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  • View in gallery

    Flowchart for integrated hydrologic flash flood analysis: indirect estimate of peak discharge, uncertainty assessment, and comparison with rainfall–runoff model results.

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    The study basin with topography and the three stream gauge stations. Locations of IPEC cross sections are also reported, with the corresponding intensities of observed geomorphic impacts.

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    Radar rainfall spatial distribution of the 25 Oct 2011 rainstorm over the Magra River basin: (a) max hourly rainfall and (b) event rainfall accumulation.

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    Coupled hydrologic–hydraulic model calibration results for the three stream gauge stations, reporting the comparisons between simulated and observed flood hydrographs and observational uncertainty bounds with 68% confidence interval.

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    Results of the rainfall–runoff simulation for the 35 IPEC sections, showing relationship between field-estimated and model-simulated (a) peak discharges and (b) unit peak discharges. Uncertainty bounds are presented for the field-estimated peak flows.

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    Relationship between estimated unit peak discharges and rainfall characteristics for the 33 considered IPEC catchments: (a) event-cumulated rainfall and (b) max hourly rainfall intensity. Fill (no fill) indicates high (moderate) rainfall basins.

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    Relationship between runoff ratio and cumulated rainfall for 22 IPEC catchments that showed consistency between field-surveyed and model-simulated peak discharges, the three gauge stations, and other Mediterranean events (Marchi et al. 2010).

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    Unit peak discharge vs drainage area for the 33 considered IPEC catchments, the three gauge stations, and other Mediterranean flash floods. The upper envelope curve for European flash floods (Gaume et al. 2009) is reported.

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Hydrometeorological Characterization of a Flash Flood Associated with Major Geomorphic Effects: Assessment of Peak Discharge Uncertainties and Analysis of the Runoff Response

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  • 1 Research Institute for Geo-hydrological Protection, National Research Council, Padua, Italy
  • | 2 Department of Land, Environment, Agriculture and Forestry, University of Padua, Agripolis, Legnaro, Italy
  • | 3 Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genoa, Genoa, Italy
  • | 4 Faculty of Science and Technology, Free University of Bozen-Bolzano, Bolzano, Italy
  • | 5 Center for Applied Geoscience, Eberhard Karls University of Tübingen, Tübingen, Germany
  • | 6 Department of Geography, Hebrew University of Jerusalem, Jerusalem, Israel
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Abstract

Postflood indirect peak flow estimates provide key information to advance understanding of flash flood hydrometeorological processes, particularly when peak observations are combined with flood simulations from a hydrological model. However, indirect peak flow estimates are affected by significant uncertainties, which are magnified when floods are associated with important geomorphic processes. The main objective of this work is to advance the integrated use of indirect peak flood estimates and hydrological model simulations by developing and testing a procedure for the assessment of the geomorphic impacts–related uncertainties. The methodology is applied to the analysis of an extreme flash flood that occurred on the Magra River system in Italy on 25 October 2011. The event produced major geomorphic effects and peak discharges close to the maxima observed for high-magnitude rainstorm events in Europe at basin scales ranging from 30 to 1000 km2. Results show that the intensity of geomorphic impacts has a significant effect on the accuracy of postflood peak discharge estimation and model-based flood response analysis. It is shown that the comparison between rainfall–runoff model simulations and indirect peak flow estimates, accounting for uncertainties, may be used to identify erroneous field-derived estimates and isolate consistent hydrological simulations. Comparison with peak discharges obtained for other Mediterranean flash floods allows the scale-dependent flood response of the Magra River system to be placed within a broader hydroclimatological context. Model analyses of the hydrologic response illustrate the role of storm structure and evolution for scale-dependent flood response.

Corresponding author e-mail: William Amponsah, william.amponsah@irpi.cnr.it

Abstract

Postflood indirect peak flow estimates provide key information to advance understanding of flash flood hydrometeorological processes, particularly when peak observations are combined with flood simulations from a hydrological model. However, indirect peak flow estimates are affected by significant uncertainties, which are magnified when floods are associated with important geomorphic processes. The main objective of this work is to advance the integrated use of indirect peak flood estimates and hydrological model simulations by developing and testing a procedure for the assessment of the geomorphic impacts–related uncertainties. The methodology is applied to the analysis of an extreme flash flood that occurred on the Magra River system in Italy on 25 October 2011. The event produced major geomorphic effects and peak discharges close to the maxima observed for high-magnitude rainstorm events in Europe at basin scales ranging from 30 to 1000 km2. Results show that the intensity of geomorphic impacts has a significant effect on the accuracy of postflood peak discharge estimation and model-based flood response analysis. It is shown that the comparison between rainfall–runoff model simulations and indirect peak flow estimates, accounting for uncertainties, may be used to identify erroneous field-derived estimates and isolate consistent hydrological simulations. Comparison with peak discharges obtained for other Mediterranean flash floods allows the scale-dependent flood response of the Magra River system to be placed within a broader hydroclimatological context. Model analyses of the hydrologic response illustrate the role of storm structure and evolution for scale-dependent flood response.

