Abstract: How to achieve the coordination and sustainable development of population, economy, society, resource, and environment system is a common problem facing all mankind. This research uses various mathematical analysis methods and GIS technology on the Gansu Province, China and its sub- regions to conduct the spatial- temporal comprehensive measurement of coordination and sustainable development of population-economy-society-resource- environment system. It makes up for the lack of the research of sustainable development form single angle, and it provides theoretical support and decision-making basis to realize a strategy for the sustainable development of Gansu Province. The results are as follows. Overall, the comprehensive level of sustainable development in Gansu Province shows gradual upwards. Among them, the level of sustainable development of economic and social subsystems is growing faster. The sustainable development level of population and environment subsystems is growing steadily, and the sustainable development level of resource subsystem fluctuates greatly. The comprehensive level of sustainable development in each city and state shows a gradual upward trend. However, the increase is limited and volatile in some areas. Among them, the development trend of sustainable development level of each subsystem is different with obvious spatial differences. The coordination development level of the five systems in Gansu Province keeps a good steady rising trend. The evolution of the coordination development level of the five systems in each city and state is basically in line with the steady growth trend. The evolution trend is basically consistent with that of the whole Gansu province. Among them, the number of regions in the state of maladjusted recession and on the verge of maladjusted recession is gradually decreasing, while the number of regions in the state of coordination development and reluctant coordination development is gradually increasing. On the whole, the gravity center of the comprehensive level of sustainable development is moving towards southeast. The comprehensive level of sustainable development in the southeastern part of Gansu Province has grown fast with strong momentum of development. The sustainable development level focuses on the subsystems distributed along the northwest-southeast direction, where the northwest-southeast migration is the dominant direction. Among them, the gravity center of the economic subsystem and population subsystem focus on the northwest distribution, while the gravity center of the resource subsystem shifts to southeast. The gravity center of the society and environment subsystems is observed to be in the middle. The gravity center of the coupling coordination degree of the five systems shifts to eastward but the migration range is not large and its evolution is relatively stable. The gravity center offset distance of coupling coordination degree in the east- west direction is greater than the north- south direction. That is, the growth rate difference of the coordination development level among the five systems in the east-west direction is greater than that in the north-south direction.

Key words: sustainable development, coupling coordination, spatial-temporal, system, index