Studies for the prevention and mitigation of floods require information on discharge and extent of inundation, commonly unavailable or uncertain, especially during extreme events. This study was initiated by the devastating flood in Tegucigalpa, the capital of Honduras, when Hurricane Mitch struck the city. In this study we hypothesized that it is possible to estimate, in a trustworthy way considering large data uncertainties, this extreme 1998 flood discharge and the extent of the inundations that followed from a combination of models and post-event measured data. Post-event data collected in 2000 and 2001 were used to estimate discharge peaks, times of peak, and high-water marks. These data were used in combination with rain data from two gauges to drive and constrain a combination of well-known modelling tools: TOPMODEL, Muskingum–Cunge–Todini routing, and the LISFLOOD-FP hydraulic model. Simulations were performed within the generalized likelihood uncertainty estimation (GLUE) uncertainty-analysis framework. The model combination predicted peak discharge, times of peaks, and more than 90 % of the observed high-water marks within the uncertainty bounds of the evaluation data. This allowed an inundation likelihood map to be produced. Observed high-water marks could not be reproduced at a few locations on the floodplain. Identifications of these locations are useful to improve model set-up, model structure, or post-event data-estimation methods. Rainfall data were of central importance in simulating the times of peak and results would be improved by a better spatial assessment of rainfall, e.g. from radar data or a denser rain-gauge network. Our study demonstrated that it was possible, considering the uncertainty in the post-event data, to reasonably reproduce the extreme Mitch flood in Tegucigalpa in spite of no hydrometric gauging during the event. The method proposed here can be part of a Bayesian framework in which more events can be added into the analysis as they become available.
Losses caused by natural hazards have a significant impact on the world economy, and floods account for around half of all
disasters globally (UN
Nearly 11 000 people were killed in Central America during Hurricane Mitch because of extreme flooding, an estimated 2.7 million lost their homes, and flood damages were estimated to more than 6 billion USD (McCown et al., 1999). This study was initiated by the flood in Tegucigalpa, the capital city of Honduras, on 30–31 October 1998 when Mitch struck the city. The estimated 500-year return period rainfall produced by Mitch (JICA, 2002) caused significant damage to Tegucigalpa, where 1000 casualties were reported and approximately 40 % of its capital stock was damaged (Angel et al., 2004; JICA, 2002). In addition to these calamities, many of Honduras' hydrological archives were swept away from their premises at SANAA (Servicio Autónomo Nacional de Acueductos y Alcantarillados) which was located close to the main channel of the upper Choluteca River.
Simulations of water-level dynamics caused by disastrous events are needed for preparedness, to produce flood-inundation maps useful for urban planning, and to prioritize investments (Pappenberger et al., 2006; Schanze, 2006). Such simulations are also relevant to better comprehend the hydraulic mechanism of large flood events in order to improve model structure (Beven et al., 2011; Jarrett, 1990). However, given that simulations of extreme floods are generally associated with limited data availability and large uncertainties, the question arises as to whether it is possible to achieve simulations that can be useful for contingency planning and prevention.
When hydrometric measurements of discharge and water levels during an event are lacking or highly inaccurate, such information may be inferred from post-event surveys. These can be done through eye-witness accounts and field campaigns (Brandimarte and Di Baldassarre, 2012; Ciervo et al., 2015; Gaume and Borga, 2008; Horritt et al., 2010; JICA, 2002; Smith et al., 2002), sometimes in combination with additional methods such as searches into historical documentation and paleo-flood techniques (Mård Karlsson et al., 2009; Smith et al., 2012; Valyrakis et al., 2015). Such surveys have been useful to estimate hydrometric data of the floods. Pictures and movies can be used to identify locations, flow type, depth, flow velocity, and discharge at the time they were taken (e.g. Ciervo et al., 2015; Le Boursicaud et al., 2016). Post-event information of channel topography and maximum water level can be used to estimate maximum peak discharge (Dalrymple and Benson, 1968; Matthai, 1968).
Post-event-estimated maximum peak discharge can be used to produce probabilistic regional envelope curves (Castellarin, 2007; Gaume et al., 2009) and discharge series for flood-frequency analysis (Cœur and Lang, 2008). These provide design-flood estimates used for inundation mapping (e.g. Brandimarte and Di Baldassarre, 2012). However, an assessment of flood development in time is required for early-warning systems (Schanze, 2006). The development of a flood in time can be obtained through a strategically planned post-event survey of peak discharge and the associated time of the peak (e.g. Delrieu et al., 2005). Detailed hydrographs can also be obtained from rainfall time series in conjunction with post-event hydrometric data, by the use of a rainfall–runoff model (RRM). A RRM in turn can be coupled with a hydraulic model to estimate the water-level development along a floodplain (Bonnifait et al., 2009; JICA, 2002; Montanari et al., 2009; Pappenberger et al., 2005a). Results from hydraulic models can be validated against post-event-estimated peak discharge, time of the peak, maximum water level, and flood-extent data (e.g. Bonnifait et al., 2009; Brandimarte and Di Baldassarre, 2012; Horritt et al., 2010).
