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ORIGINAL RESEARCH
published: 28 July 2020
doi: 10.3389/frwa.2020.00018
Frontiers in Water | www.frontiersin.org 1July 2020 | Volume 2 | Article 18
Edited by:
Chaopeng Shen,
Pennsylvania State University (PSU),
United States
Reviewed by:
Jie Niu,
Jinan University, China
Meysam Salarijazi,
Gorgan University of Agricultural
Sciences and Natural Resources, Iran
*Correspondence:
Henning Oppel
henning.oppel@rub.de
Specialty section:
This article was submitted to
Water and Hydrocomplexity,
a section of the journal
Frontiers in Water
Received: 26 March 2020
Accepted: 17 June 2020
Published: 28 July 2020
Citation:
Oppel H and Mewes B (2020) On the
Automation of Flood Event Separation
From Continuous Time Series.
Front. Water 2:18.
doi: 10.3389/frwa.2020.00018
On the Automation of Flood Event
Separation From Continuous Time
Series
Henning Oppel 1,2
*and Benjamin Mewes 2
1Center for Environmental System Research, Kassel University, Kassel, Germany, 2Institute of Hydrologic Engineering and
Water Management, Ruhr-University Bochum, Bochum, Germany
Can machine learning effectively lower the effort necessary to extract important
information from raw data for hydrological research questions? On the example of
a typical water-management task, the extraction of direct runoff flood events from
continuous hydrographs, we demonstrate how machine learning can be used to
automate the application of expert knowledge to big data sets and extract the relevant
information. In particular, we tested seven different algorithms to detect event beginning
and end solely from a given excerpt from the continuous hydrograph. First, the number
of required data points within the excerpts as well as the amount of training data has
been determined. In a local application, we were able to show that all applied Machine
learning algorithms were capable to reproduce manually defined event boundaries.
Automatically delineated events were afflicted with a relative duration error of 20 and
5% event volume. Moreover, we could show that hydrograph separation patterns could
easily be learned by the algorithms and are regionally and trans-regionally transferable
without significant performance loss. Hence, the training data sets can be very small
and trained algorithms can be applied to new catchments lacking training data. The
results showed the great potential of machine learning to extract relevant information
efficiently and, hence, lower the effort for data preprocessing for water management
studies. Moreover, the transferability of trained algorithms to other catchments is a clear
advantage to common methods.
Keywords: flood event separation, information extraction, time series, automation, data preprocessing
1. INTRODUCTION
Machine-learning has proven its capability in a vast range of applications, especially in those
cases when a certain pattern has to be revealed from a huge data archive in order to reproduce
it afterwards. Water management tasks require these capabilities in various steps. Natural and
anthropocentric processes have to be reproduced in order to model future events and behaviors
(Mount et al., 2016). Hence, machine learning (ML) has been applied in a broad range of
applications, like streamflow simulation (Shortridge et al., 2016), the interpretation of remote
sensing images (Mountrakis et al., 2011), modeling of evapotranspiration (Tabari et al., 2012),
rainfall forecasting (Yu et al., 2017), process analysis (Oppel and Schumann, 2020), and many
more. However, all water related tasks require pre-processed data. Pre-processing is in this case
defined as the extraction of the relevant information from raw data. A typical example is the need
for direct runoff flood events that have to be extracted from continuous time series of discharge.
Oppel and Mewes Automation of Flood Event Separation
This kind of information can be used for flood event research,
training of hydrological models for flood forecasting, design
tasks, etc. Despite its relevance and expense, there is no single
accepted method to efficiently automate this problem.
Especially the separation of rain fed direct runoff from the
base flow, i.e., discharge from deeper soil layers and groundwater
with higher transit times, has been subject to much scientific
work. This might be due to the fact that rain fed direct runoff
events are especially relevant for flood security (Fischer, 2018).
The most accurate way to separate direct and base flow runoff in
order to define flood events is to use tracer based methods (Klaus
and McDonnell, 2013; Weiler et al., 2017). However, tracer data
are only rarely available and are not collected on a continual basis.
Hence, their application is limited to very few case studies and is
not suitable for automated information extraction especially for
long time series.
There are three main groups of methods to extract flood
events from continuous time series: graphical methods, digital
filtering and recession based methods. Graphical approaches
(Hall, 1968; Maidment, 1993) are well-established in the water
management community, yet they rely on assumptions and
experience of the user (Mei and Anagnostou, 2015). Moreover,
these types of methods cannot be applied to large data sets
and do not allow for automation. Digital filtering techniques
overcame this drawback. These methods use a one- (Lyne
and Hollick, 1979), two- (Su, 1995; Eckhardt, 2005) or three-
parametric (Eckhardt, 2005) base equation to reproduce the
long wave response of a hydrograph. The calculated response is
treated as the baseflow, the residual of baseflow and hydrograph
is treated as the direct runoff. The intersections of baseflow
and direct runoff curves can be treated as beginning and end
of individual events. These methods are especially applicable
to extract information from long time series and allow for
automation, like Merz et al. (2006),Merz and Blöschl (2009), and
Su (1995).Gonzales et al. (2009) and Zhang et al. (2017) stated
that digital filtering techniques, especially the three-parametric
filter (Eckhardt, 2005), delivers superior results to all other
methods. However, they also pointed out that these methods
require local calibration.
