DENDROCHRONOLOGY PROGRAM LIBRARY - USERS MANUAL
by Richard L. Holmes, Laboratory of Tree-Ring Research
University of Arizona, Tucson, Arizona USA
Updated November 1994
TABLE OF CONTENTS 51 pages
Introduction to the Program Library Page 2
Data formats Page 2
General comments on using the Program Library Page 3
Program menu and sample screen Page 4
Descriptions of routines:
AGE Tree growth by age Page 6
ARI Aridity indices Page 7
ARSTAN Chronology development, statistical analysis Page 9
ART Generate artificial time series Page 21
BAR Bar plots by page or in columns Page 21
CLD Climate diagrams Page 22
COF COFECHA: Dating quality control Page 23
COL Copy selected columns Page 30
COV Coefficient of variation Page 30
CRN Chronology with unlimited series Page 30
DHL Divide series high & low Page 32
EDT Edit ring measurements Page 33
FMT Change format, manipulate data Page 35
HOM Homogeneity of meteorologic data Page 36
IMP Impact before & after event Page 38
LNP Printer plot of series Page 38
LRM List ring measurements Page 38
MAT Correlation matrices Page 39
MET Estimate missing meteorology data Page 39
MIS Estimate missing ring measurement Page 40
ORD Sort in order by selected column Page 40
PCA Principal components analysis Page 40
PRT Prepare file for laser printer Page 41
REC Reconstruct time series Page 41
RES Response and correlation function Page 41
SCA Scattergrams Page 42
SCR Scrolling plot on screen Page 42
SEA Seasonalize meteorologic data Page 43
SPL Random split of data by percent Page 43
SUR Survey data file Page 44
TSA Time series analysis Page 44
VFY Verify calibration Page 44
YUR Read casewise (column) data file Page 44
YUX Make casewise (column) data file Page 45
ZZZ Switch brightness of screen Page 45
... Output: FORTRAN / Laser printer Page 46
Disclaimer Page 46
Acknowledgments Page 46
VAX, Mainframe and PC-compatible versions Page 47
References cited Page 47
Key to tasks Page 49
INTRODUCTION TO THE PROGRAM LIBRARY
The Dendrochronology Program Library (DPL) is a set of some thirty-six
interactive computer programs which perform data processing tasks and
analysis commonly carried out in dendrochronology for chronology development
and for applications in ecology, climatology, hydrology and archeology.
Versions of the DPL have been prepared for the VAX and other mainframe
computers and for PC-compatible computers. This manual describes the
routines in the DPL.
The DPL performs tasks such as crossdating quality control and
measurement verification (COF, Program COFECHA), listing of measurements for
trouble-shooting and documentation (LRM), tree-ring data editing and
correction (EDT), estimating missing (not absent) rings (MIS), and
chronology development and analysis (Programs ARSTAN and CRN).
It also deals with monthly meteorological data, estimating missing
values (MET), checking for homogeneity between stations (HOM), and
seasonalizing climatic data (SEA). Relating tree rings and climate, it
computes response and correlation functions (RES), does calibration and
reconstructions (RES and REC), and verifies the reconstructions (VFY).
Other routines do tasks such as changing data formats and preparing or
reading casewise files (FMT, YUR and YUX), principal components analysis
(PCA), constructing correlation matrices (MAT), determining the effect of an
impact on tree growth (IMP), and inventorying data files (SUR). The
remaining routines carry out other tasks occasionally needed.
DATA FORMATS
All the programs will read data in several ASCII formats, among them
the standard formats for ring measurements and indices established by the
International Tree-Ring Data Bank (ITRDB), known also as the Tucson formats.
If the format of your data is different from any of these, you may be able
to change it with routine FMT, or you may need to reformat it in some other
way. One or more lines of text may precede the data in the files as title
lines.
Most programs also provide options for the format of output data files.
Routine FMT may be used to change data from one format to another. Routines
YUX and YUR may be used to create and to read and convert data files in
column (casewise) format.
Following is a description of several formats for input and output
files. The percentage indicates the approximate space the format requires
compared to that needed by the Compact time series format.
M = ITRDB standard ring measurement format (also called the Tucson
measurement format). Precision of data is 0.01. Format for each line is
(A8,I4,10I6), 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. If this is not the last series the next line is the first decade of
the following series. (230%
3 = Ring measurement format with precision of 0.001; dummy value at the
end of the series is -9999. (230%)
I = ITRDB standard ring index or chronology format (also called the
Tucson index format). Format for each line is (A6,I4,10(I4,I3)), where (A6)
is the chronology identification, (I4) the first year of the decade, and
(10(I4,I3)) a decade of chronology indices in units of .001, followed by the
number of tree-ring series represented by the index. If the first decade is
incomplete, the date is the beginning year of the decade ending in 0, and
the first spaces are filled with dummy values of 9990 and series numbers of
0. Following the last actual data value the decade is filled to the end
with dummy values as at the beginning of the first decade. There must be at
least one dummy value to indicate the end of the chronology, even if this
requires a new line. The first decade of the next chronology follows on the
next line. (260%)
A = Accurite ring measurement format. The DPL reads this format but
does not use it to produce new files.
C = Compact time series format. This format is recommended for most
time series because it is not limited by the scale of the data and it
conserves precision at any scale. The first line shows the number of values
and the date of the first value, followed by the series identification. To
the right is the power of ten to which the data are to be multiplied, the
data format and a code in the last column to indicate the type of format.
The format is adjusted by the program creating the file to conserve
precision while making efficient use of space. (100%)
1 = Single column of values.
2 = Two columns: year, value.
V = Two columns: value, year. Each value is identified with the year
in the second column, and series identification may appear to the right of
the first year. (530%)
S = Spreadsheet or casewise format. The DPL can both read existing
files and write new files in this format.
T = Meteorological data format, either University of Arizona style
(I4,12I5) or Lamont-Doherty style (I5,12I5). The first value is the year of
data, and the (12I5) values are monthly meteorological data read as
(12F5.1). (172%)
X = Format specified by the user. Specify the format for real
(floating point) data and include parentheses. If it is an input file, give
the number of data values. For example, the data format you would specify
for the meteorological data format is (4X,12F5.1), and if there are twenty
lines of data, respond 240 to the prompt for the number of values.
GENERAL COMMENTS ON USING THE PROGRAM LIBRARY
Either upper or lower case letters may be used in responding to
prompts. The program may be terminated at any time you are prompted for a
reply by typing a slash ("/") followed by (Enter).
Certain routines (COFECHA, ARSTAN, CRN, RES and several others)
request a run identification code of up to three letters or numbers to
identify output for printing and data files produced by the program. use
the code as the first letters of output data files. Responding with
will cause the default identification "ZZZ" to be used. New files produced
by the program combine the identification code with the routine code, and
add an extension according to the type of file, for example, ZZZCOF.OUT or
ZZZCRN.DAT.
When opening an existing file the first few lines are shown on the
screen. The program tries to determine the data format of the file. If the
determination is correct, touch , otherwise respond "N" and give the
code for the correct format from the choices listed. If the file is not to
be read as data (such as text), simply touch .
Output files for printing are identified by the extension *.OUT and
have FORTRAN carriage control, allowing them to be printed with the desired
line spacing and paging on standard line printers. Data output files have
list carriage control, so they may be typed on a screen or printed without
causing a page break when a line begins with the number "1". Files may be
prepared for printing on most printers by selecting the "..." option on the
first menu, before selecting the routine to run, or by running the output
for printing through routine PRT.
On the VAX/VMS operating system, command files may be prepared to run
one or more programs automatically as a batch. By convention these files
have the extension ".COM". The first line for each program run is a system
command beginning with a dollar sign ("$"), and the following lines are
responses exactly as you would give to the interactive program, including
responses of alone, one response per line. Program runs may be chained
together by starting with a new system command after the end of the lines
the program will read.
PROGRAM MENU AND SAMPLE SCREEN
Routines in the DPL are accessed by typing DPL and selecting the
desired routine from the menu. Programs such as ARSTAN, EVENT, EARLAT,
EXTRAP, OLDCORE, OUTBREAK, SPANFIRE, SSA and SSIZ stand alone and do not
appear on this menu. They are executed by typing DPL and the program name
(see below).
A sample run of Program COFECHA is shown here for illustration.
Responses by the user are in bold type. Some lines which appear on the
screen are omitted for brevity.
$> DPL
DENDROCHRONOLOGY PROGRAM LIBRARY
*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*
AGE Tree growth by age MIS Estimate missing ring measurement
@@@ ORD Sort in order by selected column
ARI Aridity indices PCA Principal components analysis
ART Generate artificial time series @@@
BAR Bar plots by page or in columns PRT Prepare file for laser printer
CLD Climate diagrams REC Reconstruct time series
COF COFECHA: Dating quality control RES Response and correlation function
COL Copy selected columns SCA Scattergrams
COV Coefficient of variation SCR Scrolling plot on screen
CRN Chronology with unlimited series SEA Seasonalize meteorologic data
DHL Divide series high & low SPL Random split of data by percent
EDT Edit ring measurements SUR Survey data file
FMT Change format, manipulate data TSA Time series analysis
HOM Homogeneity of meteorologic data VFY Verify calibration
IMP Impact before & after event YUR Read casewise (column) data file
LNP Printer plot of series YUX Make casewise (column) data file
LRM List ring measurements ZZZ Switch brightness of screen
MAT Correlation matrices ... Output: Fortran carriage control
MET Estimate missing meteorology data (DPL version 1.04V Day count 21671)
*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*
Select the program to run: COF
Identify job (up to 3 letters): RML
DENDROCHRONOLOGY PROGRAM LIBRARY
---------------------------------------------------------------
COF COFECHA: Dating quality control 17:07 Sat 30 APR 1994
---------------------------------------------------------------
Job RMLCOF
CROSSDATED TREE-RING SERIES
-> Name of EXISTING file: CPP.RWM
First 6 lines file CPP.RWM
Crystal Cave, CA (Ponderosa pine) 1670m to 1753m SW-W [21SEP92-1126]
169=N 1752=I CPP01A -2(26F3.0)~
437285346306262247346300275322196221183169197296302260346373506411438275226228
265287273314260147388410312393268503327288388439351126201315215277252308315311
355201298241196201232205159274224211225164210153211164121113 71153186150189 95
92144152 84123 96137130 94126139 55 98 59 59 74 34 19 42 37 65 64107128174159
....:....1....:....2....:....3....:....4....:....5....:....6....:....7....:....8
Title:
Crystal Cave, CA (Ponderosa pine) 1670m to 1753m SW-W [21SEP92-1126]
Time series span 1696 1990 295 years 40 series
File to print is RMLCOF.OUT
COF COFECHA: Dating quality control 12:16 Wed 27 APR 1994
- = [ COF ] = -
The start of a run of Program EVENT is shown here for illustration.
Responses by the user are in bold type. Note that in this example a slash
is used to exit the program before normal termination.
$> DPL EVENT
*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*
DENDROECOLOGY PROGRAM LIBRARY
P R O G R A M E V E N T
SUPERPOSED EPOCH ANALYSIS
Version 1.33V
*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*
Each year in a list of event dates is taken as a key or zero window year.
Time series values for event years and for a window of years before and after
the event years are superposed and averaged over the chronology time span.
Random simulation determines the significance of the relationship.
Identify job (up to 3 letters): RML
Provide the names of two files with
(1) Chronology or reconstruction; and
(2) List of event years in a column
CHRONOLOGY or RECONSTRUCTION
-> Name of EXISTING file: /
Exit
The following pages describe each routine.
Routine AGE Tree growth by age
Computes functions of tree growth by age of the tree rather than by a
dated chronology. Measured tree-ring series are assigned ring numbers
corresponding to the age of the tree when the ring was formed rather than a
calendar date.
For each series the initial "year" will not be a date, but the ring
number or age of the tree when that ring was produced. The first ring
outside the pith is counted as ring number one. If the pith is not present
on the sample, the ring number must be estimated. Routine EDT may be used
to adjust the initial ring number of each series.
Incremental and cumulative tree diameter and basal area are computed
and extrapolated to pith (year 1). Cubic smoothing splines with a rigidity
specified by the user are fit to provide smoothed series as well. Relevant
statistics are printed, and if desired the individual series of these
parameters are saved on disk files.
Routine ARI Aridity indices
Calculates various monthly and annual indices of aridity, also known
as bioclimatic indices, using monthly temperature and precipitation data.
The following indices are derived, generally using temperature in *C and
precipitation in mm.
Abbreviations used in the formulas:
Ta = Mean annual temperature (*C)
Tm = Mean monthly temperature (*C)
Pa = Total annual precipitation (mm)
Pm = Total monthly precipitation (mm)
TK = Temperature in degrees Kelvin (absolute)
MaxK = Mean maximum temperature of the warmest month in *K
MinK = Mean minimum temperature of the coolest month in *K
TF = Temperature in *F
Pi = Precipitation in inches
Lang's pluviofactors.
Annual index = Pa / Ta
De Martonne's annual and monthly aridity indices, a measure of the
effectiveness of precipitation or of aridity of a region.
Annual index = Pa * .1 / (Ta + 10)
Monthly index = Pm * 1.2 / (Tm + 10)
Emberger's annual coefficients, using the difference between the mean
maxima of the warmest month and the mean minima of the coolest month.
Temperatures are converted to Kelvin.
Annual coefficient =
Pa * 1000 / (((MaxK + MinK) / 2) * (MaxK - MinK))
Thornthwaite's annual P/E indices, precipitation effectiveness.
Index = Sum (n=1,12) of (Pmn * 1.64) / (Tmn + 12.2)
Thornthwaite's annual P-E indices of long-term effectiveness of
precipitation for plant growth. Temperatures below -2*C are taken as
-2*C. P-E indices over 40 are taken as 40.
Index =
10 * Sum (n=1,12) of 11.5 * (Pmin / TmFn - 10)x(10/9)
Thornthwaite's moisture provinces, from the P-E index (1931) revised in
1948 to use the moisture index. Both the classifications of 1931 and 1948
are calculated.
Thornthwaite's heat index, a function of low temperatures under cold
conditions, increasing exponentially with increments in temperature.
Index = Sum (n=1,12) of (Tmn / 5) 1.514
Thornthwaite's annual indices of long-term effectiveness of temperature
for plant growth, or thermal efficiency (T-E) index. Negative indices are
taken as zero.
Index = Sum (n=1,12) of (TmFn - 32) / 4
Thornthwaite's temperature provinces, from the T-E index (1931) revised
in 1948. Both the classifications of 1931 and 1948 are calculated.
Bhalme and Mooley annual drought index (BMI) for a selected span of
months.
Program DPLARS ARSTAN -- Chronology development, statistical analysis
A R S T A N
Guide for computer program ARSTAN, by Richard L. Holmes and Edward R. Cook
Adapted from Users Manual for Program ARSTAN, in Tree-Ring Chronologies of
Western North America: California, eastern Oregon and northern Great Basin,
by R. L. Holmes, R. K. Adams and H. C. Fritts, Laboratory of Tree-Ring
Research, University of Arizona, 1986, pages 50 to 65.
INTRODUCTION
Program ARSTAN produces chronologies from tree-ring measurement series
by detrending and indexing (standardizing) the series, then applying a
robust estimation of the mean value function to remove effects of endogenous
stand disturbances. Autoregressive modeling of index series often enhances
the common signal. Extensive statistical analysis of a common time interval
provides characterization of the data set. Three versions of the chronology
are produced, intended to contain a maximum common signal and a minimum
amount of noise. Many options are provided to enable you to tailor the
processing to a wide variety of situations and purposes.
The concept and methodology of Program ARSTAN were developed by Dr.
Edward R. Cook at the Tree-Ring Laboratory, Lamont-Doherty Earth Observatory
of Columbia University, Palisades, New York. ARSTAN includes several
concepts not previously applied to tree-ring chronology development. In
1983 Dr. Cook provided the source code for Program ARSTAN to the Laboratory
of Tree-Ring Research at the University of Arizona, where Richard L. Holmes
updated the program to ANSI standard FORTRAN-77 and in collaboration with
Dr. Cook developed several enhancements.
RUNNING PROGRAM ARSTAN
Your disk space must be sufficient for the output file for printing,
the data files to be produced, and temporary files created during execution.
If available, a scratch disk may be used; this provides large temporary
working space.
At the beginning of program execution you will be asked for initials to
identify printed output and other files produced by the program ("ZZZ" is
the default set of initials). Either upper or lower case may be used in
responding to prompts.
ARSTAN will ask for the name of the file containing the tree-ring
measurements. Next provide a title of up to 80 characters to identify this
run of the program and the chronology and other data files produced.
The menu shows current settings of values for controlling program
execution. Items in the menu are: (Initial setting appear below in
italics)
(1) Information on series in the file
(Informative only)
(2) Detrending methods (spline, least-squares regression line, negative
exponential curve or horizontal line)
(1 & 128: Detrending is negative exponential then 128-year spline)
(3) Interactive detrending of series
(Not interactive)
(4) Special treatment for selected series
(0 series for special treatment)
(5) Stabilize variance (of detrended series, chronology or both)
(No stabilization, method 0 used)
(6) Method of computing indices (division or subtraction)
(Division)
(7) Print plots of series showing 10-year means
(Not printed)
(8) List values in series on printout
(No listing)
(9) Save detrending curves, detrended series and residuals
(Not saved)
(10) Columns in series identification which identify a tree
(Columns 1 through 5)
(11) Tree summaries produced
(Not produced)
(12) Method of autoregressive modeling (same order for all, each series with
its order, constrained order or no modeling)
(Same order for all)
(13) Method for chronology computation (robust mean or arithmetic mean)
(Robust mean)
(14) Year-by-year list of chronology indices with statistics on indices
(Year-by-year list is printed)
(15) Common interval analysis of the red-noise fraction of the data (common
interval analysis of detrended series and white-noise fraction is done
automatically)
(No analysis of red-noise fraction)
(16) Number of principal components and amplitudes to save
(6 components and amplitudes saved)
Any of these values may be changed by first typing the number at the
left, then responding with the modifications desired. When no more changes
are to be made, touching alone begins processing of the data.
You have the choice of either typing in a mask for the chronology, or
allowing the program to separate trees automatically by columns in the
identification (item 10 of the menu); in the latter case just touch .
The program will compute the optimum common interval containing the
maximum possible number of data (length of common interval times number of
series included). You may accept this common interval by touching or
override the beginning and ending dates supplied by the program.
During program execution brief messages are printed on the screen to
keep you posted on the progress of the program. The full results are in the
printout file and the chronology and other data are in additional files. At
the end of execution a list is shown of files created.
CONTROL PARAMETERS IN THE MENU:
(1) Information on series in the data file. This is purely informative,
displaying the series identification, first and last year, and the length of
the series.
(2) Detrending methods
First detrending; the following options for detrending have these
effects:
1: A negative exponential curve is fit, or if it fails, a linear
regression line is fit.
2: A negative exponential curve is fit, or if it fails, a linear
regression line of negative slope or a horizontal line through the mean is
fit.
3: A linear regression line is fit.
4: A horizontal line is fit through the mean (no detrending).
5 or greater: A smoothing spline is fit with 50% frequency cutoff
of this many years.
-1: No detrending or division by the mean: measurement series are
not transformed.
Negative: A smoothing spline is fit with stiffness of this percent
of the series length. For example, if detrending is -75, the 50% cutoff
frequency is 75 percent of each series length.
0: Only a table of measurement series statistics is produced;
there is no detrending or chronology.
Second detrending option:
Curve-fitting options are the same as described for first
detrending. If you select zero, no second detrending is done.
Prior to detrending, series may be log-transformed after adding a
constant equal to one-sixth of the series mean.
The series may be normalized after detrending. If desired, the
variance of all series may be set to 1.0, thus weighing all series equally
in the chronology, whether actually complacent or sensitive.
The relative stiffness of the alternate smoothing spline may be
specified. If the curve specified for the first detrending cannot be fit,
the second detrending spline stiffness is this percent of the smoothing
spline indicated for the second detrending. For example, if the first
detrending is 1 (negative exponential curve), the second detrending is -100
(smoothing spline of stiffness equal to the series length), and the relative
stiffness is 67, first detrending is a negative exponential curve and second
is a spline of stiffness equal to the series length N x 1.0. If the
negative exponential curve cannot be fit, the first detrending is a
regression line and the second is a spline of stiffness equal to the series
length N x 1.0 x .67
The minimum smoothing spline stiffness may be set; the spline stiffness
will never be less than this value. One may not wish to fit a very flexible
spline to short series in order to conserve in the series a persistence
structure similar to that of the longer series.
(3) Interactive detrending permits you to see how the detrending curve fits
each series and to try different methods until satisfied with the result.
Statistics of the detrended series are displayed. You may cancel the
interactive detrending at any time during the run and the program will
proceed automatically, using the detrending options selected from the menu.
(4) It may be necessary to deal with some series differently. This option
enables you to indicate certain series for special treatment. The
treatments that can be specified include exceptions to the above general
curve-fitting procedure, truncation of data at either or both ends or
omission from processing. You are prompted for the treatment desired for
the selected series. Note that the series identifications are case-
sensitive.
(5) Stabilization of variance. Sometimes it is a characteristic of a site,
a species, or certain trees, that the variance changes a great deal through
time. In this situation you may wish to modify the series so that the
variance does not fluctuate so much. Program ARSTAN allows you to request
variance stabilization of each detrended index series, of the chronologies
only, or both. Options for variance stabilization include those for
detrending plus a square root transform or a log transform after adding a
constant of one-sixth of the series mean to each value.
We recommend the use of a cubic smoothing spline if the variance will
be stabilized. Here a spline is fit through the absolute departure values
from the mean and the series is divided by the spline curve values. One way
of picturing this is to imagine normalizing the detrended series to a mean
of zero, flipping the negative departures to positive (keeping track of
these), and fitting a spline to this series. The departures are divided by
the respective spline values, and the indices whose departures were
originally negative are given a negative sign. Finally the mean of the
series is added back in to yield a series with stabilized variance.
(6) Options for computing indices:
Division (ratio): measurement divided by curve value.
Subtraction (residual): measurement minus curve value.
(7) Line printer plots may be printed showing means by decade (or by a
period you specify) of measurements, detrending curves and indices for each
series.
(8) Values in individual series may be listed. You may select to list ring
measurement series, detrended index series, and/or residual series from
autoregressive modeling.
(9) Individual series may be saved on disk files in compact or measurement
format.
(10) Columns of the series identification which identify a tree. This is
used by the program in the common interval analysis and to compute tree
summaries if requested. The default columns are 1 to 5, which implies that
the first three columns are a site code and columns four and five are the
tree number. For example in a series identified as ABC08A, ABC is the site
code, 08 is the tree number, and A is the radius within the tree.
(11) You may request summaries (chronologies) of each tree. Series that
belong to the same tree are determined by the chronology mask or by the
portion of the series identification which designates the tree. The
summaries are computed by arithmetic mean and saved in the file ZZZARS.TRE.
(12) Options for autoregressive modeling method:
S: The same order autoregressive process as selected by
multivariate autoregressive modeling may be fit to each series using its
own coefficients. This is the default method.
E: Each series may be modeled as an autoregressive process where
the order is selected for the individual series by first-minimum Akaike
Information Criterion search.
C: You may override the first-minimum Akaike Information Criterion
search by specifying the order to be fit to each series.
N: You may specify that no autoregressive modeling be done. The
chronology is then computed by the standard method only.
The next question is which series to use for computing the pooled
autoregression model (default is to use all series). Responding "N"
indicates that a subset of the series is to be used. You are then prompted
to provide a mask to indicate which series are to be included in the model.
Each column of the mask corresponds sequentially to the respective series.
Enter a '1' if the series is to be used, or a '0' if it is to be bypassed.
This option may be invoked if there is reason to believe that a subset of
the series is uncontaminated by disturbance and therefore has a clean
stochastic structure for modeling and for producing the 'ARSTAN' chronology.
(13) Chronology computation may be done by means of a biweight robust mean
estimation (default), by arithmetic mean value function, or no chronology
may be requested.
(14) The printout lists each annual index of the chronology with statistics
and a line-printer plot. You may suppress printing this list.
(15) If you wish, the common interval analysis will include analysis of the
red noise fraction of the series (detrended series minus residual series).
(16) You may specify the number of eigenvectors and principal component
amplitudes to be calculated for the common interval, printed and saved in
file ZZARS.AMP. If the number entered is greater than the number of series,
all possible are saved. The default is six saved.
