A multiple spatial scales water use simulation for capturing its spatial heterogeneity through cellular automata model

Abstract

Reliable water use simulation is essential for sustainable water resource planning, especially under intensifying pressures from climate change, population growth, and socio-economic transitions. While previous studies have extensively explored water availability as supply side modeling across multiple spatial scales for its spatial heterogeneity, the water demand side remains relatively underdeveloped – often constrained by fixed spatial scales and coarse statistical data that assume spatial homogeneity. This mismatch between supply side and demand side limits the ability of existing models to accurately represent spatial heterogeneity in water use and brings uncertainty into water resource allocation strategies. To address this mismatch, we propose a novel multi-scale water use simulation framework by integrating cellular automata (CA) model with Generalized Likelihood Uncertainty Estimation (GLUE). The CA model captures the spatial heterogeneity of water use through the grid-based update rules. Two update rules are adopted – probability rule (i.e., capturing stochastic transitions via distribution fitting) and linear rule (i.e., modeling neighborhood-weighted evolution). To evaluate the impacts of spatial scale on water use heterogeneity, simulations are conducted at three spatial scales: 1 km, appropriate scale, and prefecture scale across 341 prefectures in China. Results show that both the update rule and spatial scale significantly affect spatial heterogeneity and uncertainty of water use. The probability rule can capture the broader variability but results in higher Root Mean Squared Error (RMSE) and Relative Error (RE) while the linear rule brings more stable performance with lower errors. While the 1 km scale increases uncertainty due to sensitivity to local fluctuations, and the prefecture scale suppresses spatial details, the appropriate scale offers the best trade-off between stability and spatial heterogeneity. The uncertainty quantified by GLUE, expresses as confidence intervals, varies across prefectures and spatial scales. Overall, the proposed framework offers a flexible tool for multi-scale water use simulation and highlights the critical role of spatial heterogeneity, thereby supporting adaptive water resource planning and management.