A stochastic method, the ensemble Kalman smoother (EnKS), is proposed as a linear solver in four-dimensional variational data assimilation (4DVAR). The method approaches 4DVAR for large ensembles. Regularization provides global convergence, and it is implemented as an additional artificial observation. Since the EnKS is uncoupled from the insides of the 4DVAR, any version of EnKS can be used.

The focus of this paper is to improve our studies related to the novel use of the Thorpe method applied to atmospheric boundary layer (ABL) using new data from Spanish field experiments. We analyse the time behaviour of the maximum Thorpe displacement (d_T)_max and the Thorpe-scale L_T during a day cycle. We also analyse the relation between (d_T)_max and L_T. We deduce that they confirm a power law statistically significant, with differences between convective conditions and shear-driven conditions.

Helical structures are commonplace in geophysical flows, but their effect on turbulence is still enigmatic. A novel PIV laser technique has been used to analyze helical structures in a turbulent swirling jet where the underlying shear flow is subjected to external acoustic forcing. Although the acoustic excitation had an effect on the flow field, no evidence for the existence of large-scale helical structures with maximal helicity was found.

Percolation theory can be used to find flow paths of least resistance. Applying percolation theory to drainage networks apparently allows identification of the range of exponent values describing the tortuosity of rivers in real networks, thus generating observed scaling between drainage basin area and channel length, a relationship known as Hack's law. Such a theoretical basis for Hack's law may allow interpretation of the range of exponent values based on assessment of substrate heterogeneity.

To numerically simulate the atmosphere and ocean, the large eddies are resolved on a grid, and the effect the small unresolved eddies have on the large ones is modelled. Improper modelling leads to resolution-dependent results. We solve this long-standing problem by calculating the model coefficients from high-resolution simulations, and characterise the coefficients with a set of scaling laws. Low-resolution simulations adopting these laws reproduce the statistics of the high-resolution cases.

Induced seismicity is a concern for the industries relying on fluid injection in the deep parts of the Earth’s crust. At the same time, fluid injection sites provide natural laboratories to study the impact of increased fluid pressure on earthquake generation. In this study, I show that simple geometric operations on a static stress field produced by volume change at depth explains two empirical laws of induced seismicity without having recourse to complex models derived from rock mechanics.