Parameter estimation (PE) with a global coupled data assimilation (CDA) system can improve the runs, but the improvement remains in a limited range. We have to come back to simple models to sort out the sources of noises. Incomplete observations and the chaotic nature of the atmosphere have much stronger influences on the PE through the state estimation (SE) process. Here, we propose the guidelines of how to enhance the signal-to-noise ratio under partial SE status.

NDVI and EVI vegetation indexes, estimated from satellite images, can been used to estimate root zone soil moisture. However, depending on the spatial and radiometric resolution of the sensors used, estimations could change. In this work, images taken by satellites IKONOS-2 and LANDSAT-7 of the same location are compared on the four bands involved in these vegetation indexes. The results show that spatial resolution has a similar scaling effect in the four bands, but not radiometric resolution.

Parametric excitation of edge waves with a frequency 2 times less than the frequency of surface waves propagating perpendicular to the inclined bottom are investigated in laboratory experiments. The domain of instability on the plane of surface wave parameters (amplitude–frequency) is found. The subcritical instability is observed in the system of parametrically excited edge waves. It is shown that breaking of surface waves initiates turbulent effects and can suppress the parametric generation.

This paper aims to show how the tropical circulation responds to changes of the vertical stratification of the imposed temperature that drives the model. These changes mimic the presence of water vapor cycles. Thus, for simplicity's sake we impose a periodic change of this stratification with variable periods of 10–90 days. The model responds with quasi-periodic oscillations having two or more dominant frequencies. After a long forcing time period, chaotic behavior starts to appear cyclically.

The sandpile-based model is the paradigm model of self-organized criticality (SOC), a mechanism believed to be responsible for the occurrence of scale-free (power-law) distributions in nature. One particular SOC system that is rife with power-law distributions is that of earthquakes, the most widely known of which is the Gutenberg–Richter (GR) law of earthquake energies. Here, we modify the sandpile to be of use in capturing the energy, space, and time statistics of earthquakes simultaneously.

Fluid parcels exchange water properties when coming into contact with each other, leading to mixing. The trajectory encounter volume, defined here as the volume of fluid that passes close to a reference trajectory over a finite time interval, is introduced as a measure of the mixing potential of a flow. Regions with a low encounter volume (the cores of coherent eddies) have a low mixing potential. Regions with a large encounter volume (turbulent or chaotic regions) have a high mixing potential.

Various methods in the single-spacecraft data analysis are reviewed to determine physical properties of waves, turbulent fluctuations, and wave-wave and wave-particle interactions in the space plasma environment using the magnetic field, the electric field, and the plasma data.

The influence of fluid injection on tectonic fault sliding and generation of seismic events was studied in the paper by a multi-degree-of-freedom rate-and-state friction model with a two-parametric friction law. The considered system could exhibit different types of motion. The main seismic activity could appear directly after the start of fluid injection or in the post-injection phase (after some days or months). Such an influence of injection on seismicity is observed in the real cases.

This paper evaluates the connection between winter precipitation over the Iberian Peninsula and the large-scale tropospheric mixing over the eastern Atlantic Ocean. Finite-time Lyapunov exponents (FTLEs) have been calculated from 1979 to 2008 to evaluate this mixing. Our study suggests that significant negative correlations exist between summer FTLE anomalies and winter precipitation over Portugal and Spain.

In our simulations of sea swell, we show that its evolution exhibits remarkable features of universality. At long stretches the swell ``forgets'' initial conditions and keeps its specific distribution of wave energy in scales and directions. Slow evolution of swell in time and space can be related to fundamental relationships of the so-called theory of weak turbulence that gives a solid basis for the swell prediction.

The nonlinear Schrödinger equation describing weakly rotational wave packets in a fluid in the Lagrangian coordinates is derived. Rogue effects are possible in low-vorticity waves, and the effect of vorticity is manifested in a shift of the wave number in the carrier wave. Special attention is paid to Gouyon and Gerstner waves. It is shown that this equation in the Eulerian variables can be obtained from the Lagrangian solution with an ordinary change in the horizontal coordinates.

Our work shows that a simple kinematic model is able to retain the fundamental mechanisms responsible for complex fluid parcel evolution in the stratosphere. Our analysis justifies in a controlled manner the formation of filaments eroding the polar vortex and shows that the breaking and splitting of the polar vortex is explained by the sudden growth of a planetary wave and the decay of the axisymmetric flow.

This is the first mathematical definitions of the spatial scale and its transformation based on Lebesgue measure. An Ito process-formed geophysical variable with respect to scale was also provided. The stochastic calculus for data assimilation discovered the new expressions of error caused by spatial scale transformation. The results improve the ability to understand the spatial scale transformation and related uncertainties in Earth observation, modelling and data assimilation.

We study the problem of sinking particles in a realistic oceanic flow, with major energetic structures in the mesoscale, focussing on marine biogenic particles. By using a simplified equation of motion for small particles in a mesoscale velocity field, we estimate the influence of physical processes such as the Coriolis force and the particle's inertia, and we conclude that they represent negligible corrections to passive transport by the flow, with added vertical velocity due to gravity.