The severity of floods is shaped not only by event- and catchment-specific characteristics but also depends on the river network
configuration. At the confluence of relevant tributaries with the main
river, flood event characteristics may change depending on the magnitude
and temporal match of flood waves. This superposition of flood
waves may potentially increase the flood severity downstream in the main
river. However, this aspect has not been analysed for a large set
of river confluences to date.
To fill this gap, the role of flood wave superposition in the flood
severity at downstream gauges is investigated in four large
river basins in Germany and Austria (the Elbe, the Danube, the Rhine and
the Weser). A novel methodological approach to analyse flood wave
superposition is presented and applied to mean daily discharge data from
37 triple points. A triple point consists of three gauges: one in the
tributary as well as one upstream and downstream of the confluence with the
main river respectively. At the triple points, differences and similarities in
flood wave characteristics between the main river and the tributary are
analysed in terms of the temporal match and the magnitudes of flood peaks.
At many of the confluences analysed, the tributary peaks consistently arrive
earlier than the main river peaks, although high variability in the
time lag is generally detected. No large differences in temporal matching are
detected for floods of different magnitudes. In the majority of
cases, the largest floods at the downstream gauge do not occur due to
perfect temporal match between the tributary and the main river. In terms of
spatial variability, the impact of flood wave superposition is
site-specific. Characteristic patterns of flood wave superposition are
detected for flood peaks in the Danube River, where peak discharges
largely increase due to inflow from alpine tributaries. Overall, we
conclude that the superposition of flood waves is not the driving
factor behind flood peak severity at the major confluences in Germany; however,
a few confluences show the potential for strong flood magnifications if a temporal shift in flood waves was to occur.
Introduction
Floods result from an interplay of several factors along a cascade
of processes beginning with precipitation and runoff generation in
a catchment down to river routing. Event-specific characteristics such
as the intensity and spatial patterns of precipitation exert an impact on
river discharge. The impact of a precipitation event on the timing and
magnitude of a flood is further modulated by the prevailing soil
moisture conditions in the catchment that control the timing and amount of
runoff generation . Moreover, flood patterns
are characteristic for each catchment due to the specific
physiogeographic conditions, i.e. the elevation and slope or geological
formation, that result in site-specific runoff generation
processes. In particular, floods are impacted by the river network
configuration and the related geomorphological catchment
characteristics. Several studies have indicated the impact of drainage
density (or hillslope lengths), which is related to the network
configuration, on the runoff coefficients
(e.g. ). Travel times of water to the
catchment outlet or confluence are also influenced by the
distributions of hillslope-channel lengths
. Hence, the river network configuration can lead
to a higher/lower probability of flood wave superposition
, and the impact from different tributaries to the main
river can be highly variable. Each tributary has specific catchment
characteristics and typical flood characteristics. Thus, the shape of the
flood wave can significantly change at each relevant confluence
.
According to the definition in this study, flood wave superposition is
based on both (i) a temporal match of flood peaks and (ii) a high
peak magnitude in both the main river and the
tributary. A superposition of flood waves at confluences may increase
the flood magnitude and lead to an acceleration of the flood wave
. Conversely, low or medium
discharge conditions in a tributary may prevent further aggravation of
the flood event . In a study of the
2013 flood in the Danube Basin, noted the
synchronous occurrence of flood waves at the confluence of the Salzach and
the Inn rivers in Austria. They emphasised that the Inn River flood
wave typically occurs earlier than the flood wave of the Danube at the confluence of
the Inn and the Danube rivers at the German–Austrian border. An
earlier or later flood occurrence in the tributary relative to the
main river leads to a weaker flood wave superposition due to
a temporal peak mismatch . In a simulation study,
analysed how a temporal shift
of a flood event of two tributaries to the Danube of 20 h affects the flood
peak in the main river. In one case, they showed that temporal peak
matching would increase the flood peak in the main river downstream of
the confluence by up to twice the observed value.
Although flood wave superposition could potentially impact flood
magnitudes, only a few studies have addressed this topic to date
. suggested the
possibility of decoupling the tributary and main channel waves,
i.e. enforcing a temporal shift through enhanced storage and
attenuation, as a measure for flood risk
reduction. At the lowland
confluence in the Meuse catchment, concluded that the time lag between peaks is of
minor importance due to the long duration of flood waves compared
with the typical variability of the time lags. They stated that the typical time lags are less relevant for the
impact of flood wave superposition for
long flood durations. In contrast, the time lag may be
of high importance in smaller and fast reacting catchments with
shorter flood durations. Hence, it is important to understand whether
patterns of flood wave superposition are typical for a confluence or
whether they are event-specific and change between small and large
floods.
To quantify flood wave superposition, we select triple points. These
are three gauging stations that are located close to the confluence:
one on the tributary and two on the main river, upstream and downstream
of the confluence. At these triple points, two flood event
characteristics are considered simultaneously. First, the timing of
the flood wave peak describes whether the tributary flood peak reaches
the confluence at the same time as the main flood wave or if there is
a temporal shift. Second, the flood magnitudes at all three gauges are
used for the assessment of similarities or differences in flood
intensity. Therefore, a perfect overlay of flood waves means that a high
tributary wave peak matches (in time) a high main channel peak at the
confluence.
