  Earth system models (ESMs) are fundamental for understanding Earth's complex
climate system. However, the computational demands and storage requirements of
ESM simulations limit their utility. For the newly published CESM2-LENS2 data,
which suffer from this issue, we propose a novel stochastic generator (SG) as a
practical complement to the CESM2, capable of rapidly producing emulations
closely mirroring training simulations. Our SG leverages the spherical harmonic
transformation (SHT) to shift from spatial to spectral domains, enabling
efficient low-rank approximations that significantly reduce computational and
storage costs. By accounting for axial symmetry and retaining distinct ranks
for land and ocean regions, our SG captures intricate non-stationary spatial
dependencies. Additionally, a modified Tukey g-and-h (TGH) transformation
accommodates non-Gaussianity in high-temporal-resolution data. We apply the
proposed SG to generate emulations for surface temperature simulations from the
CESM2-LENS2 data across various scales, marking the first attempt of
reproducing daily data. These emulations are then meticulously validated
against training simulations. This work offers a promising complementary
pathway for efficient climate modeling and analysis while overcoming
computational and storage limitations.
