Temporal scales and signal modeling in dendroclimatology Joel Guiot

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Joel Guiot. Temporal scales and signal modeling in dendroclimatology. Past Global Changes Mag- azine, Past Global Changes (PAGES) project, 2017, 25 (3), pp.142-143. ￿10.22498/pages.25.3.142￿. ￿insu-02269697￿

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HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. 142 SCIENCE HIGHLIGHTS: Centennial to millennial climate variability

https://doi.org/10.22498/pages.25.3.142 Temporal scales and signal modeling in dendroclimatology Joël Guiot

Tree rings are demonstrably good proxies for temperature or precipitation at timescales less than a century. Reconstruction based on multiple proxies and process-based modeling approaches are needed to estimate the climate signal at lower frequencies.

Paleoclimatological proxies "represent component of the trend. Afterwards, the method is complex and needs a large records of climate that were generated tree leaf area stabilizes, and a fairly con- number of replicated series for the same through physical, chemical and/or biologi- stant quantity of xylem is distributed along species. No method is perfect and some cal processes. Reconstructions of climate a circle of increasing diameter. This is the of them reduce the low-frequency signal rest on attempts to turn this around in geometry factor. Other low-frequency ef- excessively, while others introduce spuri- order to get back to the climate informa- fects may occur during the tree’s lifespan, ous low-frequency variations. For these tion" (Hughes et al. 2010). In most cases such as competition variations, changes in reasons, climate reconstructions tend to these reconstructions are obtained as nutriment availability and carbon concen- be biased, with either too little or too much chronological series, which are character- tration in the atmosphere, fires, infesta- low-frequency variability. ized by a time resolution depending on the tions, diseases, or genetic variability – and sedimentation or growth processes. These climate changes. All these factors result Climate reconstructions processes act as a low-pass filter and in a complex combination of low and mid Climate reconstruction consists of calculat- determine the resolution of the climatic frequency signals, which should be under- ing a regression between climate series signal. Here, I focus specifically on tree- stood and modeled to produce indices for and tree-ring series on the period where ring series. climate reconstructions. both are available (usually the last century) and to extrapolate the regression, also Pre-processing of tree-ring series The classical approach, called the stan- called transfer function, to tree-ring series Tree-ring series reproduce annual vari- dardization, consists of detrending tree- of previous centuries. These reconstruc- ability of the climate with relatively good ring time series before calibration with tions may be affected by the so-called reliability, but tree growth is the result of meteorological time series. Numerous "divergence problem". From the 1970s, numerous complex processes. Hence, like methods exist, but it is difficult to distin- the tree-ring series no longer appears to all biological proxies, tree rings record a guish the low-frequency signals related be correlated with summer temperature, combination of several climate variables. to climate from other factors (Cook and especially in the high latitudes and in some At low frequencies, the signal is affected Kairiukstis 1990). The standardization cases in the high elevations (D’Arrigo et by an age-related trend, which includes produces indices, which are defined as the al. 2008). The correlation shifts towards both geometrical and physiological fac- ratio between the raw tree ring and a theo- the summer precipitation or other climate tors. During its young phase, the tree retical model of (low-frequency) growth, factors. The shift may be caused by a builds its architectural model and leaf either calculated by nonlinear functions, change of limiting factors (climate becom- system, and then reaches its reproductive smoothing, autoregressive models or a ing warmer, trees are lacking water), an

maturity with a progressive increase of bio- function based on the biological age of effect of CO2 fertilization, air pollution, soil mass production. This is the physiological the tree (Briffa and Melvin 2011). The latter composition change (increase of nitrate), or insolation. This induces a calibration bias: if the transfer function is calibrated on the most recent period (after the 1970s), it should not be used to estimate climate variations before the 1970s. This problem triggered some worries about the value of the climate reconstructions.

Despite these risks of biases, and likely be- cause of them, numerous statistical recon- struction methods have been introduced after the pioneer paper to deconvolve the climatic signal (Fritts et al. 1971). Tree rings are indeed an interesting material for statisticians because the time series have annual resolution and they are also well replicated (a site tree-ring series is based on 20 to 50 cores).

The climate signal calibration is often based on multiple regression, but the Diagram of the process-based approach and comparison with the standard transfer function. In the Figure 1: low-frequency signal may differ depend- process-based approach, the initial probability distribution of the climate (needed to initiate the iterations) may be given by educated guess, as it is done with the class of methods called inverse modeling, or by simulation of ing on the stationarity of the time series, climate models, as it is done with the class of data assimilation methods. The standard transfer function uses the on the calibration period, the use, or not, tree-ring series as input and the climate as output. The stream is opposite to the causal relationships. of the principal components, the rescaling

PAGES MAGAZINE ∙ VOLUME 25 ∙ NO 3 ∙ December 2017 CC-BY SCIENCE HIGHLIGHTS: Centennial to millennial climate variability 143

Figure 2: Summer temperature and precipitation reconstructions at Fontainebleau, France, obtained from the inversion of the multiproxy biophysical model MAIDENiso

(Boucher et al. 2014), i.e. the MAIDEN model with an isotope simulation module. Red curves are obtained when the inversion is forced by CO2 fixed at preindustrial levels

(280 ppmv) and black curves are obtained from increasing values of CO2 from 280 ppmv in 1850, 320 ppmv in 1960 to 360 ppmv in 2000. Straight lines with corresponding colors represent the trends. Adapted from Boucher et al. (2014). done after the calibration and other varia- done separately in the low-, medium- and Conclusion tions (Bürger et al. 2006). Pseudo-proxy high-frequency bands with the appropriate In conclusion, tree-ring series have an ex- method is an interesting method to study proxies. cellent time control and an annual resolu- the behavior of the reconstruction method. tion, and are good proxies for temperature It consists (i) in generating proxy series Process-based approaches or precipitation variations (depending on from climate model simulation to which Finally, one may model the formation of their geographical position and species) at are added white noises of progressively the record by representing explicitly the sub-century timescales. At lower frequen- increased variance, (ii) in calibrating the chain of physical and biological processes cies, literature is extensive on the difficul- reconstruction method on the pseudo which lie between the climatic information ties coming from (i) the standardization proxy series, and (iii) analyzing the per- and the observed signal. Such a model procedure (age-related factors), (ii) the formance of the method in function of the may be used in "forward mode", forced by selection of model relating tree growth noise variance. A difficulty is that these climatic or other environmental data (Fig. and climate, and (iii) the calibration of the pseudo-proxies should mimic as best as 1). It may also be inverted to estimate cli- model itself. Proposed solutions are based possible the physics of the proxies used mate from observations, as in the MAIDEN on multiproxy approaches, use of appro- (Christiansen and Ljungqvist 2016). or VS-light models (Boucher et al. 2014; priate treatment of low frequencies, and, Tolwinski-Ward et al. 2014). The inverse finally, mechanistic tree-growth models. Other variables may be measured on problem is solved with a Bayesian method, tree rings and used for estimating past which estimates the posterior probabilistic AFFILIATIONS climates. They have not the same biases distribution of the climate parameters pro- CEREGE, CNRS, Aix-en-Provence, France but can have others. The tree-ring maxi- viding the observed tree growth. When the mum density has proved to be quite useful processes generating the low-frequency CONTACT Joël Guiot: [email protected] to reconstruct the summer temperature discrepancies are included in the model, it and seems to be free of age-related trends is possible to clear the climate reconstruc- REFERENCES 18 (Briffa et al. 1992). Oxygen isotopes (δ O) tion from the corresponding biases, such Acevedo W et al. (2016) Clim Dyn 46: 1909-1920 in cellulose is a potential means to recon- as the CO effect. This process is illustrated 2 Boucher E et al. (2014) Biogeosciences 11: 2014-3245 struct variables related to water (Saurer in Figure 2. Scenario A1 (black) forces the 13 Briffa K, Melvin T (2011) Dendroclimatology 5: 1-30 et al. 1997). Stable carbon isotopes (δ C) inversion with true values of CO2 concen- record the balance between stomatal tration while scenario A2 (red) forces the Briffa KR et al. (1992) J Clim 5: 735-753 conductance and photosynthetic rate, inversion with constant CO2 concentra- Bürger G et al. (2006) Tellus A 58A: 227-235 dominated at dry sites by relative humid- tion (280 ppmv). Both reconstructions are Christiansen B, Ljungqvist FC (2016) Rev Geophys 55: ity and soil water status, and at moist sites highly correlated in the high-frequency do- 40-96 by summer irradiance and temperature main. When the CO2 effect is not taken into Cook ER, Kairiukstis LA (1990) Methods of dendrochro- (McCarroll and Loader 2004). account (A2), the temperature reconstruc- nology. Applications in the environmental sci- tion has no linear trend (the differences ences. Kluwer Academic Publishers, 393pp Moberg et al. (2005) proposed to use both are not significant for the precipitation). D’Arrigo R et al. (2008) Glob Planet Change 60: 289-305 pollen data and tree rings to reconstruct As this temperature trend is also recorded Fritts HC et al. (1971) J Appl Meteorol 10: 845-864 Northern Hemisphere average tempera- in the observations (not shown here), it is Guiot J et al. (2010) PLoS One 5: e9972 ture. Pollen data are robust on low fre- important to take into account the CO2 ef- quencies, so that they could help improve fect to obtain better reconstructions in the Hughes MK et al. (2010) PAGES news 18: 87-89 the quality of the low-frequency part of low-frequency domain. Another approach McCarroll D, Loader NJ (2004) Quat Sci Rev 23: 771-801 the signal. This application used a wave- based also on process models, which Moberg A et al. (2005) Nature 433: 613-617 let analysis. A similar approach has been seems also promising, is data assimilation, Saurer M et al. (1997) Tellus Ser B 49: 80-92 used by Guiot et al. (2010) for gridded in which proxy data are used in conjunc- Tolwinski-Ward SE et al. (2014) Clim Dyn 44: 791-806 temperature in Europe, using a method of tion with model runs (Acevedo et al. 2016; spectral decomposition. A calibration is see also Fig. 1).

CC-BY PAGES MAGAZINE ∙ VOLUME 25 ∙ NO 3 ∙ December 2017