Detrending with ARSTAN
ARSTAN
•
Detrends individual tree-ring measurement series of unwanted trends,
especially age-related trends and those from local/regional
disturbances unrelated to climate.
•
Developed by Dr. Edward R. Cook of the Tree-Ring Laboratory at
Lamont-Doherty Earth Observatory, Columbia University, with
important modifications by Paul Krusic.
•
Largely a product of his dissertation research: Cook, E.R. 1985. A time
series analysis approach to tree ring standardization. Ph.D.
dissertation, The University of Arizona, Tucson, 171 pp.
•
First disseminated in late 1980s, now the
de facto standard for detrending tree-ring
measurement time series.
•
Available for free download from the TRL
software web site at Lamont-Doherty Earth
Observatory. (Note Absoft folder location
requirement.)
ARSTAN
•
Several versions of the years. Know what each can and can not do.
• CRONOL:
Stripped down version that does no pooled autogression modeling,
therefore producing only the standard and residual chronology
types.
• ARSTAN for DOS:
The standard for many years, still used by many researchers,
powerful, straight-forward, also available for download from the
Laboratory of Tree-Ring Research at the University of Arizona.
• ARSTAN for WINDOWS:
New in recent years, batch mode processing, powerful graphics,
interactive detrending capability, considerable output for diagnostics
(running rbar, individual summary statistics, table for easy input into
Excel).
•
Note that no formal User’s Manual was ever created. Ed feels users
should be knowledgeable of his dissertation. Some rudimentary guides
do exist and are often cited.
ARSTAN
•
Detrending! The advantage of the Windows version with its graphics
capabilities is that you can now visually inspect the detrending curve to
ensure the curve is doing what it is supposed to do.
•
Begin by choosing a class of detrending options, for example, negative
exponential curves and if the curve is a poor fit, then fit a straight line to
the tree-ring series (common first choice).
•
Inspect the initial choice of detrending class and ask yourself, “Are
these curves able to model the growth of the tree over time?” If not,
then choose another detrending class type, for example, 50-year
smoothing spline.
•
Three chronology types produced: (1) standard: chronology with
considerable autocorrelation (the standard for many years and still is);
(2) residual: autoregressive modeling on individual series, resulting in
no low-frequency trends whatsoever; (3) arstan: pooled autoregression
property derived from all series, assumed to be climatic in origin, then
placed back into the residual series.
•
Note: a raw chronology type is also produced.
ARSTAN
•
The ARSTAN Main Menu: Basics
•
“opt” is the option chosen for that menu item
•
A description of that menu item is found to the right
•
“plt” indicates whether or not to plot out the results from that option
•
The default option will be highlighted in brackets <n> so that simply
hitting return chooses that option
•
Help is available in most options by hitting “h for help”
•
Most important options:
•
[4] first detrending
•
[7] interactive detrend
•
[13] stabilize variance
•
[15] site-tree-core mask
•
[16] running rbar
•
[19] summary plots
ARSTAN
•
The ARSTAN Main Menu
ARSTAN
•
To demonstrate ARSTAN, I’m going to use a data set of raw
measurement series that came from a historic log structure in Meigs
County, Tennessee.
•
The samples have already been crossdated graphically and statistically
using COFECHA. The data set extends from 1707 to 1875.
•
This data set is ideal because (1) the oak trees are eastern hardwoods
that are more prone to effects of stand dynamics, and (2) in fact, the
measurements will show two major changes in growth rates unrelated
to climate, likely caused by a major forest disturbance of some type (but
unknown).
•
These unwanted trends must therefore be removed if we are to use the
master chronology from this data set in any further analyses, especially
when attempting to quantify past climate.
•
Note that we normally would have accepted the default detrending
option of negative exponential/straight line fit. This exercise
demonstrates the usefulness of interactive detrending.
ARSTAN
•
Spaghetti plot can assist in evaluating overall trend in your data set:
Note the two major changes in
growth rate for all samples = two
disturbances ca. 1778 and 1836!
ARSTAN
•
Detrending curves with mean give you an overall sense of trend:
ARSTAN
•
Running rbar and eps are important diagnostics of sample quality:
ARSTAN
•
Interactive detrending:
Straight-line fit appears
poor. Note release about
1786.
ARSTAN
•
Interactive detrending:
100-year spline fit. Release
still evident.
ARSTAN
•
Interactive detrending:
50-year spline fit. Release
effects now minimal.
ARSTAN
•
Interactive detrending:
Straight-line fit appears poor.
Note change in growth rate
about 1778 and again in 1830.
ARSTAN
•
Interactive detrending:
50-year spline fit. Still doesn’t
appear ideal. Note remaining
trend.
ARSTAN
•
Interactive detrending:
32-year spline fit. Much better
fit to this “trendy” series.
