Zacate Creek water samples were collected from ten different locations with a total of 30 samples representing three different seasons: September 2024 (fall), early March 2025 (winter), and late May 2025 (summer) (Figure 1). Surface runoff from urban areas enters the stream from all the sampling locations along the drainage network. Physical parameters such as water temperature, pH, EC, DO, and TDS were measured at the time of sampling in the field. Samples were taken in 250 mL acid-washed polyethylene bottles, and refrigerated at the laboratory of Texas A&M International University (TAMIU) and samples were packed in ice and sent to soil and water testing lab of the Texas A&M University in college station for the analysis of major base cations (Na⁺, K⁺, Mg²⁺, Ca²⁺), major anions (Cl⁻, NO 3 − , SO 4 2 − , HCO 3 − , PO 4 3 − ), hardness, alkalinity, sodium adsorption ratio (SAR) and boron. Carbonate ion was not detected in any location.

Water temperature, pH, EC, DO, and TDS were measured at the time of sampling by using handheld meter, Thermo Scientific^TM Orion Star^TM A329. Chloride was determined by ion chromatography using US EPA method 300.0 [30]. NO₃-N is measured by reduction of nitrite (NO₂-N) to nitrate by using cadmium column followed by spectrophotometric measurement [31]. Sulfate was calculated from total sulfur [31]. Ammonium (NH₄-N) was measured by spectrophotometric measurement [31]. Fluorine was determined directly using fluoride selective electrode (APHA 1989). Samples were filtered through a 0.45 µm polycarbonate filter for Na, K, Mg, Ca, S, P, Fe, Zn, Cu, Mn, As, Ba, Cd, Cr, Ni, and Pb analysis by using Inductively Coupled Plasma Emission Spectroscopy (ICP-ES) [31]. Trace element concentrations were found to be too low and were not used for modeling or further analysis. Carbonate and bicarbonate are determined by titration using sulfuric acid, alkalinity is calculated from carbonate and bicarbonate concentrations and hardness is calculated from Ca and Mg concentrations [31]. TDS is calculated by summing the cations and anions. Sodium Absorption Ratios (SAR) are calculated from sodium, calcium and magnesium concentrations. Charge balance is calculated by dividing the sum of cations by the sum of anions and it is less than 5% for all samples [31].

Physical and chemical parameters of Zacate Creek, located in Laredo, Southern Texas, were monitored from September 2024 to May 2025 to capture seasonal variations across fall, spring, and summer. Table 1 and Figure 2 summarize seasonal water temperature patterns in Zacate Creek based on 30 observations. Average temperatures vary by season, with the highest mean occurring in summer (31.8˚C) and the lowest in winter (25.6˚C), while fall shows intermediate values (26.6˚C). Summer temperatures are consistently warmer, with a relatively narrow 95% confidence interval (29.8˚C - 33.9˚C), indicating stable conditions. Winter exhibits the greatest variability, reflected in the largest standard deviation (3.9˚C) and the widest confidence interval (22.8˚C - 28.4˚C). Overall, the combined data yielded an average water temperature of 28.0˚C, with observed values ranging from 21.0˚C to 35.6˚C, highlighting clear seasonal differences in thermal conditions along the Zacate Creek.

Table 1. Seasonal variation in water temperature at Zacate Creek.

Figure 2. Average water temperature plot.

To examine seasonal variation in the physical and chemical parameters of Zacate Creek, an Analysis of Variance (ANOVA) test was performed to evaluate the null hypothesis that seasonal temperature differences exert no significant influence on the measured parameters. The first column of Table 2 lists all measured parameters under study with their respective units, while columns 2 - 4 present the seasonal mean ± standard deviation for fall, winter, and summer, respectively. Columns 5 - 7 provide the corresponding Fisher’s F-statistic, degrees of freedom (DF), and p-values. Statistically significant results, where the null hypothesis was rejected, are indicated by palm branch (⸙) in the final column.

