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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.
Content may be subject to copyright.
published: 28 July 2020
doi: 10.3389/frwa.2020.00018
Frontiers in Water | 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
Henning Oppel
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
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
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
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.
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
H= −
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:
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:
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=DM.
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:
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).
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 H3.7 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
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
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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.
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.
Frontiers in Water | 8July 2020 | Volume 2 | Article 18
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
Frontiers in Water | 9July 2020 | Volume 2 | Article 18
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
Frontiers in Water | 10 July 2020 | Volume 2 | Article 18
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.
Frontiers in Water | 11 July 2020 | Volume 2 | Article 18
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.
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.
All datasets presented in this study are included in the
article/Supplementary Material.
This study was developed and conducted by both
authors (HO and BM). HO provided the main text
Frontiers in Water | 12 July 2020 | Volume 2 | Article 18
Oppel and Mewes Automation of Flood Event Separation
body of this publication which was streamlined
by BM.
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.
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.
The Supplementary Material for this article can be found
online at:
Addor, N., Nearing, G., Prieto, C., Newman, A. J., Le Vine, N., and Clark, M. P.
(2018). A ranking of hydrological signatures based on their predictability in
space. Water Resour. Res. 54, 8792–8812. doi: 10.1029/2018WR022606
Alpaydin, E. (2010). Introduction to Machine Learning. Adaptive Computation and
Machine Learning, 2nd Edn. Cambridge, MA: MIT Press.
Blume, T., Zehe, E., and Axel, B. (2007). Rainfall–runoff response, event-based
runoff coefficients and hydrograph separation. Hydrol. Sci. J. 52, 843–862.
doi: 10.1623/hysj.52.5.843
Collischonn, W., and Fan, F. M. (2012). Defining parameters for Eckhardts digital
baseflow filter. Hydrol. Process. 27, 2614–2622. doi: 10.1002/hyp.9391
Cortes, C., and Vapnik, V. (1995). Support-vector networks. Mach. Learn. 20,
273–297. doi: 10.1007/BF00994018
Cover, T. M., and Thomas, J. A. (2006). Elements of Information Theory, 2nd Edn.
Hoboken, NJ: Wiley-Interscience.
Dahak, A., and Boutaghane, H. (2019). Identification of flow components
with the trigonometric hydrograph separation method: a case study
from Madjez Ressoul catchment, Algeria. Arab. J. Geosci. 12:463.
doi: 10.1007/s12517-019-4616-5
Eckhardt, K. (2005). How to construct recursive digital filters for baseflow
separation. Hydrol. Process. 19, 507–515. doi: 10.1002/hyp.5675
Elshorbagy, A., Corzo, G., Srinivasulu, S., and Solomatine, D. P. (2010a).
Experimental investigation of the predictive capabilities of data driven
modeling techniques in hydrology - Part 1: concepts and methodology. Hydrol.
Earth Syst. Sci. 14, 1931–1941. doi: 10.5194/hess-14-1931-2010
Elshorbagy, A., Corzo, G., Srinivasulu, S., and Solomatine, D. P. (2010b).
Experimental investigation of the predictive capabilities of data driven
modeling techniques in hydrology - Part 2: application. Hydrol. Earth Syst. Sci.
14, 1943–1961. doi: 10.5194/hess-14-1943-2010
Fischer, S. (2018). A seasonal mixed-POT model to estimate high flood
quantiles from different event types and seasons. J. Appl. Stat. 45, 2831–2847.
doi: 10.1080/02664763.2018.1441385
Furey, P. R., and Gupta, V. K. (2001). A physically based filter for separating
base flow from streamflow time series. Water Resour. Res. 37, 2709–2722.
doi: 10.1029/2001WR000243
Gong, W., Yang, D., Gupta, H. V., and Nearing, G. (2014). Estimating information
entropy for hydrological data: one-dimensional case. Water Resour. Res. 50,
5003–5018. doi: 10.1002/2014WR015874
Gonzales, A., Nonner, J., Heijkers, J., and Uhlenbrook, S. (2009). Comparison of
different base flow separation methods in a lowland catchment. Hydrol. Earth
Syst. Sci. 13, 2055–2068. doi: 10.5194/hess-13-2055-2009
Goodfellow, I., Bengio, Y., and Courville, A. (2016). Deep Learning. Cambridge,
MA: MIT Press.
Hall, F. R. (1968). Base-flow recessions-a review. Water Resour. Res. 4, 973–983.
doi: 10.1029/WR004i005p00973
Hammond, M., and Han, D. (2006). Recession curve estimation for storm event
separations. J. Hydrol. 330, 573–585. doi: 10.1016/j.jhydrol.2006.04.027
Huang, G.-B., Zhu, Q.-Y., and Siew, C.-K. (2004). “Extreme learning machine:
a new learning scheme of feedforward neural networks, in 2004 IEEE
International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541),
Vol. 2, 985–990 (Budapest). doi: 10.1109/IJCNN.2004.1380068
Kelleher, J. D., MacNamee, B., and D’Arcy, A. (2015). Fundamentals of Machine
Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case
Studies. Cambridge, MA; London: MIT Press.
Klaus, J., and McDonnell, J. J. (2013). Hydrograph separation using stable isotopes:
review and evaluation. J. Hydrol. 505, 47–64. doi: 10.1016/j.jhydrol.2013.09.006
Lyne, V., and Hollick, M. (1979). “Stochastic time-variable rainfall-runoff
modelling, in Institute of Engineers Australia National Conference (Barton,
ACT: Institute of Engineers Australia), 89–93.
Maidment, D. R., editor (1993). Handbook of Hydrology. New York, NY: McGraw-
Mei, Y., and Anagnostou, E. N. (2015). A hydrograph separation method based
on information from rainfall and runoff records. J. Hydrol. 523, 636–649.
doi: 10.1016/j.jhydrol.2015.01.083
Merz, R., and Blöschl, G. (2009). A regional analysis of event runoff coefficients
with respect to climate and catchment characteristics in Austria. Water Resour.
Res. 45. doi: 10.1029/2008WR007163
Merz, R., Blöschl, G., and Parajka, J. (2006). Spatio-temporal variability of event
runoff coefficients. J. Hydrol. 331, 591–604. doi: 10.1016/j.jhydrol.2006.06.008
Minns, A. W., and Hall, M. J. (2005). “Artifical neuronal network concepts in
hydrology, in Encyclopedia of Hydrological Sciences, Vol. 1, ed M. G. Anderson
(Chichester: Wiley), 307–319. doi: 10.1002/0470848944.hsa018
Mount, N. J., Maier, H. R., Toth, E., Elshorbagy, A., Solomatine, D., Chang,
F.-J., et al. (2016). Data-driven modelling approaches for socio-hydrology:
opportunities and challenges within the Panta Rhei science plan. Hydrol. Sci.
J. 8, 1–17. doi: 10.1080/02626667.2016.1159683
Mountrakis, G., Im, J., and Ogole, C. (2011). Support vector machines in
remote sensing: a review. ISPRS J. Photogrammetry Remote Sens. 66, 247–259.
doi: 10.1016/j.isprsjprs.2010.11.001
Oppel, H., and Schumann, A. (2020). Machine learning based identification
of dominant controls on runoff dynamics. Hydrol. Process. 34, 1–16.
doi: 10.1002/hyp.13740
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O.,
et al. (2011). Scikit-learn: machine learning in python. J. Mach. Learn. Res. 12,
Scott, D. W. (1979). On optimal and data-based histograms. Biometrika 66,
605–610. doi: 10.1093/biomet/66.3.605
Shannon, C. E. (1948). A mathematical theory of communication. Bell Syst. Tech.
J. 27, 379–423. doi: 10.1002/j.1538-7305.1948.tb01338.x
Sharma, A., and Mehrotra, R. (2014). An information theoretic alternative to
model a natural system using observational information alone. Water Resour.
Res. 50, 650–660. doi: 10.1002/2013WR013845
Shortridge, J. E., Guikema, S. D., and Zaitchik, B. F. (2016). Machine learning
methods for empirical streamflow simulation: a comparison of model accuracy,
interpretability, and uncertainty in seasonal watersheds. Hydrol. Earth Syst. Sci.
20, 2611–2628. doi: 10.5194/hess-20-2611-2016
Solomatine, D. P., and Ostfeld, A. (2008). Data-driven modelling: some
past experiences and new approaches. J. Hydroinform. 10, 3–22.
doi: 10.2166/hydro.2008.015
Frontiers in Water | 13 July 2020 | Volume 2 | Article 18
Oppel and Mewes Automation of Flood Event Separation
Stewart, M. K. (2015). Promising new baseflow separation and recession analysis
methods applied to streamflow at Glendhu catchment, New Zealand. Hydrol.
Earth Syst. Sci. 19, 2587–2603. doi: 10.5194/hess-19-2587-2015
Su, N. (1995). The unit hydrograph model for hydrograph separation. Environ. Int.
21, 509–515. doi: 10.1016/0160-4120(95)00050-U
Tabari, H., Kisi, O., Ezani, A., and Talaee, P. H. (2012). SVM, ANFIS, regression
and climate based models for reference evapotranspiration modeling using
limited climatic data in a semi-arid highland environment. J. Hydrol.
