Hydrogeological mapping of fracture networks using earth observation data to improve rainfall–runoff modeling in arid mountains, Saudi Arabia

1 Introduction

Mapping of geological lineaments such as faults, joints, and fractures is an important approach in the field of hydrology for rainfall–runoff response analysis because faults act as water storage and cause changes in groundwater. A geological lineament is a linear feature on the earth’s surface that shows a straight or nearly straight feature and is found on different geological structures [1,2]. Remote sensing application for the detection of geological lineament is useful for hydrogeological study [3,4,5,6,7,8], geological hazards research for earthquakes and landslides [9,10,11,12,13,14] and hot springs [13,15].

Remote sensing data from optical and radar systems are often employed for lineament extraction and characterization of active faults. Modern optical sensors favored by certain researchers include Landsat thematic mapper, enhanced thematic mapper, Operational Land Imager (OLI)/thermal infrared sensor, advanced spaceborne thermal emission and reflection radiometer and Sentinel 2 [16]. Sentinel 1, interferometric synthetic aperture radar, advanced land observing satellite, phased array L-band synthetic aperture radar, and digital elevation model are examples of radar-based sensors that have been widely used for lineament and active fault characterization [14,17].

Analysis and mapping of geological lineament have been performed in arid and sub-arid regions due to sparse vegetation and exposure of bedrock [18,19]. Lineament studies performed in Saudi Arabia include Wajid Group [20], North East of Wadi Ar Rika Quadrangle [21], Bulghah area [22], Neom mega-project area [23,24], southern Arabian Shield [25], Al Qunfudhah Area [26], and Wadi Fatima [27].

Remote sensing imaging provides an effective tool for identifying geological features like lineaments and is valuable for mapping lithology [28,29]. Studies show several remote sensing and geographical information system (GIS) techniques to delineate, analyze, and identify geologic lineament features, including manual approaches, semi-automatic methods, and automatic methods [30]. Manual lineament feature extraction approach is performed by using human operating visualization, and extraction utilizes image enhancement techniques, e.g., manual digitization, visual analysis and interpretation, band ratio, directional filtering, and transformation [31,32,33]. Semi-automated geological lineament extraction is the process of lineament detection and identification based on some digital image analysis techniques and visual interpretation [30]. The lineaments can be obtained using digital image analysis after pre-processing and enhancement, and the user may also choose to manually modify any discovered lineaments [34]. The extraction of lineaments is automated using computer software. The automated processing includes enhancement, filtering, edge detection, and finally, lineament extraction [30]. There are several methods and algorithms used by different researchers for automatic linear extraction, i.e., lineament extraction and stripe statistical analysis [35], High Transform [36], TecLines [37], segment tracing algorithm [37], lineament detection and analysis [38], and Canny algorithm [39]. The Canny algorithm will be used to perform linear extraction, comparing curve number (CN) and rainfall–runoff response.

The second stage of the research is to perform the calculation of the Natural Resources Conservation Service Curve Number (NRCS-CN) and analyze rainfall and runoff in the study area [40]. The CN method depends on land use and soil type parameters to calculate and predict runoff potential. The most often used approach for determining the direct runoff depth, Q, from a given storm rainfall depth, P, is the NRCS-CN method. The United States Department of Agriculture Soil Conservation Service developed the approach in 1954 [41].

A previous study showed relatively large values of CN that have been observed between 61 and 99. CN values were calculated using rainfall and runoff data from certain gauged catchments in Saudi Arabia’s western area (Yiba catchment and its sub-basins) [42].

Among the benefits of CN include its ability to anticipate the link between rainfall and runoff, as well as its responsiveness to the main characteristics of runoff-producing catchments, such as soil type, land use, surface condition, and antecedent moisture condition [43,44]. However, complex rainfall–runoff correlations that are not always reflected in a single metric come from the dynamic nature of rainfall patterns, including volume, severity, and frequency, as well as landscape and soil features [45]. The empirical approaches, like the Soil Conservation Service Curve Number (NRCS-CN), have only yielded limited and untested system information in complicated basins [46]. In addition, the NRCS-CN also has some limitations such as lack of a land slope factor, and an improvement has been done by Shi and Wang [47].

