Parsimonious Model of Groundwater Recharge Potential as Seen Related with Two Topographic Indices and the Leaf Area Index

Abstract

A concise model, utilizing the threshold values of closed depressions, the convergence index, and the leaf area index (LAI) that play a significant role in modeling vegetation–atmosphere interactions and understanding the impact of vegetation on the hydrological cycle, was employed to pinpoint potential aquifer recharge centroids. The LAI index served as a geographic mask, linking centroid locations to soil vegetation cover. Analyzing a paired subsample of 500 centroids for each strata (true and false), we observed that maximum values of true centroids, indicating potential groundwater recharge, correlated with the presence of abundant vegetation (0.074 < LAI < 0.639). Conversely, lower LAI values were associated with sparse vegetation in false centroids (0.01 < LAI < 0.590). The study’s findings hold promising implications for aquifer management, biodiversity conservation, hydric planning, and land use protection, making a substantial contribution to the field. The recharge hypothesis is theoretically sound and empirically supported to propose that areas of high topographic convergence and closed depressions are potential water recharge zones, and these locations may exhibit permanent or denser vegetation, reflected as higher LAI values. This happens because water accumulates or lingers in these zones, soil moisture is maintained more consistently, and plant roots access water for longer periods, even during dry seasons. Vegetation becomes more resilient and persistent (possibly even forming phreatophytes—plants accessing groundwater). Additionally, there is potential for expanding the research by incorporating field observations, including tracking the routes of surface and subsurface runoff and determining arrival times to the aquifer. Such studies are increasingly vital for addressing contemporary environmental and water resource challenges.

1. Introduction

Groundwater is stored in geological reservoirs (aquifers) made of rocks and deposits from different geological ages and types [1]. Aquifers consisting mainly of carbonate and evaporite rocks with unconsolidated sediments that originate from the deposition of geological material through weathering are referred to as karst aquifers [2,3]. A parsimonious model can be explained in essence as an explanatory model that forecasts on the basis of as few variables as possible. This indicates that the model being developed or used in the research is intentionally kept simple and straightforward. A parsimonious model typically includes only the most essential variables and parameters necessary to achieve the research objectives. The aim is to avoid unnecessary complexity while still obtaining meaningful results.

The systematic classification of geo relief, its components and associations, and its regional structuring is one of the prerequisites for understanding geoscientific systems in different temporal and spatial dimensions [4]. In this sense, it is a two-dimensional surface in three-dimensional space [5]. On the other hand, the geo-relief can be understood as the surface of a body formed by the near-surface subsurface, which the authors of [6] called a three-dimensional geomorphospheric complex. A useful tool in the interpretation of several properties of geo relief exhibited by natural networks results in a convergence index. In geomorphology, geo relief is understood as the interface between the lithosphere/pedosphere and the atmosphere/hydrosphere dimensions [4]. In any of its forms, water is a valuable resource for life and its use is vital for sustainable development. Affording assured water resources for agricultural and domestic activities is a seemingly tough task in areas of scarce water sources and uneven rainfall distribution [6,7]. The hydrogeological conditions of Chiapas are as varied and complex as its topography. The state’s geology, climate, and relief create a mosaic of surface water systems and groundwater regimes. Groundwater varies by region, with productive alluvial aquifers in the Central Depression, limited fractured-rock systems in the highlands, and complex karst aquifers in the north.

Groundwater is a renewable source and the most important hydric resource for the sustainability of current and future generations. It is the stabilizing factor of production chains, especially in areas with rainfall deficits and limited water storage infrastructure, and it is essential to improve socio-economic development in rural and urban areas. A report from UNESCO [8] stated that about 2.5 billion people around the world depend merely on groundwater sources in many activities, such as domestic use and industrial and agricultural purposes. The variability in groundwater recharge affects freshwater availability [9]. The spatiotemporal assessment of groundwater recharge is becoming a critical concern due to data scarcity in different climatic regions [10]. Recharging becomes effective if the infiltration is concentrated at a given time and space [11]. Groundwater recharge requires detailed assessments of scientific principles governing groundwater flow processes [12]. Groundwater recharge is focused in topographic depressions, which receive lateral inputs of snowmelt runoff in addition to vertical inputs of precipitation [13]. The growth in population and the corresponding increase in water demand will lead to much higher groundwater consumption [14], so aquifer sustainable management is mandatory.

The assessment of groundwater recharge (i.e., the downward movement that crosses the vadose zone and enters the saturated zone) is a key element of water resources management [15,16], but its response to extreme climate change has a large degree of uncertainty [17,18]. In most regions, rainfall events have been observed as randomness, with strong spatial variation in frequency and intensity. All of these could affect runoff and infiltration [19], and subsequently groundwater recharge. Previous studies on climate change impacts on groundwater recharge were mostly conducted in temperate regions [20,21,22], with a few exceptions in tropical regions—for example, in Mexico. Hence, there is a need to advance our understanding of climate change effects on groundwater recharge in tropical regions.

