1. Introduction
Despite numerous international water agreements, treaties, and joint cooperation protocols (more than 688) aiming to shed light on cooperation issues and prevent uncontrolled disputes [
1], recent history reveals grey areas among riparian states concerning the management of their shared waters. The Nile transboundary river basin serves as a characteristic example of the water conflict situation among Ethiopia, Sudan, and Egypt. However, the water conflicts are non-violent components of the political conflict regarding the management of the Nile River’s water [
2], since international frameworks and research on water conflict and cooperation, aimed at mitigating and adapting to water problems, have played a crucial role in recent decades in smoothing out tensions and preventing violent conflicts [
3]. Nonetheless, the risk of conflict remains and will potentially increase as the population grows, water use intensifies, and climate change is un unmet reality [
4]. Coordinated and cooperative management of international rivers can be secured when it is based on solid ground derived using knowledge of the hydrosystem’s data and behavior [
3,
5], as clearly mentioned in the United Nation Economic Commission for Europe convention on the protection and use of transboundary watercourses and international lakes [
6].
According to the latest data, there are currently 286 international river basins globally shared by 151 countries [
7]. At the European scale, there are 72 designated transboundary basins, with Greece sharing the waters of five rivers with neighboring countries. The water governance of the countries that further belong to the European Union (EU) is strictly controlled by the well-known Water Framework Directive (WFD) and implemented through the River Basin Management Plans (RBMPs) [
8]. The outputs of these strategic documents are based on water-related data and information, and expressed through environmental and water balance indexes. However, WFD’s primary aim is water quality rather than quantity issues, resulting in limited knowledge about the available river runoffs in several EU Member States. For instance, in Greece, the transboundary rivers and their tributaries are not regularly monitored, making them either completely or partially ungauged [
9]. Moreover, and despite the emergence of spatiotemporal coverage from remote sensing water-related products, their validation and ground truth rely on observations [
10,
11]. The limitation on discharge observations could thus compromise the precision of the RBMPs’ outputs and pose an obstacle to sustainable and coordinated management of the transboundary waters.
The use of large-scale hydrological models (LSMs) is an emerging advancement in Earth system modeling and climate impact assessment [
12], since they address water management challenges, such as global water security, by expanding the scope of modeling from the catchment scale to continental and global domains [
13]. Initially designed for flood predictions and early warning systems across large geographical areas [
14], LSMs have seen their utility expand to include long-term simulations across diverse environments when provided with relevant long-term input time series [
9]. LSMs, much like traditional catchment-scale models, rely on a variety of input parameters, such as topographic characteristics, meteorological variables, and land uses, which are sourced from global datasets [
15]. Moreover, the computational capabilities of modern computers enable the simultaneous modeling of various spatiotemporal resolutions representing multiple river basins [
16,
17]. However, unlike catchment models, LSMs are typically only partially calibrated due to the limited availability of gauges compared to the vast number of catchments that need to be simulated. Therefore, these models are based on efficient parameter regionalization, which involves transferring well-defined model parameterization to basins lacking gauge stations but with similar characteristics [
18], while their validation primarily relies on flow signatures [
19]. In the context of international rivers, LSMs prove particularly valuable, as the lack of knowledge about neighboring riparian waters, coupled with limited communication channels [
20], poses a significant challenge to hydrological simulations at transboundary watershed scales.
Bias correction of meteorological and hydrometric datasets is crucial in hydrology because of input uncertainty, such as measurement errors, model uncertainty, and parametric uncertainty [
21,
22]. Nowadays, bias correction has become a compulsory process when integrating hydrological models with climate change datasets, which inherently contain biases from systematic and random errors derived by the climate models [
23]. Pierce et al. [
24] applied four bias-correction methods, including quantile mapping, to daily maximum temperature and precipitation data from 21 Global Climate Models (GCMs) to assess their impact on the GCMs’ climate change signal. Ghimire et al. [
25] tested eight bias-correction methods, ranging from simple to complex, to improve hydrological simulation at multiple timescales. The authors concluded that linear scaling and parametric and nonparametric empirical quantile mapping methods produced highly satisfactory hydrological performance. Shrestha et al. [
26] demonstrated that, in their case study basin and with the utilized Regional Climate Models (RCMs), simplified bias-correction methods, such as linear scaling, can perform as effectively as more advanced ones such as quantile mapping. However, little evidence exists on the optimal bias-correction method since it depends on the examined variable, the case study area physiography and extent, and the quality and quantity of the available data [
27].