CN is considered a sensitive parameter in the hydrological field such as runoff estimation and design of stormwater management systems. It should be estimated accurately. Hydrologists use soil conservation service tables to estimate CNs, which have a high degree of subjectivity. The NRCS-CN approach supposes a constant land cover condition over time and does not include geological features (fractures, fissures) in the modeling concept, which these features are very significant in hydrological systems and can influence infiltration rates and runoff. The current hydrological model considers mountains as impermeable surfaces, resulting in a high curve number (CN) value, which can lead to unrealistic hydrological responses in certain scenarios [48]. However, mountain areas contain fractures and cracks may contribute to the infiltration process. In such cases, method adjustments are needed to accurately account for fractures and fissures in mountainous areas. From previous studies in the literature, lineament and fracture density have been found to be utilized as one of the factors for analyzing groundwater potential (GWP) in different regions worldwide. Its significance in hydrological studies lies in its role as pathways for the movement of groundwater. Lineaments can be described as permeable zones and are positively associated with high GWP. In the same context, a study conducted by Akinluyi et al. [6] in southwestern Nigeria seeks to investigate the influence of lineaments on the groundwater yield of the basement terrain of Ondo State using optical remote sensing. This research assists in optimizing hydrogeological investigation to predict GWP based on structural lineaments and hydro-lithological characteristics. A recent study was carried out in the western part of Saudi Arabia, showed the CN value ranges between 45 and 85 at the initial abstraction ratio, λ = 0.2 and transmission losses, which are common in arid environments, are accounted for by the low CN values [49]. This transmission loss probably happened due to the occurrence of the high degree of permeability of the alluvium in the wadi and the geological fractures in the mountainous rocks in which the water infiltrated easily toward the ground.

This research will investigate the link between hydrological response and geological features in arid basins and will focus on the influence of local fracture density on CN and runoff. The integration of remote sensing and GIS technology will be employed for the automatic extraction of geological lineaments (including fractures and faults) based on the method used in previous studies [1,50]. Then, a best-fitting technique, based on the least-squares method (LSM), will be used to find out the empirical relationship between CN and line density, and therefore, an optimum range of CN range will be obtained.

The study aims to explore the effect of geological features on hydrological characterization and to quantify their impacts on CN and rainfall–runoff response in arid regions. Understanding this relationship is vital for making informed decisions about land development, water resource management, and climate change adaptation.

2 Study area

The study area is located in the southwestern part of Saudi Arabia (Figure 1). This region is particularly found in the eastern part of the Asir escarpment, with an elevation reaching up to 300 m that extends from the Red Sea coast. The climate conditions are arid and subarid, with extreme temperatures. The essential elements of climate parameters are wind speed, sunshine duration, temperature, relative humidity, and rainfall. In this research, five basins, namely, Yiba, Al Lith, Liyya, Habawnah, and Tabalah, are proposed to be investigated. Except for the two basins Habawnah and Tabalah, all basins drain toward the Red Sea, whereas these two basins drain toward the Rub al Khali from the mountainous region. In the research area, several measuring devices were used. Over the basins, there are around 100 rainfall gauges. Each of these basins is divided into sub-basins, and a total of 19 sub-basins are found. The annual pan evaporation is 3,955 mm, with the mean monthly evaporation ranging between 176 and 498 mm. Rainfall in Saudi Arabia is small and irregular, but it can be heavy and widespread during local storms. Due to its geographic location in the subtropical zone, the western region of Saudi Arabia receives a modest quantity of rainfall with a lengthy history of dry times [51]. The average annual rainfall of the basin is 187 mm. Most of the rainfall occurs in March, April, and May.

Figure 1

Location map of the study area.

In this study, 161 rainfall–runoff events during the years 1984–1987 were examined. The data are collected from the Ministry of Environment, Water, and Agriculture, Saudi Arabia.

