Groundwater recharge estimation using water table fluctuation and empirical methods

Surface water resources are currently unable to meet the rising water demand due to rapid urbanization, economic development, and climatic variability (Wada & Bierkens 2014; Kummu et al. 2016; Mersha et al. 2018). Hence, groundwater is used as an alternative source of water supply, food production, and economic development. Many uses of groundwater are preferred sources because of their high quality and low cost (Custodio et al. 2016). Groundwater overexploitation has been reported in various places around the world (Pophare et al. 2014; Shahid et al. 2015; Chang et al. 2017; Figueroa-Miranda et al. 2018; Molle et al. 2018; Lili et al. 2020). The rate of groundwater overuse and depletion coupled with increasing population pressure and climate change will challenge the sustainable use of the resource for future generations (Schewe et al. 2014; Zhou et al. 2016). The water withdrawals have exceeded the natural replenishment rates. This could be attributed to land degradation. If the degradation trend continues, 95% of the Earth's land areas could become degraded by 2050 (GEF 2022). Thus, the resultant groundwater levels decline. Groundwater recharge is necessary for the sustainability of groundwater extraction. However, a portion of the rainfall contributing to recharge remains incomplete.

Quantitative measurement of natural groundwater recharge and discharge is one of the prerequisites for effective groundwater resource management. Natural groundwater recharge is the fraction of total precipitation falling on the earth's surface that infiltrates and eventually reaches the water table in the unsaturated zone. Groundwater recharge is the most important hydrologic element for determining the availability and sustainability of groundwater resources (Vu & Merkel 2019; Sanford 2002). Recharge is a major component of the groundwater system and has important implications for water resource management strategies (Tan et al. 2014). An accurate quantification of recharge is extremely important to sustain long-term groundwater use, genuine groundwater allocation decisions, and assess the risk of groundwater contamination (Ebrahimi et al. 2016; Ali & Mubarak 2017).

Different studies employ different groundwater recharge estimation methodologies at different spatiotemporal scales. The methods for estimating groundwater recharge range from simple to complicated. Recharge has been determined using a water table fluctuation (WTF) method (Delottier et al. 2018), empirical methods (Falalakis & Gemitzi 2020; Andualem et al. 2021), an integrated surface water and groundwater modeling approach (Chemingui et al. 2015), baseflow separation (Coes et al. 2007), soil moisture budget (Noorduijn et al. 2018), water balance method (Dhungel & Fiedler 2016), lysimeter (Zhang et al. 2020; Gong et al. 2021), seepage meter (Michael et al. 2003), Darcy's method (Yin et al. 2011), chloride mass balance (Yin et al. 2011; Crosbie et al. 2018), stable isotopes (Jesiya et al. 2021), modeling approach (Ebrahimi et al. 2016; Mogaji & Lim 2020), geographic information system (GIS)-based approach and satellite imageries (Batelaan & De Smedt 2007), etc. According to Healy & Cook (2002), the application of multiple recharge estimation methods increases the accuracy of recharge estimates.

Despite multiple methodologies being employed to estimate the recharge, this field of determination remains challenging due to natural and man-made factors such as surface and subsurface interaction, soil characteristics, geologic heterogeneity, landscape slope, land use, land cover, climate change, anthropogenic factors, and so on (Holman 2006; Choi et al. 2012; Wu et al. 2021). The researcher's experience and the availability of the desired data set influence the method of estimation used. WTF and empirical equations are presented in this research. The most widely used method for determining recharge is the WTF method, which requires knowledge of specific yield and changes in water levels over time. This approach has the benefit of being straightforward and unaffected by the mechanism through which water passes through the unsaturated zone. Multiple equations are used in the empirical technique that accounts for precipitation as a function of recharge. The objective of this research was, therefore, to better understand the groundwater recharge using the WTF and empirical methods in the sub-humid Ethiopian highlands.

For a 4-year period from 2013 to 2016, precipitation was monitored during the monsoon rain phase from June to September. From July through November 2014, the perched groundwater table levels were measured in the piezometers. In the same year, infiltration tests were conducted using a single-ring infiltrometer in the watershed. The measurement was conducted by taking four tests at three distinct slope positions, and the steady-state infiltration values were informed. The detailed procedure of data collection is explained as follows.

Precipitation: During the 4-year monsoon phase from June to September, rainfall depths were measured every 5 min using an automatic tipping bucket rain gauge installed in the watershed's center. In addition, a manual rain gauge was placed in the watershed's center to record daily rainfall if the automatic gauge failed to do so.

