Multi-Resolution Variational Analysis (MRVA): High-resolution data fusion over global surface

The Multi-Resolution Variational Analysis method was developed to merge satellite sea surface temperature (SST) measurements with drastically different spatial resolution and coverage. MRVA is a hybrid of the variational analysis technique used commonly in geophysical data interpolation/assimilation and multiresolution analysis technique based on orthonormal wavelet decomposition, where the former addresses the irregular-sampling and uncertainty estimation issues while the latter provides a mathematical framework to control the interpolation scale (internal resolution) for each data set as well as inter-sensor bias corrections. Satellite-based SST data are indeed irregularly-sampled by different sensor types. The microwave (MW) sensors have typically coarser 25-km resolution than the infra-red (IR) sensors which can resolve down to a 1-km scale. However, the IR-based measurements are prone to data voids due to cloud contamination, which does not affect MW sensors nearly as much. Scientific and operational needs for the SST data cover a wide range of spatial and temporal scales. For example, a regional or global mean is often examined over a long time period in climate studies, while SST snapshots of sub-kilometer resolution may be required in biological applications. The focus of the Multi-scale Ultra-high Resolution (MUR) SST analysis project is to produce a high-resolution daily SST field based on the satellite retrieval data to address these variety of needs. The MRVA method was applied to merge these satellite data to produce the MUR SST analysis over a 1-km global grid at a daily frequency. The power spectral density of SST displays a self-similar (power-law) characteristic, and MUR SST shows consistency with this characteristic over a wider range of wavenumber spectrum due to its higher internal resolution. Capability to reproduce such empirical characteristics is a strength of the MRVA technique.