Upper limits of flash flood stream power in Europe

GEOMOR-05435; No of Pages 10 Geomorphology xxx (2015) xxx–xxx Contents lists available at ScienceDirect Geomorphology journal homepage: www.elsevier.com/locate/geomorph Upper limits of flash flood stream power in Europe Lorenzo Marchi a,⁎, Marco Cavalli a, William Amponsah a,b, Marco Borga b, Stefano Crema a a b CNR IRPI, Corso Stati Uniti 4, 35127 Padova, Italy Department of Land, Environment, Agriculture and Forestry, University of Padova, Campus Agripolis, Viale dell'Università 16, 35020 Legnaro PD, Italy a r t i c l e i n f o Article history: Received 4 May 2015 Received in revised form 2 November 2015 Accepted 8 November 2015 Available online xxxx Keywords: River Flash flood Peak discharge Channel slope Stream power Geomorphic changes a b s t r a c t Flash floods are characterized by strong spatial gradients of rainfall inputs that hit different parts of a river basin with different intensity. Stream power values associated with flash floods therefore show spatial variations that depend on geological controls on channel geometry and sediment characteristics, as well as on the variations of flood intensity: this stresses the need for a field approach that takes into account the variability of the controlling factors. Post-flood assessment of peak discharge after major floods makes it possible to analyse stream power in fluvial systems affected by flash floods. This study analyses the stream power of seven intense (return period of rainfall N100 years at least in some sectors of the river basin) flash floods that occurred in mountainous basins of central and southern Europe from 2007 to 2014. In most of the analysed cross sections, high values of unit stream power were observed; this is consistent with the high severity of the studied floods. The highest values of crosssectional stream power and unit stream power usually occur in Mediterranean regions. This is mainly ascribed to the larger peak discharges that characterize flash floods in these regions. The variability of unit stream power with catchment area is clearly nonlinear and has been represented by log-quadratic relations. The values of catchment area at which maximum values of unit stream power occur show relevant differences among the studied floods and are linked to the spatial scale of the events. Values of stream power are generally consistent with observed geomorphic changes in the studied cross sections: bedrock channels show the highest values of unit stream power but no visible erosion, whereas major erosion has been observed in alluvial channels. Exceptions to this general pattern, which mostly occur in semi-alluvial cross sections, urge the recognition of local or event-specific conditions that increase the resistance of channel bed and banks to erosion or, like short flow duration, reduce the geomorphic effectiveness of the flood. © 2015 Elsevier B.V. All rights reserved. 1. Introduction Stream power, which incorporates river discharge and channel morphological setting to express river energy expenditure, has been proposed as an index of the geomorphic work of major floods (e.g., Baker and Costa, 1987; Magilligan, 1992; Thompson and Croke, 2013) as well as of near-bankfull flows (Knighton, 1999; Fonstad, 2003). Stream power related to bankfull discharge permits homogeneous comparisons of geomorphic work between different parts of a channel network. However, stream power assessment for rare, large floods provides important insights on river energy expenditure for events that are often responsible for major and abrupt morphological changes in the fluvial system. Baker and Costa (1987) computed the stream power of extreme historical floods and paleofloods in the U.S. and underlined the complexity of the relationships between energy expenditure and accomplished geomorphic work. These authors noted that boulder and bedrock channels are modified only by rare, paroxysmal floods, ⁎ Corresponding author. E-mail address: lorenzo.marchi@irpi.cnr.it (L. Marchi). whereas modest flows may play a major role in rivers where channel bed and banks feature fine materials mobilisable by smaller, more frequent floods. Baker and Costa (1987) also identified an upper envelope in the plot of unit stream power (i.e., the energy expenditure per unit area of the channel bed) versus catchment area for catastrophic floods: the envelope is curvilinear, with maxima at 10–50 km2 approximately. Subsequent studies on stream power of major floods largely built on the pioneering work by Baker and Costa (1987). Miller (1990), based on the study of several historical floods in the central Appalachians in the eastern U.S., indicates a value of unit stream power of 300 W m−2 as ‘a reasonable minimum estimate’ of the threshold to be exceeded for producing severe floodplain erosion. However, he noted that, because of the complex interactions between local site characteristics and flood flow, stream power is a rather poor predictor of erosion at individual locations. Magilligan (1992) also referred to a value of unit stream power of 300 W m−2 as an approximate minimum threshold for significant channel adjustment and analysed the flood frequency (expressed as the ratio of peak discharge to Q100) above which this threshold is likely to be exceeded. Several authors (see Barker et al., 2009 and references therein) have observed and discussed variations of stream power, both analysing http://dx.doi.org/10.1016/j.geomorph.2015.11.005 0169-555X/© 2015 Elsevier B.V. All rights reserved. Please cite this article as: Marchi, L., et al., Upper limits of flash flood stream power in Europe, Geomorphology (2015), http://dx.doi.org/10.1016/ j.geomorph.2015.11.005 2 L. Marchi et al. / Geomorphology xxx (2015) xxx–xxx downstream variations along a channel and comparing values observed in different streams. Assessing the downstream variations of stream power can provide useful insights on its relationships with morphological changes along the longitudinal profile of channel reaches. Curvilinear trends of stream power for varying catchment area, already observed by Baker and Costa (1987) for the upper envelope of unit stream power of extreme floods in different river basins, have been observed for downstream variations of cross-sectional stream power and unit stream power for bankfull or near-bankfull discharge (Lecce, 1997; Knighton, 1999; Fonstad, 2003). Recent papers (Barker et al., 2009; Krapesch et al., 2011; Vocal Ferencevic and Ashmore, 2012; Thompson and Croke, 2013; Parker et al., 2014; Bizzi and Lerner, 2015) have analysed the variability of stream power and other hydraulic and topographic variables by means of geographic information systems and by using high-resolution digital elevation models; this has enabled significant advances in the spatially distributed representation of the factors that control channel adjustment. Costa and O'Connor (1995) observed that floods of very short duration (‘flash floods in small basins that rise quickly and are gone in a matter of minutes’ Costa and O'Connor, 1995, p. 55) may produce limited landform changes, notwithstanding high values of peak discharge and maximum stream power; whereas the most effective floods combine high peak discharge (and, hence, large maximum stream power) with long duration. A major role in the capability of floods to produce important geomorphic effects was attributed by Costa and O'Connor (1995) to flow duration and total energy expenditure, computed by integrating the stream power per unit channel width over the flood hydrograph. Magilligan et al. (2015) performed a detailed analysis of the hydraulic and geomorphic processes/effects produced by the tropical storm Irene in two gravel-bed rivers of the northeastern U.S. and refined the interpretation of the role of flood duration proposed by Costa and O'Connor (1995): short duration, high peak discharge floods may actually show limited erosivity and produce little channel widening but have major sedimentological effects, including entrainment and transport of coarse sediment and its deposition across floodplains. Another recent contribution aimed at improving the capability of hydraulic parameters in predicting channel changes is the new metric related to the stress on bends developed by Buraas et al. (2014), which has been successfully applied, in combination with stream power, in two gravel-bed rivers of the northeastern U.S. affected by a major flood. Among the various types of floods, flash floods are particularly interesting in connection with Costa and O'Connor's (1995) observations concerning the role of duration and cumulative energy expenditure for flood effectiveness. Flash floods are associated with short, highintensity rainfalls, mainly of convective origin that occur locally. As such, flash floods usually affect basins b 1000 km2, with response times typically less than one day. Runoff rates often far exceed those of other flood types as a result of the rapid response of the catchments to intense rainfall, modulated by soil moisture and soil hydraulic properties. Flash floods are often associated with complex orography, in that relief may affect flash flood occurrence in specific catchments by a combination of two mechanisms: orographic effects augmenting precipitation and anchoring convection, and steep relief promoting rapid concentration of streamflow (Marchi et al., 2010). Owing to these reasons, flash floods are often geomorphically effective floods at catchment scales b1000–2000 km2, producing significant changes in the pre-flood landforms that persist over several years and that could not have been accomplished by less intense and long-duration floods (Hicks et al., 2005). The small spatial and temporal scales of flash floods, relative to the sampling characteristics of conventional rain and discharge measurement networks, make these events particularly difficult to observe (Borga et al., 2008). In an investigation of 25 major flash floods that occurred in Europe, Marchi et al. (2010) showed that less than one-half of the cases were properly documented by conventional stage measurements. Moreover, streamgauge measurements of flash floods are almost absent at basin area b 100 km2, which is of great interest for stream power analysis. Consequently, the assessment of flash flood stream power is remarkably rare. A further motivation is the great variability of the geomorphic effects of flash floods, which urges investigations on the relationships with hydraulic conditions and the geological and morphological settings of affected channels. This paper presents cross-sectional and unit stream power values for a sample of recent, intense (return period N100 years) flash floods in Europe and discusses possible climatic and morphological controls on stream power values and geomorphic effects of the studied floods. The aims of the study are to extend experimental information on stream power of flash floods and its relationships with the geomorphic effects produced in different climatic and geographical regions of central and southern Europe where such data are still rather sparse. The large spatial variability of precipitation forcing and geomorphological settings associated with the occurrence of flash floods in complex terrains implies that the associated geomorphic response would vary even within small catchments and makes the assessment and analysis of controlling factors, including stream power, particularly challenging. Spatially distributed analysis of stream power for flash floods can provide a metric of energy expenditure for these events and helps to explore the relationships with geomorphic impacts along the channel network. 2. Flash floods and stream power data The database consists of seven flash floods that occurred in Europe from 2007 to 2014 under different climates and in catchments of different morphological settings. Fig. 1 shows the location and related climate classification according to Köppen–Geiger (Peel et al., 2007) of the studied flash floods, whose main characteristics are reported in Table 1. The criteria adopted for flash flood selection are high intensity (the recurrence interval of the flood-generating rainfall exceeds 100 years at least for some rainfall duration and in some sectors of the river basin) and availability of data collected and validated by means of homogeneous procedures; the sample includes only rainfall-caused floods. Data were collected for 110 cross sections; the number of cross sections per event ranges between 2 (Vizze) and 24 (Magra), mostly depending on the overall area impacted by the flood. Only two cross sections were surveyed in Vizze, which were considered sufficient to document the flood in the main river, whereas the tributaries were affected by debris flow. The catchments corresponding to the surveyed cross sections range in area between 0.5 and 1981 km2; however, only two catchments are larger than 1000 km2 in size, which fits the space scale definition of flash flood adopted in this study (see also Gaume et al., 2009; Marchi et al., 2010). The duration of the events is linked to the maximal drainage areas, with the rainstorms lasting 20 h or more in the case of those impacting areas larger than 500 km2 (Argens, Magra, and Cedrino–Posada). Interestingly, these three events occurred in the Mediterranean region. This is consistent with observations by Gaume et al. (2009) and Marchi et al. (2010), who noted that the spatial extent and duration of the flash flood events is generally smaller for continental floods with respect to those occurring in the Mediterranean area. Actually, shorter duration and smaller affected areas characterize the floods in continental and alpine areas (Starzel, Selška Sora, and Vizze), as well as the Lierza. The Lierza catchment (Fig. 1) is located in a hilly area of northern Italy; although Lierza lies close to the Adriatic sea, the local climate lacks typical features of Mediterranean areas and is classified as humid subtropical (Cfa) according to the Köppen–Geiger classification (Peel et al., 2007). The maximal local channel slope at the surveyed sites can be divided into two main groups: the first with the steepest slopes ranging between 0.015 and 0.040 (Starzel, Vizze, Cedrino–Posada, and Lierza) and the second with that between 0.06 and 0.15 (Selška Sora, Argens, and Magra). The maximal unit peak discharges can also be divided into two main groups: the first includes events with the values varying between 10.0 and 11.7 m3 s− 1 km− 2 Please cite this article as: Marchi, L., et al., Upper limits of flash flood stream power in Europe, Geomorphology (2015), http://dx.doi.org/10.1016/ j.geomorph.2015.11.005 L. Marchi et al. / Geomorphology xxx (2015) xxx–xxx 3 Fig. 1. Location map of the studied flash floods; climate classification according to Köppen–Geiger (Peel et al., 2007). (Selška Sora, Argens, and Starzel) and the second those with much larger maximal unit peak discharges, between 25.6 and 28.2 m3 s−1 km−2 (Magra, Cedrino–Posada, and Lierza). The case of Vizze, with unit peak discharges around 1 m3 s−1 km−2, is representative of flash floods in the dry, internal core of the Alps, where rainfall rates and unit peak discharges are less intense compared to other regions, nonetheless representing locally extreme values. Most cross sections are unconfined or partially confined, whereas confined cross sections are limited to some headwater channel reaches. The different classes of channel confinement are almost evenly distributed in the study cases, with the exception of Vizze where both surveyed cross sections are unconfined. For each flash flood, a comprehensive hydrological and geomorphological analysis has been performed. It includes rainfall estimation based on rain gauge and weather radar data, collection of recorded water level and discharge data from streamgauge stations, post-flood assessment of peak discharge in ungauged catchments, and a consistency check of rainfall and discharge data performed through the application of a rainfall-runoff model (Marchi et al., 2009). Post-flood field surveys played a central role in the analysis of the studied flash floods and the collection of stream power data, especially in small ungauged basins. The slope conveyance method (Gaume and Borga, 2008) was used for the indirect estimation of the flood peaks. This method requires a topographical survey of high water marks (corresponding to flood levels), channel bed slope, cross-sectional geometry, and estimation of flow roughness and finally computes the discharge by means of the one-dimensional Manning–Strickler equation, which assumes a uniform flow along a channel reach according to the following formula: Q ¼ A  K  Rh 2=3  Se 1=2 ð1Þ where Q (m3 s−1) is the peak discharge, A (m2) is the wetted crosssectional area, Rh (m) is the hydraulic radius, Se (m m−1) is the energy slope, and K is the Manning–Strickler roughness coefficient. The K coefficient is estimated based on the channel cross-sectional characteristics (mainly river bed materials and riparian vegetation). The approximations Please cite this article as: Marchi, L., et al., Upper limits of flash flood stream power in Europe, Geomorphology (2015), http://dx.doi.org/10.1016/ j.geomorph.2015.11.005 4 L. Marchi et al. / Geomorphology xxx (2015) xxx–xxx Table 1 Summary data on the studied flash floods. River basin (Country) Date of occurrence Storm duration (h) No. of cross sections Catchment area (km2) Mean (Min — Max) Unit peak discharge (m3 s−1 km−2) Mean (Min — Max) Local channel slope (m/m) Mean (Min — Max) Prevailing lithology Previous studies Selška Sora (Slovenia) 18.09.2007 16.5 21 02.06.2008 8 17 Argens (France) 15.06.2010 20 22 Magra (Italy) 18.10.2011 24 24 4.4 (1.5–10.8) 3.0 (0.8. -11.7) 3.7 (0.7–10.0) 12.0 (2.3–28.2) 0.022 (0.005–0.060) 0.019 (0.005–0.040) 0.017 (0.003–0.075) 0.029 (0.002–0.150) Limestone, schist and shale Limestone, marls and claystone Limestone and granite Sandstone and mudstone Marchi et al. (2009) Starzel (Germany) 29.8 (1.9–147) 28.1 (1.0–120) 232.2 (3.0–1981) 81.9 (0.5–956) Vizze (Italy) 4–5.08.2012 8 2 59.1 (45.2–73) 1.3 (1.1–1.5) 0.015 (0.014–0.015) Cedrino–Posada (Italy) 18.11.2013 24 17 Lierza (Italy) 02.08.2014 184.6 (3.9–550) 4.7 (1.5–12.2) 13.4 (6.2–25.6) 18.1 (12.2–27.6) 0.014 (0.003–0.03) 0.025 (0.010–0.040) 1.5 7 implicit in this approach, and in its application to post-flood assessment of intense flash floods, are discussed by Marchi et al. (2009). In this paper, we use the term cross-sectional stream power for the power per unit channel length and unit stream power for the power per unit wetted area. Peak discharge, longitudinal slope, and channel width enabled computation of cross-sectional stream power and unit stream power for all surveyed cross sections. A spatially distributed representation of stream power variability across different catchments hit by the studied flash floods was thus obtained. Cross-sectional stream power Ω (W m−1), which represents the rate of energy expenditure per unit channel length, was computed as: Ω ¼ γ  Se  Q Niedda et al. (2015) channel conditions for Magra, Cedrino–Posada, and Lierza floods. The cross sections were categorised to elucidate the relationships between the morphological characteristics of the cross sections and the geomorphic effects. The following four classes have been used for cross section classification (Fig. 2): • bedrock: the cross section is entirely on bedrock (thin sediment cover can be present); • semi-alluvial: this class includes cross sections consisting of alluvial material and bedrock; it also includes alluvial cross sections partially reinforced with riprap and revetment walls; • alluvial: the cross section entirely consists of alluvial material; and • artificial: lined channels, channel banks protected with riprap, etc. ð2Þ where γ (9810 N m−3) is the specific weight of water, Q (m3 s−1) is the peak discharge, and Se (m m−1) is the energy slope. Unit stream power ω (W m−2), which represents the energy expenditure per unit area of the channel bed, is calculated as cross-sectional stream power relative to channel width W (m): ω ¼ γ  Se  ðQ=W Þ: Gneiss, Micaschist, Calcschist, Amphibolite Limestone and granite Marls, claystone, conglomerates Ruiz-Villanueva et al. (2012) Payrastre et al. (2012) Mondini et al. (2014); Nardi and Rinaldi (2015) Rinaldi et al. (2015) ð3Þ The channel width required for the estimation of unit stream power is obtained as the width of the water surface corresponding to the flood level. Only a few of the cross sections of our sample are located along the same channel; whereas most of them, although belonging to the same river systems, are located in different catchments. As a consequence, our analysis does not provide insights on the downstream variation of stream power but indicates the variability among catchments of different size hit by the same flood and among floods that occurred under different climates and in basins of different morphological characteristics. The relationships between the morphological characteristics of the cross sections and the geomorphic effects produced by the flood have been analysed for the three most recent events (Magra, Cedrino–Posada, and Lierza). A common feature of these floods is their high intensity, demonstrated by high unit peak discharges (Table 1). Excluding the other floods, mostly characterized by lower unit peak discharges, has permitted us to reduce the bias in the relationships between crosssectional characteristics and erosion processes caused by differences in flood magnitude. The geomorphological settings of the cross sections were investigated by means of aerial photo interpretation and field surveys; aerial photos have also enabled recognition of pre-flood The geomorphic effects, essentially represented by channel widening owing to fluvial entrainment and bank erosion/failure have been grouped into three classes of intensity: • negligible; • small to moderate channel widening dominated by fluvial entrainment; and • major: large channel widening, major erosion and/or failure of banks, and erosion of the floodplain. 3. Results The relationships between peak discharge versus basin area (Fig. 3A) permit recognition of an upper envelope, which is defined by floods in the Cedrino–Posada, Magra, and Lierza rivers. The pattern is linear on logarithmic scales, as expected for the relationship between these two variables, which is commonly represented by means of a power relationship (Castellarin, 2007, and references therein; Gaume et al., 2009). The relationship of channel slope with basin area (Fig. 3B) shows a large variability within each of the studied cases. Moreover, we can see that high slopes are common in the channels of the Magra, which shows also the highest mean value of channel slope (Table 1), and of the Argens. The scatterplot outlines a nonlinear (in the log–log plot) variation of channel slope with drainage area; a marked decrease occurs for larger areas (approximately above 100 km2). As observed by Lecce (1997), the nonlinear relationship between channel slope and drainage area imparts a nonlinear pattern also to the relationships between cross-sectional stream power and catchment area. Please cite this article as: Marchi, L., et al., Upper limits of flash flood stream power in Europe, Geomorphology (2015), http://dx.doi.org/10.1016/ j.geomorph.2015.11.005 L. Marchi et al. / Geomorphology xxx (2015) xxx–xxx 5 Fig. 2. Examples of channel cross sections: (A) bedrock, (B) semi-alluvial, (C) alluvial, (D) artificial. The relationships with hydrologic and topographic controlling factors have permitted exploring the variability of stream power between floods and within each flood event. In the scatterplot of cross-sectional stream power versus basin area (Fig. 4A), two floods (Cedrino–Posada rivers and Magra River) define the upper boundary of the distribution for most basin sizes, with the third Mediterranean flood (Argens) featuring lower values. For small basin areas, the stream power of the Lierza flood approaches the values observed in the Magra. When the small basin size is taken into account, the Lierza is characterized by rather low values of channel slope (Fig. 3B). This did not preclude the occurrence of high values of cross-sectional stream power for this flood (Fig. 4A), inasmuch as the extreme peak discharge observed in this small stream balanced slope conditions not favourable to the formation of high-energy flows. The lowest values are observed for the Starzel flood, which defines the lower envelope of the relationship between cross-sectional stream power and catchment area. The relationship is nonlinear in the log–log plot: the increase of crosssectional stream power shows a pronounced attenuation for the largest drainage areas. Similar to what was observed for cross-sectional stream power, the highest values of unit stream power occur for the Mediterranean flash floods of the Magra and Cedrino–Posada (Fig. 4B). The flood of the Cedrino–Posada shows very high values also for large drainage areas, for which Magra and Argens (the most similar as to climate settings and size of involved river basins) show a remarkable decrease of unit stream power. The nonlinear variation of unit stream power with catchment area has been interpolated by Lecce (1997) using power functions or logquadratic functions. The application of log-quadratic regression to six flash floods of our sample (Vizze basin was excluded because data are available for two cross sections only) is shown in Fig. 5. In four out of the six cases, the log-quadratic fitting permits a satisfactory Fig. 3. Scatterplots of peak discharge (A) and local channel slope (B) versus catchment area. Please cite this article as: Marchi, L., et al., Upper limits of flash flood stream power in Europe, Geomorphology (2015), http://dx.doi.org/10.1016/ j.geomorph.2015.11.005 6 L. Marchi et al. / Geomorphology xxx (2015) xxx–xxx Fig. 4. Scatterplot of cross-sectional stream power (A) and unit stream power (B) versus catchment area. Fig. 5. Log-quadratic interpolation between unit stream power and catchment area for six studied flash floods. Please cite this article as: Marchi, L., et al., Upper limits of flash flood stream power in Europe, Geomorphology (2015), http://dx.doi.org/10.1016/ j.geomorph.2015.11.005 L. Marchi et al. / Geomorphology xxx (2015) xxx–xxx interpretation of the dependence of unit stream power on basin area, although the explained variance is rather low. Because of small sample sizes and uneven distribution of drainage areas within some samples, single cases may have a major impact on the representation of the relationship between unit stream power and drainage area. This is clearly visible in the Magra: one small catchment (0.5 km2, indicated by an arrow in Fig. 5D), which lies in the sector of the basin that received the most intense rainfall, is drained by a steep bedrock channel (Fig. 2A) and is not balanced by other catchments of similar size with different morphological characteristics. This catchment biases the value of maximum unit stream power toward small-sized basins (dashed line in Fig. 5D). This catchment was retained in the database and used in all other analyses as it can be deemed representative of high values of stream power attained in small, steep bedrock channels. However, it was not considered for fitting the regression of unit stream power with basin area (continuous line in Fig. 5D). A decrease of unit stream power with increasing basin area is not clearly visible for the Cedrino–Posada flood (Fig. 5E). The variance explained by a logquadratic regression for the Cedrino–Posada flood is very low and only marginally higher than that of a power relationship that would indicate a slight increase of unit stream power with increasing basin area. This can be partly ascribed to the large extent of flood-generating convective bands, which produced very high values of peak discharge even for large drainage areas. Moreover, the lowermost, low-slope channel reaches, which could have shown a decrease of unit stream power because of the low slope near the river outlet to the sea, have not been surveyed because the flood discharge was altered by the presence of reservoirs. A similar pattern (i.e., the absence of a clearly defined decrease of unit stream power with increasing drainage area) was observed in the Lierza (Fig. 5F), where it can be attributed to the structural controls on local channel slope, which frequently cause very gentle slopes even for small drainage areas. The drainage area at which the log-quadratic regression identifies maximum values of unit stream power shows relevant differences between the six studied floods and ranges from 6.4 km2 for the Lierza to 94 and 123 km2 for the Argens and the Cedrino–Posada, respectively. The areas corresponding to the highest values of unit stream power depend on the extent of the rainstorm that triggered the flood and on the spatial organization of the drainage network affected. Significantly, in the Magra flood, notwithstanding the large total area of the drainage basin considered (more than 900 km2 in the main stream and 500 km2 in its main tributary), the log-quadratic interpolation indicates the maximum value of unit stream power for a drainage area of 18 km2, closer to the floods of the Selška Sora and Starzel (14 and 12 km2, respectively) than to the other large-extent Mediterranean floods. This can be attributed to the spatial distribution of the rainfall that caused the flood of 25 October 2011 in the Magra River, which occurred with the highest intensity in a narrow belt that covered the right tributaries of the main river and the central sector of its most important tributary, the Vara River (Rinaldi et al., 2015). As a consequence, very intense flash floods occurred in several catchments that drain areas up to 40 km2 approximately (Mondini et al., 2014; Rinaldi et al., 2015) and are characterized by relatively steep and narrow channels, thus resulting in high values of unit stream power. The peak discharge in the main channels, although relevant, was attenuated by the limited contribution from the sectors of their drainage basins that had received significantly lower rainfall amounts. Accordingly, unit stream power peaked at small drainage areas and substantially decreased in the largest basins. Table 2 reports the number of cross sections and the average value of unit stream power for each combination of geomorphic effects and cross section type. The studied flash floods caused geomorphic changes in almost all erodible (alluvial) and partly erodible (semi-alluvial) cross sections. Major erosion prevailed in alluvial cross sections, whereas smaller erosion was mostly observed in semi-alluvial cross sections. Local conditions, such as extremely short duration of the flood combined with erosion-resistant channel banks consisting of cohesive 7 Table 2 Unit stream power values for different cross-section classes and observed geomorphic response. Unit stream power (W m−2) No. of cross sections Mean Std. Dev. 9 5 0 1452 2060 762 1375 Semi-alluvial Major Small-moderate Negligible 4 16 3 1862 1763 893 565 1023 385 Bedrock Major Small-moderate Negligible 0 0 4 4195 1859 Artificial Major Small-moderate Negligible 0 0 7 1170 364 Alluvial Major Small-moderate Negligible sediment and channel bed consisting of coarse material (cobbles and boulders), may explain the absence of appreciable erosion in three semi-alluvial cross sections in spite of a remarkable average value of unit stream power of 893 W m−2. Not surprisingly, no perceivable geomorphic effects were observed in erosion-resistant bedrock and artificial cross sections. Although the small sample size hampers the significance of this comparison, we note the large difference in unit stream power between bedrock and artificial cross sections, with the bedrock featuring much higher values. The lower value of unit stream power observed in artificial cross sections is ascribed to lower channel slope (mean slope of 0.047 for bedrock and 0.015 for artificial cross sections). 4. Discussion As recalled in Introduction, Costa and O'Connor (1995) and, more recently, Magilligan et al. (2015) have stressed the importance of flow duration as a measure of the distribution of stream power throughout a flood hydrograph, in combination with maximum flow rate, for determining the geomorphic effectiveness of floods. Even in the domain of flash floods, flow duration may show remarkable variability from event to event, mainly depending on rainstorm characteristics. Homogeneous data on flood duration were not available for all studied floods, and thus integrating stream power with flood hydrographs was not possible. However, rainstorm duration (Table 1) provides a surrogate of flood duration. Mediterranean flash floods (Argens, Magra, and Cedrino–Posada), in addition to high peak discharge, also feature longer duration than flash floods studied in the other considered regions, so they meet both favourable conditions to cause significant landform changes (Costa and O'Connor, 1995). The flash flood in the small catchment of the Lierza, caused by a rainstorm that lasted only 1.5 h, lies at the opposite end of flood duration range. The limited channel erosion observed in semi-alluvial cross sections of the Lierza, in spite of high values of cross-sectional and unit stream power (Fig. 4), is in agreement with the reduced capability of short-duration floods to produce significant channel changes. Field observations in the Lierza, however, showed overbank pebble deposits in channel reaches where undisturbed riparian vegetation witnessed the absence of channel widening (Fig. 6). Such evidence of intense sediment transport supports the study of Magilligan et al. (2015), which distinguishes sedimentological effects from erosive impacts: in the Lierza, short flood duration (and erosion-resistant cohesive channel banks) prevented significant Please cite this article as: Marchi, L., et al., Upper limits of flash flood stream power in Europe, Geomorphology (2015), http://dx.doi.org/10.1016/ j.geomorph.2015.11.005 8 L. Marchi et al. / Geomorphology xxx (2015) xxx–xxx Fig. 6. Overbank gravel and cobble deposits along the Lierza creek. (A) Travelled path (muddy marks on the grass and elongated deposit), (B) detail of the deposit. channel and bank erosion, but readily mobilisable channel bed sediment was entrained and transported. In this study, post-flood channel width was used for unit stream power assessment because it was possible to carefully measure it in the field and it is consistent with topographic and hydraulic variables related to peak discharge computation, whereas pre-flood channel width was not known in several of the studied cross sections for the Selška Sora, Starzel, and Argens floods. Possible problems in the use of post-flood width for channel cross sections where significant widening has occurred during the flood must be mentioned. Since channel widening may occur, entirely or in part, during the recession phase of the flood, post-flood channel width may underestimate the maximum value of unit stream power. Moreover, in cross sections affected by relevant widening the estimation of peak discharge is affected by major uncertainties. The check of discharge values based on rainfallrunoff modelling has permitted discarding some cross sections in which gross inconsistencies arose. Other cross sections affected by large widening, which have passed the model-based consistency check, have been retained for the analysis. The studied flash floods are usually characterized by very high values of unit stream power, which in 88% of the considered cross sections exceeds the value of 300 W m−2 indicated by Miller (1990) and referred to in other studies (Magilligan, 1992; Nanson and Croke, 1992) as the minimum threshold for major erosion. Such high values of unit stream power agree with the occurrence of relevant erosion in most alluvial cross sections. However, other alluvial and semi-alluvial cross sections show minor erosion (Table 2), or even lack evidence of erosion, as we mentioned in the previous section for three semialluvial cross sections. This can be mainly imputed to local conditions (e.g., bank cohesion) that increased the resistance of channel banks to erosion or to short flood duration that reduced the geomorphic effectiveness of streamflow, particularly in the case of the Lierza (Table 1). The rather loose correspondence between unit stream power and channel erosion for the studied cross sections confirms its limited suitability as an index of geomorphic action of floods at specific locations (e.g., Miller, 1990). Buraas et al. (2014) demonstrated the effectiveness of parameters related to the stress in bends in assessing channel reaches susceptible to widening. The cross sections analysed in this study, however, are mostly located in straight channel reaches, which provide the best conditions for indirect peak discharge estimation by means of the slope-conveyance method (Gaume and Borga, 2008): this limits in our study the suitability of the stress on bend metric developed by Buraas et al. (2014), which better applies to more complex reach geometries. Closer relationships between unit stream power and geomorphic changes in channel could be identified at channel reach scale. For instance, Krapesch et al. (2011) found that unit stream power computed on pre-flood channel width satisfactorily predicted channel widening caused by catastrophic floods in gravelbed rivers of Austria. Working at reach scale permits avoiding, or at least averaging, the effects of local conditions that may affect stream power values and the geomorphic effects of the flood (Krapesch et al., 2011; Parker et al., 2014; Nardi and Rinaldi, 2015). In turn, analysis at the scale of cross sections for which discharge data are available, although potentially prone to bias in stream power computation because of local conditions, has the advantage of relying on detailed observations of water level and cross-sectional geometry, derived from either streamflow gauging or, as in the case of this study, on post-flood observations validated through model-based consistency verification. Cross-sectional scale enables an overview of stream power variability between different catchments in which field analysis at channel reach scale could be difficult because of logistic and economic constraints. Moreover, the assessment of discharge and stream power at selected channel cross sections may serve to ‘anchor’ the analysis of stream power and geomorphic response at channel reach scale to specific sites where detailed measurements and hydraulic estimates have been conducted. The differences in cross-sectional stream power and unit stream power observed between the studied flash floods can be mainly ascribed to different flood intensity, which is higher in Mediterranean regions (Table 1) as noticed in previous studies (Gaume et al., 2009; Marchi et al., 2010). It is possible to note that values of unit stream power in several cross sections of the Argens, Magra, and Cedrino–Posada exceed the values (212–2134 W m−2) reported by Grodek et al. (2012) for an extreme flash flood that caused intense channel erosion in small streams of the Mediterranean climatic region of Israel. In the range of drainage area from approximately 10 to 50 km2, where Baker and Costa (1987) observed the most powerful floods, Fig. 7. Comparison of unit stream power for small drainage areas: data from Baker and Costa (1987) and two catchments in the Magra (M) and Argens (A). Please cite this article as: Marchi, L., et al., Upper limits of flash flood stream power in