INTRODUCTION

Superposed epoch analysis (SEA) is a powerful tool used to determine the
degree, strength, and/or influence a particular variable has prior to and
during a certain event, under the assumption that the selected variable
has some degree of influence upon that type of event.  In most portions
of the United States and North America, fire events are closely
associated not only with the immediate weather patterns, but also with
overall climate trends for the past several years.  The problem to be
overcome is the quantification of the degree of influence of climate on
observed fire events: given a set of years in which climate has certain
characteristics (e.g. dry from one year to the next), what is the
likelihood that a fire event will result, and what can we say about the
possible severity of that fire event?

In fire history analyses, the event type is the record of fire years
while the variable considered largely responsible for that event (as well
as for the severity of the fire event) is climate.  In the FHX2 system,
two variables are required.  The first is a list of fire years created
using the Composite Axis Export function as described in the Graphics
Module documentation.  The second variable can be: (1) a tree-ring
chronology that spans the length of the desired period, or (2) an actual
reconstruction of a particular climate variable based on a local
tree-ring chronology.  The format for the fire event years is created by
the software, while the format for the climate or tree-ring data is
Decadal format.  Tree-ring chronologies produced by the standardization
programs CRONOL and ARSTAN produce chronologies in a format compatible
with the FHEVENT program.

In SEA, fire years are superimposed one on top of another.  The climate
prior to, during, and succeeding these fire years is also superimposed as
well, resulting in a "window" of n number of years encasing the fire year
(year "zero" in the window).  The climatic characteristics are then
averaged across all fire year events, as well as for all years prior to
and succeeding the fire year.  To determine various levels of confidence,
bootstrapping methods are employed on simulated events (windows picked at
random) to provide robust estimates based on the actual data themselves. 
Bootstrapping is preferred because of the often low number of fire events
that must be analyzed.  The result is the quantification of average
climate conditions that existed prior to and during the fire year.

To begin the SEA, select "E" from the FHX2 Main Menu or type "fhevent" at
the DOS prompt.  The SEA in the FHX2 system works in two modes.  The
first is the "direct" mode begun when running the program from the DOS
prompt.  In this situation, the user must enter all information according
to the Event Program Menu.  The second mode is "interactive," and begins
by typing "E" from the Main Menu of the FHX2 system.  The SEA Main Menu
opens, and the user can enter the options needed by the Event Program. 
Once the options have been entered, the user can select "G" from the SEA
Menu to begin the analyses.

The Event Program will always try to read input from an initialization
file prior to conducting the analyses.  If no initialization file exists,
default settings will be used, and the user must change these as required
for the analysis.  The SEA program is memory-intensive, and occasionally
may not operate from the FHX2 Main Menu.  In this case, the information
can be entered, the FHX2 system exited, and the Event program run from
the DOS prompt.  If not enough memory is available, the user may wish to
consider optimizing the memory of the computer using MemMaker (DOS 6.0
and later) or any commercially-available software (see the general FHX2
documentation for more information on memory optimization).

THE SEA MAIN MENU

After selecting "E" from the Main Menu, a new window opens for the SEA. 
All options in the window must be activated before the SEA program will
operate.  When entering information, note that the fields have certain
fixed lengths.  The program will not allow the user to enter information
over the necessary length. The following options are available in this
window:

Job ID
The Job ID must be entered by selecting "J" from this menu.  By default,
the ID is set to "ZZZ" but this may be changed by the user.  The Job ID
simply identifies a particular run of the Event program and should be
unique for each run to allow the user to identify that run.

Chronology file
This is the file that contains the independent variable, and can be
either a tree-ring chronology developed from nearby trees or an actual
climate reconstruction based on the same or nearby trees.  The chronology
file must be in an acceptable format that is internationally recognized,
such as ITRDB (the most common) or Decadal format.  If these types of
data are not easily available, the user may wish to obtain nearby
chronologies from the International Tree-Ring Data Bank (ITRDB) which
contains tree-ring data in an acceptable format.  More information about
the ITRDB can be obtained by writing: Bruce Bauer, Paleoclimate Program,
NOAA/NGDC, 325 Broadway E/GC, Boulder, CO 80303 USA, or by e-mail:
bab@mail.ngdc.noaa.gov, or by telephone 303-497-6280, 303-497-6513 (fax).

Fire events file
This is the name of the file that contains the list of fire years as
developed from the Composite Axis in the Graphics Module.  The user
should refer to that documentation for more information regarding the
exporting of the fire event information.  The file name should also be
unique and easily identifiable.

Title for this run
This option allows the user to enter a title that helps identify exactly
what is being analyzed (e.g. "MLC Reconstruction vs Malpais Fires").