The calibration process limits the application of a digital
filter to its fitted catchment. Moreover, the missing physical
reasoning of the parameters introduced parameter uncertainty
to the process (Furey and Gupta, 2001; Blume et al., 2007;
Stewart, 2015). Recession based methods try to overcome the
lack of physical reasoning (Tallaksen, 1995; Hammond and Han,
2006; Mei and Anagnostou, 2015; Dahak and Boutaghane, 2019).
They either rely on a linear (Blume et al., 2007) or non-linear
(Wittenberg and Aksoy, 2010) connection between storage and
the active process that defines the hydrograph. Other methods
try to estimate the parameters of digital filter from the recession
curves (Collischonn and Fan, 2012; Mei and Anagnostou, 2015;
Stewart, 2015). The drawback of these approaches is the missing
automation. Stewart (2015) analyzed several recession curves and
their connections to the separation of direct runoff and base
flow. Although a connection between direct runoff and base flow
was identified, they also found that recession analysis relying
on streamflow data solely can be misleading. Under different
conditions of the catchment different processes are active, and
hence, the connection between storage and runoff changes.
Beside this process uncertainty most methods require calibration
just like digital filtering techniques and cannot be transferred to
other basins.
As already pointed out, the common methods either lack a
way to automate them or they require local calibration. Either
way, the effort to extract the relevant information is high.
Another drawback is that especially the physically based methods
search for the true separation of direct runoff and base flow. But,
in some cases this might not be the target of a separation. For
example: if the task is to evaluate just the first peak of each flood
event, no common method can adopt to that target. The power
of ML algorithms to detect patterns and to reproduce them in
further application could be a solution to this topic. Thiesen et al.
(2019) demonstrated that data-driven approaches with different
predicors can be applied to the task of hydrograph separation.
They found that models using discharge as predictors returned
the best results. Although their automated flood event separation
performed well, they required a large amount of training data
which is limiting the applicability of their approach. Thiesen
et al. (2019) estimated a label (flood event / no flood event) for
each time step of the continuous time series and, hence, searched
for the true separation of direct runoff and base flow. As stated
before, this might not be applicable in all cases. Therefore we
assumed that the event, i.e., the time stamp of the flood peak is
known, but the time of event beginning and end are unknown.
In the first part of the study we assessed which part of a flood
hydrograph is relevant to determine the begin and end of the
event. Based on a training set generated by expert knowledge
we analyzed how many points from a hydrograph excerpt are
needed to estimate the event boundaries. Moreover, we analyzed
which machine learning algorithms are suitable for this type of
problem and how many training data is required to automate the
separation process. A major shortcoming of common methods
is the local bound applicability. Therefore, we tested if trained
algorithms could successfully be applied in new catchments on a
regional and trans-regional scale.
2. MATERIALS AND METHODS
In this section we will shortly introduce the case study basins of
the Upper Main and the Regen. In the subsequent section, the
ML algorithms and their settings will be presented. This section
is completed with the introduction of the entropy concept and
the performance criteria used to evaluate the ML-algorithms.
2.1. Data
For this study, continuous time series from 15 gauges in south-
east Germany have been used. Five gauges from the basin of the
Upper Main have been used for local application and the tests
on required training data and predictors. Additional five gauges
from the Upper Main basin and five other gauges from the Regen
basin have been used for regional and trans-regional validation
of the trained algorithms solely. The time series had an hourly
temporal resolution and covered the time span from 2001 to 2007
in the Upper Main basin, 1999 to 2012 in the Regen basin.
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Oppel and Mewes Automation of Flood Event Separation
FIGURE 1 | Flood events observed at gauge Friedersdorf with manual defined markers of event begin tBand end tEto capture direct runoff.
We assumed that users know what kind of flood events they
are interested in and just needs to automate the process of
separation (Moreover, the process of peak identification can be
automated with a peak-over-threshold (POT) method). Hence,
we defined the time stamps of five highest discharge peaks per
year as the events of interest. The number of five events per year
has been chosen to create a large data basis while maintaining
the focus on floods. To create a training and validation data
set beginning tBand end tEof each event have been defined
manually. Due to the focus on flood events our strategy for
manual flood separation was to capture begin and end of direct
runoff. Although precipitation data was available, we excluded
it on purpose to focus on the hydrographs. The begin of the
direct runoff tBwas defined as the first significant increase
of discharge prior to the peak. The end of direct runoff tE
was defined as either the last change of slope of the recession
curve starting from the peak before the next rise, or the last
ordinate of the recession curve before the next event (compare
Figure 1). Target variables tBand tEwere defined as difference
between the time stamp of the peak and the time stamp of the
events begin/end.