This research focuses on transboundary river basins that lack extensive spatiotemporal monitoring information, and its objectives are threefold. Firstly, it aims to assess the applicability of two well-known large-scale hydrological models (LSMs) to the transboundary river basins of Greece. Secondly, this research seeks to validate which model can more accurately represent the discharge status of these rivers. Finally, it aims to demonstrate the dependence of the downstream basins on upstream waters, an issue that has not been quantified in detail before in the case study basins. To achieve these goals, LSM data representing the rivers’ discharges at the basins’ outlet and on the political borders of the riparian states are initially compared with available observations. The LSMs’ data series are then bias corrected and the synthetic time series are re-evaluated in comparison to observed data. The methodology underscores the applicability of LSMs in transboundary rivers to produce reliable discharge time series. It can be applied to any international basin and the outputs can support the development of reliable approaches focused on cooperative policies and decision frameworks, particularly in the era of climate change.
4. Discussion
Within the present study, we assess the applicability of two large-scale hydrology models (LSMs), namely the LISFLOOD and E-HYPE models, in accurately representing water volumes, focusing on the five transboundary river basins of Greece. The literature indicates that only a very limited number of scholars have utilized and validated the performance of these models in Greece and in its international waters. For instance, Skoulikaris and Piliouras [
9], and Skoulikaris [
36], evaluated E-HYPE’s performance solely for the Vardar/Axios river basin, while Mentzafou et al. [
61] used the specific model’s simulated discharges as those that occur in seven national rivers, but without any validation. Notably, although LISFLOOD outputs form part of the EU Climate Data Store produced by the European Flood Awareness System (EFWS) as part of the Copernicus Programme [
62], the model has yet to be utilized and evaluated in Greece. At the same time, to the best of the author’s knowledge, none of the specific LSMs have been utilized by the riparian states sharing their waters with Greece. Hence, we consider our approach novel in (i) using two LSMs in the transboundary river basins of Greece, which cover a large area of the Balkan Peninsula, (ii) validating the performance of these LSMs for selective case studies, and thus proposing solutions for situations of data scarcity or in ungauged basins, (iii) demonstrating, for the first time with the use of long-term discharge datasets, the dependance of the downstream parts of the basins to the upstream waters, and (iv) advocating for the use of LSMs as tools for integrated management of international waters.
The data analysis demonstrated, as anticipated, varying performance among the selected LSMs (see
Figure 4). However, in most case study basins, the simulated interannual mean and median flows align between the two models. Notably, there were cases, such as in the Struma/Strymonas river basin, where significant disparities, such as more than 50% difference in averaged discharges, were observed between the outputs. Additionally, it was found that, in certain basins, the LISFLOOD model employs a low-flow threshold, resulting in inadequate attribution of minimum flows. This finding aligns with the research conducted by Gudmundsson et al. [
12], where the assessment of nine LSMs, forced by the same meteorological variables, against observed runoff from 426 small catchments in Europe, demonstrates that while LSMs generally capture the interannual variability of mean flow well, differences in model performance become more pronounced for low-flow percentiles. Additionally, Donnelly et al. [
31] highlight that models’ outputs are improved with increasing catchment size due to the lesser impact of water regulation strategies on hydrosystem behavior compared to the frequent runoff peaks observed in smaller catchments.
