speleothem rings   Dee & Neil Pederson
  Aug 28, 2003 20:28 PDT 


there was a recent paper in quaternary research led by julio
betancourt and tom swetnam comparing drought reconstructions in new
mexico derived by speleothems and tree-rings. there was no detectable
relation between the tree-ring and speleothem reconstructions.

there are many possibilities on why there was no relation between
the two types of records. if anyone is interested in this report, i
can supply the reference when i get back to the office next week.


neil
Speleothem Rings   Ed Frank
  Sep 29, 2003 20:19 PDT 

Don,

You ask for my take on a paper entitled, “A Test of the Annual
Resolution” in Stalagmites Using Tree Rings”. I suppose the easiest
thing to do would be to say interesting and ignore it, or to trash the
paper completely, but I will try to do a fair evaluation.

One of the main considerations is a difference in mind set between two
different groups of scientists. One group are geologists the other
tree-ring researches. In the paper cited (Polyak and Asmeron, 2001)
they found more than 1600 bands in a stalagmite radioactively dated as
between 2796 +/- 88 and 835 +/- 25 years in age dated via u series
dating. On the face of it, if you would assume the dates are correct
and temporarily ignore the variance, then you have a period of 1961
years +/- 113, with only 1600 bands. Of course the rings in the
stalagmite do not correspond 1 to 1 with the calendar years and hence
will not correlate 1 to 1 with tree ring dates. 

In a later series in
the same stalagmite they found approx 300 bands subsequent to 432 +/- 13
yBP. Obviously these do not correlate 1 for 1 either. Somehow the
authors of this papery decided that they would select a certain time
period 1570-1839 and decided that 270 of those stalagmite rings should
correlate with these dates as determined via tree rings. I am not sure
how they decided on that number or why that number should be correct,
especially given that there are not the same number of rings as there
are years in the time sequence, or why those rings in particular should
be selected. If they had a rationale it was not presented in the paper.
The entire concept of mathematical correlations between the tree ring
data and the stalagmite rings is silly and is pointless. It is obvious
from the beginning that they do not correlate well.

Given all that it comes down to a mind-set. If in a 1900 year period,
a river, say the Nile River, in the spring flooded 1600 times, I would
call that an annual flood event. It is not strictly annual in the
chronological sense, but during the preponderance of years this event
took place. So while the rings may not be chronologically precise, they
generally represent the growth of the speleothem during a single year,
the vast majority of the years are represented, hence they are annual
rings.   Suggesting that a new name be used to describe the periodicity
of these rings is ridiculous. Data and interpretations must be
evaluated within the context of usage, why create an entire additional
layer of terminology?

I think using tree ring correlations to figure out how stalagmite ring
work is the way to go. It can give clues as to what the rings mean,
clues as to where there might be extra rings, or rings missing,
strengths and weaknesses of the technique. But all in all this paper
was a rather pathetic attempt.

Since it was clear that there was not going to be a good correlation to
begin with, then what was the point of the exercise? I would suggest
that it was simply to allow the authors to engage in subjective
speculation and rampant pontification in the guise of doing real
science. Quaternary Research is a decent publication, I am not sure how
this thing got published.   

I don’t believe that anyone, especially in the case of this stalagmite
is suggesting that the stalagmite can be dated by simply counting the
rings. In the case of these stalagmites or stalactites, especially in
hanging dates beyond the tree ring chronology, the resolution of the
actual age of the speleothem can not be greater than the resolution of
the dating technique. There are ways of decreasing the error associated
with uranium series dating, increased counting times for some types,
better labs for others, but these dates can only be resolved so far.

Does this mean the speleothems are useless for environmental
interpretation. Not really. For the periods near the uranium series
dated rings, the age for adjacent rings have about the same error
margin. If the number of rings is close to that of the number of rings,
then the rings, particularly near the dated ring sections, can be used
as a good proxy for annual events. Averaging data over a period, say
ten years or the error range of the dating, as a running plot should
still show longer term events, potential extra rings and missing rings
would be averaged out over the longer period and not create as much
noise in the data.   The resolution will not be as good as tree rings
which infallibly produce rings year after year, but certainly good
enough to produce useful data.

Another point is if you are looking at relative annual variations, then
in most cases it is reasonable to treat each ring as an annual ring, and
most of the time you will be right. resolution of the data in the terms
of the rings is different from the accuracy of the dating on the rings.
You may even be able to distinguish where a ring is missing. So it
needs work to figure out how to use the speleothem data, but it has good
potential. Other chemical traces or isotopic variations may provide
more useful climatological data than the width of speleothem rings. It
is a field worth keeping you eye on. More on this later.

Ed
RE: Speleothem Rings   Ed Frank
  Oct 01, 2003 14:41 PDT 

Bob,

Speleothems like stalagmites and stalactites have nothing to do with the
ground water table. These features form in the Vadose zone- the area
above the water table. So it has little to do with the level of the
water table, although periods of dry weather may affect features in the
vadose zone as well as drop the water table at the same time. During
dry periods over seasons or months or even years there may not be enough
water to flow down all of the possible water paths from the surface to
the cave chamber in which the speleothems form. Thus while some
speleothems may grow during a dry period because they are along a
preferred flow path, others will dry up. If the the normal wet season
is particularly dry then some speleothems will not receive any water at
all.

I could see this on Isla de Mona, Puerto Rico. During most of the times
I have visited the island most of the spel3othems in the caves, and the
caves were reasonably well decorated, looked dry and desiccated, and
were dusty to the touch. However during a large rain event all of these
speleothems became active and wet. For those whose drip water feeding
them was saturated with caco3, they only would grow and could only
potentially add rings during periods when it was very wet. Others
received water on a more continuous basis and would have the potential
for more rings. As a caveat probably only those with nearly continuous
flow would be good candidates for developing the concentric rings
demonstrated by the stalagmites in question, but periods of several
years of hiatus in which growth did not take pace is not out of the
question.

The key would be to see if there was some way to identify these hiatuses
in the cross section of the stal.. The other possibilities for missing
rings include maybe the technique was not sensitive enough or set at a
sufficient resolution to detect thin rings, or that two adjacent growth
periods may have had a virtually identical coloration and were not
distinguished in the analysis. Again, that is something that could be
looked at if you had the original stal to examine.

Ed Frank


dbhg-@comcast.net wrote:
 
Ed:

    What would lead to missing speleothem rings? Dry spells leading to
    lower ground water?

Re: Speleothem Rings   Neil
  Oct 02, 2003 08:27 PDT 


I reckon the primary stimulation for the comparison between tree-rings and speleothem rings was that the authors of the speleo paper [published in Science] made no comparisons to prior drought research in New Mexico. There is plenty to review or at least comment on for drought records in the American SW. I would guess the authors of the tree-rings vs speleothems felt snubbed by the lack of acknowledgement in the review of New Mexico drought history; like the speleothems trumped the tree-rings. When reviewing a subject in the scientific literature, it is proper and instructive to point out similarities and differences with other studies in the region.

I haven't looked at the paper in a long time, but I do not think that the two records even agreed upon the major historical drought events. So, it begged the question, "what is the coherency between these records?" and "at what time frequency do they agree?"

Paleo proxies have different strengths and weaknesses. Ideally, we should be able to use each in concert to better understand the Earth system. I wouldn't say the comparison was silly and pointless. These types of comparisons are necessary because they will teach us what parts of the the Earth climate system each proxy is reflecting and what more we need to learn. The Earth system is complex. We need all the proxies in our current tool kit and we need to know what each proxy is saying.

Neil
Re: Speleothem Rings   Don Bertolette
  Oct 01, 2003 19:49 PDT 

Ed-
Would these speleothem rings register the year that we first sent nuclear
particles (globally) into our atmosphere?
With perhaps a period of delay before 'percolating' down to the cave
environment?
-Don
RE: Speleothem Rings   Ed Frank
  Oct 02, 2003 19:03 PDT 

Generally I would expect that the delay between the rain and the drip
would be a matter of minutes to weeks. It would be very uncommon to find
delays greater than that. If you want to find rings then you need drips
with a short retention time for the water otherwise any variations would
be smoothed out. I doubt that the large stalagmites in Carlsbad's Big
Room at -740 feet have a delay of more than a few weeks if that. I
don't know that the subject has been studied in detail. So yes the
rings would show a big blip associated with nuclear weapons use,
particularly in c14 incorporated into the calcite.

Particles are another question. particles tend to be filtered out of the
water. If the flow is direct enough to carry particles through, then the
saturation index of the calcite may not be high enough to precipitate
calcite upon entering the cave atmosphere. Some transport does take
place, and some stal is dirtier than others, but these are not ideal for
speleothem research because of the detrital material present.

Ed
Re: Speleothem Rings   Greentr-@aol.com
  Oct 02, 2003 09:03 PDT 
I have followed this thread the last 2 days (I just signed onto your Group).
I've asked this question off ListServ, let me again ask it on, "What are
Speleothem Rings?" Since none of my forestry & arboriculture glossaries have this
term listed, I'm assuming this is of another science or discipline (geology,
sendimentary deposits, etc.). I have searched a number of websites, but all
have assumed the reader is up on these things. For the one uninformed ENTS
member, could someone throw me a bone here. Thanks,
Randy Cyr
Greenville, SC
RE: Speleothem Rings   Ed Frank
  Oct 02, 2003 20:01 PDT 

ENTS

Speleothems are secondary mineral deposits formed inside of caves.
There are dozens of different speleothems with differing shapes, and
compositions. The most common and the ones relevant here are those made
of calcite (or aragonite a pseudomorph with the same composition). The
three most common speleothems are stalactites which look like icicles
hanging from the ceiling, stalagmites which grow like fat posts from the
ground and flowstone, which forms waterfall-like deposits on the
surfaces of cave wall. Stalactites (Cling tight to the ceiling)
Stalagmites (Grow mighty from the ground) Many speleothems are variants
of these basic features or combinations of them. A column is formed
when a stalactite and stalagmite grow together.

Rain falls from the sky. Generally it hold dissolved CO2 at
atmospheric concentrations and pressure. When it hits the ground it
sinks into the soil. Soil concentrations of CO2 are much higher. The
water picks up more co2 and this forms a weak carbonic acid solution.
This solution is aggressive (meaning it has the potential to dissolve)
to calcite. If the rock below is limestone, made up of calcite mineral,
the water with the increased co2 will try to dissolve it. The water
moves down through the limestone along cracks and fractures. This is
called secondary permeability. Primary permeability allows water to
pass through the matrix of the rock itself between particles. Limestone
has virtually no primary permeability, so movement is virtually entirely
along cracks and fractures. As it flows, this aggressive water
dissolves calcite from the surfaces of the cracks. These cracks may be
large in size or microscopic. If it flows far enough it will eventually
become saturated with dissolved calcite.

If the flow path of the water then intersects a cave, an open area in
the subsurface, then things change. The atmosphere of the cave is
generally almost the same as the surface atmosphere with respect to co2
concentration. Caves breath and air passes in and out with wind and
pressure changes. The water will form a drop on the ceiling of the
cave. The water contains dissolved co2 at a higher partial pressure
than the cave atmosphere, so it degasses. With the loss of co2, the
droplet is able to hold less dissolved calcite, so the calcite
precipitates from the droplet. Depending on the situation this
precipitation may take place on the cave ceiling forming a ring of
precipitated calcite, and eventually a stalactite. In other situations
the drop will fall before the calcite precipitates. When it hits the
ground the droplet splatters into many smaller droplets. With greater
surface area these droplets de-gas faster, lose some of their dissolved
co2 and precipitate calcite from solution eventually forming a
stalagmite.

On the ceiling these little rings will add layer upon layer, ring upon
ring, and slowly lengthen to form a narrow hollow tube. These are
called soda straws, because of their similarity in size to soda straws,
and because they are hollow. Water flows down the inside of the tube
and deposits a new ring at the base of the tube where it first
encounters the cave atmosphere.   These soda straws can grow to many
feet in length until their own weigh or disturbance will cause them to
fracture. Generally before they reach great length they will plug up.
Then the water flows along the outside of the tube forming the common
carrot shaped stalactite. The deposition is concentric. Calcite is
first deposited in one place, then as that point is now higher, the next
drop flows somewhere else, and deposits its load of calcite, etc. It is
a self regulating system that assures that calcite is evenly deposited
around the perimeter of the stalactite.

Pure calcite is clear. Impurities and gas bubbles give it some color.
In speleothems the major source of color are organic dyes, like tannin,
etc that give them some color. The production of these organic dyes is
related to activity on the surface, plant growth, decay, autumn,
rainfall. These activities are seasonal.    Therefore as calcite
incorporating these dyes is deposited in the speleothems, there is a
color variation in the stalactites and stalagmites that is also
seasonal. Since they deposit the calcite uniformly around the exterior
of the stalactite (and stalagmite) These seasonal color variations are
deposited in concentric bands or rings around the stalactite. These
are the rings the posts are talking about.