As the spatial arrangement of the chosen gauges shows
(Figure 2), training and validation gauges have been selected
to cover similar relationships of neighboring and nested
catchments. Additionally, the training and validation sets have
been compiled to cover the same ranges of catchments area. Each
set comprises small catchments with an area between 10 and 100
km2and large catchments with an area between 100 and 1,400
km2(compare Table 1).
The transferability of trained ML algorithms was analyzed by
using a regional model strategy. The ML algorithms were trained
with the data from the five gauges from the Training data set,
defined in Table 1. All Training gauges were located in the upper
Main basin. For validation the trained algorithms were used to
estimate tBand tEfor flood events observed at gauges from the
regional and trans-regional data set (compare Table 1).
2.2. Machine Learning Algorithms
The No-free-Lunch-Theorem pays its tribute to the plethora of
available ML-algorithms and reduces the problem of choice to
an optimization problem: If an algorithm performs well on a
certain class of problems then it necessarily pays for that with
degraded performance on the set of all remaining problems. A
certain algorithm is more or less suitable for a specific problem
(Wolpert and Macready, 1997). Accordingly, several approaches
have to be taken into account in parallel. Additionally, Elshorbagy
et al. (2010a,b) found that a single algorithm is not able to
cover the whole range of hydrologic variability. Hence, they
recommended to use an ensemble of algorithms for water related
tasks. In order to assess which type of algorithm is suitable to the
addressed task of this study we used seven different algorithms
(provided by Pedregosa et al., 2011 as Python package scikit-
learn), representing five different algorithm structures.
Artificial neuronal networks (ANN) are the most commonly
applied ML algorithms which is also true for hydrological
applications (Minns and Hall, 2005; Solomatine and Ostfeld,
2008). The structure of an ANN is inspired by the structure
of the human brain (Goodfellow et al., 2016). Multiple input
features are connected through multiple neurons on a variable
number of hidden layers with the output of the network. The
output neuron represents the target variable of the regression
(or classification) task. The hidden layers of the ANN define
the level of abstraction of the problem. The more layers, the
more abstraction is given to the input features (Alpaydin, 2010).
Because this study addressed the topic of pattern recognition in
hydrographs with a, to this point, unknown degree of abstraction,
ANNs with different numbers of hidden layers have been applied.
Specifically, an ANN with a single and an ANN with two hidden
layers have been applied. The number of neurons per layer
has been adjusted during the training process. Both regressors
were based on the multi-layer perceptron and used a stochastic
gradient descent for optimization (Goodfellow et al., 2016).
Additionally, an Extreme Learning Machine (ELM) was added
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Oppel and Mewes Automation of Flood Event Separation
FIGURE 2 | Case study basins of the Upper Main (upper left) and Regen (lower right) in south-east Germany. Five gauges (triangle) have been used for local
application and as training data for (trans-) regional application (circle).
TABLE 1 | Gauges and catchment areas in the case study regions.
Training Reg. Validation Tr.Validation
Gauge Area [km2] Gauge Area [km2] Gauge Area [km2]
Bad Berneck 99.7 Bayreuth 340.3 Chamerau 1356.5
Gampelmuehle 62.2 Coburg 346.3 Kothmaissling 405
Lohr 165.3 Friedersdorf 11.1 Koetzing 224.4
Unterlangenstadt 713.9 Schlehenmuehle 70.95 Teisnach 626.6
Untersteinach 73.5 Wallenfels 96.45 Zwiesel 293.4
to the group of used algorithms. The ELM is a special type
of ANN (Guang-Bin Huang et al., 2004) that was designed for
a faster learning process. In a classic ANN each connection
between neurons is assigned with a weight that is updated in
the optimization process. An ELM has fixed weights for the
connection between hidden layer and the output neuron. Only
the remaining connections are optimized during the training
process. Due to this simplification, the ELM learns faster while
regression outputs remain stable (Guang-Bin Huang et al., 2004).
The three types of neuronal networks are accompanied by
4 other algorithms. As a representative for the similarity-based
algorithms the K-nearest-neighbor (KNN) algorithms has been
applied (Kelleher et al., 2015). Here, no model in the common
sense is trained. For regression, the KNN uses the predictors to
define similarity between the elements of a new data set and the
known cases of the training data. The output is then defined as
the average of the k-nearest elements. In this study, kwas defined
iteratively during the training process within a range of [5;10].