Europe, Geomorphology (2015), http://dx.doi.org/10.1016/ j.geomorph.2015.11.005 L. Marchi et al. / Geomorphology xxx (2015) xxx–xxx with peak values of unit stream power often above 10,000 W m−2, the floods studied in central and southern Europe show definitely lower values (Figs. 4B and 5). If we consider the smallest (b 5 km2) catchments, however, one small bedrock channel in the Magra River basin has greater stream power than four catchments of similar size, whereas a bedrock channel in the Argens is exceeded only by two out of the seven extreme floods (six of them in bedrock channels, one not known) reported by Baker and Costa (1987) for this range of drainage area (Fig. 7). Because data on stream power in steep channels draining small catchments are still scanty, further investigations could contribute to better understanding of the energy expenditure in these headwater streams where channel processes closely interact with hillslopes and, depending on sediment supply, water floods may turn into debris flows. Within each flood, the variability of stream power is controlled by hydrologic and topographic factors. The catchments in the sectors most severely hit by the flood obviously feature high peak discharge and high stream power, whereas the nonlinear change in channel slope with increasing drainage area contributes to attenuating the increase of cross-sectional stream power. Local topographic conditions may alter these general patterns as discussed for the Magra river flash flood (Fig. 5D). Log-quadratic interpolation (Lecce, 1997) has proved capable to interpret the curvilinear variation of unit stream power with catchment area, but the variance explained by the regression equation is generally low. Differently from the data analysed by Lecce (1997), which derived from bankfull discharge at different cross sections along the same channels, our database mainly consists of data collected in different catchments for each flash flood. The variability in geolithological conditions among different catchments, which is usually higher than between different parts of the same catchment, increases also the variability of stream power, causing its weaker correlation with drainage area. Moreover, data analysed in this study relate to flash floods, which are characterized by strong spatial variation in rainfall rate and hence in the intensity of flood response, even between adjacent catchments. This factor also causes the variability of stream power to be higher than the one resulting for downstream variation at bankfull discharge. A further factor that may influence the relationships between unit stream power and catchment area is the cross-section widening caused by the flood. As discussed above, the use of postflood channel width may have caused underestimation of maximum value of unit stream power in the cross sections where channel widening occurred. In the plot of unit stream power against drainage area, this leads to the values of stream power lower than those observed in catchments of similar size for cross sections that did not feature relevant morphological changes. The drainage basin area at which unit stream power shows the highest values varies between the studied floods and is apparently controlled by the area hit by the flood, with Mediterranean flash floods featuring the largest drainage areas. This result could partly be influenced by the choice of the sample of studied catchments, especially regarding the selection of the river sections that drain the largest areas. We remind, however, that homogeneous criteria have been adopted in the selection of the surveyed areas. Although the largest basins also may include catchments that received relatively smaller amounts of rainfall, in all studied events the lowermost analysed cross sections have been chosen close to the basin's sector most severely hit by the flood. 5. Concluding remarks Four principal observations arise from this study. • Data on stream power for seven major flash floods in different hydroclimatic regions of central and southern Europe have been gathered by means of post-flood surveys; data collection has involved 110 cross sections draining catchments from 0.5 to 1981 km2. • The highest values of cross-sectional stream power and of unit stream power occur in Mediterranean regions and are mainly ascribed to the 9 large peak discharges that characterize flash floods in these regions. Mediterranean flash floods also feature longer duration (surrogated by rainstorm duration) than flash floods in alpine and continental regions. Channel slope, although of great importance for local variability of stream power, is not responsible for systematic differences between the study areas. • The variability of unit stream power with catchment area has been represented by log-quadratic relations. The values of catchment area corresponding to the maximum values of unit stream power show relevant differences between the studied floods and are linked to the spatial extent of the events. • If compared to threshold values reported in the literature, unit stream power in most cross sections is able to induce major channel changes. Actual occurrence of such changes has been qualitatively classified into three classes and has been compared with cross-section characteristics (alluvial, semi-alluvial, bedrock, and artificially reinforced cross sections). The results confirm the findings of previous studies on the dominant control of cross-section characteristics on morphological changes, with bedrock and artificially reinforced channel banks undergoing negligible erosion despite high stream power values, and on alluvial channels prone to significant widening. Acknowledgements The authors wish to thank Francesco Comiti for useful discussion on cross-section classification, Eric Gaume for providing data on the Argens flash flood, and Marcello Niedda for his collaboration in the analysis of the Cedrino–Posada flood. This paper is a contribution to the project HyMeX (HYdrological cycle in the Mediterranean EXperiment) (www. hymex.org). The research on the Magra flash flood was partly supported by the Autorità di Bacino Interregionale del Fiume Magra and the NextData Project (Italian Ministry of University and Research). The PhD fellowship of William Amponsah at the University of Padova has been funded by CNR IRPI. The comments of two anonymous reviewers helped improve this paper. References Baker, V.R., Costa, J.E., 1987. Flood power. In: Mayer, L., Nash, D. (Eds.), Catastrophic Flooding. Allen & Unwin, Boston, pp. 1–20. Barker, D.M., Lawler, D.M., Knight, D.W., Morris, D.G., Davies, H.N., Stewart, E.J., 2009. Longitudinal distributions of river flood power: the combined automated flood, elevation and stream power (CAFES) methodology. Earth Surf. Process. Landf. 34, 280–290. Bizzi, S., Lerner, D.N., 2015. The use of stream power as an indicator of channel sensitivity to erosion and deposition processes. River Res. Appl. 31, 16–17. http://dx.doi.org/10. 1002/rra.2717. Borga, M., Gaume, E., Creutin, J.D., Marchi, L., 2008. Surveying flash floods: gauging the ungauged extremes. Hydrol. Process. 22, 3883–3885. Buraas, E.M., Renshaw, C.E., Magilligan, F.J., Dade, W.B., 2014. Impact of reach geometry on stream channel sensitivity to extreme floods. Earth Surf. Process. Landf. 39, 1778–1789. Castellarin, A., 2007. Probabilistic envelope curves for design flood estimation at ungauged sites. Water Resour. Res. 43, W04406. Costa, J.E., O'Connor, J.E., 1995. Geomorphologically effective floods. In: Costa, J.E., Miller, A.J., Potter, K.P., Wilcock, P.R. (Eds.), Natural and Anthropogenic Influences in Fluvial Geomorphology (The Wolman Volume)AGU Geophysical Monograph 89. American Geophysical Union, Washington, D.C., pp. 45–56. Fonstad, M.A., 2003. Spatial variation in the power of mountain streams in the Sangre de Cristo mountains, New Mexico. Geomorphology 55, 75–96. http://dx.doi.org/10. 1016/S0169-555X(03)00133-8. Gaume, E., Borga, M., 2008. Post-flood field investigations in upland catchments after major flash floods: proposal of a methodology and illustrations. J. Flood Risk Manage. 1, 175–189. Gaume, E., Bain, V., Bernardara, P., Newinger, O., Barbuc, M., Bateman, A., Blaškovičová, L., Blöschl, G., Borga, M., Dumitrescu, A., Daliakopoulos, I., Garcia, J., Irimescu, A., Kohnova, S., Koutroulis, A., Marchi, L., Matreata, S., Medina, V., Preciso, E., SempereTorres, D., Stancalie, G., Szolgay, J., Tsanis, I., Velasco, D., Viglione, A., 2009. A compilation of data on European flash floods. J. Hydrol. 367, 70–78. http://dx.doi.org/10. 1016/j.jhydrol.2008.12.028. Grodek, T., Jacoby, Y., Morin, E., Katz, O., 2012. Effectiveness of exceptional rainstorms on a small Mediterranean basin. Geomorphology 159-160, 156–168. Please cite this article as: Marchi, L., et al., Upper limits of flash flood stream power in Europe, Geomorphology (2015), http://dx.doi.org/10.1016/ j.geomorph.2015.11.005 10 L. Marchi et al. / Geomorphology xxx (2015) xxx–xxx Hicks, N.S., Smith, J.A., Miller, A.J., Nelson, P.A., 2005. Catastrophic flooding from an orographic thunderstorm in the central Appalachians. Water Resour. Res. 41, W12428. Knighton, A.D., 1999. Downstream variation in stream power. Geomorphology 29, 293–306. Krapesch, G., Hauer, C., Habersack, H., 2011. Scale orientated analysis of river width changes due to extreme flood hazards. Nat. Hazards Earth Syst. Sci. 11, 2137–2147. Lecce, S.A., 1997. Nonlinear downstream changes in stream power on Winsconsin's Blue River. Ann. Assoc. Am. Geogr. 87, 471–486. Magilligan, F.J., 1992. Thresholds and the spatial variability of flood power during extreme floods. Geomorphology 5, 373–390. Magilligan, F.J., Buraas, E.M., Renshaw, C.E., 2015. The efficacy of stream power and flow duration on geomorphic responses to catastrophic flooding. Geomorphology 228, 175–188. http://dx.doi.org/10.1016/j.geomorph.2014.08.016. Marchi, L., Borga, M., Preciso, E., Gaume, E., 2010. Characterisation of selected extreme flash floods in Europe and implications for flood risk management. J. Hydrol. 394, 118–133. Marchi, L., Borga, M., Preciso, E., Sangati, M., Gaume, E., Bain, V., Delrieu, G., Bonnifait, L., Pogačnik, N., 2009. Comprehensive post-event survey of a flash flood in Western Slovenia: observation strategy and lessons learned. Hydrol. Process. 23, 3761–3770. Miller, A.J., 1990. Flood hydrology and geomorphic effectiveness in the central Appalachians. Earth Surf. Process. Landf. 15, 119–134. Mondini, A.C., Viero, A., Cavalli, M., Marchi, L., Herrera, G., Guzzetti, F., 2014. Comparison of event landslide inventories: the Pogliaschina catchment test case, Italy. Nat. Hazards Earth Syst. Sci. 14, 1749–1759. Nanson, G.C., Croke, J.C., 1992. A genetic classification of floodplains. Geomorphology 4, 459–486. Nardi, L., Rinaldi, M., 2015. Spatio-temporal patterns of channel changes in response to a major flood event: the case of the Magra River (central-northern Italy). Earth Surf. Process. Landf. 40, 326–339. http://dx.doi.org/10.1002/esp.3636. Niedda, M., Amponsah, W., Marchi, L., Zoccatelli, D., Marra, F., Crema, S., Pirastru, M., Marrosu, R., Borga, M., 2015. Il ciclone Cleopatra del 18 novembre 2013 in Sardegna: analisi e modellazione dell'evento di piena. Quaderni di Idronomia Montana 32/1, pp. 47–58 (in Italian). Parker, C., Thorne, C.R., Clifford, N.J., 2014. Development of ST:REAM: a reach-based stream power balance approach for predicting alluvial river channel adjustment. Earth Surf. Process. Landf. 40, 403–413. Payrastre, O., Gaume, E., Javelle, P., Janet, B., Fourmigué, P., Lefort, P., Martin, A., Boudevillain, B., Brunet, P., Delrieu, G., Marchi, L., Aubert, Y., Dautrey, E., Durand, L., Lang, M., Boissier, L., Douvinet, J., Martin, C., Ruin, I., HYMEX TTO2D team, 2012. Analyse hydrologique de la catastrophe du 15 juin 2010 dans la région de Draguignan (Var, France). Congrès SHF: Evènements extrêmes fluviaux et maritimes, Paris, 1–2 février 2012, pp. 1–8. Peel, M.C., Finlayson, B.L., McMahon, T.A., 2007. Updated world map of the Köppen– Geiger climate classification. Hydrol. Earth Syst. Sci. 11 (5), 1633–1644. Rinaldi, M., Amponsah, W., Benvenuti, M., Borga, M., Comiti, F., Lucía, A., Nardi, L., Righini, M., 2015. An integrated approach for investigating geomorphic response to extreme events: methodological framework and application to the October 2011 flood in the Magra River catchment, Italy. Earth Surf. Process. Landf. (under review). Ruiz-Villanueva, V., Borga, M., Zoccatelli, D., Marchi, L., Gaume, E., Ehret, U., 2012. Extreme flood response to short-duration convective rainfall in South-West Germany. Hydrol. Earth Syst. Sci. 16, 1543–1559. Thompson, C., Croke, J., 2013. Geomorphic effects, flood power, and channel competence of a catastrophic flood in confined and unconfined reaches of the upper Lockyer valley, southeast Queensland, Australia. Geomorphology 197, 156–169. Vocal Ferencevic, M., Ashmore, P., 2012. Creating and evaluating digital elevation modelbased stream-power map as a stream power assessment tool. River Res. Appl. 28, 1394–1416. Please cite this article as: Marchi, L., et al., Upper limits of flash flood stream power in Europe, Geomorphology (2015), http://dx.doi.org/10.1016/ j.geomorph.2015.11.005