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Current trends in the optimization of hydraulic flood simulations in ungauged steep rivers

Conference Paper

Current trends in the optimization of hydraulic flood simulations in ungauged steep rivers

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The numerical tools simulating flood events must be accurate, in order to provide useful data, and computationally efficient, to facilitate informed decision-making during a flood. One of the main limitations of modelling software at the present time is the CPU time needed to perform simulations over complex spatial domains. Recent studies show that the models lack the necessary implementations to take advantage of the parallelism available on current hardware, which hinders their use in interesting applications such as real-time flood forecasting, calibration and uncertainty analysis, or visualization and gamification of floods for improved risk communication. For instance, methods based on artificial intelligence have contributed highly to the state-of-the-art of flood simulations, providing better performance and cost-effective solutions than complex hydrodynamic fluid solvers. The current study provides an overview of strategies dedicated to the optimization of hydraulic flood simulations suitable for ungauged steep rivers, which are not extensively studied.
Content may be subject to copyright.
River Flow 2020 Uijttewaal et al (eds)
© 2020 Taylor & Francis Group, London, ISBN 978-0-367-62773-7
Current trends in the optimization of hydraulic flood simulations
in ungauged steep rivers
A. Moraru, N. Rüther & O. Bruland
Department of Civil and Environmental Engineering, Norwegian University of Science and Technology
(NTNU), Trondheim, Norway
ABSTRACT: The numerical tools simulating flood events must be accurate, in order to pro-
vide useful data, and computationally efficient, to facilitate informed decision-making during
a flood. One of the main limitations of modelling software at the present time is the CPU time
needed to perform simulations over complex spatial domains. Recent studies show that the
models lack the necessary implementations to take advantage of the parallelism available on
current hardware, which hinders their use in interesting applications such as real-time flood
forecasting, calibration and uncertainty analysis, or visualization and gamification of floods
for improved risk communication. For instance, methods based on artificial intelligence have
contributed highly to the state-of-the-art of flood simulations, providing better performance
and cost-effective solutions than complex hydrodynamic fluid solvers. The current study pro-
vides an overview of strategies dedicated to the optimization of hydraulic flood simulations
suitable for ungauged steep rivers, which are not extensively studied.
1 INTRODUCTION
As part of its strategy to improve the scientific dissemination of flash floods affecting small,
ungauged steep rivers in Norway and worldwide, the World of Wild Waters project aims at
potential real-time simulation-based solutions, where the output is both physically and visu-
ally realistic and enables an accurate flood risk assessment and its effective communication to
the stakeholders, whom are oftentimes not part of the scientific community (Moraru et al.
2019a). Complex hydrodynamics affecting steep rivers call for more efficient hydrodynamic
fluid simulations. The prediction accuracy required to implement risk alleviation measures is,
however, a core issue when addressing flood risk assessment. Another important challenge in
small catchments is the lack of reliable historical hydrology and high-resolution terrain data.
2 PROBLEM CHARACTERIZATION AND SIMPLIFICATION
At the beginning of any flood analysis, its key to use the best input data available and define
well the problem at hand, as this will condition both the time invested in simulating and the
usability of the results.
2.1 Optimal terrain data
Given that oftentimes we do not have at hand high resolution topographic data of small
ungauged rivers, especially pre- and post-flood, when the river geometry is affected, Dey et al.
(2019) and references therein described the Bathymetric Improvement Efficiency (BIE) index.
BIE estimated quantitatively the effect of different bathymetric models in the simulated
hydraulics as opposed to ideal LiDAR data and suggested that small rivers can be modelled
using simple cross-sectional shapes without unreasonable compromise in precision. If these
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rivers are also steep, hence of low sinuosity (< 1.5), and presenting high flow regimes (e.g.
flood), bathymetric models of low-moderate cost and moderate-high efficiency (i.e. with field
survey involved up- and downstream) are preferred over a costly and overly dense survey. On
similar lines, Azizian & Brocca (2020) compared the effect of refining different remotely
sensed-DEMs with field measurements on resulting water surface elevation (WSE) and flood
inundation area. They learnt that the error could be reduced by nearly 40% if the DEM was
corrected.
Now, it is worth wondering about the most effective representation of river geometry. The
optimal spacing between cross-sections clearly depends on the hydraulic problem at hand. For
instance, cross-sectional spacing is key when bathymetry is derived from cross-sectional sur-
veys. Also, a not dense enough spacing incurs in the risk of the cross-sections not being
located at hydraulic controls (see, e.g. Grimaldi et al. 2018, Tonina et al. 2019, and references
therein). However, the relevance of these hydraulic controls, as well as the observed differ-
ences between simulated hydraulic parameters, is flow regime-dependent (i.e. the hydro-
dynamics during a high discharge relegate the influence exerted by the topography to a second
plane as compared to that exerted during low flows). On the other hand, simple channel
morphologies allow a sparser location of cross-sections than complex morphologies. If
wanted to reduce the density of cross-sections used and save surveying and computing time,
one very good indicator would be to use the average channel width (W* in Tonina et al. 2019
and references therein; represented in blue color in Figure 1 left) and sample 2W* for simple
morphologies, and 1W* for complex morphologies. For example, the cross-sectional spacing
used in Moraru et al. (2019b) was between <2W* - 4W* approx. (Figure 1 left, distance
between green cross-sections), which increased the uncertainty of the model as opposed to an
ideally 0.5W* - 1W* (Figure 1 left, distance between consecutive green and purple cross-
sections), yet the computational time saved was considerable.
2.2 Model dimensionality and scale
As exemplified by Glock et al. (2019), flow velocities simulated by 1D-models result in the
largest overestimation especially at the banks due to their area-averaged approach, followed
by 2D-models, which present depth-averaged flow velocities, usually higher than the near-wall
flow velocities used in 3D-models (Figure 1 right). The differences between these models, how-
ever, decreased with increasing discharge, and this seemed to be case-independent. Their study
was not applied to steep rivers, and the dynamics observed might not be replicable in such
cases. The models used in flood analysis present a similar uncertainty, nevertheless, as the
equations solved for steep and milder slopes are the same. The flexible mapping engine used
by Hadimlioglu & King (2019) to visualize water depth resulting from 3D-simulations pro-
vided an increased efficiency by means of allowing adaptive resolution and the possibility to
Figure 1. Left: optimal cross-sectional spacing recommended by Tonina et al. 2019 and references
therein (pink) versus spacing used in Moraru et al. 2019b (yellow). Right: comparison of hydrodynamic
model overestimation and uncertainty. The higher the dimensionality of the model, the closer we get to
the accuracy of eld observations.
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select the representation type dynamically. They achieved a higher precision of water level
description using quadtrees and allowing the system to select the most suitable representation
based on the demanded level of detail. However, their model did not include a dynamic
change of parameters over time (e.g. changes in discharge, no real-time).
2.3 Coupled GIS-remote sensing-numerical simulations
Some approaches to reduce computing effort tackle river morphology and software demands.
This section addresses the potential use of two types of critical points, morphological and
numerical or hydraulic, and their implication in flood simulation speed and precision.
2.3.1 Identification of critical points
Morphological critical points are defined as locations where the river would experience back-
water effect or failure during a flood due to the rivers morphological characteristics. Among
these are either side of structures (e.g. bridges, culverts), areas of significant planform vari-
ation (i.e. near geomorphic features), areas with potential sediment accumulation and many
others. This information can be represented by means of geomorphic indexes (Table 1) that
contain key river features and can be easily and reliably (Moraru et al. 2018) extracted from
either GIS analysis or remote sensing techniques. Concentrating the main controlling factors
to river response during an extreme event in fewer parameters allows, for instance, using finer
simulation grids or lower model dimensionality in the critical points and running coarser
simulations in the rest of the studied reaches (Moraru et al. 2019b). Integrating the data pro-
vided by these indexes in an algorithm together with an orthophoto image processing, where
structures are identified and added automatically into the calculation of the hydraulic param-
eters and inundation area, would allow potential extrapolation to other study cases.
