The RCS-modelLed "hockey-stick" chronology of Yamal: what went wrong?
Dendroclimatology is a discipline that focuses on studying past, present and even future climate from tree-rings. Dendroclimatology (Climate oriented
tree-ring science) has been publicly critisized for unproper use of tree-ring data. Public discussion in Finland was active in the beginning of 2010. Reporter
Martti Backman in a MOT TV documentary called
Climate catastrophe cancelled (produced by YLE, a Finnish Broadcasting
Company), criticised on tree-ring science adopted in the on-going IPCC climate research.
Statistician Steve McIntyre had previously analysed a dataset of a Larix tree-ring chronology collected in the Russian Yamal region.
According to his results the 'hockey stick" shaped results derived from those data were "nonsense" (e.g. Yamal: A “Divergence” Problem).
Inspired by the worldwide debate initiated by the e-mail leakage "Climategate" and the "Yamal divergence" conclusions of McIntyre, Backman decided to prepare a TV documentary on the subject.
Kari Mielikäinen, Professor of Growth and Yield, and Senior Researcher Mauri Timonen (the author) from Metla (Finnish Forest Research Institute) were asked to give an expert opinion about the climatic interpretation of the Yamal chronology. Well, having a decades long experience in tree growth modelling, applying RCS (Regional Curve Standardisation) as our standard tool in our growth trend studies, and also having an active role in method development (e.g. Ultimate RCS modelling), we may have some understanding on the subject. Finnish Lapland is rather close to the Yamal Peninsula (1600 km) and there grows our timberline Scots pine at around the same latitude. But as we don't recognise any "hockey stick" like climate patterns here, doing some analysis with the Yamal tree-ring data ia a very interesting case to us. I hope my longish story triggers some discussion on the challenges and great possibilities of Dendroclimatic modelling.
How to expose climatic variations from tree-rings?
Some people perhaps think it might not be possible to determine long term (low-frequency) climate fluctuations from tree-rings and make reliable climatic interpretations based on them. That's not however the case: there are at least 150 climatically sensitive tree species around the world that correspond with good correlation to local climatic conditions.
We Finnish tree-ring researchers go on working with our over 7600 years long tree-ring chronology and the related data of timberline Scots pine. This research material is composed of living trees, snags, stumps, building material and a number of megafossils (subfossils). The climatic signal extracted from tree-rings of Scots pine, e.g. ring width correlation with June-July temperature, is considered to be even one of the most accurate known proxies in the world!
Exposing climatic signals from tree-rings is not straightforward. There are many pitfalls to avoid in the different stages of modelling. The growth process of tree-rings can be described by Ed Cook's conceptual aggregate model. To an experienced dendrochronologist applying properly this simple basic model, climatic signal extraction is not a significant problem.
There are two approaches for exposing climatic signals from tree-rings: Single Tree Standardization (STS) and Regional Curve Standardisation (RCS).
The first step in applying STS is to standardise separately (define a mean ring width - age curve relationship) each tree-ring series (Fig. 6 on the right).
Then the tree-ring widths have to be transformed to tree-ring indices by a simple techniques of dividing the observed ring-widths by the modelled values. If using percentages,
the values have to be multiplied by 100. Therefore, if the observed value coincides with the curve value, the index will be 100. The values exceeding 100 refer to better growth conditions and vice versa.
STS fits well for exposing annual (High-Frequency) and decadal (Medium-Frequency) climatic variation. As a rule of thumb, STS makes it possible to identify climatic periods (cycles, trends) about half of the individual series length in maximum. As the oldest Finnish Scots pines reach the age of about 800 years, STS can expose ca. 400 years long cycles or trends in maximum.
Our RCS method uses the whole data (or a dataset created by BFM filtering, Fig. 4) for defining an average growth model (Fig. 6). The idea in RCS modelling is to describe a non-climatic mean ring width - age curve. Cook's Conceptual Linear Aggregate Model gives a good idea for the variables to be considered in modelling.
All the samples covering the whole 1000-yr period (Fig. 6) were used for building a joint average growth model (ring width - age model) (Fig. 8). When climate during some period is warmer than normal, annual ring-width averages are higher compared to the values of the standardised growth curve (indices > 100) and vice versa.
SAMPLE SIZE AND ACCURACY OF RING-WIDTH/INDEX ESTIMATE
A less discussed question in tree-ring science is proper sample size. There is actually no final common answer available, because the needed sample size depends largely on the investigated issue: tree-ring width, tree-ring density, isotopes stored in tree-rings etc. Defining a proper sample size for a specific ring-width data, however, is the most challenging task, because tree growth is determined by a large number of internal and external growth factors (as described in Cook's Conceptual Linear Aggregate Model).
Properly sized tree-ring data needed for climate modelling may be based purely on statistical sampling. It may, however, not always be the best fit for two reasons: 1) sample size gets large and costly to process; 2) unknown growth factors bring extra noise to data (e.g. insect damage, storms, floods, fellings and other human activities), which is hard to handle in analyses. We prefer collecting cost-effective tree-ring data based on carefully considered predefined information. The benefits of this kind approach are smaller sample size and better data quality (less noise).