CHRONOLOGY COMPUTATION
You may use all series for the chronology (default), or select series
to be included. If all series are to be used, the series belonging to the
same tree may be determined automatically by the program for common interval
analysis and/or tree summaries by leaving the chronology mask blank (see
item 10 in the menu above).
If not all series are to enter the chronology, or an inconsistent
method is used for identifying trees, a mask is entered into columns 1 to
80. Each column corresponds to a series sequence number. For common
interval analysis, series from a given tree are coded sequentially '1', '2',
'3', etc. This coding is necessary for calculating the average correlation
for pairs within and between trees, and for computing the signal-to-noise
ratio. Zeroes embedded in the mask cause those series to be excluded from
the chronology.
COMMON INTERVAL ANALYSIS
Program ARSTAN will compute the optimum common interval, containing the
maximum possible number of data in a rectangular matrix (length of common
interval times number of series). If this is acceptable, respond with ;
otherwise type "N" and provide first and last years for the desired common
interval analysis.
WHAT PROGRAM ARSTAN DOES
Program ARSTAN performs the following tasks:
(1) These files are opened in ITRDB index (I) format or Compact (C) format
and may be saved for future use:
ZZZARS.OUT Output for printing
ZZZARS.CRN Tree-ring chronologies (I)
ZZZARS.SDV Standard deviations of chronology indices (C)
ZZZARS.AMP Principal component amplitudes (C)
ZZZARS.MSM * Ring measurement series (C)
ZZZARS.CV1 * First detrending curves (C)
ZZZARS.IN1 * Series after single detrending (C)
ZZZARS.CV2 * Second detrending curves (C)
ZZZARS.IN2 * Series after second detrending (C)
ZZZARS.RSD * Residuals from autoregressive modeling (C)
ZZZARS.TRE * Summary (chronology) of each tree (I)
ZZZARS.PLO * File for plotting in Program PAGEPLOT (M)
* (File created on request only)
(2) The menu is printed showing the run control options you have specified.
(3) Ring measurement data series are read. For each series:
(a) Detrending is performed as specified. A curve is fit to each
measurement series to model biological growth trend, and the measurement
values are divided by the curve values to produce a detrended series.
(b) Decade means plots are printed if requested.
(c) Variance of the series is stabilized if requested.
(d) The detrended series is saved on disk file if requested.
(4) Ring measurements and/or indices of each series are listed if
requested.
(5) Statistics of each series before and after detrending are printed.
(6) Multivariate autoregressive modeling is performed. The following are
computed in the autoregressive modeling:
(a) Lag-product sum matrices
(b) Pooled lag-product sums
(c) Pooled autocorrelations
(d) Yule-Walker estimates of pooled autoregression
(e) Akaike Information Criterion (AIC)
(f) Autoregression coefficients based on first-minimum AIC search
(unless constrained) and selected autoregressive modeling order
(g) Impulse response function weights of the pooled autoregression
process
(h) Box-Pierce two standard error limits of residual
autocorrelation function based on the pooled autoregression coefficients.
(7) Univariate autoregressive modeling is performed, fitting an
autoregressive process of the selected order to each series, and the
following are computed for the residual series:
(a) Statistics for each series;
(b) Autoregressive coefficients for each series and the variance
explained by autoregression;
(c) Normalized residuals which are outliers over three standard
deviations from mean.
(8) Multivariate autoregressive modeling is performed on the residual
series to determine if residual multivariate lag effects remain. The
following are computed as before:
(a) Lag-product sum matrices
(b) Pooled lag-product sums
(c) Pooled autocorrelations
(d) Yule-Walker estimates of pooled autoregression
(e) Akaike Information Criterion (AIC) and selected order of
autoregression.
If no significant multivariate persistence remains after the univariate
fitting, the selected autoregression order is now zero.
(9) The 'STNDRD' version of the chronology is computed. Detrended
(standardized) tree-ring index series are combined into a mean value
function of all series or of those selected in the chronology mask. Means
for each year are computed as either the biweight robust estimate or the
arithmetic mean (Cook, 1985). The biweight mean is an integral part of the
ARSTAN methodology and is strongly recommended to remove effects of
endogenous stand disturbances and to enhance the common signal contained in
the data. Statistics on the chronology are printed, including the
distribution of values, autocorrelation structure and the gain or loss in
efficiency of robust estimation of the mean. If you request that no
autoregressive modeling be done, this is the only version of the chronology
produced.
(10) The 'RESID' (residual) version of the chronology is computed in the
same manner as the STNDRD version, this time using the residual series
resulting from step (7) above. Robust estimation of the mean value function
produces a chronology with a strong common signal and without persistence.
The same statistics are also printed for this chronology.
The portion of the residual chronology containing four or more series
is modeled up to the autoregressive order selected in the first multivariate
autoregressive modeling in step (6f). If the first-minimum AIC search
results in a selected order greater than zero, the entire residual
chronology is whitened using the auto-regressive coefficients from this
modeling. Statistics on the resulting white noise residual chronology
version are printed, including distribution of values and autocorrelation
structure.
(11) Using the autoregressive coefficients selected in the first
multivariate autoregressive modeling in step (6f), the pooled autoregression
(persistence) model is reincorporated into the residual chronology to
produce the 'ARSTAN' chronology. Statistics on the chronology are printed,
including distribution of yearly values and autocorrelation structure.
(12) A comparison is made between the 'STNDRD' and 'ARSTAN' versions of the
chronology to determine if the standard error has been reduced in the
chronology by autoregressive modeling.
(13) A common interval analysis is done with all detrended series covering
the time interval specified for this analysis. This interval may be the
optimum computed by the program or an interval you specify. The optimum
common interval is the maximum time span which is covered by the maximum
number of radial index series (the largest rectangular matrix). It is the
period of time for which this product of the length of the interval times
the number of series completely covering this interval is the greatest.
This effectively omits from the analysis those spans of years for which
there is a minimum of comparative data. The resulting interval contains the
greatest number of tree rings possible for analysis.
If autoregressive modeling is done, the common interval may be
shortened in the early part by a number of years equal to the order of
autoregressive modeling, in order to include the same series in this
analysis and in the residual analysis described in (14) below.
The following are computed for the detrended series for the common
interval:
(a) statistics on individual detrended series and on the 'STNDRD'
chronology version;
(b) correlations between each series and the chronology;
(c) average correlation for all pairs of series: those between
trees, those within trees and those between the series and the chronology;
(d) signal-to-noise ratio based on number of trees;
(e) estimated agreement of the sample chronology variance with
that of the theoretical population chronology, and of samples of reduced
replication (Wigley, Briffa and Jones, 1984);
(f) eigenvalues, eigenvectors and amplitudes for the requested
number of principal components; these are written on the *.AMP file.
(14) A common interval analysis is carried out as in step (13), using the
individual residual series and the 'RESID' chronology version. The residual
series are the results of autoregressive modeling of the detrended series
and contain approximately equal amounts of variance at all wavelengths; by
analogy to light wave frequencies these are white noise series, and the
analysis describes the white noise fraction of the unmodeled individual
series and chronology.
(15) If red-noise fraction analysis is requested, the residual version
(autoregressively modeled) of each series and the chronology used in (14) is
subtracted from its detrended version used in (13) to produce series
containing only the variance that was removed by autoregressive modeling. A
common interval analysis is done on these series.
(16) Each version of the chronology is printed in the standard format for
publication.
(17) A one-page summary is produced of key statistics of the chronologies.
The summary may be photocopied for your file.
COMMENTS ON RUNNING PROGRAM ARSTAN
In Program ARSTAN, careful selection should be made among the available
options. Do not rely on the initial settings as the recommended method.
Detrending is intended to remove overall trend in tree-ring measurement
series, and to remove part of the variance at very low frequencies
approaching the length of the series. Information on climatic variance at
these very low frequencies is not contained in the time series in any case.
Detrending causes the time series characteristics of the various measurement
series to be more similar to each other, and prepares them for subsequent
autoregressive modeling. If the detrending is successful in accomplishing
the task of removing a large proportion of the non-climatic variability,
autoregressive modeling may only marginally change the time series
characteristics of the 'STNDRD' chronology version when producing the
'ARSTAN' version.
Fritts (1976, p. 254-290) discusses the concept and reasons for
detrending tree-ring series. Further discussion is given by Holmes et al.
(1986) in sections titled "Standardization and chronology development,"
"Effects of undiscovered absent rings" and "Evaluating standardization
procedures," and in Appendix 2.
In detrending, three curve-fitting techniques are commonly used:
(1) 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
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 but the fit is often better in the early part
than in the later part of the time series.
(2) LINEAR REGRESSION LINE.
The simplest detrending method is to fit a least squares regression
line through the data. 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.
(3) CUBIC SMOOTHING SPLINE.
This method smoothly fits a succession of cubic polynomial curves to
the data in one pass; it is not an iterative process. It follows the path
of the data much as a draftsman's flexible ruler would do. Its elegance
lies in its predictability and in the certainty of its time series behavior.
The amount of variance to be removed at a particular frequency can be
precisely specified; it will remove variance of lower frequencies (longer
wavelengths) with a transition to little or no removal of variance of higher
frequencies (shorter wavelengths). Thus its flexibility can be exactly
specified and is almost infinitely adjustable. In Program ARSTAN, the
flexibility specified is the 50 percent cutoff wavelength (Cook and Peters
1981).
When plotting tree-ring data and the curves fit to them we have
observed that frequently the curves do not fit ideally. When the data
appear to be a typical "die-away" process a negative exponential curve often
fits well the earliest third or so of a series where the slope is steeply
negative and the curvature is strong. Toward the middle and later parts of
the series it may tend to ride along for many decades almost entirely above
or below the actual values of tree growth, yielding long stretches of low or
high indices. On the other hand, a very stiff cubic spline (50 percent
frequency cutoff at 300 years or more) may follow the data far better than
the negative exponential curve for the later two-thirds of the series, but
it may be too stiff to follow the bend in the steeply downward trending
early part of the series.
A two-stage process of detrending frequently solves this problem by
first fitting a negative exponential curve, then fitting to the resulting
indices a cubic spline of a stiffness adequate to follow the local mean of
the data without removing variance in the desired range of frequencies, and
again calculating the indices.
When you give a number for spline rigidity a table is printed on the
screen and on output showing the distribution of variance at several
wavelengths, for example:
Rigidity of SPLINE <32>: 20
Percent of variance in indices from spline where
indices contain 50.00% of variance at wavelength of 20.00 years
Wavelength Variance Wavelength Variance Wavelength Variance
6.34 99.0% 15.19 75.0% 28.29 20.0%
8.01 97.5% 16.81 66.7% 34.64 10.0%
9.59 95.0% 20.00 50.0% 41.76 5.0%
11.54 90.0% 23.79 33.3% 49.98 2.5%
14.14 80.0% 26.32 25.0% 63.09 1.0%
VERSIONS OF THE CHRONOLOGY
The *.CRN file created by the program contains three versions of the
site chronologies with different time-series characteristics.
(1) 'STNDRD' version.
A chronology is computed of series of tree-ring data that have been
detrended by curve-fitting to remove a large part of the variance due to
causes other than climate. Program ARSTAN provides several choices of how
this chronology is computed: single or two-stage detrending of measurement
series may be done with a variety of options; indices for a series may be
computed either as ratios (by division) or as residuals (by subtraction);
variance may be stabilized; and the mean value function may be computed
either as arithmetic means or as biweight robust estimated means to remove
effects of endogenous stand disturbances and to enhance the common signal.
If no autoregressive modeling is done, the STNDRD chronology is the only
version produced.
(2) 'RESID' version.
The residual version is produced in the same manner as the STNDRD
version, but in this case the series averaged are residuals from
autoregressive modeling of the detrended measurement series. Robust
estimation of the mean value function produces a chronology with a strong
common signal and without persistence.
If modeling of the residual chronology reveals that it is an
autoregressive process, the chronology is whitened by modeling the portion
of the chronology containing four or more series, and applying the model to
the entire residual chronology. This produces the 'RESID' version. If the
initial residual chronology is not an autoregressive process it is not
modeled. The earliest date of the RESID version may be one or more years
later than the STNDRD, depending on the order of the AR model and of the
rewhitening process.
(3) 'ARSTAN' version.
