
==== Front
MethodsX
MethodsX
MethodsX
2215-0161
Elsevier

S2215-0161(24)00367-4
10.1016/j.mex.2024.102916
102916
Earth and Planetary Science
Optimal interpolation approach for groundwater depth estimation
Yasin Kalid Hassen kalidh84@gmail.com
ab⁎
Gelete Tadele Bedo b
Iguala Anteneh Derribew c
Kebede Erana d
a Department of Remote Sensing, Space Science and Geospatial Institute, Entoto Observatory and Research Center (EORC), P.O. Box 33679, Addis Ababa, Ethiopia
b Geo-Information Science Program, School of Geography and Environmental Studies, Haramaya University, P.O. Box 138, 3220, Dire Dawa, Ethiopia
c Center for Rural Development, Oromia State University, P.O. Box 209, Batu, Ethiopia
d School of Plant Sciences, College of Agriculture and Environmental Sciences, Haramaya University, P.O. Box 138, 3220, Dire Dawa, Ethiopia
⁎ Corresponding author. kalidh84@gmail.com
15 8 2024
12 2024
15 8 2024
13 10291622 5 2024
14 8 2024
© 2024 The Author(s)
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
In arid and semi-arid regions where surface water resources are scarce, groundwater is crucial. Accurate mapping of groundwater depth is vital for sustainable management practices. This study evaluated the performance of three spatial interpolation techniques – inverse distance weighting (IDW), ordinary kriging (OK), and radial basis functions (RBF) – in predicting groundwater depth distribution across Dire Dawa City, Ethiopia. The results demonstrated the superiority of the RBF method, exhibiting the lowest RMSE (3.21 m), MAE (0.16 m), and the highest R2 (0.99) compared to IDW and OK. The IDW method emerged as the next best performer (RMSE = 4.68 m, MAE = 0.16 m, R2= 0.97), followed by OK (RMSE = 5.32 m, MAE = 0.42 m, R2= 0.95). The RBF's superior accuracy aligns with findings from other semi-arid regions, underscoring its suitability for data-scarce areas like Dire Dawa. This comparative evaluation provides valuable insights for selecting the optimal interpolation method for groundwater depth mapping, supporting informed decision-making in local water resource management.

The methodological approach comprised:• Implementation of three interpolation techniques, namely, inverse distance weighting (IDW), ordinary kriging (OK), and radial basis functions (RBF), utilizing 56 groundwater depth measurements from locations dispersed throughout the study area.

• Cross-validation through randomly withholding 20 % of the data for validation purposes.

• Comparison of the techniques based on statistical measures of accuracy, including root mean square error (RMSE), mean absolute error (MAE), and the coefficient of determination (R2).

Graphical abstract

Image, graphical abstract

Method name

Ordinary Kriging (OK), Inverse distance weighting (IDW), and Radial basis function (RBF)
Keywords

Geostatistics
Hydrogeology
Kriging
Inverse distance weighting
Radial basis functions
==== Body
pmcSpecifications tableSubject area:	Earth and Planetary Sciences	
More specific subject area:	Earth and Planetary Sciences	
Name of your method:	Ordinary Kriging (OK), Inverse distance weighting (IDW), and Radial basis function (RBF).	
Name and reference of original method:	N/A	
Resource availability:	Data available within the article	

Background

Groundwater is pivotal in sustaining human life and fostering sustainable development, particularly in regions grappling with water scarcity and increasing populations [1]. Accurately estimating groundwater depth is paramount for effective water resource management, agricultural planning, and environmental protection [2]. Despite recent advancements in groundwater assessment techniques, significant knowledge gaps persist in our understanding of how spatial interpolation methods perform under diverse hydrogeological conditions, especially in semi-arid regions. These gaps encompass the limited comparative studies of spatial interpolation techniques in varied geological settings, particularly in semi-arid areas of developing countries [3]. Furthermore, there is a lack of understanding of how different interpolation methods perform under varying data densities and complex hydrogeological conditions. Additionally, a lack of region-specific guidelines for selecting the most appropriate interpolation method for groundwater depth estimation hinders effective water management strategies [4].

