Estimating groundwater recharge rates in the Upper Awash Basin, Ethiopia under different combinations of model complexity and objective functions

Groundwater recharge is a key component of the water balance, and as a result, accurate quantification of the rate of natural groundwater recharge is essential for sustainable groundwater resource management. The total groundwater resource in Africa is estimated to be 0.66 million km³ (MacDonald et al. 2021), and this resource is unevenly distributed in the continent with the largest groundwater volumes found in North African countries such as Libya, Algeria, Egypt, and Sudan. Ethiopia has 30 billion cubic meters of groundwater resources (Kidanewold et al. 2014). This resource plays a vital role in supplying water for irrigation, drinking, and other purposes in arid and semi-arid regions of the nation. However, the increasing population and climate change lead to excessive withdrawal of groundwater in the region and pose a serious problem in sustainably utilizing groundwater resources. Therefore, accurate estimation of groundwater recharge rates is crucial for assessing water security and developing reliable groundwater resource management plans.

The volume of rainwater that reaches the water table cannot be immediately and reliably measured, making it difficult to estimate groundwater recharge rates (Scanlon et al. 2002). There are several ways to measure groundwater recharge rates; however, each technique has inherent weaknesses due to various factors that affect the recharge rate, such as climate, geomorphology, litho-structural setting, and water table. Instead, several approaches are available to estimate the rate of groundwater recharge. Therefore, it is recommended to use multiple methods to estimate the recharge rate and compare the results to increase the reliability of the estimates. These approaches include the water balance approach (Baye et al. 2012; Azagegn 2014; Mechal et al. 2015; Neil 2015; Gidafie et al. 2016; Izady et al. 2017; Birhanu et al. 2018; Tenalem 2019; Yun et al. 2023), baseflow separation approach (Berehanu et al. 2017), water-level fluctuation approach (Healy & Cook 2002; Baye 2009), chloride mass balance (Scanlon et al. 2006; Dassi 2010; Azagegn 2014; Berehanu et al. 2017), AMBHAS_1D model (Verma et al. 2023), environmental trace and stable isotopes (Li et al. 2017; Parlov et al. 2019), and the Analytic Hierarchy Process model (Varouchakis et al. 2022). However, there is no widely applicable method available for estimating groundwater recharge rates because of the complexity of the groundwater system and the large variation of factors affecting the recharge rates. Therefore, it is recommended to use multiple methods to estimate recharge rates and compare the results to increase the reliability of the estimates.

Numerous previous studies have been undertaken to estimate groundwater recharge rates in the Upper Awash basin of Ethiopia using various approaches. For example, Baye (2009) applied a water table fluctuation approach to estimate the rate of groundwater recharge, and they found that the annual water recharge of the Upper Awash Basin is 90 mm/year. Similarly, Azagegn (2014) used the water balance approach, a different hydrologic model, to quantify groundwater recharge rates in the Upper Awash basin of Ethiopia, and they reported about 82.5 mm/year. The results of these studies, particularly the water balance approach, provide inconsistent results, and thus further studies need to be conducted in the study basin. The reason for the inconsistent results in the water balance approach may be associated with the structure of the model, the level of model complexity, and the applied objective functions.

Hydrologic models play a vital role in estimating groundwater recharge and support the well-informed decision on the sustainable management of these resources. A wide variety of hydrologic models with different mode complexities, structure, parameters, and input data are available to model the groundwater recharge rate. Given that the selection of a hydrologic model for quantifying the groundwater recharge rate has been challenging, it is important to understand the effect of different levels of model complexities and objective functions in estimating groundwater recharge rates. Therefore, the present study uses the HBV-light model to quantify the rate of groundwater recharge in the Upper Awash basin of Ethiopia under different levels of model complexities and objective functions. A total of 10 combinations of model complexities and objective functions were used for the analysis.

In this study, groundwater recharge model calibration was applied for both levels of model complexity and model objective functions. The Nash–Sutcliffe efficiency (NSE) was used as the objective function in the MC-based calibration approach to adjust nine HBV-light model parameters (Table 1). The HBV-light model runs for 10,000, and therefore the best parameter sets (1,000 from 10,000 parameter sets) were selected based on the NSE value, 0.6. Among the 1,000 parameter sets, a single parameter set with the highest NSE value was applied to simulate groundwater recharge. However, it is vital to notice that the hydrological model calibration employing a single fine-tuned parameter set results in equifinality (Uhlenbrook & Leibundgut 1999; Choi & Beven 2007), which is not taken under consideration within the current study. The HBV-light model was calibrated for the period 1986–2008 during which 1986–1987 is a warm-up period. The model validation was employed from 2009 through 2013 using independent datasets.