These bands can form in some cases in a single major rainfall event.
It is possible that two rings may form if there are two wet periods and
two growth seasons on the surface. Rings may be missing if the
stalactite did not get water in a particular season, or if there was
insufficient difference in the color to distinguish a color difference.
Most stalactites have rings, but they are not prominent in every case.
Only a few are good candidates for trying to find annual or near annual
rings. Given these limitations, speleothem rings have enormous
potential for environmental interpretations as some may contain records
for hundreds of thousands of years.

Robert Leverett wrote:
 
Randy:

    I suspect you just asked the question for a lot of folks. Ed, if it
isn't too much of a job, could you go a step farther and give a
layperson definition for various common cave formations? We'd all
appreciate it immensely. Thanks in advance.
Speleothem Rings   Ed Frank
  Oct 26, 2003 19:24 PST 

A few weeks ago we were having a discussion about speleothem rings and
how they could be correlated to tree ring chronologies.   offered a lot of
opinions and a review of a published paper of which I thought less than
highly. I promised to put my money where my mouth is and tell all of
you how I would approach the problem. I have been thinking about it for
some time, but just sat down and wrote this out this evening. I am sure
I could polish it more, but...

If any of you want to offer me a graduate assistantship or research
position to pursue this, I would not be adverse to the offer.
------------------------------------------------

Tree Ring and Speleothem Ring Interpretations

Statement of Problem
Literature Review
Dendrochronology
Speleothem Rings
Speleothem Rings/Tree Ring Comparisons
Selection of samples/sample location
Detection of Rings
Methodology
Visual Inspection
Are rings uniform in thickness around entire speleothem?
Annual Nature of Rings
Age Dating
Increase Accuracy
Data Presentation
Correlation between tree rings and speleothems
Stratigraphy analogy
Moving ring correlations
Identifying Problem Areas
Can you distinguish additional rings?
Can you distinguish areas with missing rings?
Do these areas correspond to particular characteristic of tree rings
chronology?
Dealing with missing data
Surveying analogy
Cyclical pattern to infer duration of missing area?
Is missing data important for the purpose you are using it for?
Other types of climatic data
Pollen
Stable Isotopes
Fluid Inclusions
Conclusions

Statement of Problem: Tree rings provide a useful analog for climatic
data over the duration of the tree chronology of a few thousand years.
Speleothems also have annual rings. Speleothem rings potentially can
establish a chronology over many thousands to hundreds of thousands of
years. The problem is that rings are often missing from a particular
speleothem and it is unclear that the thickness of the rings has any
meaningful relationship to overall climatic conditions. Can tree ring
data be used to calibrate speleothem data so that it can be used for
meaningful annual climatic interpretations, and can the problem of
missing rings be dealt with so that the resulting annual interpretations
can be used for climatic interpretations over the longer time span of
the speleothem record beyond that available to tree ring records.

Literature Review: The literature of dendrochronology is extensive. A
literature review would be conducted to provide a background
understanding of dendrochronology, its strengths and weaknesses, and
implied assumptions used in making the correlation climatic
interpretations. Specifically literature related to the establishment
of a tree ring chronology in the area of the study would be reviewed in
detail. The literature relating to speleothem rings is much less
extensive. A review of most of the speleothem literature would be
feasible. Literature discussing the relationships between tree rings
and speleothem rings is limited and an attempt should be made to review
virtually all of this material.

Selection of samples/Selection of location: Speleothem samples need to
be found in an area with a well established dendrochronological record.
Several specimens from different areas could be selected to allow the
comparison of results between the samples. In general actually having
the speleothem sample is critical because the suggested protocol
requires a reevaluation of the sample as problem areas are identified by
making correlations with tree ring chronologies. Some samples are
clearly better than others. In most caves there are speleothems already
broken by previous visitors. Using these specimens for the analysis not
only promotes cave conservation by not damaging other speleothems, but
allows the collector to visually inspect the broken surface of the
speleothem for rings prior to collection. Also specimens that have
undergone extensive recrystalization can be avoided prior to collection.
Specimens with dark, heavy rings are not good because they suggest a
large amount of non-calcitic material may have been incorporated into
the speleothem, a potential cause for age dating irregularities. Good
sized specimens, light in color, with faint but distinguishable rings,
with no signs of recrystalization or inclusions, are best are the best.


Detection of rings: a number of techniques have been used to distinguish
rings in speleothems. The literature review would help determine the
optimum methodology for ring detection. At the moment the best method
seems to be done using an optical scanner. The thresholds fro what is
or is not identified as a ring using the methodology would need to be
examined with test scans using several different parameters. A ring
would be marked by a certain amount of change in color, transmission, or
reflectivity over a certain area. Manual visual inspection would need
to be made of the specimen to augment to mechanical scanning. The
mechanical scanning reduces personal variability in interpreting what is
seen, and may be able to distinguish finer changes than an individual
may detect. However a person is generally better at pattern recognition
than are computer devices and could potentially detect rings not
detected by the optical scan or detect items such as an individual
crystal that may have falsely detected as a ring. One area to examine
is whether the ring thickness is uniform around the entire circumference
of the speleothem. Generally they are, but is it true in the case of
this particular sample. Can what appears to be a single ring in one
area be resolved as several rings in another area?

Annual Nature of the Rings: The rings are annual in nature. This is a
base assumption that must be made in order for the interpretation of the
rings to have any meaning. It is fair to say that they represent a
single cycle of seasons. Rings may be missing. Thus ten rings may
represent fifteen years, but that does not mean that each ring represent
1 ½ years, each ring represents one year, and five one year rings are
missing. It is possible that more than one ring may form in a single
season, and this should be considered. However I believe this to be the
exception rather than the rule and unless there is evidence otherwise
the rings should be interpreted as being annual.

Dating Methodology: There are several methods that could be used for age
dating speleothems. For the purpose of comparison the method yielding
the best date resolution should be used. In some methods longer
analysis periods or larger samples will yield more precise dates.
Methods available include: C14, Uranium /Thorium, Potassium/Argon,
Uranium decay and possibly some others. There are different assumptions
and different limitations for each dating methodology. Samples would be
selected so that all material for a particular dating attempt came from
a single band. Thicker bands would provide larger sample amounts.
Samples should be selected from bands near the outer edge and toward the
inner portion of the speleothem. A caution is that it doesn’t do any
good to select points for dating that are outside the range of the
available dendrochronological record for the sample area. Every effort
must be made to assure the greatest accuracy of the dates, the greater
the accuracy and precision the fewer variables must be accounted for in
the data interpretation.

Data Presentation: The data set generated is essentially ring thickness
versus a year in time. The data should be presented as a bar graph
because that is the nature of the data. It should not be presented as a
line graph nor as variation from a mean value as has been done in some
instances. A line graph distorts the visual presentation data to some
degree, lows are undervalued, highs are overvalued, and anomalous
readings are given a quazi-reality by the smooth curves of the line
graph. I am not sure that variations from an average thickness value,
whether it represents a numerical average, the most common value, or the
point at which an equal number of values are above and below. It is an
interpretation to present the data in such a format at this point, and
I am not sure that any of those are critical values for interpretation.
Speleothem ring thickness should decrease in thickness over time if the
deposition rate remains constant, because the outer rings have a greater
volume than the inner rings.

Correlation between tree rings and speleothem rings: A simple one to one
correlation, as was used in Bentencourt et al (2002) is meaningless
because rings are missing from the speleothem data set. There are
several ways to deal with the problem. The problem here is to define
the areas or constrain the areas in which rings are missing in the
speleothem data. In geology the layers of rock present underground
often change in grain size, thickness, and type across an area as
represented in core samples or exposed section. These are still subject
to correlation. First if there are any distinguishing beds present in
both core samples these can be correlated. Then often additional beds
that can be correlated using in the areas constrained by these
distinctive marker beds. Then rocks tend to change in a certain
sequence, so correlations are made based upon changes between core sets
based upon this sequential change. Eventually working from the marker
beds up and down the areas where beds that are completely missing become
more and more constrained. One method to use would be to graphically
correlate the two data sets using any distinctive features present in
both data sets. It may not be workable, but it is something to test.

A second method would be to attempt to correlate statistically a short
segment containing a limited number of rings with the tree ring data
set. Then move one ring over and try to correlate that set with the
tree ring data. Eventually you should be able to match most of the
small sets of rings sequentially with the tree ring data. Those
sections with missing rings would correlate less well and could
potentially be identified. This method is not perfect because there may
be multiple places a single section may have a high correlation. But it
must not only correlate well, but it must fit sequentially with the
other sets. This will work so long as the number of speleothem rings is
high enough to make a meaningful correlation, and that the interval
between missing rings is generally greater than the number of rings used
for the analysis.

