Examining the Influence of Landscape Patch Shapes on River Water Quality

Abstract

River water quality can be affected by a range of factors, including both point and non-point sources of pollution. Of these factors, changes in land use and land cover are particularly significant, as they can alter the structure of the landscape and consequently impact water quality in rivers. To investigate the relationship between patch shapes, a measure of landscape structure, and river water quality at the catchment scale, this study utilized spatial data from 39 catchments in the southern basin of the Caspian Sea. This study employed stepwise multivariate regression modeling to explore how changes in landscape structure, which can be measured by landscape metrics including the shape index, the contiguity index, the fractal dimension index, the perimeter–area ratio, and the related circumscribing circle, impact water quality variables. Four regression models—linear, exponential, logarithmic, and power models—were evaluated, and the most appropriate model for each water quality variable was determined using the Akaike information criterion. To validate the models, three groups of accuracy metrics were employed, and Monte Carlo simulation was utilized to analyze the models’ behavior. This study found that landscape structure metrics could explain up to 71% and 82% of the variations in the measures of TDS and Mg, respectively, and the shape index, the contiguity index, and fractal metric were particularly significant in predicting water quality. Moreover, this study verified the accuracy of the models and revealed that changes in landscape structure, such as a decline in patch continuity and an increase in patch complexity, can impact river water quality. The findings of this study suggest optimizing landscape structure metrics in land use planning to reduce river pollution and improve water quality.

1. Introduction

River water quality is subject to constant change due to various pollutants and human and natural activities, such as topography [1], soil [2], drainage density [3], temperature [4], and land use changes [5,6], which include agricultural [7] and urban development [3]. The decline in river water quality is now a significant environmental concern due to human activities, such as the expansion of urban and rural areas [3,8], changes in land use [9,10], and the depletion of wetlands and water bodies to access cheaper land for human needs [11,12]. These activities have been well documented in numerous studies [1,2,3,6,7,12,13].

Studies have shown that land use and land cover changes significantly impact the hydrological cycle of river catchments [14,15]. Human activities, such as urban development and agricultural expansion, can intensify water pollution problems in catchments [16,17]. Therefore, there is an undeniable relationship between land cover and river water quality. The composition of land use and land cover plays a crucial role in determining river water quality [18,19,20]. Changes in land use and land cover patterns affect the water cycle, which ultimately impacts water quality in rivers [14,21,22]. Human activities and economic and social driving forces can cause changes in land use and land cover patterns, further affecting the water cycle and water quality in rivers [23,24,25,26,27]. The interaction between land use/land cover patterns and economic and social activities can significantly impact the ecological systems of rivers, resulting in changes in water quality at the catchment scale [28,29,30]. This implies that changes in these patterns can have a cumulative effect on river water quality. Given that non-point pollution is a major contributor to water pollution, the impact of land use/land cover patterns should be taken into account [31,32].

The structure, composition, and configuration of landscapes can impact hydrological processes such as rainfall–runoff, energy flow, material cycle, and nutrients at the catchment scale [22,33,34,35]. These features of the landscape have extensively been studied in relation to water quality, with research highlighting the importance of landscape patterns in shaping these processes [33,36,37,38,39,40]. Existing research works have been focused on the relationship between changes in landscape composition and water quantity and quality in rivers, with numerous studies documenting this relationship [3,7,8,41,42,43,44]. However, there is a lack of studies investigating the relationship between changes in landscape structure and river water quantity and quality. This study hence aims to address this gap by investigating whether changes in the patch shapes of the landscape are significantly related to river water quality at the catchment scale. This study also seeks to identify which landscape structure-related metrics can better explain the total variations in river water quality variables by developing appropriate regression models.

2. Materials and Methods

2.1. Study Area

The research was conducted in the southwestern part of the Caspian Sea basin, which includes the Aras and Qezel Ozen rivers. The study area consisted of 39 catchments and sub-catchments (Figure 1), which were selected based on the availability of hydrometric stations and water quality monitoring programs. These stations were located at various elevations ranging from 334 to 2120 m. The average size of the catchments and sub-catchments was 658.8 ± 1505.6 km², with an average discharge of 0.72 ± 0.9 m³·s⁻¹. The primary land cover/land use in the study area was moderate-density grassland, which accounted for 27% of the area, and the non-irrigated arable land was the second most common land use, covering 19% of the area.

