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Abstract Causal inference in complex systems has been largely promoted by the proposal of some advanced temporal causation models. However, temporal models have serious limitations when time series data are not available or present insignificant variations, which causes a common challenge for earth system science. Meanwhile, there are few spatial causation models for fully exploring the rich spatial cross-sectional data in Earth systems. The generalized embedding theorem proves that observations can be combined together to construct the state space of the dynamic system, and if two variables are from the same dynamic system, they are causally linked. Inspired by this, here we show a Geographical Convergent Cross Mapping (GCCM) model for spatial causal inference with spatial cross-sectional data-based cross-mapping prediction in reconstructed state space. Three typical cases, where clearly existing causations cannot be measured through temporal models, demonstrate that GCCM could detect weak-moderate causations when the correlation is not significant. When the coupling between two variables is significant and strong, GCCM is advantageous in identifying the primary causation direction and better revealing the bidirectional asymmetric causation, overcoming the mirroring effect.