Groundwater recharge rate depends on several geological and climatic factors, including soil infiltration capacity, the porosity and permeability of the water-bearing geological formations, the spatial−temporal distribution, frequency and intensity of rainfall events, air and soil temperature, wind conditions prevailing in the area, and the composition of biotic communities. The spatial distribution of recharge is largely dependent on the balance between infiltration and evapotranspiration [13]. In humid regions, where precipitation exceeds potential evaporation, recharge can occur over wide areas within the landscape, and it is considered “direct” [23]. In contrast, in arid and semi-arid regions, where potential evaporation exceeds precipitation, recharge is restricted to localized areas [13]. In these areas, the lateral transfer of surface water increases infiltration in localized areas such as ephemeral ponds [24] and intermittent streams [25]. This mode of recharge is called “localized” or “focused” [26]. Focused recharge may occur in humid regions, but it is most dominant in arid and semi-arid regions. What is appreciated is that it may be associated with the geographic location of sites with geologic properties that facilitate the rate of aquifer recharge. The relevance of knowing the value of the rate of water recharge to the aquifer, can achieve a greater added value when associated with the coordinate pair of geological permeability properties, which would facilitate estimating how relevant the site is to facilitate the rate of aquifer recharge.

Enclosed topographic depressions can occur in virtually any lithology. These ground depressions are regarded as the most common landforms of karst in many landscapes. They can have varied genetic origins ranging from a single basic genetic process (dissolution) especially in the formation of dolines (or sinkholes, the smallest) in karst terrains because of the relative high solubility of carbonates, gypsum and evaporites [27] to a complex polygenetic origin. They range in diameter from centimeters, a few meters to hundreds of meters, exhibiting the well-known functions of storing runoff water, recharging soil moisture, shallow groundwater, and providing food and habitat for many organisms [28,29].

The kilometric-scale depressions as reported in [30], include inter alia, rift basins, volcanic fault depressions, fault depressions [31], large-scale playa lakes [32,33], salt weathering in desert environments [34], tectonic basins created by reverse faults [35], lithospheric flexural subsidence basins [36], intra-montane basins [37] and large poljes [38].

Closed depressions that are intermediate between dolines and solution pans are covered in [39]. Larger depressions are uvalas (coalescence of dolines) and poljes [40]. Collapse and subsidence are two other common processes in the formation of dolines [29]. Tiankengs are large collapse pits (giant collapse dolines) and their origin implies mechanical instability and the chemical removal of collapsed rock [41]. Collapse dolines [42] have the same origin but they are smaller in size. Potholes or entrance pits are usually formed by the collapse of cave roofs [43].

The convergence index is a terrain parameter which shows the structure of the relief as a set of convergent areas (channels) and divergent areas (ridges) [44]; it is a measure of how the flow in a cell diverges (convergence index in negative and positive values). It represents the agreement of aspect direction of the surrounding cells with the theoretical matrix direction. The convergence index is the mean (or weighted mean, if weights are used) aspect difference between real aspect and theoretical maximum divergent direction matrix representing the ideal peak. The convergence index is very useful for the analysis of lineaments, especially those represented by ridges or channel systems as well as a valley recognition tool.

The aim of this manuscript is to delineate potential aquifer recharge centroids by utilizing the degree of spatial organization within a convergence/divergence matrix, the closed depressions and vegetation expression. This approach allows us to predict the likely locations of aquifer recharge zones. The significance and potential impact of this study is also highlighted, as follows, (a) aquifer management: this research will provide valuable insights for aquifer management. Identifying potential recharge centroids can assist in optimizing the use and preservation of groundwater resources, which is crucial for sustainable water management. (b) Biodiversity conservation. Understanding the relationships between landscape features, such as closed depressions and aquifer recharge zones, can contribute to biodiversity conservation efforts. These findings may help protect ecosystems that depend on groundwater resources. (c) Hydric planning: the study has implications for hydric planning, particularly in regions where water resources are limited or subject to stress. Predicting aquifer recharge locations is essential for effective water resource planning. (d) Land use protection: the information provided can inform land use planning decisions. Identifying areas with high potential for aquifer recharge can influence land use policies to prevent activities that might compromise water quality or quantity. (e) Baseline information: this research establishes a baseline of critical information that can be used for various environmental and land management programs. This baseline is essential for future monitoring, assessment, and decision-making.

2. Materials and Methods

2.1. Description of the Study Area

The state of Chiapas, located in southeastern, Mexico, has some of the most varied and dramatic topographic relief in the country, ranging from sea level to volcanic peaks over 4000 m above sea level (masl) in the Northern Mountains and Sierra Madre de Chiapas. This relief contributes to its diverse ecosystems and climate expression (Figure 1).

Chiapas spans an area of 73,612 km². Two major rivers, the Usumacinta and Grijalva, traverse the state, effectively dividing it into seven distinct biodiverse areas [46]. These areas exhibit variations in terms of climate, land quality, economic activities, and demographics. Chiapas is known for its diverse economy, influenced by its varied geography and natural resources. The state is a significant producer of hydroelectric energy, generating approximately 50% of Mexico’s hydroelectric power through seven dams: La Angostura, Malpaso, Peñitas, Chicoasén, Bombaná, Schoina, and José Cecilio Valle [47]. Agriculture plays a pivotal role in Chiapas, with the state being the leading producer of coffee and bananas in Mexico. It also ranks second in the production of papaya, mango, and cocoa, as well as third in tobacco production. Chiapas is the third-largest beef producer and the fourth-largest honey producer in Mexico.

Geographically situated in the tropical zone, Chiapas experiences a wide range of climates due to its orographic configuration. These climates vary from sub-humid temperate to warm humid, and the region receives rainfall throughout the year. Overall, Chiapas is a region of great ecological diversity and economic significance in Mexico. Its varied geography, coupled with its abundant natural resources, plays a crucial role in shaping its unique climatic conditions and supporting a wide range of economic activities, particularly in agriculture and energy production.

The geology of the State of Chiapas (Figure 2) has been described by several authors as consisting of a pre-Mesozoic metamorphic and sedimentary basement, a sequence of Mesozoic sedimentary rocks and a sequence of volcanic and Cenozoic sedimentary and igneous rocks [48]. The oldest of the pre-Mesozoic units are Proterozoic granites, diorites, and gneisses [49,50,51]. These units are covered by a sequence of sedimentary deposits, and metamorphic rocks (serpentinites, schists, quarzites and gneisses) [50,51,52]. These rocks are in turn intruded by gabbros, granodiorite, diorite and granite rocks of the Chiapas Batholith (or granitic Chiapas Massif), which outcrops mainly in the southwest portion of Chiapas [51]. The Mesozoic units are composed of a sequence of marine and continental clastic-carbonate deposits from Triassic–Jurassic to Upper Cretaceous in age. These deposits outcrop in the north-central part of the State forming steep mountains [52]. The Cenozoic sequence (Paleocene to Pliocene) rests on Mesozoic rocks and consists principally of igneous and sedimentary rocks. Rock permeability is delineated in

Table 1. The geology of rocks plays a crucial role in groundwater recharge. The ability of rocks to transmit water, known as permeability, is generally associated with facilitating groundwater recharge.

Type	Characteristics
Sandstone	Sandstone is often highly permeable due to its well-connected pore spaces. Water can flow through sandstone relatively easily, promoting groundwater recharge.
Limestone (e.g., karst)	Limestone is known for developing karst landscapes, characterized by features like sinkholes, caves, and underground rivers. These features enhance water infiltration and contribute to groundwater recharge.
Gravel and conglomerate	Rocks composed of gravel and conglomerate have high porosity, allowing water to move through the interconnected pore spaces. This facilitates groundwater movement and recharge.
Fractured igneous and metamorphic rocks	While igneous and metamorphic rocks are generally less porous, fractures and faults within these rocks can create pathways for water. Fractured rocks contribute to localized groundwater recharge.
Volcanic rocks (e.g., basalt)	Volcanic rocks often have vesicles (voids left by gas bubbles) and fractures that enhance permeability, supporting groundwater movement.
Sedimentary deposits (alluvial and fluvial)	Alluvial and fluvial deposits, such as those found in river valleys, often consist of well-sorted sediments like sand and gravel. These sediments promote both surface water infiltration and groundwater recharge.
Porous and permeable sedimentary rocks (e.g., sand and siltstone)	Sedimentary rocks with well-defined pore spaces, such as sandstone and siltstone, allow the movement of water. These rocks can contribute to groundwater recharge.

.

According with Figure 2, there are 32 types of geology that prevail. Classified by area (ha) with respect to the total area (7.26 Mha), limestone (37.13%), granite (14.67%), sandstone shale (12.95), alluvial (12.82%), sandstone-siltstone (6.09%), and sandstone (4.90%) dominate the geologic landscape. The rest of the strata represented on Figure 1 fulfil the remaining 11.43% of the total.

2.2. Topographic Indices and Leaf Area Index (LAI)

Groundwater potential recharge (GWPR) is highlighted as a crucial factor that supports various activities, including domestic, agriculture, and industrial activities [53]. It accomplishes this by allowing rainwater to infiltrate the ground, replenishing groundwater resources. This is a critical aspect of water resource management. The lithological (related to rock and soil types) and land use characteristics in the region under study are described as having low variability. This suggests that the geological and land use features in the area may be relatively uniform (Figure 2 and Figure 3). The closed depression index identifies pits or depressions in the terrain where water may accumulate but cannot drain out (i.e., they are surrounded by higher elevation). Closed depression features are usually considered to be primarily phenomena of the vadose zone [41]. With this constraint, deep air-filled depressions are only possible in regions with deep water tables. The horizontal transport system at the base of large collapse structures may be a free surface stream, but it could also be a conduit in the phreatic zone through model runoff retention, flood zones or temporary lakes. There exist water-filled closed depression features such as the cenotes of the Yucatan Peninsula in eastern Mexico, which may have originated as vadose zone features, before being flooded by post-Pleistocene sea level rise. An exceptional feature is Zacatón in Tamaulipas, Mexico [54]. The general use of the closed depression index is to detect sinks, potholes, or kettle holes.

