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Inspired from Climate Engine platform, I want to calculate Standardize Precipitation Index based on this paper, where each rainfall datasets are fitted to the gamma function to define the relationship of probability to rainfall.

I have try to write a code in GEE to calculate 3-month SPI, so far using simple equation where SPI = (current rainfall - LongTermAverage) / StDev spi = rainfall_now.subtract(ltamean).divide(ltastd). I have difficulties on how to fitted the data to gamma function in GEE, is there any reference or example about this?

Map.setCenter(109.738, -7.347, 7);

// We will compare for a 1-month period of CHIRPS data 
var start = 31+28; 

// Long term average (LTA) can be generated directly from the pre-calculated Rainfall
var lta = ee.ImageCollection('UCSB-CHG/CHIRPS/PENTAD')
  .filter(ee.Filter.dayOfYear(start, start + 31))
  .filterDate('1981-01-01', '2019-12-31');

var ltamean = lta.select('precipitation').mean();
var ltastd = lta.reduce(ee.Reducer.stdDev());

// same for this year
var latest = ee.ImageCollection('UCSB-CHG/CHIRPS/PENTAD')
  .filter(ee.Filter.dayOfYear(start, start + 31))
  .filterDate('2020-01-01', '2020-05-01');

var rainfall_now = latest.select('precipitation').mean();

// add the various layers and layer combination 
Map.addLayer(rainfall_now, rainfall_viz, 'JFM 2020', false);
Map.addLayer(ltamean, rainfall_viz, 'LTA', false);
Map.addLayer(ltastd, rainfall_viz, 'STDev', false);

// Calculating rainfall anomaly and standardized precipitation index 
var anomaly = rainfall_now.divide(ltamean).multiply(100);
var spi = rainfall_now.subtract(ltamean).divide(ltastd);

// Define a colour table
var red2blue = ['a60027','de3e2c','fa8b50','ffd485','e1e1e1','d3edf5','90c4de','5183bd','313694']
var rainfall_viz = {min:0, max:25, palette: ['B8810B', 'CB8C08', 'FFE47E','FFF2C1', 'DAF7A6', 'D2FFFF', '2DE7E7', '00B9D6', '008BD6', '006399']};
var rainanom_viz = {min:0, max:200, palette: red2blue};
var spicolor = ['760005','ec0013','ffa938','fdd28a','fefe53','ffffff','a2fd6e','00b44a','008180','2a23eb','a21fec'];
var spi_viz = {min:-2, max:2, palette: spicolor};

// Add the image to the map using both the color ramp and interval schemes.
Map.addLayer(anomaly, rainanom_viz, 'Anomaly (JFM2020-LTA)');
Map.addLayer(spi, spi_viz, 'SPI JFM2020');

For reference, attached is the spreadsheet file, that I frequently used to calculate SPI3 that incorporate gamma function and normal inverse in the calculation.

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That is a limitation with GEE. More details and code are provided here in this regards: https://un-spider.org/advisory-support/recommended-practices/recommended-practice-drought-monitoring-spi/step-by-step

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