Calibration of floodplain roughness and estimation of flood discharge based on tree-ring evidence and hydraulic modelling

Summary

The roughness calibration of floodplain and channels represents an important issue for flood studies. This paper discusses the genesis of scars on trees and their use as benchmarks in roughness calibration. In addition, it presents a methodology to reconstruct unrecorded flood discharge in the Alberche basin of the Spanish Central System. The study is based on the combined use of dendrogeomorphic evidence (i.e. scars on trees), data from the Navaluenga flow gauge (Avila Province) as well as a 1D/2D coupled numerical hydraulic model. A total of 49 scars have been analyzed with dendrogeomorphic techniques. Scar dates are in concert with seven flood events documented in the systematic record (i.e. 1989, 1993, 1996, 2000, 2002, 2003, and 2005). We were also able to identify an additional event dated to 1970, which is before the flow gauge was installed at Navaluenga. Based on the rating curve obtained from the flow gauge, cross-sectional area and data from hydraulic modelling, we cannot find a statistically significant difference between water depths registered at the flow gauge and scar heights on trees (p-value > 0.05), indicating that scars would have been generated through the impact of floating wood and that scars on trees would represent a valuable and accurate proxy for water depth reconstruction. Under this premise, we have estimated the peak discharge of the 1970 flood event to 1684.3 ± 519.2 m³ s⁻¹; which renders this event the largest documented flood for the Alberche River at Navaluenga. In a last analytical step, we discuss the use of scars on trees as benchmark for roughness calibration in ungauged or shortly recorded basins and address the added value of dendrogeomorphic data in flood frequency analysis.

Introduction

Developing reliable hydraulic flood models that provide accurate estimates of flood hazards in urban areas are essential to define the best strategies for flood risk mitigation (Enzel et al., 1993, de Kok and Grossmann, 2010). Recently, computational developments have allowed modelling of large and complex floodplains based on the use of 1D/2D coupled hydraulic models (Tayefi et al., 2007, Leandro et al., 2009, Roca et al., 2008) based on Saint–Venant (1D or unsteady 2D flow simulations; Chow, 1959, Souhar and Faure, 2009) as well as Navier–Stokes depth-averaged equations (steady 2D flow simulations; Denlinger et al., 2002, Duan and Nanda, 2006).

Out of all hydraulic parameters involved in the process, roughness coefficients represent, probably, one of the keys for a realistic numerical simulation of open channel flows, but remain especially difficult to determine (Cook, 1987, Kidson et al., 2005, Thorndycraft et al., 2005, Werner et al., 2005, Zhu and Zhang, 2009) as they are influenced by many factors (Chow, 1959, Aldridge and Garrett, 1973). It is estimated that a 50% error in roughness coefficients could imply an error of nearly 40% in peak discharge estimation (Kidson et al., 2002, Sudhaus et al., 2008).

For decades, the assignment of roughness coefficients in natural channels has been performed by comparing cross-sectional areas and river profiles with photographs of typical river and creek cross-sections (see: Barnes, 1967, Arcement and Schenider, 1989) or by means of empirical equations (Chow, 1959, Yen, 2002). However, in the case of unrecorded floods that occurred without instrumental recording and where documentary or observational sources are lacking (i.e. palaeohydrology sensu Baker, 2008), the assignment of “palaeo-roughness coefficients” represents a major challenge. Frequently, the approaches used to assign roughness values may have several drawbacks and shortcomings for flood studies. Some of the main difficulties include the characterization of historical floods, which is not always possible due to the lack of visual or written data to infer maximum flood stage. In the case of empirical approaches, difficulties also arise due to limited values of channel gradient or hydraulic radius (Ferguson, 2007, Ferguson, 2010), relative submergence of vegetation and boulders (Bathurst, 1993) or due to the need to define a critical flow (Grant, 1997, Tinkler, 1997, Comiti et al., 2009) which it is not always easy in natural reaches. As a result, the estimation of roughness coefficients necessary for the development and the appropriate use of hydraulic models remains particularly difficult, especially when dealing with (exceptionally) large flood events (Wohl, 1998).

Despite the use of new technologies for assessing the physical roughness parameters in river channel such as Terrestrial Laser Scanners (TLS; Hodge et al., 2009a, Hodge et al., 2009b, Heritage and Milan, 2009, Antonarakis et al., 2009) or Light Detection and Range (LiDAR; Casas et al., 2010, Colmenárez et al., 2010), several issues remain: (i) laser beams used for topography are not operational below the water surface, so roughness in the main channel cannot be properly measured in the case of permanent rivers; and (ii) with the exception of bedrock channels, river beds will only represent current roughness conditions, rendering an appropriate estimation of “palaeo-roughness coefficients” impossible.

So far, dendrogeomorphic evidence (i.e. scars on trees; Stoffel et al., 2010) preserved on riparian vegetation has remained an unexplored alternative for roughness calibration and as a palaeostage indicator (PSI; Jarrett and England, 2002, Benito and Thorndycraft, 2004). Dendrogeomorphology benefits from the fact that impacts of past torrential and fluvial activity will be preserved in the growth-ring record of riparian trees (Simon et al., 2004, Stoffel and Wilford, in press) and that palaeo-events can thus be dated with (sub-) annual resolution (Gottesfeld and Gottesfeld, 1990, St. George and Nielsen, 2003, Stoffel and Beniston, 2006, Ballesteros et al., 2010a, Ballesteros et al., 2010b, Ruiz-Villanueva et al., 2010). Tree-ring records of impacted trees have been used successfully in the past for flood discharge or magnitude estimations of events in high gradient streams (Stoffel, 2010, Ballesteros et al., 2011), but they have never been utilized for the assessment and calibration of floodplain roughness in fluvial systems.

The key for past flood research is the establishment of relations between PSI and high water marks (HWM), thus addressing the question of when the flood hydrograph was generating PSI. Previous research suggests that observed deviations between PSI (i.e. scars on trees) and HWM (i.e. fresh floating wood) are lower in low-gradient (i.e. 0.196 ± 0.03 m; Gottesfeld, 1996 – 0.005 m/m) than in high-gradient streams (i.e. −0.6 to 1.5 m in Yanosky and Jarrett, 2002 – 0.04 m/m; −0.88 to 1.35 m in Ballesteros et al., 2011 – 0.2 m/m). Although more work is required to characterize this relationship and to avoid the influence of possible local effects (Jarrett and England, 2002), it can be assumed that the stream gradient and the type of material available for transport could be the principal factors contributing to inaccuracy in estimations.

The main objective of this paper is to study the genesis of scars on trees and their use for spatial roughness calibration in fluvial channels so as to improve the input data for unrecorded flood discharge estimations based on hydraulic models. To this end, we analyzed 44 riparian trees growing on the banks of the Alberche river in the Spanish Central System. The sampled trees exhibited 49 scars and the distribution of scar heights was checked against water depths measured at the local flow gauge using non-parametric statistical tests. In a final step, based on the calibrated hydraulic model, a flood event reconstructed by dendrogeomorphology and older than the local flow gauge record was modelled using only tree-ring data.