Corresponding author e-mail: William Amponsah, william.amponsah@irpi.cnr.it

1. Introduction

Flash floods are often associated with landscapes characterized by significant relief (Marchi et al. 2010). Topographic relief is important since it may affect flash flood occurrence by the combination of two main mechanisms, namely, (i) orographically enhanced precipitation and convection anchoring and (ii) rapid concentration of streamflow in the channel network. Given the association of large runoff generation and steep topography, it is not surprising that, where abundant sediment is available for entrainment, flash floods are associated with debris flows, erosion, and sediment transport (Borga et al. 2014; Bodoque et al. 2015). In spite of the pervasive multihazard nature of extreme hydrogeomorphic processes, hydrologic and geomorphic observations concerning these processes are scarce. Reasons are related to the small space–time scales of flash flood occurrence, which limit the availability of hydrometeorological monitoring sites in the impacted catchments, and to the intensity of the runoff and geomorphic processes themselves, which limit the reliability of available stream gauge data and of postflood peak discharge estimates (Marchi et al. 2009). The lack of flash flood discharge data from stream gauge observations has been documented by Marchi et al. (2010) in an investigation of 25 major flash flood events that occurred in Europe in the last 20 years. They found that less than one-half of the cases were documented by means of conventional stage measurements, with the other cases based on indirect peak discharge estimation from postflood surveys. These surveys therefore play a major role in gathering flood peak magnitude and timing along the channel network, with the objective to advance understanding of flash floods and causative processes (Lumbroso and Gaume 2012).

The indirect estimation of peak discharge is carried out by means of various approaches, such as slope–area, flow-over-dam, or slope–conveyance methods (Dalrymple and Benson 1967). Among these, the slope–conveyance method (Gaume and Borga 2008), which attempts to identify the energy slope based on high-water marks (HWMs) and provides a flow velocity assessment by means of the Manning–Strickler equation under the assumption of uniform flow, has often been applied in intensive postflood surveys thanks to its easiness of application and flexibility (Lumbroso and Gaume 2012). Marchi et al. (2010) have shown the advantages of integrating the indirect peak discharge estimates with rainfall–runoff model simulations. With the integrated hydrologic flash flood analysis proposed here, simulated flood hydrographs are first compared with indirect peak discharge estimates, then rainfall–runoff model analysis is carried out where simulated flood hydrographs are consistent with field-derived peak observations. The first step permits one to assess the consistency between the various sources of rainfall and discharge observation, whereas the second allows one to evaluate the water balance at the event scale and to provide estimates of the runoff coefficients (ratio of event runoff to event rainfall). Analysis of event runoff coefficients may provide essential insight on how different landscapes “filter” rainfall to generate runoff and how the observed differences can be explained by catchment characteristics (Blume et al. 2007; Norbiato et al. 2009). A critical step in the integrated flash flood analysis is to quantify how field estimates and rainfall–runoff modeled peak flows are close enough, taking into account the relevant uncertainties.

Flood-triggered geomorphic processes may place considerable limitations on the reliability of indirect methods for peak estimation (Gaume and Borga 2008). For instance, scour and/or fill may occur after the HWMs are left by the current. The effect is that the cross-sectional geometry surveyed after the flood is different from the one existing at the time of the peak flow. Since geomorphic impacts are typically more severe in subbasins where runoff generation is more intense, these errors may have a considerable impact on the integrated hydrologic flash flood analysis. In spite of the impact of these errors, formal attempts to evaluate the uncertainties affecting indirect peak discharge estimate are relatively scarce (Kirby 1987; Jarrett 1987; McCuen and Knight 2006; Stewart et al. 2012; Lumbroso and Gaume 2012).

The main objective of this work is to advance the methodology for the integrated hydrologic flash flood analysis by developing and testing a procedure for the assessment of the geomorphic impacts–related uncertainties. These uncertainties are integrated into a recently developed method for uncertainty assessment of the slope–conveyance indirect peak flow estimates (Amponsah et al. 2016, manuscript submitted to J. Hydrol.). The methodology is applied to the 25 October 2011 flash flood in the Magra River basin in Italy, which provides a template for the examination of major, flash flood–related geomorphic impacts and the relevant associated uncertainties. For this event, accurate field surveys are available to evaluate geomorphic impacts (Marchi et al. 2016; Rinaldi et al. 2016).

2. Characterization of uncertainty in postflood peak flow estimates associated with major geomorphic impacts

Whenever postflood peak estimates are carried out in mountainous basins, one of the most important tasks is to properly assess the characteristics of the flow process under study. For example, historically, a number of debris flows in mountain drainage basins have been analyzed as water floods (Costa and Jarrett 1981). This kind of misidentification may lead to large errors in postflood assessment, because debris flows and hyperconcentrated flows (Pierson 2005) have distinctive features that require specific estimation methods (Hungr et al. 1984; Prochaska et al. 2008; Bodoque et al. 2011).

A second factor is related to the causative processes leading to the flood peaks. Some flood peaks are caused by failure of landslide dams or other types of channel obstructions with subsequent dam-break flow (O’Connor et al. 2013; Ruiz-Villanueva et al. 2013). Flood peaks caused by the failure of landslides and large wood jams are not directly related to runoff-generation processes and should not be used for comparison with the results of rainfall–runoff models.

Even when a postflood estimate passes the consistency checks in relation to flow type and channel obstruction, it is important to carry out an uncertainty assessment, which includes assessment of factors related to erosion and/or channel aggradation. These processes may modify the postflood river cross-sectional geometry with respect to the peak time, when HWMs were made. To cope with these issues, we extended a recently introduced linear error analysis of slope–conveyance indirect peak flow estimates (Amponsah et al. 2016, manuscript submitted to J. Hydrol.) to characterize uncertainties related to hydrogeomorphic impacts. Given the difficulties in the individual determination of these uncertainties, we decided to take a comparative observational approach based on the stratification of the intensity of the geomorphic impacts of the flood into three classes. Based on earlier work by Marchi et al. (2016), the three classes are defined as follows: class 1 is negligible geomorphic effects with no significant scour/fill or widening of the cross section, class 2 is small to moderate geomorphic effects with small scour/fill and limited widening of the cross section, and class 3 is major geomorphic effects with significant scour/fill and visible channel erosion/aggradation. These classes are defined over the whole flood-impacted region. Given the influence that changes in bed geometry and morphology may have on flow resistance (Ferguson 2007; Church and Ferguson 2015), the classification of geomorphic impacts provides information on the uncertainty assessment of the roughness.