Infiltration measurements: The soil's infiltration capacity was measured at 12 different places. The measurements were taken at three slope positions: valley bottoms with slopes ranging from 0 to 6%, mid-slopes with slopes ranging from 7 to 15%, and upslopes with a slope greater than 15%. Each slope position was located on various land uses and land cover types. A single-ring infiltrometer was driven, on average, about 10 cm into the earth. When the water in the ring depth changed with time, the measurement was taken. The measurements were continuous until the flow rate remained constant and the steady-state infiltration capacity was measured. A plastic ruler was used to measure the depth of the water. The median soil infiltration capacity was calculated using simple descriptive statistics.

Water table measurements: In 2014, the dynamics of the perched groundwater table were investigated. Twenty-one piezometers were manually installed to a maximum depth of 4.23 m up to the impermeable layer. To represent the entire watershed, the piezometers were deployed along six transects. The slope locations are also taken into account by the piezometers, with the assumption that the recharge is variable for different slope positions. Five piezometers were installed on the downslope, and eight piezometers were installed on the mid- and upslopes, respectively. Instrumented piezometer depths ranged from 1.2 m on the watershed's upslope, where basalt bedrock is at shallow soil depth, to 4.23 m in the valley bottom, where a saprolite layer is at 4–6 m depth. The piezometers were made of PVC pipes with a diameter of 5 cm. The pipes were capped at the bottom to prevent sediment from entering and at the top to prevent rain from entering. Early in the morning and late in the afternoon, the water level in the piezometers was measured. The daily water table depth was calculated using the average of the two measurements.

Recharge estimation: Groundwater recharge occurs when a portion of the precipitation on the ground surface infiltrates into the soil and reaches the water table. Groundwater recharge estimation is one of the most difficult measurements. However, using a variety of methodologies, the most accurate estimate could be approximated. Different researchers employ different recharge estimating methodologies. The following sections explain the selected groundwater estimation methods that include WTF and empirical methods.

During the recharge period, the equation assumes that water arriving at the water table is instantaneously stored and that all other components are zero. This assumption is most valid for short periods of time, such as a few hours or days, and this is the time frame in which the method should be used. Because of its simplicity, ease of usage, and insensitivity to the water-flowing mechanism in the unsaturated zone, the choice of the WTF technique is appealing. The specific yield is determined by the ratio of the volume of water drained by gravity after field capacity. A linkage between outflow and groundwater levels could be used to calculate an accurate estimate of specific yield (Olmsted & Hely 1962). Keeping this in mind, S_y values were derived from Addisie et al. (2020)'s study applying the Thornthwaite Mather (TM) approach of estimating discharge and water table in the same watershed. Accordingly, the S_y values range from 0.045 to 0.3. These values are solely represented for each piezometer location. For this study, the average number of piezometers per slope position was considered. The same is true for the whole watershed.

Empirical methods: The rainwater that reaches the ground might not fully infiltrate or contribute to the groundwater since some portions will evaporate, transpire, and convert to runoff from the watershed. The infiltrating rainwater enters the pore spaces in the soil and/or percolates downwards to recharge the aquifer. The empirical formulae developed for different locations estimate the recharge from a portion of the incoming rainfall. For this study, nine equations were tested to estimate the recharge. These include the Chaturvedi formula, the Modified Chaturvedi, Sehgal, Krishna Rao, Kirchner, Bredenkamp, Bhattacharjee, Kumar and Seethapathi, and Maxey and Eakin equations (Maxey & Eakin 1949; Krishna Rao 1970; Chaturvedi 1973; Kirchner et al. 1991; Bredenkamp et al. 1995; Kumar & Seethapathi 2002). The formulae were selected because the equations developed in the Indian monsoon climate and the humid tropical climate were similar to the study area. In addition, empirical equations have been applied for the estimation of groundwater recharge worldwide. The advantage of using the empirical equations is that there is no representative observed groundwater recharge in the study area.

The Chaturvedi formula was estimating recharge based on the water level fluctuation method and with respect to the rainfall amount. The Chaturvedi formula was used in India, where the climate is tropical, similar to the study area. This formula was later modified by the work at the U.P. Irrigation Research Institute. According to this equation, there is a lower limit of the rainfall below which the recharge due to rainfall is zero. Therefore, the rainfall recharge will be zero at P = 14 inches. The lower limit accounts for the runoff, soil moisture deficit, interception, and evaporation losses (Abdullahi et al. 2016).