Table 2. Seasonal ANOVA results for physical and chemical parameters of Zacate Creek.

Note: ^⸙ = Statistically significant.

The one-way ANOVA results indicate that most physical and chemical parameters of Zacate Creek do not show statistically significant seasonal differences (p > 0.05), including pH, Dissolved Oxygen (DO), Electrical Conductivity (EC), Total Dissolved Solids (TDS), Na⁺, K⁺, Ca²⁺, Cl⁻, SO 4 2 − , PO 4 3 − , SAR, Boron (B), and Charge Balance (CB). In contrast, five parameters exhibit significant seasonal variation: Mg²⁺ (p = 0.025), NO 3 − (p < 0.001), HCO 3 − (p = 0.003), hardness (p = 0.027), and alkalinity (p = 0.007). Several other parameters (e.g., Ca²⁺, Cl⁻, TDS, CB) show near-significant trends (0.05 < p < 0.10) but do not meet the conventional significance threshold.

Interpretation of Significant Parameters with Bonferroni Results

Bonferroni post hoc comparisons clarify that the observed seasonal effects are primarily driven by winter-summer contrasts. Magnesium concentrations are significantly higher in winter than in summer, suggesting enhanced mineral input or reduced dilution during colder months. Nitrate shows a pronounced winter peak, with fall and summer not differing significantly, indicating seasonally elevated nutrient loading or reduced biological uptake in winter. Similarly, HCO 3 − , hardness, and alkalinity are all significantly greater in winter compared to summer, reflecting increased carbonate weathering influence, reduced streamflow dilution, or groundwater contributions during winter conditions. Collectively, these results highlight winter as the season with elevated ionic strength and nutrient levels, while summer conditions reflect comparatively diluted or biologically moderated water chemistry in Zacate Creek.

To avoid redundancy and improve clarity in presenting the 18 × 18 bivariate correlation and regression analyses of Zacate Creek water, this study focuses exclusively on highly correlated variable pairs. Accordingly, only pairs with an absolute Pearson correlation coefficient of |r| ≥ 0.85 were selected for further examination. Table 3 summarizes the 41 highly correlated pairs, reporting their corresponding Pearson correlation coefficients and their predictive models that highlight the dominant interrelationships governing the hydrochemical behavior along Zacate Creek.

Table 3. Correlation and regression analyses of highly correlated variable pairs (|r| ≥ 0.85).

NB: EC = Electrical Conductivity; TDS = Total Dissolved Solids; SAR = Sodium Adsorption Ratio.

Model Illustration and Interpretation: To aid readers in understanding the representation and interpretation of the regression models summarized in Table 3,Model 1 is presented here as an illustrative example. This model describes the linear relationship between Electrical Conductivity (EC) and Total Dissolved Solids (TDS) in Zacate Creek water.

The fitted regression equation is:

with a coefficient of determination (R² = 0.956).

The high R² value indicates that 95.6% of the total variability in EC is explained solely by TDS, while only 4.4% of the variability remains unexplained, reflecting an exceptionally strong linear association between these two parameters which obviously we expect.

The slope (1.215) represents the rate of change in EC with respect to TDS. Specifically,for every one-unit increase in TDS, EC increases on average by 1.215 units, indicating that EC responds strongly and proportionally to changes in dissolved solids. This relationship underscores the dominant role of dissolved ionic constituents in controlling the electrical conductivity of Zacate Creek water.

Furthermore, the p-value (<0.001) associated with the regression slope indicates that the relationship between EC and TDS is highly statistically significant. Consequently, the null hypothesis that EC and TDS are independent is rejected, confirming a strong and meaningful linear dependence between the two variables, which is obvious for these two parameters. Figure 3 represents the graphics of the equation.

Figure 3. Bivariate relationship between EC and TDS.