2.2. Data Acquisition

The data on river water quality, including TDS (total dissolved solids), EC (electrical conductivity), HCO₃⁻ (bicarbonate), Ca²⁺ (calcium), Mg²⁺ (magnesium), and Na⁺ (sodium), were obtained from the regional authority responsible for water resources management. The land use and land cover map used in this study was obtained from the Ardabil Natural Resources and Watershed Management, with a scale of 1:25,000 and produced in 2020. The digital elevation model used in this study, with a scale of 1:50,000, was obtained from the Iran National Cartographic Center.

2.3. Research Methodology

The catchment boundaries were delineated in the study area using the hydrology extension in ArcGIS 10.8, with the aid of the digital elevation model (DEM) [45], and verified by referring to topographic maps (1:50,000) from Iran National Cartographic Center (2022). Land use and land cover maps were generated by overlaying the land use/land cover map with the catchment boundaries. The land use/land cover map was reclassified into thirteen classes using the Corine land use/land cover nomenclature [46], which includes various types of land such as irrigated land, arable land, urban areas, grasslands, forests, outcrops, water bodies, shrublands, and transitional woodlands. Landscape structure-related metrics were calculated for each catchment using these land use maps. The ten-year mean values (2010–2020) of water quality variables were then used to investigate the relationship between changes in water quality and changes in landscape structure in the catchments.

2.4. Calculation of Landscape Metrics

At the catchment scale, landscape structure-related metrics such as the shape index (Shp), the fractal dimension index (Frac), the perimeter–area ratio (Para), the related circumscribing circle (RCC), and the contiguity index (Contig) were computed for each land use/land cover class. The properties and descriptions of the metrics utilized are presented in

Table 1. The formulas, description and ranges of the landscape metrics.

Name	Description	Formula
Shape Index	For a square-shaped patch, the value of the index is equal to 0, but for an irregular shape-patch, it is ∞ [47].	$\mathrm{Shp}=\frac{1}{\mathrm{Ni}}{\displaystyle \sum }\frac{\mathrm{Li}}{4\sqrt{\mathrm{Ai}}}$
Fractal Dimension Index	The index ranges between 1 for a regular (square) patch and 2 for an irregular (convoluted) patch [48,49].	$\mathrm{Frac}=\frac{2\ln \left(0.25{ \mathrm{P}}_{\mathrm{ij}}\right)}{{\mathrm{Ln} \mathrm{a}}_{\mathrm{ij}}}$
Perimeter–Area Ratio	The farther the ratio is from 1, the more the patch deviates from the isodiametric shape [48,50].	$\mathrm{Para}=\frac{{\mathrm{P}}_{\mathrm{ij}}}{{\mathrm{A}}_{\mathrm{ij}}} \mathrm{and} \mathrm{para}>0$
Related Circumscribing Circle	It varies from 0 for a convoluted patch to 1 for an elongated patch [49].	$\mathrm{RCC}=1-\left(\frac{{\mathrm{a}}_{\mathrm{ij}}}{{\mathrm{a}}_{\mathrm{ij}}^{\mathrm{s}}}\right)$
Contiguity Index	The value of metric varies between 0 for a one-pixel patch and 1 for a connected patch [50].	$\mathrm{Contig}=\frac{\left[\frac{{{\displaystyle \sum }}_{\mathrm{r}=1}^{\mathrm{z}}{\mathrm{C}}_{\mathrm{ijr}}}{{\mathrm{a}}_{\mathrm{ij}}}\right]-1}{\mathrm{v}-1}$

.

2.5. Statistical Calculations

Multivariable regression modeling (MLR) was applied to investigate the relationship between water quality variables and landscape metrics. The available data were randomly divided into a calibration subset (70%) and a validation subset (30%). Four types of structural regression models—linear, exponential, logarithmic, and power models—were fitted for each water quality variable using each landscape metric with the calibration subset data. Collinearity between independent variables in the developed models was examined using the variance inflation factor (VIF). A VIF value less than 10 indicates the absence of collinearity in the model [51,52]. The Akaike information criterion (AIC) was used to determine the most appropriate model among the fitted models. The AIC is a metric that indicates the closeness of a developed model to the reality of the system. It is calculated based on the number of variables in the model, the number of samples, and the sum of squares of the model’s error. The formula for calculating AIC is given in Equation (1),

$${\mathrm{AIC}}_{\mathrm{c}}=\mathrm{n}\left(\log \frac{\mathrm{RSS}}{\mathrm{n}}\right)+2\mathrm{K}+\left(\frac{2\mathrm{k}\left(\mathrm{K}+1\right)}{\mathrm{n}-\mathrm{K}-1}\right)$$

(1)

where AIC is the value of the Akaike information criterion, K is the number of variables, n is the number of samples, and RSS is the sum of squares of the model’s error [53]. To determine the appropriateness of the regression models, one-to-one plots were drawn using measured and predicted data, and the r² statistic and p ≤ 0.05 were used as criteria. To quantify the appropriateness of the models, absolute model error metrics and relative model error estimation metrics [54] were calculated using the verification data subset (

Table 2. Information of validation metrics.

Type	Metric	Equation	Range
Relative Error Models	Mean Relative Error (MRE)	$\mathrm{MRE}=\frac{1}{\mathrm{n}}{\displaystyle {\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}}{\left(\frac{{\mathrm{O}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{i}}}{{\mathrm{O}}_{\mathrm{i}}}\right)}^2$	0–∞
	Mean Absolute Relative Error (MARE)	$\mathrm{MARE}=\frac{1}{\mathrm{n}}{\displaystyle {\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}}\frac{\left|{\mathrm{O}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{i}}\right|}{{\mathrm{O}}_{\mathrm{i}}}$	0–∞
	Relative Absolute Error (RAE)	$\mathrm{RAE}={\displaystyle {\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}}(\left|{\mathrm{O}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{i}}\right|/{\displaystyle {\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}}\left|{\mathrm{O}}_{\mathrm{i}}-\overline{\mathrm{O}}\right|$	0–∞
Model Efficiency	Coefficient of Determination (r2)	${\mathrm{r}}^2=\frac{\mathrm{n}({\displaystyle \sum }\mathrm{xy})-({\displaystyle \sum }\mathrm{x})({\displaystyle \sum }\mathrm{y})}{\sqrt{\left[\mathrm{n}{\displaystyle \sum }{\mathrm{x}}^2-{({\displaystyle \sum }\mathrm{x})}^2\right]\left[\mathrm{n}{\displaystyle \sum }{\mathrm{y}}^2-{({\displaystyle \sum }\mathrm{y})}^2\right]}}$	0–1
	Consistency Index (IA)	$IA={\displaystyle {\displaystyle \sum }_{i=1}^n}\left(O_i-P_i\right)/{\displaystyle {\displaystyle \sum }_{i=1}^n}{\left(\left|P_i-\overline{O}\right|+\left|O_i-\overline{O}\right|\right)}^2$	0–∞
	Coefficient of Efficiency (CE)	$CE=1-{\displaystyle {\displaystyle \sum }_{i=1}^n}{\left(O_i-P_i\right)}^2/{\displaystyle {\displaystyle \sum }_{i=1}^n}{\left( O_i-\overline{O}\right)}^2$	0–∞
Absolute Error Models	Root Mean Square Error (RMSE)	$\mathrm{RMSE}=\sqrt{{\displaystyle {\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}}{({\mathrm{O}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{i}})}^2/\mathrm{n}}$	0–∞
	Mean Error (ME)	$\mathrm{ME}=\frac{1}{\mathrm{n}}{\displaystyle {\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}}({\mathrm{O}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{i}})$	0–∞
	Mean Absolute Error (MAE)	$\mathrm{MAE}=\frac{1}{\mathrm{n}}{\displaystyle {\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{n}}}\left|{\mathrm{O}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{i}}\right|$	0–∞

).

2.6. Uncertainty Analysis

Performing uncertainty analysis is crucial in modeling [55] as it helps to understand how the model behaves under different conditions by considering all possible uncertainties in input variables [56]. The analysis focuses on identifying potential outcomes of a model. Therefore, in this study, the Monte Carlo simulation approach [57] was used to determine how well the developed models can predict water quality in the catchment. The simulation involved defining the model, determining descriptive statistics and statistical distribution of dependent and independent variables, generating random data (15,000 in this case), simulating model responses using the generated data, and obtaining the probabilistic behavior of the model. The possible behavior of the model was inferred by determining the cumulative distribution function of the simulated outputs [58].

