Advanced data assimilation methods are complex and computationally expensive. We compare two simpler methods, diffusive back-and-forth nudging and concave–convex nonlinearity, which account for change over time with the potential of providing accurate results with a reduced computational cost. We evaluate the accuracy of the two methods by implementing them within simple chaotic models. We conclude that the length and frequency of observations impact which method is better suited for a problem.

With seismic data, we observed high-frequency internal waves (HIWs) with amplitudes of around 10 m. A shoaling thermocline and gentle slope suggest that HIWs result from fission. Remote sensing data support this. Strong shear caused Ri  below 0.25 over 20–30 km, indicating instability. HIWs enhance mixing, averaging 10^-4 m²s^-1, revealing a new energy cascade from shoaling waves to turbulence, and enhancing our understanding of energy dissipation and mixing in the northern South China Sea.

The shapes of clouds viewed from space reflect vertical and horizontal motions in the atmosphere. We theorize that, globally, cloud perimeter complexity is related to the dimension of turbulence also governed by horizontal and vertical motions. We find agreement between theory and observations from various satellites and a numerical model and, remarkably, that the theory applies globally using only basic planetary physical parameters from the smallest scales of turbulence to the planetary scale.

This study presents a new approach to simulating large ocean density waves that travel long distances without breaking down. This new approach ensures that these waves are depicted more accurately and realistically in our models. This is particularly useful for understanding wave behavior in lakes with distinct water layers, which can help predict natural phenomena and their effects on environments like swash zones, where waves meet the shore.

We investigated how machine learning can forecast extreme vegetation responses to weather. Examining four models, no single one stood out as the best, though "echo state networks" showed minor advantages. Our results indicate that while these tools are able to generally model vegetation states, they face challenges under extreme conditions. This underlines the potential of artificial intelligence in ecosystem modeling, also pinpointing areas that need further research.