Post-event data have been used with deterministic calibration within hydraulic models (e.g. Horritt et al., 2010; JICA, 2002), and for coupling RRMs with hydraulic models (e.g. Ciervo et al., 2015). Using post-event data, Bonnifait et al. (2009) present a multi-variable assessment to find a group of best parameter sets for the TOPMODEL RRM and a 1-D hydraulic model. Borga et al. (2008) and Pappenberger et al. (2006) suggest that post-event data should be used within an uncertainty-analysis framework given their large uncertainties. Di Baldassarre et al. (2010) discussed the advantages of distributed uncertainty mapping, as first proposed by Romanowicz and Beven (1998), in comparison with deterministic mapping. Uncertainty-analysis techniques have been used to account for uncertainty in hydraulic models (Aronica et al., 1998; Bozzi et al., 2015; Brandimarte and Di Baldassarre, 2012; Pappenberger et al., 2005a, 2007) and for the coupling of a RRM with a hydraulic model (Montanari et al., 2009; Pappenberger et al., 2005a) using event-measured data.
Study area and data location; topography data from the Shuttle Radar Topography Mission (SRTM).
Uncertainty-analysis techniques account for possible errors involved in the modelling process, e.g. errors in model parameters and input data, due to lack of knowledge of their true values, spatio-temporal variability, or inaccurate estimation, and errors related to limited knowledge of the behaviour of the real system, i.e. epistemic uncertainty (Beven, 2016, 2009). Thus, in uncertainty-analysis techniques, uncertainties can be associated with several sources that interact among them, in which each interaction is associated with a likelihood dependent on how well it fits the observations. The formal Bayesian approach is a widely used method for uncertainty analysis, with different set-ups available (e.g. Smith and Roberts, 1993). Bayesian techniques have been commonly applied in hydraulic and hydrological modelling (e.g. Hall et al., 2011; Renard et al., 2008) and can be used within a global sensitivity analysis (see summaries by Iooss and Lemaître, 2015, and Sarrazin et al., 2016) to assess the effect of each source of uncertainty on the output (e.g. Abily et al., 2016). An informal Bayesian approach is the generalized likelihood uncertainty estimation (GLUE) framework (Beven and Binley, 1992), which differs in the way likelihood is defined and in that it does not require prior knowledge on the correlations or distributions of the parameter errors, yet with GLUE it is possible to get posterior information in the parameter combinations. In this study we hypothesize that it is possible to reasonably estimate, considering the large uncertainties in the observations, the extreme 1998 flood discharge in Tegucigalpa and the extent of the inundations that followed, from a combination of models and post-event data. We are aware of works that use the combination of hydraulic models and RRMs to assess flood dynamics or others that use post-event data to calibrate either RRMs or hydraulic models, both deterministic and through uncertainty analyses. We are not aware of any previous study combining a RRM, hydraulic modelling, and post-event data within an uncertainty-analysis framework to prove that reasonable estimation of an extreme flood is possible when hydrometric data are lacking. The methodology suggested in this paper integrates TOPMODEL (Beven and Kirkby, 1979; Kirkby, 1997), Muskingum–Cunge–Todini (MCT) (Todini, 2007) routing, and the LISFLOOD-FP (Neal et al., 2012a) hydraulic modelling tool in a GLUE framework.
The study area is the floodplain at Tegucigalpa, approximately 13
An airborne light-detection and ranging (lidar) survey in Tegucigalpa
was conducted in 2000 by the University of Texas in
cooperation with the US Geological Survey (USGS) during their survey in Honduras in response to Hurricane Mitch (Mastin,
2002). They generated a 1.5
Geometry set-up for hydraulic simulation at the Tegucigalpa floodplain. Lidar data from Mastin (2002).
The topography of the Tegucigalpa floodplain upstream sub-catchments was available from the 90
Upstream of the Tegucigalpa floodplain, two stations measured hourly rainfall during the Mitch event (Figs. 1 and 3). One of the stations is operated by Servicio Meteorológico Nacional (SMN, national weather service) and the other by the Universidad Nacional Autónoma de Honduras (UNAH).
