Numerical weather prediction involves numerically solving the mathematical equations, which describe the geophysical flow, by transforming them so that they can be computed. Through this transformation, it appears that the equations actually solved by the machine are then a modified version of the original equations, introducing an error that contributes to the model error. This work helps to characterize the covariance of the model error that is due to this modification of the equations.

To infer information of an unknown quantity that helps to understand an associated system better and to predict future outcomes, observations and a physical model that connects the data points to the unknown parameter are typically used as information sources. Yet this problem is often very challenging due to the fact that the unknown is generally high dimensional, the data are sparse and the model can be non-linear. We propose a novel approach to address these challenges.

Fluid parcels transported in complicated flows often contain subsets of particles that stay close over finite time intervals. We propose a new method for detecting finite-time coherent sets based on the density-based clustering technique of ordering points to identify the clustering structure (OPTICS). Unlike previous methods, our method has an intrinsic notion of coherent sets at different spatial scales. OPTICS is readily implemented in the SciPy sklearn package, making it easy to use.

An unprecedented amount of rainfall data is available nowadays, such as ensemble model output, weather radar estimates, and in situ observations from networks of both traditional and opportunistic sensors. Nevertheless, the exact amount of precipitation, to some extent, eludes our knowledge. The objective of our study is precipitation reconstruction through the combination of numerical model outputs with observations from multiple data sources.

The ensemble-based variational method is a method for solving nonlinear data assimilation problems by using an ensemble of multiple simulation results. Although this method is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, can also be solved by applying this method iteratively. This paper reformulated this iterative algorithm to analyze its behavior in high-dimensional nonlinear problems and discuss the convergence.

The assimilation of observations using standard algorithms can lead to a violation of physical laws (e.g. mass conservation), which is shown to have a detrimental impact on the system's forecast. We use a neural network (NN) to correct this mass violation, using training data generated from expensive algorithms that can constrain such physical properties. We found that, in an idealized set-up, the NN can match the performance of these expensive algorithms at negligible computational costs.

Recently, various models have been developed, including the fractional Brownian motion (fBm), to analyse the stochastic properties of geodetic time series, together with the estimated geophysical signals. The noise spectrum of these time series is generally modelled as a mixed spectrum, with a sum of white and coloured noise. Here, we are interested in modelling the residual time series after deterministically subtracting geophysical signals from the observations with the Lévy processes.

This paper proposes two improvements to the use of Trajectory-Adaptive Multilevel Sampling, a rare-event algorithm which computes noise-induced transition probabilities. The first improvement uses locally linearised dynamics in order to reduce the arbitrariness associated with defining what constitutes a transition. The second improvement uses empirical transition paths accumulated at high noise in order to formulate the score function which determines the performance of the algorithm.

This paper introduces a tool for data-driven discovery of early warning signs of critical transitions in ice shelves from remote sensing data. Our directed spectral clustering method considers an asymmetric affinity matrix along with the associated directed graph Laplacian. We applied our approach to reprocessing the ice velocity data and remote sensing satellite images of the Larsen C ice shelf.