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3.MODIS_TFA_Day.js
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3.MODIS_TFA_Day.js
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// This code uses Temporal Fourier Analysis to build 365 images, for each day of year,
// of the climatological tempratures based on the day (or night) temperatures.
var coleccion_imagenes=require('users/corfobbppciren2023/Humedad_de_Suelo:1.coleccion_imagenes.js');
var table = coleccion_imagenes.tabla;
// Choose here either day or night band
var Temperature_Band = 'LST_Day_1km';
// Insert here the coordinates of the area of interest.
var geometria = table; //Valparaíso
// Change the path to your own assets folder
var Assets_path = 'users/corfobbppciren2023/MODIS_LST_TFA_Valparaiso_'
var collection = 'MODIS/061/MOD11A1'; //MOD11A1
// The number of cycles per year to model.
var harmonics = 3;
// Make a list of harmonic frequencies to model.
// These also serve as band name suffixes.
var harmonicFrequencies = ee.List.sequence(1, harmonics);
// Function to get a sequence of band names for harmonic terms.
var getNames = function(base, list) {
return ee.List(list).map(function(i) {
return ee.String(base).cat(ee.Number(i).int());
});
};
// Construct lists of names for the harmonic terms.
var cosNames = getNames('cos_', harmonicFrequencies);
var sinNames = getNames('sin_', harmonicFrequencies);
var k2celsius = function(image) {
return image.multiply(ee.Image(0.02))
.subtract(ee.Image(273.15)) //convert Kelvin to Celsius
.set('system:time_start', image.get('system:time_start'));
};
// Function to compute the specified number of harmonics
// and add them as bands.
// for p = 0, Nharmonics-1 do begin
// a[p] = a[p] + 2*TS_t*cos(2*!pi*(p+1)*(t+1)/N)
// b[p] = b[p] + 2*TS_t*sin(2*!pi*(p+1)*(t+1)/N)
var addHarmonics = function(freqs) {
return function(image) {
// Make an image of frequencies.
var frequencies = ee.Image.constant(freqs);
// This band should represent lst.
var lst = ee.Image(image).select(Temperature_Band);
// This band should represent days from start.
var time = ee.Image(image).select('t');
// Get the cosine terms.
var cosines = lst.multiply(2.0).multiply((frequencies.multiply(2.0 * Math.PI).multiply(time).divide(365.0)).cos())
.rename(cosNames);
// Get the sin terms.
var sines = lst.multiply(2.0).multiply((frequencies.multiply(2.0 * Math.PI).multiply(time).divide(365.0)).sin())
.rename(sinNames);
return image.addBands(cosines).addBands(sines);
};
};
var LST = ee.ImageCollection(ee.List.sequence(1, 365).map(function (doy){
return ee.ImageCollection(collection)
.select(Temperature_Band)
.filter(ee.Filter.calendarRange(doy, doy, 'day_of_year'))
// .filter(ee.Filter.eq('start_hour', 12))
.map(k2celsius)
.mean()
.set({doy: doy})
.addBands(ee.Image(ee.Number(doy)).rename('t'))
// .map(addHarmonics(harmonicFrequencies));
}))
LST = LST.map(addHarmonics(harmonicFrequencies));
// a = a / N_TS
// b = b / N_TS
var num_days = 365;//ee.Date(lastDay).difference(ee.Date(firstDay), 'day');
var a_coef_1 = LST.select('cos_1').sum().divide(num_days);
var a_coef_2 = LST.select('cos_2').sum().divide(num_days);
var a_coef_3 = LST.select('cos_3').sum().divide(num_days);
var b_coef_1 = LST.select('sin_1').sum().divide(num_days);
var b_coef_2 = LST.select('sin_2').sum().divide(num_days);
var b_coef_3 = LST.select('sin_3').sum().divide(num_days);
// ; ========================================
// ; prepare the first 3 harmonics of the TFA
// ; ========================================
// H0 = total(TS) / N_TS ;mean
// FTA = MAKE_ARRAY(N_TS, /FLOAT, VALUE=0.)
// H = MAKE_ARRAY(Nharmonics, N_TS, /FLOAT, VALUE=0.)
// omega = MAKE_ARRAY(Nharmonics, /FLOAT, VALUE=0.)
// Phase = MAKE_ARRAY(Nharmonics, /FLOAT, VALUE=0.)
// Amplitude = MAKE_ARRAY(Nharmonics, /FLOAT, VALUE=0.)
// for p = 0, Nharmonics-1 do begin
// omega[p] = 2. * !pi * (p+1) / N
// Phase[p] = atan( -b[p], a[p] )
// Amplitude[p] = sqrt( a[p]^2 + b[p]^2 )
var H0 = LST.select(Temperature_Band).mean();
// Get the omega terms.
var omega_1 = ee.Image(1.0).multiply(2.0 * Math.PI).divide(365.0);
var omega_2 = ee.Image(2.0).multiply(2.0 * Math.PI).divide(365.0);
var omega_3 = ee.Image(3.0).multiply(2.0 * Math.PI).divide(365.0);
var phase_1 = a_coef_1.atan2(b_coef_1.multiply(ee.Image(-1.0)));
var phase_2 = a_coef_2.atan2(b_coef_2.multiply(ee.Image(-1.0)));
var phase_3 = a_coef_3.atan2(b_coef_3.multiply(ee.Image(-1.0)));
var amplitude_1 = (a_coef_1.pow(2).add(b_coef_1.pow(2))).sqrt();
var amplitude_2 = (a_coef_2.pow(2).add(b_coef_2.pow(2))).sqrt();
var amplitude_3 = (a_coef_3.pow(2).add(b_coef_3.pow(2))).sqrt();
// for t = 0, N_TS-1 do begin
// H[p,t] = Amplitude[p] * cos(omega[p]*(t+1) + Phase[p])
// Function to add a H band.
var addH = function(image) {
var H_1 = amplitude_1.multiply((omega_1.multiply(image.select('t')).add(phase_1)).cos()).rename('H_1');
var H_2 = amplitude_2.multiply((omega_2.multiply(image.select('t')).add(phase_2)).cos()).rename('H_2');
var H_3 = amplitude_3.multiply((omega_3.multiply(image.select('t')).add(phase_3)).cos()).rename('H_3');
// FTA[t] = H0 + H[0,t] + H[1,t] + H[2,t]
var TFA = H0.add(H_1).add(H_2).add(H_3).rename('TFA');
var Anomalies = TFA.subtract(image.select(Temperature_Band)).rename('Anomalies');
return image.addBands(TFA).addBands(Anomalies);
};
var LST_TFA = LST.map(addH);
// Define the visualization parameters.
var vizParams = {
bands: ['mean', 'phase', 'amplitude'],
min: [285.0,2.0,5.0],
max: [295.0,3.0,10.0],
gamma: [1.0, 1.0, 1.0]
};
//display the image.
var img = ee.Image(H0.addBands(phase_1).addBands(amplitude_1).rename('mean', 'phase', 'amplitude'));
// Map.addLayer(img, vizParams, 'RGB');
//Iterating over the image collection using this function....
var TFA_Images = LST_TFA.select('TFA')
.sort('t')
.iterate(function(img, all) {
return ee.Image(all).addBands(img);
}, ee.Image().select());
exports.TFA_Images = TFA_Images;
exports.Assets_path = Assets_path;
exports.Temperature_Band = Temperature_Band;
exports.geometria = geometria;