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<statisticalFunctions>
               <statisticalFunction function="boxPlot"/>
</statisticalFunctions>

Calendar aggregation

Aggregation by calendar day (00.00h-24.00h)

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Config example:

<statisticalFunctions>
<statisticalFunction function="calendarAggregation">
			<movingAccumulationTimeSpan                             <timeStep id="daily"/>
                              <timeStep id="weekly"/>
                              <timeStep id="monthly"/>
                              <timeStep id="seasons"/>
               </statisticalFunction>
</statisticalFunctions>

Calendar aggregation

Aggregation by calendar day (00.00h-24.00h)

unit="week" multiplier="1"/>
			<movingAccumulationTimeSpan unit="week" multiplier="2"/>
			<movingAccumulationTimeSpan unit="week" multiplier="4"/>
			<movingAccumulationTimeSpan unit="week" multiplier="12"/>
			<movingAccumulationTimeSpan unit="day" multiplier="365"/>
		</statisticalFunction>

In addition to the calender aggregation, there is also the option for accumulationAggregation and relativeAggregation. There is also a very similar function called accumulationInterval where the accumulation is displayed at every timestep (for configuration see example above).

Moving average

Moving average where the value is stamped at the end of each averaging period.

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Config example:

<statisticalFunctions>
		<statisticalFunction function="movingAverage" ignoreMissings="true">
			<movingAccumulationTimeSpan unit="hour" multiplier="1"/>
			<movingAccumulationTimeSpan unit="hour" multiplier="3"/>
			<movingAccumulationTimeSpan unit="hour" multiplier="6"/>
			<movingAccumulationTimeSpan unit="hour" multiplier="12"/>
		</statisticalFunction>

Central moving average

Moving average where the value is stamped in the middle of each averaging period.

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Config example:

<statisticalFunctions>
		<statisticalFunction function="calendarAggregation">
			<movingAccumulationTimeSpan unit="week" multiplier="1"/centralMovingAverage" ignoreMissings="true">
			<movingAccumulationTimeSpan unit="weekhour" multiplier="21"/>
			<movingAccumulationTimeSpan unit="weekhour" multiplier="43"/>
			<movingAccumulationTimeSpan unit="weekhour" multiplier="126"/>
			<movingAccumulationTimeSpan unit="dayhour" multiplier="36512"/>
		</statisticalFunction>

In addition to the calender aggregation, there is also the option for accumulationAggregation and relativeAggregation. There is also a very similar function called accumulationInterval where the accumulation is displayed at every timestep (for configuration see example above).

Moving average

Moving average where the value is stamped at the end of each averaging period.

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Config example:

Differences

Displays the difference between two selected series

Config example:

<statisticalFunctions>
		<statisticalFunction function="movingAverage" ignoreMissings="true">
			<movingAccumulationTimeSpan unit="hour" multiplier="1"/>
			<movingAccumulationTimeSpan unit="hour" multiplier="3"/>
			<movingAccumulationTimeSpan unit="hour" multiplier="6"/>
			<movingAccumulationTimeSpan unit="hour" multiplier="12"/>
		</statisticalFunction>

Central moving average

Moving average where the value is stamped in the middle of each averaging period.

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Config example:

...

<statisticalFunctions>
		<statisticalFunction function="centralMovingAverage" ignoreMissings="true">
			<movingAccumulationTimeSpan unit="hour" multiplier="1"/>
			<movingAccumulationTimeSpan unit="hour" multiplier="3"/>
			<movingAccumulationTimeSpan unit="hour" multiplier="6"/>
			<movingAccumulationTimeSpan unit="hour" multiplier="12"/>
		</statisticalFunction>

differences"/>

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If you configure Differences statistical function, the following options will become available in plot:

• Reference level.
  This option is always available. It compares the values of the TimeSeriesSet to a value you can specify by typing into the box marked <enter value>, and displays the difference: TimeSeriesSet value - reference value.
• Compare runs (available since 2020.01)
  This option is only available if you have opened/selected at least 2 different runs for each timeSeriesSet in the display. The number can be greater than 2, and does not need to be the same number for all timeSeries. (For example 2 different runs for parameter A, and 3 for B). As reference level, the oldest of this runs is selected, and the difference compared to this run is displayed. (Run value - reference run value)
• Select timeSeries as reference level
  This option is available if you have at least two different time series open in the plot. They can be different runs, but they do not need to be. The difference between the Time series and reference time series will be displayed. (TimeSeries value - reference TimeSeries value)

If the checkbox "Relative difference(%)" is checked, the relative difference will be displayed (in %). This is available for all three options.  100*(TimeSeries value - reference TimeSeries value)/reference TimeSeries value.  If the reference value is 0, N.a.N will be the result.

