Shaping a baseflow model through multiple regression analysis: the Çoruh watershed example Open Access

The amount of usable drinking water per capita in Turkey was 1,652 m³ in 2000, 1,544 m³ in 2009, and 1,346 m³ in 2020. In terms of per capita usable drinking water potential, Turkey is among the countries that are under water stress DSİ (2021) (DSİ: State Hydraulic Works), and it is understood that there will be significant reductions in streamflow and groundwater from now on. The current climate changes and the model predictions for future changes point to the significance of using water resources efficiently and effectively. To do so, it is essential to have better estimations for planning and managing the water resources.

Only correct projections and appropriate planning efforts will make it possible to keep water under control, utilize it in the best possible way, and preserve it for future generations. In order to make the projections and planning correct and appropriate, it is necessary to estimate the water flow accurately. It is also important to estimate the amount of water in the baseflow, which decreases, especially in the summer months. It is widely known that the flow passing through a stream's cross-section consists of three types: surface, subsurface and underground flows. Baseflow is composed of the lag part of surface flow and subsurface flow Bayazıt (2001).

Baseflow feeds streams and ponds through underground water flow and is less variable than other flows. It is also the most significant water supply for streams in arid seasons. In order to better understand baseflow and its parameters, it is necessary to know the flow components. In this respect, Arnold et al. (1998) developed the SWAT model, based on open spatial parameters, to estimate total streamflow and groundwater flow. Following them, Perkins & Sophocleous (1999) developed water models such as SWATMOD by combining it with the MODFLOW model, which simulates underground water flow and river-aquifer interaction. However, running such models requires a wide data network, which must include climate, river and land use data, and this situation is limited to research areas and high-level studies in practice.

Researchers in the literature have used many and various other methods to divide the streamflow into its basic components. For example, Brodie et al. (2005) compared graphic methods and data processing techniques and determined that digital filtering methods stand out from other methods for developing hydrological-based algorithms. In a study conducted by Nathan & McMahon (1990) in the United States of America (USA), four graphical methods and five digital filtering methods were used in 1815 watersheds. The digital filtering methods gave better results in 1145 watersheds and the researchers found that this method is more suitable for the USA.

Piggott et al. (2005) examined the UKIH method and revised UKIH methods, and proved that these methods are as efficient as other approaches in baseflow calculations and give accurate results. Similarly, a study by Aksoy et al. (2009) in the Western Black Sea region of Turkey compared the UKIH method, filtered UKIH methods and revised UKIH methods to determine their superior aspects. Singh et al. (2019) conducted studies to determine the overall baseflow in New Zealand to assist in its watershed ecology management and water resources planning. Regression models were developed in Minnesota, USA, by Cherkauer & Ansari (2005) and, similarly, by Lorenz & Delin (2007) for the southeastern Wisconsin region, to determine the parameters of baseflow and other flows; they used climate, geomorphological and soil properties to develop the regression models. Zhang et al. (2013) used a digital filtering method to separate the baseflow and create regression models.

In recent studies, regression models have been developed to determine the baseflow and which property (or properties) that impacts the watershed is more important for predicting the baseflow. He et al. (2016) studied the Eastern China Changle River watershed to construct a model that depended on meteorological factors to distinguish the contribution of baseflow to the total flow. Fouad et al. (2018) studied 918 watersheds in the USA to construct a model based on the physical and meteorological factors that influence baseflow. Zhang et al. (2020) used regression models to predict baseflow in their study of 596 watersheds in Australia. Similarly, Rumsey et al. (2020) employed regression models to determine the best model for predicting the baseflow in 12 different regions of the USA's Rio Grande watershed. Aboelnour et al. (2021) worked on constructing a regression model based on the watershed and geological characteristics of 130 river regions in Texas, USA.

Many studies were done solely to determine baseflow. Examples of the studies that used the UKIH model are given below:

• A hydrograph separation method based on information from rainfall and runoff records – Mei & Anagnostou (2015),

• An approach to improve direct runoff estimates and reduce uncertainty in the calculated groundwater component in water balances of large lakes – Wiebe et al. (2015),

• Evaluating relative merits of four baseflow separation methods in Eastern Australia – Zhang et al. (2017),

• Estimating groundwater discharge to a lowland alluvial stream using methods at point-, reach-, and catchment-scale – Frederiksen et al. (2018),

• Simulation and forecasting of stream flows using machine learning models coupled with base flow separation – Tongal & Booij (2018),

• Uncertainty assessment in baseflow nonpoint source pollution prediction: The impacts of hydrographic separation methods, data sources and baseflow period assumptions – Zhu et al. (2019),

• Baseflow estimation for catchments in the Loess Plateau, China – Zhang et al. (2019),

• Evaluation of baseflow modelling structure in monthly water balance models using 443 Australian catchments – Cheng et al. (2020),

• Evaluation of typical methods for baseflow separation in the contiguous United States – Xie et al. (2020).