3. Results

Figure 2 presents the summary of landscape structure metrics, including mean and standard deviation calculations. The shape index reveals that water bodies and rock outrages have a regular shape, while shrubland and low-density broad-leaved forest patches exhibit the highest level of shape irregularity. The fractal dimension index, which measures patch shape complexity, indicates low variation for all land use/land cover classes, except for the low-density broad-leaved forest.

Modeling Results

Four regression models for water quality variables have been fitted using the landscape structure-related metrics. The most appropriate models, which are based on the Akaike information criterion, are as follows:

$$Log TDS=-0.499LogQ+0.975Log\left(Shap{e}_{Df}\right)+3.849$$

$$Log EC=-0.493LogQ+0.962Log \left(Shap{e}_{Df}\right)+3.996$$

$$Log HC{O}_3=-0.252LogQ+7.101Log \left(FRA{C}_{If}\right)-7.171Log \left(FRA{C}_{G1}\right)+2.874Log \left(FRA{C}_{TW}\right)+2.921$$

$$Log Ca=-0.366LogQ+0.829Log \left(Shap{e}_{Df}\right)+2.572$$

$$Log Mg=-0.485LogQ-0.877Log \left(CONTI{G}_{G2}\right)+2.63$$

$$Log Na=-0.768LogQ-1.54Log \left(CONTI{G}_{G2}\right)+3.801$$

where

• Q the discharge in m³·yr⁻¹·ha⁻¹,
• $Shap{e}_{Df}$ the shape index of the non-irrigated arable land,
• $Fra{c}_{if}$ the fractal dimension index of the permanently irrigated land,
• $Fra{c}_{G1}$ the fractal dimension index of the high-density grassland,
• $Fra{c}_{TW}$ the fractal dimension index of the transitional woodlands, and
• $CONTI{G}_{G2}$ stands for the contiguity index of the moderate-density grassland.

This study has found that three out of five landscape metrics, namely the shape index, the fractal dimension index, and the contiguity index, are able to explain the changes in water quality variables. The developed regression models were able to explain between 71% and 82% of the total variation in TDS and magnesium, respectively, with a significance level of p ≤ 0.05. Additionally, 5 out of 13 land use/land cover classes, including moderate-density grassland, non-irrigated arable land, permanently irrigated land, high-density grassland, and transitional woodlands, were identified as significant explanatory variables for changes in water quality.

Table 3. Details of the regression models for the water quality variables.

Model		Coefficients						Collinearity Statistics
Model	Variable	B	Std. Error	Beta	r2	t	Sig.	Tolerance	VIF
TDS	Constant	3.849	0.177		0. 81	21.730	0.000
	Discharge	−0.499	0.044	−0.829		−11.226	0.000	0.947	1.056
	Shape Df	0.975	0.337	0.214		2.895	0.006	0.947	1.056
EC	Constant	3.996	0.178		0.81	22.494	0.000
	Discharge	−0.493	0.045	−0.827		−11.069	0.000	0.947	1.056
	Shape Df	0.962	0.338	0.213		2.846	0.007	0.947	1.056
HCO3	Constant	2.921	0.146		0.78	20.074	0.000
	Discharge	−0.252	0.033	−0.651		−7.707	0.000	0.904	1.106
	FRAC Ir	7.101	1.314	0.467		5.402	0.000	0.863	1.158
	FRAC G1	−7.171	1.513	−0.420		−4.740	0.000	0.822	1.217
	FRAC TW	2.874	1.080	0.225		2.662	0.012	0.903	1.108
Ca	Constant	2.572	0.165		0.74	15.553	0.000
	Discharge	−0.366	0.041	−0.775		−8.818	0.000	0.947	1.056
	Shape Df	0.829	0.315	0.232		2.636	0.012	0.947	1.056
Mg	Constant	2.630	0.149		0.71	17.648	0.000
	Discharge	−0.485	0.051	−0.857		−9.535	0.000	0.973	1.027
	CONTIG G2	−0.877	0.409	−0.193		−2.144	0.039	0.973	1.027
Na	Constant	3.801	0.182		0.81	20.907	0.000
	Discharge	−0.768	0.062	−0.909		−12.390	0.000	0.973	1.027
	CONTIG G2	−1.540	0.499	−0.227		−3.086	0.004	0.973	1.027

summarizes the regression models selected for each water quality variable and their respective model recognition coefficients. The statistical analysis revealed a significant relationship between the water quality variables and independent variables, with no multiple collinearities among the independent variables. Figure 3 depicts a scatter plot of the observed versus predicted values of water quality, indicating that over 75% of the data falls within the significant area [59].