Hourly rainfall on 30–31 October 1998 at SMN station (grey bars), UNAH station (black outlined bars), average of the two stations (asterisks), and measured outflow at Concepción reservoir (continuous line).
Post-event estimated peak discharge and time of peaks.
Discharge at three locations was estimated post-event by Smith et al. (2002) using the standard USGS techniques by Benson and Dalrymple (1967). The peaks at the Chiquito River and the Grande River (points 1 and 2 in Figs. 1 and 2 and Table 1) were estimated using the width-contraction analysis that uses the continuity and energy equations between a cross section approaching the contraction section under a bridge (Matthai, 1968). The peak at Choluteca (point 3) was estimated using the slope-area analysis, in which discharge is computed on the basis of the uniform-flow equation involving channel geometry, high-water marks, and roughness coefficients (Dalrymple and Benson, 1968). The measurements of discharge using the width-contraction analysis and the slope-area analysis can be associated with a 25 % error for unfavourable field-data conditions (Benson and Dalrymple, 1967), but up to 100 % overestimation might be associated with the slope-area analysis for slopes greater than 0.2 % (Jarrett, 1987).
A deterministic reproduction of the flood produced by Hurricane Mitch was done by JICA (2002) by setting a rainfall–runoff analysis using a linear reservoir model driven with hourly rainfall data from the SMN station. The produced hydrograph was used as input for the 1-D Mike 11 modelling tool (DHI, 2000) for unsteady flow conditions. In addition to the flood extent (Fig. 2), JICA (2002) reported the maximum peak discharge at the points 4, 5, and 7 in Figs. 1 and 2 and Table 1.
Controlled flow release through the spillway at the Concepción reservoir was conducted and recorded by SANAA during
the Mitch event (Fig. 3). The outflow over Los Laureles dam was not recorded. However, SANAA reported that its gate was
overtopped at 22:30 LT on 30 October, reaching a maximum of approximately 1200
High-water marks during the Mitch flood were surveyed post-event by JICA (2002); the data were obtained by interviewing residents who experienced the event. The survey was carried out at the same locations where the topographic cross sections were made (Fig. 2).
An inspection of the consistency of the data was done prior to the analysis. The inspection was done by plotting the maximum water-level profile to detect possible outliers. The consistency in timing and magnitude along the river network for the post-event maximum peak discharge was also checked. The flood-wave peak and time of the peak were expected to be larger and later downstream from the river confluences respectively.
To quantify the propagation of uncertainty, the GLUE method was used. The assumptions of more formal statistical approaches can not be justified in data-scarce cases with high epistemic uncertainties. Within the GLUE methodology, parameter sets were generated using a Monte Carlo technique, assuming a uniform prior distribution of the parameters.
Behavioural parameter sets, those that perform well in predicting the observations, were selected using a likelihood
measure that reflected the performance of individual simulations with respect to one or several evaluation variables
(
Fuzzy membership function for evaluation of model performance:
Scheme of the modelling framework used to reproduce an extreme flood event using post-event-estimated data to drive and constrain a combination of modelling tools within an uncertainty-analysis framework.
Precipitation (bars) and 100 class hydrographs chosen from the behavioural ones (black plots) for five sub-catchments upstream of the floodplain. Predictive range of the 100% probability limits for all hydrograph simulations (grey shaded area) and rectangles representing the fuzzy set to allow for uncertainty for peak discharge and time of the peak for the sub-catchments of the Chiquito, Guacerique, and Grande rivers.
The dynamic of the water level along the river channel and floodplain was reproduced with the sub-grid channel formulation of the LISFLOOD-FP hydrodynamic model (Neal et al., 2012a). The model requires flow hydrographs as upstream boundary conditions, which were generated using the TOPMODEL RRM (Beven and Kirkby, 1979; Kirkby, 1997) as in Fuentes-Andino et al., (2017) (Appendix A) together with the Muskingum–Cunge–Todini (MCT) flood-routing approach (Todini, 2007) (Appendix B). A scheme of the modelling framework is shown in Fig. 5.
Topographic information is a basis to set up TOPMODEL, which was one reason to select it in our mountainous catchment. Additionally, the version used here (Fuentes-Andino et al., 2017) has been shown to improve model prediction by considering the uncertainty associated with the spatially averaged estimation of rainfall. The mass-conservative version of the Muskingun–Cunge routing, the MCT, was incorporated to consider the sudden release of water from the Concepción reservoir, and it was chosen since a more complex routing could not be applied given the lack of data in the upstream area of the floodplain. The effect of Los Laureles dam on simulating the hydrograph of the Guacerique River sub-catchment was assumed to be negligible since the dam was overtopped long before the most intensive period of the storm.