Figure 2 (top two images) shows the selected rainfall–runoff events (hyetographs and hydrographs) at certain sites in distinct basins. The figure demonstrates the typical shape of the hydrographs in Saudi Arabia. The storms have common characteristics, such as shorter durations (between 4 and 6 h), and the amount of rainfall is not significant. The resulting runoff hydrographs exhibit a sharp overall shape, with steep and sharp rising limbs and quickly decreasing falling limbs. These features are typical of the arid environment in Saudi Arabia [52]. The runoff duration for the Al Lith Basin on December 19, 1984, at station J418 was 4 h. In contrast, for the Yiba Basin, during a specific event on August 19, 1985, the runoff duration was 22 h. Figure 2 (bottom two images) shows the monthly rainfall–runoff time series, which indicates minimal to no rainfall.

Figure 2

Top two images are selected rainfall–runoff events (hyetographs and hydrographs), and the bottom two images are monthly rainfall–runoff events (Ministry of Environment, Water, and Agriculture, Saudi Arabia).

3 Geological and tectonic setting

The Asir cliff in the western portion of the Arabian shield is made up of crystalline igneous and metamorphic rocks that are thought to be Pre-Cambrian in age and slope northeast, east, and southeast topographically and structurally [53]. The study region is geologically located in the Asir escarpment, which is part of the Arabian-Nubian Shield (ANS), and the formation dates to the Neoproterozoic age [54]. Due to uplift and erosion along the Red Sea’s sides in the Oligocene and earlier, the ANS, which is located in northeastern Africa and western Arabia, exposed crystalline basement rocks that are mostly Neoproterozoic in age [55].

Rock units in Wadi Al Lith, such as the Quaternary Deposit (alluvium), represent 9% of the total catchment; most of the area is covered by diorite and gabbro, whereas in Wadi Tabalah and Yiba, the area is mainly made up of tonalite and quartz diorite. The rock units in Wadi Habawnah (Figure 3b) are made up of around 10% pyritic, graphitic slate, and schist, 10% or less dacitic crystal and lithic tuff, 30% slate and wacke, and 50% greenstone and andesitic flow rocks. Mafic to felsic sills and a discontinuous strip of flinty porphyritic rhyolite or dacite along the quadrangle’s western boundary make up the unit. In Wadi Yiba, minor folds, bedding, and foliation often have geometries and orientations that correspond to the larger N-S trending fold [56].

Figure 3

Geological setting of study basins: (a) Al Lith, (b) Tabalah, (c) Yiba, (d) Habawnah, and (e) Liyyah.

According to Wheater et al. [57], annual precipitation is closely correlated with altitude; in Saudi Arabia, Asir Mountain receives the most precipitation [26,58]. The variation of the geological fractures present in the study basins influences the range of values of NRCS-CN values. The ability of bedrock to transmit water is influenced by three fracture characteristics: fracture aperture, connectedness, and density. Bedrock close to the surface often has wider apertures and a higher fracture density due to unloading and weathering processes [59].

4 Land use/land cover (LULC)

Classification of LULC plays a crucial role in rainfall–runoff modeling and water resource management. Accurately identifying LULC provides insights for a deeper understanding of patterns, changes, and impacts on the hydrological regime [60]. Classification of LULC has been made using Landsat 8 image (OLI) access via Earth Explorer website (https://earthexplorer.usgs.gov/). A supervised classification was performed to select training sites for different LULC regions. The maximum-likelihood classification is a popular method for supervised classification [61,62]. ENVI software was used to perform LULC map in the region. In this approach, we determine the spectral responses of established land cover categories, such as vegetation, alluvium, and rocks (used as training classes). The software then assigns each pixel in the image to the land cover type that most closely matches its spectral response. Therefore, the study region is classified into three major classes, such as rock, alluvium, and vegetation. To estimate the CN, the percentages of each LULC were calculated as shown in Table 1. Furthermore, enhancement, interpretation, and mapping were conducted within a GIS environment. In hydrological modeling, the CN parameter is used to evaluate a given land area’s potential for runoff depending on the features of the land cover. The CN was computed by considering the proportion of each kind of LULC, which provides important details about the hydrological response of the catchment. According to our classification except for the Liyyah (the alluvial deposits represent 40% of the study area), all other regions are characterized by a rock coverage exceeding 70%. Additionally, the Tabalah and Habawnah basins exhibit a relatively lower extent of vegetation coverage (Figure 4).

