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Balancing the tradeoff between economy, energy, environment, water resources and carbon emissions has become the major challenge for sustainable development. In this study, a fuzzy multi-objective method is developed by integrating multi-objective programming, fuzzy linear programming and multiple scenarios. The developed approach can tackle multiple uncertainties and complexities existing in economy–energy–environment system, random carbon dioxide emission and water consumption control policies mix. Results disclose that (1) policy orientation and carbon emission control policy can achieve both carbon and water resource control goals, and water resource control policies are relatively unnecessary; (2) the tertiary sector will become the leading industry, accounting for more than three quarters of the total output value, the construction industry will also overgrow, and the proportion of the manufacturing industry will drop significantly; (3) coal still dominates in the energy production and total quantity consumed, and petroleum consumption will fall, coal accounts for about 75 percent of total energy consumption and electricity for about 15 percent; (4) according to different sources, carbon dioxide emissions are mainly from coal and electricity utilization. Coal’s contribution gradually rose to 65 percent, while electricity dropped from 35 percent to 30 percent. For each industry, the mining industry, the electricity industry and the tertiary sector are the primary sources. (5) the sulfur dioxide control policy and carbon dioxide control policy has a strong correlation, and nitrogen oxide control policies have a specific correlation with them. The water resource control policy and particulate matter control policy are relatively independent.

Under climate change, the ability of water bodies to maintain ecology and human activities becomes more fragile, leading to water shortages. The change in the carrying capacity of the water environment further intensifies the management difficulties of the resource-environment-economic system. This study aims to establish a comprehensive framework that integrates an interval fuzzy program and water environmental carrying capacity assessment model to obtain the optimal state of the energy-water-carbon coupling system by promoting industrial structure adjustment. It is demonstrated that a 10 % reduction in carbon emissions leads to a 15 % increase in the water environmental carrying capacity of the Huangshui watershed. Under the influence of climate change, total energy consumption and carbon emissions show a downward trend. Water consumption per unit of output, energy consumption and carbon emission management policies are highly related and are the main control points for policymakers. The developed model simultaneously considers industrial structure optimization and water environment carrying capacity, and assists in formulating the energy-water-carbon balanced management policies to promote the sustainability of the regional environ-economic system.

The identification of factors that may be forcing ecological observations to approach the upper boundary provides insight into potential mechanisms affecting driver-response relationships, and can help inform ecosystem management, but has rarely been explored. In this study, we propose a novel framework integrating quantile regression with interpretable machine learning. In the first stage of the framework, we estimate the upper boundary of a driver-response relationship using quantile regression. Next, we calculate “potentials” of the response variable depending on the driver, which are defined as vertical distances from the estimated upper boundary of the relationship to observations in the driver-response variable scatter plot. Finally, we identify key factors impacting the potential using a machine learning model. We illustrate the necessary steps to implement the framework using the total phosphorus (TP)-Chlorophyll a(CHL) relationship in lakes across the continental US. We found that the nitrogen to phosphorus ratio (N:P), annual average precipitation, total nitrogen (TN), and summer average air temperature were key factors impacting the potential of CHL depending on TP. We further revealed important implications of our findings for lake eutrophication management. The important role of N:P and TN on the potential highlights the co-limitation of phosphorus and nitrogen and indicates the need for dual nutrient criteria. Future wetter and/or warmer climate scenarios can decrease the potential which may reduce the efficacy of lake eutrophication management. The novel framework advances the application of quantile regression to identify factors driving observations to approach the upper boundary of driver-response relationships.