**1. Introduction**

This paper presents the problem of reservoir operation in the specific conditions of lowland areas. The paper focuses on special type of reservoir, whose construction has become rather popular. These are two-stage reservoirs, consisting of a preliminary sedimentation zone and a main zone. Only the main zone stores water for basic purposes of reservoir operation. The popularity of the two-stage reservoir is related to the fact that its construction reflects the nature of the reservoir sedimentation process. This feature simplifies removal of sediments without raising additional problems in the reservoir operation. Because in the past such solutions were not very popular and have become quite popular recently, the functioning of two-stage reservoirs is not understood at a satisfactory level.

The water resources in Poland compared to other European countries are relatively limited. Hence, it is important to build water reservoirs improving water balance, environmental water conditions, as well as microclimate. Typical reservoirs may be used for different purposes including drinking water supply, industrial water supply, and flood protection. Building reservoirs is economically profitable due to the production of electricity in water power plants. Reservoirs also may play an important role in tourism or as elements of the inland waterway.

The Wielkopolska (Great Poland) district is the region with the lowest rainfalls level in Poland. This is the reason why small retention is intensively developed in this area. There are 38 reservoirs classified as small retention objects. According to the Polish regulations, these are the reservoirs with storage smaller than 5 hm3. In Wielkopolska, there are also two large reservoirs with storage exceeding

5 hm<sup>3</sup> [1]. The number of reservoirs indicates the significance of the discussed problem. Additionally, it is worth noting the economic importance of the reservoirs.

Operation of the water reservoir may cause several problems. In general, processes which are difficult to control occur in the reservoir and around it. Two problems are common for small and large reservoirs. These are, (1) erosion downstream of the reservoir dam, and (2) sediment deposition in the backward part of the inflowing river [2–4]. These processes occur relatively fast and cause a direct threat of reservoir catastrophe [3,5]. Although the processes occurring in the entire reservoir volume are also very important, they are slower and less visible in general [4–7]. The sediment transport in equilibrium conditions, occurring in the inflowing river, changes when water flows into the reservoir. The sediment transport potential rapidly decreases and the stream is not able to transport the same amount of sediments. Suspended and bed-loaded grains are deposited, creating alluvial fans and deltas in the inlet part of the reservoir. The density currents influence the water circulation in the reservoir. Finally, the fine sediments deposited in the deeper parts of the reservoir reduce the available volume and change the operational conditions in the longer time horizon [8–12]. In the inlet part of the reservoir, the deposition causes a decrease in the local depths and expansion of the riparian vegetation [6,13]. In two-stage reservoirs, these processes occur in the preliminary sedimentation zone. Water pollutants are also inhibited there, which improves water quality in the main part of the reservoir. However, pollutants are frequently deposited in the sediments (e.g., heavy metals) [14–17].

The object analyzed is the Stare Miasto reservoir, located in the Powa river in central Poland. This is a lowland reservoir with specific construction of the bottom. There is a preliminary zone separated from the rest of the reservoir by an internal dam. The flow between the upper and lower parts of the reservoir is limited. The upper part is usually smaller and plays the role of the initial sediment container, whereas the lower part is greater and it is designed to provide water for the main purpose of the reservoir operation. Hence, the lower part is usually called the main reservoir. There are basic reservoir capacities (i.e., active conservation storage, flood storage capacity, flood surcharge capacity, as well as dead storage). The described solution is one of the methods applied for prevention of sedimentation and water quality degradation in reservoirs [11,18,19]. Such an approach is not prohibitively expensive, though there are also some drawbacks. From the economic point of view, separation of the upper part means the loss of its conservation or flood storage. For this reason, broad research on such reservoirs, describing their operational conditions, seems worthwhile.

Taking into account the simplicity of the described concept, it is expected that such reservoirs will be built more frequently. In literature such objects have been rarely analyzed. Two other problems are discussed: (a) water and sediment quality [15–17,19,20]; (b) reservoir sedimentation [4,5,11,21–23]. These two processes make the described reservoir construction so attractive. Today a number of two-stage reservoirs in Poland can be found, for example, the Poraj reservoir in the Warta river, the Rydzyny reservoir in the Sama river, Kowalskie Lake in the Główna river, or the new concept of the Wielowie´s Klasztorna reservoir in the Prosna river.

The basic feature of lowland reservoirs is very good vertical mixing of heat and dissolved substances. It means the lack of temperature stratification and uniform distribution of solutes along the depth. Due to the small depths, density currents caused by temperature and salinity gradients should not be present in such reservoirs. As reported by Krenkel et al. [24], the processes of heat and dissolved mass exchange in reservoirs without stratification vary in horizontal dimensions as in rivers.

Measurements and field surveys provide limited information on the spatial as well as temporal scale. The sampling techniques provide point information. Detailed description of the spatial distributions of investigated parameters (e.g., velocities, temperature, etc.) requires a huge number of such measurements and, obviously, it is time-consuming and expensive. A similar problem arises when the temporal variability of the selected parameters is formulated. The duration of the analyzed processes is important. The description of their dynamics requires continuous measurements or very frequent momentary measurements. Hence, the application of mathematical modeling in the analysis may help. Different types of models for description of river and reservoir dynamics have been applied for many years. One-dimensional (1D) unsteady flow models are the simplest models applied for reservoirs [25,26]. However, models of this kind are able to reconstruct properly only the variability of the depth in the reservoir. Other hydraulic parameters (e.g., velocities, shear stress, etc.) are determined approximately. Modeling of other processes in 1D mode for reservoirs is burdened with significant inaccuracies. Because of this, 2D and 3D modeling is more frequently used for analysis of reservoirs. In the lowland reservoir, 2D models are preferred due to relatively small depths [25,27–30]. Such an approach enables determination of quite accurate spatial distributions of basic hydraulic variables (e.g., depth and velocity) and parameters dependent on their values (e.g., shear stress, stream power, and others) [29,30]. More accurate reconstruction of the hydraulic variables range is also the basis for modeling of other processes (e.g., transport of pollutants or sediment transport). The field measurements impact the construction of the model during the procedure of identification and verification. The final product is a model giving results (e.g., depth, velocities, etc.), consistent with observations in the field. It may be applied for test computations and forecasting. Such a model may support analysis of spatial and temporal variability of the investigated variables.

The purpose of the present research is to analyze two-stage reservoir operation, with its hydraulic and operational problems. The presented approach is based on the 2D simulations of a hydrodynamic model made for a flood scenario selected from historical data. The flood wave observed between 10 April and 19 July of 2014 is used. The attention is focused on three variables identified as the measures of potential hazards: (1) magnitude of flow velocity, (2) shear stress, and (3) stream power. The role of the flow velocity in morphodynamical changes in rivers and reservoirs is well known. Such processes as sediment deposition and erosion are observed in locations of significant velocity changes (e.g., reservoir inlets, contractions in channels, etc.). The shear stress describes these processes better with the so-called incipient motion criteria. In such objects as reservoirs, the shear stresses have specific distributions, and they may be concentrated near hydraulic obstacles (e.g., dams and bridge piers). The stream power is a combination of velocity and shear stress, with potential to link the features of both variables. Hence the stream power is a basis of many sediment transport formulae applied for modeling of sediment deposition and erosion in rivers and reservoirs. The spatial distributions of these variables are confronted with the known locations of threats (e.g., internal dam almost crashed in 2014). The main assumption is that the careful analysis of such spatial distributions may help to prevent undesirable threats in the stage of reservoir design. The analyses are made for three bathymetries reconstructed for the years 2006, 2013, and 2018. The comparison of velocity, shear stress, and stream power distributions in these three moments of time could help to understand better the nature of processes responsible for morphodynamic changes in the reservoir.

#### **2. Case Study System**

Taking into account the purpose of the research, quite a specific object, the Stare Miasto reservoir in the Powa river, was chosen as a case study. The Powa is a moderately sized river flowing in the lowland of Great Poland province in the central part of Poland. The Stare Miasto reservoir was built as an element of the small retention program [31]. The purposes of this program are the improvement of watershed capacity, flood and drought protection, and prevention of a decrease in the groundwater table. The analyzed reservoir has been in operation since 2006. It is divided into two parts (Figure 1), with an internal dam located at km 12 + 000 of the Powa river. There is a regulated sluice applied to control flow through the dam. The upper zone works as a sediment trap.

The inundation area of the upper part is 27 ha and its storage equals 0.294 hm3. The lower part is the so-called main reservoir. This part is additionally split into two internal parts by highway A2 (Figure 1), running from Pozna ´n to Warsaw [32]. The watershed area of the Stare Miasto reservoir in the cross-section of the main dam is 299.7 km2. The average depth of the reservoir is 2.4 m. The estimated length of this object is 4.5 km. The inundation area for the minimum headwater level (MinPP = 92.0 m a.s.l.) is 75.77 ha. For the normal headwater level (NPP = 93.5 m a.s.l.) the inundation area is 90.68 ha. The maximum headwater level (MaxPP) is 94.0 m a.s.l. The total reservoir capacity is 2.159 hm3. The active conservation storage is 1.216 hm3. The inundation area of the upper zone is 13.62% of the total water surface area. The land use in the neighborhood of the reservoir agriculture. Because the usefulness of the terrain is limited, crop production has been stopped in this region [32,33]. The reservoir is working in an annual compensation cycle, which may cause annual variation in the water level, from MinPP to NPP. The operational water level is from 92.00 m a.s.l. to 94.00 m a.s.l. The reservoir is filled in March and the water surface is kept at the level of NPP until the end of October. After October, the main reservoir is emptied to the level of MinPP. To protect the inlet part from degradation and sediment accumulation, the water surface in the upper part is kept at the NPP level for the entire year.

**Figure 1.** Chosen case study—Stare Miasto reservoir on the Powa river: (**a**) The reservoir and its main elements—internal dam, highway bridge, and main dam; (**b**) the watershed with main elements—river, reservoirs, and gauge station.

**Figure 2.** Variability of discharge at the Posoka gauge station, (**a**) for the period 1971–2017; (**b**) for the year 2014.

In the Powa river there is one gauge station called Posoka (Figure 1b). This is located downstream of the reservoir at km 3 + 900 of the Powa course. The watershed area in the cross-section of the gauge is 332 km2. The characteristic flows were determined on the basis of recorded observations at this gauge station during the period 1975–2017 [34]. The results are presented in Figure 2. The total minimum observed was 0.006 m3/s, while the total maximum was 42.6 m3/s. The mean flow was about 1.15 m3/s. During the time of reservoir operation, from 2006 to 2017, the maximum flow of 28.5 m3/s (Figure 2b) occurred in 2014. The minimum and mean flows did not differ much from those estimated for the entire period. In the analyzed period, the average annual outflow from the reservoir was 36.9 hm3.
