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The goal of this paper is to obtain probabilistic predictions of a partially observed dynamical system, without knowing the model equations. It is illustrated using the 3-dimensional Lorenz system where only two components are observed. In the era of deep learning and large datasets, the proposed data-driven procedure is low-cost, easy to implement, using linear and Gaussian assumptions, and requires only a small amount of data.

We have evaluated three metaheuristic algorithms PSO, GWO and vPSOGWO using resistivity data. An enormous solution is assessed and the best-fitted solutions are chosen. The posterior PDF with 68.27 % CI, a mean and posterior solution, and correlation and covariance matrix were calculated for the assessment of the uncertainty, stability and mean model and found that vPSOGWO provides reliable and consistently better results which is correlated well with borehole information.

In this paper, we introduced a sample-based algorithm to obtain the CNOPs. Compared with the classical adjoint-based method, this approach is easier to implement and reduces the required storage for the basic state. When we reduce the number of samples to some extent, it reduces the computation markedly more when using the sample-based method, which can guarantee that the CNOP obtained is nearly consistent with some minor fluctuating errors oscillating in spatial distribution.

We've trained a machine learning system, based on data assimilation and data driven forecasting fundamentals, to predict 'shallow water' fluid dynamics, such as atmosphere, using limited amounts of data from regional measurements within a twin experiment. The model performs well and is robust to noise, leveraging intuition of physical dynamics at play in the shallow water system to help the machine learning system contextualize the data.

Non-equilibrium is dominant in geophysical and climate phenomena. Most of the processes that characterize energy flow occur far from equilibrium. These range from very large systems, such as weather patterns or ocean currents that remain far from equilibrium, owing to an influx of energy, to biological structures. During the last decades progress in non—equilibrium physics came from the study of very rare fluctuations and this paper provides an introduction to these theoretical developments.

Past and future climate change at regional scales is a result of both human influences and natural (internal) variability. Here, we provide an overview of recent advances in climate modeling and physical understanding that has led to new insights into their respective roles, illustrated with original results for European climate. Our findings highlight the confounding role of internal variability in attribution, climate model evaluation and accuracy of future projections.

Accurate estimation of error statistics required for data assimilation remains an ongoing challenge, as statistical assumptions are required to solve the estimation problem. This paper provides a conceptual view on the statistical error estimation problem in the light of increasing amount of available datasets. It is found that the total number of required assumptions increases with the number of overlapping datasets, but the relative amount of error statistics which can be estimated increases.

Rainfall is erratic and difficult to predict. Thus random models are often used to describe rainfall events. Since many of these random models are based more on statistics than physical laws, it is desirable to develop connections between the random statistical models and the underlying physics of rain. Here, a physics-based model is shown to converge to a statistics-based model, which helps to provide a physical basis for the statistics-based model.

This work is a theoretical contribution that provides equations for understanding uncertainty prediction applied in air quality where multiple chemical species can interact. A simplified minimal test-bed is introduced that shows the ability our equations to reproduce the statistics estimated from an ensemble of forecast. While the latter estimation is the state of the art, solving equations is numerically less costly, depending on the number of chemical species, and motivates this research.

The feasibility of physics-based forecasting of earthquakes depends on how well models can be calibrated to represent earthquake scenarios given uncertainties in both models and data. Our study investigates whether data assimilation can estimate current and future fault states in the presence of a bias in the friction parameter.