USE OF THE IDW INTERPOLATION METHOD FOR THE MAPPING OF FLOW AND ELECTRICAL CONDUCTIVITY OF GROUNDWATER IN THE STATE OF CEARÁ

ABSTRACT

Water scarcity in semiarid regions requires the efficient management of groundwater for population growth and regional development. Evaluating the flow rate variability and electrical conductivity (EC) of deep wells is crucial because these parameters indicate the availability and quality of water. This study aimed to map the spatial distribution of these data in the state of Ceará via information from the Geological Survey of Brazil and the inverse distance weighting (IDW) method. A total of 6,018 flow data points and 9,434 EC data points were used for interpolation in SAGA software. The mean flow was 5.45 m³/h, and the EC was 2.21 dS/m. An exponential semi-variogram was the best model for spatial interpolation. Geomorphological factors, aquifer types and environmental conditions influence the distribution of parameters. Regions with more weathered soils presented greater water storage potential. The Salgado, Baixo Jaguaribe and Coreaú Basins had the highest quantitative groundwater potentials. It is concluded that the methodology used is effective in guiding public policies and water management strategies.

KEYWORDS
semiarid; groundwater; geostatistics

INTRODUCTION

In the northeastern semiarid region of Brazil, water is a scarce and vital resource that directly influences life and economic activities in the region (Sousa et al., 2022). Thus, the efficient management of this resource is essential to ensure environmental sustainability and water security (Lopes et al., 2021). In this context, the availability of groundwater plays a crucial role in meeting water demands, especially during periods of prolonged drought (Carvalho et al., 2022).

Deep wells represent valuable infrastructure for groundwater extraction in arid and semiarid regions. Deep drilling allows access to deeper aquifers that are often more protected against surface contamination. However, the effectiveness of these wells is intrinsically linked to the geological, hydrogeological and geographical characteristics of the region (Haaf et al., 2020).

In semiarid regions, groundwater plays an essential role in domestic supply and agricultural irrigation (Kate et al., 2020). According to a survey by the Brazilian Geological Survey (SGB), the state of Ceará has 36,409 extraction points registered in the Groundwater Information System (SIAGAS), the majority (94%) consisting of tubular wells that serve various regions of the world. (Cavalcante et al., 2024). In this context, concern with water quality becomes increasingly relevant, as its contamination compromises both its availability and suitability for use (Chaves et al., 2019; Andrade et al., 2016). Thus, the analysis of variables such as flow rate and electrical conductivity (EC) is essential to ensure the feasibility and safety of the use of these water resources (Carvalho et al., 2020).

Geostatistics is a set of quantitative techniques aimed at modeling regionalized variables with spatial and/or temporal dependence (Karami et al., 2018). Its application in the evaluation of the water quality of deep wells is effective because it offers robust analyses and clear spatial visualizations. This approach allows for the precise evaluation of parameters such as flow rate and electrical conductivity, thus contributing to the management of water resources (Maroufpoor et al., 2020). Khouni et al. (2021) used inverse distance-weighted interpolation via geostatistics to evaluate the surface water quality in Wadi El Bey, which is located in Tunisia.

The intrinsic importance of these topics lies in the pressing need to ensure sustainable access to water and preserve the quality of water resources, thus ensuring food security and the well-being of communities and regional economic development. The efficient management of deep wells, combined with a detailed understanding of the variables involved, directly contributes to the resilience of regions subject to adverse weather conditions (Nunes et al., 2023). In this context, improving monitoring practices is essential for the sustainable and effective management of groundwater resources in a region. Therefore, the objective of this study was to quantify, map and evaluate the groundwater flow and electrical conductivity in Ceará, Brazil, via the inverse distance weighting (IDW) interpolator and geoprocessing technique.

MATERIAL AND METHODS

The study area comprises the State of Ceará (Figure 1), which is located entirely in the intertropical region of Brazil, very close to the equator, between parallels 2.5° and 8° South latitude and meridians 37° and 42° West longitude. In addition, the state is located in the Northeast Region of Brazil, with the Atlantic Ocean to the north, the state of Piauí to the west, and the states of Rio Grande do Norte and Paraíba and Pernambuco to the south and east (IPECE, 2021).

FIGURE 1
Map of the state of Ceará and the presentation of the deep wells evaluated in this study.

According to the Brazilian Institute of Geography and Statistics IBGE (2022), the state has a total area of 148,894,447 km² and is divided politically and administratively into 184 municipalities, with a total of 8,794,957 inhabitants. In percentage terms, its area corresponds to 9.58% of the area of the Northeast Region, 1.75% of the Brazilian territory, and it is predominantly located in a semiarid region (93%).

According to the Köppen classification (1948), Ceará has two main climate types: BSh—hot semiarid, which dominates most of the state (95.10%), especially in the central and southwestern regions—and Aw'—tropical rainy hot‒humid, with rains concentrated in the summer and autumn, predominant along the coast, in the northern, eastern and southeastern areas (IBGE, 2022). The region located in the semiarid region has rainfall concentrated between the months of February and April and rainfall rates between 500 and 800 mm. In addition, the region is characterized by high solar incidence and water scarcity, with an average annual temperature of 27 °C.

There is a great diversity of soil classes in the state due to pedogenesis (Pereira et al., 2019).

To characterize the physical and hydrogeological aspects of the State of Ceará, secondary data from technical publications of the Ceará Foundation of Meteorology and Water Resources (FUNCEME, 2018), as well as recent studies on regional geology (Cajazeiras, 2020; Pinheiro et al., 2023), were used (Rodrigues et al., 2023). Data on the distribution of soil classes and aquifer typology were systematized through a literature review and cartographic analysis by considering the geospatial basis of the state.

The soil classification followed the criteria of the Brazilian Soil Classification System, with the following predominant classes being identified: ultosols, latosols, luvisols, neosols and planosols. The information on the aquifers was organized according to the predominant typology (fissures, sedimentary and karsts), including data on productivity and physicochemical characteristics (Figure 2).

FIGURE 2
Mapping of aquifers in the State of Ceará.

To elaborate the flow and electrical conductivity maps, the data available from the collection of the Geological Survey of Brazil - SGB were used. The digital database consisted of vector files with the location and sampling value of the flow rate (m³ h^-1) and electrical conductivity (dS m^-1) variables. After verifying that they had any abnormalities, the data were interpolated via the IDW method via SAGA 7.8.2 software for three different weighting functions, namely, the exponential, Gaussian and power inverse distances (Equation (1)).

$Z\left(x\right)=\frac{\sum _{i=1}^n\frac{z\left(xi\right)}{d(x,xi{)}^p}}{\sum _{i=1}^n\frac{1}{d(x,xi{)}^p}}$

Where:

Z(x) is the interpolated value at point x;

Z(xi) is the known value at the sampling point xi;

d (x, xi) is the distance between the unknown point x and the sample point xi;

p is the power parameter (or exponent), which controls the influence of distance;

n is the number of sampling points used in the interpolation.

A total of 6018 flow data points and 9434 EC data points were used. The evaluation of the best fitted semi-variogram model was based on the separation of data for calibration (75%) and validation (25%). Through the data obtained by the validation, it was possible to evaluate the

performance of the interpolator via the decision criterion of the lowest value of the square root of the mean error (RMSE), which was defined by Legates & McCabe (1999), which indicates the standard deviation of the errors of the models determined to evaluate which model is more representative.

$\text{RMSE}=\sqrt{\sum (Oi-Ei{)}^2/j}$

in which,

Hi – nth actual observed value (sample);

Ei – nth value estimated via the method (interpolated);

J – Number of observations;

RMSE – Square root of the mean error.

The RMSE is a measure of the average magnitude of the estimated errors; it has positive values in all circumstances, and the lower this value is, i.e., closer to zero, the more adjusted the estimated values are (Hodson, 2022).

RESULTS AND DISCUSSION

The results of the descriptive analysis for the EC and flow data are presented in Table 1. The average of the flow data is approximately 5.44 m³ h^-1. However, there is a relatively high dispersion around the mean, as indicated by the values of variance and standard deviation. The median is also significantly lower than the mean, suggesting that there are high extreme values pulling the mean up.

TABLE 1
Descriptive statistics of the flow rate and electrical conductivity data of the deep wells.

Parameters	Flow (m3/h)	EC (dS/m)
Mean	5.45	2.21
Standard error	0.16	0.29
Median	2.4	1.31
Fashion	1.00	0.25
Standard deviation	13.10	2.85
Sample variance	171.82	8.11
Kurtosis	180.85	32.82
Asymmetry	10.76	4.11
Minimum	0.10	0.01
Maximum	348.50	55.00
Count	6018	9440

The electrical conductivity also shows significant positive skewness, with predominantly low values (approximately 0.25 dS m^-1) but some extremely high EC observations. Kurtosis and skewness indicate that extremely high salinity events affect the distribution, as occurs with flow. This variation in the EC values of groundwater in the state was also reported by Bezerra et al. (2018), who reported values ranging from 0.064 to 23.8 dS m^-1.

The skewness values for both parameters are considerably different from zero. The kurtosis is also very high for both variables. On the basis of these statistical metrics, the flow rate and electrical conductivity data do not follow a normal distribution and exhibit significant skewness and kurtosis characteristics. For the flow, the variation between the minimum (0.10 m³ h^-1) and the maximum (348.50 m³ h^-1) is quite significant, indicating a wide dispersion in the water flows of the deep wells evaluated.

In the case of electrical conductivity (EC), the variation between the minimum (0.01 dS m^-1) and maximum (55.00 dS m^-1) values is also considerable, suggesting great diversity in the chemical composition or salinity of the species. The data show a large variation between the minimum and maximum values for both parameters, which suggests a wide range of values within the sample and indicates heterogeneity in the data.

The State of Ceará has a high diversity of geomorphological features, which are mainly composed of reliefs modeled on sedimentary and crystalline rocks with different development periods (Braga et al., 2018). These conditions strongly influence the amplitude of the minimum and maximum values of EC and flow; thus, different results can be obtained on the basis of the region where the collection was performed.

The RMSE values obtained for the three weighting models applied in the IDW method are presented in Table 2. For both parameters, the exponential model results in a lower RMSE, indicating a better fit to the interpolated data. The exponential model describes a specific spatial dependence between the data, which means that the correlation between the points decreases exponentially as the distance between them increases. This implies that the values tend to change on the basis of spatial variations.

TABLE 2
RMSE values obtained for the semivariogram models applied to the flow and EC data via the IDW method.

Model Type	IDW Vazão (m3 h-1)	IDW CE (dS m-1)
	RMSE	RMSE
Exponential	9.55	2.35
Gaussian	9.71	2.40
Inverse Power	10.03	2.42

The spatial distribution map of the flow rate data from the deep wells for the Gaussian weighting functions (Figure 3a), inverse power distance (Figure 3b) and exponential model (Figure 3c) can be observed. For all the models, the most comprehensive class was the one that classified the flow as greater than 1 m³ h^-1 and less than 4 m³ h^-1. The values that cover the means reported in the present study are as expected.

FIGURE 3
Interpolation of flow rate data via the IDW method for data from deep wells located in the state of Ceará: (a) Gaussian model, (b) power inverse distance model and (c) exponential model.

Notably, despite the smaller occupied territory, the highest total flows explored in Ceará come from sedimentary aquifer wells. Araújo et al. (2005) reported that 77% of the total flow explored in the state comes from wells in the sediment. The spatial concentration of underground water availability is also evident, as the most productive wells are in the most extreme regions of the state.

In general, the three weighting functions presented a similar characterization, with the regions of the Salgado Basin, Baixo Jaguaribe, and Coreaú and the coastal Basin having the greatest potential, exceeding values of 12 m³ h^-1 (Figure 4).

FIGURE 4
Spatial distribution of water flow data from tubular wells via the IDW interpolation method for the exponential weighting function.

The flow rate of a well is strongly influenced by the type of underlying aquifer. Granular aquifers, which are composed of permeable sedimentary rocks, generally have greater water storage capacities than do crystalline aquifers because of their greater porosities and permeabilities. This results in greater groundwater flow in regions where these aquifers predominate, as indicated by the darker coloration in Figure 4 than in the aquifer areas shown in Figure 2. In addition, factors such as slope, soil type, rainfall, land use and occupation, and altitude are also key aspects for understanding groundwater storage and well flow (Nogueira, 2017).

The slope of the terrain is a determining factor in the identification of potential groundwater zones (Ganesan & Subramaniyan, 2024). In areas of uneven relief, surface runoff during rainfall events is more intense, hindering the recharge of aquifers. Kumar et al. (2016), when mapping potential groundwater zones in Killinochi, Sri Lanka, reported that regions with flatter relief (0°–2°) favored slow runoff, prolonged recharge and greater flow. This pattern also helps explain the high flow rates of the tubular wells in the Chapada do Araripe (Salgado Basin) and Chapada do Apodi (Lower Jaguaribe Basin) regions.

The lowest flow rates from the tubular wells were recorded in the Sertões de Crateús Basin, which is located in a crystalline basement region. In this area, the low infiltration capacity of soils, aggravated by moisture losses in anthropic areas, significantly compromises aquifer recharge, which is an essential factor in sustaining the flow of groundwater extraction (Santos et al., 2021). Recharge is directly linked to weather conditions, especially rainfall. Data from FUNCEME (2018) show that, in the last 14 years, the average annual rainfall in the region has ranged from 200–1000 mm, with a predominance of values ranging from 400–700 mm, which limits the natural replacement of aquifers.

Regarding water availability, Araújo et al. (2005) reported results similar to those of the present study. They reported that 74% of the total well flow in the state comes from the Salgado River Basin and the Metropolitan Basin, whereas the middle Jaguaribe and Banabuiú River Basins contribute only approximately 2%.

Maps of the spatial distribution of electrical conductivity for the state of Ceará can be observed in Figure 5 via the IDW interpolation method with Gaussian (Figure 5a), power inverse distance (Figure 5b) and exponential (Figure 5c) models. The models have distinct interfaces: the Gaussian model classifies a greater number of areas with ECs greater than 5 dS m^-1 than the inverse power distance model does. In addition, the latter presents more condensed areas with similar EC values.

FIGURE 5
Interpolation of EC data via the IDW method for data from deep wells located in the state of Ceará: (a) Gaussian model, (b) power inverse distance model and (c) exponential model.

The highest values of electrical conductivity for water from deep wells were observed in locations occupied by crystalline aquifers. Several factors can influence the electrical conductivity values of groundwater. For example, the crystalline basement of rocks predominates in much of the state (Figure 2). Crystalline aquifers are characterized by the presence of fissures, where groundwater is stored. Owing to its solubility potential, this water dissolves the minerals present in the rock material, resulting in high concentrations of salts (Teramoto et al., 2018). In addition, the climate and physical and chemical environments have considerable influences on water quality. The Banabuiú, lower Jaguaribe and metropolitan basins have the potential for high electrical conductivity (EC) values in the region, with records above 5 dS m^-1 (Figure 6).

FIGURE 6
Spatial distribution of the electrical conductivity data of water from tubular wells via the IDW interpolation method for the exponential weighting function.

The Salgado and Serra da Ibiapaba basins had the lowest EC values over a wider range; both have basement sedimentary aquifers, and this type of aquifer favors water movement, reducing the period of contact with the rocks present. How can the types of minerals present in rocks influence lower concentrations of electrical conductivity (Neves et al., 2024)? The local lithology is responsible for the concentration of substances dissolved in the water, and the concentration increases as the water percolates through the soil profile (Andrade et al., 2010).

One of the main challenges for the implementation of groundwater policies in Ceará is the frequency of wells with high salinity, wherein waters have a concentration of salts higher than the acceptable level for consumption (Araújo et al., 2005; Santos et al., 2011; Fernandes et al., 2010; Silva et al., 2011). This problem is so serious that the Federal Government created the ‘Freshwater Program’, which aims to provide access to quality water for human consumption through the use of groundwater. Thus, the geostatistics presented in these maps have been shown to be a very valuable tool for water management in the state.

CONCLUSIONS

An analysis of groundwater flow and electrical conductivity in the state of Ceará, Brazil, revealed significant variations resulting from complex interactions among physical, chemical and climatic factors. The regions with crystalline basements were particularly vulnerable, with water scarcity and low flow rates in most of the territory. The application of an IDW interpolator proved to be effective in the geospatial representation of these parameters, contributing to the understanding of the distribution and quality of groundwater in the state. In view of these results, future studies should consider the application of different interpolation methods, aiming to further improve the accuracy of the analyses and support the sustainable management of water resources in the semiarid region of Ceará.

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• FUNDING:
  This study was financed in part by the National Council for Scientific and Technological Development (CNPq), process nos. 311886/2020-5, 420885/2023-4, and 316421/2023-5; the Coordination for the Improvement of Higher Education Personnel (CAPES) — Finance Code 001; the Ceará Foundation for Support to Scientific and Technological Development (FUNCAP); and the Brazilian Geological Survey (CPRM) for providing the data used in this study.

Edited by

• Area Editor:
  Welington Gonzaga do Vale

Publication Dates

• Publication in this collection
  19 Sept 2025
• Date of issue
  Aug 2025

History

• Received
  15 Oct 2024
• Accepted
  30 June 2025