From Figure 3, closed depressions in the landscape are typically areas where water can accumulate, often forming small ponds or wetlands. These depressions can serve as natural collection points for precipitation, allowing water to slowly infiltrate into the underlying aquifers and also to explode a vegetation patch. Understanding the geological characteristics of an area is essential for assessing its groundwater recharge potential. Geological surveys, hydrogeological studies, and the analysis of aquifer properties provide valuable insights into the role of rocks in groundwater recharge. Close depression maps are useful for evaluating geomorphological diversity and can be integrated into geomorphological maps as part of a geodiversity inventory [55]. Geodiversity assessments help in understanding the geological and geomorphological richness of a region. A commonly used form of the closed depression index is as follows:

$$CDI=z_s-z_p$$

(1)

where Z_s = elevation of the lowest saddle or spill point surrounding the depression, stands for the elevation of the pit or lowest point inside the depression. This difference gives the depth of the depression before it can overflow. In some GIS-based implementations, CDI is computed over raster cells, and a threshold is used to filter out insignificant depressions (e.g., noise due to DEM resolution). To secure the representativeness of CDI index, the domain was “filled” using the Planchon–Darboux fill algorithm. The method applied is based on a radically different approach that first adds a thick layer of water over all the DEM and then drains excess water [56].

The convergence index (CI) also known as topographic wetness index (TWI) in certain contexts, is slightly different (Figure 4). The CI is designed to quantify how much terrain converges or diverges at a specific point—i.e., how likely it is for water to accumulate or disperse there. A high convergence stands for valleys, channels, and potential flow accumulation zones, whilst low or negative convergence represent ridges, hilltops, or dispersal zones. A general form of CI is as follows:

$$CI=-{\displaystyle \frac{{\partial }^{2}z}{{\partial x}^2}}-{\displaystyle \frac{{\partial }^{2}z}{{\partial y}^2}}$$

(2)

This is effectively the Laplacian of the elevation field z, representing the second spatial derivative. In essence, it measures curvature: whether a surface is bowl-shaped (positive convergence) or dome-shaped (negative convergence).

The convergence index is a measure that indicates how surface water flows or converges within a particular area. A high convergence index suggests that water is likely to flow toward a central point, which can be indicative of potential recharge areas.

The LAI is a dimensionless quantity that represents the leaf surface area per unit ground area.

$$LAI={\displaystyle \frac{Total Leaf Area}{Ground Surface Area}}$$

(3)

It is a strong proxy for vegetation density, transpiration, biomass, and photosynthetic activity. High LAI values suggest lush, dense vegetation; low values suggest sparse or seasonal vegetation. LAI is defined as the one-sided green leaf area per unit ground area in broadleaf canopies and as one-half the total needle surface area per unit ground area in coniferous canopies [57]. According to [58], the LAI values range between 0.0 (bare land, ploughed fields, urban areas, and rock) and about 0.8 (deciduous/mixed forest). For biotic studies, the combination of LAI and the fraction of photosynthetic active radiation (fPAR; 400–700 nm) absorbed by the green elements of a vegetation canopy [59] is relevant and, in theory, its values maximize the presence of vegetation patches which coincide with runoff convergence points.

2.3. Model’s Parameters

QGIS (v. 3.30.3-‘s-Hertogenbosch), is a widely used open-source geographic information system (GIS) software that is valuable for geospatial data analysis and mapping. The raster calculator tool in QGIS allows users to perform mathematical operations on raster data, making it a valuable tool for spatial analysis and modeling. The model’s expression follows the SQL (structured query language). This suggests that SQL-like queries or expressions are being used to manipulate and analyze spatial data in the GIS environment. Four specific models are being used, and they are based on different combinations of minimum and maximum threshold values for closed depressions and the convergence index. These models likely serve different analytical purposes or scenarios. The technical approach involves using a script, which is likely a mathematical or algorithmic representation of the models. Threshold values for closed depressions and the convergence index are provided in

Table 2. These thresholds likely determine the criteria for feature selection or classifying data in the models. Cells that meet these pre-defined criteria may unveil the presence of spatial patterns.

Model ID	Closed Depressions (Unitless; Rank)	Convergence Index (Unitless; Rank)
Model l *	40–80	−5.61–10.95
Model 2	80–120	10.95–14.00
Model 3	120–200	14.00–18.00
Model 4	200–266	18.00–30.00

* (“Closed depressions@1” ≥ 40 and “Closed depressions@1” ≤ 80) and (“Convergence Index@1” ≥ −5.61 and “Convergence Index@1” ≤ 10.95).