Figure 4

LULC map: (a) Al Lith, (b) Tabalah, (c) Yiba, (d) Habawnah, and (e) Liyyah.

5 Methodology

To accomplish the research task, four major stages are conducted. The first stage is the extraction of the geological lineaments using remote sensing and GIS technology; the second stage is estimating CN from rainfall–runoff data; the third stage is developing a relationship between CN and lineament density (LD); and the final stage is evaluating the developed equations on hydrological response. The workflow chart of the study is shown in Figure 5.

Figure 5

Flow chart of the methodology.

The extraction of geological lineament will be performed further in three different steps. The first step is the selection of the initial input of data for the lineament’s extraction. Satellite data, aerial images, and geological ground data, among other sources, can be used to identify and map lineaments. Satellite data were chosen as the best alternative for lineament mapping and extraction in this investigation. The next step is the extraction and mapping of lineaments from satellite images. Convolution filtering and multiband analysis methods for lineament extraction are used. The evaluation of the lineament thematic maps is the final phase. The LD map, direction map, intersection length map, and orientation analysis map are among these maps. The algorithm of LINE consists of three stages: edge detection, thresholding, and curve extraction. Edge detection of remote sensing is one of the most important methods in lineament extraction [63]. In an image, the edges surrounding various objects contain the most valuable information. The Canny edge detection algorithm is another effective tool for detecting edges in an image. The effectiveness of the lineament plots is confirmed by comparing them with the geological map.

The next step is related to the validation of the geological lineaments with the tectonic structures of the geological maps. A visual interpretation was made between the extracted and existing lineaments and faults, and then, they were plotted using the rose diagram to determine their direction and orientation. The LD will be performed using GIS techniques, to quantify the characteristics of the identified lineaments, to verify the consistency between existing tectonic structures (field data from maps) and extracted data from satellite images, and to incorporate it in the hydrologic model [14].

The second stage is calculating the NRCS-CN from rainfall–runoff events. The NRCS-CN method is based on the principle of mass conservation between precipitation, initial abstraction, runoff, and infiltration. The method is given by [64]

where Q is the direct runoff depth (effective rainfall), P is the rainfall depth of the event, λ is the initial abstraction ratio, and S is the potential maximum retention of a given catchment.

P and Q pairs are immediately used to determine the maximum possible retention, S, describing the catchment as

The aforementioned formula becomes the common quadratic formula for S if λ = 0.2 (the common value) [65]:

Once we obtain the value of S, CN is calculated as

The CN obtained from the aforementioned analysis is called CN event (CN_e) and is related to P, Q, and λ :

Using remote sensing techniques, we shall estimate the % P a proportional percentage of alluvium and % P r proportional percentage of rock, and then, the composite CN can be expressed as

where CN c is the composite CN, CN a is the CN for alluvium, and CN r is the CN for rock unit. These values are unknown, and they will be evaluated through the method of least-squares optimization problem given in the following:

where i is the event number, and n is the total number of events.

The estimated effective rainfall Q ˆ is calculated by the flowing equation:

The estimated and observed effective rainfall was compared for all basins to assess the performance of the NRCS-CN model.

The observed CN ( CN r ) for rock units obtained from equation (8) is going to be related to rock characteristics such as the density of fractures. Then, a best-fitting technique (based on the LSM) is used to find out the empirical relationship between CN r and line density.

The verification of the developed equations for quantifying the effect of faults and geological lineaments on rainfall–runoff response is implemented. The developed equation for CN r and line density is employed to estimate CN c (CN composite) for the whole catchment area. Therefore, the composite CN c is used for calculating the expected runoff and then compared with observed runoff via a scatter plot and consequently to obtain the errors. This analysis was performed through some statistical methods such as root mean square error (RMSE), correlation coefficient (r), coefficient of determination (R ²), and the percentage of data outbound the lower and upper ninety-five % (±95%) confidence limits to validate the outcome of the results.