The fitted models for each water quality variable were validated using a validation data subset, which accounted for 30% of the remaining data. Validation metrics including absolute model error estimation, model efficiency, and model relative error estimation were used, and have been shown in

Table 4. Values of the validation metrics for the regression models of the water quality variables.

Model	Relative Error Model			Model Efficiency			Absolute Error Model
	MRE	MARE	RAE	IA	CE	r2	RMSE	ME	MAE
TDS	−0.02	0.04	0.54	0.93	0.78	0.82	0.15	−0.04	0.1
EC	−0.02	0.03	0.54	0.93	0.78	0.82	0.14	−0.04	0.1
HCO3	0.01	0.03	0.7	0.91	0.68	0.71	0.09	0.01	0.07
Ca	−0.03	0.05	0.59	0.93	0.76	0.81	0.11	−0.04	0.08
Mg	−0.03	0.08	0.62	0.92	0.71	0.74	0.14	−0.03	0.1
Na	−0.01	0.12	0.71	0.91	0.7	0.7	0.24	0.01	0.18

MRE = mean relative error (MRE), MARE = mean absolute relative error, RAE = relative volumetric error, IA = consistency index, CE = coefficient of efficiency, r² = coefficient of determination, RMSE = root mean square error, ME = mean error, and MAE = mean absolute error.

. The results indicated that all fitted models were reliable and accurate in predicting water quality variables. The coefficient of determination (r²), which was greater than 0.6, showed a relatively acceptable correlation between the predicted and observed water quality values during the validation stage. Furthermore, the root mean square error (RMSE), which is an indicator of model error, was low for all the fitted regression models. Specifically, the RMSE for TDS, EC, HCO₃, Ca, Mg, and Na models were 0.15, 0.14, 0.09, 0.11, 0.14, and 0.24, respectively.

Monte Carlo simulation was performed to analyze the uncertainty in the regression models (

Table 5. Results of optimal statistical distribution for the variables of the regression models.

Variable		Model Variable	Statistical	Kolmogorov Smirnov		Statistical
			Distribution	Statistics	p-Value	Variables
TDS	A prior statistics	Discharge	Wakeby	0.08914	0.88883	α = 1531 β = 0.19338 γ = 40.077 δ = 0.93225 ζ = −46.396
		Shape Df	Weibull	0.0936	0.85262	α = 8.3969 β = 2.0382 γ = 0
	Posterior statistics	Yobs.	Lognormal (3P)	0.08334	0.92856	α = 0.88486 μ = 5.9758 γ = 45.878
		YSim.	Gen.Extreme value	0.05299	0.99964	κ = 0.46215 σ = 0.09705 μ = 0.19072
EC	A prior statistics	Discharge	Wakeby	0.08914	0.88883	α = 1531 β = 0.19338 γ = 40.077 δ = 0.93225 ζ = −46.396
		Shape Df	Weibull	0.0936	0.85262	α = 8.3969 β = 2.0382 γ = 0
	Posterior statistics	Yobs.	Frechet	0.06909	0.98592	α = 2.3788 β = 804.97 γ = −305.53
		YSim.	Burr (4P)	0.00645	0.5588	κ= 0.20543 α = 11.513 β = 0.28681 γ = −0.1404
HCO3	A prior statistics	Discharge	Wakeby	0.08914	0.88883	α = 1531 β = 0.19338 γ = 40.077 δ = 0.93225 ζ = −46.396
		FRAC Ir	Cauchy	0.07862	0.9539	σ = 0.01357 μ = 1.1324
		FRAC G1	Dagum	0.09029	0.87996	κ = 0.15021 α = 291.26 β = 1.1397 γ = 0
		FRAC PF	Uniform	0.4395	2.9227 × 10−7	α = −0.55009 β = 0.99785
		Yobs.	Hypersecant	0.0765	0.9632	α = 85.625 μ = 196.75
	Posterior statistics	YSim.	Dagum	0.03255	4.8608 × 10−9	κ = 0.17951 α = 1.9836 β = 0.47046 γ = 0
Ca	A prior statistics	Discharge	Wakeby	0.08914	0.88883	α = 1531 β = 0.19338 γ = 40.077 δ = 0.93225 ζ = −46.396
		Shape Df	Weibull	0.0936	0.85262	α = 8.3969 β = 2.0382 γ = 0
		Yobs.	Frechet	0.0661	0.99133	α = 4.4327 β = 107.45 γ = −63.329
	Posterior statistics	YSim.	Burr (4P)	0.00833	0.26122	κ = 0.27613 α = 10.854 β = 0.3897 γ = −0.13997
Mg	A prior statistics	Discharge	Wakeby	0.08914	0.88883	α = 1531 β = 0.19338 γ = 40.077 δ = 0.93225 ζ = −46.396
		Contig G2	Gen.Logistic	0.07469	0.9701	κ = −0.52828 α = 0.05592 μ = 0.88399
		Yobs.	Gen.Extreme value	0.05299	0.99964	κ = 0.21042 σ = 10.558 μ = 15.286
	Posterior statistics	YSim.	Burr (4P)	0.00806	0.30806	κ = 0.27851 α = 8.8673 β = 0.09248 γ = −0.0424
Na	A prior statistics	Discharge	Wakeby	0.08914	0.88883	α = 1531 β = 0.19338 g = 40.077 δ = 0.93225 ζ = −46.396
		Contig G2	Gen.Logistic	0.07469	0.9701	κ = −0.52828 α = 0.05592 μ = 0.88399
		Yobs.	Fatigue life (3P)	0.07012	0.9836	α = 1.4239 β = 39.534 γ = 3.4162
	Posterior statistics	YSim.	Gen.Extreme value	0.00964	0.1372	κ = 0.85562 σ = 0.01478 μ = 0.0184

