Clim Past 10 437ndash449 2014wwwclim-pastnet104372014doi105194cp-10-437-2014copy Author(s) 2014 CC Attribution 30 License

Climate of the Past

Open A

ccess

Forward modelling of tree-ring width and comparisonwith a global network of tree-ring chronologies

P Breitenmoser12 S Broumlnnimann12 and D Frank23

1Institute of Geography Climatology and Meteorology University of Bern Bern Switzerland2Oeschger Centre for Climate Change Research University of Bern Bern Switzerland3Swiss Federal Institute for Forest Snow and Landscape Research (WSL) Birmensdorf Switzerland

Correspondence toP Breitenmoser (breitenmosergiubunibech)

Received 30 June 2013 ndash Published in Clim Past Discuss 18 July 2013Revised 25 January 2014 ndash Accepted 28 January 2014 ndash Published 11 March 2014

Abstract We investigate relationships between climate andtree-ring data on a global scale using the process-basedVaganovndashShashkin Lite (VSL) forward model of tree-ringwidth formation The VSL model requires as inputs only lat-itude monthly mean temperature and monthly accumulatedprecipitation Hence this simple process-based model en-ables ring-width simulation at any location where monthlyclimate records exist In this study we analyse the growthresponse of simulated tree rings to monthly climate condi-tions obtained from the CRU TS31 data set back to 1901Our key aims are (a) to assess the VSL model performanceby examining the relations between simulated and observedgrowth at 2287 globally distributed sites (b) indentify opti-mal growth parameters found during the model calibrationand (c) to evaluate the potential of the VSL model as anobservation operator for data-assimilation-based reconstruc-tions of climate from tree-ring width The assessment of thegrowth-onset threshold temperature of approximately 4ndash6Cfor most sites and species using a Bayesian estimation ap-proach complements other studies on the lower temperaturelimits where plant growth may be sustained Our results sug-gest that the VSL model skilfully simulates site level tree-ring series in response to climate forcing for a wide rangeof environmental conditions and species Spatial aggregationof the tree-ring chronologies to reduce non-climatic noise atthe site level yielded notable improvements in the coherencebetween modelled and actual growth The resulting distinctand coherent patterns of significant relationships betweenthe aggregated and simulated series further demonstrate theVSL modelrsquos ability to skilfully capture the climatic signal

contained in tree-ring series Finally we propose that theVSL model can be used as an observation operator in dataassimilation approaches to reconstruct past climate

1 Introduction

Information derived from tree rings is one of the most pow-erful tools available for studying past climatic variability aswell as identifying fundamental relationships between treegrowth and climate (eg Fritts 1976 Briffa et al 2002ab IPCC 2007) Tree-ring archives offer many advantagesfor climate reconstructions including their wide spatial dis-tribution annual resolution calendar-exact dating and highclimate sensitivity (Hughes 2002 Jones et al 2009) How-ever relationships between tree growth and climate are com-plex and classical calibration methods (ie establishing astatistical relationship between instrumental and proxy dataduring their period of overlap) are limited for several rea-sons Firstly empirical methods generally treat climate as afunction of the proxy rather than quantify how proxy sig-nals are driven by climate variability Secondly statisticalcalibration is bound by the assumption that the relation be-tween proxies and the target variable is stationary and in-dependent of other climate variables ndash conditions that maynot be adequately met (Raible et al 2006) Thirdly mosttree-ring-based reconstructions are limited to geographic re-gions where growth variability is predominantly constrainedby a single environmental variable For example tempera-ture reconstructions are limited to regions where growth is

Published by Copernicus Publications on behalf of the European Geosciences Union

438 P Breitenmoser et al Forward modelling of tree-ring width

primarily limited by cold temperatures This leaves the vastareas away from high mountains and high-latitude environ-ments poorly represented by high-quality temperature proxydata (Wahl and Frank 2012)

In recent years data assimilation approaches have foundan increasingly important role in palaeoclimatic reconstruc-tion efforts (Hughes and Ammann 2009 Trouet et al 2009Goosse et al 2010 Widmann et al 2010 Franke et al2011 Bhend et al 2012 Tingley et al 2012 Steiger etal 2014 for an introduction and overview see Hakim etal (2013) and Broumlnnimann et al (2013)) Combining infor-mation from climate models and proxy archives also includ-ing associated errors and their covariance provides a physi-cally plausible representation of past climate consistent withavailable proxy data An observation operator which ex-presses the proxy as a function of the model data is the for-mal link between model and proxy data So-called forwardproxy models (process-based or empirical) could potentiallybe used as an observation operator in data assimilation ap-proaches (Hughes and Ammann 2009)