Parameter values for koutside the specified range were tested, but
rarely proved to be a better alternative. In order to accelerate the
training of the KNN, the comparatively small parameter space
was chosen. A Support Vector Machine (SVM) algorithm, an
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Oppel and Mewes Automation of Flood Event Separation
error-based approach, has also been used in this study. The SVM
fits a M-dimensional regression model to the given problem,
where Mcan be greater than the dimension of the original
feature space. To maintain a reasonable computation time, the
SVM focuses on data points outside a certain margin around the
regression line, the so-called support vectors (Cortes and Vapnik,
1995). Another type of ML-algorithm included in this study was
a Classification and Regression Tree (CART). Regression trees
are built node per node with a successive reduction of regression
error between the estimates and the true values. CART-regressors
have been used as base estimators for a Random Forest (RF)
that has been used additionally in this study. The RFs consisted
of 1,000 regression trees, each trained with a randomly chosen
subset of the given training data. The average of all regression
results is returned as estimate of the RF. We applied the RF due
to its common application in hydrological studies (Yu et al., 2017;
Addor et al., 2018; Oppel and Schumann, 2020). Moreover, the
use of an ensemble regressor accounts for the recommendations
of Elshorbagy et al. (2010a). Details on implementation are
provided by Pedregosa et al. (2011).
The applied algorithms face several inherent problems and
advantages, so the right choice of a suiting algorithm depends
on the available data and the problem to be solved. SVMs,
for example, work perfectly if the margin of the separating
vector is small. Thus, they tend to overfit if that is not the
case in the data they are trained on. Moreover, the choice of
the internal kernel is not trivial and has impact on the results
and the training behavior. CART trees are very comprehensible
models and quickly converging models, but tend to overfit, so
the remaining degrees of freedom have to be considered for an
interpretation of CART results. RF on the other hand reduce
to vulnerability of overfitting, yet the build less comprehensible
outcomes due to the large number of possible model trees. ANNs
are robust against overfitting, but require more data to converge
in complex situations than the other approaches. ELM inherits
the advantages and problems of ANNs and SVM. KNN converge
very quickly and are often a suitable method. Nevertheless, the
general ability of KNN for ML prediction requires information on
internal structure of the data and its internal clustering of groups.
2.3. Shannon Entropy
The entropy concept, introduced by Shannon (1948), is the
underlying concept of information theory (Cover and Thomas,
2006). Shannon’s entropy concept is used to determine the
information content within a given data set. Entropy His
calculated for a discrete random variable Xwith possible values
x1,...,xnby:
H= −
n
X
i=1
P(xi)logbP(xi) (1)
where P(xi) is the probability that Xtakes exactly the value
xi. The basis bof the log-function can take any value, but is
usually set to b=2, which gives Hthe unit bit. As Equation
(1) shows, the entropy value is a measure for uncertainty of the
considered variable. If all samples drawn from Xwould take the
same value, the probability of this value would be 1 and hence the
entropy would be equal to 0.0, because one would be absolutely
certain about the outcome of new samples drawn from X. The
entropy increases to a value of 1.0 if the sample would be equally
distributed on two outcomes (Kelleher et al., 2015). The higher
the entropy, the wider the histogram of Xis spread.
The problem with Equation (1) is that it can only be applied
to discrete data. Unfortunately most hydrological relevant data
is continuous. This was also the case in this study, because the
ordinates of the hydrograph are intended to determine the events
temporal boundaries. Gong et al. (2014) showed that the use of
frequency histograms, which is also refereed as Bin Counting, is
a feasible and reliable approach to represent the continuous as a
discrete distribution function. To apply Bin Counting the width
of bins has to be determined. Scott (1979) proposed the following
estimator for the optimal bin-width h∗:
h∗=3.49σN−1/3(2)
where σis the standard deviation of the data and Nis the number
of samples. We followed the recommendations of Scott (1979)
and Gong et al. (2014) and used Bin Counting to calculate the
entropy of the predictor and target variables.
2.4. Performance Criteria
Estimation errors manifest as differences between estimated and
manually defined time stamps of event begin and end, resulting
in different event metrics duration and volume. The deviations of
these metrics were used to define the performance criteria. First,
the mean volume reproduction MVR was defined as follows:
MVR =
N
P
i−1
VEst;i
VMan;i
N(3)
where Nis the number of considered events and Vis the
estimated (Est) or manual defined (Man) event volume. The
MVR is defined within [0; + inf] with an optimal value of 1. The
second metric accounts for the duration of the event. For each
event two sets of time stamps are available: set Mcontaining all
time stamps of the manually separated event, and Dcontaining all
time stamps of the estimated event. Time stamps within both sets
are correctly ascertained time stamps by the ML-algorithm. This
set Ican be expressed as the intersection of both sets I=D∩M.
Temporal coverage of an estimated event has been calculated
as the ratio of the cardinalities of Iand M, i.e., the ratio of
correctly ascertained time stamps and the true number of event
time stamps:
COV =|D∩M|
|M|=|I|
|M|(4)
Temporal coverage COV is defined on [0;1] with an optimal
value of 1. Note that COV only accounts for errors of time
stamps, not the actual event duration. An estimate of event
boundaries that sets event begin and end wrong, but outside of
the true event boundaries, has a coverage equal to 1. However,
the error will be accompanied by an MVR greater than one. The
combined evaluation of COV and MVR reveals that the time
stamps were set outside the true event boundaries.
