Atmospheric radio sounding analysis using a Savitzky-Golay low-pass filter working with irregularly sampled data.
The sounding.py python script
reads data from an atmospheric radio-sounding
(in this case from file example_data.txt).
The data is a table in the ASCII format structured by several columns,
delimited by spaces.
The program does not assumes a specific number of columns, instead it works by trying to read an header with the variables names. This function will not work unless the following variable names are found:
Time, Alt_AGL, Press, Temp, DP, VTemp, RelHum, Mix_Rat, WSpeed
The data is processed and a Savitzky-Golay low-pass filter is applied to smooth some vertical profiles (wind speed and temperature) and to extract both the smoothed profiles and its derivatives.
The savitzky_golay_lowpassfilter.py
python script contains functions that apply a Savitzky-Golay low-pass filter
to irregularly sampled data.
F, dF, ddF = savgol_irregular_brute (f, x, xwindow, order=4, deriv=2)This function applies the Savitzky-Golay filter in a brute force way. For each record in the input data, a polynomial is fitted, meaning a matrix is pseudo-inverted to solve the least-squares problem.
The original technique assumes a signal with uniform sampling and only one matrix is pseudo-inverted, independently of the number of records in the input data.
F, dF, ddF = savgol_irregular_interp (f, x, xwindow, order=4, deriv=2, dx=None)This function applies the Savitzky-Golay filter, linearly interpolating the input data to regularize it. Although a polynomial is fitted to each record of the input data, the least-squares problem requires only one coefficients matrix, thus the pseudo-invertion of the matrix is performed only once. The exception is for recors at the boundaries, where a polynomial is fitted for each reacord.
A Savitzky, MJE Golay, (1964). Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, vol. 36(8):1627-1639.
The code runs with either python 2 and 3. Simply run:
./sounding.py