The VaganovndashShashkin (VS Vaganov et al 2006 2011)process-based forward model has been demonstrated to skil-fully simulate tree-ring width in North America and Siberia(Anchukaitis et al 2006 Evans et al 2006 Vaganov etal 2011) China (Shi et al 2008 Zhang et al 2011)and Tunisia (Touchan et al 2012) This forward-model oftree-ring growth was developed to quantify tree-ring forma-tion as a function of climate and environmental variables(Vaganov et al 2006 2011) Yet applications generatingldquopseudo ring-widthrdquo series from global climate models haveso far been hindered by the complexity of forward modelsneeded to accomplish this task Recently Tolwinski-Wardet al (2011a b) introduced a simplified model version (theso-called VaganovndashShashkin Lite (VSL) model) that skil-fully reproduced climate-driven variability in North Amer-ican tree-ring width chronologies This simple and efficientmodel of non-linear climatic controls on tree-ring width re-quires only latitude monthly temperature and monthly pre-cipitation as inputs and has the potential to simulate treerings across a wide range of environments species and spa-tial scales The VSL model may thus theoretically serve as alink between the proxy data and climate variables in any re-construction methodology that can support use of a forwardmodel

The goals of this study are to (a) to assess the VSL modelperformance by examining the relations between simulatedand observed growth at 2287 globally distributed sites (b)identify optimal growth parameters found during the modelcalibration and (c) to evaluate the potential of the VSLmodel as an observation operator for data-assimilation-basedreconstructions of climate from tree-ring width This studyis the first report examining the VSL modelrsquos application ona global scale and thereby across a wide range of speciesand site conditions using a gridded data set based on directobservations from meteorological stations All raw tree-ring

Fig 1 Locations of the 2287 tree-ring width chronologies(TRWITRDB) and the correlation coefficients between TRWITRDBand TRWVSL for 1901ndash1970

width measurements from the International Tree Ring DataBank (ITRDB) are processed and analysed in a consistentmanner

The paper is organised as follows we provide a brief in-troduction to the climate data the structure and parameterisa-tions of the VSL model and the tree-ring chronologies Themain results and discussion detailing the coherence betweenobserved and simulated growth and associated climatic con-trols across space and over time are then presented Finallybased on our findings we discuss possible pathways of howtree-ring data could be used in data assimilation and climatereconstruction contexts

2 Data and methods

21 Climate data

The climate data used to simulate tree-ring growth aremonthly CRU TS31 mean near-surface temperature andCRU TS311 precipitation data sets from the Climatic Re-search Unit (CRU Mitchell and Jones 2005) These datacover the global land surface (except for Antarctica) at a05

times 05 spatial resolution from 1901 to 2009 (updatedfrom Mitchell and Jones 2005httpbadcnercacukdatacru) and are based on direct observations from meteorologi-cal stations It should be kept in mind that the temporal andspatial density of the underlying observations is variable Forinstance comparison of the available network of tree rings(see Fig 1 for locations) with instrumental station records(see Jones et al (1997) and Frank et al (2007) for griddedtemperature data) shows that both the instrumental and tree-ring networks are dense for the European Alps On the otherhand tree-ring chronologies are much more prevalent in theboreal zone such as in the vast areas of Siberia and northernCanada However both instrumental and tree-ring networksare both very sparse for most tropical regions One exceptionis India where instrumental data dominate over the available

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

438 P Breitenmoser et al Forward modelling of tree-ring width

primarily limited by cold temperatures This leaves the vastareas away from high mountains and high-latitude environ-ments poorly represented by high-quality temperature proxydata (Wahl and Frank 2012)

In recent years data assimilation approaches have foundan increasingly important role in palaeoclimatic reconstruc-tion efforts (Hughes and Ammann 2009 Trouet et al 2009Goosse et al 2010 Widmann et al 2010 Franke et al2011 Bhend et al 2012 Tingley et al 2012 Steiger etal 2014 for an introduction and overview see Hakim etal (2013) and Broumlnnimann et al (2013)) Combining infor-mation from climate models and proxy archives also includ-ing associated errors and their covariance provides a physi-cally plausible representation of past climate consistent withavailable proxy data An observation operator which ex-presses the proxy as a function of the model data is the for-mal link between model and proxy data So-called forwardproxy models (process-based or empirical) could potentiallybe used as an observation operator in data assimilation ap-proaches (Hughes and Ammann 2009)

