| The biota and physical structures of ecosystem provide a wide variety of marketable goods. Moreover, society is increasingly recognizing the myriad life support functions, the observable manifestations of ecosystem processes that ecosystems provide and without which human civilizations could not thrive. The research on theory and method of ecological carrying capacity (ECC) in ecosystem is not only hot issues in the field of ecological economics research, but also the core of its research, and the main supporting theory on sustainable development. The comprehensive study on ECC theory, methods and application is not only the development of important scientific and theoretical significance to ecological economics, but also an important guiding significance to the reality to regional economic sustainable development.Based on the use of natural resources, aims at the regional ecological and economic sustainable development, in accordance with the key issues in quantitative study on ecosystem services, combining ECC and sustainable economic development research, this paper studies deeply the new evaluation method biophysical of the ECC in recent years which International concern about-Ecological Footprint(EF) Method. The paper put forward a new theoretical framework, based on the EF method's basic theory, evaluation, mathematical model and its advantages and disadvantages of analysis, combining with the principle of emergy analysis, establishes such as emergy footprint index system with the new methods, ECC of the theoretical framework, quantitative models and dynamic time for a systematic evaluation of the comprehensive study, and the value of ecosystem services and risk analysis of organic combination of ecological risk assessment carried out innovative research in ecosystem services in Gansu Province, empirical analysis be carried out. The main conclusions of the study are as follows:1. From the social development, the simple review and analysis on the relation of the development of the human history and the ECC has been made. As a result of the productivity level, the relation on the development of the society economy and ECC is different on each kind of social stage. Meanwhile this paper has conducted the systematic research on the rationale of ECC analysis.2. Emergy analysis has been developed over the past 20 years by H.T.Odum. Based on the energy flows of the ecosystem, applying the emergy theory and methods, the emergy EF on the quantitative research of Gansu ecological-economic systems has performed in order to study its sustainability. The emergy flow of Gansu was divided into 5 parts:emergy flow of renewable resources, emergy flow of products of renewable resources, emergy flow of non-renewable resources, emergy flow of money and emergy flow of waste.3. From the methods and models, the EF method is a static evaluation method, in the quantitative evaluation, analysis and prediction of a long sequence of the dynamic trend of ECC deficiencies. In order to adapt to the quantitative study on the dynamic trend of ECC, this article in the time scale, establishes the time dynamic model on EF and ECC, proposed change rates and scissors differences two quantitative indicators, two indicators of a mathematical model and analysis methods used to measure and analyze the ECC demand and supply of dynamic development trends and their differences.4. Based on the ECC and evaluation of indicators and the emergy EF method, the eco-pressure index of mathematical models and analysis methods are proposed. The use of the proposed new system of quantitative indicators and dynamic analysis model in time series on the ECC to carry out an empirical study of Gansu Province in 1980-2006 of the calculation and analysis of the province, the ecological budget time dynamic development trends, results showed that:Since 1993, the province's EF than the ECC, the state is ecological deficit. The per capita ECC was sustained in 1980-2006 to reduce the trend, the scissors difference of per capita EF and ECC in 1980-2006 in the province increases every year. This show that the two trends of the EF and ECC is growing over the same period. These conclusions are that the ECC in Gansu Province in the year-on-year gap between supply and demand gap, eco-overload volume increases every year, people in the growing contradiction, human use of natural assets have far exceeded the threshold of ECC of Gansu Province in the overall state of unsustainable development.For the next 14 years, the paper predicts the ECC of the evaluation index and ecological budget time to the dynamic trend analysis in Gansu province. The results showed that in the next 14 years in Gansu province ECC for, and development trend of the differences will continue to increase. The per capita ecological deficit will continue to increase year by year, eco-overload is becoming increasingly serious. To change this trend of development in Gansu province, man must gradually reduce construction sites and fossil energy consumption, based on the use of scientific and technological advances constantly improve productivity levels, to achieve future sustainable development.5.Combining quantitative of emergy EF and the EVR model and the information diffusion model, this paper carries on example research on ERA based on the emergy EF in the ecosystem. The paper calculates the emergy value of ecosystem services in Gansu province and use the EVR model to estimate value of ecosystem services at risk under certain confidence level. As was stated above, it provides theoretical data and quantitative analysis data for the sustainable development of the Gansu province.6. According to the above quantitative analysis research, this article proposed the Gansu Province ecology supporting capacity realizes continues the load bearing the essential countermeasure, namely enhances the ecology supporting capacity supplies, reduces the Gansu Province EF (ecology supporting capacity demand), realizes the Gansu Province economic society sustainable development. Finally to the ecology supporting capacity theory, the method study has carried on the forecast. It pointed out that the EF method will undergo the unceasing improvement and the consummation to formulate the sustainable development plan strategic analysis tool from a research tool development. |