The empirical equation further applied for different levels of rainfall amount:

R_e = 0.20*(P−400) for areas with annual rainfall between 400 and 600 mm.

R_e = 0.25*(P−400) for areas with P between 600 and 1,000.

R_e = 0.35*(P−600) for areas with P above 2,000 mm.

For this study, the area receives annual rainfall in the range of 600–1,000 mm; the recharge estimation considered the equation, R_e = 0.25*(P−400).

Maxey & Eakin's (1949) computation involves the estimation of mean annual precipitation for the sub-basin, followed by scaling these volumes by a factor representing losses by evaporation and surface water runoff, and then summing the recharge for the whole basin. The empirical relationship between average annual precipitation and recharge using recharge coefficient values ranges from 0 to 25%. This study considers the values estimated by the Groundwater Estimation Committee Norms for describing the alluvial area recharge which could be taken as 20–25% of rainfall for sandy areas and 10–20% for areas with high clay content (more than 40% clay). For this study, the values of 20% were used since the study area represents the alluvial area with high clay content. Table 1 indicates the details of each equation. All the selected empirical equations consider the annual rainfall as a function of groundwater recharge.

The formula of Kumar & Seethapathi (2002) is similar to the Chaturvedi empirical formula derived by fitting the estimated values of rainfall recharge and the corresponding values of rainfall in the monsoon rainy season using the nonlinear regression equation. In addition, Sehgal developed the equation based on the regression analysis.

The recharge coefficients from individual equations were recalculated, assuming that the recharge from WTF was reliable and could accurately forecast the recharge coefficient employed in the empirical equations for the study area. The recharge coefficient is defined as the ratio of recharge to effective rainfall, which reflects the amount of effective rainfall that contributes to groundwater aquifers expressed in percentage.

Soil infiltration rates were measured at different slopes in the watershed for the year 2014, and the resultant values varied significantly based on their positions. Steady-state infiltration rates ranged from 8 to 162 mm h⁻¹ (Figure 3). The median infiltration rate was 45 mm h⁻¹. Infiltration measurements show that the upslope areas have greater rates of infiltration than the mid- and downslopes. Figure 3 indicates the comparison between rainfall intensity and infiltration rate. The result shows that the median infiltration rate is exceeded by rainfall intensity on the upslope less than 20% of the time but less than 2% of the time on the down and mid-slopes. This indicates that most of the incoming rainfall infiltrates in the upslope and the remaining runoff. That is the water recharging the groundwater table in the downhill saturated area. The water that does not evaporate in the upper slope areas will recharge the groundwater.

Estimating groundwater recharge has been done using a variety of methods. These techniques generate estimates on a variety of time and space scales, and they cover a wide range of complexity. The accurate calculation of groundwater recharge is difficult in today's state of scientific understanding. As a result, using several estimation methods is highly advantageous and could be an indicator of accuracy (Healy & Cook 2002). WTF techniques and empirical equations are the two most commonly applicable methods used for estimating the recharge and are addressed in detail in the subsequent sections.

The recharge from WTF is estimated with the assumption that the mechanisms by which water travels in the watershed vary depending on the slope position. Therefore, the median recharge values are reported both at each slope class and at the watershed scale. The water table observation was carried out during the monsoon rainy season (July–October) when 61% of the annual rainfall falls. The change in the water table depth (Δh) at each slope position is determined using 31, 21, and 26 turning points for down-, mid-, and upslopes, respectively. For the whole watershed, 26 points are used for recharge determination (Figure S2). The recharge values from the down-, mid-, and upslopes of the total rainfall were 11.6, 14.5, and 22.4%, respectively, with an average of 16.1% (Table 2). The recharge from the whole watershed was 17.7%. Recharge for the watershed is fundamentally represented by a unique value of 89.7 mm (16.9%), taking the average of the two methods (Tables 2 and 3). The WTF method is best applied for short-term water level rises that occur in response to precipitation events. These conditions usually occur in regions with shallow water table depths. Seasonal fluctuations in groundwater levels are common due to seasonal precipitation, evapotranspiration, and irrigation. There is no irrigation or pumping practice in the study area, and more than 64% of the land is the cultivated land with a low evapotranspiration rate. The recharge estimate in the upslope was higher. However, the soils on the upslope were shallow, and we expect more evaporation and lower recharge than the other slope positions in the landscape. The higher infiltration rate in the upslope, on the other hand, contributes to a 22.73% increase in recharge (Table 2).

