditions for for the the benchmark benchmark model,model, no no supply, supply, Y Y = =2 × 2 10×5 10m3). m ). 320 320320 Left bank Right bank Left bank Right bank Bed,Left bank initial In-townRight bank bridges 310 Bed,Bed, initial initial In-townIn-town bridges bridges 310310 Bed, final Bed, final - S-J Bed,Bed, final final Bed,Bed, finalfinal - -S-J S-J 300 300300

elevation (m) elevation 290 elevation (m) elevation elevation (m) elevation 290290 280 280280 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000distance (m) 1500 2000 2500 distancedistance (m) (m) Figure 17. Model of the design flood scenario: sensitivity to the sediment transport formula Figure 17. Model of the design flood scenario: sensitivity to the sediment transport formula FigureFigure(S‐J 17. = equation17.Model Model by of [36]).of the the design design flood flood scenario: scenario: sensitivitysensitivity to the sediment transport transport formula formula (S‐J = equation by [36]). (S-J(S =‐ equationJ = equation by by [36 [36]).]). The maximum elevation reached by water was higher than the left bank close to the Garibaldi The maximum elevation reached by water was higher than the left bank close to the Garibaldi bridge,The maximumindicating thatelevation the town reached would by bewater flooded was byhigher an event than analogousthe left bank to closethe scenario to the Garibaldiunder Thebridge, maximum indicating elevation that the reachedtown would by water be flooded was higherby an event than theanalogous left bank to the close scenario to the under Garibaldi bridge,consideration indicating (see that Figure the 4 townfor the would location be at flooded which inundation by an event would analogous be expected to the to start). scenario Present under bridge,resultsconsideration indicating also confirm (see that Figure thea major town4 for importance the would location be of at flooded accountingwhich inundation by anfor eventthe would sediment analogous be expected transport to to the instart). scenariothe Presenthazard under considerationresults also confirm(see Figure a major 4 for importancethe location of at accountingwhich inundation for the wouldsediment be transportexpected toin start).the hazard Present considerationresultsassessment, also (see confirm if one Figure considers a 4major for thethat importance location the same at dischargeof which accounting inundationhydrograph for the would sediment correspond be expected transport to a to freeboardin start). the hazard Present of 1.9assessment, m at the if oneGaribaldi considers bridge that inthe a same clear discharge‐water hydraulic hydrograph model. would For correspond the present to ascenario, freeboard the of resultsassessment, also confirm if one considers a major importancethat the same of discharge accounting hydrograph for the would sediment correspond transport to a in freeboard the hazard of outflowing1.9 m at the discharge Garibaldi was bridge estimated in a inclear an ‐uncoupledwater hydraulic way with model. respect For tothe the present hydro ‐scenario,morphologic the assessment,1.9 m at ifthe one Garibaldi considers bridge that the in samea clear discharge‐water hydraulic hydrograph model. would For correspond the present to scenario, a freeboard the of model.outflowing At some discharge selected was times estimated along inthe an process, uncoupled the instantaneousway with respect profile to theof the hydro free‐ morphologicsurface was 1.9 moutflowing at the Garibaldi discharge bridge was in estimated a clear-water in an hydraulic uncoupled model. way with For therespect present to the scenario, hydro‐ themorphologic outflowing usedmodel. to Atcompute some selectedthe outflowing times along discharge the process, by treating the instantaneous the left bank ofprofile the riverof the as free a succession surface was of discharge was estimated in an uncoupled way with respect to the hydro-morphologic model. At some model.lateralused toAt weirs compute some (the selected thereader outflowing times is directed along discharge theto [43]process, by fortreating morethe instantaneous thedetails). left bank An of outflowingprofile the river of theashydrograph a free succession surface was of was selected times along the process, the instantaneous profile of the free surface was used to compute the usedobtained,lateral to computeweirs starting (the the atreader outflowinga time is ofdirected 26 discharge h from to [43]the by beginning fortreating more thedetails).of theleft event bank An andoutflowingof the with river a peakhydrograph as a ofsuccession 117 mwas3/s of 3 outflowinglateral(Figureobtained, weirs discharge 18). starting (the byreader at treatinga time is ofdirected the 26 lefth from bankto [43]the of beginningfor the rivermore asofdetails). athe succession event An and outflowing of with lateral a peak weirshydrograph of (the117 m reader /swas is directedobtained,(Figure to [ 43 18).starting] for more at a details).time of 26 An h outflowing from the beginning hydrograph of the was event obtained, and with starting a peak at a of time 117 of m 263/s h from(Figure the beginning 18). 800 of the event and with a peak of 117 m3/s (Figure 18). 800 design hydrograph design hydrograph /s) 800600 3 outflow

/s) 600 3 designoutflow hydrograph 400 /s) 600 3 400 outflow 200

discharge (m 400 200 discharge (m 0 200

discharge (m 0 0 102030405060 0 102030405060 time (hours) 0 time (hours) 0 102030405060 Figure 18. Design flood and outflow hydrographs. Figure 18. Design floodtime and (hours) outflow hydrographs.