The pooled model of autoregression is reincorporated into the RESID
version to produce the ARSTAN chronology. The pooled autoregression
contains the persistence common and synchronous among a large proportion of
series from the site, without including that found in only one or a very few
series (Cook, 1985). It is intended to contain the strongest climatic
signal possible. The earliest date of the ARSTAN chronology is usually the
same year as the STNDRD, or if the RESID version required whitening, it is
intermediate between the STNDRD and RESID versions.
EIGENVALUES, EIGENVECTORS AND PRINCIPAL COMPONENTS
If common interval analysis is done, the eigenvalues and the requested
number of eigenvectors and principal component amplitudes for the common
interval are written on the *.AMP file (default is to save four series).
Eigenvalues, eigenvectors and principal component amplitudes are produced
independently for the detrended series and the residual series.
FLOW CHART FOR PROGRAM ARSTAN Output files*
Read file of ring measurement series * * *
*
Perform first detrending on each series
* First curve fit: _ARS.CV1*
* Indices from first curve fit: _ARS.IN1*
*
Perform second detrending on each series (default)
* Second curve fit to first indices: _ARS.CV2*
* Indices from second curve fit: _ARS.IN2*
*
Stabilize variance of each series (optional)
* Indices with variance stabilized: _ARS.IN2*
*
Edit some series within program (optional)
* Ring measurements, edited: _ARS.MSM*
*
Compute pooled autoregressive model of persistence for the entire site
(default)
*
Model each series to the selected autoregressive order
* Residuals from autoregressive modeling: _ARS.RSD*
*
Tree-ring chronologies are produced in three versions:
*
Compute STANDARD chronology using robust (or arithmetic) estimation of mean
of detrended series
* Standard chronology: _ARS.CRN (or _ARS.STD*)
Compute RESIDUAL chronology using robust (or arithmetic) estimation of mean
of modeled series;
rewhiten residual chronology if it has significant autocorrelation
* Residual chronology: _ARS.CRN (or _ARS.RES*)
Return the pooled persistence model to the residual chronology to produce
the ARSTAN chronology
* ARSTAN chronology: _ARS.CRN (or _ARS.ARS*)
*
Perform statistical analysis of a common time interval
Statistical analyses of tree-ring series are performed for a time interval
entirely covered by many or most or occasionally all of the series. The
interval may be a time span selected by the user or the optimum time span
calculated by the program. The optimum span is that which includes the
largest possible number of rings, calculated as the length of the span in
years times the number of series covering the span.
Common interval analyses are done separately on the detrended ring-
measurement series and on the autoregressively modeled series (white noise),
and at the user's option, on the difference between the detrended and the
modeled series (red noise).
Principal components analysis is done for each common interval analysis
Eigenvalues, eigenvectors and principal components: _ARS.AMP
A large variety of statistics is calculated and written on the output for
printing. The chronologies are listed and the last page is a summary of
statistics.
* * * Output for printing: _ARS.OUT
* _ARS.xxx underscore stands for the user's three-letter identification.
* _ARS.xxx* Starred files are produced only at the user's request.
Routine ART Generate artificial time series
Generates a file of artificial time series to simulate tree-ring or
other series. A random series is first created, with which all artificial
series will "crossdate."
The normality of the distribution depends on the number of random
values with a flat distribution (all values equally probable) that are
averaged to approximate a normal distribution. Around 12 values gives a
distribution close to normal. The fewer the number of values averaged the
flatter is the distribution; the greater the number of values averaged, the
more the distribution clusters around the midpoint.
Three types of distribution may be chosen:
0: Normalized, with mean of zero.
1: Indexed, with mean of one.
2: Negative values are changed to positive, giving a positively
skewed distribution.
3: A constant is added to values in the time series to raise the
smallest value to zero, thus there are no negative values.
You give the first and last year of each series, and provide an
approximate first-order autocorrelation. Choose a proportion of noise to be
added, which will make the series correlate less well with others as more
noise is added. A cosine wave may be added to the series, specifying
period, phase and magnitude of the wave.
Each series of generated data is self-documented and an unlimited
number of series may be produced.
Routine BAR Bar plots by page or in columns
Makes bar plots of tree-ring or other time series in the same style as
the bar plot of the master dating chronology produced in Program COF
(COFECHA). In a file containing several series you may elect to plot or
skip each series.
Routine BAR produces bar plots page by page as in Program COFECHA; or
in continuous columns, up to ten in parallel on the page.
Each series is filtered by fitting a flexible cubic smoothing spline,
then dividing the series by the spline curve values to remove trend and long
waves. The resulting plots are similar to skeleton plots, except that
longer bars in a bar plot indicate wide rings rather than narrow ones as in
a skeleton plot.
The plot shows the date of each ring and its relative width by the
length of the bar. At the end of the bar is an alphabetic code: each letter
progressing through the alphabet indicates a quarter standard deviation from
the local mean. Lower-case letters indicate rings narrower than the local
mean, upper-case letters wider than the local mean; "@" indicates very close
to the local mean. The length of bars is selected so that there is an equal
number of bars of each length.
Bar plots may be used as a quick graphic presentation of a time series,
to assist in crossdating as a skeleton plot is used, or to pinpoint the
exact year of problems in crossdating or measurement.
Program CLD Climate diagrams
Climate diagrams are produced from monthly temperature and/or
precipitation data. You may elect to produce climate diagrams either for a
span of years or for selected individual years.
These diagrams permit rapid visual assessment of the climatic character
of a year compared to the long-term average, since both values are displayed
together.
The first diagram shows the average monthly temperature and/or
precipitation for the entire time span of data. Means for each month are
shown by a "T" for temperature and "P" for precipitation.
The diagrams which follow are for individual years. On the diagram for
a given year the monthly values are plotted in upper-case "T" or "P" and the
average monthly values for the entire span of data in lower-case "t" or "r".
The interval displayed for each year covers 16 months from January through
April of the following year.
Program COF COFECHA -- Crossdating and measurement quality control
C O F E C H A
Guide for computer program COFECHA, by Richard L. Holmes
Adapted from Quality Control of Crossdating and Measuring: A Users Manual
for Program COFECHA, in Tree-Ring Chronologies of Western North America:
California, eastern Oregon and northern Great Basin, by R. L. Holmes, R. K.
Adams and H. C. Fritts, Laboratory of Tree-Ring Research, University of
Arizona, 1986, pages 41 to 49.
INTRODUCTION
Program COFECHA performs data quality control on a set of tree-ring
measurements, verifying crossdating among ring measurement series and
indicating possible dating or measurement problems. The printout from
COFECHA provides documentation demonstrating the quality of crossdating
within a tree-ring site.
Program COFECHA serves as a tool for the identification and
documentation of portions of a tree-ring data set that may have dating
errors or important errors in measurement. It may also be used to check
crossdating among chronologies from sites within a region.
For each series a note is made of segments which correlate poorly with
the corresponding segments of the master dating series (the mean of all
other series) or which correlate higher at a position other than the
position as dated. Single values are noted which have the effect of
strongly lowering or raising the correlation of the series with the mean of
all other series. Divergent year-to-year changes, absent rings and
statistical outliers are listed. Basic statistics for each series appear in
a table.
If there are series of difficult or questionable dating you may find
their probable dating by putting them in a second data file. If the dating
for the site is unknown, you may determine preliminary best-fit
relationships among the series by giving their file name as the second file
with a blank name for the first file.
At many research centers Program COFECHA has saved a great deal of
personnel time by providing reliable quality control and archival
documentation of crossdating. It may be especially useful to an
investigator working alone or in a small group, or in dealing with
unfamiliar species.
RUNNING PROGRAM COFECHA
COFECHA will ask for the name of the file containing dated tree-ring
measurement series. Next it will ask for a second file of undated or
counted measurement series, which will be examined separately. If there are
series of difficult or questionable dating you may find their probable
dating by including them in this second data file. If the crossdating for
the site is entirely unknown, preliminary best-fit relationships among the
series may be determined by including them in the second file, giving a
blank name (respond with alone) for the first file. If no file of
undated measurements is to be examined, touch without giving a file
name
You may give a title to identify this run of the program.
A menu shows the current setting of parameters for running the
program. Any of these values may be changed by first typing the number
appearing at the left, then responding with the modification desired. When
no more changes are to be made, touching alone begins processing of the
data. Often very few or no changes need be made to the default values.
Menu for Program COFECHA:
Select number or first letter to modify: Current values
1 Rigidity of SPLINE for filtering 32
2 SEGMENT length to examine 50 lagged 25
3 AUTOREGRESSIVE MODEL A
4 TRANSFORM series to logarithms Y
5 CRITICAL level of correlation 0.3281
6 MASTER dating series, save N
7 LIST ring measurements N
8 Parts of output to print 1234567
Brief messages on the screen are intended to keep you posted on the progress
of the program. On termination of the program a summary message is shown.
The results for printing are in the file ZZZCOF.OUT (assuming ZZZ are the
initials given).
WHAT PROGRAM COFECHA DOES
Before crossdating and measurement problems are identified the data are
transformed by the program so as to enhance those time-series
characteristics which are related to crossdating, while minimizing the
features unrelated to the task. The following steps are performed on each
series of tree-ring measurements:
(1) A cubic smoothing spline with 50% cutoff of 32 years is fit to the
series, and each value of the series is divided by the corresponding value
of the spline curve, resulting in a series without trend or long waves and
with a mean of 1. In short, low-frequency variance is removed from the
series.
If you give a negative number for spline rigidity, there is no
transformation of the series: no spline, no autoregressive modeling and no
log-transform.
Experience with data sets from several regions suggests that the
optimum job of discovering errors is done by using a smoothing spline with
50% frequency response of around 32 years. A more rigid spline may leave
too much long-term variance in the series, and the resulting filtered series
may still contain information unrelated to the dating pattern.
(2) The persistence of the smoothed series is removed by
autoregressive modeling, thus removing short waves which may remain after
the spline fit. This step makes the series conform more closely to the
assumption of the Pearson correlation that the values are serially
independent; the crossdating match stands out more sharply thereby. Robert
Monserud (1986) makes an interesting analysis of this concept.
Autoregressive modeling decreases the effect of varying the spline frequency
response, although a very flexible spline (less than about 20 years) may add
spurious high-order autocorrelation to the series. This step may be omitted
at the user’s option.
(3) The logarithm of each value in the series is taken after adding a
constant of one-sixth of the mean. The constant is added to avoid the
possibility of taking the logarithm of zero (which is negative infinity) in
the case of a locally absent ring. The aim of the log transform is to weigh
proportional differences in ring measurement more nearly equally; a minor
disadvantage is that after log transformation the distribution of values in
the series is negatively skewed. This step may be omitted at the user’s
option.
Filtering with a smoothing spline, modeling and log-transformation, by
removing low-frequency variance and persistence and examining only the high-
frequency variance proportional to ring widths, mathematically simulates
human perception on visual examination of a ring series for crossdating.
(4) The transformed measurement series is saved on a direct-access
file for subsequent processing. The series is added to an accumulating
series and a counter series is incremented for the time interval.
(5) After all series have been transformed, the accumulated series is
divided by the counter series to give an arithmetic mean value function of
all transformed dated series. The resulting master dating series is
intended to embody the crossdating characteristics of the site, and may be
saved for further analysis.
(6) Each transformed series is tested against the master dating
series. The master series is first adjusted by removing the component
contributed by the series under consideration to avoid comparing it against
itself.
The series is tested segment by segment against the adjusted master
series for crossdating and general measuring accuracy, by calculating
correlations for each 50-year segment of the series under examination with
the master series matched at the point of crossdating. For each segment the
correlation is verified to be positive and significant at the 99% level.
The correlation is also checked to see that it is higher when matched as
dated than at any position shifted up to ten years earlier (-10) or later
(+10) from the dating. Experience indicates that ten years on either side
is adequate to locate most crossdating errors, and will also catch errors
made by skipping or repeating a decade while measuring.
The default critical level of correlation below which segments will be
flagged are:
Length of Correlation at
segment 99% confidence level
10 0.7155
15 0.5923
20 0.5155
25 0.4622
30 0.4226
35 0.3916
40 0.3665
50 0.3281
60 0.2997
70 0.2776
80 0.2597
90 0.2449
100 0.2324
120 0.2122
Successive segments are lagged 25 years, giving a 50% overlap. In
order to test to the ends of the series, the first segment begins with the
first year of the series and the last ends with the last year; all segments
are of the same length. Intermediate segments begin on years evenly
divisible by the lag. The overlap of the first two and the last two
segments is therefore usually greater than the lag.