Studies estimating recharge from WTF are constrained by uncertainty in specific yield (Obuobie et al. 2012). The pumping test is considered reliable; however, Dietrich et al. (2018) argued that there is no accepted method for its estimation. This could indicate that there is a great variation, for example, within a soil textural class using multiple methods. With this uncertainty, the study used the S_y values from the TM procedure. The S_y values predicted from each piezometer water level at different slope positions represent the watershed well (Addisie et al. 2020). Hence, the S_y values from the 21 piezometers range between 0.045 and 0.3. The WTF was ideal for estimating the watershed recharge as this method requires a sharp rise and fall of the water level in the piezometer. The recession curves were carefully plotted to avoid personal bias as the method has a subjective concern.

Nine empirical equations were selected and employed to estimate the recharge of the watershed for the 4-year period (2013–2016). The selected formulas and the corresponding recharge values are summarized in Table 3. As indicated in the table, the estimated recharge values are in the range of 6–39% (Table 3). This shows that the Krishna equation was underestimated in 2015 and Sehgal was overestimated in 2013. The overall empirical equation average recharge was 18.9% (Tables 3 and 4). Surprisingly, the estimated recharge using the modified Chaturvedi value in 2014 had a similar recharge to the WTF (8.98 mm, 16.9%). Observing the overall recharge values, the modified Chaturvedi has a similar result for the 4-year average (16.9%), followed by Bredenkamp (15.2%). Generally, from the average of the empirical equations, about 19% of the rainfall has the potential to recharge the groundwater aquifer in the Ene-Chilala watershed.

When comparing the recharge from WTF to the average empirical equation, the empirical equation deviates by about 1.8%. Considering the WTF method is more scientific and realistic (Maréchal et al. 2006), the study here recalculates the recharge coefficients of the empirical equations using the WTF recharge values. The old coefficient values were then recalculated using the existing individual equation using the average estimated recharge value from the WTF method. Then, the modified coefficient value of the equations is determined as indicated in Table 4.

In summary, water table depth and recharge are determined by averaging (Alemie et al. 2019). Rainfall is the principal source of replenishment of soil moisture in the soil water system and recharges groundwater. The recharge depends upon the rate and duration of rainfall. During the onset of the rainfall, the majority of the rain runoff, and in July and August, more rainfall infiltrated. The infiltrated water is stored in the soil profile and moves further downslope as interflow occurs, hence the rise in groundwater, especially in the downslope. The response of the rise and fall of the groundwater table corresponds with the amount of rainfall. Recharge and rainfall correlation demonstrates a clear relationship for the four rainy seasons using the average recharge estimated from empirical equations. The rainfall–recharge correlation shows a linear relationship with a coefficient of determination, R² = 0.99 with the equation R_e = 2.86P−10.98 (Figure S2). Many studies, including all the empirical equations developed on the assumption of rainfall and recharge, have a strong relationship.

To estimate groundwater recharge in the Ene-Chilala watershed, data were collected at the field scale, including rainfall, infiltration, and groundwater-level between the monsoon rain seasons of June and November. The interactions between rainfall, infiltration, groundwater, and recharge were examined. The Ene-Chilala watershed, like other watersheds in the sub-humid highlands, is characterized by interflow on the upslope and eventually saturates the downslope areas. The infiltration rate on the upslope was greater, followed by the mid- and downslopes. The greater infiltration rate facilitates interflow toward the downslope. In the downslope, this process raises the perched groundwater table near the surface for a longer period of time than in the upper slopes. The recharge was estimated using the WTF and empirical equations provide an average rate of recharge estimate. Although recharge estimation is a challenging task, the application of various techniques is advisable. Despite the variation in estimated values of recharge, the average values from different slope positions could be taken as an ideal value of recharge for the watershed. The empirical equations can also be applied with the modified coefficients from the WTF method. This study suggests that the modified Chaturvedi equation could be utilized to estimate natural recharge for similar watersheds that do not have observed recharge measurements. In order to arrive at sound recharge estimates, long-term seasonal and spatial groundwater data collection should be employed for sustainable groundwater management efforts.

The author gratefully thanks the sources of financing this work including the USAID-PEER project (AID-OAA-A-11-00012); International Foundation for Science (W/5844-1); and Norman E. Borlaug Leadership Enhancement in Agriculture Program Borlaug (LEAP-016258-82). The author specially thanks the people living in the watershed and data collectors.

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

The authors declare there is no conflict.