[M-GI29] Data assimilation: A fundamental approach in geosciences

[MGI29-05] Non-Gaussian measure in Gaussian filtering problems

*Tianfeng Hou^1,2,3, Hideyuki Sakamoto¹, Toshiki Teramura⁴, Takemasa Miyoshi^1,2,3 (1.Data Assimilation Research Team, RIKEN Center for Computational Science, Kobe, Japan, 2.RIKEN Prediction Science Laboratory, Kobe, Japan, 3.RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program, Kobe, Japan, 4.Research Institute for Computational Science Co. Ltd, Tokyo, Japan)

Keywords:Data assimilation, non-Gaussian measure, Ensemble Kalman Filter, Lorenz 63 model, mean-error, replica-mean

Data assimilation has been widely used in a multitude of disciplines, since it has the potential to provide a better prediction of chaotic systems by combining numerical simulation and observations. A wide variety of data assimilation approaches have been developed in many fields over the last few decades. Among these, the Ensemble Kalman Filter is found effective with high dimensional systems, because it can avoid at least partially the curse of dimensionality. However, in cases when a critical event happens such as the sudden downpour in the field of numerical weather prediction, the state probability density function may become highly non-Gaussian, and as a result, it can lead to an inaccurate estimation of the system. Therefore, the evaluation of the Gaussian assumption is very important in an Ensemble Kalman Filter. In this research, the Lorenz 63 model is used as a representative chaotic dynamic system, and the bias of the Ensemble Kalman Filter estimation is treated as a non-Gaussian measure. More specifically, a new replica-mean technique is introduced and both the mean-error (ME) and the mean of the root-mean-squared-error (RMSE) for each replica are calculated as the bias indicators. The results show that the RMSE-ME plot can reflect the qualitative change from the linear domain to the nonlinear domain and the attractor maximum of ME can represent this transition better than the RMSE. Therefore, we conclude that the temporal inhomogeneity of unpredictability occurs even on a minimal setting of data assimilation using the Lorenz three-variable model. In addition, it is also illustrated that when the non-Gaussianity is due to the finite covariance, there is a region where the maximum of ME should be scaled as ME ∝ R^(γ/γ_0 ). Where, R and γ represent the observation interval and the observation error, respectively. Therefore, we conclude that both observation interval and observation error will affect the non-Gaussian measure in an EnKF, and we call this scaling “weak non-Gaussian scaling”.