Uncertainty estimation of simulated water levels for the Mitch flood event in TegucigalpaD. Fuentes1,2, S. Halldin1, C-Y. Xu1,3 and L-C. Lundin1

1 Department of Earth Sciences, Uppsala University, Villavägen 16, SE-752 36 Uppsala, Sweden2 Instituto de Ciencias de la Tierra, Universidad Nacional Autónoma de Honduras, Blv. Suyapa, Ciudad Universitaria, Tegucigalpa, Honduras

3Department of Geosciences, University of Oslo, P O Box 1047, Blindern, NO-0316, Oslo, NorwayContact: diana.fuentes.geo.uu.se

Water-surface profiles for the hurricane Mitch event were estimated by assuming steady gradually varied flow conditions in the one-dimensional HEC-RAS hydraulic model. Parameter uncertainty of the model was investigated using the generalized likelihood uncertainty estimation (GLUE, Beven and Binley 1992) methodology.

2.1 DataThe data used in this study include the following :Topography: During March 2000 to April 2001, an airborne light-detection and ranging (LIDAR) survey was conducted in Tegucigalpa by the University of Texas (UT) as a cooperation with the U.S. Geological Survey (USGS) during their survey in response to hurricane Mitch in Honduras (Mastin, 2002). A 1.5 meter cell resolution digital terrain model (DTM) was generated, in addition, a ground surveys was developed to acquire detailed topography around bridges.Discharge: Two years after the Mitch event, Smith et al. (2002) indirectly estimated the peak discharge during Mitch at 16 reaches. Three of 16 peaks were estimated in the study area. The indirect method used observed high-water marks, cross-sections and hydraulic properties in the channel. Observed water levels: High water marks during Mitch were surveyed post event by JICA (2002); the data were obtained by questioning residents who experienced the hurricane. The survey was carried out at approximately 100 m intervals, at 287 points where JICA had set topographic cross-sections.

2.2 Study area and model implementationThe study area is located at the downstream end of the upper part of Choluteca River basin in Honduras. The length of the river reaches summed up to 12.9 km; channel slopes vary from 0.003 to 0.009. Totally 109 cross sections set in this work at intervals of approximately 100 m along the river system were used to extract the topography from a digital terrain model using HEC-GeoRAS software (Figure 1); also 11 bridges were set directly in HEC-RAS. The initial conditions for the Mitch flood were set according to the post-event measures of the discharge estimated by Smith et al. (2002). The only available observed data to compare simulated water elevation with were the surveyed high-water marks obtained by JICA (2002). We used 127 of 287 observed points. Observed high-water levels at the up-most and down-most cross sections in the study area was used as water surface boundary conditions in HEC-RAS.

2.3 Glue methodology

Floods induced by hurricanes are the most widespread hazard in Honduras. Floods and landslides induced by the Hurricane Mitch in 1998 left 5,000 deaths and economic losses of more than $4 billion in the country (Smith et al., 2002). The Mitch-induced flood caused severe damage particularly in Tegucigalpa, the capital city of Honduras, where 15% of the population lives in landslide or flood-hazard areas (JICA, 2002). In Tegucigalpa, as in many other places, hydrometric measurements are impossible to make during extremely large flood events; thus simulation of those events can only be evaluated by indirect measurements, for example, post-event surveys. In this work the inundation extent at the Mitch event was estimated with a hydraulic model within an uncertainty-analysis framework.

2. Materials and methods

1. Introduction 3. Results

4. Conclusions and future workThe model did not reproduce well the water elevation at 10 locations, the reason could be marked meanders bend at the river (e.g. locations 2,3,4,5 and 10 in figure 1) or the presence of a bridge (e.g. location 8). The values of the discharge for the behavioral parameter set showed that indirect methods to estimate peak discharge can overestimate the discharge up to 200%. Future work need to be done in this analysis regarding the sensitivity in the model parameters. Also a stopping criterion should be used to obtain the number of runs necessary to obtain a set of behavioral parameters that can be representative for flood prediction.

References

Table 1 Uncertain parameters, sampling range and prior distribution.

A fuzzy membership function was chosen to account for error in the evaluation data and to quantify the performance of the model at each cross section. The accuracy of observed water levels were searched by plotting observed water-surface profiles and calculating the height of waves that could not be caused by river intersections, bridges, abrupt curves in the river, or changes in the river bed. Most of the wave heights reached up to 0.8 m; however the highest one was 2.5 m. Those heights were increased by 20% to account for other unknown errors. Thus the limits for the fuzzy function were set in a way such that a simulated water level was scored from zero and up to 1 only if its discrepancy from the observed water level was smaller than 3 m, the score values varied according to the proximity to the observed water level, 0.9 m was set because of ambiguity in the observation data (Figure 2). For each of the simulations a global performance was obtained by averaging the score of each cross-section, this average was weighted by a coefficient (number of cross sections with score /total number of cross sections), thus simulation with several cross-sections with zero score will have a lower weight.

Figure 2 Membership function of simulated water level

Figure 1 Study area

Figure 3 Uncertainty boundaries prediction (shaded area) for the simulated water elevation , observation data (asterisk) and channel elevation (solid black line)

A total of 8 parameters were identified as uncertain (Table1). Combinations of parameter values were searched within a Monte Carlo sampling method, obtaining a total of 340,000parameter sets.

Beven, K., & Binley, A. (1992). The future of distributed models: model calibration and uncertainty prediction. Hydrological Processes , 6(3), 20.JICA. (2002). On flood control and landslide prevention in Tegucigalpa metropolitan area of the Republic of Honduras. Tegucigalpa.Mastin, M. C. (2002). Flood Hazard Mapping in Honduras in response to Hurricance Mitch. U.S. GEOLOGICAL SURVEY, Water-Resources Investigations .Smith, M. E., Phillips, J. V., & Spahr, N. E. (2002). Hurricane Mitch: Peak discharge for selected river reaches in Honduras. U.S. Geological Survey.

From340,000 parameter set 17,539 were behavioral. A simulation was classified as behavioral if its global performance was larger than 0.6, which means that on one extreme case at least 65% of the cross sections should be behavioral (have an score larger than zero), and for those behavioral cross sections, the discrepancy between the simulated and observed water level should be smaller than 0.9m (which is the assessed ambiguity in the evaluation data). On other extreme case, all the cross sections should be behavioral, and in average the discrepancy of the simulated and observed water level should be smaller than 1.7 m. A likelihood-weighted cumulative distribution of the behavioral simulated water elevations was used to estimate the prediction limits for the 5 and 95% quantiles.The estimated uncertain boundaries did not bracket 10 observations points along the study area (figure 3 and yellow points in figure 1). Most of the rejected simulations were due to an overestimated water elevation. None of the simulations were found to be behavioral for each of the cross sections. The best scored cross section was the down-most cross section

AcknowledgmentI want to thanks to the Swedish International Development Cooperation Agency (Sida), for supporting me through the project "Research Capacity Building in Nature-Induced Disaster Mitigation

in Central America 2008–2010". I would also like to thank to the National University in Honduras (UNAH) that also supports me in this project.