arXiv subjects

Michael Tsyrulnikov

Publications and source records attributed to Michael Tsyrulnikov.

5 recordsLinked to original sources

arXiv2024

Regularization of the ensemble Kalman filter using a non-parametric, non-stationary spatial model

The sample covariance matrix of a random vector is a good estimate of the true covariance matrix if the sample size is much larger than the length of the vector. In high-dimensional problems, this condition is never met. As a result, in high dimensions the Ensemble Kalman Filter's (EnKF) ensemble does not contain enough information to specify the prior covariance matrix accurately. This necessitates the need for regularization of the analysis (observation update) problem. We propose a regularization technique based on a new spatial model. The model is a constrained version of the general Gaussian process convolution model. The constraints include local stationarity and smoothness of local spectra. We regularize EnKF by postulating that its prior covariances obey the spatial model. Placing a hyperprior distribution on the model parameters and using the likelihood of the prior ensemble data allows for an optimized use of both the ensemble and the hyperprior. The respective estimator is shown to be consistent. Its neural Bayes implementation proved to be both accurate and computationally efficient. In simulation experiments, the new technique led to substantially better EnKF performance than several existing techniques.

physics.data-an↗

arXiv2023

Additive Model Perturbations Scaled by Physical Tendencies for Use in Ensemble Prediction

Imperfections and uncertainties in forecast models are often represented in ensemble prediction systems by stochastic perturbations of model equations. In this article, we present a new technique to generate model perturbations. The technique is termed Additive Model-uncertainty perturbations scaled by Physical Tendencies (AMPT). The generated perturbations are independent between different model variables and scaled by the local-area-averaged modulus of physical tendency. The previously developed Stochastic Pattern Generator is used to generate space and time-correlated pseudo-random fields. AMPT attempts to address some weak points of the popular model perturbation scheme known as Stochastically Perturbed Parametrization Tendencies (SPPT). Specifically, AMPT can produce non-zero perturbations even at grid points where the physical tendency is zero and avoids perfect correlations in the perturbation fields in the vertical and between different variables. Due to a non-local link from physical tendency to the local perturbation magnitude, AMPT can generate significantly greater perturbations than SPPT without causing instabilities. Relationships between biases and spreads caused by AMPT and SPPT were studied in an ensemble of forecasts. The non-hydrostatic, convection-permitting forecast model COSMO was used. In ensemble prediction experiments, AMPT perturbations led to statistically significant improvements (compared to SPPT) in probabilistic performance scores such as spread-skill relationship, CRPS, Brier Score, and ROC area for near-surface temperature. AMPT had similar but weaker effects on near-surface wind speed and mixed effects on precipitation.

physics.ao-ph↗

arXiv2020

Impact of non-stationarity on hybrid ensemble filters: A study with a doubly stochastic advection-diffusion-decay model

Effects of non-stationarity on the performance of hybrid ensemble filters are studied (by hybrid filters we mean those which blend ensemble covariances with some other regularizing covariances). To isolate effects of non-stationarity from effects due to nonlinearity (and the non-Gaussianity it causes), a new doubly stochastic advection-diffusion-decay model (DSADM) is proposed. The model is hierarchical: it is a linear stochastic partial differential equation whose coefficients are random fields defined through their own stochastic partial differential equations. DSADM generates conditionally Gaussian spatiotemporal random fields with a tunable degree of non-stationarity in space and time. DSADM allows the use of the exact Kalman filter as a baseline benchmark. In numerical experiments with DSADM as the "model of truth", the relative importance of the three kinds of covariance blending is studied: with static, time-smoothed, and space-smoothed covariances. It is shown that the stronger the non-stationarity, the less useful the static covariance matrix becomes and the more beneficial the time-smoothed covariances are. Time-smoothing of background-error covariances proved to be systematically more useful than their space-smoothing. Under non-stationarity, a filter that extends the (previously proposed by the authors) Hierarchical Bayes Ensemble Filter and accommodates the three covariance-blending techniques is shown to outperform all other configurations of the filters tested. The R code of the model and the filters is available from github.com/cyrulnic/NoStRa.

physics.data-an↗

arXiv2017

A spatio-temporal stochastic pattern generator for simulation of uncertainties in geophysical ensemble prediction and ensemble data assimilation

A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a pseudo-differential spatial operator defined on a limited area 2D or 3D domain in the Cartesian coordinate system. The generated pseudo-random fields are homogeneous and isotropic in spacetime (with the scaled vertical and temporal coordinates). The correlation functions in any spatio-temporal direction belong to the Matérn class. The spatio-temporal correlations are non-separable. A spectral-space numerical solver is implemented and accelerated exploiting properties of real-world geophysical fields, in particular, smoothness of their spatial spectra. The generator is designed to create additive or multiplicative, or other spatio-temporal perturbations that represent uncertainties in numerical prediction models in geophysics. The program code of the generator is publicly available.

physics.data-an↗

arXiv2016

A Hierarchical Bayes Ensemble Kalman Filter

A new ensemble filter that allows for the uncertainty in the prior distribution is proposed and tested. The filter relies on the conditional Gaussian distribution of the state given the model-error and predictability-error covariance matrices. The latter are treated as random matrices and updated in a hierarchical Bayes scheme along with the state. The (hyper)prior distribution of the covariance matrices is assumed to be inverse Wishart. The new Hierarchical Bayes Ensemble Filter (HBEF) assimilates ensemble members as generalized observations and allows ordinary observations to influence the covariances. The actual probability distribution of the ensemble members is allowed to be different from the true one. An approximation that leads to a practicable analysis algorithm is proposed. The new filter is studied in numerical experiments with a doubly stochastic one-variable model of "truth". The model permits the assessment of the variance of the truth and the true filtering error variance at each time instance. The HBEF is shown to outperform the EnKF and the HEnKF by Myrseth and Omre (2010) in a wide range of filtering regimes in terms of performance of its primary and secondary filter.

physics.data-an↗