6 Results and discussion

Lineaments are extracted from the Landsat 8 OLI image with band 5 specifically. The OLI multispectral sensor collects data in the visible and near-infrared, short-wave infrared, and other spectral bands. To apply lineament extraction, the image was corrected by performing radiometric calibration and atmospheric correction to mask the effects of clouds and water. LD is an essential parameter for lineament mapping.

LD is a geological or geomorphological metric that quantifies the concentration or abundance of linear features, such as faults, fractures, or other linear geological structures, within a specific area. It is typically expressed as the number of lineaments per unit area, often measured in lineaments per kilometer or lineaments per square kilometer. Because it tells us about a region’s geology and tectonic features, LD is a useful quantity in geology, geophysics, and remote sensing. Low LD may reflect relatively stable geological conditions, whereas high LD may signify regions of greater geological activity or structural complexity. It is often utilized in environmental and geological research, resource exploration, and the evaluation of geological hazards [48].

Geological faults were digitized from field observations, and the LD was generated using the line density tool in ArcGIS software and classified into sub-basins using zonal statistics.

In Al Lith and Tabalah catchments, high LD is found in diorite, tonalite, and gabbro with an average length of 1,654 and 1,700 m, respectively. Lineament extraction analysis has been performed in Wadi Al Lith for geothermal potential, which discovered that with a frequency percentage of 52% and an average lineament length of 835 m, the primary surface lineaments are structurally oriented in the north-northeast (NNE)–south-southwest (SSW) and NE–SW directions [28], whereas in Yiba and Habawnah, volcanic rocks have the highest LD with an average lineament length of 1,757 and 1,606 m, respectively. Lineament extraction is also carried out in Abha, which is nearest to Wadi Yiba. Field-structural mapping demonstrates that the Wadi Yiba region underwent at least three deformation stages (D1–D3) [56]. In Wadi Habawnah, the aquifer replenishment, storage, and leaking have considerable potential in areas with lineament densities that range from high to extremely high [66].

The geological features from field observations (geological maps) and the extracted lineaments were integrated into the RockWorks software to plot the rose diagram. Rose diagram analysis is an essential step in interpreting the spatial distribution and orientation of tectonic structures and in evaluating lineaments derived through comparison with field data. Assessing the accuracy of these measurements is crucial for reliable geological interpretations and models. As a result, the most frequent directions of extracted lineaments are identified (Figure 6).

Figure 6

Extracted lineaments superimposed on the hill-shaded map of the basin, observed faults, and line density are presented in colors: (a) Al Lith, (b) Tabalah, (c) Yiba, (d) Habawnah, and (e) Liyyah.

The extracted lineament shows a trend of two dominant directions, which are north-northwest (NNW)–south-southeast (SSE) (N20–60 W) and NNE–SSW (N0–45 E). All three wadis (excluding Habawnah and Liyyah) exhibit a general NW–SW trend, as shown in Figure 7. This suggests that the lineaments within these wadis predominantly follow a northwest–southeast orientation. Most of the major wadis that drain into the Red Sea have a NE–ENE pattern [67,68].

Figure 7

Comparison of rose diagram of lineaments extracted from remote sensing and lineaments extracted from geological maps. The small case letter (right side) indicates the extracted lineament from remote sensing data, and the left side shows the field observation taken from geological map for the five wadis – Al Lith, Tabalah, Yiba, Habawnah, and Liyyah arranged in an alphabetical order (a–e).

As a result of this study, each lineament trend may indicate an underlying tectonic and structural setting. The N–S, NNE–SSW, and NNW–SSE lineament traces discovered in the northern (Al Lith), center (Yiba and Tabalah), and southern regions (Liyyah and Habawnah) of the examined area are consistent with the N–S trending basement faults (Arabian trend). A similar trend has been seen in Jizan, which is near Wadi Habawnah, and fractures are found in sub-volcanic plutons and Asir dykes [69]. For several of the principal wadis, the NNW direction is just as significant as its conjugate perpendicular tendency [28]. In Wadi Riyan, which is located at northeast of Abha, trend analysis reveals that the principal surface fracture trend region is in the NNW and NNE and that surface geology and Landsat data also revealed minor trends in the north–south and east–west [70]. The E–W extensional tectonics are most likely responsible for this pattern.

Several extracted lineaments correlate with faults and fault zones found and depicted on geological maps. As a result, lineament analyses reveal structural patterns representing tectonic features in their actual distribution and orientation in the study area.

In Al Lith, both the field observations and extracted lineaments exhibit a similar trending orientation along the NNW–SSE direction. Similarly, in Tabalah and Wadi Yiba, the orientations were observed to be similar, except for the field-observed faults in the Tabalah catchment, which are slightly inclined toward the west direction. However, there is a discrepancy in the trend between the field observations and extracted lineaments in Wadi Liyyah. The field observations indicate a trending orientation of NNW–SSE, while the extracted lineament orientation shows toward NNE–SSW. The fundamental reason for the difference in trending orientations in Wadi Liyyah may certainly be data restrictions resulting from the catchments’ location across national borders. Part of the catchment found in Yemen, obtaining reliable and thorough data during field observations might be difficult. When compared to extracted line segments derived by software analysis, this may result in differences in the quality, accessibility, and availability of the data [71].

The second phase of the investigation involves determining the NRCS-CN value for each wadi and finding a relationship between line density and CN_r. In the first part, we have classified LULC map into three types, namely, rock, alluvium, and vegetation, and we have estimated the percentage of each class for all basins. To obtain NRCS-CN, only rock and alluvium were used, while the area of vegetation located in the alluvium and rock types were added to the alluvium and the rock area, respectively. Therefore, vegetation is not included in the analysis, while its area is added to either rock or alluvium. An initial abstraction of 0.01 was used as the best value in the arid region and the NRCS-CN table at λ = 0.2 converted into λ = 0.01 based on the regression equation developed by Farran and Elfeki [49]. This proves that λ = 0.2 is not recommended to be used in the Saudi arid environment. However, the values of NRCS-CN at λ = 0.01 seem more reasonable, since it incorporates the transmission losses that are a significant phenomenon in these mountainous arid basins. Therefore, in this study, we compare the NRCS-CN value at λ = 0.01 with line density. Figure 8 and Table 2 both display NRCS-CN values that are useful to evaluate the rainfall–runoff results.

Figure 8

CN for five wadis: (a) Al Lith, (b) Tabalah, (c) Yiba, (d) Habawnah, and (e) Liyyah.

The LSM is a minimization of the sum of squared differences between CNe and CNc (equations (5) and (6)) as well as observed direct runoff (Q) and the estimated runoff ( Q ˆ ) (equation (9)). This method gives the best estimation of the parameters. Microsoft Excel solver is used in the current study to apply the LSM. According to Table 2, in all catchments, the minimum CN is 28 and the maximum CN is 92, both of which are in Wadi Habawnah. The histogram distribution indicates a high frequency of CN between 51 and 70, and a low frequency of CN greater than 88. The average value of CN for all wadis is 57.5. Several factors influence the range of CN values; thus, geological characteristics such as fault is one of the factors that influence the CN in the catchment [72].

Different statistical techniques have been used, including RMSE, correlation coefficient (r), and coefficient of determination (R ²), to validate the outcome of the results according to Table 5 and Figure 9, which can be produced using equation (9).

Figure 9

Scatter plot shows the observed and estimated effective rainfall of Wadis Al Lith, Tabalah, Yiba, Tabalah and Liyyah catchments, and all wadis plotted in one graph.

The amount of variance in the dependent variable (seen effective rainfall) that can be explained by the independent variable (estimated effective rainfall) is measured by the coefficient of determination, which can be represented as R ².

An R-squared value and the correlation coefficient value greater than 0.94 for Al Lith and Yiba suggest that the relationship between observed and estimated effective rainfall in these catchments is highly linear and that the estimated values are closely aligned with the observed values. For the other catchments (Tabalah, Habawnah, and Liyyah), the value of the correlation coefficient and R ² is greater than 0.6. While not as high as the values for Al Lith and Yiba, an R-squared value greater than 0.6 still indicates a reasonably good linear relationship between observed and estimated effective rainfall. Therefore, the calculated effective rainfall is strongly connected with the observed values for all catchments, with Al Lith and Yiba showing especially significant relationships. This may indicate that the estimated effective rainfall is reliable and that the model that produced them works well for these catchments [73].

