A Multiscale Variational Data Assimilation Scheme: Formulation and Illustration

Abstract

A multiscale data assimilation (MS-DA) scheme is formulated for fine-resolution models. A decomposition of the cost function is derived for a set of distinct spatial scales. The decomposed cost function allows for the background error covariance to be estimated separately for the distinct spatial scales, and multi-decorrelation scales to be explicitly incorporated in the background error covariance. MS-DA minimizes the partitioned cost functions sequentially from large to small scales. The multi-decorrelation length scale background error covariance enhances the spreading of sparse observations and prevents fine structures in high-resolution observations from being overly smoothed. The decomposition of the cost function also provides an avenue for mitigating the effects of scale aliasing and representativeness errors that inherently exist in a multiscale system, thus further improving the effectiveness of the assimilation of high-resolution observations. A set of one-dimensional experiments is performed to examine the properties of the MS-DA scheme. Emphasis is placed on the assimilation of patchy high-resolution observations representing radar and satellite measurements, alongside sparse observations representing those from conventional in situ platforms. The results illustrate how MS-DA improves the effectiveness of the assimilation of both these types of observations simultaneously.

Assimilation of high-resolution sea surface temperature data into an operational nowcast/forecast system around Japan using a multi-scale three-dimensional variational scheme

“…In this case, skills of MS-3DVARs and SS3DVARs are comparable to each other (Li et al 2015a). In real situations, however, the distributions of the available data are not uniform; in particular, the high-resolution infrared SST including the Himawari-8 product involves the data missing areas due to the cloud noise (e.g., Miyazawa et al 2013), and in situ temperature and salinity data are obtained with quite coarse resolution (e.g., Miyazawa et al 2012).…”

“…The most critical change in the data assimilation process is use of multi-scale cost functions inspired by series of the recent MS-3DVAR studies (Li et al 2013(Li et al , 2015a(Li et al , 2015bMuscarella et al 2014). Here, we introduce largescale and small-scale components of the analysis increments, δX L and δX S , respectively, for estimation of the analysis temperature/salinity X a from the first guess ones X f ,…”

“…We compare the skills of a single-scale (SS-) and multiscale (MS-) 3DVAR implementations on JCOPE2. Li et al (2015a) describe an algorithm of the MS-3DVAR scheme, and they demonstrate that it reasonably assimilates the observation data with both dense and coarse distributions in the coastal oceans off Alaska (Li et al 2013) and California (Li et al 2015b) coasts. Muscarella et al (2014) briefly report that both the dense satellite and coarse in situ data are well assimilated into their ocean model in the Kuroshio Extension region.…”

“…In real situations, however, the distributions of the available data are not uniform; in particular, the high-resolution infrared SST including the Himawari-8 product involves the data missing areas due to the cloud noise (e.g., Miyazawa et al 2013), and in situ temperature and salinity data are obtained with quite coarse resolution (e.g., Miyazawa et al 2012). The MS-3DVAR scheme effectively assimilates the localized and patchy dense-distributed observation data without unrealistic smoothing and well spreads the information of the sparse-distributed data (Li et al 2015a). In terms of this viewpoint, we investigate skills in SS-3DVAR cases with different horizontal scales and compare their skills with that of MS-3DVAR.…”

Scale-dependent background-error covariance localisation

“…A somewhat related approach was developed in the context of 3DVar to treat different ranges of scales separately (e.g. Li et al, 2015). Similarly, the spatial/ spectral localisation approach of Buehner (2012) uses, within an EnVar system, background-error covariances that have been separated according to overlapping spectral wavebands with an appropriate amount of spatial localisation applied to each waveband.…”