The TOPMODEL and MCT combination assumes slope-dependent variable velocity at
a hillslope, constant velocity at a normal channel, and a variable velocity
(according to the diffusive wave model of the MCT) at the main channel (whose
length was estimated to have a minimum drainage area equal to
65
For the TOPMODEL, a network width function for each reach was created using topography from the SRTM raster. Only two rain-gauge stations were available, which made it difficult to infer the spatial distribution of rainfall. However, rainfall registered at the two stations was similar; thus, rainfall was assumed to be spatially uniform and estimated as the average of the two time series. Given the large magnitude of the event, it was expected to be associated with little spatial variation.
Uncertainty in rainfall input was taken into account by a multiplier (
All parameters were sampled from uniform distributions with ranges considered large but possible in the literature
(Table 2) and each generated parameter set was used to simulate the Chiquito,
Grande, and Guacerique river sub-catchments (outlets at points 1, 2, and 5 in
Figs. 1 and 2 and Table 1). A stopping criterion as in Pappenberger
et al. (2005b) was
used to decide the number of simulations required. For every 500 behavioural simulations added, a cumulative distribution
function (CDF) of the predicted peak discharge and one of the time of the
peak were estimated (evaluation variables; see
Sect. 3.4.1). These estimated CDFs were compared with the previous one and the number of runs was considered sufficient
when the addition of behavioural simulations did not change the CDF significantly (i.e.
Sampling parameter ranges to run the rainfall–runoff model.
Las Lomas Creek and Salada Creek (points 8 and 9 in Figs. 1 and 2) did not have data to constrain the simulations and, by proximity, the behavioural parameters found at both Grande and Chiquito were used to simulate them. This is expected to not greatly affect the system as the contributing areas for Las Lomas Creek and Salada Creek are relatively small in comparison to the three sub-catchments where post-event data were available (Fig. 1). In addition, these two areas were smaller than the threshold drainage area for applying MCT; therefore, only parameters from TOPMODEL were transferred to those sub-catchments.
To decide on behavioural hydrographs for the Chiquito, Guacerique, and Grande
river sub-catchments, the maximum peak and time of peak post-event
observations, together with their associated uncertainty, were used (refer to
points 1, 2, and 5 in
Table 1). The assumed uncertainty range was
To reduce computational costs and avoid redundancy, 100 representative hydrographs (class hydrographs) were obtained for
each sub-catchment by clustering the full behavioural ensemble. Clustering was done using the K-means flat algorithm also
called Lloyd's algorithm, originally developed by Lloyd (2006), described in
Madhulatha (2012), and with a tool available for use
at Mathworks (2011). Following the K-means algorithm, the number of groups (
The LISFLOOD-FP was used to propagate the flood waves along the channels and
across the floodplain. Here the sub-grid channel formulation following Neal
et al. (2012a) was used, where the floodplain and the channel have a 2-D
square grid
representation and flow is conveyed using the local inertia formulation (de Almeida et al., 2012). Thus, the continuity
equation (Eq. 1) and a simplified version of the momentum equation (where the convective-acceleration term was assumed
negligible) (Eq. 2) were used to keep the continuity of mass and momentum respectively in each cell and between cells.
Equations (1) and (2) are solved using an explicit forward difference scheme on a staggered grid (Bates et al., 2010) which requires fewer numerical operations (about an order of magnitude) than a full 2-D dynamic model (Neal et al., 2012b). The former numerical procedure was computationally more efficient than the latter and therefore more suitable for uncertainty analysis. In addition, the model-grid representation made it possible to obtain the discharge and water-level time series output at any grid along the channel or floodplain.
The basic input data for the LISFLOOD-FP are topography, hydrographs at the upstream boundary conditions, a downstream
boundary condition, and Manning roughness coefficients. To use as topographic
input to the model, the lidar data were
aggregated to 21
Uncertainty of the input hydrographs at each of the upstream boundary conditions was considered by sampling from the
100 class hydrographs. By assuming normal flow, the overall downstream valley slope,
Using a one-at-a-time (OAT) design for sensitivity analysis, the effect that
uncertainty in the channel depth and channel
width (through a multiplying factor) had on the outputs was explored, which led to the incorporation of the channel-width
multiplier (
Sampling range of parameters to run the hydraulic model.
