The production of spatially accurate representations of potential inundation is often limited by the lack of available data as well as model complexity. We present in this paper a new approach for rapid inundation mapping, MHYST, which is well adapted for data-scarce areas; it combines hydraulic geometry concepts for channels and DEM data for floodplains. Its originality lies in the fact that it does not work at the cross section scale but computes effective geometrical properties to describe the reach scale. Combining reach-scale geometrical properties with 1-D steady-state flow equations, MHYST computes a topographically coherent relation between the “height above nearest drainage” and streamflow. This relation can then be used on a past or future event to produce inundation maps. The MHYST approach is tested here on an extreme flood event that occurred in France in May–June 2016. The results indicate that it has a tendency to slightly underestimate inundation extents, although efficiency criteria values are clearly encouraging. The spatial distribution of model performance is discussed and it shows that the model can perform very well on most reaches, but has difficulties modelling the more complex, urbanised reaches. MHYST should not be seen as a rival to detailed inundation studies, but as a first approximation able to rapidly provide inundation maps in data-scarce areas.

Floods are a recurring phenomenon in France: in September 2014, intense rainfall affected the south of the country, leading to several deaths and about EUR 0.6 billion worth of damage. The following year, in October, about 20 people died in the south-east due to massive flooding, which caused a loss of EUR 0.5 billion. Then, in June 2016, large-scale flooding occurred over the Seine and Loire catchments, mainly affecting their tributaries and resulting in four deaths at a cost of EUR 1.4 billion. These are only examples which underline the value of flood inundation mapping to anticipate the impact of such events. Public authorities and insurance companies are showing a growing interest in the field of rapid inundation modelling, and for the development of simple methods, that would work for any river with easily available data.

Flood hazard assessment usually combines rainfall observations or
simulations, a hydrological model, streamflow simulations or observations,
and an inundation model in order to generate inundation extents, height maps
and sometimes other information (e.g. velocities). Traditionally, flood
inundation models are derived from the shallow water equations (SWEs) in one
or two dimensions (the so-called hydraulic models), with various
simplifications that have proved to give satisfying results. For instance,
the Regional Flood Model (RFM), probably one of the most comprehensive
approaches published so far, is made of four parts

Not all hydraulic models need to have this degree of complexity. It is indeed
possible to neglect specific parts of the SWEs depending on the situation.
Usually, 2-D models use the complete Saint-Venant equations while 1-D models
often disregard one or several terms, leading, for instance, to the diffusive
wave or kinematic wave approximations

LISFLOOD-FP

However, these examples concern relatively small and well-instrumented
reaches and assessing flood hazard at a larger scale may require different
approaches.

The lack of precise data (especially for channel cross sections) and the
computing time required by numerical methods for solving the SWE motivated
the development of potentially alternative methods, mostly based on DEM
analysis. For instance, the rapid flood spreading method

MHYST, the method presented in this paper, is a simplified approach developed with the aim of rapidly producing inundation maps in data-scarce areas. It combines (i) concepts of hydraulic geometry to characterise channel geometry and (ii) DEM-derived relative elevations to characterise the floodplain; it does not work at the cross section scale but computes effective geometrical properties representative of the reach scale. Combining reach-scale geometrical properties with simplified steady-state hydraulic laws allows one to rapidly generate flood inundation maps while ensuring reach-scale coherence. After describing the method and the calibration dataset, MHYST is compared against the inundation extent observed for the major event that occurred in May–June 2016 in France. The last section discusses the spatial distribution of performance and the impact of uncertainties on the results obtained.

The MHYST model stands for

The initial step consists of processing the digital elevation model (DEM) in order (i) to obtain a flowing drainage direction map, (ii) to identify the subcatchments (corresponding to the river reaches), and (iii) to compute the height above nearest drainage (HAND) in each subcatchment. This initial processing is the basis of the floodplain analysis in MHYST. To compute the drainage direction map, we used the D8 method from the Flow Direction function provided by ArcGIS 10.3. It computes the drainage direction by calculating the steepest slope from the eight possible directions for a given cell.

Figure

Processing of DEM and calculation of the HAND value for a hypothetical catchment.

