Koopman Analysis of Sea Surface Temperature with a Signature Kernel
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918387255345152 |
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| author | Sugiura, Nozomi Osafune, Satoshi Kouketsu, Shinya |
| author_facet | Sugiura, Nozomi Osafune, Satoshi Kouketsu, Shinya |
| contents | We develop a trajectory-based Koopman method for sea surface temperature (SST) that lifts annual SST segments using a signature kernel -- a reproducing kernel Hilbert space (RKHS) kernel that compares paths via iterated-integral features -- and learns the one-year shift operator. By operating on annual trajectory segments rather than instantaneous fields, the method encodes finite-time history, which helps capture memory effects in SST-only evolution. The resulting operator improves out-of-sample multi-year forecast skill relative to a climatology baseline and reveals coherent spectral modes. We implement the approach via kernel extended dynamic mode decomposition (EDMD) on signature-kernel Gram matrices, yielding a single pipeline for forecasting and spectral diagnostics of high-dimensional SST dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19494 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Koopman Analysis of Sea Surface Temperature with a Signature Kernel Sugiura, Nozomi Osafune, Satoshi Kouketsu, Shinya Atmospheric and Oceanic Physics Data Analysis, Statistics and Probability We develop a trajectory-based Koopman method for sea surface temperature (SST) that lifts annual SST segments using a signature kernel -- a reproducing kernel Hilbert space (RKHS) kernel that compares paths via iterated-integral features -- and learns the one-year shift operator. By operating on annual trajectory segments rather than instantaneous fields, the method encodes finite-time history, which helps capture memory effects in SST-only evolution. The resulting operator improves out-of-sample multi-year forecast skill relative to a climatology baseline and reveals coherent spectral modes. We implement the approach via kernel extended dynamic mode decomposition (EDMD) on signature-kernel Gram matrices, yielding a single pipeline for forecasting and spectral diagnostics of high-dimensional SST dynamics. |
| title | Koopman Analysis of Sea Surface Temperature with a Signature Kernel |
| topic | Atmospheric and Oceanic Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2602.19494 |