.

The structure likely contains the mathematical expression SQL used in the models, which specify how the model’s parameters are named. Threshold, also known as a threshold (cutoff), is the value used as a reference for the selected feature. The choice of threshold values is crucial and can significantly affect output results. Sensitivity analysis by varying the thresholds can provide insights into the robustness of our results.

2.4. Model Outputs

A graphical summary–research process to locate the centroids of potential recharge points is presented in Figure 5.

3. Results

The outputs of the proposed models are thematic maps in TIFF format. These thematic maps are binary, containing values of either 0 or 1. A value of 0 indicates a “false” model output. This means that the pixel or location in the map does not meet the specified conditions or criteria set by the model. A value of 1 indicates a “true” model output. In this case, the pixel or location on the map satisfies the conditions or criteria defined by the model. This approach is common in spatial analysis to delineate areas of interest or significance based on specified criteria.

The results of the four models indicate variations in the presence of false (0 s) and true values (1 s). Models 2, 3, and 4 dropped all false values, meaning that they did not classify any pixels as meeting the model criteria. Model 1, on the other hand, yielded both false and positive results. It included the largest closed depressions and the peak concentration of surface runoff. The total number of pixels where the models were run was 1,733,076. Of this total, the output of Model 1 was 13,848 centroids (Figure 6).

The thematic map depicted in Figure 6 serves two main purposes. (1) Evaluation of geomorphological diversity; the map represents the closed depressions, which are a key component of geomorphological diversity and geodiversity [30]. Geodiversity is the diversity of geological and geomorphological features within an area. (2) Surface runoff location; this also indicates where surface runoff coincides with the presence of closed depressions.

3.1. Model Clarification Conditions

The clarification conditions of the model pertain to the explicit criteria or rules employed by the proposed models to decide whether a pixel or cell on the output map should be assigned a value of 1 (true) or 0 (false). Integrating LAI with CI and CDI, which stand for: identifying areas of potential water accumulation due to terrain-driven flow (CI), identifying isolated pits where water may collect and stagnate (no outlet; CDI). In essence, mapping hydrological sinks or convergence zones. These areas are, by nature, more hydrologically favorable—they are more likely to retain water, leading to higher soil moisture, particularly in semi-arid or seasonally dry environments. These conditions hinge on the amalgamation of threshold values for closed depressions and the convergence index, as previously discussed. The LAI was incorporated into the analysis to associate the coordinate data of the centroids with the condition of the soil cover vegetation. The serial database of 241 days (1 January 2023 to 30 August 2023) was generated. The origin of this index is the MODIS product MCD15A2H v006. The MCD15A2H Level 4, is an 8-day composite dataset with 500 m pixel size [58]. The algorithm chooses the best pixel available from all the acquisitions of both MODIS sensors located on NASA’s Terra and Aqua satellites from within the 8-day period.

To analyze the patterns within the dataset, we partitioned the entire dataset into consistent samples of 500 elements for both false and true centroids, as illustrated in Figure 5. While the sample size may not have been determined for statistical representativeness, our assumption was that all centroids adhered to the categorization generated by Model 1. Subsequently, we computed overall statistics, encompassing minimum, maximum, and average values, based on this subset of data.

3.2. Random Selection Points

Associating the outcomes of Model 1, both true and false values, with the LAI is pertinent. We can presume that the LAI is correlated with soil moisture concentration and soil vegetation cover. The thematic map of the 500 records subsampled of each condition is presented in Figure 7.

Figure 7 illustrates the selection points for the subsample. This subsample is proportionate to both strata, capturing variability within false and true centroids. It was generated randomly to prevent the introduction of bias, and the distribution of water bodies was considered in the process. Although there is not a specific number ensuring the subsample’s representativeness, given the exploratory nature of this manuscript, this sample size is deemed adequate. As depicted in Figure 6, a significant portion of false coordinate pairs are situated at a distance from water bodies. In contrast, true centroids are predominantly located on or very close to bodies of water

In

Table 3. Statistics are associated with the LAI index, including minimum, maximum, and average values from the subsampled data.

