Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1403.3874

An approach for analyzing the ensemble mean from a dynamic point of view

Wang Pengfei
View original source ↗Read source document ↗Export metadata ↓

Abstract

Simultaneous ensemble mean equations (LEMEs) for the Lorenz model are obtained, enabling us to analyze the properties of the ensemble mean from a dynamical point of view. The qualitative analysis for the two-sample and n-sample LEMEs show the locations and number of stable points are different from the Lorenz equations (LEs), and the results are validated by numerical experiments. The analysis for the eigenmatrix of the stable points of LEMEs indicates that the stability of these stable points is similar to the LEs'. The eigenmatrix for non-stable points can be obtained too, but the eigenvalues depend not only on the value of the mean variable but also the other n-1 sample equation's variable, and thus for these points there may be different stabilities compared to the LEs'. The divergence of the LEMEs' flow has a negative value, which is the same as the LEs', and thus the trajectory in phase space approaches zero and the trajectory will be attracted to a low-level dimensional curved surface, i.e., the LEMEs have the attractor property, but the structure of the attractor is not the same as the LEs'.

Explore related subjects

physics.ao-phnlin.CD

Keep this discovery

BibTeXRIS

Wang Pengfei. 2014-03-16. An approach for analyzing the ensemble mean from a dynamic point of view. https://arxiv.org/abs/1403.3874

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Windowed Envelope Statistics for Time-Domain Significant Wave Height Estimation From HF Radar

Significant wave height (SWH) retrieval from high-frequency (HF) radar typically relies on a weak second-order Doppler continuum that is sensitive to noise, interference, and spectral leakage. This letter presents a Windowed Envelope Statistics Estimator (WESE) that operates directly on beam-formed time-domain voltages. A second-order term obtained from a Neumann expansion of the rough-surface field equation motivates quadratic compensation of localized radar features. WESE extracts the mean, standard deviation, or variance from overlapping windows of the in-phase, quadrature, or envelope-magnitude sequence, followed by quadratic compensation, rank ordering, least-squares regression, and causal smoothing. Evaluation used 335 synchronized hourly observations from a 13.385 MHz, 12-element WERA system at Argentia, Newfoundland and Labrador. The optimal configuration used quadrature variance, a 16-sample window, 896 retained chronological samples, and 30-h smoothing, achieving an RMSE of 0.152 m and a Pearson correlation of 0.978. This represents RMSE reductions of 32.1% and 18.7% relative to previously reported linear and second-order compensated ordered-statistics models, respectively. The results demonstrate robust time-domain SWH estimation without explicit Doppler-spectrum construction.

physics.ao-ph↗
arXiv2026

KiloDA: Reconstructing kilometer-scale near-surface wind states from sparse station observations

Accurate kilometer-scale near-surface winds are important for understanding atmospheric processes over complex terrain, yet remain difficult to reconstruct from sparse and unevenly distributed observations. Here we introduce KiloDA, a diffusion framework for hourly kilometer-scale wind reconstruction from surface stations. KiloDA learns the statistical distribution and spatial structure of wind fields from historical 3-km Weather Research and Forecasting (WRF) model forecasts. At each reconstruction time, no contemporaneous WRF field is used. Instead, station observations provide the only constraints on the current atmospheric state and guide posterior sampling from the learned prior. In idealized WRF experiments, KiloDA recovers localized wind structures when only 0.24% of grid cells are observed and shows an overall advantage over conventional interpolation across terrain conditions and wind speed regimes. This capability largely transfers to real observations. In a fully withheld region, KiloDA reduces the median wind speed root mean square error (RMSE) by 19% relative to ERA5 reanalysis, using only observations outside the region, with the largest improvements over high-elevation and high-relief terrain. A random station holdout further confirms that this advantage extends across different complex-terrain locations and holdout configurations. These results show that historical model archives can provide useful structural knowledge for reconstructing kilometer-scale wind fields from sparse observations without requiring an accurate model estimate of the current atmospheric state.

physics.ao-ph↗