). The cumulative density function (CDF), F(x), was used to determine the probability of the variable X being less than or equal to x (F(x) = Pr(X ≤ x)) [60]. In this study, the CDF was used to determine the probability of the model outputs being less than zero (Pr(Output) < 0), as only positive values would have any significance for the water quality variables. The researchers evaluated the behavior of the models based on the CDF values, as shown in Figure 4.

4. Discussion

Water quality modeling is a complex task that requires analyzing the impact of change in land use and land cover on water quality. While previous studies have focused on the relationship between water quality and the composition of land use and land cover classes, it is also important to consider the structural characteristics of the landscape, such as the shape and configuration of landscape patches. By incorporating these landscape features into water quality models as quantitative variables, we can gain a deeper understanding of ecological processes and nutrient transfer between sources and sinks. This information is critical for planning the sustainability of land and water resources, as it provides valuable insights into how different landscape structures affect water quality.

The results of this study are consistent with previous works that have shown the suitability of landscape structure metrics as predictors for analyzing water quality status. These findings are in agreement with [36,61,62]. For instance, Xiao and Ji (2012) [62] found that landscape metrics could explain 56% of the variance in water quality variables. However, the ability to explain the variability in water quality variables can differ based on the specific environmental settings and features of the study area. Therefore, it is essential to consider the regional characteristics as well as the temporal and spatial scales on which previous studies were conducted, as noted in [39,63].

The composition, structure, and configuration of landscapes in catchments affect their functions and services, including the regulation of water quality. However, human interventions for resource exploitation have caused changes in landscape functions and services, including the regulation of water quality [64,65]. Our study found that changes in water quality variables are indirectly related to the specific discharge, meaning that increasing the specific discharge values lead to a decrease in the measure of water quality variable. The average shape index of non-irrigated arable land patches has a significant direct relationship with changes in the mean values of TDS, EC, and Ca. The shape index ranges from 1 to infinity [48], with low values indicating square-shaped patches and high values indicating more irregular shapes [66]. This metric represents a simple way to measure the complexity of a patch, with higher values indicating more irregular shapes [49]. In the studied catchments, the irregular shape of non-irrigated arable land patches led to an increase in TDS, EC, and Ca values. The spatial structure and pattern of landscapes, including extent, distribution, and intensity, are important factors in understanding catchment hydrological processes [67].

The shape index has proven to be an effective metric for predicting water quality variables. It measures the complexity of landscape shapes [68] and can provide insight into the irregularity or regularity of patches. In this study, the average shape index for the studied catchments was found to be 2.17 ± 0.54. The shape index is calculated based on the deviation of a given shape from a standard shape of the same size [47]. The shape of a patch can have implications for its function in a hydrological context, and understanding the regularity or irregularity of landscape shapes can provide valuable insights for landscape hydrology [69].

According to Uuemaa et al. (2011) [68], the shape index of landscape patches is a crucial factor influenced by human activities. In addition to the shape index, two other landscape metrics, the fractal dimension index and the continuity index, were also found to be effective in explaining changes in the mean values of HCO₃, Mg, and Na variables in the study area. The fractal dimension index of the various landscape patches in the river catchments, including permanently irrigated land, high-density grassland, and transitional woodlands, was found to be highly correlated with changes in the measure of HCO₃ in the rivers, explaining about 78% of the total variations. In particular, an increase in the mean values of the fractal dimension index of high-density grassland patches was associated with a decrease in the measure of HCO₃ in the rivers, suggesting that more complex shapes in these patches led to the lower measure of HCO₃. The fractal dimension index measures shape complexity on a scale from 1 to 2, with values closer to 1 indicating regular or square shapes and values closer to 2 indicating more irregular shapes [48,49]. The values of fractal dimensions in the study area were mostly in the range of 1.09 to 1.13, indicating regular shapes for the landscape patches. This regularity may be due to the regular division of land in the study area and the transformation of barren and grassland areas into agricultural land.

The contiguity index is inversely proportional to the mean measure of Mg in the river water for moderate-density grassland patches. If there is a higher degree of fragmentation and dispersion among the patches, the concentration of Mg in the study catchments is expected to increase. The presence of connected patches can help to reduce the amount of rock weathering, which is a source of Mg in the water. This relationship between the contiguity index and water quality is also true for predicting sodium variable in the study area. The contiguity index measures the spatial continuity and connectivity of cells within patches and land use/land cover in a catchment [10]. It ranges from 0 to 1 [48], with a higher value indicating more spatially connected and extensive patches and vice versa [49]. The contiguity index can be used to evaluate patch shape and boundary by assessing the spatial connectedness of cells within a patch or patches of a certain landscape category [50].

Our study revealed that the continuity among patches of moderate-density grassland has resulted in a decrease in the release of magnesium and sodium, leading to improved water quality and the functioning of water ecosystems. This finding is consistent with the results of previous studies [10,22]. Additionally, Sullivan et al. (2004) [70] reported that fragmentation of landscape into smaller areas increases interconnections between drainages, which in turn increases discharge and carrying capacity of rivers.

The changes in landscape structure have had a significant impact on water quality variables in the study catchments. The conversion of natural ecosystems into irrigated and arable lands, urban areas, and forest and grassland, as well as the decrease in the existing forest area by 50 [71], has led to a loss of ecosystem balance and reduced the continuity, shape complexity, and disintegration of the landscape. This has, in turn, affected the quality of river water. However, maintaining the continuity of patches of the same landscape class and larger geometric shapes in the landscape can be effective in reducing the negative effects. Human activities intensify the edge effects of the landscape, making irregularly shaped patches more susceptible to negative effects. Circular patches of a certain size are considered the most stable and resistant against external negative effects from an ecological point of view [72].

Based on the findings the present study, optimizing the shape of landscape metrics can be considered one of possible approach to mitigate the negative impacts on water quality and pollution at catchment scale. This can have an effect on the structure and function of the landscape network by altering the connections between its components, such as patches and corridors. The relationship between the spatial patterns and processes of the landscape is important in understanding how it changes [73]. By adjusting the structural metrics of the landscape, it is possible to manage and improve the quality of water resources in the study area.

5. Conclusions

This study explored the connection between the alteration in landscape patches and river water quality. Through the development of multivariate regression models, it was discovered that the shape index, fractal index, and the contiguity index of five metrics are significant variables that affect river water quality. Spatial features of landscape patterns were found to be influential in modeling water quality variables. The shape index was found to have a greater impact on TDS, EC, and Ca. Magnesium and sodium concentrations in rivers and streams were found to increase due to discontinuity in moderate-density rangeland patches. Additionally, regular non-irrigated arable land patches and continuous moderate-density rangeland patches significantly reduce nutrient and pollutant leaching from the landscape into rivers. This study’s findings suggest that changes in land use planning processes should be carefully considered since the shape of different land use/land cover classes can significantly impact the landscape nutrient leaching process and, in turn, affect river water quality.