This document discusses uncertainty and confidence in tree-ring records as climate proxies at multi-decadal to centennial timescales. It examines how confidence estimates are often based on annual to decadal correlations, but errors may increase at longer timescales. Case studies from Yamal and Polar Urals compare tree-ring records from different sites, growth rates, and species to evaluate confidence over centuries to millennia. Larger and more widespread samples are needed to reliably reconstruct climate over the longest timescales.

1. Uncertainty & confidence in
tree‐ring records at
mul5‐decadal to centennial 5mescales
Tim Osborn
Clima5c Research Unit, School of Environmental Sciences, UEA
with contribu5ons from
Keith Briffa and Tom Melvin
TwiGer: @TimOsbornClim
3 September 2015

2. Tree‐ring measurements as climate proxies
Problems include:
• Biological proxy
– Mul5ple controlling processes (T, light, moisture, nutrients etc.)
– Age effects
Advantages include:
• Precise, absolute da5ng
– Possible because mul5ple samples with annual resolu5on &
strong common signal allows cross‐da5ng
• Mul5ple samples
– Stronger climate signal and allows uncertainty es5mates

3. Realis5c error es5mates for
proxy data & climate reconstruc5ons
Interes6ng challenge, combining process understanding
with sta6s6cal analysis
– Great poten5al for sta5s5cal analysis for tree‐rings because we
have large samples with precise, absolute da5ng
Two components (this talk focusses on first one):
• Confidence in the proxy record itself
• Confidence in the clima5c interpreta5on & reconstruc5on

4. Es5ma5ng confidence in tree‐ring records ..1
Centennial–millennial ambi6on but approaches oDen only
measure annual–decadal behaviour
– (1) Expressed Popula5on Signal (EPS)
– where n = sample size (number of trees sampled)
– and rbar = mean inter‐series correla5on
– But rbar determined mostly by annual–decadal common signal
– (2) Calibra5on and verifica5on against climate observa5ons
– But result determined mostly by annual–decadal correspondence
because limited length of instrumental record
Esper et al. (2004) Climate reconstruc5ons: low‐frequency ambi5on and high‐frequency ra5fica5on. EOS 85, 113‐120
Wigley et al. (1984) On the average value of correlated 5me series… J Clim Appl Meteor 23, 201‐213
EPS !
nr
1+ n "1( )r

5. Es5ma5ng confidence in tree‐ring records ..2
Errors tend to diminish from annual to decadal 6mescales,
but may then increase again out to longer 6mescales
– Different mean growth rates, differences between trees’ life
cycles, uncertainty in the expected growth–age curve
Centennial–millennial confidence can only be assessed by
considering agreement between independent long records
Briffa et al. (2013) Reassessing the evidence for tree‐growth and inferred temperature change… QSR 72, 83‐107

6. Yamalia case study: Yamal & Polar Urals
Living & sub‐fossil Larix sibirica trees
Polar Urals: TRW & MXD
Yamal: TRW, but bigger sample
Fig. 1, Briffa et al. (2013) QSR
Yamal: 473 sub‐fossil, 160 living
Polar Urals: 61 sub‐fossil (+18 for MXD), 62 living

7. Yamal chronology:
Full sample mean &
standard error

8. Fig. 9, Briffa et al. (2013) QSR
Red/Black: two versions of the overall mean chronology (thin lines where < 6 trees sampled)
Cyan: +/‐2 SE of the mean for 50‐year smoothed data. Grey: sample counts
1000 1400 1800 2000
400 BC 0 400 CE 800

9. Yamal chronology:
Calibrated JJ temperature
reconstruc5on with error
components

10. Fig. 11, Briffa et al. (2013) QSR
Red/Black: two versions of the overall mean chronology (thin lines where < 6 trees sampled)
Cyan: +/‐2 SE of the mean for 50‐year smoothed data. Grey: sample counts
1000 1400 1800 2000

11. Yamal chronology:
Compare different sites
Only for recent centuries where mul6ple
sites with living trees are available

12. Fig. 2, Briffa et al. (2013) QSR
Mean chronology for each site and SUB for sub‐fossil (thin lines where < 4 trees sampled)
1600 1800 2000
1600 1800 2000

