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• A nonlinear discrete grey model is developed to assess the intervention effect. • A new intervention effect-based nonlinear discrete grey forecasting model is designed. • Effect of a carbon emissions trading scheme on emissions intensity is assessed. • The novel model can predict carbon emissions intensity under policy intervention. • Empirical results demonstrate the novel model's excellent forecasting performance. In the context of severe global warming, accurately exploring the trend of carbon emissions intensity (CEI) changes is of great significance for mitigating climate change issues. The implementation of China's Carbon Emissions Trading Scheme (ETS) in 2013 is a policy intervention aimed at influencing CEI. The impact of intervention events makes forecasting a complex problem, which poses significant challenges to the construction of forecasting models. We first develop a quadratic time-varying nonlinear discrete grey model (QDNDGM(1,1)) to assess the intervention effect of the ETS policy. Then, a novel intervention effect-based quadratic time-varying nonlinear discrete grey model (IE-QDNDGM(1,1)) is developed to conduct the prediction under intervention effect, including an intervention term. The Whale Optimization Algorithm (WOA) is used to calculate a nonlinear parameter. We assess the intervention effect of the ETS policy in China and find that it can indeed reduce CEI. We verify the IE-QDNDGM(1,1) model's superiority by comparing its predictive performance with that of three grey models, one statistical technique, and one artificial intelligence model. The comparative study shows the proposed model's excellent fitting and prediction performance. An ablation experiment is conducted to validate the design of the IE-QDNDGM(1,1) model. Policy implications of the ETS intervention effect are discussed. [ABSTRACT FROM AUTHOR]