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 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 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 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 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.

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 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 Interactive detrending:

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:

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-da std cle-da std cle-da std cle-da std cle-da std cle-da std cle-da std cle-da std cle-da std cle-da std cle-da std cle-da std cle-da std cle-da std cle-da std cle-da std cle-da std cle-da 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-da res cle-da res cle-da res cle-da res cle-da res cle-da res cle-da res cle-da res cle-da res cle-da res cle-da res cle-da res cle-da res cle-da res cle-da res cle-da res cle-da res cle-da res ARSTAN Chronologies are in ITRDB or Index format:

year num seg age raw std res ars ARSTAN Chronologies are also placed in columns for easy import into Excel in a separate file:

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 CLE CLE001B CLE001C CLE002B CLE002C CLE CLE003B CLE003C CLE CLE004A CLE004B CLE ARSTAN A separate file is created to archive the series detrending option: year corrs rbar sdev serr eps cores A separate file is created to archive the rbar and eps information: