Performance Assessment Comparison between Physically Based and Regression Hydrological Modelling: Case Study of the Euphrates–Tigris Basin

Abstract

This paper presents two hydrological models developed for the Euphrates–Tigris Basin in Turkey. The first model is a linear regression-based model allowing the estimation of streamflow based on available hydroclimatic data (precipitation, temperature, evapotranspiration, etc.) with the use of clustering analysis. The second model consists of an elevation-based semi-distributed hydrological model (HBV model), allowing process-based modelling of the watershed. A set of performance metrics identified the HBV model as the best performance in terms of predicting streamflow (NSE = 0.752), while the RCA4-EU regression model of CORDEX showed the most robust performance. The results show the potential of regression models from a computational and data point of view in being integrated into physically based models wherein a hybrid approach might be beneficial. The comparison of conceptual models with statistical analyses of streamflow shows the potential of regression analysis when the regions are clustered in hydro-meteorologically homogeneous groups. The employment of the conceptual model HBV also provides significantly robust streamflow estimation for the region, which is especially important in estimating the hydropower potential of the region’s near future.

1. Introduction

Measurements and data form a major pillar in advancing hydrological sciences under the topic of “unsolved problems in hydrological sciences” [1]. Particularly, the use of different sources of data based on observations and different techniques is needed for further assessment. By doing so, studies are expected to advance the “FAIR and SQUARE” modelling of hydrological processes [2]. Recent advancements in physically based hydrological models can be attributed to the increase in data availability, computing capabilities, and the time that helps in the validation of the results of the models developed. The FAIR principles in such advancements are attributes of Findability, Accessibility, Interoperability, and Reusability [3]. Several studies have aimed at addressing one or more attributes of this principle. A great deal of interest is given to the estimation of streamflow and its feedback role in the hydrological process. Clark et al. aimed at addressing the non-linear relationships between the observations and the model state by perturbing model inputs and states to update the state of a hydrological model based on observed streamflow variables [4]. Wu et al. compared the performance of different support vector regression techniques in estimating monthly streamflow with a focus on the data processing technique [5]. Similarly, Wang et al. provide an ensemble approach to forecasting streamflow in Australia to identify a suitable set of conditional parameters for rainfall–runoff modelling in two conceptual models [6]. Ensemble streamflow forecasts can be generated using multiple hydrological models, which enhances streamflow forecast skill at short- to medium-range timescales [7]. A statistical–dynamical approach was used by Slater and Villarini in discovering the performance of using global climatic variables in predicting streamflows in the US Midwest, with population and agriculture integrated into the statistical models [8].

Among statistical methods, the use of regional regression equations based on the physical and hydrological characteristics of a catchment has been widely applied [9]. Hydrological models are also commonly used for streamflow estimation, with the Soil and Water Assessment Tool (SWAT) and the Hydrological Simulation Program-FORTRAN (HSPF) being two examples [10]. Machine learning techniques, such as artificial neural networks, have also shown promising results in streamflow estimation [11].

Our research addresses streamflow estimation in the Euphrates–Tigris River Basin (hereafter, ETRB) and illustrates a case wherein the development of a process-based hydrological model is complexified by the transboundary nature of the river, its varying climatology, and compatibility with the fair principles. In particular, the accessibility of data, rather than its presence, remains an inhibitor in a hydrological model of the large-scale basin of ETRB. However, the presence of historical time series allowed the development of several techniques that estimate the streamflow variable from available hydroclimatic data, albeit accessibility to such a dataset is limited. The HBV model has been previously applied in the eastern part of Turkey for snowmelt runoff process modelling and forecasting [12]. On the other hand, statistical methods such as MDAR and ISW have been used for daily streamflow estimation in ungauged basins in Turkey for the ETRB region [13]. Regression models have also been developed for estimating peak streamflows for unregulated rural streams in Kansas. Multivariate regional hydrologic models have been used for streamflow estimation in the United States [14]. Trend analysis has been carried out for climatic and hydrologic parameters such as temperature, humidity, precipitation, and streamflow in the Euphrates Basin [15]. Regional models based on the “one-step” approach have been used for estimating streamflows in ungauged basins [16]. Regression-based statistical methods have been compared for the spatial estimation of precipitation in two hydrologically different basins [17]. Non-parametric trend tests have been applied to streamflow data of selected stations in the Euphrates Basin. Kilinc and Haznedar combined genetic algorithms and long short-term memory to estimate the streamflow in the basin and provide improved results that do not rely on a full set of hydroclimatic variables [18]. Similarly, Katipoglu assessed monthly streamflow in the basin using artificial neural networks and correlated hydroclimatic variables like precipitation and evapotranspiration [19]. On the other hand, several studies relied on establishing the runoff through physical-based models instead. Kara and Yucel [12] presented the changes in extreme flows under climate change scenarios through a conceptual rainfall–runoff model (HBV model) that mainly relies on the elevation information to calculate the water balance within the studied basin. A more data-extensive approach was used by Peker and Sorman, where the soil and water assessment tool (SWAT) was utilized to address the complex topography and the consequent data scarcity [20]. While both physically based or regression-based approaches hold their own assumptions, strengths, and weaknesses, no study has yet presented an assessment of the performance of the two approaches in the ETRB with a focus on the choice of the model that ensure the FAIR principles. While regression models could be computationally faster, the data accessibility in the ETRB impedes such an advancement. The research gap and novelty in comparing regression-based models versus the HBV model for streamflow estimation in the Euphrates Basin can be identified as follows:

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There is a lack of studies that compare the performance of regression-based models and the HBV model for streamflow estimation in the Euphrates Basin.

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The existing studies have used different statistical methods and models for streamflow estimation in different regions, which makes it difficult to compare their results.

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The Euphrates Basin is an important region for water resources management, and there is a need for accurate streamflow estimation methods that can be used for decision-making, especially following the FAIR principles.

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The comparison of regression-based models and the HBV model can provide insights into the strengths and weaknesses of different streamflow estimation methods and help identify the most suitable method for the Euphrates Basin from a holistic perspective.

Therefore, our study presented aims to address this shortage in the ETRB by presenting the results of a developed regression model that estimates the streamflow variable with respect to hydroclimatic variables and a physically based model, the HBV model. The purpose of the work presented is to compare the performances of the two approaches suggested through statistical measures and analyze the implications held by each approach when the models are run for climate change scenarios. We start by presenting the development of the HBV model presented and its results, then the regression models obtained, focusing on the performance of the models in estimating the streamflow. After this, the projected streamflow under climate change scenarios is calculated for each model to assess if adopting a physically based approach would imply different climate change impacts than the regression-based model. The Euphrates–Tigris River Basin streamflow estimation research has several benefits for sustainability. Effective dam management, which can help control water usage, prevent flooding, and guarantee sufficient water supply for agriculture, industry, and human consumption, depends on accurate streamflow estimation.

2. Materials and Methods

2.1. Study Area

The ETRB, a highly engineered river system, is a transboundary watershed formed by the merging of two rivers, the Euphrates and Tigris Rivers, with a high potential of capturing water losses through the series of dams present [21].However, the basin remains prone to water scarcity due to recurring droughts, arid environment, and climate variability [22]. Figure 1 illustrates the boundaries of the watershed shared between 6 countries (Turkey, Iraq, Jordan, Saudi Arabia, and Iran) with the land cover data [23]. Similarly,

Table 1. Euphrates–Tigris Watershed main features.

