Time above threshold statistical models
The SEPEM server hosts three types of
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.
- fluence and peak flux modelling;
- time above threshold (this page);
- event duration.
The models require an underlying time series on which to base the analysis. On SEPEM there are two types of input available:
- Data tables
When a data table has been selected, the page reloads again to display a
selection menu with the available channels. Only channels with proton, ion or electron fluxes are shown.
- Response functions
When a response function has been selected, the page reloads again to
display additional selections, when applicable. For
SEU response functions, no further selection is needed. For
Mulassis response functions, the effect parameter and layer have to be specified. Response functions 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.
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.
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.
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.
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.
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.
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:
- event list: the start and stop times of the episodes during which the threshold is exceeded, plus the time integrated and peak values;
- model files: the probability curves in text format.
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:
- Distribution fits
- Duration: provides all three fits (Poisson, time-dependent Poisson and Levy) to the event duration data (regardless of which was selected) using two logarithmic axes. If the best fit distribution is not the one selected then a model re-run should be considered changing the distribution. If none of the distributions are well fit the event definition parameters should be altered (especially the minimum duration).
- Waiting time: provides all three fits (Poisson, time-dependent Poisson and Levy) to the event waiting times, defined as the time between the end of one event and the start of the next event. For this definition of waiting times to be valid for modelling, event durations must also be considered, which they are for the virtual timelines method. If the best fit distribution is not the one selected then a model re-run should be considered changing the distribution.
- Departures: provides a plot of the differences between the logarithms of the sample data in the event list and the distribution fits. The closer to zero the better and the higher size numbers are the more important for the modelling output.
- Probability curves
The confidence level is one minus the probability of exceeding given on the ordinate so 0.1 corresponds to 90% confidence, 0.01 corresponds to 99% confidence and 0.001 corresponds to 99.9% confidence that the stated peak flux will not be exceeded over the mission lifetime.
- Total duration: provides the total length of time over the various mission lengths that the input threshold is likely to be exceeded over a wide range of confidence levels on double logarithmic axes.
- Longest duration: provides the longest continuous time period over the various mission lengths during which the input threshold is likely to be exceeded over a wide range of confidence levels on double logarithmic axes.
Last modified on: 2 October 2011.