A multi-scale and ungridded representation of data products

Remote sensing data have irregular sampling patterns primarily due to sensor tracks. These data are typically interpolated to a regular grid for further use. "Gridding" is usually performed by relocating each data sample to its nearest grid-point or grid-box, often followed by an averaging procedure. A fundamental problem with such a practice is that the geolocation information is truncated, often distorting subgrid-scale features. Another issue is that a single grid resolution is often chosen to interpolate over some sparsely sampled regions at the expense of the information available over densely sampled regions. To address these issues, we introduce the multi-resolution variational analysis (MRVA) method, developed by modifying the multiresolution analysis (a loss-less signal decomposition based on orthonormal wavelets) for the irregularly sampled data. MRVA represents the interpolated fields using the wavelet coefficients at multiple scales. The multi-scale representation allows the interpolation scheme to be adaptable to spatially heterogeneous sampling patterns, since, unlike the Fourier basis, a wavelet basis possesses spatial specificity. Because the wavelet basis is a continuous function, an MRVA field can be sampled anywhere (gridless), facilitating validation of the interpolated field against another irregularly sampled data set. It also allows packaging of the interpolated field at any specified set of locations, enabling server-side subsetting that optimizes file size for efficient delivery. Due to losslessness, the wavelet coefficients also allow efficient storage, independent from the resolution of the output grid; the storage size depends only on the physical feature scale. The MRVA method has been applied to sea surface wind, temperature, and salinity data sets so far and is used for production of the Multi-scale Ultra-high Resolution (MUR) sea surface temperature data.