Data assimilation techniques and modelling uncertainty in geosciences

Abstract

"You cannot step into the same river twice"1. Perhaps this ancient quote is the best phrase to describe the dynamic nature of the earth system. If we regard the earth as a several mixed systems, we want to know the state of the system at any time. The state could be time-evolving, complex (such as atmosphere) or simple and finding the current state requires complete knowledge of all aspects of the system. On one hand, the Measurements (in situ and satellite data) are often with errors and incomplete. On the other hand, the modelling cannot be exact; therefore, the optimal combination of the measurements with the model information is the best choice to estimate the true state of the system. Data assimilation (DA) methods are powerful tools to combine observations and a numerical model. Actually, DA is an interaction between uncertainty analysis, physical modelling and mathematical algorithms. DA improves knowledge of the past, present or future system states. DA provides a forecast the state of complex systems and better scientific understanding of calibration, validation, data errors and their probability distributions. Nowadays, the high performance and capabilities of DA have led to extensive use of it in different sciences such as meteorology, oceanography, hydrology and nuclear cores. In this paper, after a brief overview of the DA history and a comparison with conventional statistical methods, investigated the accuracy and computational efficiency of two main classical algorithms of DA involving stochastic DA (BLUE2 and Kalman filter) and variational DA (3D and4D-Var), then evaluated quantification and modelling of the errors. Finally, some of DA applications in geosciences and the challenges facing the DA are discussed.