The Loess Plateau is a vast region in the northwest of China, covering an area of approximately 640,000 square kilometers. It is characterized by unique geological landscapes, diverse ecosystems, and significant economic and cultural value. However, rapid population growth, urbanization, and industrialization processes have led to environmental degradation and ecological imbalances in this region. It faces urgent environmental challenges such as soil erosion, land degradation, desertification, and water resource shortages.To assess the ecological livability of the Loess Plateau and determine sustainable development strategies, the utilization of remote sensing and geographic spatial analysis techniques proves to be powerful tools for assessment and monitoring. Existing research faces several issues, including the lack of scalability and comprehensiveness in ecological livability evaluation indicators, model temporal limitations, susceptibility to subjective factors, and a lack of macroscopic perspective. Moreover, the uncertainty of ecological livability models has not been considered. Leveraging the Google Earth Engine cloud platform, this study introduces various uncertainty quantification techniques for the first time to comprehensively consider the reliability of model results.

Uncertainty is classified into two sources, cognitive uncertainty and random uncertainty, and quantitative analysis of uncertainty in the model is performed using uncertainty quantification methods such as Monte Carlo, Latin Hypercube, and generalized chaotic polynomial methods. These methods effectively simulate randomness and human subjectivity in the evaluation model, providing a more comprehensive understanding of evaluation results. The Monte Carlo method employs random sampling techniques to generate numerous possible scenarios and calculates the ecological livability evaluation results for each scenario to examine the potential range of variations in evaluation results. The Latin Hypercube method introduces Latin Hypercube sampling techniques on the basis of Monte Carlo, making samples more uniform and diverse, enhancing the precision and stability of evaluation results. Additionally, the generalized chaotic polynomial method models uncertainty as a nonlinear polynomial function from chaotic theory, further revealing the degree of uncertainty in evaluation results by analyzing the characteristics of chaotic functions.

Through these uncertainty quantification methods, quantitative analysis of uncertainty in the model is performed, and through statistical indicators and sensitivity analysis, a deeper investigation into the extent and major sources of uncertainty's impact on evaluation results is conducted. With the quantification and analysis of uncertainty mentioned above, the study effectively handles and assesses uncertainty in the evaluation model, enhancing the credibility and applicability of the model. These methods and analyses provide more reliable scientific support for ecological livability assessment in the Loess Plateau region, offering robust assistance for sustainable development and ecological conservation.