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Oppel and Mewes Automation of Flood Event Separation
FIGURE 3 | Entropy values of the data sets Hconsidering a varying number of ordinates from hydrographs (number of ordinates considered on the abscissa).
3. RESULTS
In this section, the analysis regarding the automation of the
flood event hydrograph separation will be presented. Section 3.1
presents the selection of the ML-predictors, i.e., the number of
hydrograph ordinates necessary to predict the event boundaries.
This is followed by the results of the local application of the
ML-algorithms (section 3.2).
3.1. Predictor Selection
As predictors for the estimation of event boundaries (time
stamps of beginning and end of a flood event), we intended
to use the ordinates of the hydrograph itself. Therefore, we
had to determine the required amount of ordinates to achieve
satisfactory results, while keeping the amount of predictors as low
as possible to minimize the training effort of the ML-algorithms.
In other words we wanted to focus on the necessary
hydrograph components to determine flood begin and end. In
course of the graphical, manual separation (section 2.1) we
observed that we mainly paid attention to the shape of the
hydrograph in comparison to its closer hydrological context for
our decisions. Transferring this to the numerical data of the
hydrographs (Q) means that the set of hydrograph ordinate
with the highest uncertainty about Qconveyed the highest
amount of relevant information to the separation process. In
order to determine the length of these sets we performed an
entropy analysis for different lengths of sets (see below). We
used the entropy metric to evaluate the information content
H, because its values quantifies the uncertainty of a data set
(compare section 2.3).
Although Hcalculated separately for the predictor and the
target variable set allowed us to compare the information within
the data, they do not tell us if these information coincide. The
common approach to quantify the shared information content
of data sets is to use the mutual information (MI) (Sharma
and Mehrotra, 2014). The MI-value concept evaluates the joint
probability distribution of two (or more) data sets and evaluates
the information obtained from the predictor data set about the
target data set. Due to the high dimension of our predictor data
set (number of hydrograph ordinates between 10 and 600), the
joint probability distributions could not be estimated. Hence,
the concept of MI was not applicable. Hence, we relied on H
calculated for target and predictor sets separately, to evaluate the
predictor data sets. We assumed that an entropy value of the
predictor set similar to the entropy of the target variable set is
a necessary but not sufficient condition for an optimal predictor.
First, we calculated the entropy of the target variables for
manually separated events, the time stamps of event beginning
and end. Equation (1) and (2) were applied to all available data
sets. We obtained average entropy values of HA=1.55 bit for
the event beginnings and HE=2.15 bit for event ends. The
standard deviation of HAand HEbetween the considered sub-
basins was σ(HA)=0.15 and σ(HE)=0.39. The entropy values
showed that the position of the flood beginning (in relation to
the peak) is afflicted with less uncertainty than the end of the
flood. A result that is in concordance with our experience from
the manual flood separation.
In the second step of the analysis we calculated the entropy for
different predictor data sets. The first data set evaluated consisted
of 10 hydrograph ordinates, half of the ordinates prior to the
peak the other half succeeded the peak. The amount of ordinates
was increased incrementally up to 600 ordinates. The obtained
entropy values showed that the data sets contained the highest
entropy if only a few ordinates were used (Figure 3). Data sets
with 10–50 ordinates, regardless of the sub-basin, showed an
entropy value of H≥3.7 bit which is equal to the sum of
HAand HE. With an increasing amount of data the entropy
values decreased significantly. With 500 data points considered,
the entropy values lowered to a range of [2.0, 3.5] bit and did not
change any further with increasing data points.
In order to evaluate our assumption of the connection
between equal entropy values and predictive performance, a
test with different ML-algorithms in all sub-basins was carried
out. Each data set was split randomly into training data (50%)
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Oppel and Mewes Automation of Flood Event Separation
FIGURE 4 | Dependence of the number of hydrograph ordinates and the mean volume reproduction (MVR) and temporal coverage (COV) of automatically separated
flood events. Application of a trained RF in sub-basin Bad-Berneck.
FIGURE 5 | Hydrographs for two flood events at gauge Lohr with manually and automated defined markers of event begin tBand end tE.
and validation data (50%). Each ML-algorithm was trained and
validated with the MVR (Equation 3) and COV (Equation 4).
To minimize uncertainty due to the choice of training data, the
evaluation was repeated 10-times for each data set. The obtained
results were comparable in all applications. For the majority of
catchments the best MVR-results (median and variance) were
achieved with 40 or 50 ordinates used as predictors and the
optimal COV with 50 ordinates. As an example the results of
RF application in catchment Bad Berneck are shown in Figure 4
(Results for all other algorithms and catchments can be found in
the Supplementary Material).
Based on the experimental results and the evaluation of the
entropy values we chose 40 ordinates, 20 prior to the peak
and 20 succeeding the peak, as the predictor data set for the
following analysis.
3.2. Automated Flood Hydrograph
Separation
For each data set from the catchments marked as training gauges
in Table 1 and Figure 2, we tested if flood hydrograph separation
could be automated by means of ML. Like in the previous section,
we randomly chose 50% of the available flood event data for
training of the algorithms. Their performance was validated with
withheld data from the respective gauge. Again, the procedure
has been repeated to lower the uncertainty due to the randomly
chosen subsets. In this case, 500 iterations were performed. For
each event of the validation data, tBand tEwere estimated with
all available ML-algorithms (Figure 5).
The results showed that the ML-algorithms were able to
perform the required automation task. However, they tended
to overestimate the volume of the events (Figure 6), while the
temporal coverage was met in the most cases (Figure 7). Only
the ANN1 and ANN2 did not match the temporal extend of the
events. The combination of a COV lower than 1 and MVR greater
than 1 (compare Figure 5, right panel) showed that one time
stamp was set too close to the peak, while the other was set too
far from to peak. Giving a low coverage of the event and high
volume error. In these cases it was the event start that was set too
close to the peak and the end was set too far. A different behavior
is visible in the results of the ELM and KNN. While the COV is
Frontiers in Water | www.frontiersin.org 7July 2020 | Volume 2 | Article 18
Oppel and Mewes Automation of Flood Event Separation
FIGURE 6 | Mean volume reproduction (MVR) of the validation flood events in local application of trained artificial neuronal network with 1- (ANN1) and 2-hidden
layers (ANN2), regression tree (CART), extreme learning machine (ELM), k-nearest-neighbor (KNN), random forest (RF), and support vector machine (SVM).
FIGURE 7 | Temporal coverage (COV) of the validation flood event duration in local application of trained artificial neuronal network with 1- (ANN1) and 2-hidden layers
(ANN2), regression tree (CART), extreme learning machine (ELM), k-nearest-neighbor (KNN), random forest (RF), and support vector machine (SVM).
close to 1, the MVR shows an average overestimation of event
volume of 20%. This shows that ELM and KNN separated too
long flood events. The best results were obtained with the RF and
the SVM.
The results also showed regional dependence of the model
error. Independent from the chosen algorithm, Bad Berneck
showed the highest volume errors, while Gampelmuehle showed
the highest COV errors. It is striking that Gampelmuehle on
the other hand showed one of the lowest volume errors, and
Bad Berneck the lowest COV errors. Contrary to that, the three
remaining basins showed comparable results for both criteria. An
explanation for this observation lies within the response time of
these catchments. In comparison to the other hydrographs, they
are significantly more flashier and the duration of the flood events
is significantly shorter.
4. DISCUSSIONS
The presented results showed that ML is in general capable
to automate the considered task. But several choices, like
the amount of training data have to be discussed and the
transferability of trained algorithms has to be tested. This sections
provides discussions on these topics.
4.1. Training Data
The results showed that all algorithms could be used in local
application to automate the task of flood event separation from
continuous time series. Yet, the true benefit of the automation
is unclear, because we randomly selected the size of the training
data set. A true benefit for automation would be a minimal
requirement of training data, because this would minimize the
manual effort for separation. The results in section 3.2 showed
that we could at least half the manual effort. But how many
manually separated flood events are really necessary to train
the algorithms?
To answer these questions, an iterative analysis has been
performed. First, 25% of the available flood events were randomly
chosen as validation data set and removed from the data
pool. In the succeeding steps a variable amount of training
data was chosen from this pool to train the ML-algorithms.
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Oppel and Mewes Automation of Flood Event Separation
FIGURE 8 | Dependence of mean volume reproduction (MVR)/temporal coverage (COV) and size of the training data set of a random forest (RF) and an extreme
learning machine (ELM). Uncertainty belts drawn in gray scales for different probabilities (50, 80, 90%). The amount of training data has been raised incrementally to
train the algorithms and were validated in each step with the same data set, containing 25% of the available data.
In each step, the trained algorithms were validated with the
same validation data set. In order to minimize uncertainty
due to the randomly chosen data sets, this procedure was
repeated 500 times.
The results showed that the required amount of training
data was surprisingly low for all algorithms. The median
MVR reached the optimum of MVR =1.0 with the
lowest amount of uncertainty with only 20–30% percent used
training data (Figure 8, full plot with all ML-algorithms in the
Supplementary Material). This was true for all ML-algorithms
used in this study. The results for the COV criterion were
similar to these findings. But in contrast to the MVR criterion,
the uncertainty decreased slightly with increasing training data.
The combined evaluation of MVR and COV showed different
types of estimation errors. With a small data set the duration of
the separated flood events is afflicted with higher uncertainty,
while the true volume of the event is more likely to be
met and vice versa for larger data sets. However, the orders
of magnitude differ. The certainty of event duration does
not increase to the same extent as the uncertainty of the
volume increases.
Note that in this study only 20 events per sub-basin were
available, which means that a training data set of 4–5 manually
separated flood events was a sufficient training data set for the
automation of the task.
4.2. Transferability
In this section we present the results of the conducted test on
the ability to transfer the trained algorithms to other catchments.
First, a regional transfer has been tested. Here, we used the data
sets from the local application (sections 3.2, 4.1) to train the ML-
algorithms and validated their performance at five new gauges in
the same basin, i.e., regional neighborhood (Figure 2). Likewise
to the procedure in section 4.1, we analyzed the impact of training
data on the performance. Here, we had a total of 117 flood events
for training and validated with the individual data sets from the
new five catchments.
The performance of the ANN1 and ANN2 stabilized at
30–40% of used data for both criteria (Figure 9). Estimates
from both algorithms reached a median MVR ≈1.05 and a
median COV ≤0.8. A similar performance was achieved with
the ELM and the KNN, only that the obtained COV values
were larger than 0.8. Additionally, the ELM and KNN showed
faster learning than all other algorithms. Results stabilized at
approx. 5% of used training data. Further changes in median
performances and the uncertainty belts with increasing training
data were insignificant. The only algorithm that showed constant
improvement, i.e., a reduction of the uncertainty belt, was the
RF. However, this improvement was accompanied by a steady
increase of volume. With all available data used for training,
the volume was overestimated by approx. 10%. The concept of
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Oppel and Mewes Automation of Flood Event Separation
FIGURE 9 | Dependence of mean volume reproduction (MVR)/temporal coverage (COV) and size of the training data set for different ML-algorithms in regional
application. Uncertainty belts with different probabilities (50, 80, 90%) drawn for MVR in red scales, for COV in blue scales. The amount of training data has been
raised incrementally to train the algorithms. Validation was performed on data sets in regional neighborhood of the training data sources in the Main basin.
support vectors, as used in the SVM, proved to be not useful in
this case. Recall that the support vector defines a range around
the M-dimensional regression “line” and all data points falling
within the defined range are excluded from the optimization.
This focus on the outliners of the problem resulted in the inferior
performance of the SVM (Figure 9). Note that the results of the
CART algorithm are not shown in Figure 9, because the results
are similar to the results of the KNN, but with a median MVR =
1.1 and median COV =0.75.
In summary, the results showed that even with a small data
set automated hydrograph separation could be performed in
regional application. Neural network estimators (ELM, ANN1
and ANN2) and similarity-based estimators (KNN) performed
best. Flood event duration estimates were afflicted with median
bias of 20%. However, this mismatch of event duration did not
result in a significant volume error (5% overestimation with
ELM & KNN). Our results showed that a training data set of 35
manually separated flood events was needed to train ANNs, only
the ELM and KNN should be used with less available data.
Based on this results, we asked if the algorithms could be
applied to catchments of another basin, i.e., if the trained
algorithms could be used in a trans-regional application. Likewise
to the regional application, trained algorithms were used to
estimate the time stamps of event begin and end of the
floods events, but in this case for catchments in the Regen
basin (Figure 2). The results of the trans-regional applications
approved our findings of the regional application (Figure 10).
Again, the ANN1 and ANN2 required 30-40% of the data to reach
stable results. ELM and KNN, again, required less training data.
Contrary to the regional application, the median MVR of the
RF converged toward the optimum value of 1.0 with increasing
data. Again, a training data set of approx. 35 flood events was
sufficient to automate the task of hydrograph separation, even in
a trans-regional application.
4.3. Hydrograph Similarity
Our results showed that we could successfully apply an ELM
or KNN trained with data from five basins in the Upper Main
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Oppel and Mewes Automation of Flood Event Separation
FIGURE 10 | Dependence of mean volume reproduction (MVR)/temporal coverage (COV) and size of the training data set for different ML-algorithms in trans-regional
application. Uncertainty belts with different probabilities (50, 80, 90%) drawn for MVR in red scales, for COV in blue scales. The amount of training data has been
raised incrementally to train the algorithms. Validation was performed on data sets in the Regen basin.
to other sub-basins within the same catchment and in another
catchment. This brought up the question: why did it work?
A trained, i.e., calibrated model can only be applied to other
data without significant performance decrease if the patterns,
i.e., variance, within the new data matches the training data.
In the previous analysis we proved that our trained models
could be applied without performance decrease. Hence, we made
the hypothesis that the hydrographs within the training and
validation data set, i.e., their variance was similar. As stated
in section 3.1 the entropy concept is a good tool to assess
the information, i.e., the variance within data sets. Hence, we
analyzed the entropy of the training and validation data sets in
order to test our hypothesis.
Although entropy quantifies the amount of information, it
cannot assess the actual information and is, hence, not applicable
to evaluate the equivalence of two data sets. But, if redundant
information is added to a data set its entropy value decreases
(compare section 2.3). We exploited this behavior of the entropy
metric to assess the information equivalence of the training and
validation data sets.
We incrementally enlarged a merged data set comprising
hydrographs from the training data and one of the validation
data sets (regional/transregional). In each step we added a
single hydrograph to the data set and calculated the entropy
value (Equation 1). First we added all training hydrographs,
then we added the validation hydrographs. In order to assess
the uncertainty of H, due to data availability we repeated this
procedure 500 times, in each iteration only used 50% of the
available data (randomly selected).