FigureFigure 18. 18.Design Design ﬂood flood and and outﬂow outflow hydrographs.hydrographs.

Water 2016, 8, 597 13 of 16

6. Concluding Remarks This study documented an application of a numerical model towards flood hazard assessment for a mountain river with intense sediment aggradation increasing the expected water levels for any flow rate. The importance of appropriately accounting for sediment transport was proven by comparing the maximum elevation of the free surface for a clear-water and a hydro-morphologic modeling approach. It was demonstrated that even though the hazard perspective was related to a design flood event, insight into the appropriate model parameterization could be obtained from analyses of the hydro-morphologic behaviour of the river over a longer term considering flow rates in the yearly duration curve. These ordinary conditions represent initial conditions for the unsteady process of the flood wave propagation and all of its consequences. The model parameterization obtained from the preliminary analysis was first validated against the records of a past event and then exploited for the simulation of a design flood scenario with a 100-year return period. Using such a return period is a standard practice in Italy. Investigating the effect of flow rates with different probability would also be an interesting topic, that shall be accounted for in follow-up work but that does not alter the modeling procedure proposed in this study. The sediment supply into the river reach used in the computations was modeled assuming a dynamic equilibrium at the upstream boundary. Previous studies and appropriate sensitivity analyses performed in this work demonstrated that the sediment aggradation depth in the in-town reach of the river was however independent of the sediment supply at the upstream boundary, provided that the length of the computational reach was enough in light of the duration of the event. Under such a condition, the event dynamics is characterized by a redistribution of sediment already present in the water course before the event rather than on migration of the sediment supplied upstream. From a modeling point of view, a low sensitivity to the values of yielded sediment volume would significantly reduce the uncertainty related with short-term modeling. On the other hand, a major role of antecedent conditions would be consequently inferred. This part of the process, however, still needs further research. The issue of sediment connectivity has indeed received particular attention in recent years (e.g., [44–46]) and it might be worth recalling here that a similar behaviour has been also argued for water, as measurements showed that the water reaching a downstream section is present in the basin substrate before an event rather than the water arriving during the event (e.g., [47,48]). Modeling the undergoing processes at a greater spatial resolution (i.e., raster cell) over long time spans could thus also support the assessment of suitable initial states. The sensitivity of the modeling results to several parameters was assessed, resulting in a satisfactory reliability of the procedure. The sediment size can have a major influence on the simulated hydro-morphologic behaviour of the river. In the present case, a parameterization of the sediment size based on the analysis of the yearly sediment transport was proposed. The modeling approach was here applied to a design event for a 100-year flow hydrograph, but the sequence could be equally conditioned with forecasted flow rates in a warning system (e.g., [49]). According to [15], two major drawbacks of forecasting and warning tools currently used in the study site are that (i) discharge forecasts are not connected with inundation models and (ii) sediment aggradation is not considered. The modeling sequence presented in this study can effectively connect discharge forecasting and inundation models accounting for sediment transport and aggradation of the river bed, thus meeting a significant public demand. Further research on urban inundation (using a two-dimensional, unsteady hydraulic model) and damage modeling (using a model recently proposed by [50]) is presently in progress as a follow-up step of a simulation sequence. Such pieces of information shall support design of risk mitigation (i.e., damage reduction) strategies by authorities in charge. A most important shortcoming of the approach documented here is its deterministic nature, with a consequent lack of consideration for uncertainty issues. On the one hand, for the present study site the hydro-morphologic model took advantage of existing data and was calibrated based on the latter, thus mitigating the effects of uncertainty. On the other hand, uncertainty issues shall be Water 2016, 8, 597 14 of 16 key topics for follow-up research. In this respect, one can first consider that analyses dealing with non-gauged case studies would suffer from a much larger uncertainty in the hydraulic modeling. Second, the correspondence between water discharges/volumes and sediment transport volumes is far from being deterministic (e.g., [5,51,52]). Examples of probabilistic treatment of sediment supply are appearing (e.g., [53]), which can be further exploited as a step forward for an appropriate treatment of uncertainty.

Acknowledgments: The open-access publication fee was covered thanks to liberal funding from the Comune di Lecco, Italy. Author Contributions: Alessio Radice, Laura Longoni and Monica Papini conceived and designed the study; Laura Longoni, Monica Papini and Davide Brambilla collected the relevant data for the hydro-graphic catchments; Alessio Radice and Vladislav Ivov Ivanov performed the hydro-morphologic modeling for the flows in the duration curve and for the flood events, respectively; Alessio Radice wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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