ARSTAN
•
Interactive detrending:
Linear fit. Not bad but fails to
model early trends.
ARSTAN
•
Interactive detrending:
32-year spline. We should consider
removing 1724 to 1738.
ARSTAN
•
Interactive detrending:
Linear fit. This looks appropriate.
ARSTAN
•
Interactive detrending:
Linear fit doesn’t look appropriate.
ARSTAN
•
Interactive detrending:
32-year spline is much better.
ARSTAN
•
Interactive detrending:
Only negative exponential curve fit,
but does not model trend well.
ARSTAN
•
Interactive detrending:
32-year spline is a much better fit.
ARSTAN
•
Note 32-year spline now fit to the raw measurement series:
ARSTAN
•
Note AR(1) model used to add back autocorrelation to residual series,
as this is likely a climatic signal:
ARSTAN
•
Finally, you obtain very nice graphs of your final chronologies:
ARSTAN
•
Chronologies are in ITRDB or Index format:
cle-dated.txt -- no data title -cle-dated.txt -- no data title -cle-dated.txt -- no data title -cle-da17079990 09990 09990 09990
cle-da17102257 32097 31351 31181
cle-da1720 738 3 676 31132 31138
cle-da1730 609 12 791 12 722 12 802
cle-da1740 964 121211 121110 12 989
cle-da1750 887 12 804 12 932 121048
cle-da1760 814 121081 12 822 12 938
cle-da1770 990 12 931 12 789 12 726
cle-da17801354 12 895 121069 12 961
cle-da17901009 121018 12 870 121221
cle-da18001103 12 824 12 982 12 935
cle-da1810 893 121018 12 836 12 921
cle-da18201011 12 854 12 758 12 908
cle-da18301061 12 993 12 866 12 902
cle-da18401082 121212 121297 121343
cle-da18501112 12 934 121140 12 916
cle-da18601213 11 938 111052 111140
cle-da18701042 9 998 8 787 8 905
cle-dated.txt -- no data title -cle-dated.txt -- no data title -cle-dated.txt -- no data title -cle-da17079990 09990 09990 09990
cle-da17101821 3 966 3 841 3 949
cle-da1720 977 3 841 31347 31059
cle-da1730 487 12 919 12 852 12 939
cle-da1740 936 121210 121007 12 919
cle-da1750 948 12 871 121094 121096
cle-da1760 876 121204 12 798 121035
cle-da17701056 12 951 12 848 12 854
cle-da17801336 12 759 121162 12 951
cle-da1790 903 12 982 12 859 121293
cle-da18001167 12 780 121076 12 951
cle-da18101001 121077 12 847 121002
cle-da18201024 12 878 12 842 121034
cle-da18301071 12 982 12 880 12 955
cle-da18401118 121176 121185 121168
cle-da18501094 12 869 121166 12 867
cle-da18601254 11 838 111089 111123
cle-da1870 985 9 999 8 784 81035
09990
3 666
31357
12 757
12 991
12 781
12 921
12 557
12 698
121103
12 961
121052
12 905
12 671
121124
12 851
111041
71098
09990
3 570
81292
12 589
121375
12 696
12 993
12 598
12 795
121018
121112
12 922
12 716
121010
121151
12 936
111005
61158
09990
3 721
121657
12 736
121137
12 850
12 941
12 694
121286
12 852
12 948
12 756
12 788
121313
121275
12 903
10 946
39990
09990
3 542
31211
12 844
121001
12 802
12 976
12 689
12 705
121018
12 992
121110
12 959
12 701
12 926
12 889
11 983
71088
09990
3 838
81103
12 695
121405
12 827
121031
12 839
12 940
12 941
121101
12 907
12 788
121169
121104
121013
111011
61119
09990
3 928
121500
12 959
12 992
121011
12 956
12 862
121381
12 832
12 880
12 803
12 913
121283
121289
12 937
10 998
39990
1st itrdb line missing
2nd itrdb line missing
3rd itrdb line missing
02074 31554 31835 3
3 817 3 745 3 632 3
121051 121227 121320 12
121060 12 910 121172 12
121132 12 803 12 888 12
12 931 12 920 12 886 12
121000 121145 12 792 12
12 629 12 701 121067 12
121358 121431 121156 12
121080 121037 12 842 12
12 840 121054 12 847 12
12 948 12 979 12 979 12
12 927 121028 12 949 12
121108 121097 12 881 12
121208 121285 121005 12
111103 11 986 11 920 11
91008 9 865 91175 9
09990 09990 09990 0
1st itrdb line missing
2nd itrdb line missing
3rd itrdb line missing
01697 3 720 31535 3
31059 3 827 3 797 3
12 825 121118 121148 12
121196 12 832 121166 12
121051 12 778 121013 12
121027 12 959 12 949 12
12 995 121137 12 768 12
12 779 12 893 121210 12
121217 121251 12 950 12
121117 121006 12 850 12
12 881 121136 12 841 12
121060 121013 12 996 12
121042 121073 12 957 12
12 934 121041 12 816 12
121019 121178 12 860 12
111158 11 916 11 940 11
91080 9 883 91240 9
09990 09990 09990 0
std
std
std
std
std
std
std
std
std
std
std
std
std
std
std
std
std
std
std
std
std
res
res
res
res
res
res
res
res
res
res
res
res
res
res
res
res
res
res
res
res
res
ARSTAN
•
Chronologies are also placed in columns for easy import into
Excel in a separate file:
year
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
num
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
3.
8.
12.
12.
12.
12.
12.
12.
12.
12.
12.
12.
12.
12.
12.
12.
12.
seg
160.333
160.333
160.333
160.333
160.333
160.333
160.333
160.333
160.333
160.333
160.333
160.333
160.333
160.333
160.333
160.333
160.333
154.250
151.417
151.417
151.417
151.417
151.417
151.417
151.417
151.417
151.417
151.417
151.417
151.417
151.417
151.417
151.417
age
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
11.000
12.000
13.000
14.000
15.000
16.000
17.000
7.375
5.917
6.917
7.917
8.917
9.917
10.917
11.917
12.917
13.917
14.917
15.917
16.917
17.917
18.917
19.917
raw
2.153
1.297
1.535
2.073
1.700
1.163
0.961
0.562
0.543
0.611
0.772
0.672
0.562
0.610
0.608
0.939
0.946
1.156
1.054
1.339
0.938
1.062
1.046
0.461
0.638
0.562
0.592
0.584
0.440
0.565
0.874
0.690
0.892
std
2.074
1.554
1.835
2.257
2.097
1.351
1.181
0.666
0.570
0.721
0.817
0.745
0.632
0.738
0.676
1.132
1.138
1.357
1.292
1.657
1.051
1.227
1.320
0.609
0.791
0.722
0.802
0.757
0.589
0.736
1.060
0.910
1.172
res
1.697
0.720
1.535
1.821
0.966
0.841
0.949
0.542
0.838
0.928
1.059
0.827
0.797
0.977
0.841
1.347
1.059
1.211
1.103
1.500
0.825
1.118
1.148
0.487
0.919
0.852
0.939
0.844
0.695
0.959
1.196
0.832
1.166
ars
1.882
1.176
1.626
2.144
1.556
1.128
1.016
0.550
0.606
0.725
0.917
0.784
0.686
0.815
0.746
1.216
1.171
1.300
1.258
1.633
1.152
1.196
1.249
0.616
0.720
0.708
0.788
0.734
0.558
0.731
1.057
0.861
1.094
ARSTAN
•
A separate file is created to archive the series detrending option:
num
ify
yfp
idt
isb
ics
num
1
2
3
4
5
6
7
8
9
10
11
12
•
=
=
=
=
=
=
number of series
ident = series identification
first year of time series
ily = last year of time series
years from pith for rcs
itn = transform (>3 = power*1000)
series detrending options
ips = series ar model order options
stabilize variance options
icu = use (1) or do not use (0)
save (1) or do not save (0)
cpa = common period analysis series
-- do not delete these lines -ident
ify
ily
yfp
itn
idt
ips
isb
icu
ics
cpa
CLE001
1707 1865
0
0
100
0
0
1
1
1
CLE001B
1707 1870
0
0
4
0
0
1
1
2
CLE001C
1707 1864
0
0
4
0
0
1
1
3
CLE002B
1725 1855
0
0
32
0
0
1
1
4
CLE002C
1724 1874
0
0
4
0
0
1
1
5
CLE003
1725 1874
0
0
32
0
0
1
1
6
CLE003B
1725 1875
0
0
4
0
0
1
1
7
CLE003C
1725 1875
0
0
4
0
0
1
1
8
CLE004
1724 1873
0
0
32
0
0
1
1
9
CLE004A
1724 1874
0
0
4
0
0
1
1
10
CLE004B
1724 1875
0
0
4
0
0
1
1
11
CLE005
1724 1872
0
0
32
0
0
1
1
12
A separate file is created to archive the rbar and eps information:
year
1727.
1760.
1790.
1820.
1850.
corrs
3.
66.
66.
66.
36.
rbar
0.8298
0.3649
0.5555
0.4073
0.4689
sdev
0.0835
0.2102
0.1576
0.1519
0.1640
serr
0.0482
0.0259
0.0194
0.0187
0.0273
eps
0.9752
0.8733
0.9375
0.8918
0.9098
cores
8.07
12.00
12.00
12.00
11.43