We introduce a sample-based algorithm to obtain the conditional nonlinear optimal perturbations. Compared with the classical adjoint-based method, it is easier to implement and reduces the required storage for the basic state. When we reduce the number of samples to some extent, it reduces the computation markedly more when using the sample-based method, which can guarantee that the CNOP obtained is nearly consistent with some minor fluctuating errors oscillating in spatial distribution.

Electron holes have been reported in space plasmas along with suprathermal plasmas far from Maxwellian equilibrium. In particular, electron distributions with elongated suprathermal distributions (kappa distributions) are of current interest for space plasmas. This work considers regularized kappa distributions, which are well beyond the Maxwellian equilibrium and show a harder suprathermal electron population.

In the ensemble Kalman filter, the ensemble space may not fully capture the forecast errors due to the limited ensemble size and systematic model errors, which affect the accuracy of analysis and prediction. This study proposes a new algorithm to use cost-free pseudomembers to expand the ensemble space effectively and improve analysis accuracy during the analysis step, without increasing the ensemble size during forecasting.

We present a novel, efficient method for identifying climate tipping point threshold values of CO₂ beyond which rapid and irreversible changes occur. We use a simple model of Arctic sea ice to demonstrate the method’s efficacy and its potential for use in state-of-the-art global climate models that are too expensive to run for this purpose using current methods. The ability to detect tipping points will improve our preparedness for rapid changes that may occur under future climate change.

How big is a cloud? and How long does the weather last? require scaling to answer. We review the advances in scaling that have occurred over the last 4 decades: (a) intermittency (multifractality) and (b) stratified and rotating scaling notions (generalized scale invariance). Although scaling theory and the data are now voluminous, atmospheric phenomena are too often viewed through an outdated scalebound lens, and turbulence remains confined to isotropic theories of little relevance.

Accurate estimation of the error statistics required for data assimilation remains an ongoing challenge, as statistical assumptions are required to solve the estimation problem. This work provides a conceptual view of the statistical error estimation problem in light of the increasing number of available datasets. We found that the total number of required assumptions increases with the number of overlapping datasets, but the relative number of error statistics that can be estimated increases.