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Article
Design Flood Estimation: Exploring the Potentials
and Limitations of Two Alternative Approaches
Kenechukwu Okoli 1,2 , Korbinian Breinl 2,3, Maurizio Mazzoleni 1,2 and
Giuliano Di Baldassarre 1, 2, *
1Department of Earth Sciences, Uppsala University, Villavägen 16, 752 36 Uppsala, Sweden;
kenechukwu.okoli@geo.uu.se (K.O.); maurizio.mazzoleni@geo.uu.se (M.M.)
2Centre of Natural Hazards and Disaster Science (CNDS), Villavägen 16, 752 36 Uppsala, Sweden;
breinl@hydro.tuwien.ac.at
3Institute of Hydraulic Engineering and Water Resources Management, TU Vienna, Karlsplatz 13/222,
1040 Vienna, Austria
*Correspondence: giuliano.dibaldassarre@geo.uu.se
Received: 22 February 2019; Accepted: 4 April 2019; Published: 9 April 2019
Abstract:
The design of flood defence structures requires the estimation of flood water levels
corresponding to a given probability of exceedance, or return period. In river flood management,
this estimation is often done by statistically analysing the frequency of flood discharge peaks.
This typically requires three main steps. First, direct measurements of annual maximum water
levels at a river cross-section are converted into annual maximum flows by using a rating curve.
Second, a probability distribution function is fitted to these annual maximum flows to derive the
design peak flow corresponding to a given return period. Third, the design peak flow is used as
input to a hydraulic model to derive the corresponding design flood level. Each of these three
steps is associated with significant uncertainty that affects the accuracy of estimated design flood
levels. Here, we propose a simulation framework to compare this common approach (based on the
frequency analysis of annual maximum flows) with an alternative approach based on the frequency
analysis of annual maximum water levels. The rationale behind this study is that high water levels
are directly measured, and they often come along with less uncertainty than river flows. While this
alternative approach is common for storm surge and coastal flooding, the potential of this approach
in the context of river flooding has not been sufficiently explored. Our framework is based on the
generation of synthetic data to perform a numerical experiment and compare the accuracy and
precision of estimated design flood levels based on either annual maximum river flows (common
approach) or annual maximum water levels (alternative approach).
Keywords: flood defence; design floods; peak levels; peak flows; uncertainty
1. Introduction
The design of river flood defence requires the estimation of potential flood levels [
1
,
2
]. In the past,
this was done by keeping track of the historical water levels, which were then used for the design of
flood protection measures [
3
]. For example, flood walls in Rome were raised at the end of the 19th
century to about one meter above the maximum water level that was reached during the catastrophic
1870 flood event [4]. More recently, as hydrology has progressed, river flows (instead of water levels)
have been used more and more by water engineers, as river discharge is more useful than water levels
for the study of hydrological processes and water management applications [
5
]. As a result, the design
of defence structures to prevent river flooding is currently based on the analysis of flood discharge
peaks. More specifically, the estimation of design flood levels often consists of three main steps: (i)
Water 2019,11, 729; doi:10.3390/w11040729 www.mdpi.com/journal/water
Water 2019,11, 729 2 of 11
Time series of annual maximum flows are derived from (directly measured) annual maximum water
levels using a rating curve; (ii) river discharges corresponding to the desired return periods (hereafter
“design peak flows”) are derived from annual maximum flows by means of one or more probability
distribution functions; and (iii) design flood levels are estimated by using hydraulic models to simulate
design peak flows [
6
]. As such, this common approach requires a cascade of three types of models:
A rating curve, a probability distribution function, and a hydraulic model. Numerous studies have
shown that significant uncertainty affects each of these three steps.
First, direct measurements of river flows are not error free [
7
]. Systematic and random errors
affect these measurements as a result of wrong calibration and precision limitations of measuring
instruments. Pelletier [
8
] provided a comprehensive discussion about sources of errors that affect
direct measurements of stream flows and concluded that their combined effect is around 8% at the
95% confidence level. Other studies report error estimates of about 5% as a result of an improvement
in measurement techniques [
9
]. In contrast, water levels are measured more accurately and errors
are considered to be around
±
3 mm at the 95% confidence level [
10
]. Schmidt [
11
] reported the
uncertainty of a single water level gauge to vary from 3 to 14 mm. As such, the uncertainty in the direct
measurements of water levels is minimal, and essentially negligible for medium-to-large rivers [12].
Second, river discharge is almost never directly observed, especially during flood conditions.
Measurements of water levels are typically converted into river flows by using analytical functions
often referred to as rating curves [
13
]. Rating curves are often derived by fitting a model to a limited
number of direct measurements of river flow (Q) and corresponding water stage (h) [
14
]. The power
law model is commonly used in hydrology to define the relationship between water level and river
flow, i.e., the so-called stage-discharge relation [
15
]. While the uncertainty in the direct measurements
of river flows is limited, with expected errors of around 5%, river flow values derived using the rating
curve (Q*) are affected by additional sources of uncertainty [
7
], which can lead to very high errors
(over 30%) during high flow conditions [7,16].
Third, the significant uncertainty present in estimated peak flows derived from a rating curve
can be exacerbated when probability models are used to derive design events with a given probability
of occurrence, as discussed extensively in the literature [
17
–
22
]. Indeed, on top of the measurement
errors and rating curve uncertainty discussed above, additional sources of uncertainty affect the design
peak flow due to: (i) The choice of a probability distribution function and a parameter estimation
method [
23
–
25
]; (ii) the assumptions about randomness, homogeneity, and independence; and (iii) the
type of sample, i.e., peak-over-threshold versus annual maximum flows [26].
Fourth, the recent literature has shown that hydraulic models are also affected by significant
uncertainty [
27
,
28
], especially when used for conditions different from the ones they were calibrated
for [
29
,
30
]. This is often the case as extreme flood conditions are rare (by definition) and therefore
hydraulic models are typically calibrated by parameterizing the Manning’s roughness coefficients to
reproduce more common flow conditions.
Hence, the propagation of uncertainty from measurement errors to design flood levels through
this cascade of three models (rating curve, statistical analysis, hydraulic modelling) can negatively
affect the precision and accuracy of design flood levels, thereby limiting the reliability of flood risk
assessment and defence measures based on these uncertain estimations.
An alternative approach to derive design flood levels is to fit probability distribution functions
directly to the time series of annual maximum water levels. As a matter of fact, high water levels
are the only type of data that is directly measured and they typically have high precision and
accuracy
[10–12]
. Such an approach is relatively common in modelling coastal floods caused by
storm surge events
[31–33]
. A similar approach has been developed to estimate extreme ground water
levels by Fürst et al. [
34
]. Apart from the technical note published by Dyhouse [
35
], there are no studies
exploring the potential of frequency analysis of water level peaks in the context of river flooding,
despite direct analysis of high water levels being the traditional approach used by Egyptians, Romans,
and other past civilizations [3].
Water 2019,11, 729 3 of 11
Thus, we provide a new simulation framework to compare two approaches for the estimation of
design flood levels (Figure 1): (i) The common three-step approach based on flood discharge peaks;
and (ii) the alternative approach based on flood level peaks. This paper also discusses opportunities
and limitations of these two alternative approaches.
Water 2019, 11, x FOR PEER REVIEW 3 of 11
Thus, we provide a new simulation framework to compare two approaches for the estimation
of design flood levels (Figure 1): (i) The common three-step approach based on flood discharge peaks;
and (ii) the alternative approach based on flood level peaks. This paper also discusses opportunities
and limitations of these two alternative approaches.
Figure 1. Virtual experiment proposed in this study. Graphical representation of the simulation
framework to compare the estimation of design flood levels based on two alternative approaches.
2. Methodology
Case studies cannot allow insights about the potential and limitations of estimating design
floods based on flood level peaks instead of flood discharge peaks, as the real design flood is
obviously unknown. Thus, we propose a virtual experiment based on the use of synthetic data. A
Comparison &
Errors
Annual Maximum
Water Levels
Common approach
(based on flood discharge peaks)
Alternative approach
(based on flood level peaks)
Rating
Curve
Probability
Model
Annual Maximum
Flows
Design Peak Flow
Hydraulic
Model
Design Flood Level
Design Flood Level
Probability
Model
Design Peak Flow Design Flood Level
(Reference Value)
Parent
Distribution
Hydraulic
Model
(B)(A)
(D)
(E) (F)
(G)
Synthetic
Estimated
Annual Maximum
Flows
Hydraulic
Model
(C)
Parent
Distribution
Figure 1.
Virtual experiment proposed in this study. Graphical representation of the simulation
framework to compare the estimation of design flood levels based on two alternative approaches.
2. Methodology
Case studies cannot allow insights about the potential and limitations of estimating design
floods based on flood level peaks instead of flood discharge peaks, as the real design flood is
obviously unknown. Thus, we propose a virtual experiment based on the use of synthetic data.
A fundamental assumption of the proposed experiment is that a well-established parent distribution
and a well-established hydraulic model of a river reach are used to generate synthetic data, which
enables a comparison of the estimates provided by the two approaches.
Water 2019,11, 729 4 of 11
Our Monte-Carlo simulation framework consists of the following steps (Figure 1):
We start by assuming a well-established probability distribution function as the Parent Distribution
(Figure 1), and use it to generate the design peak flow with a return period of Tyears (step A).
We then apply a well-established Hydraulic Model to propagate the design peak flow generated in
step A, to derive a synthetic T-year design flood level (step B). This value is used as a reference (i.e.,
the “truth”) for comparing the two different approaches.
The Parent Distribution is likewise used to generate a sample of synthetic annual maximum flows
with a length of Myears (step C). This sample from step C is then converted into the synthetic annual
maximum water levels with the Hydraulic Model (step D). These water levels are assumed to be a
typically observed sample, as they are often the only direct measurements available in the real world.
The water levels are the key input for the two approaches:
Common approach (Figure 1, E): The synthetic annual maximum water levels are converted into
estimated annual maximum water flows by using a rating curve. Then, a Probability Model is used to fit
these annual maximum flows and estimate the design peak flows for a T-year return period. Lastly,
these design peak flows are propagated by the Hydraulic Model to estimate a T-year design flood level.
Alternative approach (Figure 1, F): The sample of annual maximum levels obtained in step D is
directly fed into a Probability Model (Figure 1) to estimate a T-year design flood level.
The design flood levels estimated in step E (common approach) and step F (alternative approach)
are compared (step G). Errors are defined as differences between these two estimates and the synthetic
design flood level estimated in step B is used as a reference value.
Steps (C–G) are repeated Ntimes to explore the role of sampling.
3. Example Application
A 98 km reach of the Po River between Cremona and Borgoforte (Italy), and a floodplain confined
by two continuous levee systems was investigated. Its width varies from 400 m to 4 km [
6
]. A high
quality 2 m digital terrain model (DTM) of the middle-lower portion of the Po River (covering an
extension of about 350 km) was made available by the Po River Basin Authority. Information regarding
the river geometry essential for hydraulic modelling was extracted from the DTM. A 90 year record of
annual maximum flows (1920–2009) at the gauge station of Pontelagoscuro was available and used in
this study.
3.1. Hydraulic Modelling
The 1D hydrodynamic Hydrologic Engineering Center’s River Analysis System (HEC-RAS)
model [
36
] was applied for simulating the hydraulic behaviour of the 98 km reach of the Po River
between Cremona and Borgoforte under steady flow conditions. A calibrated 1D hydrodynamic
model by Brandimarte and Di Baldassarre [
6
] was used in this study as the Hydraulic Model. Many
studies have used HEC-RAS for hydraulic modelling in simulating flows in natural rivers [
37
–
41
].
The river geometry is described by 88 cross sections extracted from the DTM. HEC-RAS solves the
governing equations for gradually varied flow, and water profiles are computed using the standard
step procedure. Details about the HEC-RAS model code can be found in the Hydraulic Reference
Manual [
36
]. The modelling exercise neglects the effects of unsteady flow and sediment transport that
can influence the stage–discharge relationship at a given location.
3.2. Rating Curve
To replicate the typical estimation of design flood levels using frequency analysis of the flood
discharge peaks (as shown in Figure 1), it is necessary to estimate the rating curve information at any
given cross-section along the river. We applied the hydraulic model to derive a number of synthetic
pairs (h,Q), which were then used to parameterize the estimated rating curve equation. The synthetic
rating curve was derived by simulating in HEC-RAS flows ranging from 100 m
3
/s to 1000 m
3
/s with
steps of 100 m
3
/s, followed by simulations of discharge ranging from 1000 m
3
/s to 13,000 m
3
/s with
Water 2019,11, 729 5 of 11
steps of 1000 m
3
/s. After that, the estimated rating curve was assessed by fitting the synthetic data
pairs
(Q,h)
using a power law relationship between the water level and river flow. Data pairs
(Q,h)
for the statistical fit are discharge data ranging from 1000 m
3
/s to 6000 m
3
/s (with steps of 1000 m
3
/s)
and their corresponding stages derived from the hydraulic simulations. The power law relationship is
expressed as:
Q∗=(h−h0)b(1)
where Q* is the estimated river flow,
h0
is the cease-to-flow stage,
h
is the measured water stage, and
C
and
b
are calibration parameters that can be determined by the method of non-linear least squares.
Once the power law relationship is established, one can extrapolate to higher flow values.
The two rating curves are shown in Figure 2and the full circles represent the data pairs
(Q,h)
used in deriving the estimated rating curve. Figure 2refers to two cross-sections at 58 and 68 km
downstream of Cremona. Extrapolation beyond the range of measurements leads to a systematic
underestimation of discharges for this particular case.
Water 2019, 11, x FOR PEER REVIEW 5 of 11
rating curve was derived by simulating in HEC-RAS flows ranging from 100 m3/s to 1000 m3/s with
steps of 100 m3/s, followed by simulations of discharge ranging from 1000 m3/s to 13,000 m3/s with
steps of 1000 m3/s. After that, the estimated rating curve was assessed by fitting the synthetic data
pairs (𝑄,ℎ) using a power law relationship between the water level and river flow. Data pairs (𝑄,ℎ)
for the statistical fit are discharge data ranging from 1000 m3/s to 6000 m3/s (with steps of 1000 m3/s)
and their corresponding stages derived from the hydraulic simulations. The power law relationship
is expressed as:
𝑄
∗
=
(
ℎ
−
ℎ
)
(1)
where Q* is the estimated river flow, ℎ is the cease-to-flow stage, ℎ is the measured water stage,
and 𝐶 and 𝑏 are calibration parameters that can be determined by the method of non-linear least
squares. Once the power law relationship is established, one can extrapolate to higher flow values.
The two rating curves are shown in Figure 2 and the full circles represent the data pairs (𝑄,ℎ)
used in deriving the estimated rating curve. Figure 2 refers to two cross-sections at 58 and 68 km
downstream of Cremona. Extrapolation beyond the range of measurements leads to a systematic
underestimation of discharges for this particular case.
3.3. Parent Distribution
The GEV distribution, as defined by Jenkinson [42] and parameterised using a 90-year record of
annual maximum flows available from a gauging station along the Po River, was assumed to be the
Parent Distribution. Our justification for selecting the GEV as a parent lies with the fact that the focus
is on modelling the block maxima of water levels, and the theoretical arguments from extreme value
theory are considered sufficient for this task, assuming that the discharge, 𝑄, follows a GEV
distribution, 𝑄 ~GEV(𝜉,𝛼,𝑘), ξ, α, and 𝑘 are the location, scale, and shape parameters, respectively.
The tail behaviour of the GEV distribution is influenced by the value of the shape parameter and
generally falls in three classes: The Gumbel type (𝑘 = 0) is characterised by a light upper tail, the
Frechet type (𝑘 > 0) has a heavy upper tail, and the Weibull type has (𝑘 < 0) and is bounded
above. Hence, GEV encompasses three asymptotic distributions that can be selected to model the
right tail of a distribution and as such is a grand-parent.
(A)
Water 2019, 11, x FOR PEER REVIEW 6 of 11
(B)
Figure 2. Synthetic and estimated rating curves derived using the Hydrologic Engineering Center’s
River Analysis System (HEC-RAS) model and the power law models for two cross-sections located
58 km (A) and 68 km (B) downstream of Cremona (Po River, Italy).