These knowledge gaps give rise to several pressing needs in groundwater management. Foremost among these is the demand for accurate, cost-effective methods to estimate groundwater depth in areas with limited data availability. This need is closely followed by the requirement for robust comparative analyses of interpolation techniques in challenging environments, such as semi-arid urban areas experiencing rapid development. Moreover, there is a growing demand for actionable insights to guide policymakers and water resource managers in selecting the most suitable interpolation methods for their contexts [5].

Researchers has employed various interpolators to address this issue, including geometrical, statistical, spatial statistics, functional, stochastic, physical, and integrated techniques [1,2,[6], [7], [8]]. However, the accuracy of these methods in capturing the spatial continuities between dispersed sample sites remains a challenge, necessitating a comparative analysis to identify the most effective approach [[8], [9], [10], [11]]. In this regard, methods such as inverse distance weighting (IDW), ordinary Kriging (OK), and radial basis function (RBF) have been proposed as potential solutions that account for spatial autocorrelation and provide reliable estimates even in regions with limited data [4,7,8,[12], [13], [14]]. Nonetheless, the efficacy of these techniques is not uniform; it is significantly influenced by the geological and climatic context of the study area, as well as by the size of the area, the density of sampling, and the spatial structure inherent to the groundwater system [15,16]. Therefore, a nuanced application of these methods, tailored to the specific conditions of the study area, is essential for accurate groundwater analysis.

The city of Dire Dawa, Ethiopia, presents an ideal case study to address these knowledge gaps and unmet needs [17]. As an urban center grappling with water scarcity due to its semi-arid climate and rapid industrialization, Dire Dawa epitomizes the challenges many developing regions face worldwide. The city's semi-arid climate, characterized by erratic rainfall patterns and extended dry seasons, exacerbates the pressure on groundwater resources [18,19]. These conditions make Dire Dawa a critical and relevant context for evaluating the performance of different interpolation methods. To tackle the identified knowledge gaps and unmet needs, this study aims to systematically assess and compare the performance of IDW, OK, and RBF interpolation methods for groundwater depth estimation in the semi-arid urban environment of Dire Dawa, Ethiopia. By evaluating the accuracy of these interpolation methods, the research seeks to select the optimal interpolation technique based on available data.

The methodology employed in this study involves a rigorous comparison of IDW, OK, and RBF methods, with accuracy validated using statistical techniques such as coefficient of determination (R2), mean absolute error (MAE), and root mean square error (RMSE). This approach allows for a nuanced understanding of each method's strengths and limitations in the specific context of Dire Dawa, offering valuable guidance for future applications in similar semi-arid urban environments. The findings of this study have substantial implications for enhancing our comprehension of groundwater dynamics and improving the precision of groundwater depth estimations. This research aims to comprehensively evaluate IDW, OK, and RBF techniques for groundwater depth estimation in challenging environments by addressing the critical gap in comparative studies of spatial interpolation methods in semi-arid regions, particularly Ethiopia.

Method details

Study area

Dire Dawa City, one of Ethiopia's two chartered cities, is located in the eastern part of the country, around 515 km from the capital Addis Ababa. Situated between 9°30′−9°37′N latitude and 41°45′−41°54′E longitude, it covers an area of 1332.62 km2 with diverse topography including mountains (45 %) and low-lying flat lands (35 %) (Fig. 1) [20]. Groundwater is the region's primary water supply, but it is severely overexploited due to excessive pumping rates of around 400 l/s to meet urban needs [21]. The city has numerous private shallow and deep wells, highlighting the significance of groundwater management.Fig. 1 The study area's geographical location: (a) Ethiopia's relative position on the African continent; (b) the precise location of Dire Dawa City in eastern Ethiopia; and (c) the administrative wards and city boundaries within Dire Dawa with groundwater site.

Fig 1

Dataset

The data utilized in this study was procured from multiple sources, encompassing various Federal sector organizations within the Dire Dawa Administration Council (DDAC). These organizations include the Ministry of Water Resources (MoWR), Water Well Drilling Enterprise, Ethiopian Institute of Geological Surveys (EIGS), Water Work Design and Supervision Enterprise (WWDSE), DDAC of Water Mines and Energy Office, and Hara Water Supply Emergency Project. As essential institutions in Ethiopia's water sector, these organizations possess invaluable insights into water resources, related hydrological data, and their management. The dataset, comprising groundwater depth measurements from 56 sites acquired from these organizations, served to predict groundwater depth using various interpolation techniques and facilitate a comparative analysis of selected modeling approaches (Table 1).Table 1 Groundwater location points and corresponding water level measurements across Dire Dawa city.