During a hydraulic simulation, the failure of the numerical simulation is often presented as
a warning message and its subsequent suspension. This can either be due to i) an error in the
set-up (e.g. not defining boundary conditions everywhere needed, too many iterations are run
for a given time-step, the maximum prescribed divergence is not reasonable or does not
respect the Continuity requirements, the set calculation time is too large, insufficient grid reso-
lution, inadequate Strouhal number, uniform roughness coefficients do not capture the spatial
variations, etc.), ii) the lack of numerical solution to the equation or iii) an unacceptable error
to the proposed solution. It is essential identifying errors in the computing process as soon as
possible to minimize them or ensure that they are within the desired precision range. Prefer-
ably, the program would include a break to stop the simulation at the earliest possible if no
solution is found. It is desired that the program allows automatic set-up update and iterates
when the software gives a numerical model warning and crashes or requires denser cross-
sections. This would save unnecessary long computing time for unacceptable results but also
facilitate resuming the simulation after an issue arises.
Table 1 . Some geomorphic indexes used as indicators for ood analysis. See references for acronyms.
Geomorphic
index Estimation Considered values References
Width ratio
(Wr)
Wr ¼Waf
Wbf Wr > 1 for erosion Moraru et al. 2018, Ruiz-Villanueva et al.
2018, Scorpio et al. 2018, and references
therein
Relative sec-
tion ratio
(Wxs)
Wxs ¼Wn
Wn1ðÞ
Wxs > 1.1 for expansions,
Wxs < 0.9 for contractions
Usman 2019
Width to
depth ratio
(W/D)
W=D¼W
DW/D < 12 for V-shaped
channels
Usman 2019
Bend
curvature
A, W, M, R,
ϕ,θ,t
Dependent on bend angle
and material
Murniningsih 2018
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3 CODING AND FLUID SIMULATIONS
3.1 Algorithms and efficiency
Adjoint optimization permits computing the gradient or total derivative between two vari-
ables, for instance, the minimum difference between field observations and simulated values.
It requires less iterations than finite differences (e.g. in Watanabe et al. 2018, after 10 iter-
ations the total cost function was minimized) or integrating sensitivity equations, and the com-
puting on CPU is fast enough to enable real-time decision-making. Another advantage of this
method is that the algorithm iterates after updating the control variables, and it can be used
for both hydrologic (i.e. hydrograph) and hydraulic (i.e. water surface and velocity) model-
ling, which ensures double validation.
3.2 Computation parallelization on GPU/CPU
Echeverribar et al. (2018) carried out ca. 30 times faster 2D-simulations on a very large study
area by means of running a 21 days-long flood model on GPU instead of CPU. This made the
model very affordable and highlighted that the compromise in precision was especially due to
the quality of the bathymetric input data. Tafuni et al. (2018) and references therein, on the
other hand, have successfully applied some of the most advanced optimizations of the CUDA
architecture and GPU to modelling open boundary conditions in Smoothed Particle Hydro-
dynamics (SPH). This method is very versatile, can be highly parallelized on hybrid architec-
tures and applied to both complex 2D- and 3D-simulations.
González-Cao et al. (2019) and references therein optimized the original code for the model-
ling software Iber Aula, achieving to compute 24h of detailed 2D-simulation time in less than
10 minutes on CPU using GPU parallelization on the Nvidia CUDA platform, when the ori-
ginal version would have needed at least 15h (i.e. the improved code runs up to 100 times
quicker). If this code implemented data locality-ordering algorithms and/or excluding dry cells
during the computation, the results could be obtained even more efficiently. Furthermore,
when coupling the optimized hydraulic model with a hydrologic model for an extended area,
they successfully modelled a 3 days-forecast within 1h. They learnt, however, that the
hydraulic model is the most computational greedy in their system. Fortunately, this is not
area-dependent, and the running time does not increase significantly with the number of areas
analyzed (if parallel computing hardware is available). An expected challenge for this coupled
hydrologic-hydraulic system is, nevertheless, its suitability in ungauged regions. Many regions
lack high resolution topographic data and/or reliable historical hydrologic data. It is key to
simplify data requirements to greatest extent to adapt its application to any river in the world.
4 ARTIFICIAL INTELLIGENCE IN FLASH FLOOD ANALYSIS
Flood modelling can be implemented by means of Artificial Intelligence (AI) algorithms even in
data-scarce and ungauged regions, where flood analysis may be a challenge. Using documented
flooded points as an input in the AI model provides an analysis of the relationships between
flood episodes and environmental and topo-hydrological factors controlling rivers response.
4.1 AI and field data collection
The versatility of AI has been recently proved by Khan et al. (2019), whom built a multiple
sensor field station that enabled to monitor several environmental variables indicating potential
flooding and reduced the uncertainty of gathered data by 30% in comparison to using individual
sensors. This was achieved by filtering out collected data using the scaled conjugate gradient
method and validating their results against Multi-Layer Perceptron (MLP) models of flooding
false alarms. The implication of their research is crucial in real-time monitoring and flood warn-
ing, as well as in understanding the reliability of field data used in numerical simulations.
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4.2 AI and fluid simulations
The conceptual scheme in Figure 2 represents the usability of AI if previous hydraulic simula-
tions are available to train the algorithm. If field data is collected by a sensor and then used as
input of numerical simulations (a. and b. in Figure 2), hydraulic parameters can be estimated.
Many numerical simulations need to be run for all the possible combinations given the known
input data to train an AI algorithm properly (b. and c. in Figure 2). Now, if all the variables
that control the river response during a flood are available, analyzed and narrowed down to
fewer parameters (e.g. see geomorphic indexes in Table 1), the number of required numerical
simulations needed to base the algorithm training on would be reduced. The numerical simu-
lations are very slow computing and the training of the Neural Network algorithm (e.g. DNN
or MLP, Figure 2 right) is very time-greedy too. However, once its been trained and valid-
ated, the algorithm will take significantly shorter than the numerical model to obtain a similar
result if properly trained (i.e. using reliable training input). The output of the algorithm will
emulate the results of the numerical simulations, nevertheless, not the real worlds behavior,
as the numerical simulationsresults will be used in the training. The algorithm could also be
trained based on field data instead of simulated data, but this would be much costlier.
Once the algorithm has been trained, validated and the uncertainty has been analyzed and
discussed, the algorithm can be refined by using some reliable historical field data. Now, the
results of these AI simulations cannot be extrapolated to any other study case from which
data has not been considered in the training process. However, if new data from a new case is
fed into the already refined algorithm and trained again, given that both cases have similar
characteristics and expected behavior, the performance of the algorithm in the new case could
be compared against the observed behavior. This process is called «transfer learning» (Figure
2 right), as part of the learned knowledge based on the numerical simulations can be removed
and a new batch of (field) data can be incorporated for the subsequent round of training. The
algorithm would expectedly perform better after the second training round. This is currently
a challenge in the AI field.
4.3 AI and image processing
Rapid processing of flood documentation, such as images and videos captured by affected
population and/or aerial imagery surveyed by the authorities, could contribute to more
Figure 2. Conceptual scheme of the application of articial intelligence algorithms to the hydraulic
simulation of oods and its renement and extrapolation through transfer learning.
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effective real-time emergency management (Lohumi & Roy 2019). The analysis of such data
with binary classification methods (i.e. Support Vector Machines, SVM) combined with Prin-
ciple Component Analysis (PCA) produces speedier identification of flooded areas (Akshya &
Priyadarsini 2019). Similar information could be expected if imagery surveyed during a flood
event was analyzed with Neural Network methods, which would present a better tradeoff in
terms of modelling time and achieved precision if the simulation was run on GPU and a High-
Performance Computing platform (HPC; as in González-Cao et al. 2019 and references
therein).
4.4 AI and Internet of Things (IoT)
Radial Basis Function Neural Network were applied by Kartika et al. (2019) to simulate
floods based on publicly available hydrologic databases, and the results could be sent to an
android application via IoT. This would help connect rapid flood prediction systems with the
end-users in real-time, contributing to on-site flood risk management if reliable public infor-
mation was provided efficiently.
5 DISCUSSION AND CONCLUDING REMARKS
Small, ungauged steep rivers are more sensitive to extreme rainfalls than large rivers. Topog-
raphy, as the main driver of water flow, affects considerably the accuracy of hydraulic simula-
tions of steep rivers. Slight differences in topographic features control eventually the flow
paths and resulting water depths. Hence, the availability of high-resolution bathymetry and
observed data for model verification makes it possible to evaluate the uncertainty, providing
valuable criteria in selecting suitable models for flood analysis. Small rivers oftentimes lack
high-resolution topographic and historical hydrologic data, which hampers their study. For
instance, Norway has a complex topography that makes extrapolating data from nearby
gauging stations to small ungauged rivers unreliable. Also, sediment load and bed load affect
the flow velocity significantly, but reliable data regarding sediment transport during flash
floods is seldom available. Using numerical modelling results as basis for the management
and implementation of flood protection and mitigation measures in these rivers is, therefore,
challenging.
A thorough characterization of the study case and flood event at hand, as well as its simpli-
fication, would allow focusing the computational effort into the key controlling factors of
river response during an extreme hydrologic event. Furthermore, if the original code of the
numerical model is optimized, a similar improvement in numerical efficiency could be
achieved through code development as through parallelization (Neal et al. 2018). The disad-
vantage of the restructuring the code, however, is that some of its areas could not run effi-
ciently in parallel (e.g. structures) or must run sequentially (e.g. calculations of Momentum
and Continuity). The highest optimization rates were obtained in High Performance Comput-
ing (HPC) platforms (e.g. González-Cao et al. 2019), yet these are unaffordable in small com-
munities. If the results matched, for example, 60% to 90% of the floodplain coverage
presented by the national emergency authorities and were obtained with the computational
efficiency required in emergency response, the most cost-effective technique would be
desirable.
One advantage of using artificial intelligence in flood analysis is the multiple machine learn-
ing methods available and their ability to replicate satisfactorily the events the algorithm is
trained for. The goal of implementing AI simulations in the study of flash floods within
WoWW is to use transfer learning to extrapolate flood analysis in a river with reliable data
available to data-scarce rivers (Figure 2 right). The obvious limitation and uncertainty would
always come from the training and validation data, and this is challenging in the case of
ungauged rivers. An AI algorithm needs intensive and data-reliable training, otherwise it will
learn and simulate processes that do not necessarily occur in nature nor can be of use in
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applied hydraulic engineering cases. If the data used for training were relatively similar in
characteristics, this does not guarantee the extrapolation to cases with much different dynam-
ics. Additionally, there is fairly more literature available on the application of AI to hydro-
logic modelling than to hydraulic simulations despite the similarity of the models used in both
hydrologic and hydraulic simulations.
ACKNOWLEDGEMENTS
Thanks to P. Salvo Rossi for the introduction to AI and brainstorming in the simplest and
most insightful way. This publication is part of the World of Wild Waters (WoWW) project,
which falls under the umbrella of Norwegian University of Science and Technology
(NTNU)s Digital Transformation initiative.
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... The river's geometry was modified and its slope was virtualized into constant values along the modelled reach to identify the influence of other parameters in the river response. The results of such study and its applications are described in detail in (Moraru et al., 2019(Moraru et al., , 2020. Such critical areas have the potential of being further combined into a locally refined, yet faster-solving, model. ...
... GPU computing, as well as the use of ML, are state-of-the-art optimization techniques (Moraru et al., 2020). The computing tool used for numerical modelling will determine greatly the performance of the model, nevertheless. ...
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... The river's geometry was modified and its slope was virtualized into constant values along the modelled reach to identify the influence of other parameters in the river response. The results of such study and its applications are described in detail in (Moraru et al., 2019(Moraru et al., , 2020. Such critical areas have the potential of being further combined into a locally refined, yet faster-solving, model. ...
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