The Analog Data Assimilation

Abstract

International audienceIn light of growing interest in data-driven methods for oceanic, atmospheric and climate sciences, this work focuses on the field of data assimilation and presents the Analog Data Assimilation (AnDA). The proposed framework produces a reconstruction of the system dynamics in a fully data-driven manner where no explicit knowledge of the dynamical model is required. Instead, a representative catalog of trajectories of the system is assumed to be available. Based on this catalog, the analog data assimilation combines the non-parametric sampling of the dynamics using analog forecasting methods with ensemble-based assimilation techniques. This study explores different analog forecasting strategies and derives both ensemble Kalman and particle filtering versions of the proposed analog data assimilation approach. Numerical experiments are examined for two chaotic dynamical systems, namely Lorenz-63 and Lorenz-96 systems. The performance of the analog data assimilation is discussed with respect to classical model-driven assimilation. A Matlab toolbox and Python library of the AnDA are provided to help further research building upon the present findings

Spatio-temporal interpolation of altimeter-derived SSH fields using analog data assimilation: A case-study in the south china sea

“…where Z(P i , t) refers to the P × P patch centered in i for field Z at time t. Following AnDA scheme [8], A is an analog dynamical model [9]. It retrieves exemplars in a reference catalog similar to the current state at time t − 1 to sample forecasts at time t. Y is the observation field, i.e.…”

“…The AnEnKS represents a version of the classical Ensemble Kalman Filter and Smoother (EnKF/EnKS) adapted to analog based data assimilation. The reader is invited to see [8] for more details. As stated early in the paragraph, we consider overlapping regions patches, however, to reduce the computational complexity we do not consider all possible positions, a stride of str = 15 is used to move from one patch to the other either horizontally or vertically.…”

“…We use optimal interpolation code from [12], and the Analog Data Assimilation toolbox [8] (Python Library can be found at https: //github.com/ptandeo/AnDA and the Matlab toolbox can be obtained by sending an email to the corresponding author).…”

“…Here, we investigate such a data-driven approach, namely analog data assimilation (AnDA) framework introduced recently [8]. AnDA combines analog forecasting methods [9] and stochastic data assimilation algorithms.…”

“…AnDA combines analog forecasting methods [9] and stochastic data assimilation algorithms. In [8], we considered an application to Lorenz 63 and Lorenz 96 models, which involve rather low-dimensional state space (<100). By contrast, we consider here a more challenging problem as gridded SSH field involves significantly higher-dimensional state space, typically above 10 5 .…”