13. Fig. 2, Briffa et al. (2013) QSR
Mean chronology for each site and SUB for sub‐fossil (thin lines where < 4 trees sampled)
BoGom panel smoothed with a 20‐yr spline
1600 1800 2000
1600 1800 2000

14. Yamal chronology:
Compare different growth
rate samples
Two independent chronologies by alloca6ng
half samples to each group based on their
mean growth rate aDer removing age
effects & common (climate) signals

15. Ring age (yr) 50 100 200 300 400
0 500 1000 1500 2000
Fig. 3, Briffa et al. (2013) QSR ‐ Mean chronology for each growth‐rate class (thin lines where < 8 trees sampled)

16. Yamal chronology:
Compare with Polar Urals
Two Polar Urals records (TRW & MXD) but
both have much smaller sample sizes &
span only 1 millennium
MXD sensi6ve to a longer summer season

17. Fig. 3, Briffa et al. (2013) QSR
Mean chronology for each growth‐rate class (thin lines where < 8 trees sampled)

18. Fig. 3, Briffa et al. (2013) QSR
Mean chronology for each growth‐rate class (thin lines where < 8 trees sampled)
r( Yamal , Polar Urals) = 0.82 (< 15 yr) 0.78 (15–100 yr) 0.69 (> 100 yr)
r( Yamal , Polar MXD) = 0.55 (< 15 yr) 0.72 (15–100 yr) 0.52 (> 100 yr)

19. Closing remarks
Confidence in tree‐ring records on century‐to‐millennium
6mescales:
– Don’t assume they are reliable. Evaluate them
– Don’t assume errors are random. Try to iden5fy systema5c biases
– Larger samples are needed to establish confidence at the longest
5mescales
– Clear advantage of tree‐rings: mul5ple, precisely dated samples
Scope to extend this by collabora6on with sta6s6cians
– using hierarchical sta5s5cal models of the data genera5ng process
– extension to spa5o‐temporal models (this example is one site, but a
widespread network exists across parts of the NH)

20. Spare slides relevant
for some ques5ons

21. Qilian Mountains case study: NE Tibetan Plateau
Fig. 1, Yang et al. (2014) PNAS
1203 sub‐fossil + living
Qilian Juniper, very long lived, slow growing, TRW only

22. Qilian chronology:
Compare different
sites
Living and archaeological samples

23. Fig. SB2, Yang et al. (2014) PNAS

24. Fig. SB2, Yang et al. (2014) PNAS

25. Qilian chronology:
Compare different growth
rate samples
Four independent chronologies by alloca6ng
quarter of samples to each group based on
their mean growth rate aDer removing age
effects & common (climate) signals

26. Fig. SB9, Yang et al. (2014) PNAS

27. Fig. SB10, Yang et al. (2014) PNAS

28.
Sampling sites near the edge of a
species’ ecological range to
obtain a single dominant
growth control
Near the la6tudinal or eleva6onal tree line
(can also reduce influence of stand dynamics where
this coincides with a more open canopy forest)

29. Magnified view
Pine tree
Processed wood core

30. Natural archives of past climate?

31. Trees cannot grow above/beyond their tree-line
In very cold regions, tree growth is limited by temperature

32.
Polar Urals root samples
Difference in mean ring width between
bole (trunk) & root collar samples can
result in biased tree‐ring record

33. Example of sampling bole (trunk) at “breast height”
Tom Melvin, Northern Norway, 1 June 1999

34. Example of root collar with large diameter than the bole
Remnant Scots Pine, near Torneträsk, Sweden

35. Polar Urals TRW record: original used bole
samples, “update” included root collar samples

36.
Iden5fying previous periods
with elevated tree mortality
End‐aligned spans of tree samples, but note that
sub‐fossil segments may not be complete
(outer rings not preserved, pith not sampled)

37. Khadytla River
One of the living-tree
sites in the Yamal region

38. -6000 -4000 -2000 0 2000
Year BC/AD
0
100
200
300
400
500
600
700
800
900
Numberofstackedsamples
Example for Tornetrask, northern Sweden