[M-GI26] Data assimilation: A fundamental approach in geosciences

[MGI26-P04] Functional data assimilation to make use of high resolution data

*Shin ya Nakano^1,2 (1.The Institute of Statistical Mathematics, 2.Graduate Institute for Advanced Studies, SOKENDAI)

Keywords:data assimilation, ensemble Kalman filter, functional data analysis

Assuming that the variance of the observation noise for each measurement is fixed, the likelihood function becomes sharper as the number of observations increases. This means that the estimates with huge data tends to mostly rely on the observations and ignore the dynamical model. High spatial resolution data are also regarded as a huge data set. The estimates with high resolution data would thus be totally based on the observations. When the spatial resolution of the observations is higher than that of the model ability, the estimates with data assimilation may be overfitted to the observed data and the prediction based on the assimilation result can become poor. Considering the fact that model errors do not depends on the spatial resolution of the observation, it would be appropriate to construct the observation model so that the sharpness of the likelihood is independent from the spatial resolution of the observation. We devise an approach in which the observation is treated as a spatial function. Data assimilation is then achieved by using the inner product on the functional space. This formulation is free from the spatial resolution of the observation. The results with the proposed approach will be demonstrated.