Dynamic web map tile generation for data cubes
Most modern web maps display raster or image data using some derivation of the Slippy Map convention. In Slippy Map style web maps, the globe is divided into a set of tiles at different zoom levels. At zoom level zero, one tile covers the globe, and each subsequent zoom level divides previous tile into four. Traditionally, a more or less static, two dimensional raster dataset is reprojected in the web-mercator projection and then preprocessed into tiles for each zoom level (up to a maximum zoom level reflective of the resolution of the source raster). Preparing this tile cache can be a very computationally expensive process resulting in a very large dataset which must be stored. Alternatively, tile generation can be done on-the-fly but results in significantly slower map loading.
"Data cubes" are multidimensional ("n-D") data arrays (a.k.a. "tensors") which can be thought of as a stack of 2D raster images. A data cube has a consistent grid in space (x and y) and one or more additional dimensions - commonly things like time, elevation/altitude, and data variable. Data cubes can be stored as sets of 2D rasters (e.g. geotiffs) or in n-D data array formats such as NetCDF.
Pre-computing a tile cache to serve each permutation of data cube dimensions (besides x and y) can quickly become extremely expensive. The problem grows exponentially when one additionally considers the possible calculations which can be done over a data cube's dimensions, for example:
- differencing surface temperatures across two dates in time,
- summing precipitation a period of time, or
- performing calculations across multi-spectral satellite imagery bands
The Tilecube library is built upon the realization that the process of reprojecting a dataset and regridding from the source data grid to a given web map tile is a linear transformation (in the case of most regridding algorithms). The transformation matrix to generate a given web map tile depends only on the input grid and, once calculated, can be applied to any input data. This means that for any data cube, we can pre-compute a single tile cache of transformation matrices, which is similar effort to calculating a tile cache for a single 2D raster extracted from the data cube. A simple (and fast) matrix multiplication will then generate a tile for any input data, be it selected from a dimension of the data cube or calculated on-the-fly.