The VaganovndashShashkin (VS Vaganov et al 2006 2011)process-based forward model has been demonstrated to skil-fully simulate tree-ring width in North America and Siberia(Anchukaitis et al 2006 Evans et al 2006 Vaganov etal 2011) China (Shi et al 2008 Zhang et al 2011)and Tunisia (Touchan et al 2012) This forward-model oftree-ring growth was developed to quantify tree-ring forma-tion as a function of climate and environmental variables(Vaganov et al 2006 2011) Yet applications generatingldquopseudo ring-widthrdquo series from global climate models haveso far been hindered by the complexity of forward modelsneeded to accomplish this task Recently Tolwinski-Wardet al (2011a b) introduced a simplified model version (theso-called VaganovndashShashkin Lite (VSL) model) that skil-fully reproduced climate-driven variability in North Amer-ican tree-ring width chronologies This simple and efficientmodel of non-linear climatic controls on tree-ring width re-quires only latitude monthly temperature and monthly pre-cipitation as inputs and has the potential to simulate treerings across a wide range of environments species and spa-tial scales The VSL model may thus theoretically serve as alink between the proxy data and climate variables in any re-construction methodology that can support use of a forwardmodel

The goals of this study are to (a) to assess the VSL modelperformance by examining the relations between simulatedand observed growth at 2287 globally distributed sites (b)identify optimal growth parameters found during the modelcalibration and (c) to evaluate the potential of the VSLmodel as an observation operator for data-assimilation-basedreconstructions of climate from tree-ring width This studyis the first report examining the VSL modelrsquos application ona global scale and thereby across a wide range of speciesand site conditions using a gridded data set based on directobservations from meteorological stations All raw tree-ring

Fig 1 Locations of the 2287 tree-ring width chronologies(TRWITRDB) and the correlation coefficients between TRWITRDBand TRWVSL for 1901ndash1970

width measurements from the International Tree Ring DataBank (ITRDB) are processed and analysed in a consistentmanner

The paper is organised as follows we provide a brief in-troduction to the climate data the structure and parameterisa-tions of the VSL model and the tree-ring chronologies Themain results and discussion detailing the coherence betweenobserved and simulated growth and associated climatic con-trols across space and over time are then presented Finallybased on our findings we discuss possible pathways of howtree-ring data could be used in data assimilation and climatereconstruction contexts

2 Data and methods

21 Climate data

The climate data used to simulate tree-ring growth aremonthly CRU TS31 mean near-surface temperature andCRU TS311 precipitation data sets from the Climatic Re-search Unit (CRU Mitchell and Jones 2005) These datacover the global land surface (except for Antarctica) at a05

times 05 spatial resolution from 1901 to 2009 (updatedfrom Mitchell and Jones 2005httpbadcnercacukdatacru) and are based on direct observations from meteorologi-cal stations It should be kept in mind that the temporal andspatial density of the underlying observations is variable Forinstance comparison of the available network of tree rings(see Fig 1 for locations) with instrumental station records(see Jones et al (1997) and Frank et al (2007) for griddedtemperature data) shows that both the instrumental and tree-ring networks are dense for the European Alps On the otherhand tree-ring chronologies are much more prevalent in theboreal zone such as in the vast areas of Siberia and northernCanada However both instrumental and tree-ring networksare both very sparse for most tropical regions One exceptionis India where instrumental data dominate over the available

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 439

tree-ring network Note that sites of tree-ring chronologiesare on average located 164 m higher than the elevation ofthe corresponding CRU grid cell Correction for elevationaldifferences requires knowledge of the site-specific climato-logical lapse rate and is therefore difficult to achieve (egtests assuming a constant moist-adiabatic lapse rate on asite-by-site basis did not improve fits between tree-ring andmodel data) and was not further considered

22 Forward model description the VSL model

We use the VaganovndashShashkin Lite (VSL) model and aBayesian parameter estimation approach (Tolwinski-Wardet al 2013) to produce synthetic tree-ring chronolo-gies (Tolwinski-Ward et al 2011a b version 23 acces-sible from httpwwwncdcnoaagovpaleosoftlibsoftlibhtml) The VSL model only requires monthly mean tem-perature accumulated precipitation and latitude to modelgrowth A further 12 adjustable parameters are required re-lated to climatic limitations on growth parameterisations forsoil moisture availability and the calendar periods when an-nual increment of wood is responsive to climate The net ef-fect of the dominating non-linear climatic controls on treegrowth are implemented in terms of the principle of limitingfactors and threshold growth response functions