What is the correct sample size and how many independent data sets should be collected for the requested accuracy? Proper solution requires a conceptual understanding in terms of validity and reliability. Validity describes how well the collected data set represents the question setting. Reliability is linked to statistical sample sizing.
We, in our climate analyses, set the minimum accuracy of the annual ring-width or tree-ring index estimate to at least a ± 10% level at 5% risk. We usually define sample size based on the coefficient of variation as shown in Fig. 5. The formula may not be ideal for this purpose, but it, however, gives an objective tool for taking into consideration the variability of local climate. According to the table, a ± 10% accuracy requirement at 5% risk level counts at the Finnish pine timberline at least 50 observations per year. One can ask whether a 10 % accuracy is adequate for correlating tree-ring indices with instrumental measurements. Well, it is worth discussing; collecting even larger data sets would not at all be a bad idea!
A method called Box Filling Method (BFM, Fig. 4) is useful for creating balanced RCS datasets. There are three dimensions in the BFM approach: calendar year, cambium age and number of samples. If "box filling" is done successfully, there is also a good chance to build a reliable RCS model.
But note: BFM improves only the reliability, not the validity of data! That is why attention has also to be paid to the homogeneity of growing conditions of the sample trees. As often happens, sample trees are collected from a variety of sites. This may lead to misinterpretations and completely wrong conclusions!
Also a single storm or some other natural event (e.g. insect outbreak) may have a strong effect on sample trees. A change in stand structure may invoke a drastic growth reaction to the nearby survivors, which can be erraneously interpreted as a common climatic signal. In order to avoid these kinds of pitfalls, a number of separate data sets over the investigated region should be collected (Fig. 1). Not until after testing all the data sets and chronologies over the whole region and comparing the results to previous studies, the worst climatic misinterpretations may be recognised. But that still does not necessarily provide the answer to the original question setting of data validity.
About supralong chronologies
The Russian 4000-yr Yamal chronology of Larix was completed in the ADVANCE-10K EU Project in 1996-1999 and published in Holocene 2002 (Briffa et al. 2002). The same project and paper introduced also the Finnish 7520-yr chronology of timberline Scots pine (Eronen et al. 2002), the Swedish 7400-yr Tornetrask chronology of Scots pine (Grudd et al. 2002) and the German 10479-yr chronology of Oak (Friedrich et al. 2002). The Finnish chronology was later on extended to 5634 BC (Helama et al. 2008). For more details, check the newspaper article in Helsingin Sanomat Muinainen ilmasto oli aaltoliikettä (Ancient climate was of cyclic origin; sorry, only in Finnish).
The ring-width data of the Yamal chronology, as checked by Cofecha's Quality Control and Check (output), seems to be of the highest quality. Cofecha, which is a leading dating and tree-ring data quality checking program of the ITRDB DPL library, reports only four flags and shows exceptionally high interseries correlation (r=0.771). For those wanting to check the contents of the Finnish supralong chronology data, enclosed some information: Cofecha summary and some overall documentary: paper of evaluation and some poster presentations: a, b and c. Included also a User Guide to COFECHA output files.
Some comments on the Yamal Chronology
Climatic interpretation of the Yamal chronology has triggered a lot of discussion for its hockey stick shaped curve. There was no hockey stick in the earlier climatic presentation of the Yamal chronology by Hantemirov et al. 2002 (Abstract). The hockey stick was reported later on, in 2009 Briffa's paper. Why did Briffa get different results compared to Hantemirov et al.? Some possible reasons can be listed: 1) Different methodologies: Hantemirov applied the so called Corridor Method, but Briffa his fine-tuned RCS method. 2) Cambium age distribution over time (calendar year range) in the Yamal data is unbalanced because the oldest tree-rings appear only during the last couple of hundred years. A good data for building basic RCS ring width - cambium age models requests an evenly distributed data, both over the cambium age and the calendar year. Accepting all the available ring-width data for model processing inevitably results an unbalanced time-related age distribution, which may lead to strange results as seen in the Yamal case.
As explained earlier, BFM makes it possible to create optimal data sets for high-quality RCS modelling. This method, in combination with careful randomising in sampling, allows to create several replicated subdatas. This benefits RCS to be tested with several independent data subsets. The examples here show the importance of Age Banding (Fig. 8) to be applied in the RCS method. Age Banding, i.e. limiting ring-age within the frames of a data set, greatly balances the tree-ring data needed for the basic RCS ring-width age modelling (Fig. 9).
This important view of RCS modelling should be noted: RCS is highly dependent on successful ring width - ring age modelling. Poor data (like in the case of the Yamal modelling problems) may lead to biased models and misleading conclusions. Ignoring the role of ring age in RCS modelling in fact seems to be a major problem in Dendrochronology. The Yamal chronology data is a typical example of a dataset with distorted age distribution over time (calendar year) causing "funny" results.