Comparing LD and CN involves assessing the relationship or correlation between these two geospatial parameters. LD, as previously mentioned, quantifies the concentration of linear geological features within a given area, while the CN is a hydrological parameter used to assess runoff potential and soil infiltration characteristics in a catchment. Based on each sub-catchment, comparisons of line density and CN have been made, as shown in Figure 10. The coefficients of determination (R ²) are carried out to determine the relationship between the distribution of CNs and LD. Therefore, all wadis suggest an inverse relationship between CN and LD, according to the findings. A negative correlation between LD and high CNs suggests that areas with more geological features (lineaments) may have better surface infiltration characteristics and lower runoff potential. This could indicate that the presence of geological features enhances soil permeability, allowing water to infiltrate into the ground more effectively. Areas with higher LD and lower CNs may be favorable for groundwater recharge [52]. The geological features could act as pathways for water to enter and replenish the groundwater aquifers beneath the surface.

Figure 10

Scatter plot between line density and CN for rock. The black dotted line indicates the trend line for the data, and the data are represented by red dots.

Wadi Al-Lith shows the highest R ², equal to 0.72. Wadis Habawnah and Tabalah provide a moderate correlation for estimation, while poor correlations are observed in Wadi Yiba and Wadi Liyyah between the fracture density and the CN. The graphs c, d, and e show a high variability between CN and line density, which is reflected in the low R ²; therefore, more data is needed to verify this relation in further research. The lack of geological information, particularly upstream of Wadi Liyyah, does not make it possible to accurately assess the fractures present in the mountain. This basin shows that there are limited geological faults in the area that have been observed, making it impossible to map the fault pattern outside of the territory of the country and indicating that trends between CN and extract lineament are not well correlated.

The linear trend is shown to be the best when compared with other models and provides the highest R ². The developed linear equations with low R ² can be improved in the future by having more data.

The scatter plot in Figure 11 demonstrates that the observed and calculated CNs for rocks exhibit a somewhat positive linear relationship. The R ² value in this instance is 0.66. Even if the R ² number is not particularly high, it still indicates some degree of connection between the two variables. The correlation coefficient between the CN values is 0.68. The correlation coefficient “r” measures the strength of a linear relationship between two variables. A value of 0.68 indicates a moderately strong positive linear correlation between the observed and estimated CNs.

Figure 11

Scatter plot between observed and estimated CN for rocks.

We calculated the estimated effective rainfall and plotted it against the observed effective rainfall using the developed equation (Table 3) and applied it to each sub-catchment to validate the equations. To obtain the estimated effective rainfall, the observed CN of rock ( CN r ) would be replaced by the estimated CN ( CN ˆ r ) as shown in equation (10) (Table 4):

The scatter plot in Figure 12 and the statistical analysis of the developed model in Table 5 show that in Wadi Al Lith and Wadi Yiba, the coefficient of determination (R-squared) between estimated effective rainfall and observed effective rainfall is significantly higher than in the other wadis, where it is higher than to 0.52. The RMSE of less than 2.10 mm indicates a strong and highly linear relationship between the estimated and observed effective rainfall in Wadi Habawnah and Wadi Tabalah. In these two wadis, the models used for estimating effective rainfall seem to be reliable.

Figure 12

Scatter plot between observed effective rainfall and estimated effective rainfall based on the developed equations of the CN of rock with LD (Table 3).

This low RMSE value suggests that the variability in observed effective rainfall can be explained by the estimated values, which is a strong indication of the model’s reliability. However, in the other wadis (Yiba, Al Lith, and Liyyah), the RMSE value of greater than 5.50 mm suggests a moderate linear relationship between estimated and observed effective rainfall. This might indicate that the models used for estimating effective rainfall in these wadis are reasonably accurate [74].

