1. Detrending with ARSTAN

2. 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.)

3. 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.

4. 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.

5. 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 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

6. ARSTAN The ARSTAN Main Menu

7. 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.

8. 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!

9. ARSTAN Detrending curves with mean give you an overall sense of trend:

10. ARSTAN Running rbar and eps are important diagnostics of sample quality:

11. ARSTAN Interactive detrending: Straight-line fit appears poor. Note release about 1786.

12. ARSTAN Interactive detrending: 100-year spline fit. Release still evident.

13. ARSTAN Interactive detrending: 50-year spline fit. Release effects now minimal.

14. ARSTAN Interactive detrending: Straight-line fit appears poor. Note change in growth rate about 1778 and again in 1830.

15. 50-year spline fit. Still doesn’t appear ideal. Note remaining trend. ARSTAN Interactive detrending:

16. 32-year spline fit. Much better fit to this “trendy” series. ARSTAN Interactive detrending:

17. Linear fit. Not bad but fails to model early trends. ARSTAN Interactive detrending:

18. 32-year spline. We should consider removing 1724 to 1738. ARSTAN Interactive detrending:

19. Linear fit. This looks appropriate. ARSTAN Interactive detrending:

20. Linear fit doesn’t look appropriate. ARSTAN Interactive detrending:

21. 32-year spline is much better. ARSTAN Interactive detrending:

22. Only negative exponential curve fit, but does not model trend well. ARSTAN Interactive detrending:

23. 32-year spline is a much better fit. ARSTAN Interactive detrending:

24. ARSTAN Note 32-year spline now fit to the raw measurement series:

25. ARSTAN Note AR(1) model used to add back autocorrelation to residual series, as this is likely a climatic signal:

26. ARSTAN Finally, you obtain very nice graphs of your final chronologies:

27. cle-dated.txt -- no data title -- 1st itrdb line missing std cle-dated.txt -- no data title -- 2nd itrdb line missing std cle-dated.txt -- no data title -- 3rd itrdb line missing std cle-da17079990 09990 09990 09990 09990 09990 09990 02074 31554 31835 3 std cle-da17102257 32097 31351 31181 3 666 3 570 3 721 3 817 3 745 3 632 3 std cle-da1720 738 3 676 31132 31138 31357 81292 121657 121051 121227 121320 12 std cle-da1730 609 12 791 12 722 12 802 12 757 12 589 12 736 121060 12 910 121172 12 std cle-da1740 964 121211 121110 12 989 12 991 121375 121137 121132 12 803 12 888 12 std cle-da1750 887 12 804 12 932 121048 12 781 12 696 12 850 12 931 12 920 12 886 12 std cle-da1760 814 121081 12 822 12 938 12 921 12 993 12 941 121000 121145 12 792 12 std cle-da1770 990 12 931 12 789 12 726 12 557 12 598 12 694 12 629 12 701 121067 12 std cle-da17801354 12 895 121069 12 961 12 698 12 795 121286 121358 121431 121156 12 std cle-da17901009 121018 12 870 121221 121103 121018 12 852 121080 121037 12 842 12 std cle-da18001103 12 824 12 982 12 935 12 961 121112 12 948 12 840 121054 12 847 12 std cle-da1810 893 121018 12 836 12 921 121052 12 922 12 756 12 948 12 979 12 979 12 std cle-da18201011 12 854 12 758 12 908 12 905 12 716 12 788 12 927 121028 12 949 12 std cle-da18301061 12 993 12 866 12 902 12 671 121010 121313 121108 121097 12 881 12 std cle-da18401082 121212 121297 121343 121124 121151 121275 121208 121285 121005 12 std cle-da18501112 12 934 121140 12 916 12 851 12 936 12 903 111103 11 986 11 920 11 std cle-da18601213 11 938 111052 111140 111041 111005 10 946 91008 9 865 91175 9 std cle-da18701042 9 998 8 787 8 905 71098 61158 39990 09990 09990 09990 0 std cle-dated.txt -- no data title -- 1st itrdb line missing res cle-dated.txt -- no data title -- 2nd itrdb line missing res cle-dated.txt -- no data title -- 3rd itrdb line missing res cle-da17079990 09990 09990 09990 09990 09990 09990 01697 3 720 31535 3 res cle-da17101821 3 966 3 841 3 949 3 542 3 838 3 928 31059 3 827 3 797 3 res cle-da1720 977 3 841 31347 31059 31211 81103 121500 12 825 121118 121148 12 res cle-da1730 487 12 919 12 852 12 939 12 844 12 695 12 959 121196 12 832 121166 12 res cle-da1740 936 121210 121007 12 919 121001 121405 12 992 121051 12 778 121013 12 res cle-da1750 948 12 871 121094 121096 12 802 12 827 121011 121027 12 959 12 949 12 res cle-da1760 876 121204 12 798 121035 12 976 121031 12 956 12 995 121137 12 768 12 res cle-da17701056 12 951 12 848 12 854 12 689 12 839 12 862 12 779 12 893 121210 12 res cle-da17801336 12 759 121162 12 951 12 705 12 940 121381 121217 121251 12 950 12 res cle-da1790 903 12 982 12 859 121293 121018 12 941 12 832 121117 121006 12 850 12 res cle-da18001167 12 780 121076 12 951 12 992 121101 12 880 12 881 121136 12 841 12 res cle-da18101001 121077 12 847 121002 121110 12 907 12 803 121060 121013 12 996 12 res cle-da18201024 12 878 12 842 121034 12 959 12 788 12 913 121042 121073 12 957 12 res cle-da18301071 12 982 12 880 12 955 12 701 121169 121283 12 934 121041 12 816 12 res cle-da18401118 121176 121185 121168 12 926 121104 121289 121019 121178 12 860 12 res cle-da18501094 12 869 121166 12 867 12 889 121013 12 937 111158 11 916 11 940 11 res cle-da18601254 11 838 111089 111123 11 983 111011 10 998 91080 9 883 91240 9 res cle-da1870 985 9 999 8 784 81035 71088 61119 39990 09990 09990 09990 0 res ARSTAN Chronologies are in ITRDB or Index format:

28. year num seg age raw std res ars 1707 3. 160.333 1.000 2.153 2.074 1.697 1.882 1708 3. 160.333 2.000 1.297 1.554 0.720 1.176 1709 3. 160.333 3.000 1.535 1.835 1.535 1.626 1710 3. 160.333 4.000 2.073 2.257 1.821 2.144 1711 3. 160.333 5.000 1.700 2.097 0.966 1.556 1712 3. 160.333 6.000 1.163 1.351 0.841 1.128 1713 3. 160.333 7.000 0.961 1.181 0.949 1.016 1714 3. 160.333 8.000 0.562 0.666 0.542 0.550 1715 3. 160.333 9.000 0.543 0.570 0.838 0.606 1716 3. 160.333 10.000 0.611 0.721 0.928 0.725 1717 3. 160.333 11.000 0.772 0.817 1.059 0.917 1718 3. 160.333 12.000 0.672 0.745 0.827 0.784 1719 3. 160.333 13.000 0.562 0.632 0.797 0.686 1720 3. 160.333 14.000 0.610 0.738 0.977 0.815 1721 3. 160.333 15.000 0.608 0.676 0.841 0.746 1722 3. 160.333 16.000 0.939 1.132 1.347 1.216 1723 3. 160.333 17.000 0.946 1.138 1.059 1.171 1724 8. 154.250 7.375 1.156 1.357 1.211 1.300 1725 12. 151.417 5.917 1.054 1.292 1.103 1.258 1726 12. 151.417 6.917 1.339 1.657 1.500 1.633 1727 12. 151.417 7.917 0.938 1.051 0.825 1.152 1728 12. 151.417 8.917 1.062 1.227 1.118 1.196 1729 12. 151.417 9.917 1.046 1.320 1.148 1.249 1730 12. 151.417 10.917 0.461 0.609 0.487 0.616 1731 12. 151.417 11.917 0.638 0.791 0.919 0.720 1732 12. 151.417 12.917 0.562 0.722 0.852 0.708 1733 12. 151.417 13.917 0.592 0.802 0.939 0.788 1734 12. 151.417 14.917 0.584 0.757 0.844 0.734 1735 12. 151.417 15.917 0.440 0.589 0.695 0.558 1736 12. 151.417 16.917 0.565 0.736 0.959 0.731 1737 12. 151.417 17.917 0.874 1.060 1.196 1.057 1738 12. 151.417 18.917 0.690 0.910 0.832 0.861 1739 12. 151.417 19.917 0.892 1.172 1.166 1.094 ARSTAN Chronologies are also placed in columns for easy import into Excel in a separate file:

29. num = number of series ident = series identification ify = first year of time series ily = last year of time series yfp = years from pith for rcs itn = transform (>3 = power*1000) idt = series detrending options ips = series ar model order options isb = stabilize variance options icu = use (1) or do not use (0) ics = save (1) or do not save (0) cpa = common period analysis series -- do not delete these lines -- num ident ify ily yfp itn idt ips isb icu ics cpa 1 CLE001 1707 1865 0 0 100 0 0 1 1 1 2 CLE001B 1707 1870 0 0 4 0 0 1 1 2 3 CLE001C 1707 1864 0 0 4 0 0 1 1 3 4 CLE002B 1725 1855 0 0 32 0 0 1 1 4 5 CLE002C 1724 1874 0 0 4 0 0 1 1 5 6 CLE003 1725 1874 0 0 32 0 0 1 1 6 7 CLE003B 1725 1875 0 0 4 0 0 1 1 7 8 CLE003C 1725 1875 0 0 4 0 0 1 1 8 9 CLE004 1724 1873 0 0 32 0 0 1 1 9 10 CLE004A 1724 1874 0 0 4 0 0 1 1 10 11 CLE004B 1724 1875 0 0 4 0 0 1 1 11 12 CLE005 1724 1872 0 0 32 0 0 1 1 12 ARSTAN A separate file is created to archive the series detrending option: year corrs rbar sdev serr eps cores 1727. 3. 0.8298 0.0835 0.0482 0.9752 8.07 1760. 66. 0.3649 0.2102 0.0259 0.8733 12.00 1790. 66. 0.5555 0.1576 0.0194 0.9375 12.00 1820. 66. 0.4073 0.1519 0.0187 0.8918 12.00 1850. 36. 0.4689 0.1640 0.0273 0.9098 11.43 A separate file is created to archive the rbar and eps information: