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The MannKendall algorithm first calculates several statistics on the timeseries. Missing values are ignored.
Mann-Kendall statistic S
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{latex}
\(S=\sum\limits_{k=1}^{N-1}\sum\limits_{l=k+1}^{N}sign(x_l-x_k)\)
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Variance S
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S
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where
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{latex}g{latex}the number of tied data in the p-th group
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{latex}h{latex}the number of multiple data in the qth time period
Z statistic
Z=
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\( \frac{S-1}{\sqrt{VAR(S)}}\)
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{latex}Z=0{latex} |
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Z=\( \frac{S+1}{\sqrt{VAR(S)}}\)
{latex}Slope
In classical MannKendall tests Slope is the median of the slopes which is a very reliable estimator of the slope even when there are lots of missing values. The calculation of this value is expensive in terms of memory and requires N * (N-1) / 2 memory where N is the number of non-missing input values. In order to prevent memory problems, it is recommended that a limited amount of input values is used. If the option logSensSlope is set to false, the average slope is used to estimate the slope which is less accurate than the median but requires N memory.
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where delta is defined as
Wiki Markup {latex}delta = inverseCDF(1 - confidenceCoefficient) if two-tailed{latex}
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Configuration
- id: identifier of the check.
- checkRelativePeriod: The period to run the trend test for.
- variableDefinition: Definition of time series. Each time series is processed independently.
- inputVariable:Identifier of a variable of which timeseries the flags will be used as input (neighbouring locations). Refers to a time series set defined in the variableDefinitions.
- outputVariable: Identifier of a variable for which timeseries the outputFlag has to be updated in case the thresholds are exceeded (observed values). Refers to a time series set defined in the variableDefinitions.
- logSensSlope: Includes Sen's slope in the logging (default true). For large number of steps the algorithm for determining Sen's slope requires lots of memory. To resolve out of memory problems, set this option to false. The difference is that no longer the median of the slopes is used to estimate the slope (classical mann kendall), but instead the average of the slopes is used as slope estimator.
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