The slope–conveyance method (Gaume and Borga 2008) requires the surveys of HWMs, channel bed slope, cross-sectional geometry, and estimation of flow roughness at one river section to compute peak discharge by means of the one-dimensional Manning–Strickler equation as follows:
e1
where is the wetted cross-sectional area, is the hydraulic radius, is the water surface fall over reach length , and is the roughness coefficient.

The linear error analysis permits us to explicitly take into account the effects of discrepancies between the “true” values of a number of variables and the corresponding measured or estimated values. The effect of these error sources on the accuracy of the computed peak discharge is estimated by a first-order error analysis using a Taylor series approximation of the discharge equation and the equation for the variance of a sum of correlated random variates (Kirby 1987).

The first-order error analysis of the slope–conveyance method accounts for six observational error sources affecting the measurement or estimation of the following variables: water surface fall , reach length , section width , section mean depth , scour/fill after flood peak , and roughness parameter . The error variance in the computed peak discharge can be treated in a Taylor series approximation as follows:
e2
where represents the variances in the change in generic variable z. The terms and , which represent the variances in the change in measured cross-sectional area and wetted perimeter P, respectively, incorporate the errors in the measurements of the section width, section mean depths, and scour. The scour is assumed to be of constant depth across the section. Fill is treated as negative scour. Errors in the surveying of HWMs and of the cross sections are distinguished because the measurements of ground points and of HWMs are characterized by different accuracies. The development of Eq. (2) leads to the following relationship:
e3
where is the number of ground points used to survey the cross-sectional geometry and the term indicates the relative error variance associated with the variable . The coefficients in Eq. (3) are obtained through a partial derivative of Eq. (1). Measurement errors in section mean depths and scour are expressed in terms of relative error variances and , respectively, referenced to mean depth , whereas the errors in section width are expressed in terms of relative error variance referenced to , that is, the average spacing between ground points. From Eq. (3), the observational error variance depends on the measurement uncertainties (, , , and ), on the uncertainties in the evaluation of the roughness parameter , and on the impact of the geomorphic effects . The standard deviation obtained from Eq. (3) is used to derive confidence intervals for the field-estimated peak flows. Flood peak simulations obtained from one or more hydrological models may then be compared with these uncertainty ranges both to identify field-based estimates that require further investigations and to retain/reject the hydrological simulations for the studied cross section. Figure 1 presents a flowchart for the integrated hydrologic flash flood analysis, with inclusion of characterization of flood-caused geomorphic impacts, related uncertainties, and subsequent comparison with results from rainfall–runoff models driven by high-resolution radar rainfall estimates.
Fig. 1.
Fig. 1.

Flowchart for integrated hydrologic flash flood analysis: indirect estimate of peak discharge, uncertainty assessment, and comparison with rainfall–runoff model results.

Citation: Journal of Hydrometeorology 17, 12; 10.1175/JHM-D-16-0081.1

3. The 25 October 2011 flash flood in the Magra River basin

The Magra River basin (Fig. 2) is located in central-northern Italy, at the border between the Tuscany and Liguria regions, with highest elevation at 1900 m MSL, and drains to the Ligurian Sea. The total drainage area of the study basin is 1717 km2, of which the Vara River (the major tributary of the Magra River) drains 605 km2. The climate is Mediterranean with dry summer and abundant precipitation occurring from autumn to early spring. Precipitation in the basin is monitored by means of a network of 41 rain gauge stations, with approximately 40 km2 per rain gauge. The basin is also covered by the weather radar located on Mt. Settepani (1386 m MSL) at 80 km to the west of the basin. The mean annual precipitation of the river system accumulates up to 1770 mm and reaches 3000 mm in the upper parts of the basin due to orographic effects. The geology of the basin mostly consists of arenaceous and muddy bedrock, featuring low permeability and high erodibility. Three main land-use classes can be identified within the study basin: forest (>80% of the total area), agricultural lands (predominant in the valley floor), and urbanized areas and infrastructure.

Fig. 2.
Fig. 2.

The study basin with topography and the three stream gauge stations. Locations of IPEC cross sections are also reported, with the corresponding intensities of observed geomorphic impacts.

Citation: Journal of Hydrometeorology 17, 12; 10.1175/JHM-D-16-0081.1

The severe weather event that struck the basin on 25 October 2011 was associated with a large depression positioned off Ireland’s western shore since the day before. The atmospheric scenario was a southwesterly flow on the storm’s right wing (warm front), channeled between Italy and the Sardinia/Corsica east coast and moistened by warm Mediterranean water, which transported a significant amount of water vapor into the study area. At the mesoscale, local steep topography was the trigger for the onset of an organized and self-regenerating mesoscale convective system (MCS) that lasted for 24 h starting at 0100 central European time (CET; Rebora et al. 2013). Event rainfall was associated with narrow southwest–northeast-oriented convective band, which produced event rainfall accumulation up to 540 mm.

