From d1dc77c510047b2c9bf4aeeac3ced852af53d5e8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Peter=20L=C3=BCnenschlo=C3=9F?= <peter.luenenschloss@ufz.de>
Date: Tue, 4 Aug 2020 08:08:26 +0200
Subject: [PATCH] Delete BreakDetection.md
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-# Break Detection
-
-## Index
-[breaks_flagSpektrumBased](#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](docs/ParameterDescriptions.md#offset-strings) | `"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](docs/ParameterDescriptions.md#offset-strings) | `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](docs/funcs/TimeSeriesHarmonization.md)
-
-
-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.
-
--
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