A segment length of 50 years provides sufficient degrees of freedom so
that there are few segments where very high or low correlation occurs by
chance, and the correlation at 99% significance is low enough that few
segments are flagged unnecessarily. Yet 50 years is short enough to allow
detection of dating errors of a few years in length, and thus allow the
dendrochronologist to narrow the search for dating problems. The length of
segments may be decreased for short series (but less than 30 years is not
recommended) or lengthened to 100 years or more for long series in species
with relatively weak crossdating or widely separated key crossdating years
such as Sequioadendron giganteum.
If in any time interval a major proportion of the series that make up
the master series are incorrectly dated, the master series itself may not
contain the correct dating pattern, and most or all of the series will show
low correlation for that interval. Test runs of the program show that if
there are sufficient samples, more than half may be erroneously dated in a
given time interval, so long as they are not systematically misdated in the
same way, and the program will still correctly identify those series
containing errors while not flagging the correct series. Thus the inclusion
among the dated series of some with severe errors, though not to be
preferred, generally does not destroy the dating pattern.
The level of correlation among correctly crossdated ring measurement
series may differ with tree species, geographic area, site homogeneity,
amount of stand competition, and degree of disturbance. Through time a
given tree may suffer differing amounts of stress from competition with
other trees for light and moisture, competition for moisture with ground
cover, access to soil by the roots, and disturbances such as fire and insect
attack. This could cause the tree growth pattern through time to become
either more similar to or more divergent from that of other trees. For
these reasons, Program COFECHA does not provide precise accept/reject
criteria for making objective decisions as to whether a series has been
crossdated correctly throughout, but rather is to be used as a tool to
assist the researcher in verifying the dating and measurement accuracy.
Because visual characteristics of tree rings contain many clues to
crossdating in addition to ring width, the program results should not be
used as a substitute for visual crossdating on the wood sample. COFECHA is
intended to assist data quality control by thoroughly examining all series
from the first to the last value (the end of a series which extends beyond
all others cannot be checked). It thus gives the dendrochronologist an
independent tool to confirm the accuracy of dating and measurement. It may
be used to assist in deciding to accept or reject series or portions of
series for inclusion in a site chronology or for other analyses.
At the end of a run of Program COFECHA a brief summary appears; the
summary is also printed on output:
****************************************
*C* Number of dated series 40 *C*
*O* Master series 1696 1990 295 yrs *O*
*F* Total rings in all series 7096 *F*
*E* Total dated rings checked 7068 *E*
*C* Series intercorrelation 0.643 *C*
*H* Average mean sensitivity 0.288 *H*
*A* Segments, possible problems 7 *A*
****************************************
PRINTED OUTPUT FROM PROGRAM COFECHA
Output from Program COFECHA appears in seven or eight parts:
Part 1: Title page, options selected, summary, absent rings by series
Part 2: Histogram of time spans
Part 3: Master series with sample depth and absent rings
Part 4: Bar plot of Master Dating Series
Part 5: Correlation of each series with Master
Part 6: Potential problems: low correlation, divergent year-to-year
changes, absent rings, outliers
Part 7: Descriptive statistics
Part 8: Undated series adjustments for highest correlations
(this part is produced if there is a file of undated series)
The following paragraphs describe the results printed on the output.
PART 1. The cover page shows the name(s) of the data file(s), the run
title, and a list of contents of the printout. The menu is printed showing
the options selected and below it is a brief summary of the results and a
count of absent rings by year. On the following page a histogram shows in
graphic form the time span covered by each dated series. Next, the master
series in normalized form (mean = 0, standard deviation = 1) is listed along
with the number of individual series contributing to the value for each
year. Following this is a bar plot of the master series which serves as a
visual aid to verification of crossdating. The bar plot is similar to a
skeleton plot, but wider rings are indicated by longer bars. The relative
width of all rings is shown along with an alphabetic code; lower-case
letters indicate rings narrower than the local mean, upper-case wider than
the local mean. The symbol "@" indicates that the value is very close to
the local mean; each letter progressing through the alphabet indicates an
additional quarter standard deviation from the mean. The bar plot may
assist in finding the exact year of problems in crossdating or measurement.
PART 2. Correlations of each segment of the series with the master are
printed in a table. Given a segment length of 50 years, correlation values
are underlined and flagged with "A" if they are less than 0.3281,
representing the 99% confidence level of significance in a one-tail test of
the distribution of the correlation coefficient with 48 degrees of freedom.
Correlations are flagged with a "B" if a correlation at some position other
than as dated gives a higher correlation with the master series. At the
right margin are the number of flagged correlations and total number of
segments for the series.
PART 3. Potential problems in dated series are reported here. All
information pertaining to questions about a given series appears together.
[A] A line is printed for any segment which correlates higher at some
position other than where it was dated, or which correlates below the 99%
confidence level. This line shows the correlation of the segment at each
position from -10 to +10. The value as dated (position +0) is underlined,
and the highest correlation is underlined and bracketed. The position of
highest correlation is also printed in the column labeled "High". For
clarity, an open dashed line separates non-consecutive segments.
Crossdating may be erroneous in the segments listed. Crossdating
errors are often indicated by the occurrence of a low correlation at the
dated position (+0) and a much higher correlation at some position near the
dated position, for example at +1, -1, +2 or -2. If the misdating continues
for more than a few rings, two or more successive segments may correlate
higher at the same nonzero position. A value of -2, for example, suggests
that moving the dating back two years will give a higher correlation;
possibly two rings (locally absent?) may not have been recorded at the later
end of the flagged segments. If there are unflagged segments prior to the
flagged ones, two extra rings may have been recorded (double or false?) at
the early end of the segments. If the highest correlation is at position
+10 or -10, the measurer may have skipped a decade or repeated it.
[B] For the entire series and for segments listed in [A] above, the
effect on the correlation with the master series is listed for the rings
whose presence most lowers or raises the correlation. A ring that either
lowers or raises the correlation of a segment, particularly if its absolute
value is greater than about .07, may indicate a measuring error or an
especially wide or narrow ring that is misdated.
[C] Year-to-year differences in ring measurement are shown where they
diverge by 4.0 standard deviations or more from the mean of the year-to-year
differences of the other series for the same pair of years. This
information may help to locate problems to the exact year.
[D] Locally absent rings (years with zero-value measurements) are
listed.
[E] Rings are listed which are statistical outliers, defined for this
purpose as being more than +3.0 standard deviations larger or more than -4.5
standard deviations smaller than the mean of the other series for that year.
These individual rings are possible sources of dating or measurement error.
The listing of a segment or a ring in this section indicates that there
may be an error in crossdating or one or more large errors in measuring.
Most measurement errors will have the effect of lowering the correlations of
the segments in which they occur. Listed segments may be candidates for
remeasurement to check for errors in the original measurements. Dates of
locally absent rings (zero values) should be independently confirmed since
they are determined by judgment rather than from direct observation.
A disturbance to the growth of the tree may produce a listing. A fire
or other disturbance, sudden removal of competition, severe insect
infestation or other environmental changes abruptly affecting the tree in
question differently from others in the stand, may cause ring growth to be
anomalous for one or a few years, and thus produce low correlation in one or
two segments of the series and divergent year-to-year changes. This
phenomenon was noted by L. O. White (personal communication), who observed
in his collection of Pinus lambertiana from the Mendocino National Forest in
California that evidence of fire often occurred within segments of
measurement series with somewhat low correlation in Program COFECHA; these
segments were nevertheless correctly dated.
We recommend a close examination of Part 3 of the output to confirm
correct crossdating and to select those portions of series in which the
dating and measurement should be checked. After corrections are made,
Program COFECHA should be run on the clean measurement data set to confirm
and document the correct crossdating of the site collection.
PART 4. This is a table of descriptive statistics of the ring
measurement series. Included are the total number of segments in each
series and how many segments were found to have potential problems. The
mean correlation of the series with the master series is given, along with
standard time series statistics of the measurement before and after
transformation, including the order of the autoregressive model (AR) applied
to the series.
PART 5. Date adjustment for unknown series. If there is a second data
file with undated ring measurement series, a section appears whose purpose
is to find the most probable dating of the unknown series which cannot be
confidently dated by skeleton plot or other commonly used techniques.
Tentatively dated series may be included here. Possible crossdating matches
for these series are indicated. This section is very similar in concept to
M. L. Parker's (1967 and 1971) Shifting Unit Dating Program.
For the unknown series as with the dated series, correlations are
calculated for 50-year segments of the counted series lagged successively 25
years, but here the segments are tested at every position from beginning to
end of the master dating series. For each segment the eleven highest-
correlating positions are shown (the eleven best matches), starting with the
highest ("Corr #1"), along with the number of years to add to the counted
series to obtain the indicated match. If the same number appears
consistently in one of the "Add" columns of the #1, #2 or #3 correlation
there is a high probability that the correct dating of the series may be
obtained by adding this number to the count of each ring. The dating should
of course be verified on the wood sample, since there are many clues to
crossdating in addition to ring width. At the end of the section dealing
with a series is a tabulation of the segment adjustments which appear three
or more times with their mean correlation.
Further discussion is given by Holmes et al. (1986) in sections titled
"Crossdating, measurement and related procedures" and "Effects of
undiscovered absent rings," and in Appendix 1.
Routine COL Copy selected columns
Selected spans of columns are copied from one file into a new file.
The new file may contain up to 256 columns.
Either List carriage control (for data) or FORTRAN carriage control
(for printed output) may be selected for the new file. If desired, the new
file may have leading blanks. Trailing blanks are trimmed from the new
file.
If for example you give 9 and 72 as the first and last columns to take
for the first segment, and columns 1 to 8 for the second segment, then
request that the new file start in column 3, the resulting file will have
columns 9 to 72 from the old file in columns 3 to 66 of the new file, and
columns 1 to 8 from the old file in columns 67 to 74 in the new file.
Routine COV Coefficient of variation
Coefficients of variation (CV) are computed for a chronology:
CV = 100 x Standard deviation / Mean
The coefficients are saved as a time series on a disk file. Input files are
the *.CRN (chronology) and the *.SDV (standard deviation) files produced by
Program ARSTAN.
Program CRN (CRONOL) Chronology with unlimited series
Program CRONOL produces a chronology in two versions from a set of
crossdated tree-ring measurement series by detrending each series then
computing a chronology (a mean series) intended to contain a maximum common
signal and a minimum amount of noise. Careful selection should be made
among the options depending on the characteristics of your data and what
aspects of the data you will study. Do not rely on the initial settings as
the recommended method.
(1) The Standard version of the chronology is derived by first detrending
the measurement series, fitting to each series a curve to model biological
growth trend, and dividing out the growth model. The chronology is then
computed as a biweight robust mean or arithmetic mean of the detrended
individual series.
(2) The Residual version of the chronology is derived by performing
autoregressive modeling on the detrended ring measurement series. The
biweight robust mean or arithmetic mean of the residual (white noise) series
is a chronology with a strong common signal and without persistence.
Program CRONOL includes mainly concepts and methodology developed by Dr.
Edward R. Cook at the Tree-Ring Laboratory, Lamont-Doherty Earth Observatory
of Columbia University, Palisades, New York. Most of the details of Program
CRN are explained more fully in the section on Program ARSTAN.
RUNNING PROGRAM CRONOL
CRONOL will ask for the name of the file containing the tree-ring
measurements. Next provide a title of up to 60 characters to identify the
printed output of the program and the chronologies produced.
The menu shows current settings of values for controlling program execution.
Items in the menu are as follows; initial settings appear in parentheses:
(1) Detrending methods: choice of one- or two-step detrending by a smoothing
spline, least-squares regression line, negative exponential curve or
horizontal line through the mean
(128: First detrending: 128-year spline;
0: Second detrending: none)
(2) Stabilize variance of detrended series, chronology or both
(No stabilization, method 0 used)
(3) Print chronologies in vertical list format in addition to standard
publication form
(Print chronology only in publication form)
Any of these values may be changed by first typing the number at the left,
then responding with the modifications desired. When no more changes are to
be made, touching alone begins processing of the data.
During program execution brief messages are printed on the screen to keep
you posted on the progress of the program. The full results are in the
output file for printing and the two chronology files.
CONTROL PARAMETERS IN THE MENU
(1) Detrending methods
First detrending; the following options for detrending, described more fully
in the section on Program ARSTAN, have these effects:
1: A negative exponential curve is fit; if it fails, a linear
regression line is fit.