Most studies before 2007 only estimated baseflow because their access to the required data was restricted, but more recent studies have become more and more comprehensive. With the development of geographic information systems and digitalization, access to data became easier, and especially in the last 10–15 years, a higher number of watershed characteristics were included, and results were more accurate. This accuracy facilitated a more precise determination of the elements that comprise total flow.

This study correlated baseflow to watershed characteristics, such as climate and topography. With increased digitalization, using higher-resolution digital elevation models and generating more data, we aimed to obtain greater accuracy. We used the UKIH smoothed minima method to determine baseflow and constructed regression models to find which watershed factors were relatively more important for baseflow. These models differ from the models in similar studies in that they can determine the ratio of the baseflow to the total flow and the factors that can change the baseflow. With this information, the impact of the changing environmental conditions over baseflow can be calculated and this will benefit the water facility projects based on the corresponding watershed.

According to the climate projections in reports by the Intergovernmental Panel on Climate Change (IPCC) and the results of studies conducted by the Turkish State Meteorological Service that covers 2013–2099 period:

• for the 2013–2040 period, the temperature increase is limited to 3 °C.

• for the final 2071–2099 period, according to the Representative Concentration Pathway (RCP) 4.5, especially the Aegean coasts and the Southeastern Anatolian Region, increases of 4–5 °C in summer temperature were predicted.

• according to the RCP 8.5, a countrywide increase in summer temperature was estimated to reach as high as 6 °C.

On the other hand, in both scenarios and all periods, the precipitation in the winter months was predicted to increase. Considering the expected increases in the temperature, this precipitation is not predicted to be in the form of snow or ice and, hence, it is considered that it will not contribute to the water budget of the following seasons (Demircan et al. (2014)). Therefore, it is of utmost importance to manage the water resources by soundly selecting related projects. Most of the studies on the water budget calculations for watershed management plans are based on determining the baseflow and directly building plans on this information. Nevertheless, the correct planning emphasizes determining the actual, significant factors that impact baseflow and then constructing and operating related facilities.

There are reports in the literature on several methods to determine the amount of the baseflow and its ratio to the total flow. There are graphical methods (the constant flow rate method, the constant slope method, the concave method, and the variable slope method), and continuous baseflow separation methods (the digital filtering method, the UKIH smoothed minima method, the revised UKIH smoothed minima method, and the filtered UKIH smoothed minima method). All these methods can only be used to determine baseflow. Since correct water management requires knowledge of the factors that affect the baseflow, regression analysis is required to fill this gap and uncover the significant factors.

This study employed the UKIH smoothed minima method to determine the baseflow, and multiple regression analyses to construct a model to detect significant factors. These methods were applied to the Çoruh watershed in the northeastern part of Turkey, with climate change projections. It is a significant example for studies that focus on other regions and the whole of Turkey, and will be a basis for planned studies in the future.

In the modeling phase of the baseflow, ArcGIS 10.5 software was used to determine the hydrological basin characteristics, and SPSS statistic 22 software was utilized for statistical analyses.

The smoothed minima method, one of the methods used in separating baseflow, was developed by the UKIH in 1980 and yields a value that determines the low-flow characteristics of a stream. The value is derived from the retarded part of the subsurface flow and the ground flow, and the baseflow is separated from the total flow by using the daily average flow time series data.

The factor 0.9 used in the equation is a coefficient used to estimate baseflow (Mazvimavi et al. 2004). All the time series are exposed to the same operation and their turning points are determined. Both turning points and baseflow values can be determined annually or only once by treating all the time series in this way. The turning points determined coincide with the days when total flow results from baseflow (Piggott et al. 2005). Values between the turning points are determined through linear interpolation, and baseflow is separated from total flow. However, during the application, the values determined after linear interpolation should be checked and, if there is a value higher than the daily average flow, those values should be taken as the maximum daily average flow value.

When the smoothed minima method is used in a dry stream, the condition is valid (Hisdal & Tallaksen 2003).

The BFI is a variable value between 0 and 1. As the value draws closer to 1, the value shows the percentage of baseflow in the stream bed as opposed to the total flow. The UKIH module diagram is shown in Figure 1.

