Dendrochronological Crossdating by Skeleton Plotting

Dendrochronology is the study of (ology) time (chronos), or more specifically events in past time, using trees (dendros), or more specifically the growth rings of trees. Applications in dendrochronology include ecology (e.g., reconstruction and analysis of past fires or insect outbreaks), climatology (e.g., reconstruction and analysis of past droughts or cold periods), geology (e.g., reconstruction and analysis of past earthquakes or volcanic eruptions), and anthropology (e.g., reconstruction and analysis of past human behavior). A common objective of most dendrochronological studies is to put the present in perspective of the past in order to better understand current environmental processes and conditions. Virtually all applications of dendrochronology require that the exact year of formation of each growth ring be known, and therefore dendrochronologists do not merely count rings to find out how old trees are. Rather, all rings are dated to their exact year of formation by a process called crossdating, which may also be described as pattern matching.

Crossdating is the process of matching patterns of growth variation through time across many trees. Trees living within a homogeneous stand or forest often exhibit the same annual pattern of variation through time because they all experience the same limiting factors on growth (typically climate, but other factors can also affect growth). To crossdate samples from many trees, dendrochronologists compare variation in ring width across trees to temporally align the common pattern of variation. Unfortunately, it can be difficult to compare ring-width patterns of two or more specimens of actual wood because ring growth is often microscopic and trees typically grow at differing rates. Thus, it's often difficult to observe rings from many specimens at the same time in order to crossdate them, i.e., match their patterns of variation. Accordingly, dendrochronologists have developed a method called skeleton plotting whereby growth variation of wood specimens is represented on standard graph paper and then multpiple graph strips are compare instead of actual wood. The objective of this web based presentation is to provide pertinent information about dendrochronological crossdating by skeleton plotting and then provide users the opportunity to actually try it by playing with a Java applet that realistically simulates skeleton plotting and pattern matching.

Users who are unaware of dendrochronology or inexperienced in crossdating should read and understand the accompanying web pages listed below to understand various concepts of tree growth, wood anatomy, dendrochronology, and crossdating; experienced users may also wish to review these pages. Ultimately, all users should try crossdating by skeleton plotting for yourselves. Note that while the default settings of the applet create a reasonably simple example problem, users may change various settings to make more difficult--and fully realistic--crossdating problems. Once you have a good understanding of crossdating and have succeeded at doing it with the applet, please visit the web pages of Laboratory of Tree-Ring Research at The University of Arizona to learn about research, teaching, and extension opportunities in dendrochronology.

Lastly, please take the time to give us feedback by filling in the evaluation form. We constantly revise the applet and this set of explantory pages in order to increase their teaching-learning performance. Your feedback is an important part of this revision process.

Tree Growth, Sampling, and Growth Anomalies

Trees try to apply a sheath-like cone of new wood each year over what existed from the prior year. Thus, trees grow tall from the top (and from the tips of their branches) and out from the bark. To dendrochronologically sample a tree, pencil-thin increment cores are collected from near the base of the tree and represent a single radius of growth. Cores are collected using hollow increment borers that cause reasonably little harm to the health of the tree. After proper storage (mounting into protective holders) and preparation (sanding or planing the surface) of the sample, the transverse or cross-sectional view of radial ring growth is visible. The applet randomly generates a virtual; core of rings for skeleton plotting and crossdating. Note that the virtual tree growth extends temporally from left to right across the computer monitor.

Occasionally, environmental conditions during a growing season are so extreme (e.g., a drought) that a tree can not apply a full cone of growth over all itself. Perhaps the tree can maintain leaf, root, and cambial tissues during that year but not have enough additional photosynthetic production to apply any new wood cellulose. In this case, there would be no "annual" ring for that year, and this ring-growth anomaly is called a "missing" or "absent" ring. It is not likely that every tree in a homogeneous stand will miss the ring for that year, and therefore presumably at least one of the dendrochronologically sampled trees in the stand will have at least a narrow ring for that year. By matching growth patterns across trees, missing rings can be discovered and accounted for, thus preserving the true chronology of the tree growth. In the applet, the default setting is not to allow for missing rings, but you may turn on that option and restart a new core to try a harder crossdating problem that may include any number of missing rings. If there is a missing ring, the virtual core will show nothing for it; you will have to discover the missing ring by crossdating your skeleton plot with the master chronology.

Conversely, environmental conditions during a growing season are bimodal (e.g., spring moisture from snow melt, then a dry period, then summer rains) such that a tree applies two apparently full cones of growth over all itself. In this case, there would be two "annual" rings for that year, and this ring-growth anomaly is called a "false" or "intra-annual" ring. Although the intra-annual false band often differs anatomically from the true ring boundary enough so that it may be identified by it appearance, this is not always the case. Again, it is not likely that every tree in a homogeneous stand will have a false ring for that year, and therefore presumably at least one of the dendrochronologically sampled trees in the stand will have just one ring for that year. By matching growth patterns across trees, false rings can be discovered and accounted for, thus preserving the true chronology of the tree growth. In the applet, the default setting is not to allow for false rings, but you may turn on that option and restart a new core to try a harder crossdating problem that may include one false ring. If there is a false ring, the virtual core will show it as identical to its other intra-annual band; you will have to discover the false ring by crossdating your skeleton plot with the master chronology.

Note that even with these options turn on, your randomly generated virtual core may not have a missing or false ring. By clicking the "Hint" button, you can know if these growth anomalies exist in your current problem. If they exist, then the answers to the problem will the calendar dates of the missing rings and the ring numbers of the intra-annual bands, in addition to the sample start and end years.

Conifer Ring Structure

An important thing to understand is that each tree ring comes in two parts, earlywood and latewood. As might be intuitively obvious, earlywood is composed of cells generated during the early part of the growing season while latewood is composed of cells formed during the late part of the growing season. In conifer species (e.g., pines, firs, and many others), earlywood is typically light in color while latewood is dark in color, and thus each conifer ring has two distinct bands of color. The ring and wood anatomy of hardwood species is more complicated.

In the applet, rings are simulated as if they were from a conifer, i.e., each ring starts with a light earlywood (yellow) that is followed by a dark latewood (brown). The color of latewood often varies in certain conifer species (e.g., spruces), and the applet accordingly has three different shades of latewood. Latewood color plays no other role in the applet for now, but many dendrochronologists crossdate their collections based on latewood color versus ring width in sites where ring width is complacent but latewood color (true wood density) is sensitive.

Note that in the applet the first ring is labeled with an "o" (the zeroth ring), and every 10th visible ring is marked and labeled. You may move the virtual core left and right by clicking and holding the left mouse button over the core and then moving the mouse. To see some of the very narrow rings, you may need to magnify the core series. To do this, move the area of interest to the center of the applet space (a blue line marked on the core mount) and click the core magnification setting to either 2x or 3x.

The default setting is for 61 rings (the final ring is number 60), but you may change the number of rings to be just a few (as few as 11) to be a lot (as much as 401) and restart a new crossdating problem. Keep in mind that the more rings you have, the more likely your will be to crossdate confidently and find all pertinent dates of ring formation of the answer, or vice versa. The master chronology with which you can crossdate your skeleton plot of the core is approximately six times longer that the core series, and the true crossdated match of the sample falls somewhere within the master chronology.

Sensitivity-fewest_sensitivity

Tree growth (e.g., ring width) is described as "sensitive" when it exhibits a high degree of annual variation with wide and narrow rings intermixed through time, as illustrated on the left side of the figure above and which is typical of many pine species growing in semi-arid environments (e.g., ponderosa pine of the North American Southwest). This results from having a limiting factor, climate for example, that is highly variable from year to year. When crossdating tree-ring specimens, dendrochronologists prefer sensitive growth patterns because matching patterns of relatively wide and narrows rings is easy when ample variation exists in ring width.

Conversely, tree growth is described as "complacent" when it does not exhibit a high degree of annual variation, i.e., rings are roughly the same width for many years consecutively, as illustrated on the right side of the figure above and which is typical of many tree species growing in relatively mesic environments (e.g., giant Sequoia of the Sierra Nevada of California). This results from not having a limiting factor (with respect to ring width, in this case) that is highly variable from year to year. It is more difficult to crossdate complacent tree-ring specimens because matching patterns of relatively wide and narrows rings is hard when there is not much variation in ring width.

On the applet, the default sensitivity-fewest_sensitivity setting is very sensitive (a value of 1 on the scroll bar). Try changing the setting all the way to very complacent (a value of 10 on the scroll bar) and then restart a new core to see the different levels of sensitivity-fewest_sensitivity in the randomly generated virtual tree-ring sample. Show the master chronology to also see how the time series of relative tree growth varies when you change the sensitivity-fewest_sensitivity setting. If and when you try to crossdate a complacent series, you should consider trying a longer series, i.e., one with more rings, in order to improve your likelihood of success.

