Objectives This paper aims to address the critical challenge of scale conversion in geographic information science (GIS) by proposing a novel methodology for transforming multi-scale urban waterlogging simulation data. Traditional GIS scale conversion theories primarily focus on spatial resolution adjustments but lack applicability to data generated by mechanism-based models. Such models produce outputs reflecting the intrinsic laws of natural phenomena, and scale is redefined as the degree of representation of internal mechanisms. This paper aims to identify spatial modals inherent in urban waterlogging data across varying parameter-driven scales, to develop a mathematical framework for converting simulation data between these mechanism-defined scales, and to enrich GIS scale conversion theory by integrating spatial pattern recognition and mechanism-driven transformations.

Methods 12 simulated urban waterlogging datasets are generated under distinct parameter configurations of a hydrological model. These datasets represent diverse spatial manifestations of waterlogging influenced by nonlinear interactions between rainfall, terrain, and drainage systems. Matrix decomposition techniques are employed to extract latent spatial modals from the high-dimensional simulation data. The Frobenius norm, serving as a constraint, is integrated into a similarity transformation framework to mathematically convert the weight coefficient matrices associated with these spatial models across scales. Conversion accuracy is rigorously evaluated using mean absolute error (MAE), mean squared error (MSE), and the coefficient of determination (R²).

Results The proposed method demonstrated robust performance in cross-scale waterlogging data conversion. For individual simulation events, error metrics spanned MAE from 0.04 m to 0.11 m, MSE from 0.001 m² to 0.02 m², and R² from 0.86 to 0.97, indicating consistent precision across diverse parameter conditions. Aggregate performance across all 12 scenarios yielded MAE was 0.07 m, MSE was 0.01 m², and R² was 0.95, confirming the reliability of the proposed method.

Conclusions This study advances the theory of geographic information scale conversion by establishing a mechanism-driven paradigm that transcends traditional resolution-based frameworks. The proposed method provides a generalized framework for mechanism-aware scale conversion in geographic information science, demonstrating significant applicability in disaster simulation, climate modeling, and multi-source geospatial data fusion.