A new framework for extracting coarse-grained models from time series with multiscale structure

In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales. In this work we consider the inference problem of identifying an appropriate coarse-grained model from a single time series of a multiscale system. It is known that estimators such as the maximum likelihood estimator or the quadratic variation of the path estimator can be strongly biased in this setting. Here we present a novel parametric inference methodology for problems with linear parameter dependency that does not suffer from this drawback. Furthermore, we demonstrate through a wide spectrum of examples that our methodology can be used to derive appropriate coarse-grained models from time series of partial observations of a multiscale system in an effective and systematic fashion

Sensitivity of the polar boundary layer to transient phenomena

Numerical weather prediction and climate models encounter challenges in accurately representing flow regimes in the stably stratified atmospheric boundary layer and the transitions between them, leading to an inadequate depiction of regime occupation statistics. As a consequence, existing models exhibit significant biases in near-surface temperatures at high latitudes. To explore inherent uncertainties in modeling regime transitions, the response of the near-surface temperature inversion to transient small-scale phenomena is analyzed based on a stochastic modeling approach. A sensitivity analysis is conducted by augmenting a conceptual model for near-surface temperature inversions with randomizations that account for different types of model uncertainty. The stochastic conceptual model serves as a tool to systematically investigate which types of unsteady flow features may trigger abrupt transitions in the mean boundary layer state. The findings show that the incorporation of enhanced mixing, a common practice in numerical weather prediction models, blurs the two regime characteristic of the stably stratified atmospheric boundary layer. Simulating intermittent turbulence is shown to provide a potential workaround for this issue. Including key uncertainty in models could lead to a better statistical representation of the regimes in long-term climate simulation. This would help to improve our understanding and the forecasting of climate change in high-latitude regions.</p

Pavliotis, A new framework for extracting coarse-grained models from time series with multiscale structure

Abstract In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a highdimensional dynamical system with multiple time scales. In this work we consider the inference problem of identifying an appropriate coarse-grained model from a single time series of a multiscale system. It is known that estimators such as the maximum likelihood estimator or the quadratic variation of the path estimator can be strongly biased in this setting. Here we present a novel parametric inference methodology for problems with linear parameter dependency that does not suffer from this drawback. Furthermore, we demonstrate through a wide spectrum of examples that our methodology can be used to derive appropriate coarse-grained models from time series of partial observations of a multiscale system in an effective and systematic fashion