Example Application of Crossdating

By crossdating ring growth between trees, dendrochronologists can assign the true calendar year of formation for every ring of each sample, and this chronology information then allows for various other analyses of past environmental and/or human events. In the example above, the living tree (right side) has a known bark date--the present year--which may be taken as the starting point for the chronology. After crossdating samples from living trees, a dendrochronology will extend from present back in time to some earlier year, say AD 1500.

Then, dendrochronologists often find and sample wood from dead trees (middle), either standing snags or fallen logs, that both lived for a long time and died long ago. If the dead trees lived concurrently with the living trees, then the outer ring-growth pattern of the dead trees will match (crossdate with) that of the inner portions of the living trees. Thus, the dendrochronology will be extended further back in time to an even earlier year, say AD 1200.

Lastly, archeologists often collect samples from wooden beams, uprights, and other structural parts of dwellings that were constructed, lived in, and abandoned long ago (left side). If the trees that provided the structural parts lived concurrently with the dead trees, then the outer ring-growth pattern of the structural samples will match (crossdate with) that of the inner portions of the dead trees. Thus, the dendrochronology will be extended further back in time to an even earlier year, say AD 800, and the human behavioral events of the past can be reconstructed for further archeological analysis.

Without knowing the actual year dates of formations of all rings of these samples, this application of dendrochronology would not exist. With crossdating, however, this application is possible and, indeed, dendroarcheology is a major subfield of dendrochronology. Likewise, with crossdating to know the exact year of formation of tree rings we may study past wildland fires (dendroecology), earthquakes (dendrogeomorphology), and climate changes (dendroclimatology) as well as many other environmental processes.

Example Skeleton Plot and Pattern Matching

To skeleton plot a sample onto a strip of graph paper, you simply make marks according to the relative narrowness of each ring. The graph marks range from no mark at all (not narrow) to a mark of ten graph lines in length (the most narrow). A mark of only one graph line in length would represent a ring that is only slightly narrow. Dendrochronologists typically accentuate narrow rings when skeleton plotting, as illustrated in the figure above. Note that ring #5 is quite narrow relative to its neighboring rings of the sample. The mark on the corresponding 5th line of the strip of graph paper is 8 lines long. In comparison, ring #2 is only slightly narrow and its associating graph mark is only 3 lines long. To make a normal mark on the graph paper of the applet, simply put the cursor on the correct position (vertical line) and at the height (horizontal line) you desire and then click the left mouse button.

Occasionally a very wide ring occurs (e.g., ring #15 above), prompting dendrochronologists to mark a "b" on the corresponding position (vertical line) on the graph paper to indicate that wide ring. The applet allows you to mark a "b" by selecting the wide option when drawing marks. The master chronology has "b" marks, so skeleton plotting some wide rings can be helpful for crossdating. Note also that ring #11 is merely average in width, and no mark at all is made on the 11th position of the graph strip. Average rings are simply not marked on skeleton plots. For an idea of how to make marks on your skeleton plot, look at the master chronology to see what values of ring growth merit a long mark versus no mark at all versus a "b" mark. On the master, a value of 1.0 is average and all values greater than 1.0 represent above-average growth while values less than 1.0 represent below-average growth.

Once you are done skeleton plotting your sample, show the master chronology and switch the graphs to an appropriate size for your computer monitor. To see more of the master chronology, you may change the magnification setting to have smaller graphs, which may be helpful for obtaining a bigger picture of the chronology. Then, move the master chronology left or right by clicking and holding the left mouse button in the lower portion of the chronology graph and moving the mouse. You goal now is to find where the marks on your skeleton plot match those of the master in mirror image. When you see a match, you can then determine the start and end years of the sample as well as account for ring-growth anomalies that might exist. If you have a missing ring, put a missing-ring mark in between the adjacent vertical graph lines of your skeleton plot (as with lines 16 and 17 above) and move your plot one position to the right to account for the missed year. If you have a false intra-annual band, put the false mark over the corresponding graph line of your skeleton plot (as with line 19 above) and move your skeleton plot one position to the left. Once you have determined the start and end year as well as dates of all ring anomalies, check the answer button to confirm your crossdating.

Relative Scale of Skeleton Plots

Although trees living within a homogeneous stand or forest usually exhibit the same relative patterns of growth variation through time, they often have absolute growth rates that differ substantially due to living in different microsites. Because of this, it is often difficult to compare the ring-growth variation of two or more specimens from the actual wood samples. For example, sample A from above has an average ring width of 1.0 mm while that of sample B is 2.0 mm and that of sample C is 3.0 mm. All three samples have exactly the same pattern of variation across their 20-year time spans, but it is impossible to align that pattern using the actual wood samples because of their different growth rates. To overcome this situation, dendrochronologists make skeleton plots, i.e., they represent growth variation of samples onto separate strips of standard graph paper in order to equalize the absolute scales of all specimens and thereby more easily compare growth of two or more specimens. Note that the three skeleton plots of above, representing their respective samples, are easy to compare to one another and clearly show that the pattern of variation of each sample is the same and is therefore is contemporaneous.

On the applet, you are given a strip of virtual graph paper on which you can make a skeleton plot of the ring-width variation of the series of tree rings generated for you. The applet starts with default settings of drawing (versus erasing) a normal mark (versus other marks for wide, absent, or false rings). To make a mark on the graph paper, simply put the cursor in the bottom part of the graph strip and click once with the left mouse button. To erase that or any other mark, turn on the eraser and click over the mark. Don't forget to turn on the drawer to continue making marks. Note that you can move the graph strip left or right by clicking and holding the left mouse button in the top part of the graph and moving the mouse.

To put scrollable, sizeable help comments on how to operate the applet?

Other Ways of Crossdating

There are other ways of dendrochronological crossdating besides using skeleton plots:

European skeleton:

Corridor analysis:

Character listing:

Running signs agreement:

Quantitative checks:

COFECHA

CROS

Feedback Form

After your playing with the skeleton plotting applet, we would like know these things:

Major field of study or career:
Arts Physical Sci. Natural Sci. Engineering-Tech. Social Sci. Medicine Law Other

Level of academic training:
pre high school high school college, lower division college, upper division college, post-graduate

Level of awareness of dendrochronology: 1 (none) 2 3 4 (moderate) 5 6 7 (lots)

Level of dendrochronological crossdating experience: 1 (none) 2 3 4 (moderate) 5 6 7 (lots)

Where did you first try this applet? Classroom (facilitated learning) Home or office (distance learning)

If in a classroom, did an instructor help or did you do it alone? With an instructor Alone

Did you correctly determine the start and end dates of the core using the default settings? yes no

If yes, how many tries did you need to succeed the first time? 1 2-5 6+
If no, how many times did you try using the default settings? 1 2-5 6+

Did you try a crossdating problem with only the missing-ring anomaly? yes no

If yes, did you correctly determine the missing years? yes no

If yes, how many times did you try with missing rings before succeeding? 1 2-5 6+
If no, how many times did you try with missing rings? 1 2-5 6+

Did you try a crossdating problem with only the false-ring anomaly? yes no

If yes, did you correctly determine the false ring pair? yes no

If yes, how many times did you try with false rings before succeeding? 1 2-5 6+
If no, how many times did you try with false rings? 1 2-5 6+

Did you try a crossdating problem with both missing and false rings? yes no

If yes, did you correctly determine all missing years and false rings? yes no

If yes, how many times did you try with missing and false rings before succeeding? 1 2-5 6+
If no, how many times did you try with missing and false rings? 1 2-5 6+

Did you try a crossdating problem with a different sensitivity setting (other than the default of "1")? yes no

If yes, what was the highest sensitivity setting that you tried? 2 3 4 5 6 7 8 9 10

Did you correctly find all parts of the answer at that highest setting? yes no

If yes, how many times did you try with at that sensitivity setting before succeeding? 1 2-5 6+
If no, how many times did you try at that sensitivity setting? 1 2-5 6+

Did you try a crossdating problem with a different number of rings? yes no

If yes, what was the fewest number of rings you tried (presumably less than 61)?
11 12-21 22-31 32-41 42-51 52-61
What setting of sensitivity did you try in this case?
1 2 3 4 5 6 7 8 9 10
Did you correctly determine all parts of the answer? yes no

Did you use this applet to teach crossdating in dendrochronology? yes no
If yes:

How many students were in your class? 1-5 6-10 11-20 21-50 50+

How effective was the applet as a teaching tool? 1 (not at all) 2 3 4 (intermediate) 5 6 7 (highly)

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