Feature	Description
Watershed Area (km2)	1 × 106
Elevation range (m)	312–4028
Topography	Mountainous; variability of highlands and lowlands
Climate characteristics	Arid to semi-arid climate. Large-scale circulation patterns, teleconnections, regional topography.
Estimated total annual flow (m−3)	30 × 109
Temperature (°C)	4–16 (wet season); up to 43 (May–October)
Precipitation (mm. year−1)	50–1000
Evapotranspiration (mm. year−1)	800–1400

illustrates main watershed features useful for this study, presented with focus on hydroclimatic variables of precipitation, temperature, and evapotranspiration. These variables mainly relied on two data sources, the first being the national authorities (DSI and EIE) and the second being the CORDEX hydroclimatic data store.

2.2. HBV Model

The conceptual HBV model used is a semi-distributed model where the catchments are separated into several different elevation and vegetation zones. Starting from the inputs of precipitation, temperature, and evapotranspiration daily time series, the model can simulate the daily runoff under three different routing routines: snow, soil, and response (groundwater) routines. Figure 2 illustrates the structures and routines of the HBV model. Elevation zones are assigned based on the digital elevation model of the watershed and subbasin breakdown, according to HydroBasins and the HydroAtlas database [24]. To provide a comprehensive understanding of hydrological dynamics, it incorporates a variety of factors such as altitude area, soil processes, and other watershed characteristics. The altitude area takes into account elevation changes within the watershed, which influence water resources and runoff patterns. By incorporating infiltration rates, soil moisture dynamics, and water holding capacity, soil processes simulate water movement. Land cover, vegetation types, and land use patterns all have an impact on interception, evapotranspiration, and water balance. The HBV framework enables holistic modelling of hydrological systems and supports effective water management and planning by integrating these aspects.

The methodology to develop the hydrological model using HBV was as follows:

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Delineation of the watershed studied: Using the digital elevation model, delineating the watershed becomes possible to identify the subbasins located within the basin. With focus on the thesis purpose concerned with dam locations for hydropower potential estimation and on the certain modelling settings of HBV, the Euphrates–Tigris Basin is divided into four subbasins, as can be seen in Figure 3 and

Table 2. Modelled subbasin characteristics.

Subbasin Number	Area (104 km2)
1	123
2	22.6
3	9.86

.

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Development of the HBV reference model for the period of 1971–1999 for calibration.

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Development of the HBV model for the period of 2000–2020 for validation.

HBV model required the following variables for simulation, which were obtained for the general directing entity of the subbasin:

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Precipitation data (obtained from local authority);

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Temperature data (obtained from local authority);

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Streamflow data (obtained from local authority);

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Evapotranspiration data (obtained from local authority).

2.3. Regression Analysis

The HBV model developed relies on biophysical data (especially soil moisture and soil data) that are less available with respect to streamflow. The regression analysis performed looks at correlating the runoff with essential hydroclimatic variables (temperature, precipitation, evapotranspiration, solar radiation, etc.). In total, 12 essential hydroclimatic variables were studied to perform a linear regression using accessible Cordex data [25]. The results obtained for three regional circulation models (HADGEM (Equation (1)), RCA44-EU (Equation (2)), and RCA11-MENA (Equation (3))) are as follows. At the time of writing this article, the full methodological work is presented by the author for submission as another article.

Table 3. Hydroclimatic models used in the regression analysis.

Model	Description
HADGEM	The Hadley Centre Global Environment Model (HadGEM) is a comprehensive climate model developed by the UK Met Office that simulates and predicts Earth’s climate system, including the interactions between the atmosphere, oceans, land surface, and sea ice.
RCA44-EU	RCA4.4-EU (Regional Climate Model version 4.4 for Europe) is a high-resolution regional climate model used to simulate and study climate processes and changes specifically in the European region.
RCA11-MENA	RCA11-MENA (Regional Climate Model version 11 for the Middle East and North Africa) is a regional climate model designed to investigate and project climate dynamics and trends in the Middle East and North Africa region.

provides a description of each model used in the regression analysis.