As seen in the Yamal case (Age Banding - Scatter), tree-ring age distribution over the calendar year axis does not fulfil the age restriction of 70-110 years. All the tree-ring cambium ages in the 1900s exceed 110 years, because the tree-rings of the same living trees since the 1750s were used for filling the 250-yr gap between the youngest subfossils and the present. Considering the use of BFM approach in the Yamal case, it is not possible, because there is not enough data available for passing the Age Band limitation. Arguing on this fact, my strong opinion is: the Yamal data represents a typical tree-ring dataset that never should be applied in RCS modelling! Compare some age-banded models in the poster.
The Yamal tree-ring data is technically almost flawless, but small data size easily leads to validity and reliability problems. We do can draw conclusions from annual and decadal variations, but exposing longer trends is much more challenging and the risk of misinterpretation dramatically increases. Poor cambium age distribution over time in the data prevents using Age Banding, which is an essential part of RCS modelling. If we, e.g., would like to use an age band of 70-110 years, it would not at all be possible in this case, because average cambium age increases gradually from 75 years to 250 years in the 1900s. Applying the 70-110 band would fail because of lacking observations in the 1900s! That’s because all rings are older than 110 years!
If there are plenty of tree-ring data available, it is very useful to apply BFM and create several independent or dependent data sets for advanced RCS analysis. Although RCS can not be applied properly to data sets like Yamal, indexing methods like STS and Shiyatov's Corridor Method play well. Unfortunately ordinary tree-ring indices can expose trends only about half of the life span of the oldest trees. The maximum trend or cycle length in the Yamal case would thus be some 130 years. That is not enough for identifying periods like MWP, LIA and MWP. Comparison of the RCS and STS chronologies, however, show that RCS produces a hockey stick shaped curve but the STS method not. Check the poster.
Five important principles
Heavy criticism focused on the dendroclimatic use of the Yamal chronology can be considered as a school example of how science, close to important political decision making, should not be performed. Although the Yamal chronology technically is almost flawless and it is perfect for dating purposes, its validity and reliability considering climatic modelling is poor. There are at least five important questions to be answered:
1) What is the validity of this kind of data? What do the trees actually represent? The risk they are exposing something else than climatic responses is obvious.
2) What is the reliability of the sampled data set? Knowing well that variation in tree growth at the Finnish timberline areas, expressed in terms of the coefficient of variation (CV), is 40-50 % (timberline pine in Finnish Lapland over 40 % and Larix in the Yamal peninsula over 45 %), a lot of careful investigation should be paid to sampling. And this is not enough, we definitely have also to also to consider, what kind of predefined ruling to adapt in order to maximise the climatic signal.
3) What research method is most suitable for producing proper conclusions? Considering the two climatic signal exposing methods, STS and RCS, it is crucial to make difference that STS exposes only local annual and decadal variation while RCS can expose also long-term variation. Age Banding should always play an important role in applying the both methods. Because RCS is a very data sensitive method, considerable attention should be paid for analysis of all the relevant data characteristics. If the data set does not fulfil the predefined information requested by the BFM, RCS should not be used for climatic analyses at all. This is actually the case also with the Yamal data set.
4) How to generalize results? Small data sets, as used e.g. in the Yamal case, represent only local climatic conditions, provided that the validity and reliability of the data is high enough. If not, climatic conclusions may be even locally badly misleading.
5) One more thing to be considered: the whole research process, the results and the conclusions should be exposed to public criticism before publishing. As seen every now and then, peer-reviewing does not always guarantee the proper scientific conclusions! Unfortunately.
The Finnish 7644-yr supralong timberline pine chronology
Because the Yamal region is pretty close to Finland, we tree-ring scientists are frequently asked whether our chronologies expose any hockey stick like patterns. As the enclosed graphs, referring to some preliminary results from Mielikäinen's Growth Trend Project, suggest there are no specific hockey stick patterns in these chronologies.
Finnish timberline pines grow normally, reflecting the June-July temperature variation. The observed solid temperature - growth response wipes off also the worry about any trend like divergence problems. As regards to low-frequence variation, Finnish timberline pines speak for a typical MWP-LIA-MWP pattern in their growth (Fig. 5 in this poster).
Although the "boomerang" shaped growth/temperature pattern arouses common interest, we, however, prefer to investigate the cyclic growth/climate patterns found in our pine and spruce chronologies. According to spectral analysis, the three strongest cycles exist between 81 and 95 years. That coincides with the solar based Gleissberg cyclicity (80-90 years). We hypothesise that the climatic part of tree growth at the Finnish pine timberline is mainly solar-forced, but also triggered by the cyclicly warming-cooling sea waters (AMO) and the macroclimate dynamics (NAO). The paper of Helama et al. (2010) gives an interesting introduction to this direction.
(P1) Principles in RCS modelling:
Ultimate RCS Modelling
(P2) RCS modelling applications: Growth trends in Finnish Forests
(P3) Studies with the Finnish 7644-year pine chronology: Cyclic growth of trees
(P4) Effect of tree-ring age on RCS models Age-banded models
(P5) Index comparison: Yamal RCS index <-> STS index
(P6) More to read: some echoes from the WorldDendro 2010 Conference: Activities Report
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