2: A negative exponential curve is fit; if it fails, a linear
regression line of negative slope or a horizontal line
through the mean is fit.
3: A linear regression line is fit to the data series.
4: A horizontal line is fit through the mean (no detrending).
5 or greater: A cubic smoothing spline is fit with a rigidity
(50% frequency cutoff) of this many years.
-1: No detrending or transformation of the series is done
Second detrending option:
Curve-fitting options are the same as described for the first
detrending. If you touch or type zero, no second detrending is done.
(2) Stabilization of variance.
You may request variance stabilization of each detrended index series, of
the chronologies only, or both. For variance stabilization a cubic
smoothing spline is employed of a rigidity you select.
CHRONOLOGY COMPUTATION
Program CRONOL performs the following tasks:
(1) Ring measurement data series are read, and for each series detrending
is performed as specified. One curve (or two curves in succession) is fit
to each measurement series to model biological growth trend and other low-
frequency effects you wish to remove, and the measurement values are divided
by the curve values to produce a detrended series.
(2) Variance of the series is stabilized if requested.
(3) Autoregressive modeling is done, fitting an autoregressive process to
each series of the order determined by the first minimum of the Akaike
Information Criterion. Statistics are printed on each series.
(4) The Standard version of the chronology is computed. Detrended tree-ring
index series are combined into a biweight robust mean (default) or an
arithmetic mean of the series.
(5) The Residual version of the chronology is computed in the same manner as
the Standard version, this time using the residual series resulting from
autoregressive modeling.
(6) The Standard and Residual versions of the chronology are saved on a disk
file named __CRN.DAT, or if requested in two files: __STD.CRN and __RES.CRN,
and printed on the output in the standard form for publication.
Routine DHL Divide series high & low
Splits series such as tree-ring chronologies into two new series
representing respectively the positive and the negative departures in growth
from the mean.
In the first series in the new file, values in the original series
above the mean are kept intact and values below the original mean are set
equal to the mean. In the second series in the new file, values in the
original series below the mean are kept intact and values above the original
mean are set equal to the mean. The resulting data file thus contains two
"hemi-chronologies."
To make use of these split chronologies, Program RESPO (RES) may be run
on each of them in turn. If the correlation and response functions to
climate are very similar, then probably negative departures are caused by an
opposite anomaly of the same influence which causes positive departures. If
on the other hand the correlation and response functions to climate are
dissimilar between positive and negative anomalies of growth, then the cause
of negative departures may be due to a different influence (or combination
of influences) on growth from that causing positive departures.
Routine EDT Edit ring measurements
Enables you to edit efficiently a file of tree-ring measurements or
other time series, producing a new file which incorporates the changes you
have made. Each series in the file may be copied to the new file intact, it
may be edited in one or several respects and then copied, or it may be
omitted from the new file. The new file is written at your option in
compact or measurements format. Note that if a large number of data are to
be entered, or if certain types of change are to be made, it may be easier
to use a text editor.
The program allows you to copy one or more lines from the beginning of
the existing file as headers in the new file.
In editing a time series you may display the data; insert, change or
delete values; truncate at the beginning and/or end; shift the dating
forward or back; split the series into two or more; and/or change the
identification.
The menu for editing is:
No 1 CPP01A Interval 1752 1920 169 years
C: COPY as is F: new FIRST year U: new LAST year
I: INSERT value E: ELIMINATE value R: REPLACE value
(: Cut from BEGINNING ): Cut from END P: DISPLAY data
T: Take remaining series O: OMIT series N: New identification
X: Exit program Q: Re-edit series K: COPY and re-edit
S: Copy all until .. Select:
The menu for editing presents several editing options. You may:
C: Copy the series into the new file as it is currently, edited or not.
F: Adjust the dating of the series by resetting the date of the earliest
ring.
U: Adjust the dating of the series by resetting the date of the latest
ring.
I: Insert a ring measurement value in the series, moving the earlier part
of the series backward in time ("<") or the later part of the series forward
in time (">") to make space for the inserted value.
E: Eliminate a ring measurement value in the series, moving the earlier
part of the series forward in time (">") or the later part of the series
backward in time ("<") to fill the space left by the deleted value.
R: Replace a ring measurement value, substituting another value.
(: Truncate the series by cutting off values at the beginning.
): Truncate the series by cutting off values at the end.
P: Present data on the screen, displaying 50 values with dates from any
part of the series. The date you give will appear as close as possible to
the center of the screen.
T: Take all remaining series in the old file into the new file without
further editing.
O: Omit this series from the new file, skipping to the next series in the
old file.
N: Change the identification of the series to a new string of up to eight
characters.
X: Exit the program, leaving in the new file only those series you have
copied to this point.
Q: Restore the series to the original and edit it anew. This option may
be used if you have made an error in editing.
K: Copy and re-edit. This way you may divide a series into two or more
parts by editing to leave only the first part, then copying with this option
to re-edit. You then edit the series again, this time leaving the second
part. Change the series identification with option "N" before copying it to
the new file to avoid duplication.
S: Skip ahead several series, copying them to the new file without
editing, until you reach the next series you wish to edit.
Some sample replies you may make to items on the menu, the prompt from the
program, and one possible reply:
Reply Prompt Reply
P Around what year?: 1820
I Date of value BEFORE which to insert: 1813
Value to insert: .45
Move: < early portion BACK; > late portion FORWARD: <
) LAST year to keep: 1917
F Correct date of FIRST year: 1762
N Present identification_: CPP01A
New identification _: SBE09B
C No 1 SWE09R Interval 1762 1928 167 years, COPIED
Routine FMT Change format, manipulate data
Converts data files from one format to another, with the option to
perform one or several operations on each series.
Codes and names of formats in which data may be read from an existing file
(explanation below):
C: Compact format
M: Measurements with precision of 0.01
3: Measurements with precision of 0.001
I: Index or chronology format
A: Accurite ring measurements
T: Meteorological data format
S: Spreadsheet (casewise) format
1: Single column of values
2: Two columns: year, value
V: Two columns: value, year (“Universal Vertical”)
X: User-supplied format
Formats in which data may be written to a new file (explanation below):
C: Compact format
M: Measurements with precision of 0.01
3: Measurements with precision of 0.001
I: Index or chronology format
S: Spreadsheet converted to series by column or by row
2: Two columns: year, value
V: Two columns: value, year (“Universal Vertical”)
T: Meteorological data format
K: Meteorological to separate meteorological months
W: Individual months to meteorologic format
P: Publication format for chronologies
X: User-supplied format
You may choose among any of these formats for input and output files.
See the section above on DATA FORMATS for detailed descriptions of available
formats.
OPTIONS FOR DATA MANIPULATION
In addition to reading and writing data files the program is capable of
performing several manipulations of data. When prompted for the format of a
new file, K and W are special cases.
K = Data in a file in meteorological format will be separated into series of
individual months. You may elect to have them placed consecutively in a
single file, or each month in a separate file. If desired you may select
those months to copy. (This procedure is the inverse of "W".)
W = Individual series may be combined consecutively into a single series in
meteorological format. (This procedure is the inverse of "K".)
A menu gives additional options for data manipulation:
Option Default
1 Select series to include Include all
2 Time stamp title: [10MAY94-1740] No
3 Truncate series start & end 0 0 (No truncation)
4 Minimum length of series to include 0 (No minimum)
5 Include only series covering 0 0 (Include all)
6 Adjust year dates of all series 0 (No adjustment)
7 Multiply data by constant 1.0000 (No multiplier)
8 Add constant to data 0.0000 (No constant)
9 Save sample depth from chronology No
10 Spline fit to data No 0.00
Fit cubic smoothing spline to data and save SPLINE curve or
INDICES from division. Specify spline rigidity.
11 Autoregressive modeling No
12 Normalize series No
13 Set skewness and Kurtosis to zero No
14 Convert between Fahrenheit and Celsius No
15 Separate file for each series No
If desired, the data may be multiplied by a constant and/or have a
constant added. If both, you specify which operation is done first.
If the data are chronology indices, you may elect to save also the
number of series for each index.
You may truncate at the beginning and/or end each series that surpasses
the dates you specify. By specifying both beginning and ending years you
will make a rectangular matrix of data.
To accommodate archaeological work or very long series where 8000 is
sometimes added to the date, the dating may have a positive or negative
constant added to it. Thus if a series is dated -400 to 1986, adjusting the
year date by 8000 will yield "dates" of 7600 to 9986. Conversely, if a
series is "dated" 7600 to 9986, adjusting by -8000 will give dates of -400
to 1986.
Each series may be normalized to a mean of zero and variance of one.
The first line of the original file may be copied into the new file as
a title, or you may provide a new title. Responding with when prompted
will omit a title from the new file.
Routine HOM Homogeneity of meteorologic data
Examines monthly temperature, precipitation or similar data from a pair
of meteorological stations for homogeneity. Two analyses are performed.
(1) The Mann-Kendall statistical test for randomness is performed on
the data sets. For each year the number of years following with larger
ratios (Station 1 value / Station 2 value) is calculated and these are
totaled and compared with the expected number. A pass/fail test is made for
the 90%, 95% and 99% critical limits.
Tau = 4P / (Nyr * (Nyr-1)) - 1
where P is the sum over years of the ratios beyond a given year which are
greater than the ratio for that year, and Nyr is the number of years in the
series. The 90% critical limit depends on the number of years and is such
that for 90% of all samples, the absolute value of Tau is less than the 90%
critical limit. Thus if the given Tau does not lie in this range, there is
less than a 10% chance that the ratios form a homogeneous series. The 95%
and 99% critical limits are defined similarly. Note that if a given Tau
would occur on 7% of all samples, the result would fail the 90% limit and
pass the 95% and 99% limits. Hence the 90% limit is the most stringent.
(2) A scattergram is made to enable visual assessment of the
relationship between the stations.
For temperature, since the data values are not zero-based, a
scattergram is made plotting the year versus cumulative temperature
differences (Station A minus Station B).
For precipitation, since the data values have a base of zero, a
scattergram is made plotting cumulative precipitation of Station A versus
that of Station B (double mass plot).
For both temperature and precipitation the points plotted on the
scattergram run from the lower left corner to the upper right corner. If
the stations are homogeneous, their relationship has remained constant
through time, and the points will fall close to a straight line and there
will be no change in slope.
If there is a change in slope, you may determine the year of the change
(the year is printed at each point) and its direction. If, for example,
precipitation at Station A is plotted along the horizontal and precipitation
at Station B along the vertical axis, and the slope becomes more positive
(steeper) at year T, then beginning in year T+1, either Station A began to
register relatively less precipitation than before or Station B began to
register more. This occurrence is often due to a change in type or location
of instrumentation at the meteorological station.
To determine which station has the inhomogeneity, each station must be
compared with at least two others, for example A with B, B with C, and A
with C. The station with inhomogeneous data will show a break in slope at
the same year in the same direction with both comparison stations.
If there is a jog in the scattergram plot without a change in slope,
there is a large discrepancy between the stations in the year following the
jog. This implies a probable error in the data.
Time spans may differ between the two stations, in which case the
common time span will be compared. There must not be missing values in the
common time span of either data set. (See routine MET for estimation of
missing values in monthly meteorological data.)
Routine IMP Impact before & after event
Tree-ring measurement series or chronologies are used to compare mean
growth before and after an impact or disturbance which is thought to cause a
change in growth, for example, a hailstorm or fire.
The impact year is the first year the tree will exhibit the effect of
impact. This would be the first narrow ring in the case of a negative
impact on growth. Indicate a span of years before the impact year to
establish the base rate of growth. Select a span of years after the impact
to be compared as a whole and year by year with the base rate.
Printed for each series is the growth before and after the impact in
terms of the base, as well as the mean growth in the time span after impact
compared with the base rate before impact. For each year before and after
the impact, the mean growth and index as a proportion of base growth is
shown.
In lieu of this routine you may prefer to use Program EVENT to perform
Superposed Epoch Analysis. In this program (see description) each year in a
list of event dates is taken as a key or zero window year. Time series
values for event years and for a window of years before and after the event
years are superposed and averaged over the chronology time span. Random
simulation determines the significance of the relationship.
Routine LNP Printer plot of series
Line printer plots of time series are produced for printing. Series
are displayed horizontally across the page, each value represented by a
vertical bar identified with the last digit of the year. If a series is
more than 125 values long it is continued below.