Display lows below value & Display peaks above value

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Shows all peak heights or dip depths and duration above or below a reference level. This level is set by default but can be altered in the toolbar. After adjusting, press the apply button to recalculate the peaks or dips. . From now on we will only mention the peaks and how values are above a level, but this functionality is symmetrical for the valleys and values being below a level. The default value for the reference level is set by determining the 'low' areas according to the maximum available value of the input time series array.

After setting the reference level, every continues series of values above that level is considered a peak and will be depicted as a dot in the XY plot. The X axis shows what the duration of this peak is, with this value corresponding to the amount of time entries that make up that peak. The Y axis shows the average height of the peak above the reference level. The parameter used on the Y axis is equal to that of the selected time series.

When hovering above a point in the XY plot, a tooltip will appear. Here is an overview of the tooptip format with some of the elements being optional:

• |Parameter Id| |Location Id| (|Peak duration|, |Average peak height|), Max Difference = |Max peak height|, Percentile Difference = |Percentile peak height| at time |Peak time|
• Parameter Id: Paramter Id from selected timeseries
• Location Id: Location Id from selected timeserires
• Peak duration: Number of time entries in peak
• Average peak height: Average of all differences between reference level and the time entries value
• Max peak height (optional): Maximum of all differences between reference level and the time entries value
• Percentile peak height (optional): Relation between the average and max peak height
• Peak time: Time of the first time entry in the peak

Config example:

		<statisticalFunction function="showLowsBelow"/>
		<statisticalFunction function="showPeaksAbove"/>

Display lows below value & Display peaks above value (per year and season)

(Since 2016.02) The same as the function above but then with the extension of selecting multiple different years and seasons, plus a choice of how the different seasons and years should be uniquely colored.

Unique color per season

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Unique color per year:

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Unique color per year and season:

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<statisticalFunction function="historicalShowPeaksAbove">
	<season startMonthDay="--01-01" endMonthDay="--12-31" label="Year" color="black"/>
	<season startMonthDay="--04-01" endMonthDay="--09-30" label="Grow Season" color="gray"/>		
</statisticalFunction>
<statisticalFunction function="historicalShowLowsBelow">
	<season startMonthDay="--01-01" endMonthDay="--12-31" label="Year" color="black"/>
	<season startMonthDay="--04-01" endMonthDay="--09-30" label="Grow Season" color="gray"/>		
</statisticalFunction>

Normalize duration

(Since 2016.02)  for the peaks above/below functions a checkbox is added to normalize over duration. This changes The y-axis from Normalized difference to Max difference and the X-axis from (total) duration the Normalized duration. 

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The differences between normalization can best be shown in a pictures

Normalized difference:

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Normalized duration:

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Split peaks

(Since 2016.02) for the peaks above/below functions a possibility is added to split the peaks when they have multiple local maxima.

No split:

Image Added

Split when local maxima have a low between them with a value difference of

Differences

Displays the difference between two selected series

Config example:

...

<statisticalFunction function="differences"/>

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If you configure Differences statistical function, there will be the following options available in plot:

• Reference level.
  This option is always available. It compares the values of the TimeSeriesSet to a value you can specify by typing intot the box marked <enter value>, and displayes the difference: TimeSeriesSet value - reference value.
• Compare runs (available since 2020.01)
  This option is only available if you have selected at leaset 2 different runs for each timeSeriesSet in the display. The number can be greater than 2, and does not need to be the same number for all timeSeries. (For example 2 different runs for parameter A, and 3 for B). As reference level, the oldest of this runs is selected, and the difference compared to this run is displayed. (Run value - reference run value)
• Select timeSeries as reference level
  This option is available if you have at least two different time series open in the plot. They can be different runs, but they do not need to be. The difference between the Time series and reference time series will be displayed. (TimeSeries value - reference TimeSeries value)

If the checkbox "Relative difference(%)" is checked, the relative difference will be displayed (in %). This is available for all three options.  100*(TimeSeries value - reference TimeSeries value)/reference TimeSeries value.  If the reference value is 0, N.a.N will be the result.

Display lows below value & Display peaks above value

...

Shows all peak heights or dip depths and duration above or below a reference level. This level is set by default but can be altered in the toolbar. After adjusting, press the apply button to recalculate the peaks or dips. . From now on we will only mention the peaks and how values are above a level, but this functionality is symmetrical for the valleys and values being below a level. The default value for the reference level is set by determining the 'low' areas according to the maximum available value of the input time series array.

After setting the reference level, every continues series of values above that level is considered a peak and will be depicted as a dot in the XY plot. The X axis shows what the duration of this peak is, with this value corresponding to the amount of time entries that make up that peak. The Y axis shows the average height of the peak above the reference level. The parameter used on the Y axis is equal to that of the selected time series.

