Instantaneous events¶

An instantaneous LTS event is a local maximum in time of a certain quantity, typically water level or discharge. The LTS module registers only instantaneous events which are found to be independent, i.e. they must fulfill simultaneously the following two criteria:

Interevent time criterion \(\Delta T\): two successive instantaneous events are independent if the time difference between the two events exceeds \(\Delta T\). In other words, a local maximum in a time series is an event maximum if there are no larger local maxima within \(\pm \Delta T\) of the local maximum.
Interevent level criterion \(p\) (\(0 < p < 1\)): two successive instantaneous events are independent if the smallest level between the two events becomes smaller than \(p\) times the value of the smallest of the two events.

Please note that in some cases criterion 2 needs to be applied with respect to a common zero level for the quantity. For example, for a water level in a node, the zero level would correspond to the node bottom level. In general, to identify events for water levels, the criterion 2 is applied to water depths.

Examples¶

Here are several examples of LTS event identification, using the two criteria:

Time series with two peaks A and B separated by more than the interevent time, where the trough depth h is small compared with the peak height H

Figure: Both time and level \(p \cdot H > h\) criteria are met. Here \(p = 0.5\) is used. Events A and B are identified.

Time series with two peaks A and B where the trough between them stays high, so the trough depth h is comparable with the peak height H

Figure: Time criterion is met, level criterion is not \(p \cdot H < h\). Only single event B is identified.

Time series with two narrow peaks A and B spaced closer together than the interevent time

Figure: Time criterion is not met. Only single event B is identified.

Time series with three peaks A, B and C, where the interevent time spans start at the two tallest peaks A and C

Figure: Two events A and B are identified.

Time series with three peaks A, B and C of increasing height, with overlapping interevent time spans covering all three

Figure: Single event C is identified.

Time series forming a single broad peak A carrying small high-frequency oscillations on its rising and falling limbs

Figure: Small oscillations are disregarded as events. Single event A is identified.