444–445:78–89. doi: 10.1016/j.jhydrol.2012.04.007
Tallaksen, L. (1995). A review of baseflow recession analysis. J. Hydrol. 165,
349–370. doi: 10.1016/0022-1694(94)02540-R
Thiesen, S., Darscheid, P., and Ehret, U. (2019). Identifying rainfall-runoff
events in discharge time series: a data-driven method based on information
theory. Hydrol. Earth Syst. Sci. 23, 1015–1034. doi: 10.5194/hess-23-
Weiler, M., Seibert, J., and Stahl, K. (2017). Magic components-why quantifying
rain, snowmelt, and icemelt in river discharge is not easy. Hydrol. Process. 32,
160–166. doi: 10.1002/hyp.11361
Wittenberg, H., and Aksoy, H. (2010). Groundwater intrusion into leaky sewer
systems. Water Sci. Technol. 62, 92–98. doi: 10.2166/wst.2010.287
Wolpert, D. H., and Macready, W. G. (1997). No free lunch theorems for
optimization. IEEE Trans. Evol. Comput. 1, 67–82. doi: 10.1109/4235.585893
Yu, P.-S., Yang, T.-C., Chen, S.-Y., Kuo, C.-M., and Tseng, H.-W. (2017).
Comparison of random forests and support vector machine for
real-time radar-derived rainfall forecasting. J. Hydrol. 552, 92–104.
doi: 10.1016/j.jhydrol.2017.06.020
Zhang, J., Zhang, Y., Song, J., and Cheng, L. (2017). Evaluating relative merits of
four baseflow separation methods in eastern Australia. J. Hydrol. 549, 252–263.
doi: 10.1016/j.jhydrol.2017.04.004
Conflict of Interest: The authors declare that the research was conducted in the
absence of any commercial or financial relationships that could be construed as a
potential conflict of interest.
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Frontiers in Water | 14 July 2020 | Volume 2 | Article 18
... Tarasova et al., 2018, Diederen et al., 2019, the latter focuses on the flood events only, for example by separating flood events for given flood peaks (e.g. Oppel and Mewes, 2020), which are characterised by a large increase of runoff (see German norm (DIN 4049-1, 1992). Due to the nature of such events, in Central Europe they are expected to occur seldomly within a year. ...
... However, event beginning and end are not provided directly. Instead, often additionally baseflow separation methods are applied, where it is assumed that a deviation of baseflow (the direct runoff) indicates a flood event (Oppel and Mewes, 2020). Though they are originally designed for the separation of runoff events, they are suitable in the context of floods when applied to apriori identified flood events (e.g. ...
... Recently, application of machine-learning techniques offered a new perspective on flood event separation (e.g. Thiesen et al., 2019;Oppel and Mewes, 2020). These techniques use pattern recognition to separate flood events and hence overcome the drawback of POT-based methods, that is the application of constant thresholds and the usage of baseflow separation. ...
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The classification of characteristics of flood events, like peak, volume, duration and baseflow components is essential for many hydrological applications such as multivariate flood statistics, the validation of rainfall-runoff models and comparative hydrology in general. The basis for estimations of these characteristics is formed by flood event separation. It requires an indicator for the time when a flood peak occurs as well as the definition of the beginning and end of a flood event and a subdivision of the total volume into direct and baseflow components. However, the variable nature of runoff and the multiple processes and impacts that determine rainfall-runoff relationships make a separation difficult, especially an automation of it. We propose a new statistics-based flood event separation that was developed to analyse long series of daily discharges automatically to obtain flood events for flood statistics. Moreover, the related flood-inducing precipitation is identified, allowing the estimation of the flood-inducing rainfall and the runoff coefficient. With an additional tool to manually check the separation results easily and quickly, expert knowledge can be included without much effort. The algorithm was applied to seven basins in Germany, covering alpine, mountainous and flatland catchments with different runoff processes. In a sensitivity analysis, the impact of chosen parameters was evaluated. The results show that the algorithm delivers reasonable results for all catchments and only needs manual adjustment for long timeslots with increasing or high baseflow. It reliably separates flood events only instead of all runoff events and the estimated beginning and end of an event was shifted in mean by less than one day compared to manual separation.
... Busico et al. (2018) have used the groundwater major constituents and heavy metals to perform three steps of FA separately for identifying the governing source of groundwater pollution in their study region and the obtained results precisely justified the study. Statistical techniques are widely applied in several studies dealing with the Earth systems, including hydrological events, water management tasks, climate changes, etc. by various researchers/scientists all over the world (Aslam et al. 2018;Flowers 2018;Murray et al. 2018;Rhein 2019;Oppel and Mewes 2020). However, some drawbacks have been reported while performing these statistical approaches, such as flaws in uncertainty analysis, the precision of the results, high computational cost, and the requirement of bulk amount of data (Akpoti et al. 2019;Ardabili et al. 2020). ...
