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You can also view are materials here: https://tyson-swetnam.github.io/emsi
The following pages are to help guide you through our process for calculating the Ecosystem Moisture Stress Index (EMSI) for any available EOS platform, on Google's Earth Engine.
The EMSI is derived using the formula for the standard score or z-score where the pixel (xy) or area average value, τi, of the Normalized Difference Vegetation Index (NDVI) for Julian day or period of interest (t); minus the NDVI mean (μ), divided by NDVI standard deviation (σ) for the same date/period across the entire time series or reference time period (T). A coefficient ρ is used to normalize or give a positive or negative sign to the index.
In our examples, we calculate EMSI using the familiar NDVI. Other vegetation spectral indices may be more useful for specific use cases.
The EMSI of each pixel is thus placed in its distinctive statistical location in a 'normal distribution' that is defined by all a given pixel's NDVI values for the same Julian date across the reference period.
Tracking the EMSI for a given pixel's 'phenoperiod' roughly yields, with some statistical rigor, interannual trends in (as we like to say) 'climate forcing' and are amenable to inferential analyses.