Regression analysis uses an equation to express the relationship between variables. In other words, it determines the correlation in which X_i and Y_i variables are related to each other. Regression created with two variables is called simple regression, while regression that examines the relationship between more than two variables is called multiple regression.

The equation above determines the most suitable coefficient to be used in the regression equation.

Before starting the regression analysis, the partial correlation coefficients between each independent variable and the dependent variable are calculated, and there must be a check whether these calculated partial correlation coefficients are close to 1. Being close to 1 indicates that the independent variable affects the dependent variable, and that it is appropriate to include the independent variable in the multiple regression analysis.

Hypothesis tests are performed to determine the independent variables to be used in the multiple regression model. These hypotheses are H₀ (null hypothesis) and H₁ (opposite hypothesis).

The H₀ and H₁ hypothesis tests are used not only to determine the coefficients but also in multiple regression analysis. In regression analysis, the hypotheses can be expressed as follows:

• H₀: All independent variables used in the model are statistically insignificant in explaining the dependent variable (b1 = b2 =b3 = ⋯ = bm = 0).

• H₁: At least one independent variable used in constructing the model is statistically significant in explaining the dependent variable (at least one of the values is not 0).

After the model is tested with the F test, the significance test is performed separately for each of the partial regression coefficients of the independent variables that will form the model (H₀: b_i = 0, H₁: b_i≠0 hypothesis).

By comparing the value corresponding to the t value in the distribution table with the t statistic calculated, the coefficients failing to pass the test according to the significance level are removed from the model, and the regression analysis is performed again. With this application, it is ensured that all the independent variables that can be included in the model contribute significantly to the explanation of the model.

In the regression model, it is important to define the determination coefficient (R²). R² is a coefficient in the developed model showing the degree of relationship between dependent variables and independent variables.

R² obtains values ranging from 0 and 1. As the value of R² nears 1, the capability of the chosen independent variables will increase to explain the dependent value. For instance, for R² = 0.9, the chosen independent variables can explain the dependent variable up to 90%. In this respect, the closer the R² is to 1, the more acceptable the model is. When the variables passing through all the hypothesis tests are used, increasing the R² value should constitute a valid result. If the R² value is equal to 0, the dependent variable cannot explain the independent values.

The significance of the estimation results obtained by this model depends on the conditions of some assumptions. Analyzing data carefully enables better estimation and multidimensional space evaluation (Sharma 1996). To state it simply, the validity of these assumptions reveals the accuracy of the model. Assumptions used for the relationship analyses can be summarized as follows:

• There should not be multiple linear connections between independent variables, i.e., dependency.

• There should not be dependency (autocorrelation) between estimation errors (ε).

• The variances of estimation errors (ε) should be equal.

• The distribution of errors should be normal.

The ArcGIS and SPSS programs were used to determine what watershed characteristics to include in the study at the multiple regression stage by obtaining and analyzing data from Water Affairs Authority, the Turkish State Meteorological Service, and the Ministry of Agriculture and Forestry.

The ArcGIS software was used to determine the watershed rainfall, temperature distribution, drainage field, drainage length, drainage density, drainage index, sloppiness index, mean sloppiness of the stream bed, relief, roughness number, yearly potential evapotranspiration, climate index, elevation, agricultural areas and forest and semi-natural areas by designing the digital elevation model (DEM) within the borders of the watershed in ArcGIS. The parameters to affect watershed baseflow are determined through various statistical operations.

The SPSS software was used to perform statistical operations. The contributions of these parameters to the model and model parameters were evaluated by completing a primarily correlation operation and inputting the model parameters through the linear regression menu. The decision about whether the model was appropriate was taken after the various controls and tests were administered, as indicated in Figure 2.

The Çoruh watershed chosen as the study area is in the northeast of the East Anatolia region. The surface area of 19,654.4 km² was considered significant for the region because its annual rainfall was recorded as 540 mm. As a result of applying the DEM with the ArcGIS program, the watershed area was found to be 20,047 km² and the mean annual rainfall was found to be 531.61 mm. The difference in the size of the watershed resulted from the pixel difference of DEM data with 30 m resolution. Stream networks and used flow observation stations (FOSs) of the Çoruh Basin are shown in Figure 3.