Prior (grey) and posterior (black outlined) relative frequency
distribution for the most sensitive rainfall–runoff parameters: rainfall
multiplier (
Prior and posterior relative frequency distribution (grey and black
outlined bars respectively) of the LISFLOOD-FP parameters (width factor,
slope for the downstream boundary condition, channel roughness coefficient,
and floodplain roughness coefficient:
Prior and posterior relative frequency distribution (grey and black outlined bars respectively) of simulated maximum peak and time of the peak of input hydrographs for boundary conditions.
Performance of the model in predicting high-water marks,
average (
Likelihood of high-water marks during the Mitch event, considering uncertainty in model parameters, model input, and evaluation data to drive and constrain a combination of rainfall–runoff and hydraulic modelling tools.
Likelihood of inundated area during the Mitch event on 30–31 October 1998, considering uncertainty in model parameters, model input, and evaluation data to drive and constrain a combination of rainfall–runoff and hydraulic modelling tools. The deterministic flood extent was obtained by digitalization of the flood extent in JICA (2002).
Different degrees of belief ( One degree of belief value, Two degrees of belief values, Ninety-nine degrees of belief values,
The fuzzy set values of
A parameter set was considered behavioural if the degree of belief was larger
than 0 for each of the 102 evaluation
points. For every parameter set, a global score (GS) was calculated based on a weighted average of the degrees of
belief obtained for each evaluation criterion.
Subsequently, likelihood values were obtained by scaling the global scores by a constant
From prior inspection of the data, it was found that information about the maximum peak discharge and time of the peak was consistent (i.e. in comparison to locations at the upstream reaches): discharge values and times of the peaks were larger and later at downstream locations after the confluences. A plot of the high-water marks showed sudden jumps at some observation points without any obvious physical explanation, but this is perhaps to be expected given the origin of those observations (witness accounts from memory). Thus, we did not eliminate any of the observations, but instead allowed an uncertainty range associated with all observation points.
Behavioural hydrographs to use as the upstream boundary conditions of the hydraulic model were obtained for the
sub-catchments of the Grande, Guacerique, and Chiquito rivers and, by using
behavioural sets at the Grande and Chiquito river sub-catchments, at the
Salada Creek and Las Lomas Creek sub-catchments (Fig. 6). The cumulative
distribution function (CDF) of the predicted peak discharge and of the time
of the peak of 2000, 8000, and 9000 behavioural simulation for sub-catchments
of the Chiquito, Guacerique, and Grande rivers respectively did not change
significantly by adding 500 behavioural simulations more. Thus a total of
3000, 9000, and 10 000 behavioural simulations, obtained from a total of
61 205, 60 237, and 60 833 samples respectively, were considered enough to
infer 100 class hydrographs for the Chiquito,
Guacerique,
and Grande river sub-catchments respectively. When comparing the prior and
posterior distributions of the rainfall–runoff model parameters, five out of
eight parameters were sensitive: the rainfall multiplier (
There were no simulations for which all degrees of belief were larger than 0.
Criteria
Change in the posterior distributions of the parameters showed that the channel roughness coefficient and floodplain roughness coefficient were more sensitive than the channel width factor and the slope for the downstream boundary condition (Fig. 8). Changes in the posterior distribution of the peak and time of the peak showed that the model was unsurprisingly more sensitive to input hydrographs from the larger sub-catchments than from small sub-catchments (Fig. 9). Flood-wave propagation of different input-hydrograph combinations led to prediction of two markedly different times of the peak at the floodplain, resulting in under- (over-) prediction when the earliest (latest) peak of input hydrograph combinations prevailed (Fig. 10).
There were three observed high-water marks in the Chiquito River reach that
were constantly under-predicted and outside
the uncertainty bounds of the observations (Fig. 11). The propagation from the water-level uncertainty to the flood extent
was more evident in urban areas, where the flood extent varies more with changes in the water level due to the presence of
structural features such as buildings (Fig. 12). From behavioural simulations, the 90 % confidence interval for
prediction of the discharge at the floodplain outlet was 2708 to
4619
A field campaign after a large flood event is an opportunity to collect information useful for flood forecasting and subsequent contingency planning in places where hydrometric measurements are lacking because of non-existing or broken gauges.
