Combining Multivariate Singular Spectrum Analysis and Dynamic Mode Decomposition for Daily Sea Surface Temperature Forecasting up to 60 Days Ahead in the Marmara Sea

Accurate long-range forecasting of sea surface temperature (SST) fields remains challenging because regional SST variability reflects the combined influence of recurrent seasonal behavior and shorter-term oceanographic processes. This study develops a forecasting framework combining Multivariate Singular Spectrum Analysis (MSSA) and Dynamic Mode Decomposition (DMD), hereafter referred to as MSSA-DMD, for daily SST forecasting in the Marmara Sea. The framework first represents the SST field in a reduced empirical orthogonal function (EOF) space, separates the temporal dynamics into reconstructed MSSA components, and independently propagates these components using DMD before reconstructing the full SST field. Daily Copernicus Marine Service SST data were evaluated for forecast horizons ranging from 1 to 60 days. The proposed approach was compared with Standard DMD, multivariate empirical mode decomposition (MEMD)–DMD, multivariate variational mode decomposition (MVMD)–DMD, direct inverted Transformer (iTransformer), MSSA-iTransformer, persistence, and climatology. MSSA-DMD provided the most consistent overall forecasting performance, with its advantage becoming particularly evident at extended lead times while maintaining stable spatial and temporal error characteristics. The improvement of MSSA-iTransformer over direct iTransformer further indicates that MSSA decomposition itself contributes substantially to predictive skill. Computational analysis additionally showed that MSSA-DMD achieved a considerably lower end-to-end execution cost than the iTransformer-based configurations. These findings demonstrate that decomposition-assisted reduced-order forecasting, particularly through MSSA-DMD, provides an effective accuracy–cost balance for long-range regional SST prediction.