[GIS] Reconstructing MODIS time-series applying Savitzky-Golay Filter with Python/Numpy

Question

I want to apply the 'Savitzky-Golay' (savgol) filter to my time series, MODIS dataset, to remove noise (i.e., cloud pixels, etc.) in my data. MODIS have quality flags that indicates the reliability of each pixel values or if the pixel is possibly affected by clouds. So I would like to incorporate these quality flags in my filter by putting less weight or ignoring those pixel values and let savgol filter predict the optimal pixel value. I am testing np.NaN/np.nan/isnull but it seems that it removes the element in the array, and consequently savgol filter also skip those values. I would like my resulting data to be like in the attached figure.

(https://matinbrandt.wordpress.com/2014/12/02/smoothingfiltering-a-ndvi-time-series-using-a-savitzky-golay-filter-and-r/)

Answer 1

You need to interpolate missing data before you can apply the Savitzky-Golay filter. TIMESAT is the most widely used tool for this job and they handle missing data with linear interpolation prior to applying the Savitzky-Golay filter. Assuming that you already masked cloudy and other bad observations as np.nan here is how you can interpolate a time-series with pandas.interpolate() and then apply the Savitzky-Golay filter scipy.signal.savgol_filter().

import numpy as np
import pandas as pd
from scipy.signal import savgol_filter

#create a random time series
time_series = np.random.random(50)
time_series[time_series < 0.1] = np.nan
time_series = pd.Series(time_series)

# interpolate missing data
time_series_interp = time_series.interpolate(method="linear")

# apply SavGol filter
time_series_savgol = savgol_filter(time_series_interp, window_length=7, polyorder=2)

There are of course other ways to interpolate the missing data but pandas is one of the most convenient ways to do this, especially if you want to test the effects of different interpolation algorithms.