Our study demonstrated that it was possible, in a data-scarce situation, to reproduce an extreme flood event that was within the bounds of the uncertainty in the evaluation data. Our results support those of Bonnifait et al. (2009) and Ciervo et al. (2015) about the possibility of reproducing an extreme flood event by a suitable combination of RRM and hydraulic modelling tools with only event-based rainfall data and post-event hydrometric data. Here we additionally incorporated the GLUE methodology to account for expert knowledge of uncertainties in model parameters, rainfall input, and evaluation data. Thus, the combination of a RRM with a hydraulic modelling tool within an uncertainty framework as in Montanari et al. (2009) and Pappenberger et al. (2005a) proved to be useful also in the case with only post-event-estimated hydrometric data.
After considering the uncertainties and their interaction it was possible to identify behavioural parameter sets that were used to obtain a realistic probabilistic reproduction of the flood-water level (Fig. 11) and flood extension (Fig. 12). In comparison to the deterministic estimates made by JICA (2002) using different modelling tools, in this work it was possible to obtain predictive ranges of the water level that encompassed most of the observations. The flood extent here, associated with a likelihood at each flooded cell, generally extended beyond the extent of the JICA (2002) mapping.
The combination of TOPMODEL and MCT allowed us to estimate behavioural
hydrographs for the Chiquito, Guacerique, and Grande
sub-catchments. The simulations could be constrained (Fig. 6) in spite of the wide uncertainties in the data and the
simplified assumption of the MCT routing for ungauged basins applied here. The rainfall multiplier (
The rainfall multipliers were sensitive and the means of their posterior distributions varied across sub-catchments (0.93,
1.5, and 1.3 for Chiquito, Guacerique, and Grande respectively) (Fig. 7),
suggesting that the spatial average rainfall estimated from the two available
gauges was overestimated at Chiquito and underestimated at the Guacerique and
Grande sub-catchments. The Guacerique and Grande sub-catchments are larger
and have a higher topographic elevation than the Chiquito sub-catchment.
Underestimation of rainfall for these sub-catchments might be the result of
lack of stations to
represent the rainfall spatial pattern, highly variable in the area (Westerberg et al., 2010). Thus, a simplistic account
of a space- and time-averaged rainfall multiplier as in Fuentes-Andino
et al. (2017) was also useful here to account for bias estimation of the
spatially averaged rainfall. The posterior distribution of the rainfall
multiplier at the Chiquito and
Guacerique sub-catchments clearly aggregated to different mean values. The sensitivity to the multiplier was different in
the case of the Grande sub-catchment, which also showed a different posterior marginal distribution shape for the rate of
depletion (
Different shapes of posterior marginal parameter distributions at the Grande
River sub-catchment relative to the Guacerique and Chiquito river
sub-catchments could be caused by parameter adjustment to fit the
observations or by different hydrological
processes going on in the different sub-catchments. The sudden release of water from the dam could also be a reason for
these differences. The posterior marginal parameter distributions for the Grande River sub-catchment suggest that it has
a shallower effective soil depth (low
Even if more detailed post-event observations of flood extent might do better than water levels in constraining the LISFLOOD-FP (Fewtrell et al., 2011; Horritt and Bates, 2002), the modelling tool predicted the observed high-water marks, peaks, and times of peaks well. Behavioural simulations for which the degree of belief for the peak discharge, time of the peak, and at least 90 % of predicted high-water marks (89 out of 99 observations) were above 0 were identified.
The channel and floodplain roughness coefficients were the most important parameters for the hydraulic model (Fig. 8). As roughness coefficients directly affect the estimation of discharge and water level, the impact of their uncertainty has been shown previously in other studies (Dimitriadis et al., 2016; Pappenberger et al., 2005b; Warmink and Booij, 2015; Wohl, 1998). Here, uncertainty is expected to be particularly large as these coefficients interacted with uncertain post-event estimated discharge and high-water marks and also because they were assumed to be spatially aggregated due to data limitations. For example, a more localized calibration of such coefficients could have helped to tackle the problem of localized channel erosion during flood events common in the area (Guerrero et al., 2012). Given the assumed spatial representation of the roughness coefficients and the uncertainty they are associated with, they interacted with all other sources of uncertainty in a complex way that is difficult to separate. Such complex interactions are contained implicitly in the resulting ensemble of behavioural simulations (Beven, 2016).
The effect of the input hydrographs from the Grande River and Guacerique river sub-catchments on the resulting outputs is evident in Fig. 9. Thus, as in Dimitriadis et al. (2016), here the roughness coefficients and input flow were the most important sources of uncertainties. Two peaks in the input rainfall (Fig. 3) led to two main large peaks in the hydrographs as input boundary conditions (Figs. 6 and 9). The propagation of input hydrographs along the floodplain led to under- or over-prediction of the times of peak (Fig. 10). This suggests that the spatial pattern of rainfall was not well represented by the gauge average, as also suggested by the posterior distribution of rainfall multipliers in the RRM. Since rainfall data played an important role in predicting the times of peak, investment to improve the rainfall measurement system, e.g. radar estimates or a denser rain-gauge network, should be prioritized in the study area, especially because these data are easier to collect relative to discharge in a high-magnitude event.
Some observed high-water marks were constantly largely underpredicted in the estimates by JICA (2002) and outside the prediction bounds produced here, even when allowing for significant uncertainty in the evaluation data (Fig. 11). Inspection at the points that were constantly underpredicted showed that no man-made structure could have been the reason for such disagreement. Thus the problem of predicting at those locations could be caused by the inability of the hydraulic modelling tool to simulate the system under extreme conditions where effects such as sharp river bends might have an important local effect on the flow. However, a previous experiment using the 1-D HEC-RAS model on the same river also agreed with the results obtained here, and no localized effect in the under-predicted places was obtained. Another reason for the disagreement could be large errors in the post-event data.
In general, minor errors between prediction and observations in this work could be caused by a weak spatial representation of topography and roughness coefficient, i.e. special topographic details in a highly populated area with man-made structures that could not be captured by the DEM. However, those local features might not affect the general flood extent (Haile and Rientjes, 2005).
The peak discharge at point 3 (Figs. 1 and 2) was under-predicted by most of the simulations (Fig. 10). However, the high-water mark was over-estimated at that location (Fig. 11). The reasons for this could be an over-estimation of the post-event peak discharge, or an under-estimation of the observed high-water mark, or the simplistic representation of the downstream boundary condition assumed.
A general under-prediction of the water level in the Chiquito River reach could be due to the low (perhaps under-estimated) post-event-estimated peak discharge; as in the comparison with the Grande and Guacerique sub-catchments, most of the hydrograph simulations for the former were rejected because the simulated peaks were larger than the evaluations (even considering the uncertainty) (Fig. 6). This could also be the reason for a lower rate of behavioural sets for the Chiquito River sub-catchment when comparing with the other two.
A detailed inspection of model structure, model set-up, and data at specific points where the modelling tools did not perform well even after considering possible uncertainties in the parameters, input, and evaluation data, could reveal areas for improvement.
This study was set up to demonstrate the use of post-event data and a combination of suitable RRM and hydraulic modelling tools with uncertainty analysis to reproduce an extreme flood in a data-scarce area. The behavioural ensemble found here depends on the uncertainties coming from the model structure (Dimitriadis et al., 2016), quality of the data (Pappenberger et al., 2006), topographic resolution (Haile and Rientjes, 2005), and spatial aggregation of the parameters (Beven, 1995). Considering the dependency with those sources of uncertainties and their interaction, the post-event data proved to be useful in reproducing the Hurricane Mitch flood event. High-water marks obtained from personal memories of an event are a good source of information. To decrease uncertainty of such information, institutions in charge of disaster prevention should be prepared to carry out such surveys soon after flood events when memory is fresh. In fact, soon after extreme events it is also possible to collect that information by surveying the marks left by the flood (e.g. Neal et al., 2009). Post-event-estimated peak discharge, though it is known to be associated with large uncertainties (Benson and Dalrymple, 1967; Jarrett, 1987), was a valuable source of information in this work. A higher spatial availability of flood peak discharge and time of the peak estimates would greatly benefit this methodology as it will allow a better quality control of individual estimates, to leave some of the estimates out for validation, and to estimate more localized patterns of roughness coefficients.
The use of this methodology can be done within a Bayesian framework in which the posterior distribution of the parameters is updated when more events become available. Data from more events could further reduce the predictive uncertainties and help us to learn from the flow behaviour at some localized areas where the errors were large. Post-event estimates in the future could likely also come from social-media information which is becoming gradually more available (Fraternali et al., 2012; Triglav-Čekada and Radovan, 2013).
The flood-hazard map presented here can be used by the committee in charge of disaster contingency and management in the city of Tegucigalpa (CODEM-DC) as a complement to the 5-, 10-, 25-, and 50-year return period hazard map produced in JICA (2002) and the the 50-year hazard map produced in Mastin (2002) and Mastin and Olsen (2002) for spatial planning and to prioritize investment. If real-time discharge measurements are available to calculate the initial saturation of a catchment, behavioural parameter sets updated from a range of events can be used for forecasting the flood extent as shown by Romanowicz and Beven (2003) and Montanari et al. (2009). In the absence of such measurements, a guess of the initial discharge may also work since it will not significantly affect the prediction for the intense period of the event. Furthermore, for that period, our methodology can give a better performance since calibration is done against discharge, time, and water level at the peak. It is also tempting to consider this methodology for forecasting fed both by an improved rain-gauge network and water-level information coming from social media.