3.4. Probability Model
The Gumbel distribution was selected as the Probability Model to fit samples drawn from the
parent distribution. The Gumbel distribution is quite popular among engineering practitioners for
most parts of the world. For instance, it is the distribution of choice to describe flood probabilities at
the Tiber River in Rome, Italy [43].
As such, we aim to mimic the common situation in the real world, in which simple models (the
Gumbel distribution in our example application) are used to fit reality (the GEV distribution in our
example application). Previous studies in statistical hydrology used similar research methods, by
using other simple distribution functions, such as the Lognormal, as a probability model and more
complex distribution functions, such as the Kappa and Wakeby, as parent distributions [22,24].
The GEV and Gumbel quantile function is given as
𝑋
(
𝐹
)
𝜉
+
𝛼
{
1
−
(
−
log
𝐹
)
}
/
𝑘
𝑘
≠
0
𝜉
−
𝛼
log
(
−
log
𝐹
)
𝑘
=
0
(2)
where 𝑋 represents a quantile estimate (for either discharge or water stage) corresponding to a
certain return period, in this case 100 years, while 𝐹 is the non-exceedance probability. The
parameters of the GEV were estimated by the method of maximum likelihood using the available 90
year record of annual maximum flows. These parameters were fixed and used for generating
synthetic annual maximum flows by random sampling from its inverse cumulative distribution
function. Equation (2) for the condition of 𝑘 ≠ 0, which is the quantile function for GEV, was used
to estimate the 100-year design peak flow. The 100-year peak flow was simulated using HEC-RAS to
get the estimated design flood level, ℎ.
3.5. Application of the Simulation Framework
Based on the hydraulic model (Section 3.1), rating curve (Section 3.2), parent distribution
(Section 3.3), and probability model (Section 3.5), we applied our simulation framework (Section 2)
to the 98-km reach of the Po River and by using a return period of 100 years (T = 100), repeating steps
C–G for 1000 times (N = 1000), and exploring the role of sample size by using M equal to 30, 50, and
100. A generated sample size of 30 and 50 years reflects the typical length of historical observations,
while samples of a length equal to 100 years represent an optimistic case in hydrology.
Figure 2.
Synthetic and estimated rating curves derived using the Hydrologic Engineering Center’s
River Analysis System (HEC-RAS) model and the power law models for two cross-sections located
58 km (A) and 68 km (B) downstream of Cremona (Po River, Italy).
Water 2019,11, 729 6 of 11
3.3. Parent Distribution
The GEV distribution, as defined by Jenkinson [
42
] and parameterised using a 90-year record
of annual maximum flows available from a gauging station along the Po River, was assumed to be
the Parent Distribution. Our justification for selecting the GEV as a parent lies with the fact that the
focus is on modelling the block maxima of water levels, and the theoretical arguments from extreme
value theory are considered sufficient for this task, assuming that the discharge,
Q
, follows a GEV
distribution,
Q
~GEV
(ξ,α,k)
,
ξ
,
α
, and
k
are the location, scale, and shape parameters, respectively.
The tail behaviour of the GEV distribution is influenced by the value of the shape parameter and
generally falls in three classes: The Gumbel type (
k=
0) is characterised by a light upper tail, the Frechet
type (
k>
0) has a heavy upper tail, and the Weibull type has (
k<
0) and is bounded above. Hence,
GEV encompasses three asymptotic distributions that can be selected to model the right tail of a
distribution and as such is a grand-parent.
3.4. Probability Model
The Gumbel distribution was selected as the Probability Model to fit samples drawn from the
parent distribution. The Gumbel distribution is quite popular among engineering practitioners for
most parts of the world. For instance, it is the distribution of choice to describe flood probabilities at
the Tiber River in Rome, Italy [43].
As such, we aim to mimic the common situation in the real world, in which simple models (the
Gumbel distribution in our example application) are used to fit reality (the GEV distribution in our
example application). Previous studies in statistical hydrology used similar research methods, by using
other simple distribution functions, such as the Lognormal, as a probability model and more complex
distribution functions, such as the Kappa and Wakeby, as parent distributions [22,24].
The GEV and Gumbel quantile function is given as
XT(F)(ξ+α{1−(−log F)k}/k k 6=0
ξ−αlog(−log F)k=0(2)
where
XT
represents a quantile estimate (for either discharge or water stage) corresponding to a certain
return period, in this case 100 years, while
F
is the non-exceedance probability. The parameters of
the GEV were estimated by the method of maximum likelihood using the available 90 year record
of annual maximum flows. These parameters were fixed and used for generating synthetic annual
maximum flows by random sampling from its inverse cumulative distribution function. Equation (2)
for the condition of
k6=
0, which is the quantile function for GEV, was used to estimate the 100-year
design peak flow. The 100-year peak flow was simulated using HEC-RAS to get the estimated design
flood level, h100.
3.5. Application of the Simulation Framework
Based on the hydraulic model (Section 3.1), rating curve (Section 3.2), parent distribution
(Section 3.3), and probability model (Section 3.5), we applied our simulation framework (Section 2) to
the 98-km reach of the Po River and by using a return period of 100 years (T= 100), repeating steps
C–G for 1000 times (N= 1000), and exploring the role of sample size by using Mequal to 30, 50, and
100. A generated sample size of 30 and 50 years reflects the typical length of historical observations,
while samples of a length equal to 100 years represent an optimistic case in hydrology.
4. Results
The application of the simulation framework described in Section 2and depicted in Figure 1, to a
98-km reach of the Po River (Section 3), allows us to compare the accuracy and precision of the two
approaches for the estimation of design flood levels.
Water 2019,11, 729 7 of 11
Figure 3shows boxplots of errors when the estimation of design flood levels is based on the two
methods that are considered in this study.
Water 2019, 11, x FOR PEER REVIEW 7 of 11
4. Results
The application of the simulation framework described in Section 2 and depicted in Figure 1, to
a 98-km reach of the Po River (Section 3), allows us to compare the accuracy and precision of the two
approaches for the estimation of design flood levels.
Figure 3 shows boxplots of errors when the estimation of design flood levels is based on the two
methods that are considered in this study.
(A)
(B)
Figure 3. Boxplots of error estimates for the two approaches with Gumbel distribution used for design
flood level estimation at cross-sections A and B. The red lines represent the median (50th percentile),
the lower and upper ends of the blue box represent the 25th and 75th percentile, respectively. Outliers
are represented by red dots.
The left panel of Figure 3 refers to the common approach (when the estimation is based on
annual maximum flows), and it shows a substantial underestimation, which is larger in section A,
where the rating curve has larger errors (Figure 2). Moreover, and there is no substantial
improvement in accuracy and precision after increasing the sample size from 30 to 100 years.
The right panel of Figure 3 refers to the alternative approach (when the estimation is based on
annual maximum levels), and it shows an underestimation of the design flood by 0.8 m with a more
Figure 3.
Boxplots of error estimates for the two approaches with Gumbel distribution used for design
flood level estimation at cross-sections (
A
,
B
). The red lines represent the median (50th percentile),
the lower and upper ends of the blue box represent the 25th and 75th percentile, respectively. Outliers
are represented by red dots.
The left panel of Figure 3refers to the common approach (when the estimation is based on annual
maximum flows), and it shows a substantial underestimation, which is larger in section A, where
the rating curve has larger errors (Figure 2). Moreover, and there is no substantial improvement in
accuracy and precision after increasing the sample size from 30 to 100 years.
The right panel of Figure 3refers to the alternative approach (when the estimation is based
on annual maximum levels), and it shows an underestimation of the design flood by 0.8 m with a
more significant reduction of uncertainty after increasing the sample size from 30 to 100 years. These
differences are substantial when the estimation of design flood levels is used for flood defence design
or risk assessment.
Water 2019,11, 729 8 of 11
5. Discussion
Our results demonstrate that the alternative approach can provide lower errors in assessing the
design flood level. The main advantage of the alternative approach is that less sources of uncertainty
come into play, such as the ones related to rating curve estimation and hydraulic modelling structure
and calibration [
44
,
45
]. In addition, the alternative approach can be easily implemented due to the
low data requirement, no dependency on hydraulic modelling, and computational power. Moreover,
one advantage in using high water levels is that information regarding the water stage is in abundance,
or at least it can be, given the relative ease of measuring it. Also, remote sensing using satellite altimetry
provides the opportunity to derive water stage data. Some studies have explored the direct use of
water levels (instead of river flows) in the study of ungauged catchments [
46
]. Studies focusing on
low flows, especially in large rivers, cannot be investigated using the alternative approach because of
hydraulic sensitivity at the section control [47].
Yet, conducting flood frequency analysis using water stages is not devoid of uncertainty. For rivers
with a gentle slope, water stages are heavily influenced by the downstream control (i.e., hydraulic
works, roughness, channel outfall), which might lead to backwater effects and in turn affect the accuracy
of the observed annual maximum water stage data. Water levels are also affected by backwater effects
and hydraulic jumps forming at the gauging station [
47
]. Seasonal variation in channel hydraulic
roughness affects the accuracy of observed water stages for a given discharge. Hence, the estimation
of design flood levels based on records of water levels seems to have more potential for rivers with a
subcritical flow regime and with a stable channel geometry. Di Baldassarre and Claps [
12
], for example,
showed that flood water levels in the study area considered here (i.e., Po River) are not significantly
influenced by changes in river geometry.
Moreover, while the design of levees only requires the estimation of a water level with a given
return period, the design of flood control reservoirs requires an estimation of the volume of water
corresponding to a given return period. In such a case, the analysis of flood discharges is needed.
Furthermore, using flood discharges has other advantages, including the possibility to follow regional
methods for design flood estimation, i.e., trading space for time and using multiple sites within a
homogeneous region [
48
]. On the other hand, however, hydrogeomorphic approaches can help identify
flood water levels in ungauged areas [
49
]. Table 1summarizes the main advantages and disadvantage
of the two approaches.
Table 1. Summary of pros (+) and cons (−) of the two approaches.
Various Aspects and Applications Common Approach
(Flood Discharges)
Alternative Approach
(Flood Levels)
Sources of uncertainty −+
Computational time −+
Data requirement −+
Changes in the river channel (e.g., erosion) + −
Hydraulic effects on the channel (e.g., backwater) + −
Design of levees −+
Design of flood-control reservoirs + −
Regionalization methods + −
Hydrogeomorphic methods −+
6. Conclusions
This paper presents a simulation framework (Figure 1) to compare two approaches for the
estimation of design flood levels: (i) A common one based on the frequency analysis of annual
maximum flows, and (ii) an alternative one based on the frequency analysis of annual maximum water
levels. We proposed a virtual experiment based on the use of synthetic data to gain insights about
potentials and limitations of these approaches.
Water 2019,11, 729 9 of 11
The example application demonstrates that the alternative approach can work better than the
common approach in terms of both accuracy and precision (Figure 3). These results were unavoidable
as they were associated with the specific test site, as well as the arbitrary assumptions about the
parent distribution and the hydraulic model. Still, they show that there is potential in this alternative
approach, which is essentially based on very old methods of estimating potential flood levels along
rivers in the past. This result is only partly surprising. While the use of annual maximum flows
remains theoretically more appropriate in the context of river flooding, this approach is affected by
numerous sources of uncertainty due to the use of a cascade of three models (Figure 1). As such,
we suggest complementing the common approach with an alternative estimation of design flood levels
directly based on annual maximum water levels, which are often the only type of data derived from
direct (and typically accurate) measurements.
Our work is an initial effort to compare common and alternative approaches for the estimation
of design flood levels, which we see as complementary given their corresponding pros and cons
(Table 1). The simulation framework presented here can be applied elsewhere considering more
parent/probability distribution functions, as well as data from various hydrogeomorphic conditions.
As such, it offers new opportunities to gain more understanding about the potentials and limitations
of these two alternative approaches.
Author Contributions:
K.O., writing—original draft preparation; G.D.B., M.M. and K.B., writing—review and
editing; K.O., Investigation; K.O., data curation; K.B., M.M. and G.D.B., supervision.
Funding: This research received no external funding.
Acknowledgments:
We thank Alberto Montanari and Richard Vogel for nice discussions on previous versions of
our work. Two Anonymous Reviewers are also acknowledged for constructive comments to this paper.
Conflicts of Interest: The authors declare no conflict of interest.
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