You may elect to draw a horizontal line at the mean or at any level you
specify. From a file containing several series you may select the series to
be plotted, and if desired choose to plot only a portion of the series.
Scaling of the plots is automatic.
Routine LRM List ring measurements
A listing of tree-ring measurement values is produced for all tree-ring
series in a file for printing. For each year measurements appear in a
single column, and the values in a given series may be followed
horizontally.
A diagonal bar between adjacent values indicates when the year-to-year
change in measurements exceeds 20 percent of the mean of the two values, "/"
when the change is positive, "\" when negative; nothing appears if the
adjacent values are within 20% of their mean. Absent rings are indicated by
"**AB*" so they are easily seen on the page.
The printout may be used to check crossdating and locally absent rings
and to locate unusual features, and also serves as an archival record of
tree-ring measurements.
Routine MAT Correlation matrices
Produces one or more correlation matrices for a set of time series,
using one or more time intervals you specify.
Any series not covering the specified time interval is excluded from
the correlation matrix. By default every series in the file covering the
span is included in the correlation matrix. An option permits you to select
those series you want to include.
If you give one file name, correlations will be calculated for all
possible pairs of series in the file.
If you give two file names, correlations will be calculated for each
series in file 1 with every series in file 2.
If one of the data sets is very large, give it as the second file.
Tables of correlations to three decimal places are written on a file
for printing along with the mean correlation and mean absolute correlation
for each series. You may elect to mark with an asterisk all correlation
values exceeding an absolute threshold; default () is no marking of
correlations.
Additional correlation matrices may be produced for the same data file
by specifying other time intervals.
The matrices are written on a file for printing. You may elect to save
the matrices as tables in a data file as well.
Routine MET Estimate missing meteorology data
Missing monthly meteorological data may be estimated for a small or
large number of temperature, precipitation or river flow stations. Station
data must be of the same type and should be from a homogeneous climatic
region. Missing values must be set previously either to blank or to a value
of -999 or more negative.
If for a given month no station has data, you may elect either to fill
in the mean for that month at each station, or to leave the value missing.
If data are precipitation or river flow, an estimate that results in a
negative value is set to zero.
The mean and standard deviation is calculated for each month at each
station. The departure for each month and year is then calculated and
averaged across stations to produce regional average departures for each
month and year. You may save the file of regional mean departures and/or
averages, or convert a previously made file of regional departures to
averages.
Monthly data values are estimated by calculating the value with a
departure from the mean for the month at that station equal to the average
departure of the other stations for that month and year. The standard
deviation for the month at that station is multiplied by the regional
average departure for the month and year, and the mean value for the month
at the station is added. The output for printing documents all estimated
values. New files with estimated data are produced for those stations with
missing data. If a station has no missing data, no new file is produced.
In many analyses the file of mean regional departures may be used as
meteorological data. If desired, routine MET may be run again, selecting
the option from the menu to convert a file of regional departures to
regional averages.
Routine MIS Estimate missing ring measurement
If tree-ring measurement series have single missing rings, that is, not
consecutive, routine MIS will estimate the value of each missing ring k
based on the measurements of the immediately preceding (k-1) and following
(k+1) rings and the relationship of these three rings (k-1, k, k+1) in all
other series where they are present. Missing ring measurements must be set
to a negative value before running routine MIS.
Routine ORD Sort in order by selected column
Reorders lines in a file, such as a table of data, by putting them in
ascending order by selected columns. The routine displays on the screen the
first few lines from the file to show the column structure or format.
If for example you respond with 40 and 50 for the first and last
columns, the new file will have the same lines reordered so that columns 40
to 50 appear in ascending order.
Routine PCA Principal components analysis
Principal components analysis is done on a set of time series in a
file, and eigenvalues, eigenvectors and principal components are saved,
along with output for printing.
After you give the data file name the overall time span and the optimum
time span will be displayed. The optimum time interval is the largest
possible rectangular matrix in the data set. You may select the time
interval to analyze, in which case all time series covering the interval
will be used. If you respond with to the prompt for start and/or end
of the time interval the program will select the start and/or end of the
optimum interval.
You are prompted for a 3- or 4-character mask for identification.
Ideally you should choose positions which uniquely identify each series.
For example, if a typical series identification is CPP06B where all series
start with CPP, you may want to use a mask of “...xxx” where “.” is a space
and “x” is any non-blank character. You are also rompted for a four-
character identification, which should be a general identification; in this
example you might use CPP.
The data file is easily plotted by the scattergram routine SCA (see
description). The file with extension “.EV” contains the eigenvalues and
eigenvectors, the file with extension “.PC” contains the principal
components, and the file with extension “.ID” contains the masked unique
identifications of the series.
Routine PRT Prepare file for laser printer
By default output files for printing are prepared with FORTRAN carriage
control, that is, the first character of every line is non-printing. Large
printers generally can use this form of carriage control. The special
characters for FORTRAN carriage control are effective only if they occur in
the first column:
Blank; printing continues on the next line.
0 Zero; a line is skipped before printing continues.
+ Plus; this line is overprinted on the previous line.
1 One; printing continues at the top of the next page (form feed).
Output may be prepared for laser printers using standard escape codes
by processing with Routine PRT; more efficiently, you may invoke this option
at the beginning of a program run by giving three dots (“...”) then
when the program menu appears, then selecting the routine you wish to run.
This option is described after the description of Routine ZZZ.
Routine REC Reconstruct time series
Regression coefficients and a set of predictor variables are used to
reconstruct a time series. For a valid estimation the predictors must be
the same variables as in the original calibration or regression analysis.
Two files are required. The first contains the regression coefficients
for reconstruction. Each line pertains to one predictor time series. The
first eight columns are either the identification of the predictor, left-
justified, or its sequence number in the predictor file in free format.
Following in column 9 or after is the regression coefficient for that
predictor in free format. If the intercept is given, identify it as “INT”,
left-justified. The order of the coefficients is unimportant.
The second file contains the predictor variables. Any of the formats
described above may be used for these time series.
The reconstructed time series is saved on disk file and printed in
publication format along with descriptive statistics.
Routine RES RESPO -- Response and correlation function
Program RESPO computes response functions of tree growth to climate by
means of principal components, using two methods for selecting components
for the regression. The correlation function is also calculated and printed
along with the response function. Regression weights may be saved for
subsequent plotting or for reconstruction.
If you want to print the principal component and correlation matrices,
respond "N" to the question on condensed output.
With the "E" type analysis, RESPO may be used to reconstruct a tree-
ring chronology or climate from proxy data and regression weights from a
prior run of Program RESPO.
For the tree-ring chronology, you may select a version of the
chronology (STD, RES, ARS) or by responding with to select the first
chronology in the file. If the data are for the Southern Hemisphere, where
months of meteorological data may have a calendar date later than that of
the tree ring chronology, respond "S" to adjust the chronology dates.
In giving the first and last years of analysis, remember that if the
response period selected goes back to the prior year, the first year of
analysis must be at least one year later than the first year of
meteorological data. The same is true for the chronology if prior years of
growth are to be considered. If you respond to the prompt for time interval
with the maximum possible interval will be used.
If you wish to consider for example a tree-response period from the
previous July through the current September, the response period would have
15 months. You would respond by specifying month 9 (September) as the
latest month of analysis for both temperature and precipitation, and
specifying 15 months to use. If you respond to the prompt with months
1 through 12 will be used.
You may save the values for the correlation and response function for
plotting; the file will have the name ZZZRESPO.PLT.
Program RESPO was written by Dr. Janice M. Lough of the Australian
Institute of Marine Science, Townsville, and modified for the DPL by Richard
L. Holmes.
Routine SCA Scattergrams
Produces line printer scattergram plots of pairs of data points in two
series in a file. Each point is plotted in the X-axis direction as a value
in the first series, in the Y-axis direction as a value in the second
series.
The series to be plotted need not be consecutive in the file. Several
plots may be made using the same or different pairs of data series. For
example, from the *.AMP file output by Program ARSTAN (DPLARS) Eigenvector 1
may be plotted versus Eigenvector 2, then Eigenvector 1 versus Eigenvector
3. Another example is to plot one chronology versus another to determine
years of agreement and divergence.
Symbols displayed at each point may have up to three characters. You
may elect to number the points consecutively beginning with a number of your
choice such as 1 or a year; to input from the keyboard a symbol for each
point; or to prepare beforehand a file of these symbols listed in a single
column. If you are plotting eigenvectors from a run of Program PCA, the
file with extension “.ID” is produced for this purpose.
Routine SCR Scrolling plot on screen
Time series are plotted on the screen, scrolling from top to bottom.
All or selected series in a file may be examined. The scale is adjusted so
the plot will use the entire width of the screen.
If you give one file name each series is plotted in turn, identifying
each point by the last digit of the year. If you give two file names, then
one series from each file will be plotted superimposed, the first identified
by the last digit of the year, the second by "B". If both values occupy the
same point the symbol is "#"; a symbol at the right edge of the screen shows
which value is greater (A < B or A > B). The correlation between the series
is calculated. Both series may be previously normalized at your option.
If the second file contains only one series, it will be used as a
reference series, and will be plotted superimposed on the plot for each
series in the first file.
One application is to study the detrending curves from Program ARSTAN
(DPLARS), using the output files *.MSM and *.CV1, or *.IN1 and *.CV2.
Another is to observe the general pattern of the time series, or to look for
abrupt changes or impacts on growth.
Routine SEA Seasonalize meteorologic data
Monthly meteorological data may be grouped into seasons of one or
several months, creating a new file with seasons replacing months. Up to
twelve seasons or groups of months may be chosen. They may overlap, may
include only one month, and may include months in the prior and following
years as well as the current year.
If the data are temperature, the season mean is recorded; if
precipitation or river flow, the total is recorded.
To indicate first and last months, give the number of the month: 1 to
12 for the current year, -1 to -12 for the prior year, and 13 to 24 for the
following year. For example, -7 to 3 will give a nine-month season from the
prior July through the current March, averages for temperature and totals
for precipitation or river flow; 5 to 5 will give a one-month "season"
including the current May only.
The span of each season is automatically indicated in the new file, and
routines in the Dendrochronology Program Library will read it without
difficulty.
Routine SPL Random split of file by percent
Divides a casewise data file randomly into two new files in the
proportion specified.
For example, if a file contains 127 data lines, and you specify the
proportion as .375, the first new file will have 48 data lines (37.8%)
randomly selected, the second new file the remaining 79 data lines (62.2%).
This routine may be used to select a random sample of yearly values for
calibration, reconstruction or verification as an alternative to using spans
of consecutive years.
Routine SUR Survey data file
This routine surveys one or more data files of time series. The first
few lines of the file and the identification and time span of each series
appear on the screen and the time span and common interval (if any) of the
entire data set are calculated.
The series may be viewed and listed in order as they appear in the
file, ordered by identification or by first year, by last year, or by length
of the series.
At the end of the run you may elect to keep or delete the file for
printing, which duplicates the information presented on the screen.
Routine TSA Time series analysis
Calculates descriptive statistics of time series in their entirety and
in 50% overlapping segments of a length you may specify (default is segments
of 50 values). If you give a negative number for length of segments,
analysis will be done on the entire series only.
Statistics computed include the mean, median, mean sensitivity,
variance, standard deviation, coefficient of variation, skewness, kurtosis,
autocorrelation and partial autocorrelation to ten lags, and the Ljung-Box
Portmanteau Q statistics. There is no limit to the number of series in a
file that may be processed. In addition to the printed output you may save
the statistics in a table.
Routine VFY Verify calibration
Verifies reconstructions of meteorological series or tree-ring
chronologies by comparison of actual data with estimated data for one or
more common time spans.
You provide first and last years for a calibration time interval and
for a verification time interval. Subsequently additional time intervals
may be analyzed for the same data.
Several tests are performed for significance, such as the product sum
test, correlation, reduction of error, T-value, sign-products test, and
negative first differences. Significant values are starred. Risk, drift,
variance, covariance, and difference of means between actual and estimated
data are calculated.
Routine YUR Read casewise (column) data file
Reads a file with one or several time series in column (casewise)
format, converting them into Compact, tab or measurement format as desired.
Data may be read as strict columns; in this case columns must always be
delimited by one or more spaces, or by a comma or tab character between data
columns. Otherwise you provide a FORTRAN format to read the data as real
data type, for example (F4.0,20F5.1), which will read up to 21 columns. You
may select which columns are to be read and converted, and provide
identification for each column.
