Innovative control strategy for flood mitigation through a combination of barrage management on impounded rivers and polders

The partially catastrophic effects of large floods, such as the events of 2002 and 2013 in Germany and Austria for example, clearly show the vulnerability of settlement structures along large rivers. In the case of impounded rivers with run-of-river hydropower plants, the main question is whether a reduction of floods can be achieved with flood-adapted, intelligent control of barrages - to date, the operational objective has been the safe discharge of floodwater; targeted reduction is currently an unoccupied field due to its complexity. Specifically, the interaction with the operation of a polder for flood retention is of special interest, as polders are a much-discussed and effective element of flood protection, especially at higher discharges, that directly influences the hydrograph shape. Extensive analyses and sensitivity investigations of a multitude of parameters and measured values, using a complex model system, are needed in order to investigate the reduction potential of the named technical flood protection measures and the development of control strategies relevant to practice. It is essential to base the developed controlling strategies on operationally available data, as this is the only way to make the determined reductions relevant for practical operation.

1 Introduction

In recent decades, major flood events and the associated large-scale flooding and damage have demonstrated the vulnerability of settlement structures along major rivers. The 2013 flood in Passau on the Danube and downstream in Upper Austria represented an event with an annuality of well over 100 years and record water levels due to the influence of the Inn River (Bayerisches Landesamt für Umwelt 2014; Bundesanstalt für Gewässerkunde 2013). In 2013 Passau had a population of around 49,400 people (Statistisches Bundesamt 2021). In the case of the 2013 flood, the flooding affected an area of around 241 hectares in the area of the city of Passau and resulted in total damage of around 190 million euros. The 2002 flood caused damage totaling 20 million euros in Passau (Wittmann et al. 2015).

The existing development of large rivers with chains of barrages raises the question whether flooding can be reduced by means of adapted operation and, following from this, intelligent control of barrages in flood situations. In this context, overlapping or interaction with the retention effects of polder operation is of particular interest. The effectiveness and applicability of flood-adapted barrage operation ‒ so-called barrage management ‒ including the operation of polders, are frequently discussed in research and by the public. In the present case, barrage management is understood as the intelligent lowering and increasement of the headwaters of barrages for flood retention in a chain of run-of-river hydropower plants. It should be noted that the heads of the barrages are usually between 5 and 15 m.

With regard to barrage management, the spectrum of assessment ranges from problem-free applicability with high potential for peak reduction to the impossibility of application and/or very low potential. In many cases, the assessments made are not supported by investigations or analyses and ultimately represent unfounded assessments.

However, while there is appropriate literature available on the automated operation of run-of-river hydropower plants (Chapuis 1998; Theobald 1999; Schwanenberg et al. 2014), the width of the discussion on flood mitigation is hardly reflected in the available research on the control of barrages, as the total number of publications is comparatively small. Studies on Austrian Danube barrages, described for example in Rauschenbach and Wernstedt (1999), show a general potential for flood reduction based on a known discharge hydrograph using a model-based, simulative optimization procedure. However, since the uncertainties of the forecast as input data are not addressed, this is a theoretical potential study and not an operationally applicable control system. Based on forecast data and one-dimensional simulation, Kim et al. (2021) also show flood mitigation using six barrages on the Taedong River, Democratic People’s Republic of Korea. The complex optimization options are explained in detail, but the processes are also based on forecasts. Another consideration is provided by Dettmann & Theobald (2015) for Danube floodplains in Upper Austria. Here, a 1D hydrodynamic-numerical (HN) simulation model, coupled with control elements, was used to determine a theoretical potential of mitigation through adapted barrage operation based on extensive sensitivity studies. The study was for potential assessment only and was conducted using known hydrographs; therefore, a direct derivation of operationally applicable control specifications was not performed. However, it was discussed that the development of a practical control system would be possible using operationally available data. Further investigations on the German Danube, described by Lehrstuhl und Versuchsanstalt für Wasserbau und Wasserwirtschaft (2017), show a potential for mitigation by adapted barrage operation based on 2D-HN simulations. However, this is determined based on known hydrographs and no control functions are discussed, so no applicable system emerges from this case study. A realistic mitigation by adapted barrage operation is presented by Gerke et al. (2017) for a flood-adapted operation at the Langkampfen barrage in the alpine area of the Inn River. Due to short differences of onset times in the system, flexible control specifications for a barrage were developed, which were tested simulatively with a 1D-HN model and refer to operationally available values - the boundary conditions at the investigated barrage only make a reduction up to HQ₃₀ possible. However, the described investigation refers to one barrage only.

Interesting simulation and optimization approaches are also shown for example by Jordan et al. (2012) and Diao et al. (2022) especially with the management of cascades of reservoir systems. The state of optimization techniques, which are used to solve the often multi-criteria problems in addition to flood mitigation, are intensively discussed. With regard to the transferability of these research results to the topic discussed here, a difficulty lies in the dimensions of the reservoirs under consideration. As the reservoirs of dams are much larger than the volumes of the reservoirs of barrages, the systems react much more slowly and delayed; there is no need for the precise control required for weirs of barrages. Inaccuracies in the data and signals used are therefore less significant. The use of operationally available data, which is discussed below in relation to time-sensitive barrage management, is though comparable.

The research work presented here aims to provide a detailed investigation of various ways of potentially reducing peaks: adapted barrage operation, polder operation, a combination of both, and the simulation-based development of complex control specifications. Due to the consideration of a large number of different parameters, particularly including operationally available data, these control specifications are suitable for practical operation (Dickel 2023). The investigation of the potential flood mitigation by means of barrage management and combined operation with an exemplary polder was carried out for the Inn River in Bavaria and is based on the “Retentionspotentialstudie Inn”, which was commissioned by the Bavarian State Office for the Environment.

Realistic investigation into the application of the two flood protection measures referred to and their interaction, as well as the development of practice-relevant control specifications, requires the use of a modeling tool. This modeling tool must be able to represent the interaction of the complex hydraulic processes involved in the flood event in connection with the control specifications at the hydraulic-engineering structures (Dettmann et al. 2022; Theobald 1999; Theobald et al. 2022). The control specifications developed for the adapted operation of the barrages, which are described in the following, include operationally available measured values. The performance of control specifications is event-based. The operation of the polder control is also defined analogously with reference to measured values. Based on detailed observations and analyses, the system model and the underlying method can also be applied to other river systems.

2 Numerical modeling of the impounded river system

The study used a one-dimensional hydrodynamic-numerical method, which can be coupled with Matlab/Simulink (Dettmann et al. 2022; Theobald et al. 2022). The modeling tool is flexible and allows various dependencies to be implemented as boundary conditions. The HN method is an inhouse development in C++, in which the complete unsteady Saint-Venant equations are solved using the Preissmann scheme. The double sweep method is used here (Cunge et al. 1980). Below the two Saint-Venant equations are shown. The representation of complex flow structures, such as branched systems, is possible as well as the integration of polders or other special structures.

$$\frac{\partial \text{Q}}{\partial \text{x}}+\frac{\partial \text{A}}{\partial \text{t}}=0$$

$$\frac{\partial \text{v}}{\partial \text{t}}+\text{v}\frac{\partial \text{v}}{\partial \text{x}}+\frac{\text{g}}{\text{b}}\frac{\partial \text{A}}{\partial \text{x}}=\text{g}({\text{I}}_{\text{S}\text{O}}-{\text{I}}_{\text{E}})$$

It includes a comprehensive toolbox with different types of water balance controls for single barrages or chains of barrages on impounded rivers. The modeling tool thus enables the control aspects of the operation of barrages and other hydraulic engineering structures to be represented and, at the same time, the influence of the control specifications on the flow conditions in the reservoir or in the river to be analyzed. The modeling tool was developed at the Department of Hydraulic Engineering and Water Resources Management. It has been used successfully in a large number of projects and is constantly being further developed (Dettmann et al. 2022; Theobald et al. 2022). For example, a total of 82 barrages or rather the chains of barrages formed with them in Bavaria and Upper Austria with a total modeled river length of about 1,100 km were simulated. In this modeled domain, for example, water balance controls at the barrages were considered and adapted to the special conditions in order to ensure the automated operation of the barrages and compliance with even contrary management objectives (Theobald et al. 2022). The modeling tool is also used for the development of superordinate regulation modules, which, for example, allow for the equalization of an unsteady discharge situation (Dettmann et al. 2022).

The modeled area presented in this study includes the Inn River in Bavaria from the Oberaudorf-Ebbs hydroelectric power plant (HPP) to the confluence with the Danube with a length of approx. 211 km, the power plant channel of the Töging power plant as well as the Danube section of the Jochenstein dam, as shown in Fig. 1 (left side). A total of fifteen run-of-river hydroelectric power plants, which are implemented in the connected chain model, are located on this flow section of the Inn River (Fig. 1, right side). The head of the run-of-river hydroelectric power plants considered on the Inn ranges from 5.38 to a maximum of 11.65 m and is relatively high, especially on the lower Inn, with a minimum of 9.5 m. The lengths of the reservoirs also differ and the reservoirs of the HPP Schärding-Neuhaus and Passau-Ingling show the largest spatial expansion with 16.50 and 14.60 km, respectively.

The barrages considered in the barrage management are highlighted in Fig. 1 (left side), differentiated into plants upstream (circled in orange) and downstream of the confluence with the river Salzach (circled in green). The investigated, exemplary polder location (yellow) is situated in the direct application area of the barrage management in the reservoir of the HPP Ering-Frauenstein at the lower Inn river.

Fig. 1

Modeled area of the Inn river in Bavaria with barrages (red dots) considered in barrage management, divided into barrages upstream of Salzach (circled in orange) and downstream (circled in green) as well as gauges (green dots) and location of exemplary polder (yellow); schema of Inn model on the right side

The flood genesis in the catchment area under consideration is significantly influenced by the tributary Salzach at the lower Inn from Inn km 68.3. The statistical characteristics of an HQ₁₀₀ are of comparable magnitude at the gauges Wasserburg / Inn (km 158.67) and Burghausen / Salzach (km 11.4) and correspond to Q = 2,850 m³/s and Q = 3,300 m³/s, respectively. At the gauging station Passau Ingling / Inn (km 3.1) in the confluence area of the Inn, the discharge value of HQ₁₀₀ after the confluence of Inn, Salzach and further lateral tributaries is Q = 6,800 m³/s.

The considered study area of the Inn in Bavaria represents a large river of the Alpine foreland, which is characterized by alpine influence, especially in the area of the upper model boundary. In the past, large flood events were mainly triggered by intensive and long-lasting precipitation events due to Vb weather conditions, which in some areas led to large-scale flooding with catastrophic effects. During Vb weather events, an area of low pressure moves from northern Italy towards the northeast, causing heavy precipitation especially in Central Europe due to the often very water vapor-rich air masses it carries. Research results on formation processes and dynamics were described by Messmer et al. (2015). The three past floods studied ‒ 2002, 2005 and 2013 ‒ were also caused by Vb weather conditions. The floods in the catchment area of the River Inn in Bavaria generally show different maximum discharge characteristics at the upper Inn and Salzach and a distinction can be made between Inn- and Salzach-accentuated floods. The 2005 flood examined represents an HQ₁₀₀ event for the upper Inn (gauge Wasserburg), while at the lower Inn an annuality of 10 years is slightly exceeded (gauge Passau Ingling), so that it is Inn-accentuated. The 2013 flood has an annuality of HQ₂₀ at the upper Inn and an annuality of HQ₁₀₀ at the lower Inn due to the influence of the Salzach and can thus be defined as Salzach-accentuated. The 2002 flood can also be classified as a flood influenced by the Salzach: the flood peak corresponds to an annuality of HQ₅ at the upper Inn and to a 20-50-year flood at the lower Inn.

Recorded discharge data from a total of 17 gauges in the catchment area (Fig. 1, schema on right side, named as inflows) are used for the unsteady simulation of past floods; the inflows of non-gauged catchments are defined on the basis of the discharge of neighboring catchments, which are known from a gauge measurement. For the unsteady calibration of the coherent model, the floods 2005 and 2013 were simulated, as the complete model could be calibrated for the HQ₁₀₀ in sections using the floods of 2005 and 2013. The flood 2002 also represents a large flood with good recordings, but is below HQ₁₀₀ and is therefore suitable and used for validation. The model was calibrated on the basis of a comparison of measured and visualized water level and discharge hydrographs; the Strickler coefficient is selected depending on the water level in part and changes over the longitudinal course of the branches and in the forelands. In the river channel, the values are primary between 33 and 45 m^1/3/s. Details on the calibration and validation of the model can be found in Dickel (2023). As an example for the good correspondence of the simulation results with the recorded data, measured (dotted) and simulated (solid) hydrographs at the Inn gauges Wasserburg and Passau Ingling as well as the Danube gauge Achleiten are shown in Fig. 2. Thus, a model is available for the following studies, which is representative for different discharge ranges. A 2D-HN model is also available for the Inn River. The results regarding water level and runoff of the 2D-HN model do not show a better correspondence with the measured values than the 1D-HN model; however, the 2D-HN model requires significantly longer computation times and is therefore not used any further.

Fig. 2

Comparison of measured and simulated discharge hydrographs at different gauges of the Inn and Danube of the 2002 flood validation event

As previously described, the modeling tool enables the currently valid weir operating regulations (WOR) to be implemented. In the event of a flood, the headwater level is lowered in accordance with the WOR at a total of seven of the fifteen barrages on the Inn implemented in the model. The lowering of the headwater level depends on the discharge. For example, in the event of higher discharges, the water levels in the reservoirs are lowered. Barrages are not currently managed to reduce floods on the Inn River, as considered in the scope of the study. The simulations carried out according to the WOR thus serve as a reference value to quantify the flood peak reductions determined with the developed barrage management and polder operation.

The simulation-based development and evaluation of the control specifications was carried out on the basis of a total of fifteen flood events. The past floods in the years 2002, 2005 and 2013 were simulated as well as twelve stochastic events, which were generated by the Technical University of Vienna within the scope of a subproject of the Inn study by means of stochastic precipitation-runoff modeling. These stochastic events show different annual peak discharges at the reference gauges on the Inn and Salzach and thus represent a wide spectrum of different precipitation and runoff distributions.

3 Conception of a practical control for barrage management

3.1 Basic principle

Operational regulation for flood reduction by means of adapted barrage operation ‒ barrage management ‒ consists of two processes: lowering and increasement of the headwater. The headwater level at the barrage is reduced before the flood arrives to provide volume in the reservoir that can be used for retention. By increasing the headwater level when the flood peak passes, volume is stored in the reservoir so that a reduction in the flood peak can be achieved.

Figure 3 shows the principle of barrage management as an example for the Ering-Frauenstein barrage, where the headwater level is maintained at a constant water level of 336.2 müNN according to the WOR. In the case of barrage management, the headwater level (black) is lowered by 2.0 m in this example, which leads to an increase in discharge at the barrage in the time range up to approx. simulation hour 20 in the case of barrage management (blue) compared to operation according to WOR (red). However, this increase in discharge takes place early prior to the flood in a low discharge range at approx. Q = 1,400 m³/s so as not to cause any damage. By increasing the headwater level to the regular impoundment target from hour 72, the discharge hydrograph in the flood peak area is lowered over a longer time period and the maximum discharge of the flood is reduced by ΔQ = 115 m³/s and a volume of 3.3 million m³ is retained. Due to the interaction of the eight barrages considered, the individual reductions overlap.

Fig. 3

Basic principle of barrage management

In the management concept investigated for the Inn, barrage management is carried out at eight of the fifteen barrages regarded. These are the Neuötting, Perach and Stammham plants upstream of the confluence with the River Salzach and the five plants on the lower Inn (Fig. 1). The barrages further upstream are not considered, as the implementation of barrage management is more difficult there due to morphological processes, landslides or shorter periods between the onsets of flood peaks. For the determination of control specifications and corresponding reference levels, extensive analyses and sensitivity studies have to be carried out in order to investigate the influence of different parameters and their interaction. The attainable peak reduction in barrage management depends mainly on the parameters of the lowering and increase of the headwater and corresponds to the depth of lowering or increase of the headwater height and, in particular, to the timing and gradients of the increasement process, as explained in detail below.

3.2 Simulation-based development and evaluation of control specifications

It is essential to consider the operationally available data when developing control specifications to ensure that they are practically applicable and the determined reduction reflects a realistic range. In general, the use of forecasts or measured values can be considered. Forecast data offer the advantage of a long duration up to the time of occurrence of the flood, but the existing uncertainties must be considered. For this reason, it must not be assumed that the forecast ideally predicts the hydrograph in the event of a flood when creating forecast-based control options ‒ instead, the forecasts must be considered and evaluated when creating control options in order to be able to assess the influence of their inaccuracy or reliability on the control process.

In addition to the use of forecasts, it is also possible to take measured values into account. Water level measurements are particularly suitable for this purpose, since they can be measured comparatively well even at higher discharges. When considering measured values, redundancy of measurement and information transmission must be ensured so that different measuring devices are available at the same cross-section of the river, each with independent power supply and data transmission. In addition, it is advisable to arrange and observe further reference gauges in the surrounding area to ensure and generally verify the plausibility of the measurement.

In addition to the determination of suitable, operationally available input data and suitable reference locations of e.g. gauging stations for water level measurement, various parameters and their influence must also be considered and investigated in detail for the development of control specifications. Today’s established methods of HN-modeling ‒ and especially given the short duration of the simulation runs and simultaneously sufficiently accurate modelling of the conditions in nature, 1D-HN-modeling ‒ provide the means for a broad study of variants for the development of control specifications as well as for their efficient evaluation.

3.3 Lowering of the headwater level

In order to carry out the lowering process as early as possible prior to the actual flood, a flood forecast is considered. As an example, for the analysis of available forecast data, Fig. 4 shows the evaluation of the forecasts for the 2013 flood with the LARSIM model at the Passau-Ingling HPP. The data generated from the LARSIM model during the 2013 flood was provided by the Bavarian State Office for the Environment. Larsim is a hydrological model that is used, for example, by the Bavarian Water Management Administration for operational flood forecast (Hangen-Brodersen et al. 2008). The forecast periods of 48 to 96 h are sufficiently long to be considered in the control specifications. The maximum predicted peak discharge and its time of occurrence were evaluated in comparison with the measured maximum discharge of Q = 6,691 m³/s (≈ HQ₁₀₀) at 5 pm on 03.06.2013. The size of the dots represents the ratio of predicted to observed maximum discharge. The evaluation indicates that for the hourly updated forecasts, a maximum value corresponding to 64% of the actual peak is already predicted 80 h before the peak, while the onset time of the flood peak is still predicted about 21 h too early at this time. As time progresses, the prediction converges to the real observed Q_max and the onset time of the flood peak.

Fig. 4

Evaluation of the forecasts of the LARSIM model for the 2013 flood at the Passau-Ingling HPP

In order to initiate the lowering process, which should take place as early as possible prior to the flood, it is only necessary to know whether a defined threshold value has been reached or exceeded; it is not necessary to know the exact peak discharge or its onset time. In order to evaluate the available time spans, the temporal difference between the real onset time of the peak discharge and the exceeding of different threshold values of the forecasts was performed. In the case of the 2013 flood, a discharge of an annuality of at least HQ₅ (Q = 3,700 m³/s) is predicted by the LARSIM model from 92 h prior to the real onset of the peak, and the predicted maximum discharge is permanently above Q = 3,700 m³/s from 84 h prior to the onset time. An analogous evaluation for the forecast of the 2010 flood (Q_max = 4,464 m³/s, ≈ HQ₁₀) shows that from 27 h before the measured flood peak a prediction of at least Q = 3,700 m³/s is available and the maximum predicted discharge does not decrease below the value of HQ₅ in the further course. HQ₅ therefore is a suitable value and is also published as a statistical value by the authorities in Germany.

Control specifications for the lowering process were developed based on the evaluations of the flood forecasts, knowledge of the flow behavior of the Inn River and under consideration of the influence of different parameters. Lowering of the headwater is initiated as soon as the forecast for the gauge Passau Ingling exceeds a threshold value (for example Q = 3,700 m³/s) and the discharge values at the barrage Nußdorf and/or at the gauge Laufen (Fig. 1) exceed a defined value (Q = 600 m³/s). A decrease of the forecast below the threshold value leads to a temporary suspension of the discharge process.

The definition of the parameters for the lowering and increasement processes was based on realistically implementable variables by a program of extensive simulations with a variation of the lowering depths by 10 cm in order to quantitatively evaluate the hydraulic effect in the respective barrages. The gradient of the lowering process was determined depending on structural (dams) and operational (WOR) boundary conditions and was set at 10 cm/h (except for Passau-Ingling) in accordance with the operating mode according to the WOR, so that there is no negative impact on the dams due to too fast lowering. At the Passau-Ingling HPP, the gradient of the lowering process is higher in order to maintain the specifications for operation in accordance with the WOR. The lowering of the headwater through barrage management at the three dams upstream of the mouth of the Salzach River is 1.5 m. Of these three dams, only the Perach HPP has a lowering of 0.6 m during regular operation in accordance with the WOR, i.e. an additional lowering of 0.9 m is applied here. At the barrages on the lower Inn, the headwater levels at the Braunau-Simbach HPP and the Passau-Ingling HPP are lowered by 0.5 m and by 3 m respectively during regular operation in accordance with the WOR in the event of floods. In the case of barrage management, depending on the barrage, a further 1.5 to 2.5 m of drawdown is performed in addition to the lowering of the headwater in accordance with the WOR, so that the total drawdown is between 2 and 4.5 m. At Passau-Ingling, for example, the headwater level is already lowered by 3 m during regular operation, so that only a further 1.5 m is lowered in barrage management. The drawdown in accordance with the WOR is always considered.

The comparison of the evaluations of the forecasts described above with the duration of the lowering processes ‒ corresponding to the chosen gradient and the drawdown ‒ shows that the time period between the forecast of a flood that exceeds a threshold value of, for example, Q = 3,700 m³/s is sufficient to initiate the lowering process, which on average takes approx. 20 h for a drawdown of 2 m and a gradient of 10 cm/h, at an early time. The time period between the forecast of a flood that exceeds a threshold value of, for example, Q = 3,700 m³/s is sufficient to be able to initiate the lowering process at an advanced stage.

3.4 Increase of the headwater level

The beginning of the increase of the headwater – in addition to the duration ‒ is an essential criterion for the effectiveness of the achievable flood peak reduction through the increasement process. A detailed analysis of the flood forecasts, analogous to the evaluation shown in Fig. 4, for different reference locations shows that a use of forecasts for the time-fitting initiation of the complex and time-sensitive increasement process of increasing the headwater is currently not expedient due to their inaccuracy. As a result, an approach for the development of control specifications based on upstream measured values was chosen.

Extensive analyses and sensitivity studies were done and the depencies of different values were estimated. At first, the time differences between the onset times of the flood peak at different locations in the river system (propagation time) were examined - all this depending on maximum flood peaks and the overlapping effects of the floods of Inn and Salzach. With a simulation program the influence of the parameters of drawdown and increasement gradient was then investigated as well as further dependencies (e.g. flood crest width) and a measurement-based control was developed. The evaluation with the fifteen simulated, variously pronounced flood events shows that this measurement-based control effectively reduced flood peak. The control specifications for the increasement process are based on the water level measurement at the gauges Rosenheim II (Inn km 187.2) and Laufen (Salzach km 47.5), which are marked in Fig. 1.

Three variants for the increasement process were developed based on each other, which differ in their complexity with regard to the number of signals considered as well as the specifications of time shift and gradient of the increasement process. The preferred variant III, developed from the composition of the most suitable specifications from the previously created variants I, which is rather robust e.g. without overlapping effects, and variant II, which is complex and takes a lot of signals into account, is explained below.

If a water level of HQ₅, which was determined to be suitable according to the simulations, is exceeded at both reference gauges Rosenheim II and Laufen, both water level hydrographs and thus the overlapping effects of the flood waves of the Inn and Salzach are considered in the control specifications. For this purpose, an auxiliary discharge after the confluence was determined based on the evaluation of the simulations using the maximum water levels at Inn and Salzach. A differentiation is made into Inn- or Salzach-dependent increasement processes for the determination of the start of the increase of the headwater. When considering the overlapping and thus an exceedance of HQ₅ at both reference gauges Rosenheim II and Laufen, the classification is made on the basis of the larger expected discharge of Inn or Salzach in the confluence area of the Salzach. If, however, only one water level at a reference gauge (Rosenheim II or Laufen) exceeds HQ₅, the increasement process is carried out depending on the relevant gauge. In general, the increasement process is initiated as soon as a flood is registered to be subsiding at the reference gauge(s) due to the water level dropping by a defined height.

The increasement gradient is 15, 20–25 cm/h, as usual gradients for increasement processes, and is determined depending on various parameters and simulations. For their definition, various linear regressions were generated, which include, for example, the propagation time of the flood peaks in relation to the maximum water level, the crest width of the flood peak depending on the moving average of the water level gradient and the peak discharge in relation to the maximum water level. Furthermore, the maximum discharge after the confluence of Inn and Salzach was determined as an auxiliary parameter of the discharge. A lower gradient of 15 cm/h is used if the hydrograph at the respective reference gauging station for the increasement shows a broad crest or if there is a larger difference between the onset times of the two flood waves when an overlapping is considered. In the case of broad crests, the reduction due to the increasement process accordingly extends over a longer period of time. If the calculated auxiliary discharge is above a certain discharge limit, which was determined via simulations, a higher gradient of 25 cm/h is used to generate a temporally more concentrated retention.

Once the signal of the subsiding of the flood is present at the reference level(s), the increasement process is initiated depending on further parameters ‒ e.g. maximum water level, width of the crest area, propagation times of the flood hydrographs when taking the overlapping into account ‒ whereby a time shift is considered based on the parameter size, location of the barrage and the interaction of the increasement processes at the barrages. All these values are automatically evaluated in Matlab/Simulink continuously and at specific points in time (e.g. the passage of the flood peak) as well as evaluated and forwarded using stored functions. The values and their interactions were obtained on the basis of an extensive analysis of the simulation results from the various simulation runs. The processes are initiated according to these signals. In certain cases, e.g. in the case of broad crests at the respective reference gauges, no time shift is defined and the increasement process starts at all barrages as soon as the signal about the subsiding of the flood is available.

Since the increase in the headwater with barrage management goes up to the regular impoundment target in the WOR during the passage of a flood, there is no hazard due to exceeded water levels (no overdammed backwater) compared to operation according to the WOR. Backwater effects are considered within the simulation.

3.5 Reduction of flood peaks through sole barrage management

When implementing barrage management according to the control specifications described above, the determined absolute reductions are in a range of ΔQ = 150 m³/s to 373 m³/s, which corresponds to percentage reductions of between 2 and 9%, based on the maximum discharge according to WOR at the gauge Passau Ingling (see Sect. 4.3). These discharge reductions remain at a similar height downstream of the confluence of Inn and Danube, since the flood peaks of the Inn are significantly higher.

The determined water level reductions at the Schärding gauge (related to the maximum discharge at the Passau Ingling gauge, black) and at the Passau/Danube gauge (with reference to maximum discharge at the Achleiten gauge, red) are shown in Fig. 5 for the investigated three past floods and 12 stochastic events. The effect of barrage management depends on the peak discharge of the flood as well as the hydrograph shape (e.g. crest width), whereby the possible peak reduction tends to decrease with increasing maximum discharge. Due to the total volume, about 11.5 to 20 million m³ is retained in the used reservoirs and water level reductions of 17 cm to 46 cm were determined at the Schärding gauge in the reservoir of the Passau-Ingling HPP. Directly upstream of the confluence of the Danube with the Inn at the gauge Passau/Donau the water level reductions are between 9 cm and 25 cm.

Fig. 5

Water level reduction by barrage management variant III at gauges Schärding (Inn) and Passau (Danube)

To verify the sensitivity of the developed barrage management system, various sensitivity studies were performed on different operating cases and variations of the specifications. These variations include, for example, the time shifts for the increasement process or a reduction of the drawdown (Dickel and Theobald 2022). Furthermore, different availability scenarios with malfunctioning individual plants were considered as well as the reaction to an exemplary renewed increase in the flood during the increasement process. The sensitivity studies show that the selected specifications with regard to time shifts, gradients and drawdowns are practical and well suited in their interaction, so that correspondingly high reductions of flood peaks are determined using the developed control specifications. If the drawdown is reduced by 0.5 m at the barrages of the lower Inn, the influence on the achievable retention depends on the peak discharge of the flood and a good overall reduction is also determined. The analysis finds good overall peak reduction even if individual barrages malfunction during barrage management. For the possible case of a renewed increase of the flood (e.g. for the rather unlikely case of a flood with two peaks at the Inn), a control was implemented, with which the impoundment is paused and continued when the signal is received that the flood event has subsided.

The definition and feasibility of barrage management depend on the conditions of the river and the barrages with their reservoirs. Factors that influence the possible reduction are, for example, the hydraulic conditions with regard to the volume of the reservoirs and the controllability of the barrages at higher discharges. With regard to the above-mentioned requirements, the Inn River has generally advantageous site conditions. For an implementation in practice, morphodynamic and ecological aspects have to be considered in detailed investigations, which concern, for example, the mobilization of sediments during the lowering process as well as the possible draining of shallow water zones and thus the influence on the habitat of fish and birds. Furthermore, alarm plans for flood protection are to be reviewed and, if necessary, adapted.

4 Combined operation of barrage management and polder

4.1 Implementation of an exemplary polder

In general, improved retention can be achieved by combining different flood protection measures. One important aspect is the possible interaction between the different measures and the underlying control processes, since all measures have an influence on the hydrograph shape, which in turn influences the potential retention effect of other measures. Overlapping effects in the combined operation of barrage management and polder are thus an essential aspect of the investigation of potential peak reduction. A polder was implemented in the model for this reason. The polder is located in the reservoir of the Ering-Frauenstein HPP (see Fig. 1) and is therefore in the direct operational area of the barrage management. The polder was considered as an example and not as a planned polder site.

For more realistic modeling and simulation of polder operation, different constraints were defined, e.g. the maximum polder inflow, the rate of change of the inflow depending on the water level in the polder and the hydraulic feasibility of the filling process with the presence of a sufficient gradient between the water levels of river and polder. Inlet and outlet of the exemplary polder with a total volume of 13.4 million m³ were implemented as controllable components, whereby the focus of the investigation lies on the filling process and the emptying is not simulated.

4.2 Measurement-based control specifications of the polder operation

In order to define the filling process of the polder, consideration was given to operationally available data and thus a measurement-based approach in order to operate without forecasts and the associated uncertainties. The filling process of the polder for the withdrawal of water from the Inn River is based on measured water level data from upstream reference gauges at Inn and Salzach. For the control specifications for the polder operation, the differentiation into Inn- or Salzach-accentuated floods and the consideration of overlapping and different parameters of the measured water level hydrographs is carried out in the same way as for barrage management like described, so that the filling is started as soon as flood subsidence is registered at the respective reference gauge Rosenheim II and/or Laufen. Filling begins with a specific time delay depending on the floods maximum water level and is carried out for all fifteen flood events on the basis of a predefined discharge hydrograph, which increases linearly over approximately 7.4 h, is kept constant at Q = 400 m³/s for two hours and is then reduced linearly with the same gradient, resulting in a volume to be stored of about 13.4 million m³ with a duration of the filling process of 16.7 h in total. Within the scope of sensitivity studies, different discharge hydrographs for the polder filling were considered, which differed with regard to the maximum discharge and the filling duration. The selected discharge hydrograph is applied for all flood events in the same form, regardless of the flood peak, and represents a practicable configuration due to the overall good peak reduction within the different flood simulations, but not a general optimum.

4.3 Flood peak reduction through sole and combined operation

Compared to reduction by sole barrage management (Fig. 6, crosses), sole polder operation (Fig. 6, circles) results in comparatively lower reductions of the maximum discharge in the lower flood event range, while the peak reduction determined is higher for larger floods in comparison. This is mainly due to the fact that barrage management generates a retention volume of between 11.5 and 20 million m³ in the crest area, with the retained volume tending to decrease for larger discharges. With polder operation, on the other hand, around 13.4 million m³ are available regardless of the peak discharge.

As shown in Fig. 6, the absolute peak reductions determined by a combined operation of barrage management and polder operation are significantly larger than the respective reductions with sole operation and amount to between ΔQ = 190 and 507 m³/s (quadrangles), corresponding to a percentage reduction of 4 to 12%. The reductions in the individual effects of sole operation overlap for the most part nearly additively in combined operation, as can be seen in the example of the 2013 flood. Here, the reductions in the sole operations amount to approx. ΔQ = 240 m³/s each, and the reduction for combined operation is approx. ΔQ = 440 m³/s.

Fig. 6

Absolute peak reduction of maximum discharge through sole barrage management, sole polder operation and their combination at gauge Passau Ingling

In the case of water level reductions, an almost additive overlapping of the individual effects is also evident. At the Schärding gauge in the reservoir area of the Passau-Ingling HPP (Fig. 7, crosses, with reference to gauge Passau Ingling at Inn), reductions between 23 and 68 cm were determined for combined operation, while the reductions at the gauge Passau / Danube were between 17 and 36 cm (Fig. 7, squares, with reference to the gauge Achleiten at Danube).

This means that combined operation brings about significant reductions in the neuralgic areas of Schärding and Neuhaus as well as in the city area of Passau, which are already affected by flooding and damages at lower floods. In this context, it is important to note that every centimeter of reduction in the flood peak is critical in the event of a flood.

Fig. 7

Water level reduction through combined operation of barrage management and polder at gauges Schärding (Inn) and Passau (Danube)

5 Conclusion

In the case of impounded rivers, the main question, especially after major flood events such as the 2013 flood at the Danube in Germany and Austria, arises if it is possible to use the reservoirs of the barrages for flood retention in order to reduce the flood peak by means of an intelligent control of the barrages. A literature search revealed that no studies on active flood mitigation through barrage management (targeted lowering and increasement of the headwater as an adaptive process) of run-of-river hydropower plants with low heads (below 20 m) have been documented for practical use and clearly indicates the existing need for research.

Extensive investigations and analyses, using a complex model system to represent the interactions of the operation of barrages and the flow conditions in the watercourse, were performed to consider the interrelationships between the control specifications for flood retention and discharge reduction for different floods. Operating regulations for the flood-adapted operation of barrages and the operation of an exemplary polder were then developed. Special attention was paid to operationally available data, so that the developed controlling strategies are suitable for practical operation.

The results of the study show that barrage management can contribute to flood reduction on the Inn River. In the field of flood protection and retention, barrage management is generally a complementary measure to, for example, retention areas and polders. The positive interaction with the operation of an exemplary polder in the direct area of application of barrage management and the high water level reductions at neuralgic points of the Inn and in the confluence area of the Inn and Danube, which emerged from the investigations, impressively illustrate the possible synergy effects of different flood protection measures.

In general, the method developed can also be applied to other river systems to investigate the potential for peak reduction by flood-adapted barrage operation and its superposition with further retention measures such as polders.