Focusing on the two LSMs, although they are well-established and validated models, as clearly indicated in the
Section 2, e.g., [
9,
35,
41,
42], none of the Greek national or international basin gauges, along with their relative gauges, have been utilized for validation during their development phase. Specifically, that of LISFLOOD uses only a station (out of the 693 utilized stations) in the upper part of the Struma basin for its validation [
62], while E-HYPE validation does not include sub-Danubian basins [
31]. In this regard, the research validates the two LSMs in the river basins of Southeastern Europe, demonstrating their potential to successfully simulate river discharges. The data analysis reveals that, in the Vardar/Axios basin, R
2, NSE, and KGE are 0.349, −0.657, and 0.259 for LISFLOOD, and 0.595, 0.268, and 0.574 for E-HYPE (see
Table 3 and
Table 4). For the Mesta/Nestos basin, the goodness-of-fit measures indicate that R
2, NSE, and KGE are 0.353, 0.301, and 0.507 for LISFLOOD, and 0.473, 0.308, and 0.604 for E-HYPE (see
Table 5 and
Table 6). The outputs of the E-HYPE model in both of the aforementioned case study basins coincide with those produced by the model during its development phase, as reported by Donnelly et al. [
31]. It is indicated that, for all E-HYPE’s validation stations across Europe, two-thirds had NSE greater than zero, and one-third of the stations had values greater than 0.4, which aligns with our research findings. Additionally, Donnelly et al. [
31] demonstrate that 85% of all validation stations across Europe had KGE greater than zero, with 52% having values greater than 0.5, a pattern consistent with the outputs of our current research. Regarding the LISFLOOD model, the model’s validation output demonstrates that 16% (97 out of 594 validation stations) had a negative NSE, while 78% (461 out of 594 stations) had NSE values greater than 0.2 [
62], which is consistent with the findings of the current research. Finally, in the case of the Struma/Strymonas and Maritsa/Evros/Meriç basins, the absence of current observational data necessitated an examination solely of E-HYPE’s capability to represent river runoff. In both cases, the outputs (R
2 = 0.619, NSE = 0.472, and KGE = 0.726 for the Struma/Strymonas basin, and R
2 = 0.714, NSE = 0.444, and KGE = 0.602 for the Maritsa/Evros/Meriç basin) reveal E-HYPE’s ability to accurately simulate the river discharges. However, it is essential to re-evaluate the specific model using more recent data and longer time series, since small data samples increase the likelihood of observational errors, potentially resulting in biased outcomes during model evaluation [
12].
In the bias-correction process, the methods utilized are commonly employed in surface hydrology and mathematical models’ evaluation (e.g., [
50]). Bias-correction methods resulted in an overall increase in the statistical indexes, indicating the correlation between observed and bias-corrected data. The relatively straightforward linear regression (LR) method, for instance, performed very well in the case of the Vardar/Axios and Mesta/Nestos basins. Specifically, the initial NSE values of −0.657 and 0.301 for LISFLOOD (see
Table 3 and
Table 5) became 0.423 and 0.797, respectively, while in the case of the E-HYPE model, NSE increased from 0.268 and 0.308 for the Vardar/Axios and Mesta/Nestos basins to 0.664 and 0.772, respectively (see
Table 4 and
Table 6). The same method also performed very well in the case of the Struma/Strymonas and Maritsa/Evros/Meriç basins, where NSE and KGE values for both LSMs were greater than 0.73 and 0.61, respectively (see
Table 7 and
Table 8). The quantile mapping (QM) method also had a positive impact on increasing the statistical measures, and in some cases, outperformed other methods. In the case of the LISFLOOD model, for example, KGE is constantly greater than 0.58, and in the case of the E-HYPE model, KGE is greater than 0.7, which is the best indicator among the bias-correction methods. Moreover, QM resulted in PBIAS values very close to zero (<±1.0 for all cases) indicating the excellence performance of the method. Finally, the scaling factor (SF) and delta change (DC) methods provided less satisfactory outputs, concluding that LR and QM bias-correction techniques are efficient in decreasing the LSMs’ runoff biases in the case study basins.
An important output of the research is the quantification of the dependence of the downstream parts of the case study transboundary basins on the available upstream water resources. This analysis is also considered an innovative aspect of the study, as the literature review revealed a lack of gauge stations, an issue which aligns with the research of Skoulikaris and Pilirouas [
9] at the national borders of transboundary basins, as well as a lack of documented figures (see
Table 2) about the upstream inflows. Regarding the contribution of the upper parts of the basins, in the case of the Vjosa/Aoos river basin, LISFLOOD and E-HYPE attribute 63.04% and 27.2% of the basins’ waters to upstream sources, respectively. Considering only 33% of the basin’s area belongs to Greece, it can be said that LISFLOOD partially overestimates the water inflow into Albania. In the Vardar/Axios basin, both LSMs demonstrate that the inflows from North Macedonia correspond to more than 92% of the total inflows, establishing the significant dependence of the downstream water uses on upstream waters. As for the Struma/Strymonas and Mesta/Nestos basins, which are almost equally shared between Bulgaria and Greece, both LSMs coincide that approximately 50% to 75% of the waters originate from upstream sources. This result, particularly in the case of the Mesta/Nestos basin, is validated in the literature [
30]. As far the Maritsa/Evros/Meriç basin is concerned, the LISFLOOD and E-HYPE models show that 42.53% and 70.9% of the basin waters, respectively, are coming from upstream sources. These figures are relatively small, particularly in the case of LISFLOOD, considering that Greece accounts for only 6.9% of the basin’s extent and is primarily comprised of plain areas. However, it should be noted that not all major tributaries of the river are connected in the upstream waters, and thus are not considered by the two models as upstream waters.
To sum up, the research promotes a methodology for producing realistic outputs regarding the water discharges of transboundary basins, which can further be used to trigger indexes demonstrating cooperative and conflictive interactions, such as those of the International Water Event Database (IWED) [
63]. Moreover, the outputs can lay the foundation for cooperative water management and the development of a framework for addressing scarcity and dependency, as proposed by Munia et al. [
64]. De Stefano et al. [
65] provide a thorough analysis on the transboundary basins that are more likely to experience hydro-political tensions over the coming years due to construction of large hydraulic projects, such as dams within the river course. Hence, the analysis of large-scale construction impacts on transboundary water resources is considered the advancement of the current research. Moreover, De Stefano et al. [
66] investigated the institutional resilience to water variability in transboundary basins due to climate change; thus, the investigation of transboundary water bodies’ vulnerability to climate change is also a thematic proposed to be further investigated. In terms of the research limitations, LSMs provide daily or mean simulated discharges rather than extremes [
12]; thus, the proposed methodology cannot be followed in the case of extremal analysis.
5. Conclusions
Accurate data and effective data exchange are fundamental for ensuring equitable and sustainable management of transboundary waters. This significance is underscored by Article 6 of the Convention on the Protection and Use of Transboundary Watercourses and International Lakes [
6], as well as Article 8 of the Draft Articles on the Law of Transboundary Aquifers [
67]. Furthermore, the EU, through its Water Framework Directive, recognizes information sharing as a cornerstone of integrated water resources management at national and transboundary scales [
68].
This research, in the absence of monitoring data, investigated the way LISFLOOD and E-HYPE large-scale hydrological models (LSMs) can represent the river discharges of the transboundary river basin of Greece. The E-HYPE model slightly outperformed the LISFLOOD model in most of the case study basins; however, more recent data are required to establish a more secure consideration. Overall, the outputs demonstrate that both models provide reliable outputs that are further ameliorated after correcting for bias. Among the methods used for creating unbiased time series, linear regression and quantile mapping produced outputs of high accuracy. The research is considered a methodological roadmap that can be implemented in basins where limited data are available, as well as in transboundary basins where the often-political environmental policies and frameworks between the riparian states do not facilitate the integrated modeling of the water resources.
This research, conducted in the absence of ample monitoring data, investigates how LISFLOOD and E-HYPE large-scale hydrological models (LSMs) represent the river discharges of the transboundary river basin of Greece. The E-HYPE model slightly outperforms the LISFLOOD model in most of the case study basins; however, more recent data are required to establish a more secure conclusion. Overall, the outputs demonstrate that both models provide reliable results, which are further improved after bias correction. Among the methods used for creating unbiased time series, linear regression and quantile mapping produced highly accurate outputs. The research serves as a methodological roadmap that can be implemented in basins with limited data availability, as well as in transboundary basins where political and environmental policies and frameworks between riparian states often do not facilitate the integrated modeling of water resources.