Cost effect or innovation effect? how climate physical risk works on the pressure of agricultural carbon footprint?

Climate physical risk exerts complex nonlinear effects on agricultural carbon footprint pressure (ACFP), yet the underlying cost and innovation mechanisms remain insufficiently examined. Using balanced panel data from 30 Chinese provinces over the period 2000–2023, this study empirically investigates the nonlinear impact of the Climate Physical Risk Index (CPRI) on ACFP. The findings reveal a statistically significant inverted U-shaped relationship, with a turning point at CPRI = 50.15307. Below this threshold, climate physical risk intensifies ACFP, reflecting a cost effect; above it, risk mitigates ACFP, indicating an innovation effect. Mechanism analysis shows that on the left side of the inflection point, green finance moderates the cost-induced increase in ACFP, whereas on the right side, digital inclusive finance reduces ACFP through a chain mediation pathway involving agricultural digital innovation. Moreover, the inverted U-shaped relationship is more pronounced in provinces northwest of the Hu Line and under high climate policy uncertainty. The study concludes by proposing targeted policy measures, including the deployment of differentiated financial instruments and the incorporation of ACFP into local performance evaluation systems, to promote a coordinated governance framework for pollution reduction, carbon mitigation, and climate adaptation in agriculture.