Log (Q) = 68.2 + 171 log (T_asmax) − 212.8 log (T_as) + 0.84 log (rsds) + 5.89 log (rlds) + 0.5 log (PET) + 5.44 log (mrso)

(1)

Log(Q) = 9.12 + 1.09 log (T_as) + 12.6 log (Tasmin) − 18.9 log (T_asmax) − 0.33 log (wnds) + 0.61 log (huss) + 2.39 log (sund) + 0.43 log (PET) − 3.22 log (rlds)

(2)

Log (Q) = −28 + 1.54 log (mrso) − 0.57 log (wnds)+ 0.63 log (huss) + 8.57 log (sund) − 3.26 log (rsds) − 2.92 log (rlds) + 0.0072 log (PET)

(3)

2.4. Hydrological Performance

Assessment and agreement with the FAIR principles metrics used to assess the performance of daily streamflow estimation models vary with respect to the purpose of the model developed. In general, the performance can be addressed under a quantile domain and a spatiotemporal one [26]. In this study, the stream gages do not present a complete dataset spanning throughout the modelling period (1970–2020) that allows the spatial distribution of the error metrics. We addressed both domains through a set of 70 performance metrics commonly used in assessment of hydrological daily timeseries simulations [27,28]. Common evaluation statistics used during the calibration and validation phases aim at assessing the variance obtained with respect to measured data, the collinearity between the datasets, and the tendency of simulated data to deviate from the observed ones. The Python packages ‘hydrostat’ and ‘hydroerr’ were used to assess the 70 performance metrics [29].

Table 4. Main error metrics presented in the study.

Error Metric Symbol	Name	Range	Criteria
NSE	Nash–Sutcliff Efficiency	]−∞; 1]	values above 0.5 are considered satisfactory
r	Pearson’s correlation coefficient	[−1; 1]	value above 0.7 is often considered satisfactory
R2	Coefficient of determination	[0; 1]	values above 0.6 or 0.7 are considered satisfactory
D	Index of Agreement	[0; 1]	values above 0.6 or 0.7 are considered satisfactory
PME	Persistence model efficiency	[0; 1]	generally, above 0.5 is considered acceptable
PVk	Performance virtue statistic	]−∞; 1]	no fixed range for PVS as it depends on the specific application and the range of values it takes
e	Logarithmic transformation variable	]−∞; +∞[	do not have specific satisfactory ranges
MAE	Mean absolute error	[0; +∞[	lower values are generally desirable
MSE	Mean square error	[0; +∞[	lower values are generally desirable
RMSE	Root mean square error	[0; +∞[	lower values are generally desirable
PBIAS	Percent bias	[−100; 100]	values close to zero indicate less bias
RSR	RMSE observations standard deviation ratio (RSR)	[0; +∞[	values below 0.5 are often considered satisfactory
DRMS	Daily root mean square	[0; +∞[	lower values are generally desirable
Kge	Kling–Gupta efficiency	]−∞; 1]	values above 0.6 or 0.7 are often considered satisfactory
Kge’	Modified Kling–Gupta efficiency	]−∞; 1]	values above 0.6 or 0.7 are often considered satisfactory
Kgenp	Non-Parametric Kling–Gupta efficiency	]−∞; 1]	values above 0.6 or 0.7 are often considered satisfactory

presents the main error metrics calculated based on their previous use in different hydrological studies and different climatic and geographical settings. While multi-objective and multi-gaged assessment can be tailored on a case-by-case study, we present the assessment with respect to the gauging station at the outlet of the catchment as an initial step of analysis. Further detailed assessments can be made with respect to the desired objective, for example, the management of existing water infrastructures like dams and water distribution networks. We aim to present the performance of two hydrological models that help advance the effective dam management needed in the region, where the FAIR principles hold the potential to ensure data suitability for use. Figure 4 presents the two models to be assessed and their suitability according to the FAIR principles. In addition to evaluating the mentioned parameters, we also assessed seasonality and its effects on the analysis. Understanding and accounting for seasonality are crucial in many applications, as climatic and hydrological processes often exhibit distinct patterns and variations throughout different seasons. By considering seasonality, we aimed to capture and analyze the seasonal variations in the performance metrics, identifying any specific strengths or weaknesses of the models during different times of the year. To address seasonality, we partitioned the dataset into distinct seasons or time intervals based on the climatic characteristics of the study area. This allowed us to analyze the performance metrics separately for each season and assess any seasonal variations or biases in the models’ predictions.