Table 5 and Figure 13 show the percentage of data points that fall outside the ± 95% confidence limits to better assess the developed model for all basins using the developed equations of the CN of rock with LD. As a result, a higher percentage of data points outside confidence limits is found in the Habawnah Basin (16.6%), which represents a high uncertainty compared to other basins. This highest value could be due to limitations of the data employed to evaluate the model, such as the smaller number of measured data or inaccuracies in some hydrological parameters. However, Tabalah Basin has the lowest percentage (4.34%), demonstrating less data outside the confidence limits. Overall, a combined analysis of all basins shows a relatively low number of data points falling outside the confidence bounds (6.36%). It indicates that the models used for estimating effective rainfall have a satisfactory level of reliability.

Figure 13

Scatter plot between estimated and observed effective rainfall based on the developed equations of the CN of rock with LD, with 95% confidence interval: the gray line is a line of the perfect fit; the green line represents the upper limit (95%), and the red line is the lower limit (95%).

7 Conclusions

Faults, joints, and bedrock fractures are examples of subsurface features that can have a substantial impact on an area’s ability to withstand infiltration. Highly fractured rocks or fissured soils typically have higher permeabilities, which facilitate easier water flow through them. The CN may be impacted by this greater permeability since it impacts how quickly water seeps into the ground. Due to the greater capacity of the fractured subsurface to absorb water, runoff potential is lowered in places with a high fracture density, which might result in a lower CN. The relationship between CN and geologic fractures can have significant implications for understanding and managing water resources, particularly in areas with fractured rock systems.

According to our findings, the following points can be drawn from the study:

• This study proposes an approach for quantifying and parameterizing lineament features for CN estimation in mountainous regions, and consequently, it can be used to enhance rainfall–runoff response in catchments that contain mountains with a high density of geological features.

• An automatic extraction of lineament from the Landsat image was performed. The results were validated by comparing them with the rose diagram of the observed faults, which show relatively reasonable agreement.

• Some relationships between LD and CN were established for enhancing the prediction of hydrological response with the range of applications given in Table 3 (LD range). A negative correlation between LD and high CNs suggests that areas with more geological features may have higher surface infiltration characteristics and lower runoff potential. Low values would result in arid and semi-arid regions, where strong infiltration in a dry substrate and fractured mountains causes transmission losses to be the predominant features.

• The correlation coefficient of 0.68 indicates a moderately strong positive linear correlation between observed and estimated CNs, and therefore, the developed relationship between CN and fracture density could be used by hydrologists to best management of water resources in these basins. Further research is needed to improve the developed equation in other basins in Kingdom of Saudi Arabia.

• The RMSE between estimated effective rainfall and observed effective rainfall based on the developed equations for Wadi Tabalah and Wadi Habawnah is 2.10 and 0.61 mm, respectively, which is relatively low and indicates a strong relationship between CN and lineaments density. However, a relatively high RMSE is indicated for other wadis (Yiba, Al Lith, and Liyyah), which indicates that the models used for estimating effective rainfall in these study areas may need further analysis by incorporating more data. The percentage of data points beyond the ±95% confidence limit was also calculated. According to the results, Habawnah Basin (16.6%) has a higher percentage of data points out of confidence bounds, which suggests that it has a higher level of uncertainty. The low values of confidence level derived from the developed equations for some studied basins may be attributed to a variety of factors, including the limited number of data used to assess the model, inaccuracies in certain hydrological parameters (e.g., CN), or disparities between observed and estimated values. In contrast, the lowest percentage (4.34%) is found in Tabalah Basin, indicating that there is less data outside the confidence interval. An analysis combining all basins found the number of data points outside the confidence bounds to be relatively low (6.36%), which demonstrates an adequate degree of reliability, and consequently, the model could be used for runoff estimation.

• Overall, the low values of CN in the arid catchment are interpreted by the LD available in the mountainous area together with transmission losses in the stream alluvium. The alluvial deposits and the huge mountain are the regions that can be thought of as prospective groundwater direct recharge locations.

• This study highlights the importance of fracture densities in arid catchments and their contribution to increase the infiltration rates. The results obtained in this research can be better exploited in integrated watershed management and groundwater management by incorporating more recent hydrological measurement and geological data to improve the proposed methodology.