Identifying Problem Areas: Once the areas with the missing rings have
been identified or constrained, then the speleothem needs to be
reexamined. In the area of the speleothem in which you have determined
there are missing rings, three main questions must be considered when
reevaluating the speleothem: Can you distinguish additional rings in
the area where you believe rings are missing. If so, then you can
refine your techniques to detect them in the initial examination. If
you can’t distinguish additional rings, are the areas with missing rings
distinguishable in any way? Can you use that information to pick out
other areas with potential missing rings? Do these areas with missing
rings correspond to particular characteristic of tree rings chronology?
Do they appear when there is a low rainfall period? A high rainfall
period? Or any other type of distinguishable event? If you can’t
distinguish any additional ring, nor distinguish characteristics that
might indicate that rings are missing, then it limits the usefulness of
the speleothem ring chronology interpretations.

Dealing with missing Data: If you have missing data, does that mean the
data you have is useless? Not necessarily, it depends on what you are
trying to determine using the data. If you are surveying a loop of
twenty stations, and bust on one of the measurements, your loop will not
close. How do you deal with the bad survey shot, short of resurveying
the entire loop. One method is to average the error throughout the loop
so that it closes. This makes your survey loop work, and often used by
various error correction programs, but it means that only your initial
survey point is accurate, every other station on the loop is moved from
its true position. If you can use external data to determine where the
error has occurred, such as a pattern of passages or grid of roads, then
you can keep most of your data, working forward along your survey to the
bust, and working backward from the end point to the bust, than apply
all of your correction on the erroneous reading. Then all of you data
points are correct, with the caution that data for the bust has been
applied at the correct point.

If you can identify the areas with missing data, then perhaps you can
make use of the existing data that you do have, and put it all in a
proper perspective. If the missing data is part of a cyclical pattern,
then not only could you interpolate the length of the missing data, but
estimate the value of the missing data. It would not be as good as
actual measurement, but may be suitable for your purposes.

Other types of data can be gained from speleothem analysis.
Paleoclimatic information can be gathered from speleothems. Some
speleothems have been identified with pollen embedded into the crystal
matrix. Sea level fluctuations can potentially .be measured in seaside
caves in the Bahamas and similar coastal area. Stable isotope data using
12C/13C measurements, and 16O/18O isotope ratios have been used in
paleoclimatic interpretations. Fluid inclusions have also been used to
interpret paleoclimatic information. All of these are in the
development stage. But a key to making these more useful tools is
figuring out how to use speleothem rings to make meaningful
paleoclimatic interpretations.

Ed Frank
October 26, 2003

http://www.nativetreesociety.org/
http://www.nature-web-network.com
RE: Speleothem Rings   Dale J. Luthringer
  Nov 04, 2003 05:36 PST 

Ed,

I see.

How do they find out the date minimums and maximums if they don't know
how old a sample is start with?

Dale
RE: Speleothem Rings   Ed Frank
  Nov 04, 2003 18:03 PST 

Dale,

In radiometric dating, they count the number of decay events per a
given time, per a given mass of uranium/ c14/ or whatever radioactive
element you are measuring. Decay events individually are random, but
collectively they statistically conform strictly to a smooth curve, or
logarithmic straight line whose slope is the half life of the element
being measured. Thus a date is generated based upon where the number of
decay events plots on the curve. Since the individual events are
random, there is an error bar involved. Thus the date is expressed as
1000 yBP +/- 20 years. The longer the count is taken the better the
amalgamation of random events define the exact date with a given
statistical certainty. Thus with longer counts, the error bars on
each side of the best fit date become smaller.

In Uranium/thorium counting, the actual ratio of the number of atoms
of uranium to the actual number of thorium atoms is counted. Therefore
the error bar for the dates represent the limits of the accuracy of how
well you can measure the number of atoms of each element. Better
methodologies and more sensitive instruments measure more accurately.
Another point is with larger samples, while the amount of measurement
error remains the same, the number of atoms counted increases, therefore
the ratio of error to sample size decreases, and the error bars (the +/-
number of years) around the projected date decrease in size.

Thus in radiometric dating the resolution of the date (the amount or
size of the error bars) increase, the error gets smaller, with longer
count times, and in the ratio measurement methodologies the resolution
increases, the error gets smaller, with larger sample sizes, and the
error gets smaller with better measurement techniques and equipment.
There are practical limits to how well you can define a particular date.
But is that really important, if you are off by 20 years, when you are
looking at events 100,000 years ago-- something quite feasible with
current techniques?

Ed