Table 1Well Index	Local Name	X	Y	Elev	GWL	Well Depth	SWL	
BH-09	Melka Jebdu-3	805,167	1,063,299	1131	1108	106	23	
BH-52	Railway station	813,936	1,061,662	1180	1150.23	62	29.77	
BH-54	Textile-1(old)	816,702	1,062,643	1192	1166.9	45.7	25.1	
BH-07	D/Dawa food com	814,520	1,063,426	1177	1147	115	30	
BH-15	Hafcat #2	814,941	1,063,539	1167	1167	56	0	
BH-12	Palace	814,172	1,061,499	1202	1167.9	48.8	34.1	
BH-14	Hafcat #1	814,865	1,063,384	1168	1168	86	0	
BH-56	Textile Old W-3	816,481	1,062,864	1191	1165.1	61	25.9	
BH-57	Textile No 4	816,792	1,062,510	1189	1161.6	62.5	27.4	
BH-17	Amdael #2	814,239	1,064,632	1136	1112	124	24	
BH-10	East Afri Bot#2	814,020	1,061,049	1205	1168.5	120	36.5	
BH-11	East Afri Bot#3	814,520	1,061,049	1205	1168.5	125	36.5	
BH-73	Sabian TW-8(89)	812,867	1,062,764	1155	1155	100	0	
BH-74	Sabian TW-9(89)	812,461	1,064,371	1130	1113	129.2	17	
BH-75	Sabian TW-10(89)	813,117	1,063,444	1160	1139	76	21	
BH-76	Sabian TW-11(89)	811,921	1,063,785	1150	1139	78	11	
BH-80	Genderige BH-3	805,170	1,063,115	1150	1138.45	80	11.55	
BH-21	High school	813,851	1,060,388	1212	1164	79.2	48	
BH-22	Dil Chora Hospi	813,892	1,061,139	1210	1170.9	47	39.1	
BH-23	Dire dawa food cplx	814,400	1,063,426	1170	1137	112	33	
BH-43	Sabian Pw-1	812,491	1,063,930	1147	1133.5	72.4	13.5	
BH-44	Sabian Pw-2	812,097	1,063,961	1144	1134.7	98.8	9.3	
BH-46	Sabian Pw-4	812,527	1,063,543	1163	1143.3	104.6	19.7	
BH-47	Sabian Pw-5	812,362	1,063,793	1157	1141.1	101.8	15.9	
BH-48	Sabian Pw-6	812,767	1,063,462	1174	1151.2	86.2	22.8	
BH-49	Sabian Pw-7	813,081	1,063,268	1169	1145.3	82.7	23.7	
BH-50	Sabian Pw-8	812,573	1,062,411	1190	1175	87.7	15	
BH-51	Sabian Pw-9	813,111	1,063,263	1169	1147.75	71	21.25	
BH-55	Textile-2(old)	816,573	1,062,781	1195	1176.2	61	18.8	
BH-53	Elfora	810,907	1,062,360	1210	1187.68	82	22.32	
BH-95	Prison	814,010	1,063,530	1160	1138.3	47.8	21.7	
BH-99	Municipality#1	812,440	1,061,310	1192	1166.7	33.5	25.3	
BH-100	Municipality#2	812,460	1,060,990	1197	1175.1	35	21.9	
BH-13	Amdael well #1	814,356	1,064,666	1136	1112	135	24	
BH-81	MelkaJebdu bh-1	808,534	1,064,055	1140	1140	100	0	
BH-107	Former Railway	814,025	1,061,390	1212	1174	54.9	38	
BH-83	Genderige BH-5	808,532	1,063,462	1145	1126.32	80	18.68	
BH-84	Genderige BH-6	805,945	1,063,792	1100	1082	50	18	
BH-102	Shinile milit.	814,072	1,065,654	1112	1101	119	11	
BH-105	Police training	812,730	1,061,950	1189	1167	65.6	22	
BH-112	D/D CFE	814,091	1,061,785	1200	1161	54.9	39	
BH-61	Textile Old W-8	816,460	1,062,460	1195	1150	52.6	45	
BH-63	Textile Old W10	816,025	1,062,825	1185	1144	50	41	
BH-64	Textil Old W-11	816,677	1,062,984	1175	1158	59	17	
BH-66	Textile A.W-1	814,343	1,064,427	1133	1095.7	116	37.3	
BH-68	Textile A.W. 3	814,531	1,064,064	1134	1107.58	91	26.42	
BH-85	Cement old BH-2	811,170	1,062,350	1192	1179.2	25	12.8	
BH-86	High way author	813,073	1,062,031	1190	1159.5	47.2	30.5	
BH-87	D/D R.R.C.	814,072	1,064,275	1187	1159.5	63	27.5	
BH-88	Locust control	811,806	1,062,708	1160	1139	48.7	21	
BH-111	TW5(2002)	809,796	1,064,843	1129	1095.6	124	33.4	
BH-113	Melkajebdu(old)	806,549	1,064,183	1100	1056.6	125.9	43.4	
BH-08	Melka Jebdu #2	805,241	1,063,341	0	0	95.6	0	
BH-71	Sabian TW-6(89)	812,052	1,064,343	0	0	122.3	0	
BH-45	Sabian Pw-3	812,511	1,063,930	0	0	55	0	
BH-101	Municipality#3	812,460	1,060,990	0	0	32.5	0	
Bh-62	Textile Old W-9	816,080	1,062,886	0	0	50	0	
BH-67	Textile A.W-2	814,652	1,064,390	0	0	82.3	0	

Interpolation techniques

The study utilized the ArcGIS 10.8® Geostatistical Analyst Wizard (GAW) to perform interpolation and spatial statistical analyses. The GAW encompasses two primary interpolation techniques: deterministic and geostatistical, each with its own set of methods. Most techniques within the GAW employ point data to create a surface or grid [22]. This study applied both interpolation methods to map the groundwater depth point data. Specifically, IDW and RBF were selected as deterministic techniques, while OK was chosen as the geostatistical interpolation technique.1. IDW: The IDW method derives a statistical surface from measured values at multiple points belonging to the surface. The values are calculated using a mathematical equation (Eq. (1)), with each point assigned a weight [2]. This method predicts and calculates the phenomenon's value at any point on the network based on the inverse proportion to its distance from the measured points [23]. Notably, the predicted values will not exceed the values of the samples and will be constrained by known values as the prediction decreases with distance [24]. This technique utilizes the measured data at specific locations within the area to estimate data for locations without available measurements [2]. Each point's data exerts a significant influence close to where measurements are unavailable, but its impact diminishes as it deviates from that location [25].(1) zj=∑izidijn∑i1dijn

where zj: estimated value for the unknown point at location j. dijn: distance between known point i and unknown point j. zj: value at known point i. n: user-defined Exponent for weighting.

We employed the IDW method with a power value of p = 2, also known as inverse distance squared weighting. This choice aligns with common practice in hydrogeological studies [26]. The p-value of 2 was selected because it offers a reasonable balance between the influence of nearby and distant points on the interpolation. Furthermore, we validated this choice by minimizing the RMSE through cross-validation [27].2. RBF: The RBF is the most accurate interpolation method [12]. As an exact interpolator, it predicts values identical to the measured values at the same point, and the generated surface must pass through each estimated point. However, it is essential to note that the predicted values may differ from the maximum and minimum of the measured values [27]. The five main functions of the RBF include thin-plate splines, splines with tension, fully regularized splines, multiquadric functions, and inverse multiquadric splines. Each function produces a distinct surface for interpolation with its unique shape. As the number of specified entry points increases, the surface becomes smoother, and points farther away exert a more significant influence [28]. The estimated values are based on a mathematical function that minimizes the surface curvature, resulting in a smooth surface. The smoothness of the resulting surface is determined by the smoothing parameter [4]. The RBF was calculated using a mathematical equation (Eq. (2)).(2) ∅(r)=r2+c2

where r is the distance from sample to estimation and c is the smoothing factor.

