Introduction

Over the past few decades, the world's population has grown significantly, resulting in an even greater increase in water consumption. Since the 1960s, the world's population has grown by 4 billion people, the corresponding demand for water has increased sixfold, and total water consumption has more than doubled (Otto and Leah 2020). Therefore, the need for efficient management of water resources is more urgent than ever. This problem is more intense in the Mediterranean area. The Mediterranean region has special hydrological and demographic characteristics. It is inhabited by more than 7% of the world's population and water resources are not homogeneously distributed. Water scarcity is mainly concentrated on the southern shores of the Mediterranean, but long periods of drought have been observed in the northern regions. Water scarcity has also been exacerbated by the overexploitation of available water resources, the reduction of reservoir capacity due to sediment accumulation in reservoirs, and the deterioration of surface and groundwater quality due to pollution (Kibaroğlu 2017). At the same time, the preservation of the ecosystem is another issue that has to be considered (Jorda-Capdevila et al. 2019).

In modern water resources management, hydrological simulations are used extensively in many cases. The most typical of these are related to water balance estimation, hydropower assessment, flood forecasting, water quality assessment, and, in recent years, climate change adaptation. Regarding water balance estimation, hydrological models can be used to assess the impacts of different hydrological components on the water balance (Srivastava et al. 2020; Shawul et al. 2019). To optimize hydropower generation, hydrologic models can be useful for assessing hydropower potential and better understanding reservoir operating rules (Fasipe et al. 2021; Eldardiry and Hossain 2019). For flood forecasting, hydrological models are used for both long-term (Wang et al. 2019; Sahraei et al. 2020; Wijayarathne and Coulibaly 2020) and real-time flood events (Zanchetta et al. 2020). Hydrologic models are also key components of the nonpoint source identification process and can help us to understand, assess, and predict the negative impacts of nonpoint sources on water quality (Yuan et al. 2020; Strokal et al. 2019). Climate change exacerbates the above problems and disrupts the hydrological cycles of river basins due to the increase in temperature caused by the phenomenon of global warming, which is associated with the disruption of the frequency and intensity of rainfall under given climatic conditions (IPCC 2017). This affects hydrological events and the availability of water resources (Mujere and Eslamian 2014). Therefore, climate change has led the scientific community to turn to hydrological modeling to assess, among other things, how climate change will affect river flows (Tessema et al. 2021) and to analyze the risk of climate change impacts (Swain et al. 2020).

The impacts of climate change in the Mediterranean area have been observed, analyzed, and commented on by several researchers (Cramer et al. 2018; Tramblay et al. 2020; Mimikou and Baltas 2013; Baltas and Mimikou 2005; Mimikou et al. 1999). In general, climate change is expected to result in less water being available for use in agriculture, energy production, and urban and industrial use, while riparian ecosystems will also suffer (Kibaroğlu 2017; Rocha et al. 2020). Reduced water supplies will affect major domains like agricultural production (Fraga et al. 2021; Pozo et al. 2019; Abd-Elmabod et al. 2020) and public health (Cramer et al. 2018; Linares et al. 2020). Therefore, and for the reasons mentioned above, the use of hydrological models is necessary to gain a clear understanding of the flow regime and to predict future water availability in any river basin.

All the issues mentioned so far also concern the Aliakmon River basin, which is the largest river in Greece and the main source of economic and social well-being for the people living not only in the river basin itself, but also in the adjacent areas. This is because the economic and social activities of the people living in the wider region are based on climate-sensitive sectors like agricultural production, the water supply in major urban areas, and hydropower power generation (Ministry of Environment—Special Water Secretariat 2014).

According to Lastoria (2008), hydrological models can be classified into three main categories based on how the physical processes are simulated. These model categories are lumped, distributed, and semi-distributed models. Lumped models treat the river basin as a single entity, and therefore their parameters are constant over the entire catchment area. Consequently, a lumped model can only simulate the response of the river basin at its outlet (Lastoria 2008). Distributed models, in contrast to lumped models, provide the ability to vary the watershed parameters in space at the desired resolution, which is related to the needs of the model as defined by the user. In this way, these models attempt to simulate the rainfall–runoff relationship within the watershed and, in most cases, produce fairly accurate results. The disadvantage of distributed models is that they require a very large amount of data, which is often difficult to collect (Pechlivanidis et al. 2011). Finally, semi-distributed or simplified distributed models can vary their parameters in space by dividing the basin into a number of smaller sub-basins. The main advantages of these models are that their structure is more based on physical processes compared to the structure of lumped models, and they are less demanding on input data than fully distributed models (Orellana et al. 2008). SWAT (Soil and Water Assessment Tool) (Arnold et al. 2012), HBV (Hydrologiska Byråns Vattenbalansavdelning) (Bergstrom 1995), and HEC–HMS (Hydrologic Engineering Center–Hydrologic Modeling System) (Bartles et al. 2022) are the most well-known examples of semi-distributed models.

The HEC–HMS (Hydrologic Engineering Center—Hydrologic Modeling System) model is developed by the Hydrologic Engineering Center (HEC) of the US Army Corps of Engineers (Bartles et al. 2022), and it is used to simulate the rainfall–runoff relationship for dendritic watersheds in space and time. Applications of HEC–HMS include urban flooding analysis, flood frequency analysis, flood warning system planning, reservoir spillway capacity analysis, stream restoration, etc. HEC–HMS has a user-friendly graphical user interface (GUI) and is available in the public domain, and for these reasons it has become a popular and useful tool for hydrologists. The HEC–HMS model has been used with great success to simulate river basins in many different parts of the world (Gumindoga et al. 2017; Yusop et al. 2007; Natarajan and Radhakrishnan 2019; Chea and Oeurng 2017; Bhuiyan et al. 2017; Ouédraogo et al. 2018), but the wider use of the model has been inhibited by factors such as the uncertainty involved in estimating the parameters of the model (Kalita 2008).

In this paper, HEC–HMS is used for the formulation of a simulation model of the Aliakmon River basin. More specifically, the model of the river is based entirely on free software (HEC–HMS, HEC–DSSVue, HEC–Vortex, and QGIS) and data available from free databases that are mostly available online. These free data allowed the estimation of the model parameters and helped a lot in dealing with the uncertainty in determining the model parameters. As discussed in the “Results” and “Discussion” sections, the hydrological model created shows an excellent capability to represent the flow of the river under study and could be useful for applications related to the management of the reservoirs present on the river, energy production, water supply, as well as flood forecasting. Thus, this model will be useful for the development of water management policies for the river, which, as already mentioned, is the longest river in Greece and very important for the economy and the well-being of the people that live in the area. Such management policies will, by extension, be useful for achieving Sustainable Development Goal 12 (SDG 12), thus ensuring sustainable patterns of production and consumption (United Nations 2023). In particular, the model can be used to analyze both long-term and short-term scenarios by taking advantage of the new features of the latest versions of the US Army Corp of Engineers–Hydrologic Engineering Center (HEC) software (HEC–HMS, HEC–DSSVue, HEC–Vortex), which can be scripted, giving the software the ability to automatically connect to online meteorological (forecast) databases and extract data from them.

Materials and methods

In this section, the study area is first described, and then the structure and data used to develop, calibrate, and evaluate the hydrologic model are reported. The methods selected and the assumptions made in formulating the model are then briefly described.

Study area

The model presented in the following was developed for the Aliakmon River, which is the largest river in Greece and is located entirely on Greek territory. It has a total length of 297 km, while its basin has an area of approximately 11,000 km2 (Ministry of Environment—Special Water Secretariat 2014). Figure 1 shows both the river basin and its hydrographic network. Figure 1 also shows that the river basin is essentially divided into three major sub-basins. The western one corresponds to the main stem of the river, the eastern one corresponds to the largest tributary of the Aliakmon, and there is also a central one.

Fig. 1
figure 1

Aliakmon River basin

Full size image

The topography of the Aliakmon River basin is mountainous/semi-mountainous, with an average altitude of 750 m; high peaks dominate, with some of them exceeding 2000 m. The mountainous terrain is easily distinguished by the distribution of slopes, which range from 5 to 148%, with an average slope of 18%. This, combined with the sedimentary formations, leads to intense erosion and sediment transport to the river delta. A characteristic feature of the river is the wide range of elevation differences along parts of the river basin (Ministry of Environment—Special Water Secretariat 2014). On the other hand, the climate of the study area is generally mild. Rainfall is higher in the winter months and temperatures can reach very low levels in some areas, while snow falls mainly in the mountainous areas.

On the main stem of the river there are five large reservoirs that are used for power generation and to meet the irrigation and water supply needs of the wider region. The locations of the dams and reservoirs are also shown in Fig. 1, while Table 1 presents their main characteristics (the table shows them in the order in which they are located along the river from upstream to downstream) (Karagiannidis et al. 2008; Mpakanos and Katsifarakis 2018).

Table 1 Characteristics of the Aliakmon dams and reservoirs
Full size table

The main tributary of the Aliakmon is the Almopaios River. In the past, the Almopaios River flowed into the Lake of Giannitsa, which in turn passed the waters to the Loudias River, which is located east of the Aliakmon, but in 1930 drainage works were carried out in the area, which caused the lake to dry up and the Almopaios to divert into the Aliakmon. Today, the Almopaios River joins the Aliakmon River about 40 km before its mouth, a few kilometers downstream from the last of the large dams (the Agia Varvara dam), which, as already mentioned, were built along the main stem of the river.

The surface runoff of the central part of the Aliakmonas catchment, as shown in Fig. 1, is concentrated in Lake Vegoritida. This lake used to overflow into the Almopaios River, but in recent years the level of the lake has dropped dramatically, so there is no outflow from the lake into the river.

As shown in Fig. 1, the main stem of the river is completely controlled by the dams built along its course. As will be discussed further in the following sections, this is the reason why, when estimating the river flow near its estuary, the hydrological model can be limited to simulating the flow of the Aliakmon tributary, Almopaios, by including the controlled outflows of the Asomata dam.

The outflow of the Asomata reservoir flows into the Agia Varvara regulating reservoir. From there, large quantities of water are diverted through the A0 canal (Fig. 2) to the Thessaloniki plain, mainly during the summer months, to meet the irrigation needs of the fields in the wider area. In addition, a significant amount of water (about 2–3 m3/s) is diverted to the city of Thessaloniki throughout the year to meet the city's water needs.

Fig. 2
figure 2

Agia Varvara reservoir and the irrigation channel Α0

Full size image

In addition, the Makrokhori hydroelectric power plant is located on the A0 irrigation canal. The Makrokhori hydroelectric power plant is in operation throughout the year, so the amount of water flowing through the A0 irrigation canal is greater than the irrigation needs of the area. As shown in Fig. 2, the A0 canal is connected at some point to the Aliakmnonas River in order to return the excess water that is not needed for irrigation and the water supply to this canal. Downstream of the Agia Varvara dam, a small hydroelectric power plant is installed to harness the ecological flow of the river. It has a constant flow rate of 4.5 m3/s. When the water entering the Agia Varvara reservoir from the Asomata dam is more than the water diverted to the A0 canal and the ecological flow, it overflows through the dam's spillways.

Input data

In order to develop a model in HEC–HMS, it is necessary to first define the hydrographic network of the river and the corresponding sub-basins, and then to estimate the parameters of all the methods used by the software to simulate surface runoff. Thus, a digital elevation model, the European Digital Elevation Model (EU-DEM), version 1.1, was used for the identification of the hydrographic network and sub-basins of the Aliakmon River. This digital elevation model is provided by the Copernicus service of the European Union (2016). EU-DEM v1.1 is available as Geotiff 32-bit digital image files. It is a continuous dataset covering almost all of Europe, and is divided into raster-type files, each corresponding to an area of 1000 × 1000 km. Each pixel corresponds to an area of 25 × 25 m with a vertical accuracy of ± 7 m mean square error.

To estimate the parameters of the surface runoff simulation methods, data describing the hydraulic characteristics of the soil are used. These data are provided by the European Soil Data Centre (ESDAC) of the Joint Research Centre. In the current study, the 3D Soil Hydraulic Database of Europe at 1 km and 250 m resolution was used (Tóth et al. 2017), as well as land-use data from the European Union's Copernicus service (European Union—Copernicus Land Monitoring Service—European Environment Agency (EEA) 2018). In particular, the Corine Land Cover 2018 database was used, but also the additional high-resolution layers providing information on soil imperviousness, forest and tree density, water surfaces, and grasslands.

The meteorological data used for the calibration and evaluation of the model were taken from the ERA5-Land Hourly Data from 1950 to Present database, and were obtained from the Copernicus service of the European Union (Muñoz 2022).

In addition, since no data were available on the water discharged from the dams, the approach proposed by Skoulikaris and Krestenitis (2020) was followed. Specifically, for the calibration of the model, data on electricity production (in hourly time steps) as well as data on the reservoir filling rate, available online at the website of the Greek Independent Power Transmission Operator (IPTO; https://www.admie.gr/en), were used. Based on these data, the average daily discharge of the Asomata reservoir, which is located upstream of the Agia Varvara reservoir, was estimated. In the same way, the flow diverted to the A0 canal was estimated through the electricity production of the Makrochori hydropower plant.

Figures 3 and 4 present the average daily flows estimated from the electricity production data for the year 2018 for the Asomata and Makrokhori hydropower plants, respectively. Obviously, the flow estimated for the Makrokhori hydropower plant corresponds to the total amount of water diverted from the Agia Varvara reservoir to the A0 canal, since there is no water abstraction before the aforementioned hydropower plant. A key feature of the two figures is that the flow varies greatly from day to day, mainly due to fluctuating electricity generation needs, and it also appears that there is a seasonality in the average flow rate. Finally, it is evident that the increase in flow in the period between April and September is due to an increasing demand for irrigation water.

Fig. 3
figure 3

Estimated discharge of Asomata dam based on 2018 electricity production

Full size image
Fig. 4
figure 4

Estimated flow of the A0 canal based on the 2018 electricity production of the Makrochori hydropower plant

Full size image

Regarding the quantities of water diverted from the Aliakmon River to the Loudias River basin to meet the irrigation and water supply needs, data obtained from the General Organization for the Improvement of the Plains of Thessaloniki—Lagadas were used.

Figure 5 shows the daily amount of water diverted from the Agia Varvara reservoir through the A0 canal to meet the water supply and irrigation needs. As shown in Fig. 5, during the winter months, a constant flow of 2 m3/s is diverted to meet the water supply needs of the city of Thessaloniki, while during the spring and summer months, the amount of water diverted increases and reaches 50 m3/s in July and August, which are the months with the highest demand for irrigation water. It is worth noting here that the magnitude of the irrigation demand is proportional to the increase in the flow rate observed both in the Asomata dam outflow and in the A0 canal flow rate, which, as already mentioned, are estimated from their power generation.

Fig. 5
figure 5

Water supply and irrigation needs of the Thessaloniki plain for 2018

Full size image

Figure 6 shows the estimated average daily flow of water returned to the Aliakmon River from the A0 irrigation canal. This magnitude of flow was not available anywhere but was estimated from the difference between the total daily flow of the A0 canal (Fig. 4) and the water supply and irrigation demand (Fig. 5). In Fig. 6, it is evident that the average daily flow diverted back to the Aliakmon River decreases to a very large extent during the summer period, except for some occasional cases that probably correspond to some heavy rainfall episodes that temporarily reduced the irrigation needs.

Fig. 6
figure 6

Excess flow of the A0 canal diverted back to the Aliakmon River in 2018

Full size image

Figure 7 shows the estimated average daily flow of the water released from the Agia Varvara dam, either by the small hydroelectric power plant located there which, as mentioned above, harnesses the ecological flow of the river, or by spillages of water that cannot remain in the reservoir due to its limited capacity. Figure 7 shows that the average daily flow has a minimum value of 4.5 m3/s, which corresponds to the ecological flow of the river and shows large seasonal variations that follow the variation of the flow of the Asomata dam. As there are no data available for the discharge of the Agia Varvara dam, the magnitude of the flow shown in Fig. 7 was estimated from the flows of the Asomata dam and the A0 canal, assuming that, due to the small volume of the reservoir, the volume of water remaining in it on a daily basis remains constant.

Fig. 7
figure 7

Estimated discharge of Agia Varvara dam based on the ecological discharge plus the excess water for 2018

Full size image

Finally, the calibration and evaluation of the hydrological model was based on the data from the monitoring station, which belongs to the Soil and Water Resources Institute (SWRI; Hellenic Agricultural Organization “DEMETER”) and is located near the estuary of the Aliakmon River. From the monitoring station, measurements of the river discharge were taken at half-hourly intervals from 2018 to 2021. At this point it should be emphasized that the station records the water level in the riverbed, and the flow rate is calculated through a water level–flow rate relationship estimated by the station operators.

Basin model formulation

As already mentioned, the water flow in the main stem of the river is fully controlled due to the operation of the five large reservoirs. It is obvious that for the estimation of the river discharge near the estuary it is not necessary to include the main river branch in the model. Thus, the hydrological model was formulated in HEC–HMS in the way shown in Fig. 8. In particular, it was assumed that there is a water source at the location of the Agia Varvara regulating dam, which corresponds to the outflow of the dam. For the purposes of the following analysis, the discharge from this water source is derived from the processing of the data obtained from the IPTO, as already mentioned.

Fig. 8
figure 8

The hydrologic model formed in HEC–HMS

Full size image

The formulation of a hydrological model in HEC–HMS first requires the identification of the sub-basins and the hydrographic network of the basin and then the selection of methods that replicate the physical processes that take place during the conversion of precipitation into surface runoff. The basin model was formulated using the new GIS features of HEC–HMS. Thus, the drainage network and sub-basin boundaries of the study area were defined. During this process, HEC–HMS also computes all the geometric parameters of all sub-basins and reaches, such as sub-basin area, sub-basin slope, longest flowpath length, centroidal flowpath length, and stream channel length and slope. The values of these parameters are then helpful in determining the parameter values of the simulation methods of the physical processes that take place in each sub-basin of the river basin. The physical processes selected for simulation, the methods used, and how the parameters of these methods were calculated are discussed below.

Canopy method

The canopy method is one of the elements that can be included in the simulation of sub-basins and represents the presence of plants within them (Chea and Oeurng 2017). Plants retain rainfall with their foliage, thus reducing the amount of water reaching the soil surface. The water retained by plants evaporates between two rainfall episodes and therefore does not eventually reach the watercourses. According to the HEC–HMS user manual (Bartles et al. 2022), the choice of a canopy method for the simulation of sub-basins is optional, but it should be used for continuous simulation applications. In this paper, the simple canopy method was chosen to link the hydrological model to the physical problem as accurately as possible. The estimation of the values of the method parameters for each sub-basin was done in QGIS using the land-use data (both Corine land cover and the high-resolution layers) obtained from the Copernicus Land Monitoring Service (European Union—Copernicus Land Monitoring Service—European Environment Agency (EEA) 2018). In particular, the percentage of the total area covered by vegetation and the impervious areas were calculated to estimate the amount of precipitation that can be retained by vegetation (Zinke et al. 1967).

Surface method

The surface method represents the natural process whereby rainwater is concentrated in areas where the soil is disturbed and cannot drain away from the surface (Chea and Oeurng 2017; Grimm et al. 2019). The amount of rainwater retained on the soil surface depends directly on the nature of the soil, but also on the amount of vegetation cover. For example, a field can retain quite large amounts of water. Water that accumulates on the soil surface infiltrates the soil as long as it is not saturated with water. Surface runoff will occur when the rainfall rate exceeds the infiltration rate and the cavities on the soil surface are filled with water. According to the HEC–HMS user manual (Bartles et al. 2022), the choice of a surface method for the simulation of sub-basins is optional and is usually used in continuous river flow simulation applications. In the present work, in order to link the hydrological model to the physical problem as accurately as possible, the simple surface method was chosen for use. From all of the above, and according to the literature (Pozo et al. 2019; Abd-Elmabod et al. 2020), the amount of water retained on the soil surface depends directly on the slope of the ground. Thus, the values of the method parameters for each sub-basin were calculated proportionally from the ground slope in QGIS according to the limits suggested in the literature (Pozo et al. 2019; Abd-Elmabod et al. 2020).

