Statistical Crossdating with COFECHA

COFECHA Cutting edge, high-powered statistics ensure precision in yearly assignments. Evolution: beginnings in late 1970s with Richard Holmes creating algorithms using correlation techniques. Statistical Crossdating

What is a correlation coefficient? Extremely important in geography, dendrochronology, and practically all sciences… Statistical Crossdating COFECHA

Correlation Coefficients Used to test the strength of linear association between two variables In our case, the tree-ring series being tested against all other tree-ring series. COFECHA

Correlation Coefficients

-1.0 < r < +1.0 COFECHA Correlation Coefficients = r-values

COFECHA Correlation Coefficients and Statistical Significance

COFECHA Correlation Coefficients

Mean sensitivity An important measure of how sensitive the ring widths (or densities) are, year to year. Not to be confused with variability, although the two are remotely related. Effective ranges: 0.10 to Southeastern, PNW, upper elevation trees: 0.15 to 0.20 common, 0.25 to 0.35 exceptional. Southwestern and semiarid site trees: 0.35 to 0.50 common, 0.60 to 0.80 exceptional. COFECHA

Welcome to COFECHA (Spanish for “co-date” or “crossdate”): Analyzes crossdating accuracy of all measured series. First breaks down each series into shorter segment lengths (for example, 40 yrs). Compares each segment with the same calendar segment from the average of all other series via correlation techniques. The analysis then shifts by half the segment length and compares the next 40 yr segment. Continues until the end of the series being tested. COFECHA

COFECHA: A segment that falls below the statistical significance threshold is flagged by COFECHA. It then attempts to place the errant segment in an alternate position via date adjustments. Most common alternate positions/date adjustments are what ??? Prints out diagnostics that let the user zero in on the possible ring causing the errant segment. Interseries correlation coefficient is the key benchmark of crossdating quality: Also inspect the average mean sensitivity and autocorrelation values. COFECHA

What does COFECHA do to enhance crossdating interpretation? Crossdating is a “high-frequency” process. We concentrate on the year-to-year overall patterns. Therefore, we must remove all “low-frequency” trends first = autocorrelation effects, age-related trend, possible disturbance trends. COFECHA performs three transformations on each series! 1. Fit with a 32-yr spline = maximizes interseries correlation 2. Performs autoregressive modeling to remove effects of autocorrelation = biological inertia 3. Performs log transformation to weigh proportional differences in ring measurements proportionally COFECHA

[] Dendrochronology Program Library Run TEST Program COF 14:50 Tue 18 Oct 2005 Page 1 [] [] P R O G R A M C O F E C H A Version 6.06P QUALITY CONTROL AND DATING CHECK OF TREE-RING MEASUREMENTS File of DATED series: fl003.rwl CONTENTS: 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 by year Part 4: Bar plot of Master Dating Series Part 5: Correlation by segment of each series with Master Part 6: Potential problems: low correlation, divergent year-to-year changes, absent rings, outliers Part 7: Descriptive statistics RUN CONTROL OPTIONS SELECTED VALUE 1 Cubic smoothing spline 50% wavelength cutoff for filtering 32 years 2 Segments examined are 40 years lagged successively by 20 years 3 Autoregressive model applied A Residuals are used in master dating series and testing 4 Series transformed to logarithms Y Each series log-transformed for master dating series and testing 5 CORRELATION is Pearson (parametric, quantitative) Critical correlation, 99% confidence level Master dating series saved N 7 Ring measurements listed N 8 Parts printed Absent rings are omitted from master series and segment correlations (Y) Text in file: LEN 1 O'Leno State Park QUST Text in file: LEN 2 Florida Post Oak 15M __ Text in file: LEN 3 D.Stahle M.Cleaveland Time span of Master dating series is 1852 to years Continuous time span is 1852 to years Portion with two or more series is 1854 to years **************************************** *C* Number of dated series 24 *C* *O* Master series yrs *O* *F* Total rings in all series 2540 *F* *E* Total dated rings checked 2538 *E* *C* Series intercorrelation.509 *C* *H* Average mean sensitivity.266 *H* *A* Segments, possible problems 26 *A* *** Mean length of series *** ****************************************

PART 2: TIME PLOT OF TREE-RING SERIES: 14:50 Tue 18 Oct 2005 Page Ident Seq Time-span Yrs : : : : : : : : : : : : : : : : : : : : : len01b len01a len02a len02b len03a len03b leno3c len04b len05a len05b len06a len06b len07a len08a len08b len09a len09b len10a len12a len12b len41a len41b len42a len42b : : : : : : : : : : : : : : : : : : : : :

PART 3: Master Dating Series: 14:50 Tue 18 Oct 2005 Page Year Value No Ab Year Value No Ab Year Value No Ab Year Value No Ab Year Value No Ab Year Value No Ab

PART 4: Master Bar Plot: 14:50 Tue 18 Oct 2005 Page Year Rel value Year Rel value Year Rel value Year Rel value Year Rel value Year Rel value Year Rel value Year Rel value C B B H 1952-c D G c D A 1855-c a A b a 1857o A A b 1908h F B D C G D B B E a I D a D b D A 1964f c 1915f A c 1916h G D b A C B A b 1970-e 1871-e c D 1872g b 1873-d G C b E 1974-c A a b A 1927-e a 1878-d B B a 1979-d A B a 1981h G 1932o b G A A B E B a C c B a 1887-e 1937-c 1987g a C 1889-e D b G F E B 1941-d B D a D b a c a b A 1945-d a 1947-d 1898g 1899-d b

