The popular data assimilation technique known as the ensemble Kalman filter (EnKF) suffers from sampling errors due to the limited size of the ensemble. This deficiency is usually cured by inflating the sampled error covariances and by using localization. This paper further develops and discusses the finite-size EnKF, or EnKF-N, a variant of the EnKF that does not require inflation. It expands the use of the EnKF-N to a wider range of dynamical regimes.

In this paper a new interpretation of the local finite-time Lyapunov exponent is proposed. This concept can practically assist in field experiments where samples are collected at a fixed location and it is necessary to attribute long-distance transport phenomena and location of source points to the characteristic variation of the sampled particles. Also, results of this study have the potential to aid in planning of optimal local sampling of passive particles.

The disappearance of Malaysia Airlines flight MH370 on 8 March 2014 is one of the great mysteries of our time. The most relevant aspect is that not a piece of debris was found during the intensive surface search carried out for roughly 2 months following the crash. By combining different ocean data with dynamical systems tools, we propose a revised search strategy by showing why debris could not have been expected in some targeted search areas and determining regions where debris could be.

In the present study, we investigate the scaling properties of the topography of Mars. Planetary topographic fields are well known to exhibit (mono)fractal behavior. Indeed, fractal formalism is efficient in reproducing the variability observed in topography. Our results suggest a multifractal behavior from the planetary scale down to 10 km. From 10 km to 300 m, the topography seems to be simple monofractal.

This paper shows how statistical methods can be applied to the ensemble Kalman filtering technique, a widely used method in atmospheric science and other related fields. Traditional methods for covariance localization, commonly done in the field with multiple variables, are compared to the newly proposed method with the use of a parametric localization function (proposed in statistics as a class of multivariate covariance functions) in the ensemble Kalman filter system with multiple variables.

While the negative nonlinear feedback associated with two new modes in the 5DLM can stabilize solutions, additional resolved heating processes by a third mode in the 6DLM can destabilize solutions. The findings support the view of Lorenz (1972) on the role of small-scale processes: if the flap of a butterfly’s wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado.