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Mann-Kendall statistic S
Variance S
where
is the number of groups of tied data
the number of tied data in the p-th group
- h
the number of sampling times that contain multiple data
- u_p
the number of multiple data in the qth time period
Z statistic
Z=
, if S > 0,
, if S = 0
, if S < 0,
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
delta = inverseCDF(1 - confidenceCoefficient) if two-tailed
delta = inverseCDF(1 - confidenceCoefficient / 2) if upward or downward
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.
- onErrorResumeNext When true, makes the secondary validation continue when an error logging is applied.
For each threshold,
- testTrend: either two-tailed, upward or downward (two-tailed is default)
- logLevel: Log level for the log message that is logged if a trend is detected. Can be DEBUG, INFO, WARN, ERROR or FATAL. If level is error or fatal, then the module will stop running after logging the first log message. Fatal should never be used actually.
- outputFlag Either unreliable or doubtful.
- outputMode By default the flags that need updating are updated and log events are generated for the updated flags. When this option is set to 'logs_only', the log events are generated but the flags will not be updated.
- logEventCode: Event code for the log message that is logged if a trend is detected. This event code has to contain a dot, e.g. "TimeSeries.Check", because the log message is only visible to the master controller if the event code contains a dot.
- logMessage: Log message that is logged if a trend is detected.
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