PART 5: CORRELATION OF SERIES BY SEGMENTS: 14:50 Tue 18 Oct 2005 Page Correlations of 40-year dated segments, lagged 20 years Flags: A = correlation under.3665 but highest as dated; B = correlation higher at other than dated position Seq Series Time_span len01b B.26A len01a A.29B len02a A len02b len03a len03b leno3c A 8 len04b len05a len05b B len06a A len06b A.28B 13 len07a len08a len08b B.22B 16 len09a A.34A.32A 17 len09b B.26B 18 len10a B.28B 19 len12a A 20 len12b A.36A B 21 len41a len41b A.32A 23 len42a B 24 len42b Av segment correlation

PART 6: POTENTIAL PROBLEMS: 14:50 Tue 18 Oct 2005 Page For each series with potential problems the following diagnostics may appear: [A] Correlations with master dating series of flagged 40-year segments of series filtered with 32-year spline, at every point from ten years earlier (-10) to ten years later (+10) than dated [B] Effect of those data values which most lower or raise correlation with master series Symbol following year indicates value in series is greater (>) or lesser (<) than master series value [C] Year-to-year changes very different from the mean change in other series [D] Absent rings (zero values) [E] Values which are statistical outliers from mean for the year ==================================================================================================================================== len01b 1866 to years Series 1 [A] Segment High | * * [B] Entire series, effect on correlation (.485) is: Lower 1932> > > < Higher to 1939 segment: Lower 1932> > Higher to 1959 segment: Lower 1932> > > < < < Higher [C] Year-to-year changes diverging by over 4.0 std deviations: SD [E] Outliers SD above or -4.5 SD below mean for year SD PART 5: CORRELATION OF SERIES BY SEGMENTS: 14:50 Tue 18 Oct 2005 Page Correlations of 40-year dated segments, lagged 20 years Flags: A = correlation under.3665 but highest as dated; B = correlation higher at other than dated position Seq Series Time_span len01b B.26A.57.63

PART 7: DESCRIPTIVE STATISTICS: 14:50 Tue 18 Oct 2005 Page Corr // Unfiltered \\ //---- Filtered -----\\ No. No. No. with Mean Max Std Auto Mean Max Std Auto AR Seq Series Interval Years Segmt Flags Master msmt msmt dev corr sens value dev corr () len01b len01a len02a len02b len03a len03b leno3c len04b len05a len05b len06a len06b len07a len08a len08b len09a len09b len10a len12a len12b len41a len41b len42a len42b Total or mean: = [ COFECHA TEST COF ] = -

Seq Series Time_span A.32A A.32A A B.22B A B.22B CBES3A B.29A CBES3A B.29A CBES3B B.29A CBES3B B.29A Av segment correlation Av segment correlation COFECHA

Seq Series Time_span A.32A A.32A A B.22B A B.22B B-.13B.02B.08B.07B.00B-.04B.02B.07B.14B.15B.10B B-.13B.02B.08B.07B.00B-.04B.02B.07B.14B.15B.10B CBES3A B.29A CBES3A B.29A CBES3B B.29A CBES3B B.29A Av segment correlation Av segment correlation COFECHA

to years Series 12 [A] Segment High [A] Segment High |.37* |.37* |.51* |.51* |.60* |.60* |.72* |.72* |.64* |.64* |.65* |.65* |.67* |.67* |.69* |.69* |.75* |.75* |.71* |.71* |.64* |.64* |.67* |.67* As dated = “zero shift” position COFECHA

Seq Series Time_span Seq Series Time_span A.33A A.33A A B.21B A B.21B B.14B.07B-.12B-.16B B.14B.07B-.12B-.16B CBES3A B.29A CBES3A B.29A CBES3B B.29A CBES3B B.29A Av segment correlation Av segment correlation COFECHA

to years Series to years Series 13 [A] Segment High [A] Segment High |.66* |.66* |.77* |.77* |.78* |.78* |.62* |.62* |.66* |.66* As dated = “zero shift” position COFECHA

PART 7: DESCRIPTIVE STATISTICS: 17:06 Thu 09 PART 7: DESCRIPTIVE STATISTICS: 17:06 Thu Corr // Unfiltered \\ //---- Filtered -----\\ Corr // Unfiltered \\ //---- Filtered -----\\ No. No. No. with Mean Max Std Auto Mean Max Std Auto AR No. No. No. with Mean Max Std Auto Mean Max Std Auto AR Seq Series Interval Years Segmt Flags Master msmt msmt dev corr sens value dev corr () Seq Series Interval Years Segmt Flags Master msmt msmt dev corr sens value dev corr () CBES3A CBES3A CBES3B CBES3B Total or mean: Total or mean: COFECHA

A major use of COFECHA is to date tree rings of a sample against a master chronology for a region.

COFECHA Remember, crossdating has to be convincing both graphically and statistically. Never, ever rely solely on COFECHA (direct from Richard himself). A violin