Loss method

The loss method represents the process of water infiltration into the soil. HEC–HMS can simulate the infiltration of water into the soil by several methods (Al-Mukhtar et al. 2019; Fanta and Sime 2022). Some of these methods are more suitable for simulating single rainfall events, while others are more suitable for continuous simulation. Since the scenarios presented in this paper are single rainfall events, the initial and constant method, which is suitable for simulating such events, was chosen. The parameters that need to be calculated for each sub-basin in order to apply the initial and constant method are the initial losses, the constant loss rate, and the percentage of the sub-basin area covered by impervious surfaces (Bartles et al. 2022). The values of the method parameters for each sub-basin were calculated in QGIS. The values of the initial loss and the constant loss rate were obtained by appropriately processing data from the 3D Soil Hydraulic Database of Europe at 1 km and 250 m Resolution. The percentage of the catchment area covered by impervious surfaces was obtained after processing the corresponding high-resolution raster file obtained from the Copernicus Land Monitoring Service.

Transform method

The transform method represents the surface runoff process (Fanta and Sime 2022). This method simulates the process by which rainwater that is not retained by vegetation or soil cavities is concentrated, and drains through the ground surface into basin streams. HEC–HMS has several alternative methods for simulating this process in this case as well. The method chosen for the model of the Aliakmon River basin presented in this paper is the Clark unit hydrograph method. The application of this method requires the calculation of two parameters: the time of concentration and the storage coefficient. The time of concentration is calculated using the following equation (Bartles et al. 2022):

$$\begin{array}{*{20}c} {T_{c} = 2.2 \cdot \left( {\frac{{L \cdot L_{c} }}{{\sqrt {Slope_{{10 - 85}} } }}} \right)^{{0.3}} } \\ \end{array} ,$$
(1)

where Tc is the time of concentration (h); L is the longest flow path length (mi); Lc is the centroidal flow path length (mi); and Slope10−85 is the average slope of the longest flow path when only the part of the path from the point 10% along the path to the point 85% along the path is considered (ft/mi). All the information required to calculate the time of concentration was automatically derived by HEC–HMS during the sub-basin boundary determination process. On the other hand, the storage coefficient R is calculated according to the HEC–HMS user’s manual (Bartles et al. 2022) by the following equation:

$$\begin{array}{c}\frac{R}{{T}_{\text{c}}+R}=0.65 \end{array}.$$
(2)

Baseflow method

The base flow method is the last of the methods that describe the physical processes that lead to the formation of the surface runoff. In particular, the base flow method represents the flow of water that occurs below the ground surface. It calculates the amount of rainwater that first infiltrates into the soil and then returns to the surface. Among the available baseflow methods, the linear reservoir method was chosen for use because it is the only baseflow method that conserves mass within the sub-basin (Bartles et al. 2022). The linear reservoir method assumes that there is one (or more) underground reservoir(s) that supplies water to the baseflow. The inflow to the linear reservoirs is the Infiltration or percolation computed by the loss method. To apply this method, it is necessary to determine, for each underground reservoir and each sub-basin, the parameters relating to the percentage of rainwater that initially infiltrates into the ground but eventually returns to the surface via the linear reservoir, and the time that this process takes. The values of these parameters were obtained after testing during the model calibration process.

Reach routing method

Reach elements conceptually represent the segments of the river that are modeled within HEC–HMS. Therefore, the reach routing method describes the water flow within a stream. Among the available methods for the model presented in this paper, the Muskingum–Cunge method was chosen for use. The parameters required for the application of this method were estimated through GIS, and a single value for the Manning coefficient of 0.035 was used.

Meteorological data

The meteorological data used for the calibration and the validation of the hydrological model, as already mentioned, have been obtained from the ERA5-Land Hourly Data from 1950 to Present database. These data are provided by the Copernicus service in the form of GRIB files with a horizontal resolution of 0.1° × 0.1°, i.e., a native resolution of 9 km. The grid files were processed appropriately with the HEC Vortex software to produce precipitation time series with a time step of 1 day for each sub-basin. Thus, one rain gage was created for each sub-basin for the meteorological model, and the specified hyetograph method was adopted for the precipitation.

More specifically, to calibrate the model, the corresponding data for the year 2018 were used. Then, the data for the hydrological years 2018–19, 2019–20, and 2020–21 were used to validate the model. Figure 10 shows the hyetograph of 2018, which corresponds to the rainfall received by sub-basin 47 (Fig. 9).

Fig. 9
figure 9

Precipitation time series for the year 2018 at sub-basin 47

Full size image

Evapotranspiration was also included in the simulation. The method used to simulate evapotranspiration was the Hamon method, because it is a simple method and the only requirement is the time series of the average temperature for each sub-basin, which was also obtained from the ERA5 database for the time ranges mentioned above.

Model evaluation

The model calibration and validation were conducted using computed and observed mean daily flow data at the site of the monitoring station. All parameters were adjusted by manual calibration. It should be noted that an attempt was made to calibrate the model through the optimization algorithms available in HEC–HMS. Unfortunately, the program failed to converge to a better solution, probably due to the nature of the input data.

There are many performance metrics that have been developed to evaluate the efficiency of a hydrological model calibration (Hall 2001; Krause et al. 2005; Bardsley 2013). The hydrological model was calibrated in order to achieve the best possible values for all performance metrics automatically calculated by HEC–HMS. These performance metrics are the root mean squared error ratio (RSR), Nash–Sutcliffe Efficiency (NSE), percent bias (PBIAS), and the coefficient of determination (R2) (Bartles et al. 2022). The values of these metrics were evaluated according to the evaluation criteria shown in Table 2 (Bartles et al. 2022; Singh et al. 2005; Chung et al. 2002).

Table 2 Model performance evaluation criteria (Bartles et al. 2022)
Full size table

Results

The results obtained for all the time periods studied are presented below. In particular, Fig. 10 shows the flow of the Almopaios River, while Fig. 11 shows the flow of the Aliakmon River as estimated by the model compared to the flow observed at the location of the monitoring station for 2018. Figure 10 is presented to make it clear how the river flow shown in Fig. 11 results from a combination of the inflow from the Almopaios River, the outflow from the Agia Varvara dam, and the water diverted from the A0 canal back to the Aliakmon riverbed. As shown in Fig. 11, but also in Table 3, the fit of the model to the data is very good.

Fig. 10
figure 10

Computed discharge from the Almopaios River in 2018

Full size image
Fig. 11
figure 11

Observed flow versus computed flow for 2018 (calibration period)

Full size image
Table 3 Model performance statistics for all time periods
Full size table

In particular, Table 3 shows that all the performance metrics used to evaluate the performance of the model indicate that the model provides a very good fit to the observed data for all time periods except hydrologic year 2019–20. Looking closely at Fig. 11 (but also at Figs. 12, 13, 14), we can see that the model follows the trends in the periodicity of the river flow magnitude, and it is important to note that it shows the peaks on exactly the same days. On the other hand, it is noticeable that in all the periods when the river flow increases significantly (above 150 m3/s), the model underestimates the magnitude of the flow, and moreover, as the river flow increases, the difference between the calculated flow and the observed flow increases. This is due to two possible reasons: (a) it is possible that in some cases that the Asomata dam released water through its spillways, and as a consequence these amounts of water could not be estimated through energy production; or (b) this is an indication that the water level–flow rate relationship used by the monitoring station operators overestimates the flow rate for high water levels. On the other hand, for the periods where small deviations of the river discharge values from the observed values occur, the most likely interpretation is that it is due to the assumption of a constant level of the Agia Varvara reservoir.

Fig. 12
figure 12

Observed flow versus computed flow for the hydrological year 2018–19

Full size image
Fig. 13
figure 13

Observed flow versus computed flow for the hydrological year 2019–20

Full size image
Fig. 14
figure 14

Observed flow versus computed flow for the hydrological year 2020–21

Full size image

The same pattern is present for the three hydrological years through which the reliability of the model calibration was checked. In particular, Table 3 shows that the model was assessed and found to be very good for all performance metrics for the years 2018–19 and 2020–21, while for the year 2019–20, it was assessed and found to be very good for two of the four indicators and good for the remaining two indicators.

Discussion

From the results of the simulation of the Aliakmon River flow presented in the previous section, it is clear that the hydrological model developed here provides very good performance. The model performance metrics presented in Table 3 show that the model provides very good performance for both the calibration and evaluation periods for which it has been tested (Bartles et al. 2022). It is important to emphasize here that this good model performance was achieved without the need to use an optimization model to calibrate the model parameters. This was due to the abundance of high-resolution and high-quality free data used for the initial estimation of the model parameters. This made the process of the manual calibration of the model easy and relatively short.

Similar models have been developed for many rivers around the world, and the performance of this model was similar to them (Ren and Cao 2023; Cahyono and Adidarma 2019; Verma et al. 2022; Fanta and Tadesse 2022). This model was also validated over a long period of time (3 years), as is common for similar models reported in the international literature (Chea and Oeurng 2017; Fanta and Tadesse 2022; Chakraborty and Biswas 2021). The very good performance of the model allows it to be used as a basis for the formulation of management tools for the Aliakmon River basin.

However, the greatest value of this model is its potential for use in the study of the impacts of climate change. The simulation of all physical processes included in the model will be very useful for uncertainty analysis and policy formulation (Worku et al. 2021; Das et al. 2018), and could also be combined with other modern tools that integrate new ideas into strategic planning for adaptation to the impacts of climate change (Papamichael et al. 2022).

The model presented in this paper, as outlined in Sect. “Study area,” differs from most models found in the literature because of the water diversions included in the Aliakmon River model. For this reason, it depends heavily on a wide range of data related to water use for power generation, irrigation, and water supply, which in some cases are not available. To compensate for the missing data, some assumptions have to be made. In the case of the hydrological model of the Aliakmon River, these missing data were those related to the quantities of water released from the dams through the spillways and the data on the level of the Agia Varvara reservoir. Therefore, in a similar case, one would need to obtain the relevant data and then follow the procedure described in this paper.

It follows from the previous paragraph that the performance of the model can be further improved because the daily variation of the water level of the Agia Varvara reservoir, which is a crucial influence on the model’s performance, is not yet included in the model because data on this water level variation are not freely available at this time.

On the other hand, it is obvious that, given the way the hydrological model is set up at this point, it can be used to formulate management alternatives with a daily time step. This is clearly a serious disadvantage for electricity production in particular, as it is clearly important to be able to determine more precisely when electricity will be produced during the day. However, it is also possible to improve the model and provide more detailed results regarding the time step. This seems feasible since both meteorological data (from ERA5) and electricity production data (from IPTO) are available with a time step of 1 h. In this case, it will probably be necessary to recalibrate the hydrological model, which would require the availability of data on the level of the Agia Varvara reservoir.

Conclusions

In this paper, the way in which the hydrological model of the Aliakmon River basin was formulated using the HEC–HMS software was presented in detail. The model was calibrated for 1 year and evaluated for a long time period of 3 years, and demonstrated very good performance. This model can now be considered as an essential part of a set of management tools for the Aliakmon River basin. The model can be linked to online meteorological and energy production databases and, through the development of an optimization algorithm, one could identify and promote strategic management alternatives for the Agia Varvara reservoir.

Once the coupling between the model and the optimization algorithm is completed, this new management tool can be implemented to investigate rational management scenarios for the optimal operation of the Agia Varvara reservoir, focusing on irrigation planning for the agricultural land in the region as well as flood prevention. The adjustment of the model with input data as well as climate change estimates can be implemented to take into account the possible impacts of climate change and thus evaluate the necessary adaptation measures.

Furthermore, this work has also demonstrated that HEC–HMS is still a modern and efficient tool that, in combination with the quantity, quality, and variability of freely available data, is able to produce reliable estimates of river flow. All of the above, combined with the additional features added to the latest versions of the software by its developers, such as the automatic connection to databases through which it is able to download data from the web, and with the available optimization tools, makes it an important component of a management model of a river basin, such as a digital twin of the river.

There are two issues that should be addressed in future research. The first is the fact that the model of the Aliakmon River described in this paper is essentially concerned with the management of the Agia Varvara reservoir only. This is the smallest reservoir of the river. Based on the encouraging results presented here, the hydrological model should be extended to the whole river. The second issue is the time step of the model. At this point, the simulation uses a daily time step. As discussed above, since the necessary data are available,another step to improve this model will be to adapt the model to simulate the river flow with an hourly time step.