Multi-resolution data assimilation for missing data interpolation in geophysical sequences
Résumé
Nowadays, with recent technical advances, earth's surface is monitored with a dense network of satellites. Before these satellites launching, studies about the ocean requires costly in situ observations. Thus, global ocean study was hardly possible. Nowadays, satellites record global images at differ- ent resolution of multiple ocean parameters such sea surface temperature (SST), sea surface salinity (SSS), sea surface chlorophyll (CHL) concentration, ocean altimetry. Geophys- ical satellite observations exploit different modalities (e.g., infrared (IR) sensors or micro-wave radiometry (MW) as- sociated with different resolutions as illustrated in Fig.1. In the case of SST parameter, microwave (MW) radiometry provides low resolution (25km) [1] while infrared (IR) ra- diometry delivers high resolution SST measurements (5km) [2]. In all cases, data acquisition by satellites are sensitive to the atmospheric conditions such as cloud coverage or heavy rains. Consequently observation series typically involve large percentage of missing data, high-resolution observations be- ing more affected. Besides missing data issues related to atmospheric conditions, low temporal or spatial resolution can also be assimilated to missing data problem. Thus, miss- ing data estimation in geophysical observation sequence is a critical issue [3, 4, 5]. Operational products mainly rely on statistical optimal interpolation techniques, Kalman filter- ing or smoothing techniques, or ensemble of Kalman filters [6, 4, 5, 7]. Their main drawbacks are that they require processing over very large covariance matrices, and assume statistical hypotheses such as stationarity, Gaussiannity and linearity of the dynamical model that can hardly be veri- fied in real observations. Qualitatively, the state-of-the-art missing data interpolation methods result in oversmoothed reconstruction and cannot recover fine-scale structures. As il- lustrated by SST and SSS observations in Fig.1, gains can be expected from the fusion of multi-modal and multi-resolution observations. Thus, to address the missing data interpola- tion issue, we propose a variational data assimilation model that, from multi-resolution geophysical observations, jointly estimate the missing data and an associated transport field re- lated to the parameter temporal evolution. The performance of the proposed method are evaluated on real SST and SSS observations.