... In this regard, data-driven-based ML models are well applied in water resources studies, including Geographic Information System (GIS) and Remote Sensing (RS) platform viz., hydrological flow series prediction/streamflow simulation (Atiquzzaman and Kandasamy 2018;Tongal and Booij 2018), rainfall-runoff modeling/rainfall forecasting (Yu et al. 2017;Kratzet et al. 2019), interpretation of RS images (Cresson 2018; Li et al. 2019), modeling of evapotranspiration (ET) (Granata 2019;Valipour et al. 2019), flood prediction events (Mosavi et al. 2018;Oppel and Mewes 2020;Schmidt et al. 2020), forecasting of water demand in urban (Antunes et al. 2018;Bata et al. 2020), groundwater level predictions (Yoon et al. 2016), prediction of various chemical/heavy metal concentrations in groundwater (Bhagat et al. 2020;Bui et al. 2020), water quality index prediction (Singha et al. , 2021 and many more. It is no doubt that ML has, thus, gained a lot of attention (Shen 2018), with the majority of research studies implementing ML models for prediction purposes. ...
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The present study is aimed to assess the spatial variation of groundwater quality based on the influencing hydrogeological parameters in the surrounding mining areas of India’s one of the largest coal fields, the Korba coal field, Chhattisgarh, Central India. To achieve this goal, a knowledge-driven approach with the aid of a Machine Learning (ML) decision tree-based model, i.e., Classification and Regression Tree (CART) model, was developed to predict possible factors contributing to the degradation of groundwater quality in the selected regions. A total of five influencing factors were selected viz., water table depth (WTD), groundwater drawdown (DR), slope (S), elevation (E), and distance to mines (DTM), which were considered as the important input variables. Groundwater Quality Index (GWQI) values of 216 locations within a buffer zone of 20 km centered from the coal mining area were assigned as the target variables in the CART model. The influences of these factors on groundwater quality were assessed using a recursive partitioning combined with a pruned algorithm. Results showed that the significant factors followed decreasing trend of S (34%) > DTM (23%) > WTD (16%) > DR (15%) > E (12%). The model predicted relatively higher GWQI values attributed to the available lower ground slope in the study area. Similarly, wells situated within a 3 km radius of the buffer zone had low groundwater quality apparently due to the influence of mines. Higher GWQI values were observed in the wells having low WTD value (˂7.9 m) and higher DR in the study area. The results suggested that the anthropogenic activity is one of the major sources of groundwater contamination, whereas the impact of mines was only observed within a radius of 3 km from the center of the mining areas.
... Machine learning has been widely applied in hydraulic and hydrological modeling. In this regard, it has been used to predict daily stream flow (Rasouli et al., 2012), detecting land use and land cover changes (LULC) (Nourani et al., 2018), rainfall-runoff modeling (Daliakopoulos and Tsanis, 2016), operation of the water reservoir (Bozorg-Haddad et al., 2018), groundwater of hydrological cycle (Sahu et al., 2020), and flood events (Oppel and Mewes, 2020). ...
The performance and behavior of many machine learning algorithms are stochastic because they explicitly use randomness in their procedures. Stochastic refers to a process where the outcome involves some randomness and has some uncertainty. The stochastic nature of machine learning algorithms is an essential foundational concept in machine learning and must be understood to effectively interpret the behavior of predictive models. These algorithms are practical for training and optimizing large systems with rich structures. Such algorithms have been deployed with considerable success in large-scale hydrological models. This contribution presents an overview of theoretical and practical aspects of the broad stochastic learning algorithms that can be categorized as stochastic Gradient Boosting and stochastic Gradient Descent and describe their common properties. These include well-known algorithms such as K-Means, Perceptron, Adaline, LVQ, and Multi-Layer Networks.
... In hydrological sciences, machine learning has been used in applications such as precipitation analysis (Sun and Tang, 2020), rainfall-runoff processes (Hsu et al., 1995;Minns and Hall, 1996;Dawson and Wilby, 1998;Abrahart and See, 2000;Duan et al., 2020;Oppel and Mewes, 2020), groundwater hydrology (Karandish and Šimnek, 2016;Sahu et al., 2020), reservoir hydrology (Bai et al., 2016;Mital et al., 2020), hydraulic networks (Dibike et al., 1999), river basin management (Solomatine and Ostfeld, 2008), flow mapping (Zhu and Guo, 2014), land use analysis (Loukika et al., 2021), and disaster risk management (Whitehurst et al., 2021). Explainable artificial intelligence (XAI) is a subdomain of machine learning that aid in the interpretability of machine learning models by helping users understand how their 'black-box' models operate (Maksymiuk et al., 2020;Althoff et al., 2021). ...