MHYST is mostly based on a DEM and its derivatives (drainage map and drainage
areas) and on the hydraulic equations describing a steady uniform flow at the
reach scale. This means that for a given time step (day in this case), at a
given reach, we make the approximation that the flow is constant over time
and space (this is obviously a strong simplification that we will discuss
later). Table

Representation of the
model structure: the reach-scale geometry is derived from hydraulic geometry
relationships and DEM data and is then used to compute a relation between the
threshold height

Other variables can be directly calculated from the DEM (Fig.

Typical cross section segmentation, with the cross section area of
the channel (

Representation of the reach-scale geometry derived from HAND and the
DEM.

The only unknown variables in these equations are sub-grid parameters

The fundamental equations of the MHYST model come from an experimental study
by

The streamflow

Names, units and interpretations of the variables used in the geometric and hydraulic equations of the MHYST model.

Names, units and interpretations of the free parameters of MHYST's structure.

The two Strickler coefficients add 2 degrees of freedom, and

For a given threshold height

By repeating the operation for all possible

When working on an event where only

Although this method and that of

MHYST can work with either simulated or observed flows. In this paper,
observed data from 12 measurement stations of the French HYDRO database

In this study, we used a

5

Daily observed discharges were obtained from the French HYDRO database

Maximum flood extent for the May–June 2016 event over the Loing catchment produced by the Copernicus Emergency Management Service.

Following an extremely wet month of May (namely the wettest on record for
many stations), a heavy rainfall event started on 30 May 2016 over the
centre of France, affecting the Upper and Middle Seine basin and the Middle
Loire basin. This episode lasted until 6 June and, combined with highly
saturated soils due to a series of preceding minor events, led to major flood
inundations. Over this period, overall precipitation reached

Since calibration data were available for June 2016 event, we chose to use
our model to simulate this episode and compare the results with observations.
We conducted this study over the River Loing, tributary to the River Seine,
with a catchment covering

Daily hydrograph of the River Loing at Épisy
(

To assess the model's performance, we used several criteria based on the
contingency table in Fig.

The POD (probability of detection), which is also called Correct

These ratios are particularly reliable if they are used to compare simulations and exhaustive observations. This is almost the case with Copernicus calibration data, which represent a “maximum flood extent”. However, MHYST outputs are dated, which is not the case for the observed map. This is why all daily simulated inundation extents were merged into one maximum simulated extent, meaning that we did not try to validate the temporal dynamic of the flood, but only aimed to assess its largest area. Thus, the preceding scores will only evaluate MHYST's ability to reproduce the maximum flood extent.

Contingency table gathering the different scenarios encountered during calibration (the numbers refer to pixels).

Table of forecast scores used to assess the performance
of a flood simulation. All criteria are based on the contingency table
(Fig.

Forecast scores obtained by the model on the River Loing versus
Copernicus data for all the parameter values tested,

MHYST has two free parameters (Table

To help make a decision on the optimal parametrisation of the model, we used
the following graphs, on which each (

two contour plots (Fig.

a Pareto plot (Fig.

a Pareto plot (Fig.

Last, to be able to analyse the variability of results between reaches (we
have a total of 90 reaches affected by the inundation), we also computed the
CSI and BIAS reach by reach, and produced two cumulative distribution
plots showing these results (Fig.

The fit criteria are very sensitive to the

The CSI clearly shows an optimal zone around

Another way to confirm the validity of this choice (

Last, Fig.

Pareto diagram for two forecast scores, POD and FAR. 1-FAR is used
so that each criterion evolves in the same way,

Cumulative frequency of CSI and BIAS values for all combinations of
parameters and for the 90 affected reaches. Green lines correspond to the
best combinations identified in Fig.

Figures

Reach-scale performance of

For the downstream-most part of the Loing (Fig.

The small tributary (Fig.

The orange part in the middle of the BIAS map (Fig.

Finally, the red and orange zones in the south of the presented map
(Fig.

The area identified (Fig.

Similarly to the previous area (Fig.

In that case (Fig.

In this area (Fig.

In the western part of the upstream area (Fig.

This area (Fig.

The most upstream part of the simulated area (Fig.