TYPE	False: LMn	True: LMn	DIF	False: LMean	True: LMean	DIF	False: LMx	True: LMx	DIF
Limestone (L)	0.14	0.35	0.21	0.34	0.59	0.25	0.43	0.75	0.32
Granite (G)	0.10	0.08	−0.03	0.23	0.27	0.04	0.26	0.58	0.31
Sandstone shale (SSh)	0.10	0.17	0.07	0.43	0.42	−0.01	0.52	0.56	0.04
Alluvial (Al)	0.16	0.07	−0.09	0.15	0.16	0.01	0.56	0.36	−0.20
Sandstone siltstone (Ssil)	0.02	0.09	0.07	0.23	0.31	0.08	0.34	0.48	0.14
Sandstone (S)	0.03	0.12	0.09	0.22	0.23	0.01	0.31	0.37	0.06
Andesite–intermediate volcanic crust (AIVC)	0.06	0.08	0.02	0.47	0.37	−0.11	0.57	0.61	0.04
Limestone–sandstone (Ls)	0.02	0.07	0.05	0.15	0.12	−0.03	0.19	0.26	0.07
Limestone–shale (Lsh)	0.07	0.08	0.02	0.16	0.28	0.12	0.22	0.42	0.21
Conglomerate (C)	0.02	0.10	0.07	0.17	0.19	0.02	0.19	0.37	0.18
Andesite (A)	0.04	NO DATA		0.11	NO DATA		0.19	NO DATA
Sandstone conglomerate (Sc)	0.05	NO DATA		0.17	NO DATA		0.21	NO DATA
Metamorphic complex (Mc)	0.14	NO DATA		0.21	NO DATA		0.24	NO DATA
Shale (Sh)	0.06	NO DATA		0.28	NO DATA		0.34	NO DATA
Granodiorite (Gr)	0.03	NO DATA		0.20	NO DATA		0.27	NO DATA
Lake	0.06	NO DATA		0.18	NO DATA		0.22	NO DATA

, a snapshot of the statistical data is presented.

From Table 3, the first six strata, which are those that occupy the largest geographic area, are located in the upper rows of the table. It is also worth noting that geologic strata of smaller geographic coverage (i.e., andesite, sandstone conglomerate, metamorphic complex, shale, granodiorite and lake) did not correspond to the true output of the model, but only to the false one (“NO DATA”). It is important to highlight the differences between the centroids that met the model specifications and those that did not (Figure 8) in the context of vegetation cover. The comparison between false/true centroids for LAI is represented in Figure 9.

In Figure 8, the contrast between the true and false centroids is evident. Of the sample centroids (397), 79% resulted in average minimum and maximum values with a positive difference; that is, for the true centroids, the minimum average of the data series was 0.074 and the maximum 0.639. On the other hand, in the set of false centroids (107), the minimum and maximum values were between 0.01 and 0.59, respectively. A comparison of the differences in LAI between minimum, maximum and mean by geologic strata is presented in Figure 9.

From Figure 9, the most conspicuous correlation between geologic strata and plant coverage manifested in the LAI:L stratum. Notably, all significant disparities in the minimum, average, and maximum values of LAI between true and false centroids were evident for the L substrate (0.21, 0.25, and 0.32, respectively).

4. Discussion

The recharge hypothesis is theoretically sound and empirically supported to propose that areas of high topographic convergence and closed depressions are potential water recharge zones, and these locations may exhibit permanent or denser vegetation, reflected as higher LAI values. This happens because water accumulates or lingers in these zones, soil moisture is maintained more consistently, and plant roots access water for longer periods, even during dry seasons. Vegetation becomes more resilient and persistent (possibly even forming phreatophytes—plants accessing groundwater). The permeability properties of parent material is quite contrasting. According to [60], the parent material plays a major role in the development of a soil and its physical and chemical properties. Limestone materials have a particularly significant influence on soil morphology, which is because of their high base saturation and calcium content, their tendency to produce alkaline soils, and their solubility in weak acids (ibidem). Despite the evidence of this relationship, we are well aware that due to the exploratory nature of this manuscript, and the subsample data, it is not feasible to reach a conclusion to support the claim that vegetation cover and permeability properties are fully related, as it would be necessary to perform complementary studies with ground measuring devices. Geology and lithology may control the long-term recharge pathways (e.g., fractured basalts or karst vs. clay), essential for understanding deep infiltration and aquifer structure. However, they do not indicate where the water enters the ground. Other indices like the topographic water index (TWI), the soil hydraulic conductivity/permeability index (SHC/P), and the geology/lithology index (G/L) are easier to compute, to predict the vertical water movement toward the aquifer, and control long-term recharge pathways. However, the TWI index is useful for runoff concentration, but weak in reflecting actual infiltration/recharge unless used in conjunction with soil and land cover data. The SHC/P index must be interpreted spatially and contextually (e.g., soil compaction from agriculture may not be reflected in soil maps). And the G/L index is foundational, especially for regional-scale studies, but needs to be combined with surface and soil indicators for local accuracy.

Karst limestone aquifers exhibit hydrological and hydrochemical heterogeneity, with common point source recharge occurring through sinkholes and fissures [61]. The observed heterogeneity in pinpointing GWPRs prompts the exploration of additional research questions. Beyond discerning their locations, researchers could delve into inquiries related to field methods for mapping both surface and subsurface runoff, thereby evaluating potential charge points and employing quantitative field methods to trace the route of subsurface runoff. While this perspective extends beyond the objectives of the current manuscript, it opens up a spectrum of options for future exploration. Based on the parsimonious nature of this study, using minimum, maximum, and average data to characterize a large dataset can provide some valuable insights, but the validity of this approach is tight on the goals of the study and characteristics of any particular analysis. In Ref. [62], the authors suggest that the minimum, maximum, and average values can help provide a high-level overview of the data’s distribution and central tendency. A general overview or the making of high-level comparisons, or summary statistics can be valid. However, if you need to make precise predictions or detailed inferences, you might need more advanced statistical methods.