The one-factor-at-a-time (OAT) method was used to analyze the sensitivity of the model parameters for different combinations of precipitation inputs and model complexity. Several studies that examined sensitivity analysis have made extensive use of this methodology (van Griensven et al. 2006; Nonki et al. 2021). To perform OAT, the model was run 1,000 times, varying one parameter while keeping the other parameters constant. The value of the best-fit parameter of the MC simulation and the corresponding range of values (Table 1) were used to perform the OAT. Based on the different objective functions such as Kling–Gupta efficiency (KGE), NSE, coefficient of determination (R²), LogNSE, and Volume Error (VE), the most influential parameters that have a strong influence on the model simulation result were identified and then refined to improve the efficiency of the model.

The hydrograph and scatter plot were used to compare the observed and simulated flows in addition to these statistical evaluation criteria. The model that performed the best in simulating recharge estimation was selected based on statistical evaluation metrics.

In this study, a sensitivity analysis was performed to determine the impact of various model parameters on the flow within the catchment area. The results indicated that the FC, LP, and BETA parameters had the greatest sensitivity across different objective functions and model complexities. These parameters were found to significantly affect the simulation of flow. On the other hand, the UZL, K0, and MAXBAS parameters had minimal influence on the model results. The results underscore the significant impact of the objective function and model complexity on parameter sensitivity. Specifically, when using the VE objective function, FC, LP, and MAXBAS consistently emerged as the most sensitive parameters across both model complexities. Conversely, PERC, UZL, K0, K1, and MAXBAS showed minimal levels of influence. When analyzing the LogNSE objective function, it was found that the semi-distributed HBV-light model was most sensitive to the K2 parameter. On the other hand, the lumped model complexity showed that BETA and PERC were the most influential parameters. It is worth noting that the sensitivity of the model parameters is greatly influenced by the methods used to conduct the sensitivity analysis (Devak & Dhanya 2017) and the objective functions chosen (Nonki et al. 2021).

Figure 7 shows the comparison of daily observed and simulated streamflow from the Hombele gauging station during the period 1 January 1988 to 31 December 2008 for calibration and 1 January 2009 to 31 December 2013 for validation for semi-distributed (a) and lumped (b) and different objective functions. We noticed errors in the streamflow measurements, which are highlighted by black circles. We provided two reasons for detecting these errors. The first reason is that in some cases, streamflow measurements were recorded even when all available rainfall inputs indicated no rainfall. This suggests that there may be observational errors in the data. It is possible that there were mistakes or inaccuracies in the process of measuring and recording streamflow, leading to these discrepancies. The second reason is related to the baseflow component, which represents the contribution of groundwater to streamflow. We noted that this component had a relatively minor impact on the daily streamflow values. This observation suggests that there may be inconsistencies in the observed data, which can affect the accuracy of the model's performance. During the calibration period, the model exhibited superior performance regardless of the combination of objective functions and model complexities. This indicates that an acceptable fit was achieved by the model's ability to calibrate its parameters to match the observed data. We did note, however, that the model's precision throughout the validation period might be lower. This is because the model is evaluated using independent data that were not used for calibration. Therefore, any discrepancies or errors in the observed data during the validation period may lead to less accurate model performance.

The findings of assessing the performance of the semi-distributed and the lumped HBV-light model in combination with the KGE objective function are shown in the following statement. The outcomes indicate the calibration scores for multiple metrics, such as R², NSE, PBIAS, KGE, and VE. The semi-distributed HBV model had calibration scores of R² = 0.79, NSE = 0.78, PBIAS = −0.3, KGE = 0.89, and VE = 0.59. The lumped HBV-light model had calibration scores of R² = 0.77, NSE = 0.76, PBIAS = −1.5, KGE = 0.88, and VE = 0.58. These evaluations show the degree of agreement between the observed data and the model-generated simulated data.

The LogNSE objective function combined with the semi-distributed and lumped HBV-light model produced the best results during model calibration. The calibration score, as measured by the R², was 0.8 (0.8), indicating a strong correlation between the observed and simulated values. The NSE score was also high at 0.79 (0.77), showing a good fit between the observed and simulated values. In contrast, the use of other performance evaluation matrices, such as KGE and PBIAS, resulted in lower model performance, particularly for the lumped model complexity levels. This suggests that these objective functions were not as effective in accurately determining the model's performance.