Reach-scale performance of

Reach-scale performance of

In order to complete our interpretation of MHYST behaviour, we conducted two
sensitivity analyses, one with the Morris method

It is possible to assess the sensitivity to the DEM in two ways: first by
aggregating our DEM from

CSI scores obtained by the model on the River Loing versus
Copernicus data for all the parameter values tested and for various
resolutions of the DEM, aggregated from the 5 m resolution DEM:

Before using the RGE 5 m DEM from IGN, we tried to use the 25 m EU-DEM from
the European Environment Agency, and it showed poorer results, because it was
not precise enough. Figure

The objective of this paper was to present and validate a simple hydraulic
model for rapid inundation mapping in data-scarce areas. MHYST is based on
DEM analyses and simple hydraulic equations, creating a reach-scale relation
between the average discharge and the average “height above nearest
drainage” which can then be used to simulate any event, past or future, as
long as streamflow information (observed or simulated) is available. This
model was calibrated against an observed exceptional flood which occurred in
2016 on the Loing River near Paris and showed results that are certainly not
perfect, but from our point of view and for our objectives quite encouraging.
Furthermore, we compared our methodology with the traditional HAND approach,
using a single threshold height of

The simple structure of MHYST allows it to be used almost anywhere with few data and only two parameters. The model can, however, be used in first approximation, when a lack of time and data restrains the use of a more complex method.

For the sake of honesty, we would like to specify the theoretical limits of
the MHYST approach:

The model equations were solved by using the hypothesis of a reach-scale steady uniform flow (probably one of the most simplifying assumptions one can make). This simplification is probably too extreme for highly complex situations, especially in the presence of dikes and bridges. Indeed, on the one hand, the DEM resolution is too coarse to precisely take into account hydraulic structures, and on the other hand, the DEBORD formulation is not sufficient to describe the interaction between the flow and these structures.

The DEM is a critical part of the model, because geometrical relationships and variables are directly related to the shape and distribution of elevations. Another DEM was actually tested as model input and showed much poorer results.

Moreover, since the channel geometry was unknown, hydraulic geometry equations were used to assess bankfull height and width, with fixed parameters from another study in the case of height, which may not be the optimum for this catchment, adding its share of uncertainty.

Finally, there is at this point no continuity equation between reaches, since the calculations were made for each reach separately. Uncertainties may therefore be higher in areas around connection points between reaches, especially if it is a confluence of rivers. One way to address this issue could be to add a continuity equation between the reaches, which might increase the overall coherence of the flood. However, at this point of the development of the model, we have not included this specificity.

Thus, the maps produced by MHYST should be seen as a maximum extent of the flood which can be used as a first and rapid estimation. To further test this approach, we consider that attention should first be given to the following: assessing the impact of the DEM choice, resolution and quality; testing the approach on a range of (less extreme) events and catchments, to better assess the range and stability of its parameters and performance; and improving the treatment of possible discontinuities between reaches.

The IGN DEM cannot be freely downloaded. Copernicus
Emergency Management Service data and the corresponding report can be
downloaded at

In order to assess the sensitivity of the model to its main parameters
(

The Morris method

Results of the Morris method applied to MHYST with a 50 m
resolution DEM on the Loing catchment for the six parameters
(

The problem might be that despite the use of a Latin hypercube sampling
method, the “good” values of the parameters never meet, i.e. when

Moreover, the issue with sensitivity analyses such as the Morris method is
that the results can be very different depending on the catchment or the
event modelled. Indeed, if the water is concentrated in the channel part for
a very steep catchment, a very flat one will on the contrary rely on the
floodplains, and so the parameterisation of the model will add more value to

The Sobol method

The results of this analysis are presented in Table

Sobol first-order indices for the six parameters of MHYST. Confidence interval is denoted as conf. int. here.

The distributions of

Sobol total-effect index for the six parameters of MHYST. Confidence interval is denoted as conf. int. here.

In order to understand why Morris and Sobol give, contrary to our initial
expectation, so little importance to

The hydraulic geometry parameters are clearly important, but if they are fixed to legitimate values estimated by observations or tables of regionalised values, their impact becomes minor in front of the Strickler coefficients.

The model presented in this paper was developed and analysed by CR during his PhD work. He also wrote the paper, which was corrected by VA and NLM.

The authors declare that they have no conflict of interest.

The first author was funded by a grant from the AXA Research Fund. Thanks are extended to Rafal Zielinksi, who helped us access data from the Copernicus Emergency Management Service. We would also like to thank the AXA Global P&C research team for their advice and our discussions on the development of simple conceptual inundation models. The MHYST model was developed using R (R Core Team, 2015) and GFortran, Gnu compiler collection (gcc) Version 4.9.2. Edited by: Roger Moussa Reviewed by: Renata Romanowicz and one anonymous referee