An Interpretable Low-Rank State-Space Model for Multi-Horizon Simulation of Large-Scale Regional Temperature Fields

Varun Kotharkar; Michael L. Stein

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arXiv · 2607.27160

An Interpretable Low-Rank State-Space Model for Multi-Horizon Simulation of Large-Scale Regional Temperature Fields

Varun Kotharkar·Michael L. Stein

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Abstract

We propose an interpretable low-rank state-space model for conditional simulation of daily regional temperature fields. The central statistical question is whether empirical orthogonal functions (EOFs) can be treated as stable large-scale features of the field rather than only as sample-dependent basis vectors for dimension reduction. The framework represents the dominant temperature field through a small number of retained EOF coefficients, models their seasonal mean and variance structure, propagates the resulting low-dimensional state with stable multivariate dynamics, and uses structured innovations to represent the remaining uncertainty. The resulting reduced-rank model is interpretable, computationally efficient, and suitable for iterative ensemble generation. It is designed to support both inference on the structure of the retained temperature state and prediction through multi-horizon probabilistic field simulation.

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BibTeX RIS

Varun Kotharkar, Michael L. Stein. 2026-07-29. An Interpretable Low-Rank State-Space Model for Multi-Horizon Simulation of Large-Scale Regional Temperature Fields. https://arxiv.org/abs/2607.27160

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