When hovering above a point in the XY plot, a tooltip will appear. Here is an overview of the tooptip format with some of the elements being optional:

• |Parameter Id| |Location Id| (|Peak duration|, |Average peak height|), Max Difference = |Max peak height|, Percentile Difference = |Percentile peak height| at time |Peak time|
• Parameter Id: Paramter Id from selected timeseries
• Location Id: Location Id from selected timeserires
• Peak duration: Number of time entries in peak
• Average peak height: Average of all differences between reference level and the time entries value
• Max peak height (optional): Maximum of all differences between reference level and the time entries value
• Percentile peak height (optional): Relation between the average and max peak height
• Peak time: Time of the first time entry in the peak

Config example:

...

		<statisticalFunction function="showLowsBelow"/>
		<statisticalFunction function="showPeaksAbove"/>

Display lows below value & Display peaks above value (per year and season)

(Since 2016.02) The same as the function above but then with the extension of selecting multiple different years and seasons, plus a choice of how the different seasons and years should be uniquely colored.

Unique color per season

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Unique color per year:

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Unique color per year and season:

Image Removed

...

<statisticalFunction function="historicalShowLowsBelow"/>
<statisticalFunction function="historicalShowPeaksAbove"/>

Normalize duration

(Since 2016.02)  for the peaks above/below functions a checkbox is added to normalize over duration. This changes The y-axis from Normalized difference to Max difference and the X-axis from (total) duration the Normalized duration. 

Image Removed

The differences between normalization can best be shown in a pictures

Normalized difference:

Image Removed

Normalized duration:

Image Removed

Split peaks

(Since 2016.02) for the peaks above/below functions a possibility is added to split the peaks when they have multiple local maxima.

No split:

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Split when local maxima have a low between them with a value difference of at least 0,001. As can be seen this results in a lot more separate peaks.

...

<statisticalFunction function="doubleMassCurve">
	<dateFormat>yyyy-MM-dd hh:mm</dateFormat>
</statisticalFunction>

/>

Duration Duration curve

A convenient way to show the variation of hydrological quantities through time may be done by means of duration curves. For the selected time period the values of the selected quantity are sorted descending (durationExceedence) or ascending (durationNonExceedence). When the duration curve is plotted in the timeseries display, the x-axis will show the entire length in time of the selected view period. Percentages are shown as duration with respect to the entire chosen view period.

...

Allows comparison of the current situation with selected previous years at the same moment within the year. CAn Can be used to compare seasonal behaviour, e.g. deficit accumulation, snow accummulation/melt, runoff.
The bottom of the window shows the full timeseries to assist in picking relevant historical years.

The function requires a multi-year historical series, where the view period on the x-axis streches stretches over multiple years before the function is selected. You can use the |<>| button to stretch the x-axis from the current view period to the full available length. The display requires a fixed season definition for the x-axis, to be included in the configuration. The user needs to select the historical year of interest to plot this against the current year. Multiple years can be selected by holding the CTRL-key. Holding the SHIFT-key will select a range of years.

...

Typically, this functionality is intended to work in combination with the Topology and the Filters, such that you can have a default set of locations which you can modify from the map or via the Filters. You can also exclude locations from the analysis by making the timeseries invisible in the graph. By default the function shows the scatterplot of the best 5 equations (lowest root mean square error). By selecting one item in the legend, this item and its confidence interval is shown.

The PCA-estimate for the basin value can be utilized in a modifier if the ModifierTypes-configuration refers to the statistical function for the default value.

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Scatter Plot

Creates a scatter plot of two selected series

Config example:

...

<statisticalFunction function="scatterPlot"/>

interval is shown.

The PCA-estimate for the basin value can be utilized in a modifier if the ModifierTypes-configuration refers to the statistical function for the default value.

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Scatter Plot

Creates a scatter plot of two selected series

Config example:

<statisticalFunction function="scatterPlot"/>

Historical Scatter Plot (per year and season)

(Since 2016.02) There is also a scatter plot available where you can select years and seasons separately and choose unique coloring

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<statisticalFunction function="historicalScatterPlot">
	<season startMonthDay="--01-01" endMonthDay="--12-31" label="Year" color="black"/>
	<season startMonthDay="--04-01" endMonthDay="--09-30" label="Grow Season" color="gray"/>
</statisticalFunction>

Historical Scatter Plot (per year and season)

(Since 2016.02) There is also a scatter plot available where you can select years and seasons separately and choose unique coloring

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<statisticalFunction function="historicalScatterPlot"/>

Show statistics for specific timeseries

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