They are particularly useful for identifying outliers, understanding data ranges, and getting a sense of the overall data patterns. However, using only these summary statistics can result in a loss of detailed information. They condense a potentially complex dataset into a few values, which might not capture nuances or variations within the data. For some analyses, this loss of detail might be acceptable, while for others, it could be a significant limitation.

Another noteworthy relationship was observed in the LAI:G substrate (−0.03, 0.04, 0.31) and LAI:Al (−0.09, 0.01, −0.20, respectively). Notably, the correlation between LAI and Al is particularly contrasting. Firstly, alluvial soils are sedimentary deposits formed by sand, silt, clay, and gravel transported to natural watercourses, a composition that is not ideal for sustaining plant communities. Secondly, as highlighted by [63], alluvial soils, despite being highly productive, are often covered with tall grasses and forest species, serving as locations for agricultural areas. Our results depict this substrate with negative differences in maximum and average parameters. In this context, alluvial sites exhibit reduced vegetation in response to the true centroids in the model parameters. However, it is essential to note that this observed condition extends beyond the scope of this manuscript, presenting an opportunity for posing new research questions. The LAI integrates vegetation density and type, which strongly influence interception losses, evapotranspiration, and soil structure through root systems, also indirectly reflecting land cover condition, management practices, and soil health.

This manuscript delves into two primary aspects of GWPR. Firstly, it explores the influence of abundant plant cover and the coinciding location of centroids where two topographic indices intersect. Vegetation influences rainfall distribution by means of throughfall and stemflow pathways [64], increases the infiltration capacity of a soil [65] and modifies soil structure [66], which commonly result in a runoff reduction. At this point, the permeability of geological formations emerges as a crucial factor in groundwater dynamics, and it appears to be associated with plant cover. On one hand, permeability determines the speed of water movement through the subsurface, impacting aquifer recharge. As observed in connection with the LAI index, this seems to indicate pronounced differences in plant cover. However, these differences are notably conspicuous in three strata within the study region: LAI:L, LAI:G, and LAI:Al. Limestone, often characterized by high permeability due to the formation of solution channels and fractures, facilitates rapid downward water movement to the aquifer, ensuring a high availability of surface water. In contrast, granite, being an igneous rock with generally low porosity and permeability, is less conducive to swift groundwater recharge. Alluvial deposits, comprising materials like gravel, sand, and silt transported by rivers, are often considered highly permeable, allowing for substantial and relatively swift groundwater recharge. However, our evidence suggests the contrary, indicating that true centroids lack robust vegetation cover. Shale, characterized by its fine-grained nature, is generally less permeable, impeding water movement. Nevertheless, the presence of fractures can enhance permeability. Conglomerate, a sedimentary rock formed from rounded or angular clasts cemented together, exhibits variable permeability. Well-cemented conglomerate may have lower permeability, while less-cemented formations with spaces between clasts could be more permeable. Andesite, an intermediate volcanic rock, demonstrates permeability influenced by factors like porosity, vesicularity (presence of gas bubbles), and degree of alteration. Generally, volcanic rocks like andesite have moderate permeability. Metamorphic rocks, resulting from the alteration of pre-existing rocks under high pressure and temperature, exhibit varying permeability influenced by factors such as the original rock type, degree of metamorphism, and presence of fractures or foliation. Granodiorite, an intrusive igneous rock, and igneous rocks, in general, tend to have lower permeability compared to some sedimentary and volcanic rocks. However, the presence of fractures or other structural features can significantly influence permeability. Critically examined, the integrated proposal of convergence index, closed depression index and LAI locates zones of water concentration, identifies microtopographic zones where water can accumulate and linger, and reflects vegetative cover expression and surface–soil interaction potential.

By combining in a concise model the data of zones of water concentration (closed depressions), zones where water can accumulate and linger (convergence index), and permanent vegetative cover, the potential locations can be found where the topographic relief is favorable for mapping the GWPR. These areas are likely to receive and retain water, allowing it to percolate into the aquifer below. This approach is valuable for aquifer management, as it helps pinpoint areas where natural recharge processes are active. It can guide decisions related to land use, water resource management, and conservation efforts to protect these critical recharge zones.

