# Paleohydraulic Reconstruction of Modern Large Floods at Subcritical Speed in a Confined Valley: Proof of Concept

## Abstract

**:**

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}, which implied an increase of Manning’s roughness coefficient from 0.04 to 0.055 s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m

^{−1/3}in less than 15 years.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}) favour the occurrence of heavy precipitation events and floods [34]. Indeed, flooding is the most damaging type of natural disaster in this area [35] with economic losses per province ranging between 200 and $1200\times {10}^{6}$ € [36]. In this study, previously undocumented extreme floods occurred since the early 20th century are analysed in a channel reach of the confined valley downstream of the Marmolejo dam (N ${38}^{\circ}$${3}^{\prime}$${31}^{\u2033}$ E ${4}^{\circ}$${11}^{\prime}$${13}^{\u2033}$), see the sketch in Figure 1.

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}(Q denotes water discharge from now on). The full reach of interest is 6 km in length and exhibits a sharp bend of approximately 140 degrees and 400 m radius that joins two straight channels of 100–200 m bankfull width. It is interpreted as a transfer area between less stable floodplains at the up- and down-stream boundaries [39,40], recall Figure 1. The slope of the channel thalweg is very low (mean value of 0.076%) leading to subcritical flow regime and downstream hydraulic control at all water discharges, referred to as backwater effect [41], as it happens in large flood flow in narrow deep bedrock streams [10]. An additional constraint in the study site is the need to minimise the impact of natural or anthropogenic channel changes, river engineering works and land-use change. Hence the dammed upstream channel reach has only been used to establish well-controlled boundary conditions, being excluded in the paleoflood study.

- The study site must be selected in order that the flood discharge increases result in large increases in the stage. Thus, the confined channel is more preferred than the floodplains. Indeed, an increase in the water discharge from 1400 to 3000 m
^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s^{−1}implies an increase in depth of 4 m in the main channel of the confined valley analysed herein (see Section 3). - It is important to find key control reaches with stable cross-sections and well-preserved high-water indicators. Subsequently, a channel with exposed slate substrate and bedrock gorge was selected in this study, allowing the use of two-dimensional shallow water equations over fixed bed in the hydraulic reconstruction [3,8].

#### 2.2. Gauging Records

#### 2.3. Imagery and Documentary Evidence

^{TM}S910 (Swiss technology); next, rating curves were obtained below the dam and at the bridge/Spa by correlating the date and time of the photo with the inferred flood stage and the water discharge (known at the dam).

#### 2.4. Sedimentary Sequences and Botanical High Watermarks

^{TM}S910, see some illustrative examples in Figure 5. Then, the highest elevation of the PSIs was positioned as a function of the streamwise distance to the dam (denoted by x). In a longitudinal downstream profile, the following sedimentary sequences were identified: erosional reach with exposed bedrock shales at the foot of the dam ($x\le 175$ m, see inset in Figure 1); imbrication of cobbles, pebbles and clasts pointing in the downstream direction few meters downstream ($175<x\le 325$ m, see Figure 5c); field of longitudinal sand bumps in mixed sand-mud ($325<x\le 425$ m, see again Figure 5c); laterally-attached sandy siltlines emplaced from suspension where flow boundaries (bridge peers, Spa building, bend and shoreline) produce markedly reduced local velocities relative to the mean channel velocity ($850<x\le 5000$ m, see e.g., solid line in Figure 4a); bar formation at natural channel bend ($2580<x\le 2630$ m, see Figure 5a); and, preservation of relatively fine-grained flood sediments deposited at tributary mouth slackwater site where the Guadalquivir flooding backflood the tributary up to a level equivalent to the mainstream flood stage ($x\approx 6000$ m).

#### 2.5. Two-Dimensional Shallow Water Modelling, Computational Mesh and Boundary Conditions

^{TM}S910). A computational mesh with a cell size thinner than 1 m was created near the spillways, see Figure 2). Far from the dam, the computational grid is coarser with characteristic edge lengths of 5 m in the channel and 10 m in the valley. The mesh of the reservoir, dam and spillway piers replicates reality. Note the similarity between the simulated geometry (Figure 2e) and the real one (Figure 2c).

## 3. Results

#### 3.1. Systematic, Historical and Paleostage Flood Records

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}and occurred in the year 1925. The data was interrupted between the years 1931 and 1949 because of the Second Spanish Republic and the Civil War (1936–1939). The second wet period developed in the sixties. The water discharge was a maximum of 2859 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}on 17 February 1963. It is remembered as the most severe inundation in the Guadalquivir River Basin. The discharge at the study site achieved a similar magnitude as recorded at the outlet of the Guadalquivir Basin (4275 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}on 19 February 1963, Alcalá del Río, Seville). It is worth pointing out that the duration of the rising-falling limb ($2000\leftrightarrow 2859$ m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}) was shorter than 24 h, whereas less severe floods (1000–2000 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}) took approximately one week. After the dry period of 1980–1995, small floods (<1000 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}) occurred between the years 1995 and 2001. Three modern floods in February 2010, December 2010 and April 2013 reached hourly average (daily average) flow discharges of 1925 (1812), 1434 (1327) and 1378 (1294) m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}, respectively. These modern events were not as extreme as the 1963 flood but, interestingly, damages were likely the same.

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. For water discharges ≥1400 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}, documentary evidence predicts 1 m deeper flows. The water surface elevation was also measured at the reservoir during the period 2009–2013, see solid dots in Figure 2b. Fluctuations of the water level at the same discharge reflect gate operations. At low water discharges (<500 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}), the water level varies between the spillway crest (185 m) and the top of tainter gate (192 m). For higher water discharges, the slope of the rating curve is well defined. Some points do not collapse because the different states of gates provoked several water elevations for the same water discharge at different times.

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}, see Figure 3b, which achieved a similar level as on 24 February 2010.

- The lack of bedforms and fine sediment deposits in the first river reach indicates a transport capacity larger than sediment supply. Only woody debris and a siltline are preserved at elevated bedrock terraces (9 m above the thalweg) or anthropogenic platforms (i.e., roads) below the dam. Surface gravel structures were formed by pebble to cobble grain-sized angular clasts. Downstream imbricated clasts support the argument of low sediment supply to sediment capacity ratio [59]. The high sediment transport capacity below the dam could be associated with the extreme turbulent intensity of the water down the spillways which was able to resuspend fine sediments [60].
- A field of sandy mud bumps developed on a bedrock bench further downstream. Bumps of cohesive mixtures of mud and sand are preserved downstream of flow obstacles (i.e., downstream flexible-wood trees such as Tamarix sp. and Fraxinus sp.). Shrubs on the bumps could initiate the accumulation of sediments as happens in obstacle dune. The bedforms resemble linear or long straight dunes. They are elongated along the longitudinal axis, being the width and height of the bumps much shorter than its longitudinal length.
- Overbank flood-deposited sediments downstream of the bridge ($x\approx 1000$ m) was identified as a sedimentary evidence of flood level with the depth of 11 m. The documentary rating curve in Figure 3a indicates that the corresponding water discharge should be $Q\gg 2000$ m
^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s^{−1}. - Bank erosion also developed further downstream, on the inner side of the natural river bend ($x\approx 2500$ m). The photograph and the 3D representation of the bend shown in Figure 5a and Figure 7b, respectively, illustrate the lateral sediment bar that formed at the bottom of the inner bank. The elevation of the sediment bar measured during fieldworks (≈178 m) is in good agreement with the LiDAR data shown in Figure 7a. The top of the riverbanks at the bend (≈182 m) is elevated 8 m above the thalweg.
- Laterally-attached sandy siltlines were deposited from the end of the bend up to the flow expansion area ($3000<x<5000$ m) during the April 2013 flood. Their locations could be readily identified in the most recent orthophoto (see the solid line in black in Figure 4a) and the elevations could be inferred based on the LiDAR data. For the sake of the brevity, the elevations are shown in Figure 6 only at the beginning and at the end of the sediment deposits.
- Botanical HWMs are depicted with green right triangles in Figure 6. Figure 5b shows an illustrative example which was identified in the flow contraction area of the outlet channel (see location in Figure 4a). These botanical records are consistent with other flow stage indicators as the top level of lateral bars and imagery for the flood occurred in April 2013.

#### 3.2. Calibration of the Numerical Model Pre- and Post-Vegetation Encroachment

^{−1/3}corresponding with a depth of flow reaching branches [62]. According to experimental observations, the free surface is horizontal in a fixed cross section. Numerical simulations (see Section 3.3) show that vegetation is homogeneous along the streamlines, although heterogeneous in the transversal direction. Subsequently, the assumption of a constant Manning’s roughness coefficient might induce some errors in the computation of the cross-section velocity profiles, which were avoided in the paleohydraulic reconstruction by using only PSI-HWMs well correlated with the flood stages.

^{−1/3}corresponds to moderate water discharges <1000 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}independently of the age of floods. Larger water discharges required higher friction factors up to 0.04 s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m

^{−1/3}for the oldest floods (1910–1930). The increase of the friction factor during flood mimics the effect of riparian vegetation on flow resistance and flood potential. Even higher friction factors were needed to simulate appropriately modern floods. Larger values of Manning’s coefficient were found out (up to 0.055 s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m

^{−1/3}for the water discharge of 2000 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}) using the rating curve of 2009–2013 floods (red circles in Figure 2b). Verification of numerical results against hydrological data further downstream is presented in Section 3.3 and Figure 6.

^{−1/3}was compared against actual results, see the dashed-dotted line in Figure 2b. The ensuing rating curve under-predicts the flow depth by a large extent (i.e., 2 m at 2500 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}) with respect to previous numerical results, corroborating backwater effects at the channel outlet that affect the flood stages far upstream (recall Figure 4a).

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. Gates were operated at lower discharges. As gates were assumed open in the numerical simulation, recall Figure 2d,e, there is obviously a disparity between reality and simulation at low water discharge. Yet, the interest is the fluvial regime at flood stage and so this fact does not affect the analysis of larger water discharges.

#### 3.3. Verification of the Simulated Floods with PSIs

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. These values correspond with inundations occurred in 2009–2013 (modern floods) and 1963 (historical flood). Taking into account that the PSI-HWMs described in Section 3.1 constrain the stages with an average error of $\pm 0.25$ m (equivalent to a Manning’s roughness uncertainty of $\pm 0.005$ s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m

^{−1/3}), and using the mean roughness values given in Section 3.2, the Manning’s friction factor was set to 0.045 and 0.055 ± 0.005 s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m

^{−1/3}to simulate modern and historical floods, respectively. So numerical results in Figure 6 show the upper and lower bounds of the simulated water surfaces.

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}and 2000–3000 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}lead to the increases in depth $1.84\pm 0.12$ m and $1.72\pm 0.12$ m, respectively. The free surface slope is much higher for $4500\le x\le 5500$ m due to the sudden expansion that occurs from the outlet channel in the confined valley to the floodplains, as shown in Figure 4a for $Q=1400$ m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}.

^{−1}, respectively, for $1400\le Q\le 2000$ m

^{3}·s

^{−1}but their correlation with bedform dimensions could not be addressed because of the nontransverse shape of bedforms, the non-uniformity of the flow field and the contrasting role of cohesive forces in flow and bed [64,65] which prevent the use of universal laws obtained in laboratory experiments under uniform and steady flow conditions [13,60].

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. Other indicators as HWMs at bridge piers, eroded riverbank levels and botanical evidence (scars on trees) are also in excellent agreement with numerical simulations. Watermarks at the bridge piers are associated with the February 2010 flood and the peak hourly average water discharge 1925 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. Probably, the instantaneous peak discharge was slightly larger which explains the good correlation with the simulation of 2000 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. Slackwater deposits at the rear of the bridge record the same water level and, consequently, are well correlated with $Q=2000$ m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. The unique indicators of the most severe flood in the last century are overbank flood-deposited sediments downstream of the bridge. As a matter of fact, the paleohydraulic reconstruction shows that this sedimentological PSI is well correlated with the water discharge $Q=3000$ m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}(17 February 1963). On the other hand, elevations of tree wounds (green right triangles) overlap with the level of the water discharge $Q=1400$ m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. Scars on trees should have been developed during the most modern inundations (April 2013) with the hourly average peak water discharge of 1378 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. No botanical evidence in Figure 6 could be correlated with the simulated profiles for $2000\le Q\le 3000$ m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. The absence of botanical marks for older, more severe floods corroborates their perishable nature [16].

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}(see cross section in Figure 7a). The water surface elevation achieves approximately 182 m and the flow depth is 7 m. On the other hand, the sediment bar on the inner side of the bend is submerged 4 m below the water surface. The velocity field depicted in Figure 7c is really complex and non-uniform at this location, reaching a maximum of 3 m$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}close to the outer riverbank and much lower values of 1.2 m$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}in the lateral bar. In contrast, the free surface slope is as low as in the rest of the channel, leading to the flow depth field in Figure 7d. The sharp decrease in velocity near the inner bank should provoke the sedimentation of sand grains and the formation of the sediment bar. Interestingly, the streamlines (solid lines in Figure 7c) do not show flow separation. The elevation of woody debris in the outer floodplain is similar to the sediment bar elevation (see Figure 6). Sediments also settled over the outer floodplain, near the bend outlet, recall Figure 4e. Once again, slackwater deposits can be attributed to the sudden decrease in velocity magnitude at this location. The velocity magnitudes achieve values consistent with the simulated ones in the sediment bar, i.e., about 1.2 m$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}.

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}along the whole reach. Leaves debris at the branches of riparian trees, see Figure 5b, indicate the same flood levels as siltlines and numerical simulation. Slackwater deposits at the sudden expansion from the confined channel to the floodplain (denoted with a triangle symbol at $x\approx 6000$ m in Figure 6) poorly constrain the flood stage (i.e., flow depth increases only 1.5 m when the water discharge varies from 1400 to 3000 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}). Floods previous to 2013 could not be identified at these locations because of soil management and the developments of the riparian vegetation cover. Anyway, the most recent flood served to verify the accuracy of the paleoflood reconstruction.

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. Vegetation encroachment developed just after upstream river impoundment, between the years 1962 and 1977 (Figure 4), which yields 10% deeper floods and an increase of Manning’s roughness coefficient from 0.04 to 0.055 s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m

^{−1/3}in less than 15 years.