Years prior to event
The next two options allow the user to identify the window of time for
the analysis based on years prior to and years following the fire event. 
With this option, the user can enter the number of years prior to the
fire event to be analyzed.  These years are of most interest in  this
analysis, because climate during these years may, in some way, have
affected the possibility of a fire event occurring.  By default, this
value is set to five years, a value found to be optimal based on analyses
conducted in the American Southwest.  The user should consider changing
this value based on current knowledge of the climate and fire system for
the local area.

Years following the fire event
This option allows the user to "close" the window.  Analyzing climate
following a fire event is useful for examining the general trend of
climate encasing the fire years.  The window must be defined to include
the fire event year in some capacity for statistical testing.  Any value
greater than one is acceptable.

Number of simulations
This option is used to designate the number of iterations used in the
simulations for the bootstrapping process to determine confidence limits. 
By default, this value is set to 1000.  For optimum analysis, the number
of simulations should always be set >500.

Beginning year of analysis
This option allows the user to enter the first year to begin the
analysis.  For ease of use and interpretation, this value is normally set
at some even value (e.g. 1600, 1750, 1800, etc.).  Note that, in the
following options, values should be entered in multiples of each other
(for example, by multiples of 50, 100, 200, etc.).  The beginning year of
the analysis can be less than or greater than the first fire year as
well.  For example, if the first fire year is 1623, the user may wish to
enter the year 1600 as the first year of analysis.

Last year of analysis
The user should enter the last year when to end the analysis.  Note that
this year can be less than the last fire year, but must be less than the
year 2005.

Starting year for segments
The SEA is conducted on segments of years.  This option allows the user
to designate on which year to begin the segment.  Usually, this value is
the same as the beginning year for the analysis.

Length of segments
By default, the segment length is set to 100 years.  The segment length
is the number of years on which to conduct the analysis.  For example, if
the beginning year for the analysis was set at 1600 and the ending year
set at 2000, with 100 year segments, then the first segment tested would
be 1600-1700.  To conduct the analysis over the full period, the segment
length should be equal to the total number of years between the beginning
and ending years.

Lag between segments
This option allows the user to lag the segments by some designated value. 
By default, this option is set to 50 years, allowing the analyses to be
conducted on 100 year segments with a 50 year overlap.  For example, in
the above example, the first segment tested would be 1600-1700, while the
second segment to be tested would be 1650-1750.  To test segments
exclusive of each other, the lag should be set to zero.

Include incomplete epochs
Occasionally, a fire event may occur close to the end of the chronology
or climatic series (i.e. the variable being investigated) such that the
number of years in the window extends beyond the end of the variable. 
The user can select whether to include these incomplete windows by
selecting "I" from the SEA Main Menu.  The default is to exclude these
incomplete epochs.

Actual/random event simulation
Two methods are available to the user for designating which type of
sampling to conduct during the simulation.  The first is actual event
simulation in which the time intervals between consecutive actual events
are calculated, then shuffled at random.  Simulated event years are then
picked with these rearranged time intervals.  The second method (the
default) is to pick simulated event years independently at random from
the variable being tested with replacement.  Note that some years may be
picked more than once.  This method is considered more statistically
sound.

Save spreadsheet/ASCII files
This option allows the output to be presented in tabular format ready for
importing into a spreadsheet or word processor.

Get/Save setting
To write all the information to the initialization file, the user should
save the settings by selecting "V" from this menu.  These may be
retrieved by selecting "G" later, and prevents the same input from having
to be re-typed.  Note that the settings are automatically saved when the
user selects "O" to run the SEA.

Go
Selecting "O" will run the SEA.  If the settings have not been saved to
the initialization file, the program will do so.  After selecting "O,"
the FHX2 system calls the program FHEVENT.  This program, by default,
will attempt to read the settings saved in the initialization file first
prior to running.

OUTPUT PRODUCED BY THE SEA MODULE

The output produced by this analysis is divided into four sections for
each segment tested.  The beginning of the output provides a summary of
the options chosen by the user.  The first part of the output provides
statistics on the climate or tree-ring variable being used ("Time Series
Statistics"). The second part of the output provides information and
summary statistics on the years prior to, during, and following the fire
years for the site being tested as designated by the window defined by
the user ("Actual Events: CBE").  This is a critical portion of the
output because the user can quickly scan the mean values in the second
column to determine the characteristics of climate during the event
window. Note also that the 95%, 99%, and 99.9% confidence limits are
provided in this portion of the output.

The third part of the output provides similar information and statistics
for the number of simulations conducted ("Simulated Events").  Windows of
similar length were randomly picked out of the entire time series and the
mean values calculated for all years, regardless whether a fire year
occurred or not.  This provides the "control" information with which to
test the information in the previous section..

The fourth portion of the output provides a graphical display of the
results.  The range of values for each year of the window is displayed as
a vertical line.  On each vertical line are symbols designating the 95%,
99%, and 99.9% confidence levels based on the simulations.  The observed
values are designated on each line as the "year" of the window.