For a specific site and given monthi growth is calculatedfrom the minimum of the growth responses to temperature(gT ) and moisture (gM) modulated by the response to inso-lation (gE)

G(i) = gE (i) lowast mingT (i) gM (i) (1)

Annual ring width is then defined as the sum of the monthlygrowth incrementsG(i) over a specified growth periodI(Tolwinski-Ward et al 2011a)

TRWVSL =

sumiisinI

G(i) (2)

In Eq (1) gE is the ratio of mean monthly day lengthL rela-tive to that in the summer solstice month at the correspondinglatitude computed using standard trigonometric approxima-tions

gE (i) =L(i)

maxL(i) (3)

The partial growth ratesgT andgM are defined as ramp func-tions with growth parameters representing climate thresh-olds below which temperatureT and moistureM are nothigh enough for growth (T1M1) and thresholds abovewhich temperature or moisture sustain non-limited growth(T2M2) Values of these partial growth responses are be-tween zero and one (Tolwinski-Ward et al 2011a)

gT (i) =

0 for T (i) le T1T (i)minusT 1T2minusT 1

for T1 lt T (i) le T2

1 for T (i) gt T2

(4)

gM (i) =

0 for M (i) le M1M(i)minusM1M2minusM1

for M1 lt M(i) le M2

1 for M (i) gt M2

(5)

Site-specific growth parameters (T1T2M1 and M2) arenecessary due to diverse environmental conditions siteecologies and species represented in this global networkAccordingly the VSL growth response function parame-ters were determined for each chronology via Bayesian pa-rameter estimation using temperature precipitation site lati-tude and ring-width data during the calibration interval Thisscheme assumes uniform priors for the growth response pa-rameters and independent normally distributed errors forthe ring-width model The median of each of the growthparameters in the resulting posterior probability distributionwas finally taken as the ldquocalibratedrdquo growth response valuesfor a particular site A more detailed description of the ap-proach can be found in Tolwinski-Ward et al (2013) TheBayesian approach is computationally efficient is able toincorporate expert knowledge about the likely values forparameters and tends to guard against model overfitting(Tolwinski-Ward et al 2013)

In addition to the above-described Bayesian approach toestimate the optimal growth parameters we also estimatedthe optimal growth parameters for every site using a sim-ple optimisation procedure as described in Tolwinski-Ward etal (2011a) Growth parameters in this optimisation approachwere sampled uniformly across intervals and the growth pa-rameter set producing the simulation that correlated most sig-nificantly with the corresponding observed series was thenused to simulate the tree-ring series (note that throughoutthis paper we use Pearsonrsquos correlation coefficients) Resultsfrom both growth parameter estimation approaches are gen-erally similar There was some evidence that the optimisa-tion approach sometimes overfit the model due to the lackof independence between the fitting procedure and the tree-ringndashVSL relationships Nevertheless the comparable resultssupport the validity of either of these approaches with somepossible advantages for the Bayesian parameter estimation(Tolwinski-Ward et al 2011a 2013)

Soil moistureM(i) is calculated from monthly tempera-ture and accumulated precipitation dataT (i) andP(i) viathe empirical Leaky Bucket model of hydrology from theNational Oceanic and Atmospheric Administrationrsquos ClimatePrediction Center (CPC) allowing for sub-monthly updatesof soil moisture to account for the non-linearity of the soilmoisture response (Huang et al 1996 Tolwinski-Ward etal 2011a codes available fromhttpwwwncdcnoaagovpaleosoftlibsoftlibhtml)

In addition to the four parameters controlling the sim-ulated growth response to temperature and soil moistureall other parameters are taken from published studies (egHuang et al 1996 van den Dool et al 2003 Fan and vanden Dool 2004 Evans et al 2006 Vaganov et al 2006

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

440 P Breitenmoser et al Forward modelling of tree-ring width

Table 1VSL model parameters

Parameter description Parameter Value

Temperature response parameters

Threshold temp forgT gt 0 T1 ε [1 C 9C]Threshold temp forgT = 1 T2 ε [10C 24C]

