BreakDetection.md

Break Detection

Index

breaks_flagSpektrumBased

breaks_flagSpektrumBased

breaks_flagSpektrumBased(thresh_rel=0.1, thresh_abs=0.01, 
                         first_der_factor=10, first_der_window="12h", 
                         scnd_der_ratio_range=0.05, scnd_der_ratio_thresh=10, 
                         smooth=True, smooth_window=None, smooth_poly_deg=2)

parameter	data type	default value	description
thresh_rel	float	0.1	Minimum relative difference between two values to consider the latter as a break candidate. See condition (1)
thresh_abs	float	0.01	Minimum absolute difference between two values to consider the latter as a break candidate. See condition (2)
first_der_factor	float	10	Multiplication factor for arithmetic mean of the first derivatives surrounding a break candidate. See condition (3).
first_der_window	offset string	"12h"	Window around a break candidate for which the arithmetic mean is calculated. See condition (3)
scnd_der_ratio_range	float	0.05	Maximum deviation from one of the ratio of the second derivatives of a break candidate and its preceding value. See condition (5)
scnd_der_ratio_thresh	float	10.0	Threshold for the ratio of the second derivatives of a break candidate and its succeeding value. See condition (5)
smooth	bool	True	Smooth the time series before differentiation using the Savitsky-Golay filter
smooth_window	offset string	None	Size of the smoothing window of the Savitsky-Golay filter. The default value None results in a window of two times the sampling rate (i.e. three values)
smooth_poly_deg	integer	2	Degree of the polynomial used for smoothing with the Savitsky-Golay filter

The function flags breaks (jumps/drops) by evaluating the derivatives of a time series.

A value

x_k

of a time series

x_t

with timestamps

t_i

, is considered to be a break, if:

1. x_k
   represents a sufficiently large relative jump:
   |\frac{x_k - x_{k-1}}{x_k}| >
   thresh_rel

2. x_k
   represents a sufficient absolute jump:
   |x_k - x_{k-1}| >
   thresh_abs

3. The dataset

   X = x_i, ..., x_{k-1}, x_{k+1}, ..., x_j
   , with
   |t_{k-1} - t_i| = |t_j - t_{k+1}| =
   first_der_window fulfills the following condition:
   |x'_k| >
   first_der_factor
   \cdot \bar{X}

   where

   \bar{X}
   denotes the arithmetic mean of
   X
   .

4. The ratio (last/this) of the second derivatives is close to 1:

   1 -
   scnd_der_ratio_range
   < |\frac{x''_{k-1}}{x_{k''}}| < 1 +
   scnd_der_ratio_range

5. The ratio (this/next) of the second derivatives is sufficiently height:

   |\frac{x''_{k}}{x''_{k+1}}| >
   scnd_der_ratio_thresh

NOTE:

• Only works for time series
• The time series is expected to be harmonized to an equidistant frequency grid

This Function is a generalization of the spectrum based spike flagging mechanism as presented in [1].

References

[1] Dorigo,W. et al.: Global Automated Quality Control of In Situ Soil Moisture Data from the international Soil Moisture Network. 2013. Vadoze Zone J. doi:10.2136/vzj2012.0097.