The Prediction in Ungauged Basins (PUB) initiative set out to improve the understanding of hydrological processes with an aim of improving hydrologic models for application in ungauged basins. With a majority of basins around the world essentially ungauged, this suggests the need to shift from calibration-based models that rely on observed streamflow data to models based on process understanding. This is especially important in natural infrastructure planning projects such as investments in the conservation of wetlands across the watershed, where the lack of streamflow data hinders the quantification of their benefits (such as flood attenuation), resulting in a difficulty in prioritization. This research sought to contribute to this growing body of literature by (a) developing visual tools and metrics for assessing flow dynamics and flood attenuation benefits of wetlands in relation to their position in the watershed, (b) examining distribution-based topographic metrics in regard to their efficacy in predicting hydrologic response and providing a methodology for examining other metrics in future studies, (c) building robust functional forms for two important catchment metrics: the width function and hypsometric curve, and (d) devising a hierarchical clustering approach to assess hydrological similarity and find analogous basins that is computationally efficient and has a potential for large-scale applications. Taken together, this study paves the way toward an analytical formulation of the geomorphological instantaneous unit hydrograph (GIUH) that can be used to assess the hydrological behavior in ungauged or data-scarce basins.
... On top of this, a peak-over-threshold criteria can be applied to consider only larger events (Norbiato et al., 2009;Tang & Carey, 2017). Recently, different studies have developed methodologies to avoid the baseflow separation (Fischer et al., 2021;Oppel & Mewes, 2020;Thiesen et al., 2019;Towler & McCreight, 2021). However, these methodologies still require the calibration of parameters or to manually train machine learning algorithms. ...
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Methodologies for rainfall‐runoff event identification from continuous time series suffer from significant subjectivity. In particular, whether they initiate the identification from rainfall or from the streamflow timeseries, they usually require baseflow separation and they need substantial modifications and parameters’ recalibration when changing temporal resolution of the data. Therefore, here we propose a novel objective methodology for event identification that is easily transferable across sites and temporal resolutions, without having to make subjective choices and adjust multiple parameters. The proposed method to identify rainfall‐runoff events is based on a time series analysis technique that simultaneously considers rainfall and streamflow time series and does not make any a priori assumptions about baseflow separation. The novel method allows also to produce a baseflow separation a posteriori by connecting the delimiters of identified streamflow events. Moreover, the proposed method can be applied at any time resolution as long as the resolution is high enough to capture the time delay between precipitation and runoff response. When comparing the results between the proposed and the traditional baseflow‐based event identification approach, we observe a good agreement in terms of event properties both at hourly and daily scale (correlation of runoff ratios between the two methods equal to 0.78 [daily data] and 0.84 [hourly data]). The analysis comparing hourly and daily event identifications with the proposed method reveals also that the novel method produces coherent events across different temporal resolutions (correlation of runoff ratios between daily and hourly data equal to 0.71).
The estimation of catchment response time (Tr) plays an important role in several hydrological and civil engineering design problems. The non-linear relationship between Tr and rainfall intensity necessitates the estimation of an event-based set of Tr values instead of a characteristic constant value. However, there is no generally accepted method to define individual rainfall-runoff events from time-series. Here we propose a new, automated method which results in the selection of rainfall-runoff events and the corresponding Tr values. The proposed method yields an event-based set of Tr values more efficiently than other existing methods and has only two parameters. The results of the new method were compared to those of a statistical and a semi-manual event selection approach. The latter calculates eight different Tr values, including the time of concentration, lag time, time to peak, and time to equilibrium. The median Tr value of the proposed method yields the strongest agreement with the median of the time elapsed between the maxima of the total rainfall and runoff with a root-mean-square error of 4.94 hours. It is also demonstrated that a median time of concentration value can be estimated as the maximum of the event based Tr values by the current method. A sensitivity analysis explores the robustness of the proposed method, and also yields the optima of its two parameters. Once calibrated, the present automated methodology dispenses with any event selection procedure.
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Understanding hydrological variability is of crucial importance for water resource management in sub-Saharan Africa (SSA). While existing studies typically focus on individual river basins, and suffer from incomplete records, this study provides a new perspective of trends and variability in hydrological flood and drought characteristics (frequency, duration, and intensity) across the entire SSA. This is achieved by: i) creating a 65-year long, complete daily streamflow dataset consisting of over 600 gauging stations; ii) quantifying changes in flood and drought characteristics between 1950 and 2014; iii) evaluating how decadal variability influences historical trends. Results of daily streamflow reconstructions using random forests provide satisfactory performance over most of SSA, except for parts of southern Africa. Using change-point and trend analyses, we identify three periods that characterise historical variations affecting hydrological extremes in western and central Africa, and some parts of southern Africa: i) the 1950s–60s and after the 1980s–90s, when floods (droughts) tend to be more (less) intense, more (less) frequent and more (less) persistent; and ii) the 1970s–80s, when floods (droughts) are less (more) intense, less (more) frequent and less (more) persistent. Finally, we reveal significant decadal variations in all flood and drought characteristics, which explain aperiodic increasing and decreasing trends. This stresses the importance of considering multiple time-periods when analysing recent trends, as previous assessments may have been unrepresentative of long-term changes.
The prediction of hydrologic conditions in watersheds has manifold applications, ranging from flood disaster preparedness to water supply and environmental flow management. In watersheds with scarce or no flow data, it is difficult to make accurate hydrologic predictions. Past work has used similarity in single-valued properties of the terrain (for example, drainage area, mean slope) as the basis to relate flow conditions in gauged watersheds to the ungauged ones. The resulting predictions show modest accuracy and have a weak physical basis. In this study, we develop a physics-informed machine learning approach to extract features that represent the hydrologic dynamics–width function and hypsometric curve. These two geomorphometric measures are computed using functional forms fitted to estimates derived from digital elevation data. Furthermore, dynamically-similar groups are identified based on results from unsupervised clustering and divergence measures. Our approach paves the way towards a flexible and scalable machine learning approach that can be used to assess hydrologic similarity and improve prediction, one informed by physics of surface flow generation and transport in watersheds. A case study involving 72 sub-watersheds in the Narmada River Basin (India) is used to illustrate the new methodology.
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Statistical learning methods offer a promising approach for low-flow regionalization. We examine seven statistical learning models (Lasso, linear, and nonlinear-model-based boosting, sparse partial least squares, principal component regression, random forest, and support vector regression) for the prediction of winter and summer low flow based on a hydrologically diverse dataset of 260 catchments in Austria. In order to produce sparse models, we adapt the recursive feature elimination for variable preselection and propose using three different variable ranking methods (conditional forest, Lasso, and linear model-based boosting) for each of the prediction models. Results are evaluated for the low-flow characteristic Q95 (Pr(Q>Q95)=0.95) standardized by catchment area using a repeated nested cross-validation scheme. We found a generally high prediction accuracy for winter (RCV2 of 0.66 to 0.7) and summer (RCV2 of 0.83 to 0.86). The models perform similarly to or slightly better than a top-kriging model that constitutes the current benchmark for the study area. The best-performing models are support vector regression (winter) and nonlinear model-based boosting (summer), but linear models exhibit similar prediction accuracy. The use of variable preselection can significantly reduce the complexity of all the models with only a small loss of performance. The so-obtained learning models are more parsimonious and thus easier to interpret and more robust when predicting at ungauged sites. A direct comparison of linear and nonlinear models reveals that nonlinear processes can be sufficiently captured by linear learning models, so there is no need to use more complex models or to add nonlinear effects. When performing low-flow regionalization in a seasonal climate, the temporal stratification into summer and winter low flows was shown to increase the predictive performance of all learning models, offering an alternative to catchment grouping that is recommended otherwise.
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Hydrological models used for flood prediction in ungauged catchments are commonly fitted to regionally transferred data. The key issue of this procedure is to identify hydrologically similar catchments. Therefore, the dominant controls for the process of interest have to be known. In this study, we applied a new machine learning based approach to identify the catchment characteristics that can be used to identify the active processes controlling runoff dynamics. A random forest (RF) regressor has been trained to estimate the drainage velocity parameters of a geomorphologic instantaneous unit hydrograph (GIUH) in ungauged catchments, based on regionally available data. We analyzed the learning procedure of the algorithm and identified preferred donor catchments for each ungauged catchment. Based on the obtained machine learning results from catchment grouping, a classification scheme for drainage network characteristics has been derived. This classification scheme has been applied in a flood forecasting case study. The results demonstrate that the RF could be trained properly with the selected donor catchments to successfully estimate the required GIUH parameters. Moreover, our results showed that drainage network characteristics can be used to identify the influence of geomorphological dispersion on the dynamics of catchment response. This article is protected by copyright. All rights reserved.
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Hydrological signatures are now used for a wide range of purposes, including catchment classification, process exploration and hydrological model calibration. The recent boost in the popularity and number of signatures has however not been accompanied by the development of clear guidance on signature selection, meaning that signature selection is often arbitrary. Here we use three complementary approaches to compare and rank 15 commonly-used signatures, which we evaluate in 671 US catchments from the CAMELS data set (Catchment Attributes and MEteorology for Large-sample Studies). Firstly, we employ machine learning (random forests) to explore how attributes characterizing the climatic conditions, topography, land cover, soil and geology influence (or not) the signatures. Secondly, we use a conceptual hydrological model (Sacramento) to critically assess which signatures are well captured by the simulations. Thirdly, we take advantage of the large sample of CAMELS catchments to characterize the spatial smoothness (using Moran's I) of the signature field. These three approaches lead to remarkably similar rankings of the signatures. We show that signatures with the noisiest spatial pattern tend to be poorly captured by hydrological simulations, that their relationship to catchments attributes are elusive (in particular they are not correlated to climatic indices like aridity) and that they are particularly sensitive to discharge uncertainties. We question the utility and reliability of those signatures in experimental and modeling hydrological studies, and we underscore the general importance of accounting for uncertainties in hydrological signatures.
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In this study, we propose a data-driven approach for automatically identifying rainfall-runoff events in discharge time series. The core of the concept is to construct and apply discrete multivariate probability distributions to obtain probabilistic predictions of each time step that is part of an event. The approach permits any data to serve as predictors, and it is non-parametric in the sense that it can handle any kind of relation between the predictor(s) and the target. Each choice of a particular predictor data set is equivalent to formulating a model hypothesis. Among competing models, the best is found by comparing their predictive power in a training data set with user-classified events. For evaluation, we use measures from information theory such as Shannon entropy and conditional entropy to select the best predictors and models and, additionally, measure the risk of overfitting via cross entropy and Kullback–Leibler divergence. As all these measures are expressed in “bit”, we can combine them to identify models with the best tradeoff between predictive power and robustness given the available data. We applied the method to data from the Dornbirner Ach catchment in Austria, distinguishing three different model types: models relying on discharge data, models using both discharge and precipitation data, and recursive models, i.e., models using their own predictions of a previous time step as an additional predictor. In the case study, the additional use of precipitation reduced predictive uncertainty only by a small amount, likely because the information provided by precipitation is already contained in the discharge data. More generally, we found that the robustness of a model quickly dropped with the increase in the number of predictors used (an effect well known as the curse of dimensionality) such that, in the end, the best model was a recursive one applying four predictors (three standard and one recursive): discharge from two distinct time steps, the relative magnitude of discharge compared with all discharge values in a surrounding 65 h time window and event predictions from the previous time step. Applying the model reduced the uncertainty in event classification by 77.8 %, decreasing conditional entropy from 0.516 to 0.114 bits. To assess the quality of the proposed method, its results were binarized and validated through a holdout method and then compared to a physically based approach. The comparison showed similar behavior of both models (both with accuracy near 90 %), and the cross-validation reinforced the quality of the proposed model. Given enough data to build data-driven models, their potential lies in the way they learn and exploit relations between data unconstrained by functional or parametric assumptions and choices. And, beyond that, the use of these models to reproduce a hydrologist's way of identifying rainfall-runoff events is just one of many potential applications.
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Flood events can be caused by several different meteorological circumstances. For example, heavy rain events often lead to short flood events with high peaks, whereas snowmelt normally results in events of very long duration with a high volume. Both event types have to be considered in the design of flood protection systems. Unfortunately, all these different event types are often included in annual maximum series (AMS) leading to inhomogeneous samples. Moreover, certain event types are underrepresented in the AMS. This is especially unsatisfactory if the most extreme events result from such an event type. Therefore, monthly maximum data are used to enlarge the information spectrum on the different event types. Of course, not all events can be included in the flood statistics because not every monthly maximum can be declared as a flood. To take this into account, a mixture Peak-over-threshold model is applied, with thresholds specifying flood events of several types that occur in a season of the year. This model is then extended to cover the seasonal type of the data. The applicability is shown in a German case study, where the impact of the single event types in different parts of a year is evaluated.
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A comprehensive data driven modeling experiment is presented in a two-part paper. In this first part, an extensive data-driven modeling experiment is proposed. The most important concerns regarding the way data driven modeling (DDM) techniques and data were handled, compared, and evaluated, and the basis on which findings and conclusions were drawn are discussed. A concise review of key articles that presented comparisons among various DDM techniques is presented. Six DDM techniques, namely, neural networks, genetic programming, evolutionary polynomial regression, support vector machines, M5 model trees, and K-nearest neighbors are proposed and explained. Multiple linear regression and naïve models are also suggested as baseline for comparison with the various techniques. Five datasets from Canada and Europe representing evapotranspiration, upper and lower layer soil moisture content, and rainfall-runoff process are described and proposed, in the second paper, for the modeling experiment. Twelve different realizations (groups) from each dataset are created by a procedure involving random sampling. Each group contains three subsets; training, cross-validation, and testing. Each modeling technique is proposed to be applied to each of the 12 groups of each dataset. This way, both prediction accuracy and uncertainty of the modeling techniques can be evaluated. The description of the datasets, the implementation of the modeling techniques, results and analysis, and the findings of the modeling experiment are deferred to the second part of this paper.
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In the past decade, machine learning methods for empirical rainfall–runoff modeling have seen extensive development and been proposed as a useful complement to physical hydrologic models, particularly in basins where data to support process-based models are limited. However, the majority of research has focused on a small number of methods, such as artificial neural networks, despite the development of multiple other approaches for non-parametric regression in recent years. Furthermore, this work has often evaluated model performance based on predictive accuracy alone, while not considering broader objectives, such as model interpretability and uncertainty, that are important if such methods are to be used for planning and management decisions. In this paper, we use multiple regression and machine learning approaches (including generalized additive models, multivariate adaptive regression splines, artificial neural networks, random forests, and M5 cubist models) to simulate monthly streamflow in five highly seasonal rivers in the highlands of Ethiopia and compare their performance in terms of predictive accuracy, error structure and bias, model interpretability, and uncertainty when faced with extreme climate conditions. While the relative predictive performance of models differed across basins, data-driven approaches were able to achieve reduced errors when compared to physical models developed for the region. Methods such as random forests and generalized additive models may have advantages in terms of visualization and interpretation of model structure, which can be useful in providing insights into physical watershed function. However, the uncertainty associated with model predictions under extreme climate conditions should be carefully evaluated, since certain models (especially generalized additive models and multivariate adaptive regression splines) become highly variable when faced with high temperatures.
Madjez Ressoul catchment constitutes an important source of fresh water and arable land in northeastern Algeria. In order to achieve better management of the catchments’ natural resources, specifically water, an advanced flood recession analysis was conducted, using the recession analysis-based trigonometric approach, which was based completely on a mathematical solution. This approach provides very useful results for the master recession curves construction. The advantage of this method in the hydrograph separation is both its non-subjectivity related to the user, and then its viability for initial use in the hydrograph separation field. Results in this real case give a better indication of groundwater flow during different drought periods, using many assessed parameters of initial discharge and relative recession time. A particular review of existing hydrograph separation techniques is used to situate the recession analysis and show its case of application relative to other techniques.
Quantifying the components of rain, snowmelt, and glacier ice melt in river discharge is an important but difficult task in hydrology. Although it forms the basis of many climate impact assessments, many published modelling results do not clearly describe how they derived the discharge components. Consequently, reported components such as absolute amounts or relative percentages of snow and ice melt from different studies are rarely comparable. This commentary revisits the differences in the terminology used, the modelling approaches, and the possible conclusions for effects at different time scales. We argue that for questions related to changes in discharge, not particle tracking, for which methodology is widely available, but instead, an “effect tracking” of the input contributions is important, that is, the representation of the signals of rainfall, snowmelt, and glacier ice melt in the discharge at the catchment outlet. We introduce and briefly describe a method for effect tracking and discuss the differences and advantages compared to other methods. This comparison supports our call to the modelling community for more precise descriptions of how the generated input contributions into a catchment from rainfall, snowmelt, and glacier ice melt are tracked through the catchments' multiple stores to finally compose the presented hydrographs.
This study aims to compare two machine learning techniques, random forests (RF) and support vector machine (SVM), for real-time radar-derived rainfall forecasting. The real-time radar-derived rainfall forecasting models use the present grid-based radar-derived rainfall as the output variable and use antecedent grid-based radar-derived rainfall, grid position (longitude and latitude) and elevation as the input variables to forecast 1- to 3-hours ahead rainfalls for all grids in a catchment. Grid-based radar-derived rainfalls of six typhoon events during 2012–2015 in three reservoir catchments of Taiwan are collected for model training and verifying. Two kinds of forecasting models are constructed and compared, which are single-mode forecasting model (SMFM) and multiple-mode forecasting model (MMFM) based on RF and SVM. The SMFM uses the same model for 1- to 3-hours ahead rainfall forecasting; the MMFM uses three different models for 1- to 3-hours ahead forecasting. According to forecasting performances, it reveals that the SMFMs give better performances than MMFMs and both SVM-based and RF-based SMFMs show satisfactory performances for 1-hour ahead forecasting. However, for 2- and 3-hours ahead forecasting, it is found that the RF-based SMFM underestimates the observed radar-derived rainfalls in most cases and the SVM-based SMFM can give better performances than RF-based SMFM.
Baseflow is the portion of streamflow that comes from shallow and deep subsurface flow, and is the key for catchment ecology and water resource management. This paper comprehensively evaluates four widely used non-tracer baseflow separation methods against tracer-based hydrograph separation for five Eastern Australian catchments. The four methods include United Kingdom Institute of Hydrology (UKIH) method and three digital filtering methods: Lyne–Hollick method, Chapman–Maxwell method and Eckhardt method. The first two filtering methods include a parameter of recession constant, and the last one has two parameters: the recession constant and the maximum baseflow index. We used an Automatic Baseflow Identification Technique (ABIT) to estimate the recession constant, which varies from 0.943 to 0.987 for the five catchments that is evidently higher than the default value of 0.925, and used the default Eckhardt and UKIH methods to estimate the maximum baseflow index, respectively. All modelling results are evaluated against the tracer-based hydrograph separation. Using the recession constant estimated from the ABIT method performs noticeably better than using the default parameter, indicated by the absolute bias reduced about 20% in average. For the two-parameter Eckhardt method, estimating the maximum baseflow index has larger effect on baseflow separation than estimating the recession constant. Compared to the different parameterisation schemes, the difference among the improved non-tracer methods is small. Using multiple passes into the Lyne–Hollick method can only slightly improve or deteriorate baseflow index estimates. Our results suggest that it is critical to get appropriate parameter(s) before applying the digital filtering methods.