DENDROECOLOGY PROGRAM LIBRARY

PROGRAM EXTRAP

Users Manual by Richard L. Holmes
Laboratory of Tree-Ring Research, University of Arizona, Tucson, Arizona  USA
August 1995

USING PROGRAM EXTRAP

      Program EXTRAP projects a growth trend established in the early part of a tree-ring record and extrapolates it forward in time to predict expected ring growth.  It is generally used to determine deviation from expected growth following a known or conjectural impact on tree growth, such as a fire, insect attack, logging, or other disturbance.

Program EXTRAP asks the user the following:

      (1)  File name for the tree-ring measurements to be processed;

      (2)  Name for a new file to contain extrapolated growth curve series;

      (3)  Name for a new file to contain detrended growth index series;

      (4)  The last year of measurements to which to fit the growth curve, that is, the last year before
            the impact or disturbance.

      Program EXTRAP reads the file of tree-ring measurements, one series at a time, processes each series to yield an extrapolated growth curve and detrended indices, and saves the curve and indices respectively in two new data files while recording information on an output file for printing.

      The portion of each series of tree-ring measurements from the beginning to the year specified by the user (the base interval) is fit with a negative exponential curve (detailed below).  If such a curve cannot be fit due either to a general upward trend in the data or to a convex upward shape of the data curve, a least-squares linear regression line is computed to fit the data (detailed below).  If there are ten years of data or less in the base interval the series is skipped, since this is too few to establish a growth trend.

      The program then uses the coefficients of the negative exponential curve or regression line to produce a curve extending for the full length of the series, that is, extrapolating the curve forward in time to include the data after the impact date.

      Tree-ring measurements are divided by the corresponding growth curve values, yielding a detrended time series of indices containing the departure from expected growth.


NEGATIVE EXPONENTIAL CURVE

A modified negative exponential curve of the form:

            Y = A * e (-B * t) + D

is fit to the data set.  An iteration procedure is used, which continues until the improvement of the fit is very small.  If the fitted curve has a negative constant (D) or a positive slope (B), the curve is rejected and a linear regression is fit to the data (Fritts et al., 1969).  The coefficients of the equation are applied to the data to estimate the growth curve, and the data are divided by the estimates to obtain indices that are intended to be stationary with a mean of 1.  The negative exponential curve conforms to a theoretical decrease in annual tree growth increments due to the geometry of an increasing trunk diameter.


LINEAR REGRESSION LINE

The simplest detrending method is to fit a least squares regression line through the data:

            Y = A * t + D

It conforms to no theoretical model of tree growth, and is probably best used on series that are relatively short or that have an unusual growth pattern that the negative exponential curve cannot accommodate.


DATA FORMAT

      Program EXTRAP reads ring measurement series from a data file in standard format for ring measurements established by the International Tree-Ring Data Bank (ITRDB), known also as the Tucson format for measurements.  If the format of your data is different from this, you may change it using Program DPL/FMT (Routine FMT in the Dendrochronology Program Library).  Output data files are also in measurement format.

      ITRDB standard ring measurement format is (A8,I4,10I6) for each line, where (A8) is the series identification, (I4) the first year of data in the decade, and (10I6) a decade of ring measurements, usually in units of .01 mm.  If the first year does not end in 0, the actual first year of data is recorded, and the first spaces for measurement values contain measurements through the year ending in 9.  Succeeding lines contain full decades of measurements from the year ending in 0 through the year ending in 9.  Following the last actual data value is a dummy value of 999 to indicate the end of the series; this may require a new line with only the dummy value.  The first decade of the next series follows on the next line.


RUNNING PROGRAM EXTRAP

      Either upper or lower case may be used in responding to prompts.  At any point where a response is requested you may quit the program by responding with a slash ("/").

      The output file for printing is EXTRAP.OUT and contains page breaks, allowing it to be printed with the desired line spacing and paging on standard printers.  Data output files have names provided by the user.


ACKNOWLEDGEMENTS

      Program EXTRAP was written at the request of graduate student Linda Mutch in February 1993 by Richard L. Holmes in ANSI Standard Fortran-77.  It is modeled after an earlier program also written by Holmes at the University of Hamburg in December 1986 for Prof. Dr. Dieter Eckstein and graduate student Ursula Bentrup.  Versions of Program EXTRAP are available for the VAX and most other mainframe computers and for IBM-PC compatible computers.


REFERENCE CITED

Fritts, H.C., Mosimann, J.E., and Bottorff, C.D.  1969.  A revised computer program for standardizing tree-ring series.  Tree-Ring Bulletin 29:15-20.