## 4. Conclusions

- Following Blocken and Gualtieri [30], high-quality experimental data are indispensable for the validation of any computational river dynamics model. Jarrett and England [14] showed that the elevation at the flood-deposited sediments nearest to channel margins provides a reliable and accurate indication of the maximum height of the flood. Hence, sedimentological HWMs can be used to check the accuracy and reliability of the 2D Saint-Venant equations in paleohydrology.
- Botanical HWMs provide valuable data for understanding recent floods and reconstructing their spatial patterns but botanical PSIs are perishable, might be washed out by more extreme floods and need to be preserved, as recently pointed out by Koenig et al. [16].
- Comparison with documentary data and imagery demonstrates that botanical and sedimentological HWMs, as well as mud-lines on man-made structures, are reliable data to indicate flood stages. Furthermore, the rating curve obtained from the combined use of 2D numerical simulations and imagery was nearly as accurate as gauging measurements.
- Overbank flood-deposited sediments are the only PSIs that record the most extreme flood. Interestingly, the simulated water depth of the largest flood in this study is much higher than in Jarrett and England’s [14] work (12 m vs. 4.5 m), and closely matches the observed flood stage, confirming previous findings on the reliability of PSI-HWMs for paleoflood studies.
- Dunes, imbricated pebbles and lateral bars are indirect indicators of the hydraulic conditions. Usually, flow depth and velocity magnitude for a given bedform dimension are deduced from dimensionless correlations under uniform and steady flow conditions [13,60]. However, PSIs are uncorrelated with these universal laws in non-uniform flows.

## Acknowledgments

## Conflicts of Interest

## References

- Baker, V.R. Paleoflood hydrology: Origin, progress, prospects. Geomorphology
**2008**, 101, 1–13. [Google Scholar] [CrossRef] - Carrivick, J.L. Application of 2D hydrodynamic modelling to high–magnitude outburst floods: An example from Kverkfjöll, Iceland. J. Hydrol.
**2006**, 321, 187–199. [Google Scholar] [CrossRef] - Bohorquez, P.; Darby, S.E. The use of one– and two–dimensional hydraulic modelling to reconstruct a glacial outburst flood in a steep Alpine valley. J. Hydrol.
**2008**, 361, 240–261. [Google Scholar] [CrossRef] - Westoby, M.J.; Glasser, N.F.; Brasington, J.; Hambrey, M.J.; Quincey, D.J.; Reynolds, J.M. Modelling outburst floods from moraine-dammed glacial lakes. Earth-Sci. Rev.
**2014**, 134, 137–159. [Google Scholar] [CrossRef] - Baker, V.R.; Benito, G.; Rudoy, A.N. Paleohydrology of late Pleistocene superflooding, Altay Mountains, Siberia. Science
**1993**, 259, 348–350. [Google Scholar] [CrossRef] [PubMed] - Herget, J. Reconstruction of Pleistocene ice-dammed lake outburst floods in the Altai Mountains, Siberia. Spec. Pap. Geol. Soc. Am.
**2005**, 386, 1–118. [Google Scholar] - Carling, P.A.; Villanueva, I.; Herget, J.; Wright, N.; Borodavko, P.; Morvan, H. Unsteady 1D and 2D hydraulic models with ice dam break for Quaternary megaflood, Altai Mountains, southern Siberia. Glob. Planet. Chang.
**2010**, 70, 24–34. [Google Scholar] [CrossRef] - Bohorquez, P.; Carling, P.A.; Herget, J. Dynamic simulation of catastrophic late Pleistocene glacial-lake drainage, Altai Mountains, central Asia. Int. Geol. Rev.
**2016**, 58, 1795–1817. [Google Scholar] [CrossRef] - Benito, G.; Lang, M.; Barriendos, M.; Llasat, M.; Francés, F.; Ouarda, T.; Thorndycraft, V.R.; Enzel, Y.; Bardossy, A.; Coeur, D.; et al. Use of systematic, palaeoflood and historical data for the improvement of flood risk estimation. Review of scientific method. Nat. Hazards
**2004**, 31, 623–643. [Google Scholar] - Baker, V.R. Paleoflood hydrology and extraordinary flood events. J. Hydrol.
**1987**, 96, 79–99. [Google Scholar] [CrossRef] - Lumbroso, D.; Gaume, E. Reducing the uncertainty in indirect estimates of extreme flash flood discharges. J. Hydrol.
**2012**, 414–415, 16–30. [Google Scholar] [CrossRef] - Bohorquez, P.; García-García, F.; Pérez-Valera, F.; Martínez-Sánchez, C. Unsteady two–dimensional paleohydraulic reconstruction of extreme floods over the last 4000 yr in Segura River, southeast Spain. J. Hydrol.
**2013**, 447, 229–239. [Google Scholar] [CrossRef] - Carling, P.A. Freshwater megaflood sedimentation: What can we learn about generic processes? Earth Sci. Rev.
**2013**, 125, 87–113. [Google Scholar] [CrossRef] - Jarrett, R.D.; England, J.F. Reliability of paleostage indicators for paleoflood studies. In Ancient Floods, Modern Hazards; House, P.K., Ebb, R.H., Baker, V.R., Levish, D.R., Eds.; Water Science and Application; American Geophysical Union: Washington, DC, USA, 2002; pp. 91–109. [Google Scholar]
- Carling, P.A.; Burr, D.M.; Johnsen, T.F.; Brennand, T.A. A review of open-channel megaflood depositional landforms on Earth and Mars. In Megaflooding on Earth and Mars; Burr, D., Carling, P.A., Baker, V.R., Eds.; Cambridge University Press: Cambridge, UK, 2009; pp. 33–49. [Google Scholar]
- Koenig, T.A.; Bruce, J.L.; O’Connor, J.; McGee, B.D.; Holmes, R.R., Jr.; Hollins, R.; Forbes, B.T.; Kohn, M.S.; Schellekens, M.; Martin, Z.W.; et al. Identifying and preserving high-water mark data. U.S. Geol. Surv. Tech. Methods
**2016**. [Google Scholar] [CrossRef] - Brázdil, R.; Kundzewicz, Z.W.; Benito, G. Historical hydrology for studying flood risk in Europe. Hydrol. Sci. J.
**2006**, 51, 739–764. [Google Scholar] [CrossRef] - Hall, J.; Arheimer, B.; Borga, M.; Brázdil, R.; Claps, P.; Kiss, A.; Kjeldsen, T.R.; Kriauciuniene, J.; Kundzewicz, Z.W.; Lang, M.; et al. Understanding flood regime changes in Europe: A state-of-the-art assessment. Hydrol. Earth Syst. Sci.
**2014**, 18, 2735–2772. [Google Scholar] [CrossRef][Green Version] - Kjeldsen, T.R.; Macdonald, N.; Lang, M.; Mediero, L.; Albuquerque, T.; Bogdanowicz, E.; Brzdil, R.; Castellarin, A.; David, V.; Flei, A.; et al. Documentary evidence of past floods in Europe and their utility in flood frequency estimation. J. Hydrol.
**2014**, 517, 963–973. [Google Scholar] [CrossRef][Green Version] - Benito, G.; Brázdil, R.; Herget, J.; Machado, M.J. Quantitative historical hydrology in Europe. Hydrol. Earth Syst. Sci.
**2015**, 19, 3517–3539. [Google Scholar] [CrossRef] - Toonen, W.H.J.; Middelkoop, H.; Konijnendijk, T.Y.M.; Macklin, M.G.; Cohen, K.M. The influence of hydroclimatic variability on flood frequency in the Lower Rhine. Earth Surf. Process. Landf.
**2016**, 41, 1266–1275. [Google Scholar] [CrossRef] - Denlinger, R.P.; O’Connell, D.R.H.; House, P.K. Robust determination of stage and discharge: An example from an extreme flood on the Verde River, Arizona. In Ancient Floods, Modern Hazards; House, P.K., Ebb, R.H., Baker, V.R., Levish, D.R., Eds.; Water Science and Application; American Geophysical Union: Washington, DC, USA, 2002; pp. 127–146. [Google Scholar]
- Alho, P.; Baker, V.R.; Smith, L.N. Paleohydraulic reconstruction of the largest Glacial Lake Missoula draining(s). Quat. Sci. Rev.
**2010**, 29, 3067–3078. [Google Scholar] [CrossRef] - Denlinger, R.P.; O’Connell, D.R.H. Simulations of cataclysmic outburst floods from Pleistocene glacial lake Missoula. Bull. Geol. Soc. Am.
**2010**, 122, 678–689. [Google Scholar] [CrossRef] - Winsemann, J.; Alho, P.; Laamanen, L.; Goseberg, N.; Lang, J.; Klostermann, J. Flow dynamics, sedimentation and erosion of glacial lake outburst floods along the Middle Pleistocene Scandinavian Ice Sheet (northern central Europe). Boreas
**2016**, 45, 260–283. [Google Scholar] [CrossRef] - Feldman, A.D. HEC models for water resources system system simulation: theory and experience. Adv. Hydrosci.
**1981**, 12, 297–423. [Google Scholar] - Herget, J.; Roggenkamp, T.; Krell, M. Estimation of peak discharges of historical floods. Hydrol. Earth Syst. Sci.
**2014**, 18, 4029–4037. [Google Scholar] [CrossRef][Green Version] - Couderc, F.; Madec, R.; Martin, N.; Monnier, J.; Vila, J.P.; Dartus, D.; Honnorat, M.; Marin, J. DassFlow: Data Assimilation for Free Surface Flows. Available online: http://www-gmm.insa-toulouse.fr/∼monnier/DassFlow (accessed on 1 September 2014).
- Monnier, J.; Couderc, F.; Dartus, D.; Larnier, K.; Madec, R.; Vila, J.P. Inverse algorithms for 2D shallow water equations in presence of wet dry fronts. Application to flood plain dynamics. Adv. Water Res.
**2016**, 97, 11–24. [Google Scholar] [CrossRef] - Blocken, B.; Gualtieri, C. Ten iterative steps for model development and evaluation applied to Computational Fluid Dynamics for Environmental Fluid Mechanics. Environ. Model. Softw.
**2012**, 33, 1–22. [Google Scholar] [CrossRef] - Darby, S.E. Effect of riparian vegetation on flow resistance and flood potential. J. Hydraul. Eng.
**1999**, 125, 443–454. [Google Scholar] [CrossRef] - Sanders, B.F. Evaluation of on-line DEMs for flood inundation modeling. Adv. Water Resour.
**2007**, 30, 1831–1843. [Google Scholar] [CrossRef] - Blayo, E.; Debreu, L. Revisiting open boundary conditions from the point of view of characteristic variables. Ocean Model.
**2005**, 9, 231–252. [Google Scholar] [CrossRef] - Barredo, J.; Saurand, D.; Llasat, M. Assessing trends in insured losses from floods in Spain 1971–2008. Nat. Hazards Earth Syst. Sci.
**2012**, 12, 1723–1729. [Google Scholar] [CrossRef][Green Version] - Benito, G.; Machado, M.J. Floods in the Iberian Peninsula. In Changes in Flood Risk in Europe; IAHS Special Publication 10; Kundzewicz, Z.W., Ed.; IAHS Press and CRC Press/Balkema: Wallingford, UK, 2012; pp. 372–383. [Google Scholar]
- Instituto Geológico y Minero de España (IGME). Análisis del Impacto de los Riegos Geológicos en España. Evaluación de Pérdidas por Terremotos e Inundaciones en el Periodo 1987–2001 y Estimación Para el Periodo 2004–2033; Instituto Geológico y Minero de España (IGME), Ministerio de Educación y Ciencia, Consorcio de Compensación de Seguros: Madrid, Spain, 2004. [Google Scholar]
- Gilbert, G.K. The transportation of débris by running water. U.S. Geol. Surv. Prof. Pap.
**1914**, 86, 263. [Google Scholar] - Baker, V.R.; Kale, V.S. The role of extreme floods in shaping bedrock channels. In Rivers over Rock: Fluvial Processes in Bedrock Channels; Tinkler, K.J., Wohl, E.E., Eds.; American Geophysical Union: Washington, DC, USA, 1998; pp. 153–165. [Google Scholar]
- Church, M. Bed material transport and the morphology of alluvial river channels. Annu. Rev. Earth Planet. Sci.
**2006**, 34, 325–354. [Google Scholar] [CrossRef] - Buffington, J.M.; Montgomery, D.R. Geomorphic classification of rivers. In Treatise on Geomorphology; Shroder, J., Wohl, E., Eds.; Fluvial Geomorphology; Academic Press: San Diego, CA, USA, 2013; Volume 9, pp. 730–767. [Google Scholar]
- Davidian, J. Computation of Water Surface Profiles in Open Channels; USGS TWRI Book 3: Application of Hydraulics. Ch. A15; United States Geological Survey: Washington, DC, USA, 1984.
- Vannéy, J.R. L’hydrologie du bas Guadalquivir; Consejo Superior de Investigaciones Científicas: Madrid, Spain, 1970. [Google Scholar]
- Sistema de Información del Anuario de Aforos. Available online: http://sig.magrama.es/aforos (accessed on 1 September 2015).
- Sistema Automático de Información Hidrológica de la Cuenca del Guadalquivir. Available online: http://www.chguadalquivir.es/saih/ (accessed on 1 September 2015).
- Pascual, G.; Bustamante, A. Catálogo Nacional de Inundaciones Históricas. Actualización; Nipo: 126-11-150-1; Ministerio del Interior: Madrid, Spain, 2011. [Google Scholar]
- Uribelarrea, D.; Benito, G. Fluvial changes of the Guadalquivir river during the Holocene in Córdoba (Southern Spain). Geomorphology
**2008**, 100, 14–31. [Google Scholar] [CrossRef] - Borja Palomo, F.D. Memoria Histórico-Crítico Sobre las Riadas o Grandes Avenidas del Guadalquivir en Sevilla, Desde Principio del Siglo XV hasta Nuestros días; Excmo. Ayto de Sevilla: Sevilla, Spain, 1877. [Google Scholar]
- Infraestructura de Datos Espaciales de Andalucía. Available online: http://www.ideandalucia.es/IDEAvisor (accessed on 1 September 2015).
- Bohorquez, P.; Aranda, V.; Calero, J.; García-García, F.; Ruiz-Ortiz, P.; Fernández, T.; Salazar, C. Floods in the Guadalquivir River (Southern Spain). In Proceedings of the International Conference on Fluvial Hydraulics, RIVER FLOW 2014, Lausanne, Switzerland, 3–5 September 2014; Schleiss, A., Cesare, G., Franca, M., Pfister, M., Eds.; CRC Press/Balkema: Leiden, The Netherlands, 2014; pp. 1711–1719. [Google Scholar]
- Wu, W. Computation River Dynamics; Taylor & Francis: London, UK, 2007. [Google Scholar]
- Courant, R.; Friedrichs, K.; Lewy, H. On the partial difference equations of mathematical physics. IBM J. Res. Dev.
**1967**, 11, 215–234. [Google Scholar] [CrossRef] - Plan Nacional de Ortofotografía Aérea, Instituto Geográfico Nacional de España. Available online: http://www.ign.es/PNOA (accessed on 1 September 2014).
- Huang, W.; Cao, Z.X.; Carling, P.A.; Pender, G. Coupled 2D hydrodynamic and sediment transport modelling of megaflood due to glacier dam-break in Altai Mountains, Southern Siberia. J. Mt. Sci.
**2014**, 11, 1442–1453. [Google Scholar] [CrossRef] - Guan, M.; Wright, N.; Sleigh, P.; Carrivick, J. Assessment of hydro-morphodynamic modelling and geomorphological impacts of a sediment-charged jökulhlaup, at Sólheimajökull, Iceland. J. Hydrol.
**2015**, 530, 336–349. [Google Scholar] [CrossRef] - Bohorquez, P.; Ancey, C. Particle diffusion in non-equilibrium bedload transport simulations. Appl. Math. Model.
**2016**, 40, 7474–7492. [Google Scholar] [CrossRef] - Heyman, J.; Bohorquez, P.; Ancey, C. Entrainment, motion and deposition of coarse particles transported by water over a sloping mobile bed. J. Geophys. Res. Earth Surf.
**2016**, 121, 1931–1952. [Google Scholar] [CrossRef] - Alho, P.; Aaltonen, J. Comparing a 1D hydraulic model with a 2D hydraulic model for the simulation of extreme glacial outburst floods. Hydrol. Process.
**2008**, 22, 1537–1547. [Google Scholar] [CrossRef] - Petts, G.E. Long-term consequences of upstream impoundment. Environ. Conserv.
**1980**, 7, 325–332. [Google Scholar] [CrossRef] - Hassan, M.; Church, M. Experiments on surface structure and partial sediment transport on a gravel bed. Water Resour. Res.
**2000**, 36, 1885–1895. [Google Scholar] [CrossRef] - Yalin, M.S.; da Silva, A.M.F. Fluvial Processes; IAHR Monograph, IAHR: Delft, The Netherlands, 2001. [Google Scholar]
- O’Connor, J.E.; Webb, R.H. Hydraulic modeling for paleoflood analysis. In Flood Geomorphology; Baker, V.R., Kochel, R.C., Patton, P.C., Eds.; John Wiley and Sons: New York, NY, USA, 1988; pp. 393–402. [Google Scholar]
- Arcement, G.J., Jr.; Schneider, V.R. Guide for Selecting Manning’s Roughness Coefficients for Natural Channels and Flood Plains; U.S. Geological Survey Water-Supply Paper; United States Government Printing Office: Denver, CO, USA, 1989; Volume 2339.
- Whitham, G.B. Linear and Nonlinear Waves; John Wiley & Sons: New York, NY, USA, 1974. [Google Scholar]
- Baas, J.H.; Davies, A.G.; Malarkey, J. Bedform development in mixed sand-mud: The contrasting role of cohesive forces in flow and bed. Geomorphology
**2013**, 182, 19–32. [Google Scholar] [CrossRef] - Baas, J.H.; Best, J.L.; Peakall, J. Predicting bedforms and primary current stratification in cohesive mixtures of mud and sand. J. Geol. Soc.
**2015**. [Google Scholar] [CrossRef] - Slater, L.J.; Singer, M.B.; Kirchner, J.W. Hydrologic versus geomorphic drivers of trends in flood hazard. Geophys. Res. Lett.
**2015**, 42, 2014GL062482. [Google Scholar] [CrossRef] - Naylor, L.A.; Spencer, T.; Lane, S.N.; Darby, S.E.; Magilligan, F.J.; Macklin, M.G.; Möller, I. Stormy Geomorphology: Geomorphic contributions in an age of climate extremes. Earth Surf. Process. Landf.
**2016**. [Google Scholar] [CrossRef]

**Figure 1.**Digital elevation model of the study site showing the Guadalquivir River in the confined valley that connects the floodplains upstream and downstream of the Marmolejo dam (N ${38}^{\circ}$${3}^{\prime}$${31}^{\u2033}$ E ${4}^{\circ}$${11}^{\prime}$${13}^{\u2033}$). The drainage area of the Guadalquivir River Basin upstream of the dam is 19,546 km

^{2}. The characteristic dimensions of the dam are: height = 20 m, crest length = 230 m, spillway crest = 186.2 m, top of tainter gate = 191.73 m, outlet channel elevation = 175.35 m, reservoir capacity = 13 Hm

^{3}and design flood = 3450 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}.

**Figure 2.**(

**a**) Flood frequency distribution and relative magnitude of the Guadalquivir river instrumental floods at Marmolejo dam; (

**b**) Rating curve upstream and downstream of the dam; (

**c**) Flooded area below Marmolejo dam on 24 February 2010 for $Q=1847$ m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. The distance between the old and new hydropower is nearly the same as the length of the dam, i.e., 195 m; (

**d**) Detail of the water surface elevation; and (

**e**) the computational mesh as for panel (

**c**) with $Q=1900$ m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}and $n=0.06$ s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m

^{−1/3}. The grid resolution is <1 m at the spillways and progressively coarser (<10 m) over the valley. The simulated water surface is nearly flat (vanishing free surface slope) few meters downstream of the dam in agreement with observations in panel (

**c**). Note the similarity between the modelled hydraulic structure and the real one as well as the modelled and observed inundated areas.

**Figure 3.**(

**a**) Rating curve at the bridge/Spa based on in situ photographs during 2009–2013 floods, botanical high-water marks (HWMs), mud-lines on bridge piers and overbank flood-deposited sediments; (

**b**) Flooded area on 18 February 1963 when the flow rate was 2200 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}.

**Figure 4.**(

**a**) Blue colour represents the inundated area obtained in the numerical simulation for the water discharge $Q=1400$ m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}with Manning’s coefficient $n=0.05$ s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m

^{−1/3}. Numbers show the location and the distance to the dam (in km) of the main paleostage indicators (PSIs). The black lines highlight the slackwater deposits of fine sediments found out along the riversides in fieldworks as well as in the 2014 orthophoto; (

**b**–

**e**) Sequence of orthophotos in the bend (white box in panel (

**a**)) showing the states before/after river regulation (1956/1977) and snapshots before/after modern floods (2007/2014). Note the absence of riparian vegetation in 1956 (panel (

**b**)), the proliferation of riparian vegetation after river regulation (panel (

**c**)) which started in 1962 with Marmolejo dam and prevails up to present days (panels (

**d**,

**e**)), and the presence of slackwater deposits in 2014 (panel (

**e**)) as a consequence the April 2013 flood.

**Figure 5.**(

**a**) Snapshot acquired with Leica DISTO

^{TM}S910 during the positioning of the top of the lateral bar in the river bend (square box in Figure 4a); (

**b**) Botanical evidence in the left bank of the hydraulic control reach: it is located within the contraction area depicted in Figure 4a. The highest watermark in the tree (8 m above the thalweg) was used as botanical evidence establishing the water level of ∼180 m at $x=5100$ m; (

**c**) Sand dune downstream a tamarisk tree and sedimentological sequence of the internal organisation of the sand dune.

**Figure 6.**Streamwise profile of the simulated water surfaces for the flow discharges: 500 ($n=0.02$ s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m

^{−1/3}), 1400 ($0.04\le n\le 0.05$ s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m

^{−1/3}), 2000 and 3000 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}($0.05\le n\le 0.06$ s$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m

^{−1/3}). The dotted line represents the thalweg profile. Symbols correspond with the PSIs in Figure 2b and Figure 3a, except empty circles and upward triangles which represent pebbles and dunes, respectively.

**Figure 7.**(

**a**) Characteristic cross section at the natural river bend shown in Figure 4b–d. Flood levels for $Q=500$ and 1400 m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}are depicted in light and dark blue, respectively; (

**b**) 3D view of the river bend (base flow level =175 m) and sediment bar shown in Figure 5a. Panels (

**c**,

**d**) show simulated values of the velocity magnitude (m$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}) and the flow depth (m) with $Q=1400$ m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}, respectively.

**Figure 8.**Details of the simulated (

**a**) flow depth; and (

**b**) velocity magnitude from the dam to the Spa ($x\le 775$ m) with $Q=1400$ m

^{3}$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$s

^{−1}. Representative streamlines and velocity vectors are also depicted.

© 2016 by the author; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bohorquez, P. Paleohydraulic Reconstruction of Modern Large Floods at Subcritical Speed in a Confined Valley: Proof of Concept. *Water* **2016**, *8*, 567.
https://doi.org/10.3390/w8120567

**AMA Style**

Bohorquez P. Paleohydraulic Reconstruction of Modern Large Floods at Subcritical Speed in a Confined Valley: Proof of Concept. *Water*. 2016; 8(12):567.
https://doi.org/10.3390/w8120567

**Chicago/Turabian Style**

Bohorquez, Patricio. 2016. "Paleohydraulic Reconstruction of Modern Large Floods at Subcritical Speed in a Confined Valley: Proof of Concept" *Water* 8, no. 12: 567.
https://doi.org/10.3390/w8120567