The combination of the NSE objective function and the semi-distributed HBV-light model produces better results compared to the lumped HBV-light model. The semi-distributed and lumped model yielded a better calibration score with an NSE of 0.8 (0.73) and a KGE of 0.88 (0.81), respectively. It is worth noting that both models performed well despite their different complexity levels. The semi-distributed model, which accounts for spatial variability in the watershed, outperformed the lumped model in terms of calibration score and overall performance. However, the lumped model, which assumes uniform characteristics throughout the watershed, still provided a reasonably accurate representation of the system.

By utilizing the MC calibration approach to determine the optimal model parameters, we were able to estimate groundwater recharge through the use of five objective functions and five evaluation matrices. Our findings indicated that recharge levels throughout the study area were dependent on the particular model configuration being utilized (Table 5). The recharge values for the semi-distributed HBV-light model ranged from 185.9 to 280.5 mm. On the other hand, the recharge values for the lumped HBV-light model ranged from 185.3 to 321.7 mm. These variations indicate that the model configuration has a significant impact on the estimated recharge values (Table 6 and Figure 8). In the study area, the recharge rate for the semi-distributed model was estimated to be 196.9 mm when the NSE objective function was utilized. However, when the KGE objective function was used, the recharge rate was estimated to be 185.9 mm. These findings emphasize the significance of the chosen objective function in determining the estimated recharge. To determine the most effective method for estimating groundwater recharge, various objective functions were evaluated. The objective functions with the highest NSE, KGE, R², VE, and lowest PBIAS values were identified as the most suitable options for estimating groundwater recharge, regardless of the complexity level of the model (Table 7). Figure 9 displays the graphical representation of annual groundwater recharge for two different model complexities and objective functions. In general, analyzing groundwater recharge through the use of different objective functions and evaluation matrices can offer useful information on recharge patterns in a particular area. The findings highlight the significance of selecting the right objective functions and model configurations to achieve precise estimates of groundwater recharge.

The study utilized the HBV-light model to determine the amount of groundwater recharge in the Hombele catchment, situated in the Upper Awash basin in Ethiopia. The objective was to compare the outcomes of groundwater recharge estimations by varying the model complexity and objective functions. Two levels of model complexities were considered in this study. The first level, known as semi-distributed model complexity, involves dividing the study area into nine elevation zones with a vertical spacing of 200 m. This allowed for consideration of orographic effects on rainfall and temperature. The second level, referred to as lumped model complexity, focuses on only one elevation zone and ignores orographic effects. A MC calibration scheme was employed to calibrate the model parameters. The calibration process aimed to find the best-fit parameters for each rainfall input, with the NSE objective function. Using this scheme, the model parameters were adjusted to better match the observed data. To evaluate how well the model estimates groundwater recharge, we used five different objective functions: NSE, KGE, PBIAS, R², and VE. By using these performance metrics, we were able to thoroughly assess the model's ability to simulate the groundwater recharge rate across various objective functions. The main objective of this study was to determine the most effective approach for estimating the groundwater recharge rate in the Hombele catchment. This was done by comparing the results obtained from various combinations of model complexities and objective functions. The analysis provided valuable insights into the reliability and accuracy of the HBV-light model in this specific context.

• Model objective functions and model complexities have a significant impact on the sensitivity of the HBV-light model parameters and objective functions.

• In most of the objective functions, the FC and LP parameters are the most sensitive model parameters when using the HBV-light model as a lumped and a semi-distributed one. MAXBAS and K0 are noninfluential model parameters in the study catchment for both model complexity and all objective functions.

• Better calibration and validation results were obtained when using a semi-distributed HBV-light model with NSE and KGE objective functions.

• The model-based recharge estimation depends on the objective function used and the levels of model complexity.

• The groundwater recharge rates in the study region range from 185.9 to 280.5 mm/year when using a semi-distributed HBV-light model and from 185.3 to 321.7 mm/year for a lumped HBV-light model.

The available data collected onsite is limited in quantity and unevenly distributed across the study area. In addition, there may be uncertainties associated with the accuracy and reliability of the observations.

To enhance the quality of this study, it is essential to establish monitoring stations capable of collecting a diverse range of climate and hydrological data. These stations should be equipped with instruments that can measure variables such as stream flow, rainfall, and temperature.

Conducting field studies and collecting comprehensive and accurate data on groundwater recharge is essential for validating and improving the results of the model used in this study. These efforts contribute to a better understanding of the hydrological processes in the study region and enhance the reliability of the study's findings and recommendations.

Overall, it is important to consider the uncertainty of model complexity and objective function while quantifying the major water balance components of the study region.

Dr. Seifu Kebede was unable to verify their authorship due to unforeseen reasons, however the Corresponding Author is able to vouch for their authorship and the Author contributed as an advisor in the Ph.D fellowship of the Corresponding Author.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.