Preprint

This preprint builds reduced-order stochastic models for time series whose statistics vary periodically, as in the annual climate cycle. It uses score-based generative methods to reproduce probability distributions while also representing temporal dependence. A demonstration with the Planet Simulator climate model uses the 20 leading principal components of surface temperature. Validation examines marginal and joint distributions, autocorrelations, and spatial coherence, with synthetic centuries generated far faster than full simulations. Readers get a framework for emulating periodically forced systems and examples of the checks needed to judge statistical and temporal fidelity.

This preprint develops a response-theory approach to tuning model parameters so that simulated statistics agree with observations. The generalized fluctuation-dissipation theorem relates small changes in parameters to changes in statistics of chosen observables. Score estimates support the calculation of these sensitivities, which can then be used in Newton-type or regularized least-squares updates. The April 2026 revision tests sensitivities of drift and diffusion parameters on analytically tractable processes and stochastic Lorenz–96 models. Readers get a principled way to construct statistical parameter sensitivities without adjoint models or separate perturbation ensembles, together with the limits imposed by linear response.

This preprint explores how observations of the ocean surface can constrain currents and buoyancy deep below it. A score-based diffusion model generates three-dimensional interior states conditioned on surface information. The method is evaluated in an idealized double-gyre simulation with 15 vertical levels, testing both mean circulation and mesoscale variability. Its reconstructions include uncertainty estimates, with skill decreasing as observations become coarser or the target depth increases. Readers get a probabilistic approach to an underdetermined ocean-observation problem and a controlled demonstration of its potential before application to real-world observations.

This preprint develops a stochastic emulator for the evolving distribution of local daily maximum temperatures in climate models. Empirical orthogonal functions provide fixed spatial patterns, while their coefficients separate seasonal changes from day-to-day fluctuations. The seasonal component depends on global mean temperature, and Gaussian stochastic processes represent correlated daily variability. Tests using CMIP6 simulations assess local distributions, changing extremes, and uncertainty arising from internal variability in unseen scenarios. Readers get an interpretable workflow for generating inexpensive spatial temperature ensembles and evaluating the statistical assumptions behind their extreme-temperature estimates.