Examples
Synthetic Data
In order to test the detection method we use a time series of synthetic data generated from a model for lake eutrophication (enrichment of an ecosystem with chemical nutrients, typically compounds containing nitrogen or phosphorus) by excessive phosphorus (Carpenter et al, 1999) to which we added a large amount of noise:
At the left we show the original data, and at the right the same data with a large amount of noise (as in Zaldivar et al., 2008).
Using this data as the input of Threshold Enhancer we where able to filter the data series and recover the position of the jump in it:
Ringkøbing Fjord
A typical example of an experimental time series with sudden jumps in the data is the one of the Ringkøbing Fjord. (Petersen et al., Ecolog. Appl., 1998)The history of the Ringkøbing Fjord demonstrates how regime shift suddenly can happen either as a consequence of many years of massive eutrophication or due to a small change in a physical parameter triggering key components of the ecosystem. The latest incidents where a total collapse in the late 1970s caused by eutrophication and a regime shift in the mid 1990s triggered by a relatively small increase in salinity. Using the data taken for the second episode we are able to test our filtering method in a real time series.
In mid summer of 1995 a collapse occurred in the Fjord as a consequence of an increased water exchange with the sea established to dilute the eutrophication of the lagoon. The salinity reached the threshold that allowed the colonization of the lagoon with soft clamps and seed production of marine plants. Due to the colonization of the Fjord by high numbers of soft clamp the biomass of phytoplankton decreased to 5% of the former level.
This drastic reduction of phytoplankton the transparency of the water (measured as Secchi depth) increased and led to an almost instant increase in the depth distribution of bottom plants.
Unprocessed Salinity and Secchi depth time series. A jump is evident in Secchi depth, but not in the salinity:
As before, by filtering this data set with ThEnhancer, jumps in the time series are made evident. This is not surprising in the case of the Secchi depth, but the jump was not evident to the naked eye in the salinity series.
Data processed by ThEnhancer:
