Introduction

Quaternary climatic fluctuations have played a fundamental role in shaping Earth's surface morphology and influencing the evolution of fluvial systems, especially in mountainous regions. These oscillations, characterized by alternating glacial and interglacial periods, have significantly altered hydrological regimes, erosion-deposition dynamics, and geomorphological development across diverse landscapes. In Iran, particularly in northwestern regions such as the Zanjanrud and Qezelozan basins, Quaternary climatic changes have left distinct geomorphic imprints, including U-shaped valleys, moraine ridges, and multiple terrace levels—features that suggest both glacial and periglacial activity.

This study focuses on detecting and validating four stages of climatic and tectonic transformation in the Arpachai Basin using sixth-degree Pearson polynomial modeling and dimensional hypsometric analysis. Unlike traditional studies that rely on international glacial stage classifications, this research emphasizes morphometric and statistical signatures of past climatic oscillations, based on topographic inflection points preserved in the river longitudinal profile.



Methodology

To achieve the research objectives, a multi-stage methodology was adopted, combining field data acquisition, spatial analysis, and mathematical modeling. Data collection involved:

Topographic maps (1:25,000 scale), Sentinel-2 satellite imagery, and Google Earth Pro for precise identification of cross-sections.

Field GPS data (UTM Zone 39N) encompassing longitude (X), latitude (Y), and elevation (H) from three cross-sectional zones: upper, middle, and lower parts of the Arpachai Basin.

Lithological and geological information derived from 1:100,000-scale geological maps provided by the Geological Survey of Iran.

All collected data were used in dimensional hypsometric analyses. Unlike traditional dimensionless hypsometry, which considers only elevation along the Y-axis, dimensional hypsometry integrates both X and Y coordinates via the Pythagorean formula:

D= √(x^2+y^2 )

This value (D ) was used as the horizontal axis, while elevation (H ) served as the vertical component in dimensional hypsometric diagrams, allowing for a more accurate representation of topographic structures.

Three cross-sections (upper, middle, and lower) were selected based on slope variation, lithological heterogeneity, and the presence of multiple geomorphic terraces. Using the Profile Tool plugin in QGIS, topographic profiles were extracted and analyzed to detect geomorphic inflection points associated with climatic and tectonic changes.

A sixth-degree polynomial model was applied to simulate the actual geomorphic profiles and identify key inflection points:

Y=a^6 x^6 〖+a〗^5 x^5+a^4 x^4+a^3 x^3+a^2 x^2+ax+a_0₀

Coefficients were optimized using the Least Squares Method, and the resulting models were statistically validated using correlation coefficient (r), coefficient of determination (R²), and effect size.

Due to limited accessibility in the middle section of the basin, pixel-coded digitization of field images and GIS-based coordinate extraction were employed to reconstruct the topographic profile. In the lower basin, 50 field survey points and UTM coordinates were combined using the Pythagorean structure to extract and analyze the corresponding topographic profile.



Results and Discussion

Analysis of the three cross-sectional profiles revealed consistent evidence of four major geomorphic edges throughout the Arpachai Basin. These edges correspond to inflection points in the river longitudinal profile and reflect significant shifts in base-level, river energy regime, and sedimentation patterns under combined climatic and tectonic influences.

These results demonstrate the robustness of the method in detecting subtle but coherent geomorphic signals across the basin. Minor discrepancies in model performance among sections were attributed to local lithological variations, differential erosion rates, and sediment deposition effects.

In the upper part of the basin, the final polynomial model was derived as:

y=(-0.1*〖10〗^(-12) ) x^6+0.000003x^5-34.682x^4+(2*〖10〗^8 ) x^3-(6*〖10〗^14 ) x^2+(9*〖10〗^20 )x-(6*〖10〗^26)

This model successfully explained over 97% of topographic variability, indicating minimal estimation error and strong explanatory power.

For the middle basin, where direct field access was limited due to steep terrain and narrow width, the following model was obtained:

y=-1.6x^6+39.2x^5-392.8x^4+1945.4x^3-4581.7x^2+5064.4x-615.92

This equation accurately simulated four geomorphic inflection points, interpreted as evolutionary stages linked to paleoclimatic oscillations.

In the lower basin, data from 50 field survey points were used to generate the following polynomial function:

y=(2*〖10〗^(-12) ) x^6-(4*〖10〗^(-5) ) x^5+408.55x^4-(2*〖10〗^9 ) x^3+(7*〖10〗^15 ) x^2-(1*〖10〗^22 )x+(8*〖10〗^27)

Here, the model achieved the highest performance, with an R² value of 98%, confirming the stability and reliability of the polynomial modeling technique.

These results indicate exceptionally high model accuracy, with all sections showing R² values above 94%, confirming the presence of four distinct geomorphic stages in the basin's evolution.

The consistency of these geomorphic signatures across all cross-sections demonstrates that the detected climatic fluctuations were recorded synchronously throughout the basin, supporting the hypothesis that the observed changes were not random or isolated, but rather large-scale spatiotemporal adjustments driven by both climatic and tectonic forces.

Minor discrepancies in model performance among sections were attributed to local lithological variations, sediment deposition effects, and differential erosion rates. However, the structural coherence of the inflection points across the basin confirms the morphoclimatic significance of the identified transitions.

The consistency of these geomorphic signatures across all cross-sections indicates that the detected climatic fluctuations were recorded simultaneously throughout the basin. This coherence supports the hypothesis that the observed changes were not random or isolated, but rather reflected large-scale spatiotemporal adjustments driven by both climatic and tectonic forces.



Conclusion

This study provides strong evidence for the presence of four distinct paleoclimatic oscillations during the Quaternary period in the Arpachai Basin. These oscillations were identified through sixth-degree polynomial modeling and dimensional hypsometry, which enabled high-resolution simulation of geomorphic profiles and statistical validation using r, R², and Effect Size.

The identified geomorphic edges represent transitions in river energy regime, base-level changes, and sediment transport dynamics, all indicative of climatic forcing. These features were consistently preserved across all three cross-sectional zones, demonstrating the basin-wide impact of Quaternary climatic fluctuations.

This research highlights the robustness of geometric and statistical methods in detecting and interpreting paleoclimatic signals in tectonically active and climatically sensitive regions. The approach used in this study can serve as a model for similar investigations in mountainous and semi-mountainous basins in Iran and other regions with complex morphoclimatic and tectonic histories.