The rainstorm of 25 October 2011 produced flash flooding in the main river channels and in several tributaries, triggering widespread landslides, especially in the sectors of the basin that were affected by the highest rainfall rates (Mondini et al. 2014). The flood caused major morphological changes in the main channel and in some tributaries (Nardi and Rinaldi 2015; Surian et al. 2016; Rinaldi et al. 2016) and recruited relevant amounts of large wood from the floodplain (Lucía et al. 2015). Several bridges were partly or fully clogged by large wood jams, with severe damages to roads, buildings, and downstream settlements; nine people died as a consequence of the flash flood.

4. Integrated hydrologic flash flood analysis

a. Radar rainfall estimation

Rainfall estimates were obtained by combining weather radar observations with rain gauge data. Reflectivity data from the original radar volume scans were elaborated using a set of algorithms and procedures described by Marra et al. (2014) in order to correct errors due to (i) partial beam blockage (Pellarin et al. 2002), (ii) signal attenuation due to heavy rain (Marra et al. 2014), (iii) vertical profile of reflectivity, and (iv) radar hardware miscalibration. Finally, radar and rain gauge measurements were merged using the adaptive multiquadric surface fitting algorithm described by Martens et al. (2013). The assessment of the quality of the final rainfall estimates was carried out by using a leave-one-out cross-validation method (Efron 1983). Two statistical parameters were computed for the comparison:
e4
and
e5
where and are the rain gauge data at station and the collocated radar estimate, respectively, σ is standard deviation, and is the number of rain gauges used in the comparison ( = 41). Adjusted radar rainfall estimates are almost unbiased at the event-accumulation scale, with a rather low FSE (0.19) and high CC (0.93).

The spatial distributions of maximum hourly rainfall intensity and total event rainfall accumulation (Fig. 3) mirror the organization around one well defined quasi-stationary convective band. This band aligned over the central portion of the Vara basin, stretching to the right tributaries of the Magra basin and covering an area of approximately 400 km2. The steadiness of this rainband led to highly variable precipitation accumulations with extreme spatial gradients up to 50 mm km−1, as well as to high correlations between the two different spatial patterns. The band mean width, defined as the distance between 5-dBZ contours on the flanks of individual precipitation bands, ranges between 6 and 8 km. The quasi-stationary convective structure produced maximum hourly rate and event-accumulation maxima up to 150 and 540 mm, respectively, with up to 300–400-yr recurrence intervals estimated for this event based on rainfall frequency analysis. The local rainfall temporal pattern was generally increasing with time until 1630–1800 CET, depending on the position in the Magra River system.

Fig. 3.
Fig. 3.

Radar rainfall spatial distribution of the 25 Oct 2011 rainstorm over the Magra River basin: (a) max hourly rainfall and (b) event rainfall accumulation.

Citation: Journal of Hydrometeorology 17, 12; 10.1175/JHM-D-16-0081.1

b. Postevent reconstruction of the flash flood response

1) Observed flood hydrographs

Flood stage measurements are available at three stream gauge stations: Vara at Nasceto, 206 km2; Vara at Piana Battolla, 549 km2; and Magra at Calamazza, 936 km2 (Fig. 2), which were transformed into discharge data using rating curves. Hydraulic simulations were used to provide estimates of the rating curve uncertainty for the stage–discharge transformation. By using the approach advanced by Di Baldassarre and Montanari (2009), we applied the 1D Hydrologic Engineering Center River Analysis System (HEC-RAS) code (Hydrologic Engineering Center 2016) for unsteady open-channel flow (Saint Venant equations) to associate uncertainty bounds (corresponding to 68% confidence intervals, that is, one standard deviation) to the observed flood hydrographs. For the peak flows, these are quantified as ±12.6%, ±18.8%, and ±23.3% for Nasceto, Piana Battolla, and Calamazza, respectively.

2) Postflood peak flow estimates and uncertainty assessment

An intensive postevent campaign (IPEC) was carried out in February and March 2012 with the objective of estimating peak discharges and characterizing geomorphic impacts of the flood in 35 ungauged tributaries of Magra and Vara Rivers (Fig. 2), featuring drainage areas between 0.5 and 77 km2. The slope–conveyance method (Gaume and Borga 2008) and the one-dimensional Manning–Strickler hydraulic equation [Eq. (1)] were used to estimate peak discharges at the surveyed cross sections. Cross sections were chosen taking into account their spatial representativeness and avoiding sites affected by local factors that could undermine indirect discharge assessment (e.g., blockage of bridges by log jams and excessive scour and fill effects).

The relative error associated with the evaluation of the scour/fill parameter was ranked into the three classes of the intensity of geomorphic impacts of the flood: negligible, small to moderate, and major (Fig. 1). The roughness relative error was based on the analysis of the various processes affecting the estimation of the Manning’s n [see Fig. 1 in Lumbroso and Gaume (2012)] and ranked according to the three geomorphic impact classes to account for the changes in bed morphology. The spatial distribution of the three classes of geomorphic impacts is reported in Fig. 2 for the IPEC sections.

While the error terms and (Table 1) are variable with the impact of geomorphic effects, the other error terms are kept constant, since they depend only on the cross-sectional geometry and HWM surveying uncertainties. The evaluation of the relative errors , , and were based on the measurement accuracy of the total station used in the surveying, whereas the value of took into consideration the errors in the selection, assessment, and surveying of the HWMs. The parameter in Eq. (3) was taken equal to 11, which represents the average number of ground points used to survey the cross-sectional geometry across the IPEC cross sections.

