Time above threshold statistical models

The SEPEM server hosts three types of statistical models:
  1. fluence and peak flux modelling;
  2. time above threshold (this page);
  3. event duration.
The three model types use the same underlying methods and assumptions, but, as the input data selection and user interaction differ significantly between, they were split up into three server pages.

Data selection

The models require an underlying time series on which to base the analysis. On SEPEM there are two types of input available:

Model selection and parameters

Once the input data have been selected, the model parameters can be specified. The time above threshold analysis employs the virtual timelines method, the new SEPEM modelling methodology which accounts for the non-negligible duration of SEP events as well as allowing the inclusion of the Levy distribution which has been shown to be a better fit in most cases and certainly more robust than the two Poisson distributions available. This method can take several hours to run.

Threshold

Instead of using an event list, the system will build on the fly a list of time intervals during which the specified threshold is exceeded. With this method, one can, for instance, evaluate the probability distributions of the durations during which the threshold will be exceeded.

The thresholds should not be set too low, which would result in a very large number of 'events' (the maximum number of events is 1,000). Setting the threshold too high could result in too few episodes (a minimum of 50 is required). As a guidance, the system lists the value range of the selected channel, and provides a default value.

For differential proton channels, the following equation is used internally to generate default values for the flux threshold for a channel of mean energy E:

fth = 5.0 * 2.70E3 * E-3.1209,

i.e. five times higher than the default thresholds used with the fluence and peak flux models.For all other input data, the default threshold value is 1/200 of the maximum value in the data series. These values serve as guidelines only. Only non-zero values are allowed.

Waiting time distribution

With the virtual timeline method, a selection must be made between three distributions to fit the waiting times between SEP events (or the reciprocal event frequencies): the Poisson, the time dependent Poisson or the Levy distribution.

A Poisson distribution (used in all major models with the exception of the early King model prior to SEPEM) assumes events are distributed randomly while the others allow for periods of higher and lower average event rates. As only the virtual timelines method allows the use of non-Poisson waiting time distributions, the user must select this option to compare the fits. The Levy function will provide a good fit in all cases and is strongly recommended by SEPEM when performing virtual timeline runs.

Duration distribution

With the virtual timeline method, a selection must be made between three distributions to fit the durations of SEP events: the Poisson (more precisely, the exponential distribution), the time dependent Poisson (Fourier transform in the time domain) and the Levy distribution. As with the waiting times, the Levy function will provide a good fit in all cases and is strongly recommended by SEPEM when performing virtual timeline runs.

Time period

At present, the system allows the use of three time periods: total time period, active years only and solar minimum (quiet years). Most models are applied to active years as it is uncertain when a mission may launch and when exactly solar cycles will begin/end. This is the strongly recommended option. Selecting quiet years only assumes that the event frequency is lower but that the flux distribution is independent of activity (possibly conservative). The total time period method ignores any solar cycle dependence and therefore assumes an average event frequency over the complete time series.

Mission lengths

It is often interesting to compare the results for various mission lengths. A minimum of 1/4 year is allowed but these results should be used with caution as the duration of a single SEP event can take up a significant portion of the time series and the complete flux profile for randomly generated events is not established. For short time periods the virtual timelines method is more likely to produce reliable results.

Up to 8 mission lengths can be specified, between 0.25 and 20 years in length. Input fields that are not required should be left blank. The system will sort the specified lengths in ascending order if required.

Note: Please keep in mind that the longer the mission lengths, the longer the run will take. Also, the analyses for each selected mission length are done independently and so the more mission lengths are selected, the longer the processing will take.

Model name and description

The user should specify a model name (which will be used as a label to identify the model run, for instance on the My SEPEM page) and a description for future reference. As the processing time for these models can be several hours, they are run in batch mode, and the outputs will be stored after completion of the run, using the name and description entered prior to pressing the Run button. The model name cannot be left blank. If a model with the same name is already stored in the database by the current user, the model results will be over-written.

Once the run has been started, no other activity (except browsing the help pages) is possible on the server (with the current user account) until the run is completed. While the process is running, a page is presented where the user can perform a refresh to check for completion, or kill the running process. The user can log out and return to the server later.

Outputs

Overview

After completion of the model run, a new pane is shown with the model outputs.

At the top of the pane, links to two types of text files are provided:

The table labelled Distribution fits contains links to plot files of the duration and waiting time distributions, plus comparison and departure plots (although only one distribution function is actually used during the analysis, all three fits are always shown to facilitate the interpretation and evaluation).

Finally, the last table provides access to plots of the probability curves for each data channel.

All output files (PNG plot files and text files) can be downloaded as a zip archive using the Supplementary outputs link: this will open a new window with a summary of the results, a table containing the main fit parameters, and a link to the Zip archive of output files. All files are stored in the database and can be retrieved at any time from the My SEPEM page.

Interpretation of results

The various plot files can be interpreted as follows:




Last modified on: 2 October 2011.