Despite the reduced number of input variables, the tested Model 1 effectively located areas within the geographic space that are likely to be of high relevance for aquifer recharge. The recharge rate is less sensitive to fluctuations in coarse soil [58]. Recharge rates vary considerably with small changes in fine soil, suggesting that soil texture plays a much bigger role in the recharge (ibidem). Ref. [67] found that soil texture causes slightly larger variations in recharge than land cover, and that the recharge decreases considerably in fine soil for all land cover types. Here are some key points to consider based on this finding. (1) The fact that the model output exhibits spatial congruence with the location of water bodies is significant. It suggests that Model 1 is capturing meaningful patterns and relationships within the landscape. This spatial congruence reinforces the credibility of the model’s predictions. (2) The recharge process is influenced by a multitude of factors, including vegetation, soil properties (chemical and physical), evapotranspiration rate, rainfall events, and many more. While the proposed Model 1 is parsimonious, it is essential to recognize the complexity of the recharge processes. Future research can explore the integration of additional variables to account for these complexities to add robustness to the model. (3) Identifying connected sinkholes on the map is a valuable insight. Sinkholes can indeed serve as important pathways for water to rapidly enter aquifers. Understanding the dynamics of conduit systems within the aquifer is crucial for assessing recharge rates and residence times. (4) The areas highlighted as potential recharge centroids have hydrogeological significance. They represent locations where water is likely to enter the aquifer, which is vital information for groundwater resource management and protection. (5) Briefly, we mention the potential for rapid transport and removal of water in conduit systems, leading to short residence times. This underscores the need for further research to not only identify recharge areas but also understand the dynamics of water movement within aquifers.

Posing New Research Questions

Studies focusing on GWPR are highly relevant, not only for their contributions to understanding hydrological processes but also for the valuable geomorphological information they provide. This research has the potential for continued improvement and expansion. By refining the proposed models, incorporating additional variables, and collaborating with experts to enhance its accuracy, the applicability of these findings in the field of aquifer recharge prediction and management might sound attractive. The definition of threshold values for the CD and CI indices and the insights gained from Model 1 is a valuable approach. It is clear that this research has the potential for further development and enhancement. However, before fully jumping to conclusions, soil type matters, human land use too, vegetation type, and depression size and depth. Some soils retain water better, irrigation or land use management can distort the signal, and some plants thrive in dry conditions with lower LAI. Here are some key points to consider for future studies:

• Defining threshold values for topographic indices was an essential step in this research. Further refinement of these thresholds can lead to more accurate identification of potential aquifer recharge zones. By refining the strata rank, we can explore different threshold values to optimize the model’s performance.
• As mentioned before, expanding the number of classes can provide a more detailed and nuanced understanding of potential recharge areas. This can help differentiate between various degrees of suitability for recharge and can be particularly useful for land management decisions.
• Adding new variables, such as soil moisture values and evapotranspiration, could enrich the analysis. The ET losses generally increase with increasing LAI across the whole soil textural gradient [58], and in combination with the soil moisture data, they can provide valuable information about the ecosystem’s capacity to facilitate groundwater recharge. Researchers have to consider how these variables interact with topographic indices.
• Improving the accuracy of location identification and the spatial distribution of potential recharge areas is a commendable goal. Fine-tuning of Model 1 and incorporating additional data could contribute to achieving this objective.
• It is necessary to validate and calibrate Model 1 using field data and observations. This step could help to ensure that the model’s predictions align with real-world conditions.
• Collaborating with experts from related fields, such as hydrology, ecology, and geology, would provide valuable insights and data sources to strengthen this research.
• The relevance of long-term monitoring to assess the actual effectiveness of identified recharge areas over time. This study can provide critical information for aquifer management and conservation efforts.

5. Conclusions

The combination of convergence, depressions and LAI indices is more dynamic, responsive to terrain conditions, and operationally useful, especially in data-scarce or arid and semi-arid environments.

It would be reasonable to infer that high CI and CDI areas, which represent water accumulation or recharge zones, might correlate with regions of permanent or dense vegetation (high LAI). The presence of such vegetation could indicate that these areas have a consistent water supply, possibly due to groundwater recharge, and would form stable ecological niches. This interplay may be a crucial piece in understanding how landscapes manage water flow and vegetation growth, with LAI helping to map the extent of permanent vegetation in these hydrologically significant zones. The visual expression of permanent vegetation in these areas, if verified, would align with the theory of them being recharge points for the water table. The proposed model, based on CD, CI, and LAI indices, demonstrates the capability to pinpoint potential groundwater recharge areas, presenting a significant contribution to hydrogeology and aquifer management, and reflects the ground-level hydrological reality better than using deep or static variables like geology on their own, especially for mapping entry points or recharge hotspots on the surface.

Our future research endeavors involve enhancing the model’s complexity by incorporating additional variables and collaborating with experts in relevant fields to achieve a more comprehensive understanding of the intricacies of aquifer recharge processes. Historically, accessing and analyzing such information posed limitations, but recent strides in computing resources and advancements in ecosystem interface computing environments have opened new avenues.

The LAI was of great help in documenting the fundamental relationship between vegetation cover and geologic strata. We found evidence of two relevant associations between vegetation cover and geologic substrate—specifically, limestone (L) and alluvial (Al). As documented in numerous research papers, L strata exhibit notable permeable properties that may foster the expansion or, at the very least, stability in vegetation cover.

Contrary to L strata, the Al strata might potentially promote more dense vegetation, but this property was not evident in our study, as it lies far beyond the goals of this manuscript.