The area's climatic characteristics resemble those prevalent in both the East Anatolia and the East Black Sea regions. The area covers a highly elevated region, where precipitation is mainly in the form of snow, and snow cover persists for most of the year. The major part of the flow results from snow melt in April, May and June. The study area includes the provinces of Bayburt, Erzurum and Artvin within its border. The length of the Çoruh River is 431 km, of which 411 km is inside the Turkish border, and the remaining 20 km is in Georgia, where it flows into the Black Sea. The river carries an average of 5.8 million m³ of sediment per year, which means the Çoruh basin has one of the highest watershed erosion rates. In addition, the Çoruh River is the fastest flowing river in Turkey.

This study used 10 flow observation stations (FOSs) that had been established in the Çoruh watershed (Table 1). The watershed baseflow rate (Q_b) of each was estimated using the daily average stream flow values obtained from the Water Affairs Authority. Monthly mean temperatures in close proximity to flow observation stations (FOSs) obtained from Turkish State Meteorology Services are listed in Table 2.

The mean daily flow rate and baseflow rate of the 10 FOSs in the watershed were determined by a study performed using UKIH smoothed minima method (Table 3).

All the characteristics of the watershed and their related variables were calculated using ArcGIS software, and the statistical values used in the study are presented in Table 4.

Correlation coefficients showing the relationships between the variables that were expected to be included in the model were calculated using SPSS software (Table 5).

The variables in the BFI equation were drainage density (DD) and temperature (T), and variables in the Q_b equation were drainage area (A), total relief (TR) and mean annual rainfall (MAR). Model determination coefficients calculated for both models are given below in a variance analysis table (Table 6) and model coefficients tables (Tables 7 and 8).

The assumptions made when calibrating the models were noted in section 2.2.1. The Variance Inflation Factor (VIF) values and Durbin-Watson (DW) statistics of the models obtained as the result of SPSS analysis of these assumptions are given in Table 9, and covariance controls, errors histogram and additive probability graphics are given in Figure 4.

The results of normality tests of the models are given in Table 10.

Relative error rates are given in Table 11.

The comparison of the estimated values in the designed models with the observed values, and the distribution of these values around the lines with little scattering, show that the model gives results close to real values. The estimated model values and the values obtained with regression analysis and the UKIH smoothed minima method are displayed for comparison in Figure 5.

Baseflow occurs as retarded flow, depending on the precipitation in the watershed, the total length of the stream network, the density of the drainage, and the steepness of the terrain. Baseflow compensates for a considerable amount of the stream flow that dries up in summer, and sometimes for all of it. However, the climate change scenarios predicted for the study area in the winter months indicate a reduction in snowfalls, and it is foreseen that the factors affecting the baseflow will change considerably. To take the changes into account in calculations for future water projects, it is important to know the present baseflow.

Each effective parameter in the estimation of baseflow can reflect various characteristics in different watershed types and, therefore, designing models unique to each watershed is expected to give more accurate results for projects in the watershed. In addition, project experts should evaluate the parameters for each model in respect of significance and R² values. Using more parameters in the project models increases the accuracy of estimations, but the relationships between parameters need to be carefully evaluated by researchers.

Digital maps of the study area were prepared at a spatial resolution of 30 m and the DEM prepared in the study gave similar results to institutional data (from the Water Affairs Authority and the Turkish State Meteorological Service). However, it is seen that resolution-based data may not give desired accurate values and improving digital data sets would contribute to making better models.

The study aimed to estimate baseflow in the Çoruh watershed using various factors, such as watershed characteristics, meteorological parameters, and hydrological properties; the following results were determined: a BFI is important to determine the ratio of the baseflow to the total flow rate. Designing the model with the variables representing negative correlation showed that baseflow in a watershed is affected most significantly by watershed characteristics. This means that the topographical characteristics of the watershed initially affect the design of the BFI model more than the meteorological parameters.

However, as the baseflow increases with precipitation, the precipitation and the areas receiving it become the most important positive elements in the design of the baseflow model, and the total relief related to the surface characteristics of the land that cause a decrease in baseflow is the most significant negative element to impact the model.

Models were accepted as statistically significant and usable for the Çoruh watershed because of the assumptions adopted, trial tests, the considerably higher R² values of the models at calibration and validation stages, the significance levels of models remaining in the desired range, the relative error range between −2.06% and 2.64% obtained at the calibration stage for the BFI model, the relative error values between 0.02% and 1.25% of BFI models at the validation stage, Q_b model error values between −21.19% and 23.75% at the calibration stage, and a relative error range between −11.49% and 12.64% at the validation stage.

Data cannot be made publicly available; readers should contact the corresponding author for details.