Table 2 Results of the triaxial analysis of urban-water interactions across the four settlements

X-axis

Historical stage judgment

Military defense→Trade expansion→Tourism transition; In-situ narrative translation

Defensive settlement→Life continuity→New-old separation;

Ex-situ symbiotic evolution

Residential settlement→Industrial development→ Post-disaster reconstruction →Tourism transition;

Catastrophic structural reconstruction

Hydraulic-based origin →Residential/trade expansion →Heritage activation; In-situ functional continuity

Y-axis

Site Adjacency

Riverside: Mainstream valley

Near river: Zagunao River tributary terrace

Riverside: Shouxi River valley

Riverside: Mountain outlet

Macro Spatial Role

Boundary definition, spatial skeleton, regional connectivity node

Ecological barrier, spatial skeleton

Ecological barrier, spatial skeleton, regional connectivity node

Boundary definition, spatial skeleton, regional connectivity node

Water Entry Mode

Outer loop→Mainstream traversing

Alpine runoff; open and underground channels

Outer loop→Outer river and inner lake

Multi-level hydraulic diversion→Moat transitioned into domestic river

Water System and Spatial Pattern

Boundary→Linear connectivity and guiding axis

Deep coupling of water network, streets, and road networks

Boundary→Reconstructed lakefront interface

Physical skeleton definition→Social life interface

Water Landscape

Ritual etiquette, frontier defense narrative

Survival defense, ethnic memory, and micro-climate regulation

Recreational consumption, ecological reshaping

Heritage activation, cultural expression, and social media landmark

Z-axis

Dominant function types

Defense orientation → Transportation and trade orientation →Cultural landscape orientation

Integrated defense, life, and ecology →Cultural landscape overlay

Production support →Reconstruction and transition orientation →Cultural landscape orientation

Hydraulic infrastructure orientation →Trade hybrid →Cultural landscape overlay