Fluence and peak flux 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 (this page);
- time above threshold;
- event duration.
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.
- Data tables of particle fluxes
When a data table has been selected, the page reloads again to display a
selection menu with the available particle species. All channels associated with the selected particle species will be used in the analysis. Only channels with differential proton, ion or electron fluxes are used.
- 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.
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).
- Fluence is the time integrated flux: the outputs will provide the probabilities of not exceeding a stated fluence over the complete mission duration (cumulative mission fluence) and over a single SEP event (listed as the worst-case event fluence).
- Peak flux will yield the peak intensity which will not be exceeded over a mission.
Three analysis methods have been implemented.
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.
- 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.
- 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.
- 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.
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.
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 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:
- event list (and, for the ESP fluence analysis, additionally the total fluence in active years): the start and stop times of the events within the epoch range of the selected data source, plus the time integrated and peak values for all data channels;
- model files: the probability curves in text format.
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:
- Distribution functions
- Lognormal: provides the lognormal fit to the channel data as displayed in the JPL model papers using a logarithmic ordinate and a normally-scaled abscissa.
- Truncated power law: provides the truncated power law fit to the channel data as displayed in the ESP model papers using double logarithmic axes which show the power law section as a straight line.
- Cut-off power law: provides the cut-off power law fit to the channel data as displayed in the MSU model papers using double logarithmic axes which show the power law section as a straight line.
- Comparison: provides all three fits to the channel data (regardless of which was selected) using one logarithmic axis and one linear axis. Please note that the high probability of not exceeding is the dominant portion of the fits for model outputs. If the fits are not good then the model should be re-run increasing the thresholds for the respective channels.
- Departures: provides a plot of the differences between the logarithms of the sample data in the event list and the flux 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.
- Cumulative fluence: provides the predicted mission cumulative fluence or flux integrated with time for a selection of mission durations over a wide range of confidence levels for each channel on double logarithmic axes.
- Worst case fluence: provides the predicted worst-case event fluence or the highest likely flux integrated with time for a single SEP event for a selection of mission durations over a wide range of confidence levels for each channel on double logarithmic axes.
- Worst case peak flux: provides the predicted worst-case peak flux or the highest likely flux intensity for a selection of mission durations over a wide range of confidence levels for each channel on double logarithmic axes.
- Duration fits
For the virtual timeline method, this table 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). The departure plots show the differences between the logarithms of the sample data in the event list and the duration distribution fits. The closer to zero the better and the higher size numbers are the more important for the modelling output.
- Waiting time fits
For the virtual timeline method, this table 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. The departure plots show the differences between the logarithms of the sample data in the event list and the waiting time distribution fits. The closer to zero the better and the higher size numbers are the more important for the modelling output.
Last modified on: 12 July 2013.