Routine YUX Make casewise (column) data file
Prepares a file that may be imported directly into most spreadsheet
programs, placing one or more time series in column (casewise) format. The
maximum number of columns is currently 79.
Series may come from one file or from several files in the same or
different formats. At your option the new file is either exclusive or
inclusive:
I: Inclusive, containing the full length of all series. If you choose
to make the new file inclusive you are prompted for a symbol of up to eight
characters for missing data (before the beginning and after the end of any
series shorter than the entire time span). If you respond with “#” then the
character is null (ASCII value zero), which is recognized as missing data by
many spreadsheet programs.
E: Exclusive, containing only the part of each series in the time
interval common to all series. A series is rejected if it does not cover
all or part of the common interval. The common interval is shortened if a
new series being added covers part but not all of the current common
interval.
The user specifies a column delimiter; this may be any single character
you type. Most commonly the delimiter is a SPACE, TAB or COMMA.
Spreadsheets commonly recognize a comma or a tab character as delimiter;
some also recognize a space.
Columns may be identified automatically with the series identification
at the head of the column (“I”); you may provide a succinct identification
for each column; or columns may have no identification. If any column
identification is blank, the identification line is not printed.
As series are read from the existing data file the identification and
time span appear on the screen and you are prompted to say whether to
include the series in the new file. You may respond “Y” for yes (default),
“N” for no, “A” to take all remaining series in the file, or “Q” to quit
this file:
CPP01A Spans 1752 1920 169 data
INCLUDE THIS SERIES? /No/All/Quit:
You may add columns of data from additional files. Responding with
will end adding columns of data.
Finally you are prompted for the name of an optional file containing
identification for the rows; this will be the first column in the new file.
Most often you will respond with , indicating there is no such file. In
this case the first column will contain year numbers.
Routine ZZZ Switch brightness of screen
ZZZ is invoked to toggle between high contrast (bright letters on a
black background; default) and low contrast (medium letters on a black
background). The Program Menu appears again to allow you to choose a
program to run.
Routine ... Output for laser printer
This symbol is invoked to toggle between preparing the output file for
printing for laser printers and for printers recognizing FORTRAN carriage
control. The last entry on the Program Menu before the version number
informs on the current status. The Program Menu appears again to allow you
to choose a program to run.
By default output files for printing are prepared with FORTRAN carriage
control, that is, the first character of every line is non-printing and
conveys instructions on printing control, generally accepted by large
printers.
Optionally, output may be prepared for laser printers using standard
escape codes. See also the description of Routine PRT above.
DISCLAIMER
Although every effort is made to ensure that the software functions
properly, no guarantee is made to this effect and we cannot be responsible
for any problems with it, including adaptation of the software to any
particular compiler or computer system.
We appreciate your comments and suggestions, and will try to help with
any problems you may encounter.
ACKNOWLEDGMENTS
The Dendrochronology Program Library was developed over several years at the
following research centers:
Laboratory of Tree-Ring Research, University of Arizona, Tucson, Arizona,
USA
Laboratorio de Dendrocronología, Centro Regional de Investigaciones
Científicas y Tecnológicas [CRICYT-Mendoza] (Regional Center for Scientific
and Technological Research), Mendoza, Argentina
Bundesforschungsanstalt für Forst- und Holzwirtschaft, Ordinariat für
Holzbiologie (Institute for Wood Biology, Federal Forest and Wood Research
Institute), Universität Hamburg, Germany
Tree Ring Laboratory, Lamont-Doherty Earth Observatory of Columbia
University, Palisades, New York, USA
Part of the work was done with the support of the U. S. National
Science Foundation. Major contributors to the programs include Edward R.
Cook of Lamont-Doherty Earth Observatory (ARSTAN), Janice M. Lough of the
Australian Institute of Marine Science, Townsville (RESPO), and Richard L.
Holmes of the University of Arizona. Many users have contributed to
additions and improvements to the programs by useful comments, helpful
suggestions and good advice.
Your suggestions and ideas on how the programs may be improved are
always welcome.
VAX, MAINFRAME AND PC-COMPATIBLE VERSIONS
The Dendrochronology Program Library is written in ANSI standard
FORTRAN-77 and was originally developed with VAX FORTRAN for the VAX/VMS
operating system. With a few modifications which are indicated in the
source code, it may be compiled and linked using any full implementation of
FORTRAN-77 and will run on VAX and other mainframe and PC-compatible
computers.
ARSTAN is compiled and linked separately from the rest of the DPL
because its memory requirements are much larger than the other programs.
These programs are designed to operate identically on all computers.
For PC-compatible computers the recommended procedure is to create a
directory such as C:\BIN for the executable files. Copy the *.EXE files
into this directory. Insert in the PATH statement in the AUTOEXEC.BAT file
the following:
C:\BIN;
In this way you can run a program from any directory by typing the
program name. Make sure that the CONFIG.SYS file contains these lines
(values for files and buffers may be somewhat larger if desired):
DEVICE=C:\DOS\ANSI.SYS (Assuming ANSI.SYS is in directory C:\DOS)
FILES=30
BUFFERS=20
The programs will run much faster if your PC-compatible computer has a
math coprocessor.
REFERENCES CITED
Cook, E.R. 1985.
A time-series analysis approach to tree-ring standardization. Ph.D.
Dissertation, Department of Geosciences, University of Arizona, Tucson.
Cook, E.R., and Peters, K. 1981.
The smoothing spline: a new approach to standardizing forest interior tree-
ring width series for dendroclimatic studies. Tree-Ring Bulletin 41:45-53.
Fritts, H.C. 1976.
Tree rings and climate. Academic Press, London, 567 pp.
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.
Holmes, R.L., Adams, R.K., and Fritts, H.C. 1986.
Tree-ring chronologies of western North America: California, eastern Oregon
and northern Great Basin, with procedures used in the chronology development
work, including users manuals for computer programs COFECHA and ARSTAN.
Chronology Series VI. Laboratory of Tree-Ring Research, University of
Arizona, Tucson.
Monserud, R.A. 1986.
Time-series analyses of tree-ring chronologies. Forest Science 32:349-372
Parker, M. L. 1971.
Dendrochronological techniques used by the Geological Survey of Canada.
Geological Survey of Canada Paper 71-25, p 26, Department of Energy, Mines
and Resources, Ottawa.
Parker, M. L. 1967.
Dendrochronology of Point of Pines. Masters Thesis, Department of
Anthropology, University of Arizona, Tucson, p 91-100.
Thornthwaite, C.W. 1948.
An approach toward a rational classification of climate. Geographical
Review 38:55-94
Thornthwaite, C.W. 1931.
The climates of North America, according to a new classification.
Geographical Review 21:633-655
Wigley, T.M.L., Briffa, K.R., and Jones, P.D. 1984.
On the average value of correlated time series, with applications in
dendroclimatology and hydrometeorology. Journal of Climate and Applied
Meteorology 23(2):201-213.
KEY TO TASKS
You may use this key to tasks by looking up an action you would like to
carry out and consulting the description of the routines or section listed.
For page numbers see the table of contents on page 1.
Task to perform Routine or section to see
Accurite measurement format FMT
Accurite measurement format, description Data formats
Add a constant to data series FMT
Bar plots in parallel columns BAR
Bar plots, one page per series BAR
Carriage control of file, Fortran COL, PRT, ..., General comments
Carriage control of file, list or text COL, PRT, ..., General comments
Casewise format FMT, YUR, YUX, Data formats
Change dating of set of series by a constant FMT
Change format of file of data series FMT
Chronology format FMT
Chronology format, description Data formats
Chronology, compute ARSTAN, CRN
Climatic data diagrams CLD
Climatic data format FMT
Climatic data format, description Data formats
Climatic data, compute regional mean MET
Climatic data, estimate missing data MET
Climatic data, seasonalize SEA
Coefficient of variation COV
Column format, several columns of data FMT, YUR, YUX
Column format, single column of data FMT
Column format, two columns of data FMT
Columns of a file, copy selected COL
Compact format FMT
Compact format, description Data formats
Constant, add or subtract from data series FMT
Constant, add/subtract from dating of series FMT
Constant, multiply or divide data series by FMT
Copy selected columns of a file COL
Correlation matrix MAT
Correlations among data series MAT
Crossdating, quality control COFECHA
Data file names General comments
Data file, description Data formats
Data quality control, crossdating COFECHA
Data series (see also time series) Data formats
Data series bar plots in parallel columns BAR
Data series bar plots, one page per series BAR
Data series in alphanumeric order of ident FMT
Data series plot for printer LNP
Data series plot on screen SCR
Data series, add/subtract constant to values FMT
Data series, edit EDT
Data series, fit cubic spline to FMT
Data series, multiply or divide by a constant FMT
Data series, plot for printer PRT
Data series, plot on screen SCR
Dating, add or subtract a constant FMT
Dating, change all series by a constant FMT
Dating, change selected series EDT
Dating, quality control COFECHA
Divide data series by a constant FMT
Edit data series EDT
Edit measurements EDT
Edit ring measurements EDT
Edit time series EDT
Eigenvectors PCA, ARSTAN
File carriage control, Fortran COL, PRT, ..., General comments
File carriage control, list or text COL, PRT, ..., General comments
File names, data files General comments
File names, output for printing PRT, General comments
File type, Fortran COL, PRT, ..., General comments
File type, list or text COL, PRT, ..., General comments
Format of data file, change FMT
Format, Accurite measurements FMT
Format, chronology FMT
Format, climatic data FMT
Format, column(s) FMT, YUR, YUX
Format, compact FMT
Format, data values in column(s) FMT, YUR, YUX
Format, index FMT
Format, measurements FMT
Format, meteorological data FMT
Format, ring measurements FMT
Format, user-defined FMT
Formats, description Data formats
Fortran file type COL, PRT, ..., General comments
Identification of data file COL, PRT, ..., General comments
Index format FMT
Index format, description Data formats
ITRDB chronology format FMT
ITRDB index format FMT
ITRDB measurement format FMT
Laser printer, prepare file for PRT
Listing of tree-ring measurements LRM
Measurement format FMT
Measurements to alphanumeric order of ident FMT
Measurements, edit EDT
Measurements, quality control COFECHA
Meteorological data diagrams CLD
Meteorological data format FMT
Meteorological data format, description Data formats
Meteorological data, compute regional mean MET
Meteorological data, estimate missing data MET
Meteorological data, seasonalize SEA
Multiply data series by a constant FMT
Plot data series for printer LNP
Plot data series on screen SCR
Plot time series for printer LNP
Plot time series on screen SCR
Plots, scatter SCA
Plots, X and Y SCA
Principal components PCA, ARSTAN
Printer, prepare file for PRT
Quality control, crossdating COFECHA
Quality control, tree-ring dating COFECHA
Quality control, tree-ring measurements COFECHA
Ring measurement bar plots in parallel columns BAR
Ring measurement bar plots, one page per series BAR
Ring measurements, alphanumeric order of ident FMT
Ring measurements, edit EDT
Ring measurements, list LRM
Ring measurements, quality control of dating COFECHA
Scattergram plots SCA
Selected columns of a file, copy COL
Skeleton plots in parallel columns BAR
Skeleton plots, one page per series BAR
Spline, fit to data series and save indices FMT
Spline, fit to data series and save spline FMT
Spreadsheet format FMT, YUR, YUX
Subtract a constant from data series FMT
Text file type COL, PRT, ..., General comments
Time series (see also data series) Data formats
Time series bar plots in parallel columns BAR
Time series bar plots, one page per series BAR
Time series data file, description Data formats
Time series in alphanumeric order of ident FMT
Time series plot for printer LNP
Time series plot on screen SCR
Time series, add/subtract constant to values FMT
Time series, edit EDT
Time series, fit cubic spline to FMT
Time series, multiply or divide by a constant FMT
Time series, plot for printer PRT
Time series, plot on screen SCR
Title for data file Data formats
Tree-ring bar plots in parallel columns BAR
Tree-ring bar plots, one page per series BAR
Tree-ring crossdating, quality control COFECHA
Tree-ring dating, quality control COFECHA
Tree-ring measurements, list LRM
Tree-ring measurements, quality control COFECHA
Tucson format (see ITRDB) Data formats
Two columns, data values in FMT
User-defined format FMT
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