Table 1.

Summary values of the error variances of peak discharge uncertainty for the three categories of geomorphic effects.

Table 1.

The confidence interval that extends one percentage standard deviation on both sides of the field-estimated peak discharge is estimated based on Eq. (3) with percentage uncertainty bounds as ±13.5%, ±23.2%, and ±37.1% for cross sections that underwent negligible, small to moderate, and major geomorphic impacts, respectively (Table 1).

c. Flash flood response modeling

1) Spatially distributed rainfall–runoff model

A distributed hydrologic model is used to examine hydrologic response associated with space–time radar rainfall variability and to check consistency with postflood indirect peak flow estimates. The Kinematic Local Excess Model (KLEM; Marchi et al. 2010) combines a grid-based runoff-generation model and a network-based hillslope and channel transport model. Runoff generation is simulated by applying the Soil Conservation Service Curve Number (SCS-CN) approach (Ponce and Hawkins 1996) to quantify the storm net rainfall total amount and using this value to estimate the effective saturated hydraulic conductivity of the Green–Ampt method (Grimaldi et al. 2013). The SCS-CN method is applied by using an infiltration storativity parameter for the overall calibration of the method [see Borga et al. (2007) for further details]. The use of this parameter allows one to calibrate a spatial distribution of CN values in order to simulate correctly the observed flood water balance.

The runoff propagation is based on the identification of drainage paths and requires the characterization of hillslope and channel paths. This is based on a channelization support area and the use of two invariant hillslope and channel flow velocities, respectively. The use of invariant channel and hillslope velocities for flash flood simulation has been discussed by Ruiz-Villanueva et al. (2012), among many others.

To account for effects due to the overflowing in the floodplains and backwater effects at confluences, the hydrologic model was coupled with the 1D model code HEC-RAS (Hydrologic Engineering Center 2016) for unsteady, open-channel flow (Saint Venant equations) in the main river system. The coupling is unidirectional, that is, the information is exchanged in one direction only, from the hydrologic model to the hydraulic model. The impact of this simplification should be limited, given the relatively small areas of the tributaries with respect to the main river (Laganier et al. 2014).

2) Model implementation: Calibration and validation

The model was manually calibrated to simulate the flood responses at the three gauged stations (Nasceto, Piana Battolla, and Calamazza; Fig. 2). A distributed CN map for the SCS-CN method was estimated based on land use and geolithological features of the study basins. The discharge data in the days before the flood were close to the average streamflow conditions for the month of October, showing that the initial soil moisture conditions were close to average seasonal conditions.

Runoff propagation parameters [(0.02 km2), (3 m s−1), and (0.2 m s−1)] were kept invariant across the study basins based on earlier works on major flash floods (Marchi et al. 2010). However, the use of a basin-invariant parameterization for the infiltration storativity parameter for the SCS-CN method produced flood simulations that were inconsistent with the observed flood hydrographs, showing that the degree of nonlinearity arising from the available data could not be reproduced by the model with spatially homogeneous parameterization. This agrees with earlier results obtained with a similar model for an extreme flash flood characterized by high rainfall spatial variability (Borga et al. 2007) and more generally with results reported by Hawkins (1993), which showed that the CN values tend to vary with the rainfall depth for the same watershed. Based on these findings, and to avoid issues with overparameterization of the model, two different parameters related to infiltration storativity parameter for the SCS-CN method were identified, stratified according to basin-average rainfall accumulation.

The whole river system at the Vara–Magra confluence was subdivided into 69 subbasins with similar sizes that flow into the main river channel. These basins were categorized as high-rainfall basin (HRB) and moderate-rainfall basin (MRB) according to the corresponding basin-average rainfall event accumulation. A threshold of 250-mm rainfall depth was used to distinguish the two categories, based on a sensitivity analysis of the coupled hydrologic and hydraulic model. The storativity parameter was calibrated in a separate way for the HRB and MRB categories. More specifically, the observed flood hydrograph at Nasceto was used to calibrate the parameter for MRB conditions. The parameter corresponding to HRB conditions was estimated by comparing simulated and observed flood hydrographs at Piana Battolla and Calamazza. The calibration of the hydraulic model was based on earlier model applications (Autorità di Bacino Interregionale del Fiume Magra 2006).

The rainfall–runoff model was validated by comparing field-estimated and model-simulated flood peaks over the IPEC basins. The model parameters identified for HRB and MRB were transposed to the catchments associated with the IPEC peak discharges to provide model simulations for the corresponding cross sections. Seventeen out of the 35 IPEC catchments are categorized as HRB. These catchments correspond to the position of the quasi-stationary convective rainfall band.

5. Results

a. Model calibration on the observed flood hydrographs

The central values of the peak discharges recorded at Nasceto, Piana Battolla, and Calamazza are equal to 350, 3000, and 4050 m3 s−1, respectively, slightly less than approximately 2-, 200-, and 100-yr recurrence intervals, based on regional peak discharge statistical assessment obtained from the Magra River basin district (Autorità di Bacino Interregionale del Fiume Magra 2006). The observed and simulated flood hydrographs for the three stream gauges are reported in Fig. 4, together with the 68% confidence intervals for the observed hydrographs. The estimated Nash–Sutcliffe efficiency scores (Nash and Sutcliffe 1970) for the comparisons are 0.90, 0.90, and 0.96 for Nasceto, Piana Battolla, and Calamazza, respectively. It is shown that the simulated peak flows are generally included within the observed uncertainty bounds, whereas the recession limbs are typically less well reproduced. The slight overestimations in simulated flood peaks at Piana Battolla and Calamazza are attributed to overbank flow to the flood plains, which was observed and documented by the IPEC team.

Fig. 4.
Fig. 4.

Coupled hydrologic–hydraulic model calibration results for the three stream gauge stations, reporting the comparisons between simulated and observed flood hydrographs and observational uncertainty bounds with 68% confidence interval.

Citation: Journal of Hydrometeorology 17, 12; 10.1175/JHM-D-16-0081.1

b. Assessment of peak discharge by means of postflood surveys

The summary of the IPEC surveys for the 35 cross sections is reported in Table 2. The uncertainty range of estimated peak discharges, which were obtained using Eq. (3) and the error terms reported in Table 1, represent the confidence interval that extends one standard deviation on both sides of the central field estimate. The central estimate results from the application of Eq. (1) with the parameters from the topographic surveys and the field evaluation of the roughness coefficient. The estimated Froude numbers were slightly lower than 1 in a number of cross sections, indicating that the flow regime was close to critical flow: this is consistent with the extreme intensity of the flood (Grant 1997; Comiti et al. 2009) and with the slope of the surveyed channel reaches, which mostly ranges from 0.02 to 0.04 m m−1.

Table 2.

Summary of the postevent survey at the IPEC cross sections. IPEC codes are reported in Fig. 2.

Table 2.

c. Comparison between field-estimated and model-simulated flood peaks over the IPEC basins

Comparisons between field-estimated and model-simulated peak and unit peak discharges for the 35 IPEC catchments are reported in Fig. 5, with the uncertainty bounds extending one percentage standard deviation on both sides of the field-estimated values. Examination of these results shows that in 22 out of the 35 IPEC catchments (12/17 for HRB and 10/18 for MRB), the model-simulated peak discharge falls within the peak flood uncertainty bound. In terms of geomorphic impact classes, the IPEC catchments with simulated peak flows included in the uncertainty bounds are distributed as follows: 9/11 for the major impacts, 7/14 for the moderate impacts, and 6/10 for the negligible impacts. The regressions in Fig. 5 show a tendency of the model to overestimate large peak flows and to underestimate moderate peak flows. This is likely due to the separate model calibration for the two rainfall depth classes, which works well in the calibration phase but performs less well in the validation phase. This suggests that the 250-mm rainfall depth is not rigidly an absolute threshold but a close approximation to discriminate the rate of runoff responses for the two rainfall amount classes.

Fig. 5.
Fig. 5.

Results of the rainfall–runoff simulation for the 35 IPEC sections, showing relationship between field-estimated and model-simulated (a) peak discharges and (b) unit peak discharges. Uncertainty bounds are presented for the field-estimated peak flows.

Citation: Journal of Hydrometeorology 17, 12; 10.1175/JHM-D-16-0081.1

The model grossly underestimated observed peak values for cross sections V07 and V08 (Fig. 5), with larger relative errors greater than threefold of the uncertainty standard deviations. This was attributed to errors in HWM assessment in these two tributaries of Vara basin closing at Nasceto because of a localized flood that occurred on 5 September 2011 and produced higher discharges than the 25 October 2011 flash flood in this sector of the basin. Thus, it is very likely that postflood peak discharges were overestimated at these two catchments that experienced moderate rainfall for this event. We therefore reject flood peak estimates for IPEC basins V07 and V08. Field estimates of peak discharges are therefore retained for 33 IPEC catchments for the subsequent analyses. Rainfall–runoff model simulations were retained only for the 22 IPEC catchments that showed consistency between model-simulated and field-estimated peak discharges for event water balance assessment.

Table 3 reports Nash–Sutcliffe efficiency scores for the comparisons of model simulations with field-estimated central values for the 33 IPEC catchments and the 22 catchments that showed consistency between field and model values as well as performance of the model for the two rainfall amount classes (HRB and MRB) and the three classes of geomorphic impacts (major, small to moderate, and negligible).

Table 3.

Nash–Sutcliffe efficiency scores for the various comparison between field-estimated and model-simulated (unit) peak discharges. The two erroneous indirect peak estimates are not included.

Table 3.

d. Peak discharges and rainfall properties

To elucidate the relationship between unit peak discharges and rainfall properties, we analyzed the distribution of field-estimated unit peak discharges with respect to the corresponding catchment-scale event-cumulated rainfall and maximum hourly rainfall intensity (Fig. 6). The analysis is carried out over the 33 IPEC basins with retained indirectly estimated peak values. The pattern of the relationships between the distribution of unit peak discharges and precipitation is very similar for both basin-average rainfall properties, which agrees well with the high correlation of the spatial patterns between 1-h maximum rainfall intensity and event-cumulated rainfall (Fig. 3).

Fig. 6.
Fig. 6.

Relationship between estimated unit peak discharges and rainfall characteristics for the 33 considered IPEC catchments: (a) event-cumulated rainfall and (b) max hourly rainfall intensity. Fill (no fill) indicates high (moderate) rainfall basins.

Citation: Journal of Hydrometeorology 17, 12; 10.1175/JHM-D-16-0081.1

Three IPEC values (P01, V01, and S11) deviate from the general linear pattern of the relationship between rainfall properties and unit peak discharges. This deviation is clearly detectable in Fig. 6b, where high rainfall intensities produced lower unit peak discharges, relative to the general pattern. These three catchments are among six IPEC catchments that received maximum hourly rainfall intensities greater than 100 mm and were characterized by very important geomorphic impacts. The geomorphic changes, most likely channel aggradation in these cross sections, could be responsible for errors and uncertainties with the postflood estimation method.

e. Water balance analysis

We computed the runoff coefficient as the ratio of the direct runoff to the event rainfall depth, based on the same procedure used in other studies (see Marchi et al. 2010) in order to make the results comparable. The analysis was focused on flood hydrographs from the rainfall–runoff model simulations obtained for the 22 IPEC catchments that showed consistency between model-simulated and field-estimated peak discharges and on observed hydrographs from the three gauge stations.

Figure 7 reports a scatterplot of event runoff coefficient against total rainfall accumulations for the studied basins and other Mediterranean flash floods obtained from Marchi et al. (2010). From Fig. 7, we can observe a similar large scatter as observed for the other events, with slight dependence of runoff coefficients on total rainfall depth. For the Magra case, runoff coefficients tend to cluster into two groups, depending on the basin-scale rainfall depths. Runoff coefficients for the 12 HRBs range between 0.51 and 0.66 (mean of 0.58; standard deviation of 0.04), whereas for the 10 MRBs they range between 0.10 and 0.48 (mean of 0.20; standard deviation of 0.11).

Fig. 7.
Fig. 7.

Relationship between runoff ratio and cumulated rainfall for 22 IPEC catchments that showed consistency between field-surveyed and model-simulated peak discharges, the three gauge stations, and other Mediterranean events (Marchi et al. 2010).

Citation: Journal of Hydrometeorology 17, 12; 10.1175/JHM-D-16-0081.1

6. Discussion

The results from the uncertainty assessment of the indirect peak discharge estimates (Tables 1 and 2), with a range in percentage standard deviations from 13.5% to 37.1%, allows one to appreciate the remarkable influence of the geomorphic impacts. Our results agree with conclusions from Kirby (1987, p. 138), who stated that “the most significant improvements in discharge accuracy can be obtained by reducing the uncertainty in the scour term.” Our estimates may be compared with those reported by Kirby (1987) for sections not specifically impacted by geomorphic effects. Kirby (1987) reported values ranging from ±16% to ±24%, even though the estimates were based on the slope–area method and not on the slope–conveyance method used here. The indirect peak discharge estimates may also be compared with those reported by Di Baldassarre and Montanari (2009), with a value of ±21% for the highest discharge value at the Po River outlet. It is also interesting to note that the uncertainties computed here with the method by Di Baldassarre and Montanari (2009) are comparable with those obtained for the indirect peak discharge estimates in the geomorphic impact classes 1 and 2.

The results reported in Table 3 and Fig. 5 exemplify the steps in the integrated hydrologic flash flood analysis. Comparison between model-simulated and field-derived peak flows (accounting for uncertainty) permits us to reconsider for analysis and then reject two field-derived peak estimates. It is interesting to observe that the two rejected peak estimates (basins V07 and V08) are placed in the low-to-moderate rainfall region for the October 2011 flood and in the small-to-moderate impact class, thus associated with low inherent uncertainty. It is only thanks to the comparison with model-based discharges that these erroneous field estimates could have been identified and rejected. The comparison also permits us to isolate 22 IPEC catchments where the model-based flood hydrographs may be considered consistent with the indirect peak estimates. The efficiency scores reported for the peak comparison over the 22 basins are very high and equal to 0.91 and 0.94 for the peak discharges and the unit peak discharges, respectively. This shows that the model permits an accurate simulation of the flood peaks over those basins. The accuracy is degraded, but not dramatically, when all 33 basins are considered, with efficiency values equal to 0.80 and 0.72 for the peak discharges and the unit peak discharges, respectively. The errors increase when moving from class 1 basins (negligible impacts) to class 3 basins (major impacts), with efficiency values for the last class equal to 0.53 and 0.28 for the peak discharges and the unit peak discharges, respectively. The increasing uncertainty in the indirectly estimated peaks with increasing intensity of geomorphic impacts plays a role in this observed behavior.

The relationship between the unit peak discharges and the rainfall characteristics (Fig. 6) provide both a basic consistency check between two fundamental flood variables and information about the flood dynamics. The case of maximum hourly rainfall intensity (Fig. 6b) is particularly interesting, because 1-h duration corresponds to the time lag at 90 km2 basin size (Marchi et al. 2010), which comprises all the IPEC basins. For this case, a well-defined linear relationship arises, with an envelope relationship that is close to the one representative of the flood response for completely saturated basins. This confirms that the flood peaks were generated during the last phase of the storms, thanks to the combination of saturated soils and increasingly severe rainfall intensity.

The values of event runoff coefficients computed for the 25 October 2011 Magra flood (Fig. 7; mean of 0.41 and standard deviation of 0.21) compare well with those reported for the Mediterranean events under similar hydroclimatic conditions (mean of 0.41 and standard deviation of 0.22; Marchi et al. 2010). These values are larger than those reported for other hydroclimatic regions in Europe, depending mostly on the features of the triggering rainfall (Marchi et al. 2010). The impact of the event rainfall is evident also for the Magra case, which exhibits a large difference between the two identified rainfall amount categories (i.e., MRB and HRB). It is not surprising that the runoff coefficient for IPEC basin V13 (classified as MRB) approaches the scatter of the HRB (Fig. 7), since this is a compound basin with its upstream sector (IPEC basin V11) lying in the HRB area.

