Accurate forecasting of Earth's dynamic systems is vital in geophysics, where neural operators offer a powerful data-driven paradigm. Standard operators often treat the Earth as a flat Euclidean plane, introducing geometric artifacts. In contrast, Spherical Neural Operators (SNOs) resolve this mismatch by operating within the spherical spectral space, naturally adapting to spherical geometries. However, for computational efficiency, existing SNOs typically rely on the rotation equivariance assumption. This assumption simplifies the transitions of physical states into isolated spectral modal evolutions, thereby over-idealizing the Earth as a homogeneous system. To solve this problem, we no longer rely on the rotation equivariance assumption that isolates spectral modal evolution, but directly derive an explicit modal interaction kernel and propose Diagonal Spherical Neural Operators named DIAGNO. DIAGNO explicitly parameterizes cross-modal interactions through spectral modal decomposition, thereby preserving the inherent heterogeneity of Earth dynamics. Furthermore, leveraging the unique diagonal structure of the spherical spectrum, we design inter- and intra-diagonal interaction mechanisms to natively capture essential zonal and meridional dynamics, respecting intrinsic geophysical regularities. Extensive experiments across simulated fluid dynamics and real-world Earth system reanalysis (including atmosphere and ocean) datasets demonstrate DIAGNO's superior capability, consistently achieving state-of-the-art performance in multi-step forecasting. Beyond this, we validate DIAGNO's practical analytical value in professional geophysical domains by assessing its fidelity in capturing climatological anomalies and maintaining physical consistency.

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