Applicability analysis of the at-many-stations hydraulic geometry method based on cross-sectional morphology

The complex cross-sectional morphology of alpine gorge rivers often reduces the stability of discharge retrieval using the at-many-stations hydraulic geometry (AMHG) method. Focusing on this problem, this study extracted cross-sectional morphological characteristics of the upper Jinshajiang River (China) during dry, normal-flow, and flood seasons from Sentinel-2 images. K-means clustering was adopted to classify the river sections into four types: unilateral open asymmetric sections (T1), bilateral open asymmetric sections (T2), bilateral open symmetric sections (T3), and symmetric narrow-deep sections (T4). Variations in the AMHG width exponent and discharge retrieval accuracy under different morphological conditions were further analyzed. Results indicated that T1 sections, characterized by moderate openness and slight asymmetry, are conducive to maintaining a stable width—discharge power-law relationship. Among them, subclass 13 exhibited better performance; except for the Batang Station, the Nash-Sutcliffe efficiency coefficient was >0.74 and the correlation coefficient was >0.90. T2 sections are strongly affected by floodplain inundation and lateral momentum exchange, resulting in high parameter dispersion. T3 and T4 sections show weak AMHG sensitivity because of energy equilibrium or topographic constraints. The dry-to-flood-season width ratio revealed a statistically significant negative correlation with the width—discharge power-law exponent b (r≈−0.66), controlling for the monotonic variation of b. In contrast, flood-season flow deviation had a statistically significant positive correlation with b (r≈0.67), causing a sharp increase in dispersion in the upper quantiles, which reflects gradient-control and threshold-amplification effects. These findings indicate that cross-sectional morphology affects AMHG parameter stability by regulating river-width response characteristics. Morphology-based classification can provide a basis for assessing AMHG applicability and selecting suitable sections in ungauged rivers in complex mountainous regions.