Table 4summarizes the multivariable regression models describing the dynamics of Zacate Creek water chemistry. Each model represents a key physicochemical parameter as a function of selected hydrochemical and ionic predictors, highlighting the interdependence among major ions, nutrients, and water quality indicators. The relatively high coefficients of determination (R² = 0.707 - 1.000) indicate strong explanatory power, reflecting systematic geochemical controls and mixing processes governing water chemistry in the creek.

The Backward Regression Method was employed for this analysis to systematically refine each model by removing statistically insignificant predictors, thereby enhancing model parsimony and interpretability. This approach minimizes multicollinearity among variables and ensures that only the most influential parameters are retained, providing a robust representation of the seasonal relationships governing the chemical composition of Zacate Creek.

Interpretation of Multivariate Models:Table 4 presents a comprehensive suite of 16 multivariate regression models, developed to predict the behavior of major physical and chemical parameters in Zacate Creek. In total, the analysis produced 16 predictive equations for parameters showing minimal seasonal dependence. Collectively, these models comprise over 119 partial regression coefficients, each quantifying the partial influence of one variable on another while holding other predictors constant. Such coefficients encode detailed information on the interconnected chemical dynamics of the pond, offering a robust empirical framework for understanding system-wide geochemical interactions.

Table 4. Spatial-multivariate models of water quality parameters in Zacate Creek.

R² values, many of which are nearly equal to 1.00, indicate an excellent level of explanation of variance in the dependent variable, suggesting high predictive reliability within the observed dataset. Each equation represents a statistical model describing the joint influence of multiple explanatory variables on the concentration of the target element. To support proper interpretation of the regression coefficients, a representative model is presented below. The same interpretive framework may then be applied to all subsequent models.

Model 6:For instance, Equation 6 models Sodium concentrations (mg·L⁻¹) throughout the year as follows:

Each regression coefficient represents the expected change in sodium concentration (Na⁺, mg·L⁻¹) associated with a one-unit increase in the corresponding predictor, while holding all other variables constant. The exceptionally high coefficient of determination (R² = 0.999) indicates that this multivariate model nearly completely explains the variability in sodium concentrations, underscoring the strong coupling between Na⁺ and the overall ionic, carbonate, and salinity framework of the Zacate Creek.

1) Regression coefficient of Mg²⁺=–0.666:A 1 mg·L⁻¹ increase in magnesium results in a 0.666 mg·L⁻¹ decrease in sodium. This inverse relationship suggests competitive ion exchange processes, where Mg²⁺ displaces Na⁺ from solution through adsorption onto sediments or clay minerals. Divalent cations such as Mg²⁺ have a higher affinity for exchange sites, thereby reducing dissolved sodium under conditions of increasing hardness.

2) Regression coefficient of Cl⁻ = +0.473:An increase of 1 mg·L⁻¹ in chloride increases Na⁺ by 0.473 mg·L⁻¹. This positive association reflects the common origin of Na⁺ and Cl⁻ from halite dissolution, evaporative concentration, or anthropogenic inputs such as irrigation return flows. Their coupled behavior is typical of salinity-driven systems and confirms sodium’s role as a dominant conservative ion.

3)Regression coefficient of NO 3 − = +1.851: A 1 mg·L⁻¹ increase in nitrate corresponds to a 1.851 mg·L⁻¹ increase in sodium. This relationship suggests that nutrient enrichment is accompanied by enhanced sodium loading, likely from agricultural runoff, fertilizer application, or wastewater inputs. Nitrate thus serves as an indicator of anthropogenic influence that simultaneously elevates Na⁺ concentrations.

4) Regression coefficient of SO 4 2 − = +0.250:Each 1 mg·L⁻¹ increase in sulfate increases sodium by 0.250 mg·L⁻¹. This moderate positive effect implies co-mobilization of sulfate and sodium through evaporite dissolution or oxidation of sulfide minerals. Under concentrated flow conditions, sulfate contributes to ionic strength without strongly suppressing Na⁺ availability.

5) Regression coefficient of Alkalinity= +0.450: A one-unit increase in alkalinity results in a 0.450 mg·L⁻¹ increase in sodium. Elevated alkalinity reflects enhanced carbonate weathering and groundwater influence, both of which are commonly associated with sodium-rich waters. This linkage highlights the role of carbonate buffering systems in sustaining dissolved Na⁺ levels.

6) Regression coefficient of SAR= +22.397: A unit increase in Sodium Adsorption Ratio leads to a substantial 22.397 mg·L⁻¹ increase in Na⁺. This strong positive relationship is expected, as SAR directly incorporates sodium concentration relative to calcium and magnesium. High SAR conditions indicate sodium dominance and reduce divalent cation control, reinforcing Na⁺ accumulation in solution.

7) Regression coefficient of B= +26.282: A 1 mg·L⁻¹ increase in boron increases sodium by 26.282 mg·L⁻¹, indicating a strong association between these constituents. Boron is commonly enriched in saline groundwater, geothermal inputs, or agricultural return flows, all of which are typically sodium rich. This relationship further supports the influence of deep or anthropogenically modified water sources.

8) Regression coefficient of CB= +2.427: An increase of 1% in charge balance increases sodium by 2.427 mg·L⁻¹. This suggests that Na⁺ plays a key role in maintaining ionic equilibrium within the system, acting as a compensatory ion when minor charge imbalances occur among measured constituents.

9) Regression coefficient ofCa²⁺ = –0.678: A 1 mg·L⁻¹ increase in calcium results in a 0.678 mg·L⁻¹ decrease in sodium. This inverse relationship reflects cation exchange and competitive geochemical controls, where increased Ca²⁺ availability suppresses Na⁺ through adsorption or precipitation-driven processes. It also indicates a transition from sodium-dominated to calcium-dominated water chemistry under higher hardness conditions.

Overall interpretation. This sodium model highlights the dominant role of salinity processes, ion exchange, and anthropogenic inputs in controlling Na⁺ concentrations. Sodium increases with indicators of salinity, nutrient enrichment, alkalinity, and boron, while being suppressed by divalent cations such as calcium and magnesium. The exceptionally high explanatory power of the model suggests that sodium behavior in the system is tightly regulated by integrated hydrogeochemical mechanisms, including evaporative concentration, groundwater mixing, agricultural return flows, and sediment-water ion exchange.

Separating the chemical concentrations of base cations and sulfate from sea-salt contributions is essential for accurately understanding their release rates from chemical weathering processes [32]. Generally elemental molar ratios in seawater are used to estimate the Sea-Salt derived ions in waters and this approach has been used by various authors in earlier studies from various regions [33]-[36].

To assess the seasonal variability of selected sea salt contributed denoted with (SS) and non-sea salt weathered denoted with asterisk (*) for major base cations and sulfate in Zacate Creek, a one-way Analysis of Variance (ANOVA) was conducted. The objective was to test the null hypothesis that seasonal temperature differences exert no statistically significant influence on these parameters. The results (Table 5) revealed distinct and statistically significant seasonal differences (p < 0.05) in all measured ions, indicating that temperature-driven processes play a critical role in regulating the geochemical behavior of Sea-Salt derived constituents.

Table 5. Seasonal variability and statistical significance of Sea-Salt contributed and weathered contributed major base cations and sulfate ions in Zacate Creek.

Note: SS = Sea-Salt contributed; (*) non-sea-salt (weathered) contributed; ^⸙ = Statistically significant.

The Sea-Salt (SS) contribution to major ions in Zacate Creek shows distinct patterns among elements and seasons. We present the individual results and interpretations for each ion for Sea-Salt contributed elements as follows.

1) Sea-Saltderived sodium (SS-Na⁺):Sea-Salt-derived sodium (SS-Na⁺) accounts for approximately half of the total sodium concentration across all seasons, with mean contributions of 49.1% in fall, 52.7% in winter, and 45.7% in summer. Although winter exhibits a slightly higher SS-Na⁺ contribution, the seasonal differences are not statistically significant (p = 0.102), indicating relatively consistent marine or evaporative influence on sodium throughout the year.

2) Sea-Salt-derived magnesium (SS-Mg²⁺): Sea-Salt-derived magnesium (SS-Mg²⁺) contributes about 42% - 45% of total magnesium across seasons, with minimal variation among fall, winter, and summer. The lack of significant seasonal difference (p = 0.701) suggests that the marine or atmospheric input of magnesium remains stable year-round and is not strongly affected by seasonal hydrological changes in the creek.

3) Sea-Salt-derived calcium (SS-Ca²⁺): In contrast, the sea-salt contribution to is very small, averaging only about 4% - 5% in all seasons, and shows no significant seasonal variation (p = 0.653). This consistently low SS-Ca²⁺ fraction indicates that calcium in Zacate Creek is overwhelmingly derived from non-marine sources, with negligible influence from sea-salt inputs regardless of season.

4) Sea-Salt-derived sulfate (SS- S O 4 2 − ): As shown in Figure 4 below, sea-salt-derived sulfate (SS- SO 4 2 − ) exhibits a comparatively low but statistically significant seasonal pattern (p = 0.007). SS- SO 4 2 − contributions are highest in winter (6.4%), slightly lower in fall (6.1%), and lowest in summer (5.2%). This seasonal decline suggests that marine or atmospheric sulfate inputs are relatively more important during cooler, higher-flow conditions, while summer conditions enhance dilution or increase the relative dominance of non-sea-salt sulfate sources in Zacate Creek.

Figure 4. Sea-Salt-derived sulfate (SS- SO 4 2 − ).

Relative Contributions of Sea-Salt and Weathering-Derived Magnesium across Zacate Creek Samples

Figure 5 below illustrates the relative contributions of Sea-Salt derived magnesium (SS-Mg²⁺) and non-sea-salt magnesium (*Mg²⁺) across ten Zacate Creek samples (ZCS 1 to ZCS 10). Each stacked bar represents the total magnesium contribution (100%), partitioned into SS-Mg²⁺ (lower, blue segment) and *Mg²⁺ (upper, orange segment), allowing direct comparison of source dominance among samples.

Figure 5. Relative contribution of sea salt contributed and non-sea salt (weathered) magnesium to the total magnesium in percentage in Zacate Creek in Laredo, Texas. SS-Mg²⁺ and *Mg²⁺ represent sea-salt and non-sea salt (weathering) contributed magnesium, respectively.

Across ZCS 1 to ZCS 6, SS-Mg²⁺ and *Mg²⁺ contribute nearly equally, with each accounting for roughly 43% - 50% of total magnesium. This near balance suggests mixed marine/atmospheric and weathering-related sources of magnesium in these samples. ZCS 7 shows a slight shift toward SS-Mg²⁺ dominance (≈53%), indicating a relatively stronger sea-salt or evaporative influence at that site.

In contrast, samples ZCS 8 to ZCS 10 display a pronounced dominance of *Mg²⁺, with non-sea-salt contributions increasing substantially from about 62% in ZCS 8 and ZCS 9 to nearly 68% in ZCS 10. Correspondingly, SS-Mg²⁺ declines to its lowest values (approximately 32% - 38%) in these samples. This trend indicates increasing influence of non-marine sources, most likely enhanced rock weathering, groundwater interaction, or localized geochemical processes contributing magnesium downstream or under changing hydrological conditions (high discharge in lower transects of the Zacate Creek) as downstream site receives urban drainage inputs from various points, so we observed relatively higher discharge than the headwater sites.

Overall, the figure highlights a clear spatial shift from relatively balanced magnesium sources in earlier samples toward strong non-sea-salt dominance in later samples, emphasizing heterogeneity in magnesium origin within Zacate Creek and suggesting increasing importance of catchment-derived weathering inputs relative to marine or atmospheric contributions.