In this study we tested the possibility of reproducing an extreme flood disaster in a data-scarce area, the devastating flood in Tegucigalpa triggered by Hurricane Mitch in 1998. It was possible to realistically reproduce this large ungauged flood event by using post-event hydrometric data in combination with rainfall data and various modelling tools, demonstrating the value of post-event field campaigns to constrain the uncertainties in estimates of hydrometric data, model parameters, and output. A methodology has been proposed where post-event-estimated data are used to drive and constrain a combination of rainfall–runoff and hydraulic modelling tools to reproduce floods within a GLUE uncertainty-analysis framework. Results of the flood extent proposed here were comparable to the deterministic mapping produced by JICA (2002) using different modelling tools. However, here more information was embedded as likelihoods of inundation associated with each cell in the floodplain.
Combining the TOPMODEL with the MCT routing to reproduce hydrographs in catchments with rapidly varied flow, e.g. release from a dam, resulted in hydrographs that were within the uncertain bounds of the observations. The predictive capability of the TOPMODEL and MCT combination warrants further exploration with more detailed and less uncertain event data. The rate and bias in the rejection of the hydrographs due to over-estimation indicated under-estimation of post-event-estimated discharge at one location. The propagation of estimated hydrographs through the 2-D hydraulic LISFLOOD-FP resulted in successful predictions of observed high-water marks, discharge peaks, and times of peaks within the uncertainty bounds for most of the evaluation variables. A few critical locations in the floodplain were identified where the model set-up could not reproduce the maximum water level. Locations of disagreement between simulations and evaluations, after considering all important sources of uncertainties, can provide information useful for improving model structure or post-event data-estimation methods. Results showed the importance that rainfall data have in simulating the times of peaks; thus, results would be improved by a better spatial assessment of rainfall. Improvements of this methodology can be done by using it within a Bayesian framework of updating the parameters' posterior distribution when more events become available. The methodology proposed here can be useful for planning, prioritizing investments, and flood forecasting.
The lidar data on Tegucigalpa described in Mastin (2002) are available on request to
the US Geological Survey (USGS). Post-event-estimated peak discharge obtained by the USGS is found in Smith et al. (2002).
Post-event-estimated peak discharge obtained by JICA (2002) is found in
The TOPMODEL scheme in Fuentes-Andino et al. (2017) used here assumes
a grid-cell distributed catchment. For any
Following the TOPMODEL concept (Beven, 1997, 2012; Kirkby, 1997), the
following assumptions are made: (a) the saturated
zone is in equilibrium with a steady recharge rate from an upslope contributing area (
Equation (A2) can be inverted to obtain an initial estimation
of
Thus, the time spent by a water particle on the surface to travel from the
The Muskingum–Cunge–Todini routing (MCT) (Todini, 2007) used in this work
was carried out using guidelines in Tewolde and Smithers (2007) to overcome
the lack of river cross-sectional data. Thus, to propagate a flood wave in
a reach of
length
The specialization factor for correction of the Courant and Reynolds number,
The Kuiper statistic (
The experiment was designed by DFA, KB, SH, CYX, and GDB. DFA carried out the experiment and performed the simulations. DFA prepared the manuscript with contributions from all co-authors.
The authors declare that they have no conflict of interest.
This research was carried out within the Universidad Nacional Autónoma de Honduras (UNAH) through agreement number 75000511–01 and the CNDS research school, supported by the Swedish International Development Cooperation Agency (Sida) through their contract with the International Science Programme (ISP) at Uppsala University (contract number: 54100006). The computations were performed on resources provided by SNIC through the Uppsala Multidisciplinary Center for Advanced Computational Science (UPPMAX) under project p2011010 and the High Performance Computing Center North (HPC2N) under project SNIC 2015/1-448. Thanks to the staff at the Servicio Meteorológico Nacional (SMN, national weather service), the Universidad Nacional Autónoma de Honduras (UNAH) and the Servicio Autónomo Nacional de Acueductos y Alcantarillados (SANAA) for their assistance in providing data for this study. Thanks to the School of Geographical Sciences at the University of Bristol for useful support regarding the LISFLOOD-FP model. Edited by: Roger Moussa Reviewed by: three anonymous referees