The aim of this study is to investigate the role of flood wave
superposition in flood severity downstream of relevant confluences in
the main rivers in Germany, including Austrian tributaries. It provides
a first analysis of the flood wave superposition problem for a large
set of river confluences. We develop and test a method to jointly
analyse temporal matching and (dis)similarities in flood peak
magnitudes between the tributary and main river (at upstream and
downstream sites). We address the following research questions:
Is the temporal match of flood waves a key factor in the occurrence of large floods?
To what extent does the peak discharge in the tributary contribute to the severity of the main river flood via wave superposition?
Is the impact of flood wave superposition higher for large floods than for small floods?
Study area and dataStudy area
Map of Germany showing the catchment elevation, major basins, rivers and gauges.
In this study, triple points from four large river basins in
Germany and Austria (the Elbe, the Rhine, the Danube and the Weser) are analysed; the selected gauges, the
main rivers and a digital elevation model
that is presented in a resampled version as
described in are shown in Fig. . The Elbe River originates in the
Czech Republic and flows through eastern Germany into the North
Sea. The middle Elbe is mainly influenced by two tributaries from the
Ore Mountains (the Mulde and the Saale, which are both left-bank tributaries). The lower Elbe flows
through the North German Plains with its major tributary the Havel
(right-bank tributary). The Rhine River originates in Switzerland and flows
northwards to the North Sea. In Switzerland, the Rhine Basin is
characterised by alpine topography and the nival flow regime. Our
analysis is mainly focused on the Upper Rhine and Middle Rhine. The largest
tributaries are the Neckar at the Upper Rhine and the Main (both from the
east; right-bank tributaries) and the Mosel (from the west; left-bank tributary) that are both at the
Middle Rhine. The Danube River drains the catchments in southern
Germany and is fed by quick-reacting steep tributaries from the German
and Austrian Alps. There are several large tributaries feeding into to the Danube
within Germany such as the Naab and the Regen from the north (left-bank tributaries) and the
Iller, Lech, Isar and Inn from the south (right-bank tributaries). The northern and
southern tributaries have different climatological and hydrological
regimes and exhibit different flow dynamics relative to the main
stream. The Weser is the only large river basin that is completely
located in Germany and originates in the Central German Uplands at the
confluence of the Werra and Fulda. It flows through the North German
Plains into the North Sea.
Triple points of the four major river basins ordered by the catchment size of the downstream gauge. The percentages in parentheses denote the share of the tributary and of the main river upstream gauge in relation to the catchment size of the downstream gauge. The last column shows the number of years for each of the triple points.
Floods in Germany are controlled by two major gradients
: (1) the elevation increases from the
lowlands in the north via the Central German Uplands up to the Alps in
the south; and (2) the climate regime changes from maritime in the western and coastal areas to more continental in the eastern parts of Germany. As
a consequence, the Weser and the Middle Rhine are characterised by winter
floods evoked by long precipitation events. Winter floods are also
dominant in the Elbe Basin and on the left side of the Danube, but
seasonal variability is higher in these regions. In the south of Germany, i.e. in
catchments on the right side of the Danube, floods mostly
occur in summer due to high precipitation and/or the snowmelt from
the Alps.
Discharge data set
The data set consists of 37 triple points (Fig. ),
for which mean daily discharge data with a time series length of more
than 30 years are available. We do not consider small catchments (area
<500km2) for which hourly discharge data would be
required due to very short catchment response times.
Table shows all of the triple points clustered by the major basins. They are manually assembled based on two criteria.
For each triple point, the catchment size of the upstream and tributary gauge is shown on a log scale. The tributary name is coloured according to the major river basins.
Firstly, the size of the tributary catchment is larger than
2 % of the downstream catchment.
The 2 % threshold was empirically estimated by investigating which tributary catchment size influences the main river peak discharge. Tributaries that are too small have no relevant impact, as the contributing flood volume is too small compared with the flood volume in the main river.
Secondly, the sum of the catchment size of the tributary (Ctrib)
and upstream gauge (Cup) is at least 70 % of the
downstream gauge (Cdown). Thus, there is a short distance
between the three gauges of a triple point to minimise the effect of
travel time lags. This criterion is needed to avoid overly large lateral
inflows to the river between the two upstream gauges and the
downstream gauge. In such cases, this inflow may dominate the
downstream behaviour, strongly reducing the value of the information
from the two upstream branches for the analysis. Due to the daily
resolution of the discharge data, a tributary peak occurring around
midnight may be recorded in the previous/next day compared with the main
stream peak. In this case, some peaks can be recorded on 2 different
days if they occur around midnight. Thus, time lags of ±1 d may
also be seen as strong superposition. At this point, we neglect the
flood wave travel time from the gauges to the confluence, or we assume it
to be within the same day for the tributary and the upstream gauge.
We have carried out an analysis on discharge data alone without using
information on overbank flow, as a detailed consideration of flood
inundation and backwater effects was not possible for this large set
of stations and events.
CRup=CupCdown
is the ratio of the upstream gauge catchment size to the downstream gauge catchment size.
CRtrib=CtribCdown
is the ratio of the tributary catchment size to the downstream gauge catchment size.
The catchment size of the downstream gauges ranges from
3803 to 139 549 km2. The ratio of the tributary
catchment size to the downstream catchment sizes (CRtrib)
varies between 4 % and 55 %. For the upstream gauges, this
ratio (CRup) ranges from 33 % to 95 %. Thus, the
relevance of the tributary and upstream gauges varies considerably between
the triple points.
Figure shows the catchment size of the upstream and tributary gauges to demonstrate the variability in the contribution of both gauges. Points along the diagonal line show a similar catchment size ratio. Among the major tributaries to the Elbe, the Mulde has much smaller catchment size compared with the Saale and the Havel. The catchment ratio of the three Rhine tributaries (the Neckar, Main and Mosel) is relatively similar. Along the Danube, the catchment ratios mostly increase downstream. The Weser confluences (the Aller, Leine and Werra) are characterised by the highest similarities in catchment sizes between the upstream and tributary gauges. Within a triple point, the upstream gauge is always the gauge on the same river, whereas the tributary gauge is on a different river branch even when the catchment size and/or mean discharge is larger in the tributary. This explains why the tributary catchment is larger than the catchment associated with the upstream gauge in a few cases.
Methods
We present four types of flood wave superposition in relation to
matches and mismatches in time and in flood magnitude using stylised
figures (Fig. ).
A perfect overlay (matching in time and with respect to peak magnitude): peaks Qp occur at all three gauges at the same time with the same relative intensity, i.e. the same specific discharge.
Temporal mismatch: there is a time lag Δtp between the flood peaks of main river and tributary gauges, while the specific discharge is the same.
Peak magnitude mismatch: there is a strong difference in specific discharge. For example, high specific discharge in the upstream gauge is compensated for by a low specific discharge in the tributary which prevents an increase in downstream flood severity.
Temporal and peak magnitude mismatch: both the peak magnitude and peak timing vary between the three gauges. Although there are no clear boundaries between these conceptual types of wave superposition, this typology is helpful to classify and describe the superposition.
Specific terminology is used to distinguish between the impact of
timing and magnitude. Flood synchronicity is defined as a temporal
match of flood peaks (types I and III). Flood amplification means that
the downstream flood magnitude increases due to the peak overlay of
upstream and tributary waves (types I, II and IV). The compensation effect
refers to the fact that a high flood magnitude in the upstream gauge is compensated for
by a low flood magnitude in the tributary or vice versa. Both cases
are characterised by a mismatch in peak magnitudes (type III).
Comparison of the four types of flood wave superposition shown for four combinations of matches and mismatches in peak magnitude and peak timing.
Our objective regarding analysing a large set of flood events is to detect
whether one of these cases dominates at a particular triple point and
how it impacts flood severity at the downstream
location. Moreover, we are interested in determining whether spatially
coherent patterns of flood wave superposition types occur in
Germany. In particular, we investigate if and where case I
(perfect overlay of all three waves) occurs and how it impacts flood
severity.
Derivation of flood peaks
For the selected 37 triple points, we consider the annual maximum flood
series (AMS) at the downstream gauge and the corresponding tributary
flood waves in the analysis. To derive flood event hydrographs, the
methodology from is modified. First, the AMS peak
at the downstream gauge is selected. Each event is characterised by
a peak value, a start and an end point. The event start point is
located between the annual maximum peak and the previous independent
peak. An independent peak is identified if it fulfils the criteria
following and : (1) the lowest
discharge between two peaks is smaller than 70 % of the
smaller peak; (2) the smaller peak is greater than 20 % of
the annual maximum peak; (3) the minimum flow between two peaks drops
below 20 % of the annual maximum flow; and (4) the time lag
between two peaks is at least 7 d. These criteria were
empirically derived by and to
prevent the identification of oscillatory peaks as independent flood
events.
To estimate the start and end point, the gradient in
discharge between 2 consecutive days is first calculated. The start point
of the flood event is then identified by tracing back the gradient
prior to the peak flow. If the gradient is lower than a predefined
threshold for 7 consecutive days, the starting date is set to the
latest date in this time window. We have empirically identified the
90th percentile of all gradients for the selected gauge as the threshold
using a trial-and-error procedure and visual inspection. If no
starting point is detected within 40 d prior to the peak flow,
the lowest discharge value in this time window is selected. The event
end point is analogously determined by looking forward from the
peak. The corresponding flood peaks of the upstream and tributary
gauge are defined as the largest discharge values within the event
period of the downstream gauge (from the start to end point).
A flood peak is characterised by two indicators: the time of peak occurrence tp and the peak discharge Qp, which are calculated for all selected events at the three gauges of each triple point. To assess flood wave superposition, the time lags Δtp, Δtp, up and Δtp, trib between the peak flows at the triple points are calculated using the following:
tp, down, which is the time of the peak of the downstream gauge;
tp, up, which is the time of the peak of the upstream gauge;
tp, trib, which is the time of the peak of the tributary gauge;
Qp, down, which is the peak discharge of the downstream gauge;
Qp, up, which is the peak discharge of the upstream gauge;
Qp, trib, which is the peak discharge of the tributary gauge.
Therefore,
Δtp=tp, up-tp, trib,
which gives the time
differences in the peak between the upstream and tributary gauge;
Δtp, up=tp, down-tp, up,
which gives the time differences in the peak between the downstream and upstream gauge; and
Δtp, trib=tp, down-tp, trib,
which gives the time differences in the peak between the downstream and tributary gauge.
Design of the analyses
The impact of flood wave superposition on flood severity in terms of the
peak magnitude and temporal match is analysed using three steps, as shown
in Fig. and described in detail below. For each
step, four examples are given. These examples do not represent the
complete spectrum; thus, Fig. does not correspond
to Fig. .
Flowchart of the analysis steps. In each column, the same flood event situation is presented.
(a) Time lags in days between the tributary and upstream peaks as density plots of time lags for all events and for the largest flood peaks (shown using shaded dots in descending order). The distance between the shaded dots is identical and represents the ranks and not the differences in peak magnitude.
(b) Representation of flood event discharges at triple points, with the colours corresponding to time lag. The grey symbols in (b) and (c) correspond to zero lag; the blue symbols represent an earlier tributary peak occurrence, and the red symbols represent a later peak occurrence. The symbol size indicates the flood magnitude at the downstream gauge. The diagonal line indicates the same specific discharge for the upstream and tributary peaks. A triangle above (below) the diagonal line indicates a higher (lower) specific discharge at the tributary compared with the upstream gauge.
(c) The representation of peak flows at the downstream, upstream and tributary gauges, with the respective coloured points corresponding to the time lag of the peaks of the upstream and tributary gauges with respect to the downstream gauge. The flood peaks are ordered by the peak magnitude at the downstream gauge in descending order.
Degree of temporal flood wave superposition
The first step investigated whether temporal flood wave
superposition is a key factor in the occurrence of large floods
(Fig. a). The degree of temporal flood wave
superposition is represented by the time lags between flood peaks at
the tributary and upstream gauges Δtp. The time
lags of all of the events at a triple point are presented as an empirical
density curve. A peaky density curve shows low variability of temporal
matching, i.e. a relatively constant time lag. A perfect temporal
flood wave superposition is indicated by Δtp=0. Additionally, we analysed whether small time lags are
(inversely) related to the magnitude for the largest events. In this
way, the hypothesis that temporal peak matching leads to larger flood
peaks is tested: the time lags of the eight largest flood
peaks are shown as shaded circles (Fig. 4a) to check whether the largest floods
are amplified due to flood wave superposition (flood synchronicity).
Four cases of temporal flood wave superposition are schematically
shown in Fig. a:
Case A1: the time lags between the tributary and upstream gauge Δtp are widely spread around zero. In contrast, the four largest floods have perfect temporal match which could potentially explain the occurrence of these large floods.
Case A2: the peak discharge occurs earlier in the tributary. Most of the largest floods also occur earlier with a constant time lag. However, the two largest floods occur when flood waves are synchronous, which suggests that temporal superposition is a relevant driver for large floods.
Case A3: as in case A1, time lags are variable around zero, but there seems to be no systematic difference in temporal matching between small and large floods.
Case A4: as in case A2, most of the flood peaks occur earlier in the tributary. Similar to case A3, the superposition of flood waves does not result in the occurrence of large floods.
The first two cases show a high
relevance of temporal flood wave superposition for the occurrence of
large floods at the downstream gauge. Here, the largest floods
coincide with zero time lag, which suggests that temporal
superposition contributes to high severity. Thus, flood synchronicity,
i.e. temporal matching of floods at the upstream and tributary gauges,
is detected for cases A1 and A2. The last two cases are examples
with a low impact of flood wave superposition.
Contribution of the tributary and main river to downstream flood severity
In the next step, the peak magnitude and temporal matching are jointly
investigated for all events of a triple point. An analysis of flood
synchronicity alone is not sufficient to evaluate flood wave
superposition; thus, an understanding of the impact of flood
amplification and an analysis of whether high discharge values at both the
tributary and upstream gauges cause an increase in flood severity at
the downstream gauge are also required. Otherwise, a low discharge magnitude either in
the tributary or upstream gauge may lead to a compensation effect and
a low downstream flood severity.
The relationship between the peak magnitude at the tributary and upstream
gauges is analysed taking their time lag and the
downstream peak magnitude into consideration (Fig. b). In this
analysis, both axes are scaled to the same specific discharge. The
diagonal line indicates the same specific discharge at the tributary
and upstream gauges. A flood peak below the 1:1 line indicates
a higher specific discharge in the main river compared with the
tributary and vice versa. The size of the triangles is scaled by the
flood magnitude at the downstream gauge, and the colour code corresponds
to the time lag between the tributary and upstream gauge. Four cases are
distinguished in Fig. b:
Case B1: the specific discharge is similar at the tributary and upstream gauge. Thus, with increasing discharge in the main river the tributary and the downstream discharges also increase.
The flood peak occurs at the tributary and upstream gauges on the same day for the four largest events (grey), whereas the tributary peak occurs earlier (blue) or later (red) for smaller flood events (here ranks 5–8). This suggests that synchronous peaks at the upstream and tributary gauges contribute to large downstream floods.
Case B2: the specific discharge is similar at the tributary and upstream gauges for most of the flood events, but the tributary peak typically occurs a few days earlier. Only the two largest flood peaks occur on the same day. High peaks in the tributary and main river lead to large floods in the downstream part of the river, and flood wave superposition clearly contributes to the amplification of the largest flood peaks.
Case B3: the specific discharge is sometimes higher and sometimes lower in the tributary. The peak sometimes occurs earlier and sometimes later, although rarely on the same day as for the upstream gauge. The flood peak severity at the downstream gauge is instead driven by the upstream and tributary flows, and the superposition plays a minor role for peak amplification.
Case B4: as in case B3, the specific discharges are variable. However, for the majority of the events, the peak occurs earlier in the tributary (dark blue triangles). The largest floods downstream are instead driven by specific flows in the tributary and upstream branches, and flood wave superposition is of minor importance for flood amplification.
Contribution of the tributary and main river to the largest downstream floods
In the last step, we analysed whether the impact of the tributary and
upstream gauges on the downstream gauge changes for different flood
magnitudes. In this way, we test whether the relevance of flood
synchronicity and flood amplification increases for large downstream
floods. In contrast to the previous analyses, the flood timing of the
tributary and upstream gauges is related to the downstream gauge. The
time lags between the upstream and downstream gauges (Δtp, up) and between tributary and downstream gauges (Δtp, trib), respectively, are coloured accordingly. This
shows whether the flood peak magnitudes at the tributary and upstream
gauges change relative to each other for the largest downstream flood
peaks.
Four cases are distinguished (Fig. c):
Case C1: high discharges at both the tributary and upstream gauge lead to high floods in the main river downstream of the confluence. For the largest floods, the flood peaks occur at all three gauges on the same day; thus, flood wave superposition enhances the flood peaks at the downstream gauge. A temporal mismatch is observed for lower-ranked flood events.
Case C2: also here, high discharges in the tributary and upstream gauges evoke large floods downstream. Due to flood wave synchronicity for the two largest events, the flood peaks at the downstream gauge are disproportionally amplified. This indicates a significant role of flood wave superposition in driving flood severity.
Case C3: the relevance of peak flows in the two upstream branches changes between different events. A relatively small flood at the upstream gauge (compared with other events) can be compensated for by a large flood in the tributary and vice versa. The synchronicity of flood peak occurrence is not systematic and is not a major driver of large floods downstream.
Case C4: the relevance of peak flows also changes between different events. However, the tributary peaks systematically occur earlier, and flood wave superposition is not a significant driver of flood severity downstream.
Cases C3 and C4 show a flood compensation effect for some
events. A high flood magnitude in the upstream gauge can be compensated for by
a low flood magnitude in the tributary and vice versa.
Results
All results are presented in separate subplots for the four major
basins (the Elbe, the Danube, the Rhine and the Weser) and are analysed consecutively.
Degree of temporal flood wave superposition
In the Elbe River basin, the tributaries generally have the lowest
degree of temporal superposition among the four basins
(Fig. ). The flood peaks in the Mulde occur about 4 d
earlier for most of the events, including large floods. The time
lags of the Saale peaks are more variable with some waves arriving few
days earlier or later than the main Elbe flood. Few large
floods show strong temporal superposition, but this is not an
unequivocal pattern: large floods also occur for preceding and
subsequent waves. The vast majority of the Havel peaks runs behind the
Elbe flood wave and appears not to control the peak magnitude
downstream. A perfect match of flood waves is detected for the
small catchment of Zschopau, where flood wave superposition enhances
the majority of flood events (case A1). Thus, all confluences in the Elbe
Basin except Zschopau belong to case A4.
In the Danube Basin, high flood synchronicity is identified in most of
the tributaries (cases A1 and A2). There is a high share of perfect
matches for several triple points (e.g. Wertach, Ziller and Naab). In
the Wertach, the largest flood peaks occur on the same day, showing
a perfect wave superposition. For the largest flood events at the
confluences of the Salzach, Regen, Naab and Isar, a perfect match or
a time lag of 1 d is observed. This suggests the strong role of
temporal wave superposition in flood generation in the lower German
Danube. This applies in particular for Salzach, where a perfect
temporal match or a time lag of 1 d is observed for the largest
events, whereas small events exhibit high variability in time lags
(case A1). Hence, at this triple point, a difference in temporal
matching is detected between small and large floods, and wave
superposition appears to enhance large floods.
In the Rhine River basin, high flood synchronicity is identified for
the small tributaries (Itz, Enz and Regnitz). They exhibit relatively
small time lag variability due to short catchment reaction times. At
the Neckar–Rhine confluence the largest flood is characterised by
strong peak synchronicity, whereas the majority of the events arrives
slightly earlier (case A2). This could indicate the enhanced role of
wave superposition. For this confluence, a higher probability of
temporal matching due to river training and flood wave acceleration
has been detected (e.g. and references
therein). The Main tributary shows the highest variability of time
lags around zero in the Rhine Basin (case A3). The largest floods
downstream of the confluence occur with the Main wave preceding or
following the Rhine flood by few days, respectively. This
indicates that large floods are not generated by temporal
superposition. The vast majority of Mosel floods occurs a few days
prior to the Rhine floods. Several floods occur at the ideal
superposition of both waves, although these are not the largest recorded
discharges.
In the Weser River basin, high flood synchronicity is found at the
smaller tributaries (Oker and Innerste). In contrast, there is high time
lag variability at the confluence of the Eder and Aller. At the Aller
confluence, the largest recorded flood is notably generated under
perfect wave matching conditions (case A2). Temporal matching is high at the
Fulda confluence (case A1) with several high floods characterised by
a time lag of 0–1 d.
Density of the time lag in days between the tributary and upstream peak. A positive time lag means that the tributary peak occurs later. The 10 largest events are shown as circles with decreasing grey colour intensity. The catchments are ordered by increasing catchment size in each subplot.
Many triple points show flood synchronicity with a sharp peak around
-1 to +1 d. For the majority of the triple points, either most
of the large floods are regularly enhanced by wave superposition (case
A1) or the superposition is not related to large floods (cases A3 and
A4). For A3 and A4, flood synchronicity is not decisive for the
generation of large floods. A strong difference in temporal matching
between all of the selected floods (AMS) and the 10 largest floods could
only be observed for a few triple points. The largest floods appear
to emerge during perfect matching of the main river and tributary
waves (e.g. Salzach, Neckar). At the Salzach, this also seems to be the
case, and we characterised it as A1. For the other cases, the causal
relationship between superposition and the emergence of the largest
floods needs to be further investigated. In the next steps, we
analysed whether these large floods are indeed generated by the strong
superposition of high floods in the tributary and upstream branches. In
this case, the wave superposition would have the potential to produce
large-magnitude floods.
Contribution of the tributary and main river to downstream flood severity
Small tributaries in the Elbe Basin (Zschopau and Bode) have a similar
specific discharge to the respective upstream gauge in the main river
(Fig. ; Fig. 4, cases B1 and B3). The Mulde River has a much
higher specific discharge than the Elbe, but its waves reach the
confluence more than 3 d prior to the main river flood peak (case
B4). The Saale and Havel tributaries have much smaller specific
discharges and, similar to the Mulde, there is a time lag of several days.
In the Danube Basin, higher specific discharges are found in the major tributaries (e.g. the Iller, Inn, Lech, Regen and
Salzach) than in the main river. There is a temporal mismatch between the Inn and the upstream
gauge, with earlier occurrence of the Inn peak. The Isar peak generally arrives
earlier than the main river peak (Fig. ). In the
Rhine Basin, high specific discharge is identified in several
tributaries (the Mosel, Neckar, Nahe, Kinzig and Tauber) with an earlier
flood peak. A different pattern is found for the Main River with
changing contributions from the Main and the upstream Rhine gauge as well as a
later peak occurrence in the tributary (case B3). For most of the
largest events, the specific discharges of either the tributary or the main
river are exceptionally high. This suggests that flood magnitudes in
the upstream branches are the major drivers of large floods downstream
rather than the wave superposition alone. In the Weser Basin, similar
specific discharges are detected for flood events in the Aller and
Fulda catchments. Overall, the tributary peaks are often later in the
Weser Basin.
The relationship of peak discharge between the upstream and tributary gauges for all selected events. The size of the triangles shows the downstream peak magnitude, normalised by the mean peak discharge: the larger the triangle, the larger the flood magnitude compared with the mean annual flood. The diagonal line delineates the same specific discharge at tributary and upstream gauges. Triangles above (below) the line represent a higher (lower) specific discharge at the tributary gauge compared with the upstream gauge. The colours express the time lag between the tributary and upstream peak: blue shows that the upstream peak occurs later, and red shows that the tributary peak occurs later.
In many cases, the analysis shows that the specific discharge is
larger in tributaries than in the main stream, but the tributary
peaks often occur earlier. The largest downstream floods (largest
triangles in Fig. 6) are often characterised by the highest specific discharges,
either in both branches or in one of them. Many subplots show
a quasi-linear relationship, often deviating from the diagonal line
that would indicate similar specific discharge
(Fig. ). Other triple points are characterised by
event-specific behaviour with varying contributions from the tributary and
upstream gauges. There is no clear indication that perfect temporal
matching (grey triangles in Fig. 6) leads to the largest floods when the
specific discharges are moderate. Hence, wave superposition does not
seem to play a major role in generating large floods in Germany.
Contribution of the tributary and main river to the largest downstream floods
The contribution of the tributaries in the Elbe Basin is variable among
tributaries and across the largest flood events
(Fig. ). While the Zwickauer Mulde has a similar
contribution to the main stream of the Freiberger Mulde (case C1), the
contribution of e.g. the Havel to the Elbe floods is minor. The strong
delay between upstream and downstream peaks in the main river around
the Saale confluence for the two largest floods (2002 and 2013) clearly
points to floodplain inundation and wave attenuation, which indeed
occurred after several dike failures.
In the Danube Basin, the largest floods are caused by much larger
peaks in the Inn tributary compared with the upstream Danube. However,
at the Inn–Danube confluence, the Danube wave has typically a 2 d
lag. At the confluence of the Salzach and Inn rivers, similar peak values are
observed. Thus, large flood peaks at the Inn confluence with the Danube
are driven by both the Inn and the Salzach. Notably, the Wörnitz,
Naab, Regen and Isar tributaries as well as the Inn (to a lesser degree) appear to behave somewhat
asynchronously with respect to the Danube floods (a “see-saw”
pattern). Large floods in the main river are typically matched by
lower floods in the tributaries and vice versa (the flood compensation
effect). At the confluence of the Lech and the Danube, high variability in the
flood peak values is detected. The largest downstream flood peaks only
occur if both rivers show large peaks. Low flood peaks in the Lech
also lead to lower values at the Danube downstream gauge. The same
situation is observed for the Regen and Naab tributaries. The
ranking of the flood peaks is largely different between the upstream and
downstream gauges due to the changing contribution from the Regen and
Naab.
In the Rhine Basin, large floods occur with relevant contributions
from the three major tributaries (the Mosel, Main and Neckar); however, the
relative contributions vary between the events (cases C3 and
C4). These tributaries and the main river flows exhibit a
“see-saw” pattern (Fig. ), where relatively low
magnitudes in the main river are compensated for by relatively large
flows in the tributaries and vice versa. For example, the flood
severity in the Rhine is partly reduced due to a relatively low flood
peak in the Mosel. Otherwise, a large flood peak in the Mosel could
increase the downstream flood peak in the Rhine. The effect of wave
superposition is not dominant in these cases either. This pattern
suggests that the extent of flood-generating storms or
their specific tracks have not been able to affect the upstream Rhine
catchment and the tributary catchments to an equal degree in the past. The largest
flood downstream of the Neckar confluence is caused by moderate main
stream and tributary flows, but here the temporal matching of the
Neckar wave is strong, which suggests the enhanced role of wave
superposition at this confluence as mentioned above.
In the Weser Basin, the contributions from upstream and the tributary are
similar at the Fulda and Aller confluences. The largest flood peaks at
the confluence of the Leine and the Aller are evoked by large flood peaks from
both upstream branches. In the majority of the cases, the Leine peak
is 1 d later and the upstream Aller peak. For the
seventh largest flood at the Leine–Aller confluence, the tributary peak is
clearly larger than the downstream peak, which indicates strong
attenuation effects due to inundation in the tributary. A flood
compensation effect is found at the confluence of the Werra and
the Fulda. Here, large discharges in the Fulda alone are not sufficient to
generate a large flood downstream.
Event peaks at the upstream, tributary and downstream gauges, shown in decreasing order according to the downstream peak discharge. The points show the timing of the upstream and tributary peak in relation to the downstream peak.
For some triple points, the flood peaks in the main river can be strongly
enhanced by inflow from the tributaries. Flood wave superposition
alone is not identified as a driver of the largest floods; however, in
a few cases at some confluences, flood wave superposition appears to
compensate for lower discharges in the upstream branches and, thus,
contributes to the generation of floods.
Discussion
In contrast to former studies using a few confluences, our study
focused on a large set of gauging stations to explain general patterns
and not on the specific characteristics of individual events.
Regarding discharge data, measurement uncertainty may be a limiting
factor for various hydrological analyses. However, we do not expect
this to have a significant impact on our results, as we analyse
flood waves and events jointly in relation to each other. We expect that
the uncertainty is similar for different events at the same gauge and
for gauges at one triple point.
The relevance of flood wave superposition for flood severity also
depends on the physiogeographic catchment characteristics and the
catchment size. concluded that flood wave
superposition is less important in large lowland rivers due to the
long duration of flood waves. In our study, flood wave superposition
may play a role at several confluences. We consider catchments ranging
across 2 orders of magnitude from lowland areas via the Central German Uplands to
alpine regions with the whole range of reaction times. Hence, there is
high variability in the time lags at the confluences and flood durations
of the incoming flood waves.
In several cases, our study has derived a time lag of some days
between the tributary and upstream peak. A perfect temporal match of
flood peaks could potentially lead to a large increase in peak
discharge. For example, in the Mulde, the two largest events (2002 and
2013) have the highest specific discharges in both streams (the Elbe and
the Mulde), but the Mulde peak occurs 4–6 d earlier. A meteorological
situation in combination with a catchment response, which would reduce
the time lag at the Mulde confluence, would be rather
dangerous. Hence, the potential for a delayed Mulde response (in
comparison to the Elbe) needs to be investigated in the
future. A possible scenario would be long lasting extreme rainfall
(e.g. a Vb cyclone; ) in combination with dry catchment
conditions in the Mulde catchment. This could result in a delayed
Mulde response and a surprisingly large flood downstream.
The sensitivity of precipitation timing and soil wetness conditions
was analysed by in a comparison of the flood waves of
the Inn and Danube rivers. The flood peak in the Inn occurs earlier than in the
Danube; however, there is some temporal variability in these
time lags among different floods. explained the lower time lag for the 2013
floods by the earlier onset of
the precipitation event in the Danube Basin compared with the Inn
catchment and by strongly saturated soils that lead to a faster
runoff response.
In order to investigate the impact of a delay in the tributary peak,
shifted the discharge time series of a tributary
to achieve temporal
matching of the flood peaks of tributary and main river in their simulation study in the Danube Basin. They showed
that flood wave superposition could highly increase the flood
peak. However, this study did not analyse whether this temporal shift
was realistic. In future, we see the need to analyse storm tracks and
precipitation patterns, which may potentially reveal if specific storm
movements could induce temporal wave matching and large floods.
Conclusions
In this study, flood wave superposition between the tributary and main
river is analysed at 37 confluences in four large basins in
Germany. Each confluence is characterised by a triple point of three
gauges (one in the tributary and two on the main river: upstream and downstream) which are
jointly analysed regarding temporal matching and similarities in
specific peak discharge during flood events. An approach is presented
to disentangle the impact from tributaries on the downstream peak flow
in terms of the temporal occurrence and peak magnitude.
The major outcomes of this study are as follows:
Flood wave superposition is not the major driver of flood peak occurrence downstream of most of the confluences analysed in this study. Flood wave superposition can be regarded as an amplification mechanism for downstream flood peaks. These are largely driven by discharges from upstream branches.
In general, the temporal superposition is sometimes constant with respect to the time lag, and there is sometimes strong variability in time lags among the floods at a specific triple point. In several cases, the tributary peaks precede the main river peak by about 2–5 d for most flood events.
Several highly relevant tributaries in terms of their contribution show a prevailing peak delay (the Mulde, Mosel and Inn), but they also show the potential for strong flood amplification if a delayed response were to occur. Future work will analyse the probability of specific storm and catchment states that are capable of reducing the time lag with a simultaneously high peak magnitude.
The impact of flood wave superposition is event-specific in terms of peak discharges in the tributary and main river. At most of the confluences, no systematic differences are observed between the small and large floods. Either all floods are enhanced systematically by wave superposition or the mechanism does not lead to extremes.
At several confluences, “see-saw” patterns of main stream and tributary flows are detected, i.e. lower flows in the main stream are compensated for by larger flows in the tributary and vice versa. These confluences show the potential to generate large floods if both upstream subcatchments react in resonance. Future work will investigate the circumstances under which such resonance is possible (different event and soil moisture patterns and different storm tracks).
Overall, we conclude that the superposition of flood waves is not the
driving factor of flood severity in Germany. The developed methodology
can be transferred to other basins and confluences and is not
region-specific.
Code and data availability
The discharge data are not able to be provided due to restrictions. Please find the MATLAB code for deriving the flood peaks for the triple points in the Supplement of this article.
The supplement related to this article is available online at: https://doi.org/10.5194/hess-24-1633-2020-supplement.
Author contributions
All authors contributed to the design of the study, the discussion of the results and writing the article. SU undertook the GIS analyses and prepared the discharge data. SV and BG implemented the flood wave separation algorithm. BG carried out the analyses and prepared the figures.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
Financial support of the FOR 2416
“Space-Time Dynamics of Extreme Floods (SPATE)” research group from the German Research Foundation (“Deutsche
Forschungsgemeinschaft”, DFG) is gratefully
acknowledged. Funding from the Austrian Science Fund (grant no. I 3174-N29) is also acknowledged. The authors thank the following authorities for
discharge data: the Federal Institute of Hydrology (BfG); the Bavarian State
Office for the Environment (LfU); the Baden-Württemberg Office of
Environment, Measurements and Environmental Protection (LUBW); the Saxony
State Office for the Environment, Agriculture and Geology (SMUL); the
Saxony-Anhalt Office for Flood Protection and Water Management (LHW); the
Hessian Agency for Nature Conservation, Environment and Geology (HLNUG); the Rhineland Palatinate Office for the Environment, Water Management and the Factory
Inspectorate (LUWG); and the Lower Saxony Office for Water Management, Coastal
Defence and Nature Conservation (NLWKN).
Financial support
This research has been supported by the German Research Foundation (DFG; grant no. FOR 2416) and the Austrian Science Fund (grant no. I 3174-N29).The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.
Review statement
This paper was edited by Markus Hrachowitz and reviewed by two anonymous referees.
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