Fluence and peak flux statistical models

The SEPEM server hosts three types of statistical models:
  1. fluence and peak flux modelling (this page);
  2. time above threshold;
  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: Finally, an event list has to be selected, either the SEPEM reference list or a list generated by the user. Prior to starting the calculation, the system will check how many events are covered by the intersection of the event list and the epoch range of the input data. If less than 50 events are found, a warning message is generated and the model run is not performed. Event lists which are not up to date cannot be selected.

Model selection and parameters

Once the input data have been selected, the model parameters can be specified.

Parameter for analysis

Two analysis parameters can be selected. Note: The time resolutions of the various available datasets are very different, with a maximum of 5 minutes. The time resolution of the SEPEM proton reference dataset is 30 minutes prior to 1984 (based on the IMP8/GME data) and 5 minutes from 1984 onwards (based on the GOES/SEM data series).

Analysis method

Three analysis methods have been implemented.
  1. Monte Carlo is the method used for cumulative fluence analysis in the well known JPL model. In SEPEM this can also be used for worst case event fluence and peak flux analysis. The model takes in the region of 30 minutes to 1 hour to run depending on the input data selected.
  2. Virtual timelines is the new SEPEM modelling methodology and 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 from 1 to 10 hours to run.
  3. The analytical ESP method is another widely used modelling technique which extrapolates results from the fitted distributions assuming a Poisson distribution of events. It takes only minutes to run in general. Although all flux distributions are shown as outputs, the model requires the use of the truncated power law for the analytical extrapolation.
If the user is interested in the fluence or peak flux fits only, it is recommended to perform a run selecting the ESP method which will provide all the plots of interest with the minimum processing time.

Flux distribution

Three distributions are available to fit the SEP event fluences and peak fluxes: the cut-off power law, the truncated power law and the lognormal distribution.It is worth doing a trial run using ESP to see the plots of all the distribution fits before selecting a distribution for the final model run (comparison plots for all channels are part of the output). However, the ESP method itself only allows the use of the truncated power law (consequently, the distribution selection is not shown for this method), so if this distribution is not desired then another analysis method (which will take a longer processing time) must be used in the final run. SEPEM recommends the cut-off power law whose fit lies between the other two at high confidence levels.

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 as it considers the duration of events based on the generated fluence or peak flux.

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.

Thresholds for event selection

Low fluence/peak flux events are often badly fit by the flux distributions. Therefore, the user should specify thresholds for each data channel: events during which a threshold is not exceeded, are removed from the event list prior to the statistical analyis. It is recommended to run the ESP method first (as this only takes a few minutes), land to study the output plots for guidance with the threshold selection for each channel, based on what will provide a good fit while keeping the highest number of events (which is statistically desirable). This parameter is very important and should not be ignored. Only non-zero values are allowed.

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

fth = 8.54E7 * E-3.1209
for a fluence analysis, and
fth = 2.70E3 * E-3.1209

for a peak flux analysis. These values can be overridden if so desired. For all other input data, the default threshold value is one thousandth of the maximum value in the data series; these values serve as guidelines only and should be evaluated as described above.

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.



After completion of the model run, a new pane is shown with the model outputs. The outputs shown depend on the selected model parameters.

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

The table labelled Distribution functions contains links to plot files of the flux distributions for each data channel, and for each of the three fit functions 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).

For the virtual timeline method, duration fits for each channel and waiting time fits are produced.

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: 12 July 2013.