Introduction
Losses caused by natural hazards have a significant impact on the world economy, and floods account for around half of all
disasters globally (UN/ISDR, 2016). Prevention and mitigation of floods require information on discharge
and extent of inundation. Such information is commonly unavailable or uncertain, especially during extreme events when
gauging equipment becomes insufficient or is lacking. Data scarcity is further aggravated in developing countries with
weak infrastructure.
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).
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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.
Method
Consistency in the post-event measured data
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.
Uncertainty and evaluation function
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
(oi). Likelihoods were inferred by using the degree of belief (di) of a trapezoidal fuzzy
membership function (Fig. 4), whose shape was chosen to account for
uncertainties in the post-event estimated values,
which are not considered crisp estimations. Thus the degree of belief for a difference smaller than a between the
simulated and post-event estimated values is equal to 1, and it declines
linearly to 0 for differences larger
than b.
Fuzzy membership function for evaluation of model performance: a
and b depend on the uncertainty associated with the
evaluation (oi).
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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.
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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.
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Modelling framework
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.
Representative hydrographs for the upstream boundary condition
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 km2). For each sub-catchment, the main channel was sub-divided
into reaches of approximately 2.5 km to execute the MCT routing. For
the MCT routing at Grande River,
the inflow for the most upstream reach was set equal to the outflow hydrograph from the reservoir, and for other
sub-catchments, to be equal to the hydrograph draining to that reach using TOPMODEL. For the subsequent reaches, this
inflow was estimated as the sum of the outflow from the MCT routing at the immediate upstream reach and the hydrograph
produced by TOPMODEL in the area draining to that reach (excluding the area draining to the upstream reaches). The
modelling time step was equal to 5 min, smaller than the estimated travel
time of the flood wave along the reach,
as required by the MCT routing.
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 (R);
in addition, uncertainty of six model
parameters was considered: the rate of decline of transmissivity (m), horizontal transmissivity (To), time
constant (td), land-use coefficient (lu), flood-wave
celerity (vc), and maximum
soil infiltration rate (imax) (Appendix A). The MCT method required information of the river slope and the
geometry of the cross sections (Appendix B). The former was approximated from
SRTM data, while the latter was inferred
here as a function of discharge using the Manning equation for a wide parabolic channel as in Tewolde and Smithers (2007),
with the channel roughness coefficient (ncu) assumed uniform
along all the reaches to make the modelling system simple and, in view of the
lack of data, to constrain localized values.
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. P<0.05) using the Kuiper (1960)
statistical test (Appendix C). This statistical test was considered suitable
since it is sensitive to changes in the tail and to the median values of the
distribution; therefore, it makes sure that the distributions did not change
along the
whole range of values.
Sampling parameter ranges to run the rainfall–runoff model.
Parameter
Abbreviation
Unit
Sampling range
Rainfall multiplier
R
(–)
0.4–2.0
Rate of decline of transmissivity
m
(m)
0.005–0.035
Horizontal transmissivity
To
(m2h-1)
0.001–20
Time constant
td
(mh-1)
1–60
Land-use coefficient
lu
(ms-1)
0.04–0.2
Flood-wave celerity
vc
(ms-1)
1.0–3.5
Maximum soil infiltration rate
imax
(mh-1)
0.005–0.03
Main channel roughness coefficient
ncu
( sm-1/3)
0.001–0.08
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.
Output evaluation
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 b=a=±50 % of the peak flow for the peak magnitude and b=a=±2.5 h for
the time of peak (Fig. 4). For the evaluation of the hydrographs, a
was set equal to b; thus, every hydrograph within the uncertainty bounds
was considered behavioural and to have an equal degree of belief. The uncertainty in peak discharge at points 1 and 2 was chosen considering, and was assumed larger than, the value suggested in Benson and
Dalrymple (1967). The discharge at point 5, although it was estimated by running a RRM by JICA (2002), was considered
reliable for calibration since its magnitude was similar to the maximum peak outflow measured at Los Laureles dam, located
in the same river and with nearly equally contributing upstream areas as in
point 5 (Fig. 1). It was expected that 50 %
of the flow uncertainty, as well as for points 1 and 2, was also reasonable at point 5. All times of peak came from the
same source, i.e. witness accounts, and there was no additional information
on their uncertainties; thus, we allowed up to 2.5 h uncertainty considering
that the survey was carried out 2 years after the event and because of the
expected
difficulties in witnesses identifying the exact times when the peak occurred.
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 (K) to cluster an ensemble of data (here the
behavioural hydrographs) were defined (here equal to 100). Then, a number of K hydrographs were randomly chosen from the
ensemble to represent the cluster centroids. Each of the hydrographs in
the ensemble was assigned to one of the centroid
hydrographs according to the smallest distance, here taken as the sum of the absolute differences between
hydrographs. Subsequently the centroid for each of the clusters was replaced
with the hydrograph whose sum of distances from all hydrographs within the
cluster is minimized; and then each hydrograph in the ensemble was assigned
to the new centroid found. The procedure of moving centroids and
assigning hydrographs to new centroids is repeated until there is no change in the clusters. To consider the extreme
cases, the hydrograph from each cluster with the largest sum of the distances to all other centroid hydrographs was
chosen.
Flood-wave propagation
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.
∂h∂t+∂Qx∂x+∂Qy∂y=0,(2a)∂Qx∂t+gASx+n2QxQxR4/3A2=0,(2b)∂Qy∂t+gASy+n2QyQyR4/3A2=0,
where Qx and Qy, and Sx and Sy
are the volumetric flow rates and the slopes respectively in the x and
y directions, h the water depth, t time, A the cross-sectional area
of flow, g gravity, n the Manning coefficient, and R the hydraulic
radius, taken as the cell cross-sectional area divided by the wetted
perimeter.
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 m cell resolution, as a trade-off between high resolution and the speed of simulations. The
surveyed cross sections and orthographic pictures from JICA (2002) were used
to define channel depth and width respectively. Test simulations of this
event were performed within the HEC-RAS 1-D hydraulic model
(Brunner,
2001) considering the topography of the bridges, and preliminary results showed that bridges had a negligible effect on
the overall flood profile. Thus, the geometry of bridges in the LISFLOOD-FP implementation was neglected by assuming
a limited and localized impact on flood levels as in e.g. Castellarin
et al. (2009), especially since the calibration data are associated with
large uncertainties so that the localized effect of structures is not
possible to detect (Fewtrell
et al., 2011).
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, bc, was used as
the downstream boundary condition. This assumption was considered in view of
the lack of hydrograph information at the downstream boundary; however,
water-level predictions at the most downstream cross sections can be
associated with larger
uncertainties due to this assumption (Pappenberger et al., 2006). Besides bc the channel-roughness
coefficient, assumed uniform along all the channel length, nc, and the floodplain-roughness coefficient
uniform along all the floodplain, nf, were also considered to be uncertain parameters. Ideally roughness
coefficients would be allowed to vary spatially to reflect changes in channel and floodplain characteristics (e.g. one
value per reach or per each side of the floodplain), but this would have led to an increased number of parameters in the
hydraulic model when there was not enough information at each reach to constrain the local roughness.
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 (wf) in the uncertainty analysis. For the hydraulic simulations, a total of 130 000 parameter
sets were sampled from a uniform distribution with ranges considered large but possible in the literature (Table 3) in the
same way as for the RRM.
Sampling range of parameters to run the hydraulic model.
Quantity
Parameter
Abbreviation
Unit
Sampling range
1
Channel width factor
wf
–
0.5–2.0
1
Slope for downstream boundary condition
bc
%
0.005–0.03
1
Channel roughness coefficient
nc
sm-1/3
0.005–0.3
1
Floodplain roughness coefficient
nf
sm-1/3
0.005–0.3
5
Hydrograph for the upstream boundary condition (100 class hydrographs)
–
units
1–100
Prior (grey) and posterior (black outlined) relative frequency
distribution for the most sensitive rainfall–runoff parameters: rainfall
multiplier (R), rate of depletion (m), time factor (td), the
main channel roughness coefficient (ncu) and the maximum soil infiltration rate (imax) for the Chiquito,
Guacerique, and Grande catchments (first, second, and third rows
respectively).
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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: wf, bc,
nc, and nf respectively).
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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.
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Performance of the model in predicting high-water marks,
average (d4-102), against predicted maximum peak discharge and two times
of peak at the Choluteca River (reference points 3 and 6 at Figs. 1 and 2 and Table 1) for
non-behavioural simulations (grey dots) and behavioural ones (black dots).
Observed values and their limits of acceptability are plotted in continuous
and dashed vertical lines respectively.
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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.
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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).
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Output evaluation
Different degrees of belief (di) (Fig. 4) were obtained by comparing the simulations with the following evaluation
data.
One degree of belief value, d1, as performance in predicting the maximum peak discharge value of point 3
(Figs. 1 and 2 and Table 1).
Two degrees of belief values, d2-3, as performance in predicting the time of the maximum peak discharge of points 3
and 6 (Figs. 1 and 2 and Table 1).
Ninety-nine degrees of belief values, d4-102, as performance in predicting maximum water levels along the main
river and two tributaries (Fig. 2).
The fuzzy set values of a and b for evaluating the simulated peak discharge were set to 20 and 50 % of observed
values respectively. Thus, for differences between observed and predicted
peak discharge within 20 % of the observation, the degree of belief was
assumed to be equal to 1, and decreased to 0 for differences larger than
50 %. These values were chosen taking into account those values suggested
by Benson and Dalrymple (1967) and Jarrett
(1987). The fuzzy set values of a and b for evaluating the time of the peak were set equal to 0.5 and 2.5 h
respectively; thus, the degree of belief for differences between observed and
predicted times of the peak smaller than 0.5 h was assumed to be equal to 1,
and it decreased to 0 to allow for up to 2.5 h of difference, an error
considered possible in the observations. And finally, the fuzzy set values of a and b for evaluating the water levels
were set equal to 0.5 and 1.8 m respectively. Thus, 0.5 m was chosen to account for error in topography
representation (Neal et al., 2009), and 1.8 m was chosen considering the magnitude of the observed water level and
that 2 years after the event witnesses' memories might have been associated
with large uncertainties.
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.
GS=∑i=1i=102widi,
where wi are the weights associated with the degrees of belief
corresponding to the observations. The weight associated with the peak
discharge and the two times of the peak data (d1-3) were set equal to
0.1 each; thus, 0.7 was the weight corresponding to the sum of the degrees of
belief associated with all the observed maximum water levels
(d4-102). A larger aggregated weight was given to predict the observed water marks in comparison to the peak
discharge and times of the peaks to reflect the larger number of observed
water marks (99) and because the focus was on predicting flood extent. The
weights could be changed according to the purpose of the study, which might
also result in
different ensembles being behavioural for different purposes (Pappenberger et al., 2007).
Subsequently, likelihood values were obtained by scaling the global scores by a constant C, so they will sum to unity
over all behavioural sets (Beven, 2009). Finally, the behavioural parameter sets were used to generate a fuzzy likelihood
water-level profile and map of the maximum flood extension during the Mitch event as in Di Baldassarre et al. (2010).
Discussion
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 (R), rate of
depletion (m), time constant (td), main channel roughness
coefficient (ncu), and maximum soil
infiltration rate (imax) were more important in selecting the resulting hydrographs (Fig. 7), whereas
horizontal transmissivity (To), land-use coefficient (lu),
and flood-wave celerity (vc) were
less sensitive.
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 (m) and the time constant (td) (Fig. 7).
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 m) and a faster channel response in
the MCT routing (low ncu) than the
other two sub-catchments. Hydrographs from a total of five sub-catchments (Fig. 6) from the TOPMODEL and MCT combination
were used as upstream boundary conditions for the hydraulic simulations.
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.