Flash flood peak observations and model analyses of hydrologic response permit us to illustrate how storm structure and evolution translate into scale-dependent flood response. To provide a hydroclimatological context for the Magra flash flood, we compared the peak discharges from the Magra event with those from extreme floods that occurred in other Mediterranean regions between 1994 and 2006 (Marchi et al. 2010) in a log–log plot of unit peak discharge versus drainage basin area (Fig. 8). The pattern of maximum unit peak discharges for the Magra flood is well organized for basin scales up to 40 km2, with unit discharges ranging between 20 and 30 m3 s−1 km−2. It is interesting to observe that this spatial scale is controlled by the shape of the convective quasi-stationary rainfall band, characterized by a mean width of 6–8 km (Fig. 3), which translates to drainage areas up to 40–60 km2. The unit peak discharges in this basin size range are close to the envelope curve developed by Gaume et al. (2009) for European flash floods. At larger basin areas, the unit peak discharges scale similarly to the envelope curve, with values for Piana Battolla and Calamazza that are 10%–15% less than those reported for the European curve.

Fig. 8.
Fig. 8.

Unit peak discharge vs drainage area for the 33 considered IPEC catchments, the three gauge stations, and other Mediterranean flash floods. The upper envelope curve for European flash floods (Gaume et al. 2009) is reported.

Citation: Journal of Hydrometeorology 17, 12; 10.1175/JHM-D-16-0081.1

7. Conclusions

The methodology for the integrated hydrologic flash flood analysis has been extended in this work to include evaluation of the geomorphic impacts–related uncertainties affecting indirectly estimated flood peaks. For this purpose, we used a linear error analysis of slope–conveyance indirect peak flow estimates that include errors related to channel erosion and/or aggradation after flood peak, to the estimation of the channel roughness and to the measurements. The 25 October 2011 flash flood in the Magra River basin in Italy, for which geomorphic impact field surveys, high-quality radar rainfall estimates, and discharge data are available, provides a template for the examination of major, flash flood–related geomorphic impacts and the relevant associated uncertainties.

The main findings of this study are summarized as follows:

  1. The uncertainties associated with the slope–conveyance indirect peak flow estimates were assessed for 35 cross sections of the Magra River based on three stratified uncertainty classes depending on the intensity of the geomorphic impact. The results from the uncertainty assessment show a variation in relative error variance from 13.5% to 37.1%, which indicates the significant influence of the geomorphic impacts. This leads to a more robust postflood analysis, with a more realistic accounting of the errors in indirect peak discharge estimates.
  2. A coupled hydrologic–hydraulic model was calibrated based on data from three stream gauges and then verified by comparing model-simulated and field-estimated peak discharges for the 35 IPEC basins, taking into account the uncertainties assessment. A comparison between simulated and estimated peak flows shows strong correlation, with 63% of the basins included in the observational uncertainty range. Integration of rainfall and discharge observations through hydrological modeling and assessment of the impacts of geomorphic effects helped to identify and reject two erroneous field estimates.
  3. A water balance analysis was carried out on the retained model simulations, with computation of the runoff coefficients. Runoff coefficients were up to 0.6 and 0.2, depending on rainfall depths, respectively, essentially influenced by the spatial rainfall organization and an existing trend of increasing runoff with event precipitation. A mean value of 0.41 for the Magra flood is comparable with other Mediterranean events (Marchi et al. 2010) that also show similar large scatter with the relationship with rainfall accumulation. Relatively high correspondence was observed for the relationship between unit peak discharges and basin-average rainfall properties (total rainfall accumulation and maximum hourly rainfall intensities), controlled by the extent of a major quasi-stationary convective band.
  4. Indirect peak flood estimates and model analyses of hydrologic response illustrate the role of storm structure and evolution for scale-dependent flood response. The spatial extent of the major convective band provides a major factor controlling the shape of the scale dependency of peak unit discharges. The values of unit peak discharge for basin areas up to 40 km2 are close to the flash flood peak envelope of Mediterranean events (Gaume et al. 2009), which is also consistent with the unit area of the banded convection.
Further research concerns the extension of the methodology presented in this paper to include uncertainties in flood response model parameterization as well as uncertainty of radar rainfall estimates. Coupling observational and modeling uncertainties would permit a comprehensive assessment of the errors that affect the various components of the approach implemented for an integrated hydrologic flash flood analysis, that is, spatially distributed surveys of flood response, radar rainfall estimation, and hydrologic modeling.

Acknowledgments

Collation of hydrometeorological data and processing of data collated through postflood surveys have been done in the framework of the NextData Project (Italian Ministry of University and Research and CNR). This work also contributes to the HyMeX programme (www.hymex.org) and was partly funded by the Hydrometeorological Data Resources and Technologies for Effective Flash Flood Forecasting (HYDRATE) project (European Commission, Sixth Framework Programme, Contract 037024). The authors wish to thank the Basin Authority of Magra River, the Hydrological Service of Regione Toscana, and the Environmental Agency of Regione Liguria for providing hydrological and geographical data. Giulia Bossi, Simone Calligaro, and Sebastiano Trevisani are acknowledged for their collaboration in field surveys. The participation of William Amponsah and Stefano Crema in this work was supported by Ph.D. fellowships funded by CNR IRPI (Grants 1681 and 2424, respectively). Ana Lucía was supported by the Kinematic of Debris Flows using Large Scale Particle Image Velocimetry (KINOFLOW) project (Autonomous Province Südtirol–Bolzano) at the Free University of Bozen-Bolzano. The comments of two anonymous reviewers helped improve this paper.

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