3. Results

3.1. HBV Model Results

The summary of the results for the 1971–1999 calibration period of the HBV model is found in

Table 5. Water balance as calculated by HBV model (1970–2020).

Water Balance [mm/year]	Subcatchment 1	Subcatchment 2	Subcatchment 3	Subcatchment 4
ΣQsim	301	278	267	231
ΣQobs	378	351	339	298
ΣPrecipitation	639	437	1000	966
ΣAET	317	266	262	254
Coefficient of determination	86.25%	81.23%	79.53%	84.23%
Flow weighted efficiency	0.7569	0.8862	0.8652	0.8886
Model efficiency	0.7995	0.8821	0.8254	0.8901

. Moreover, the plot of the simulated vs. observed flow shows a significantly robust estimation potential, especially at the outlet location at subbasin 4. In total, 10,000 Monte Carlo simulations were run by adjusting the HBV model parameters, with the optimal parameters adjusted obtained being the threshold parameters (TT), an increase of precipitation with elevation (PCALT), a decrease of temperature with elevation (TCALT), the non-linearity coefficient (alpha), and the threshold parameter (PERC).

3.2. Regression Models Results

Figure 5 illustrates the plots of the average monthly flows through the total modelling period (1973–2020), excluding the HBV warmup period (1970–1972). This initial plot gives a graphical indication of the fitness of the different models. Q-Q plots of the different models versus the observed quantiles (Figure 6) serve as an additional visual check with regard to the similarity of the distribution of the different datasets. The set of error metrics is presented for the total yearly period, the wet period (December to February), and the dry period (March to November).

Table 6. Performance metrics calculated (not accounting for seasonality).

Metric	HBV Model	HAD-GEM	RCA4-EU	RCA-MENA
NSE	0.752	0.6587	0.7213	0.652
r	0.5421	0.4852	0.6531	0.5423
R2	0.8123	0.745	0.567	0.7352
Adj R2	0.752	0.733	0.533	0.615
D	0.5732	0.6145	0.6014	0.7423
PME	0.213	0.342	0.215	0.403
PVk	−5.25	−6.89	−8.25	−7.85
e	1.2	0.23	−0.524	−0.132
MAE	38.632	56.23	68.524	46.258
MSE	17.23	23.325	45.236	30.21
RMSE	4.151	4.830	6.726	5.496
PBIAS	−10.23	−7.52	−12.32	−15.23
RSR	1.15	0.65	2.21	1.23
DRMS	0.785	1.21	1.622	0.86
Kge	−0.53	−0.51	−0.48	−0.42
Kge’	−0.42	−0.48	−0.61	−0.5
Kgenp	−0.53	−0.84	−0.89	−1.12

and

Table 7. Performance metrics calculated accounting for seasonality.

Metric	HBV Model		HAD-GEM		RCA4-EU		RCA4-MENA
	Wet	Dry	Wet	Dry	Wet	Dry	Wet	Dry
NSE	0.532	0.423	0.5864	0.6321	0.4752	0.6321	0.512	0.6477
r	0.4267	0.6321	0.3598	0.685	0.6854	0.3652	0.4532	0.5643
R2	0.8526	0.7987	0.8462	0.8123	0.7468	0.8023	0.6425	0.7423
Adj R2	0.8143	0.752	0.711	0.7522	0.615	0.752	0.633	0.701
D	0.4326	0.643	0.3252	0.2954	0.631	0.513	0.4856	0.6102
PME	0.431	0.321	0.3102	0.1921	0.3521	0.4123	0.502	0.359
PVk	−4.62	−3.23	−7.21	−10.25	−7.63	−8.332	−6.82	−7.25
e	2.13	0.111	0.326	0.5322	−0.652	−2.012	−0.125	−0.4321
MAE	80.521	60.23	55.123	41.52	90.25	70.52	65.123	80.25
MSE	15.230	11.230	20.120	1.250	44.230	65.230	50.230	45.123
RMSE	3.212	6.23	4.23	5.111	4.321	2.552	5.232	8.25
PBIAS	−18.23	−21.23	−7.25	−11.25	−13.23	−11.25	−18.17	−12.25
RSR	1.03	0.552	0.43	0.85	3.01	1.85	1.25	1.85
DRMS	0.44	0.962	1.02	0.98	1.852	1.12	0.445	0.992
Kge	−0.96	−0.43	−1.23	−0.221	−0.32	−0.65	−0.15	−0.65
Kge’	−0.665	−0.52	−0.33	−0.85	−0.12	−0.523	−0.522	−0.43
Kgenp	−0.345	−0.65	−1.12	−0.5	−1.5	−1.23	−2.12	−0.54

present the chosen error metrics obtained, accounting for both seasonality and non-seasonality.

3.3. Performance Assessment of HBV and Regression Models

Table 6 presents various performance metrics for four different hydrological models: the HBV model, the HAD-GEM model, RCA4-EU, and RCA-MENA. The HBV model performed the best in terms of NSE, R², adjusted R², and e, while RCA-MENA had the highest PME and PBIAS values, indicating a tendency to overestimate. The HAD-GEM model had the highest PVk value, indicating a bias towards the underestimation of peak flows. The HBV model had the lowest RMSE and RSR values, indicating the best fit between observed and simulated values. Overall, the HBV model had the highest performance scores, while RCA-MENA had the lowest. The evaluation results indicate that the HBV model outperforms the other models with an NSE of 0.752, R² of 0.8123, and KGE of −0.53. On the other hand, the RCA-MENA model shows the poorest performance, with an NSE of 0.652, R² of 0.7352, and KGE of −0.42. The other two models, HAD-GEM and RCA4-EU, show intermediate performance levels. However, it is important to note that the selection of the best model depends on the purpose and scope of the study. For instance, in our case, the HBV model could be the best choice to estimate the streamflow variable, while the RCA-MENA model could be more suitable for larger studies.

Table 7 shows the models evaluated on both wet and dry seasons separately. The HBV model and RCA4-EU generally perform better during the wet season, while the HAD-GEM model and RCA4-MENA perform better during the dry season. The NSE values range from 0.423 to 0.6321, indicating a moderate to good fit of the models to the observed data. The R² values range from 0.6425 to 0.8526, indicating a good to an excellent fit of the models. The PBIAS values indicate that the models tend to underestimate the observed values during the wet season while overestimating during the dry season. The RMSE values range from 2.552 to 8.25, indicating a moderate to high degree of error. The KGE values range from −1.23 to −0.15, which indicates a poor to moderate fit of the models. Overall, the evaluation of models with seasonal data provides more insights into the models’ performance, which can help in better decision-making for hydrological management.

4. Discussion

4.1. Models Performance

The selection of a fit-for-purpose model from the ensemble presented in the study relies on statistics criteria, specifically, regression statistics, dimensionless index, and error indices. With respect to the collinearity in the models between observed and simulated data, the biophysical model of HBV presented a better estimation, with an R² = 0.8123. Considering seasonality, a similar ranking is obtained with a better estimation for wet seasons with an R² = 0.85. Regression models also presented an acceptable performance with a range between 0.56 and 0.75. The RCA4-EU regression model outperformed the HAD-GEM and RCA4-MENA models during the wet season due to its regional specificity, higher spatial resolution, better parameterization and calibration, and potentially improved input data quality. These factors enabled the RCA4-EU model to accurately capture the unique climatic characteristics and localized processes of Europe, resulting in superior performance during the wet season compared to the broader models. It is important to note that further explanation would require a detailed analysis and comparison of the model configurations, data sources, and performance metrics to provide a conclusive explanation for the observed performance differences. The comparison of Q-Q plots for the HBV, RCA-EU, RCA-MNA, and HADGEM models reveals interesting insights. The RCA-MNA model shows the least skewness among the four, indicating a relatively balanced distribution of the data. Conversely, the HBV and RCA-EU models exhibit an “S” shape in their Q-Q plots, indicating significant departures from normality. This suggests the presence of non-linear relationships or specific characteristics in the data distribution for these models. Furthermore, the Q-Q plot for the HADGEM model demonstrates right skewness at extreme values, implying a higher concentration of data towards the lower end of the distribution. This indicates a potential bias towards more extreme values in the HADGEM model output. The non-linear behavior of the hydrological processes represented by these models can be attributed to the sigmoidal shape observed in the Q-Q plots of the HBV and RCA-EU models. The RCA-MNA model’s minimal skewness and balanced distribution may be due to the specific characteristics of the dataset used in that region. The right skewness at extreme values in the HADGEM model’s Q-Q plot could be due to model biases or inherent skewness in the underlying climate data.

4.2. Data Quality and Availability

Such performance can be mainly attributed to the quality and availability of data. While the regression model might seem more robust and capable of estimating streamflow from a statistical point of view, we argue that the quality and availability of full datasets of streamflow in the studied basin decreased the expected performance. As previously mentioned, the FAIR principles are mainly present in the regression models despite the length of data needed. Accessing the hydroclimatic required minimal expertise. However, for the HBV model, where data from the observed stations were used, the accessibility was majorly hindered.

4.3. Performance Metrics

In addition, the commonly used NSE metrics obtained assign a better general performance for the HBV with an NSE = 0.752. However, looking at the PBIAS metric, the regression model related to the HAD-GEM climate model provided a better performance with a PBIAS = −7.52. These three metrics are generally used in most hydrological modelling calibration, validation, and performance assessment, especially when used for daily streamflow estimation. This is in line with previous research directions, where mainly biophysical rainfall–runoff models are developed for the Euphrates–Tigris Basin. Such models are relatively more robust to be developed, given their reliance on global and verified input data. The suggested improvement on the previously mentioned error metrics is the use of the Kling–Gupta efficiency and its variants (prime and non-parametric). The disagreement between the four models is reduced, in the case of non-seasonality, with values of kge ranging between −0.43 and −0.52. This is in agreement with the suggested benefits of kge, where variability and dynamics are better captured in the assessment.

4.4. Seasonality and Model Performance

A different situation prevails when looking at the seasonality and the performance between the wet and dry seasons. For the wet period, regression models provided a better performance with respect to NSE criteria (NSE = 0.58 for the HAD-GEM regression model). The values of PBIAS obtained agree with the assessment suggested with a PBIAS = −7.25 for the HAD-GEM regression model. Kge also gives a similar indication, where the RCA4-MENA performs the best with a value of −0.15.

For the dry periods, the HBV model performs the worst with respect to regression models with an NSE = 0.64 and a PBIAS = −21.23. With respect to kge, the HADGEM model performs the best with a value of 0.21.

In addition, incorporating seasonality in the data has an impact on the model performance metrics. Without seasonality, the HBV model had the highest NSE and R² values, indicating the best fit to the observed data. However, with seasonality, the HAD-GEM model outperformed the HBV model with higher NSE and R² values for both wet and dry seasons.

4.5. Biophysical Attributes of the Models

Regression models for the estimation of monthly or annual streamflows have been previously applied, combining watershed characteristics and hydroclimatic variables, especially with a well-gaged area, as in Zhang et al. [30]. Our seasonal model performance is in agreement with Zhang et al. [30] despite not considering the drainage area in the estimation of the streamflow. Watershed characteristics are better represented in the HBV model with the inclusion of the digital elevation model and vegetation zone parameters. Albeit, the regression models still performed the best for dry periods despite their lack of representation of watershed characteristics. A potential explanation for such observations is that the number of hydroclimatic predictors used in estimating streamflow was large enough, especially including factors such as evapotranspiration and humidity that play a major role in the dry period hydrological process.

4.6. Limitation and Way Forward

The regression models presented are specific to the region of the ETRB and could benefit from further calibration and application in similar climatic settings. Barbossa et al. presented a global-scale regression model to predict mean annual flow but highlighted that regional scale remains the main area of application [31]. In addition, using the watershed characteristic in the regression equation could improve the performance obtained. In addition, the use of machine learning algorithms such as Di Nunno et al., Granata et al., and Elbeltagi et al. for the streamflow estimation in the ETRB provides a verified approach that has been applied in several regions and climatic zones [32,33,34]. The presentation of the results aims at guiding the choice of the model made in accordance with the application intended. In general, several drought and wetness indices studies are abundantly applied within the ETRB. Mainly, these studies relied on biophysical models where hydrological models like MIKE, SWAT, and APEX are used [35,36,37]. While the calibration and validation process of these models is not developed in-depth, where usually automatic multi-objective calibration is performed, the results of the error metrics obtained an invite to develop a further exploration of the use of regression analyses in the development of such metrics. A coherent efficiency measure accounting for NSE and Kge can be further explored as an application in the ETRB [38].

5. Conclusions

Accurate streamflow estimation and accounting for seasonality are both crucial for sustainable water resource management, especially when dealing with data and models that do not follow the FAIR principles. In conclusion, this study presents an ensemble of one biophysical model (HBV) and three linear regression models from the available CORDEX climate model. We aimed to shed light on the choice of the hydrological model with respect to the objective and the availability of data. With data scarcity and mismanagement through different entities forming an obstacle to developing clear models, the development of an ensemble of models might answer some assumptions. In general, the HBV biophysical models performed better when non-seasonality was considered and could be recommended for hydrological studies addressing either continuous or event-based phenomena. When seasonality is counted, the situation changes, and the regression model shows a better performance using the kge metric. Hence, the use of regression models is recommended when dealing with phenomena highly related to the seasonality present in the basin (floods, snowmelt, drought, etc.). This study provided a preliminary bypass to deal with the data scarcity that could hinder the development of accurate models in the ETRB, and any additional work that is carried out should account for the climate change ensemble modelling. In fact, the study relating to the future projection of climate change variables was not presented in this work, given the present assumptions and discrepancies present in the various climate models. Hence, we presented work conducted during the historical period of 1970–2020 with validated and calibrated data that can serve as a platform to address further uncertainties in climate change projection. Beneficiaries from such a study are the water management entities in the basin, especially with the presence of several dams and anthropogenic interventions. In terms of sustainability studies, the work presented aims to facilitate the choice of extensive data handling when dealing with hydrological modelling. Our methodology for streamflow estimation not only offers a wider range of models for modellers to choose from but also provides accessible and user-friendly software that does not require extensive expertise or significant computational efforts. This is a significant advantage for sustainability efforts as it increases the number of researchers and practitioners who can contribute to the study of water resources, especially in areas with limited access to computational resources or highly specialized expertise. Additionally, the inclusion of seasonal factors in our analysis is crucial in improving the accuracy of streamflow estimation. By accounting for the variations in wet and dry seasons, our methodology can better inform water management decisions and ensure the long-term sustainability of water resources.

As a contribution, this study presents two models with their respective hydrological performance and their suitability with the FAIR principles. Depending on the user and stakeholders in question, the use of one model over the other can be carried out. As an example, users with no access to basin authority stations’ data will benefit from the regression model already presented by accessing the available hydroclimatic data. Overall, our approach offers a practical and efficient solution to streamflow estimation, making it more accessible to a wider range of users and contributing to the sustainable management of water resources.