We utilized a spline with tension as the kernel function for the RBF interpolation. This choice was made due to its adaptability in fitting surfaces with varying smoothness. It is handy for groundwater depth estimation, where the surface may exhibit gradual and sharp changes [29]. The tension parameter was optimized to 0.006, allowing the surface to fit the data points closely while maintaining an appropriate degree of smoothness for groundwater surfaces [30].3. OK: OK is a sophisticated and reliable interpolation technique that applies statistical techniques to the data before use. Unlike deterministic methods, OK can predict unknown values that are greater or smaller than known ones but do not exceed them. The OK method is well-suited for nonlinear and linear completion [14]. As an advanced geostatistical technique, it creates an estimated statistical surface from dispersed points with z values (Eq. (3)). Kriging is a linear interpolation procedure that offers unbiased linear estimates of various values in space [6]. The semivariogram, which incorporates the autocorrelation of spatial data to create mathematical representations of the spatial correlation structures expressed by variables, is a crucial component of the Kriging model for the analysis and modeling of geostatistical data [6,28].(3) z(so)=∑i=1nγz(si)

where (so): prediction location, γ: unknown weight for the measured value at the i location, z(si): measured value at the i site, n: number of samples.

In applying OK, we utilized a logarithmic transformation of the data to address potential non-normality in the groundwater depth distribution, which is common in hydrogeological datasets [31]. A second-order trend removal was applied to account for large-scale spatial trends in the groundwater surface, with an explanatory trend of 10 to capture finer-scale variations. We selected a Gaussian kernel function and semivariogram model suitable for smoothly varying spatial phenomena like groundwater levels [32]. The nugget effect of 0.05 accounts for measurement errors and micro-scale variability, while the lag size of 593.73 was determined based on the average spacing between sampling points in our study area [27].

Method validation

The accuracy of the employed spatial interpolation techniques was evaluated using three statistical criteria: R2, MAE, and RMSE. To validate the models, 20 % of the groundwater point data was withheld during the interpolation process [3,12,23,33].a) RMSE

The RMSE is a critical parameter that indicates the accuracy of spatial analysis in remote sensing and GIS applications [33]. A lower RMSE value corresponds to more accurate estimates in areas lacking data. Cross-validation can be utilized to determine the optimal control parameters for a spatial interpolation model by minimizing the RMSE (Eq. (4)) [34].(4) RMSE=1n∑i=1n[z^(xi)−z(xi)]2

where: z(xi)is observed value at the point xi, z^(xi)is the predicted value at the point z^(xi), n is the number of samples (sum of squared errors) observed-estimated (values), and n is the number of pairs (errors).b) MAE

The MAE measures the error's magnitude and assesses the estimates' bias. Higher values indicate more significant discrepancies between observed and predicted values (Eq. (5)) [15].(5) MAE=1n∑i=1n[z^(xi)−z(xi)]

where: z(xi) is the observed value at the point xi, z^(xi)is predicted value at a point xi, n number of samples.c) R2

The R2, also known as the coefficient of determination, is expressed as the ratio of the total squares of regression to the total squares. Its value ranges from zero to one and can be calculated using the Eq. (6). The R2 value represents the square of the linear correlation coefficient [2,33].(6) R2=[∑i=1n(P1−Pave)(Q1−Qove)]2∑i=1n(P1−Pave)2∑i=1n(Q1−Qave)2

where: Qave is the mean of measured values, Pave is the mean predicted values, and n is the number of samples used for prediction.

Results and discussion

Groundwater is an essential resource in various regions worldwide, particularly in arid and semi-arid areas where surface water resources are scarce [1]. This study aimed to assess the accuracy of different interpolation methods for determining groundwater depth in Dire Dawa City, Ethiopia, a semi-arid region with limited surface water availability. The research focused on three widely used interpolation methods: OK, IDW, and RBF. A comparative analysis was conducted to gain comprehensive insight into the spatial distribution of groundwater depth and the effectiveness of these interpolation methods in capturing the study area's hydrogeological complexity.

The performance of each interpolation method was rigorously assessed using three key metrics: MAE, RMSE, and R². These metrics were selected for their complementary nature, providing a multifaceted evaluation of the accuracy and reliability of each method. The evaluation results revealed that the RBF method demonstrated superior performance, exhibiting the highest accuracy across all metrics. Specifically, the lowest MAE of 0.16, lowest RMSE of 3.21, and highest R² of 0.99 were recorded for RBF (Table 2). These results underscore the RBF method's ability to effectively balance the capture of local variations while maintaining broader regional trends in estimating groundwater depth [8].Table 2 Cross-validation results for interpolation methods.

Table 2	RBF	OK	IDW	
MAE	0.16	0.42	0.42	
RMSE	3.21	5.32	4.68	
R2	0.99	0.95	0.97	

The MAE of 0.16 for the RBF method is very low, indicating that the average difference between the predicted and observed groundwater depths is minimal. This high level of accuracy is significant for water resource managers, who rely on precise estimations to make informed decisions about groundwater management strategies. Furthermore, the RMSE of 3.21, while higher than the MAE, remains significantly lower than the values obtained using other methods. This discrepancy between the MAE and RMSE suggests that RBF is more effective at handling outliers and extreme values, providing a more robust interpolation in areas with complex hydrogeological conditions [35]. The nearly perfect R² value of 0.99 further demonstrates that the RBF method explains almost all the observed data variability, offering a highly reliable interpolation technique for groundwater depth estimation in the semi-arid context of Dire Dawa City.

In contrast, the OK and IDW methods showed comparable performance in terms of MAE, yielding a value of 0.42. This value is notably higher than that of RBF, indicating that, on average, the OK and IDW predictions deviate more significantly from the observed values. The higher MAE suggests these methods may be less suitable for applications requiring high precision in groundwater depth estimation in this region [36]. Additionally, the RMSE values for the OK and IDW methods were significantly higher than those obtained for the RBF method, indicating more significant variability in the prediction errors. In particular, the higher RMSE for the OK method suggests that it may be more sensitive to extreme values or outliers in the dataset, which could be a critical consideration in areas with complex hydrogeology or where anomalous groundwater depths are present [37].

Although the R² values for the OK and IDW methods were still relatively high, they were lower than those of the RBF method. This difference in R² values indicates that while OK and IDW are capable of interpolation techniques, they may not capture the spatial variability of groundwater depth as accurately as RBF in this specific context [1]. Interestingly, the slightly higher R² for the IDW method than the OK method suggests that it may be marginally better at capturing the overall trend of the data despite its known limitations in handling complex spatial patterns.

The spatial patterns of the interpolation methods offer valuable insights into the distribution of groundwater in Dire Dawa City (Fig. 2a-c). The OK method generated a surface with smooth transitions between areas of different groundwater depths, which could be beneficial in understanding regional trends [4]. The large red area in the north of the OK interpolation map indicates higher groundwater levels, transitioning through purple, blue, green, and yellow in the south, which suggests a general trend of decreasing groundwater depth from north to south. This pattern could be related to topography, geology, or groundwater recharge and extraction patterns, providing crucial insight for regional water resource planning and management.Fig. 2 Spatial interpolation map based on (a) OK, (b) IDW, and (c) RBF.

Fig 2

In contrast to the smooth transitions of OK, the IDW method captured more localized variations but may have overemphasized individual data points, as evidenced by the distinct circular patterns in the interpolated surface, particularly in blue and green areas (Fig. 2b). These “bull's-eye” patterns, a known characteristic of IDW, can sometimes lead to unrealistic representations of the groundwater surface [13]. However, the ability of IDW to capture local highs and lows could be valuable for identifying specific areas of concern, such as localized depressions in the water table or areas of unusually high groundwater levels [22]. This level of detail might be beneficial for targeted interventions or site-specific groundwater management strategies.

As demonstrated by its superior performance metrics, the RBF method appears to strike an optimal balance between the need for localized detail and the preservation of regional trends in groundwater depth interpolation [8]. Compared to the OK and IDW methods, the RBF interpolation displays more localized variations than OK but smoother transitions than IDW. The distinct red areas in the north and some southern portions, coupled with the complex patterns in the central and southern regions (Fig. 2c), indicate that RBF can effectively capture broad trends and local variations in groundwater depth. This balanced approach makes RBF particularly suitable for a wide range of applications in groundwater management, from local project planning to regional water resource assessments. The choice of interpolation method can significantly impact decision-making in water resource allocation and management. While the OK method provides a smoother, more generalized view that may be more suitable for regional planning and policy-making, it may overlook significant local variations critical for site-specific interventions. In contrast, the IDW and RBF methods, with their ability to capture more local detail, might be more helpful in locating specific areas needing intervention, such as zones of rapid groundwater depletion or unusual accumulation. The balance struck by RBF between local detail and regional trends makes it particularly valuable for a wide range of applications, from local project planning to regional water resource assessments.

