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Is there a standard color palette (or most commonly used in publications and other materials) for the spectral indices?

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There is no standard color palette for spectral indices. The most important is to represent the indices in a way that can understandable to someone looking at the map. Choosing a color palette is a matter of personal preference, some people prefer a range of strong tone with various (different) colors, others may prefer a range of same color (light to dark green), or a range of two colors (yellow/white to green, for example). It is recommended to choose a color that can be easily recognized on the map.

Here is some examples of NDVI color available at the web Earth Observatory: NASA, Tetracam, and New NDVI colormap

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