The results of this analysis supported our hypothesis
(Figure 11). We found that Hincreased very quickly with only
2 or 3 data sets (actual position of HMax depending of selected
hydrographs). After that Hdecreased, with some variance in
its development due to data selection. Although variance was
visible, HMax <2.5 [bit] was never exceeded with the additional
validation data, neither with the regional nor with the trans-
regional data set. Note that HMax in this analysis was lower
than the entropy values in section 3.1, because normalized
hydrographs have been used to assess the information given to
the ML-algorithms.
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Oppel and Mewes Automation of Flood Event Separation
FIGURE 11 | Development of entropy Hfor merged training and validation (regional REG/trans-regional TR) data sets. Median (black lines) and 90%-uncertainty belts
calculated by randomly adding 50% of the available hydrographs per sub-basin to the merged data set.
5. CONCLUSIONS
In this article we demonstrated how machine learning can
be used to automate the task of hydrograph separation from
continuous time series. As predictor for the used ML-algorithm
we used the ordinates of hydrograph, solely. This minimized the
effort for data pre-processing. An analysis of entropy values and
numerical experiments showed that only a short excerpt of the
hydrograph (40 values, 20 prior, and another 20 succeeding the
flood peak) were required for hourly discharge data.
Seven different ML-algorithms were trained with manually
separated flood events and were applied locally, regionally
and trans-regionally. All applications showed that machine
learning was able to extract the relevant information (flood event
duration and volume). In the local application, i.e., application
of the trained algorithms to the same catchment, RF and SVM
showed the best results. However, in regional and trans-regional
application, i.e., application to other catchments than the training
data source, estimators based on artificial neuronal networks
(ELM, ANN with 1 hidden layer) and similarity based estimator
(KNN) performed best.
Moreover, we demonstrated that the application of ML
minimizes the effort for manual data pre-processing. For local
application, data sets containing only 4–5 manually separated
events were sufficient to transfer the experts knowledge to the
algorithms. For a transfer of the trained algorithms to other
catchments lacking training data, the manual effort increased
slightly. In our applications, 35 events from 5 gauges, i.e., 7 events
per gauge transferred the required amount of information to
the ML-algorithm.
A striking observation was that the performance of flood event
separation was comparable in local, regional and trans-regional
application. With an assessment of information equivalence in
the training and validation data sets we demonstrated that the
variance of our predictors necessary to be applied to other data
sets, could be covered with our training data set. The result of
the analysis not only supported our hypothesis about information
equivalence, but also provided an explanation why our approach
to automation of event separation had a quicker learning process
than other approaches like Thiesen et al. (2019). We excluded
the majority of natural variance within the continuous time with
the focus on the events we are interested in (via POT-method).
From the time-stamp returned by POT we used the 40-discharge
ordinates around the peak as predictors for the estimation of
event beginning and end. With this procedure we focused the
ML-algorithms on the shape of the flood event and trained
it to identify its begin and end. Our results proved that this
approach delivered good results and requires a minimum amount
of manual work for training.
However, we have to focus on this topic in future works.
We excluded the transfer to other climatic conditions and we
excluded the impact of biased data. With additional data, taking
more catchments into account, we want to test the application of
trained algorithms to a wider range of possible applications than
presented in this study. Moreover, more numerical experiments
have to be carried out to evaluate the impact of the training data
and choices made by the user, for example the chosen separation
target. In this study we tried to separate the full flood event.
However, other users might be interested in other tasks. Although
our results are promising in this respect, further tests must be
carried out.
DATA AVAILABILITY STATEMENT
All datasets presented in this study are included in the
article/Supplementary Material.
AUTHOR CONTRIBUTIONS
This study was developed and conducted by both
authors (HO and BM). HO provided the main text
Frontiers in Water | www.frontiersin.org 12 July 2020 | Volume 2 | Article 18
Oppel and Mewes Automation of Flood Event Separation
body of this publication which was streamlined
by BM.
FUNDING
The financial support of the German Federal Ministry of
Education and Research (BMBF) in terms of the project
Wasserressourcen als bedeutende Faktoren der Energiewende
auf lokaler und globaler Ebene (WANDEL), a sub-project
of the Globale Ressource Wasser (GRoW) joint project
initiative (Funding number: O2WGR1430A) for HO is
gratefully acknowledged.
ACKNOWLEDGMENTS
The authors would like to thank the Bavarian Ministry of the
Environment for providing the Data used in this study. We also
like to thank Svenja Fischer for her feedback that helped to
improve this work.
SUPPLEMENTARY MATERIAL
The Supplementary Material for this article can be found
online at: https://www.frontiersin.org/articles/10.3389/frwa.
2020.00018/full#supplementary-material
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Conflict of Interest: The authors declare that the research was conducted in the
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potential conflict of interest.
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