The enhanced performance of the RBF interpolation method demonstrated in this study is consistent with the findings of numerous prior investigations conducted in arid and semi-arid regions. For example, Sun et al. [1] observed that RBF surpassed the OK and IDW methods in interpolating groundwater depths in northwest China, which shares climatic similarities with Dire Dawa City. Similarly, Raghuvanshi and Tiwari [38] indicate that RBF significantly outperformed IDW in groundwater level interpolation in the semi-arid Sagar district of India. Moreover, Adhikary & Dash [12] found RBF was more effective than IDW and OK in Delhi, India, providing further evidence to support this conclusion. Arkoc et al. [3] also reported the RBF method's success in modeling groundwater levels in Turkey's Ergene Basin compared to the IDW method. Kamińska & Grzywna [8] noted that RBF creates a more accurate representation of reality for measured groundwater levels than IDW.

The consistent findings across different geographical contexts demonstrate the robustness of RBF as an interpolation technique for estimating groundwater depth in semi-arid environments. However, it is important to recognize that the optimal interpolation method may vary based on a study area's specific hydrogeological conditions and data characteristics. Varouchakis & Hristopuos [23] found that kriging methods could outperform RBF in certain scenarios within a semi-arid region of Crete, emphasizing the need for site-specific evaluation of interpolation techniques. Although RBF's performance in Dire Dawa City is promising, it should be considered in light of the region's unique hydrogeological setting and data distribution. Antonakos & Lambrakis [28] highlighted the OK model as the most appropriate spatial interpolation method for groundwater level distribution in Greece's Korinthia Prefecture. Hua et al. [16] found OK the most accurate method for spatial interpolating groundwater depth in the Shule River basin, with data transformation enhancing its precision. Shahmohammadi-Kalalagh and Taran [4] observed that OK had the highest accuracy compared to IDW, RBF, and other models. Khazaz et al. [25] also found that OK is the optimal model for estimating groundwater levels in Haouz Plain, Morocco. These studies emphasize the importance of selecting interpolation methods best suited to the local conditions of the study area.

In light of the pressing global concern for water scarcity, especially in semi-arid regions, the study's findings on the precise interpolation capabilities of the RBF method hold considerable significance. These findings provide a solid foundation for groundwater management in semi-arid areas like Dire Dawa City. The highly accurate groundwater depth maps generated using the RBF method are critical for making informed decisions regarding groundwater extraction, protecting recharge zones, and creating sustainable water usage plans. Furthermore, these maps can establish a zoning system for regulated groundwater extraction and guide urban planning and development. The RBF method's exceptional ability to capture regional trends and local variations makes it ideal for developing early warning systems for groundwater depletion and creating targeted groundwater management policies. This research offers a robust foundation for strengthening groundwater management strategies, particularly in regions facing water scarcity challenges, by providing precise spatial information on groundwater depths.

Limitations

The results of this study, which are specific to the unique characteristics of Dire Dawa, make significant contributions to the comparative analysis of spatial interpolation methods for groundwater depth mapping. The study emphasizes the importance of evaluating various interpolation techniques based on local hydrogeological conditions and data availability. Although the developed methodological framework and criteria may not be universally applicable, they can guide similar studies in other areas, helping to select the most appropriate interpolation method for effective groundwater management. The study also acknowledges its limitations, such as the impact of sample size, spatial distribution, and local anomalies on interpolation accuracy. It recommends that future research consider these factors and incorporate auxiliary variables like topography, geology, and land use to improve the accuracy of groundwater mapping in diverse settings.

Ethics statements

This work does not use human subjects, animals, or data collected through social media as research materials.

Data availability

Data is available within the article.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

CRediT authorship contribution statement

Kalid Hassen Yasin: Methodology, Software, Formal analysis, Investigation, Resources, Data curation, Writing – original draft. Tadele Bedo Gelete: Writing – review & editing. Anteneh Derribew Iguala: Writing – review & editing. Erana Kebede: Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data is available within the article.

Acknowledgments

The authors express their gratitude to all the data providers referenced in the article for providing the necessary data for this analysis.
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