Moisture response parameters

Threshold soil moist forgM gt 0 M1 ε [001 0035] vvThreshold soil moist forgM = 1 M2 ε [01 07] vv

Soil moisture parameters

Runoff parameter 1 α 0093 monthminus1

Runoff parameter 2 micro 58 (dimensionless)Runoff parameter 3 m 4886 (dimensionless)Max moisture held by soil Wmax 08 vvMin moisture held by soil Wmin 001 vvRoot (bucket) depth dr 1000 mm

Integration window parameters

Integration start month I0 minus4Integration end month If 12

Tolwinski-Ward et al 2011a Zhang et al 2011 Touchan etal 2012) as is outlined in Table 1 which have demonstratedthe applicability of VSL for a wide range of environmentalconditions

As growth periodI we use a 16-month interval start-ing in the previous September and ending in December ofthe modelled year (previous March to current June for theSouthern Hemisphere) This integration interval accounts forsome persistence in tree-ring growth (leading to autocor-relation) and showed the best overall performance in testsfrom a subset of our data set (which are all sites in AfricaNew Zealand Tasmania Chile Mongolia southeastern AsiaAustria Norway Florida and California) This interval isfurthermore consistent with the outcomes from Tolwinski-Ward et al (2011a) in their simulations of North Americantree-ring series and with the importance of autumn phenol-ogy controlling interannual variability of net ecosystem pro-ductivity (Wu et al 2013)

23 Tree-ring chronologies

A total of 2287 standardised tree-ring chronologies wereused for our primary analyses To obtain these series weconsidered all available raw tree-ring width measurementsfrom 2918 sites from 163 different tree species from theITRDB (Grissino-Mayer and Fritts 1997httpwwwncdcnoaagovpaleotreeringhtml) Prior to further analysis weattempted to identify and correct data and metadata errorsincluding repetitive measurements feet-meter encoding in-appropriate decimal points and hyphenations incorrect serieslabelling or misplaced series positions (see Table S1 in theSupplement)

To remove the biological age trend and other lower-frequency signals that may be driven by stand dynamics

or disturbances we processed all data sets in the programARSTAN (Cook 1985) using standard dendroclimatologi-cal methods (ie detrending and standardisation to dimen-sionless growth indices) We tested different standardisationmethods on a subset of 97 locations from all six continentsand selected our detrending approach based on this subsetMethods tested include (a) a negative exponential curve andlinear regression fits (b) a smoothing spline fit with a 50 frequency response cut-off (which is the wavelength at which50 of the amplitude of a signal is retained) equal to three-fourths of a series length and (c) a smoothing spline with a200 yr frequency response cut-off These tests and Pearsonrsquoscorrelation analyses between the differently standardised se-ries and the monthly climate parameters led us to favour a hi-erarchical approach fitting negative exponential curves andlinear regression curves of any slope were applied as first-order detrending options but if these two methods were notsuitable (eg because values of a fitted curve approachedzero) a smoothing spline was fit with a 50 cut-off fre-quency at 75 of each series length The detrending meth-ods applied allow retention of climate-related signals in anygiven chronology of the order of the median segment lengthof the constituent tree-ring series (Cook et al 1995)

Combining multiple measurements into a single ring-width chronology should then ideally represent a coherentclimate signal of a particular species at a site (Cook et al1990) Standard chronologies (TRWITRDB) of all these siteswere developed by a biweight robust mean estimate (Cook etal 1990) and the variance was stabilised to minimise arte-facts from changing sample size through time (Osborn etal 1997 Frank et al 2007) Further we required that thesample depth of a chronology (number of samples from treesused for every point in time) is alwaysge 8 and that the 1901ndash1970 interval was fully covered by tree-ring data These cri-teria resulted in the 2287 chronologies for further analyses

24 Aggregation of observed tree-ring chronologies

In addition to comparing individual observed and VSL-modelled chronologies we further analysed whether thesignal-to-noise ratio can be enhanced by aggregating severalneighbouring observed series into one ldquosuper-chronologyrdquowhich subsequently is modelled with VSL

Aggregation of chronologies is performed using a searchradiusR of 200 and 600 km centred at each land grid cellof the CRU climate data set The former radius approximatesthe grid resolution of many global climate models and the lat-ter reflects a typical decorrelation length scale in large-scaleprecipitation and temperature fields We do not use greatlyexpanded search radii like Cook et al (2010) or Ljungqvistet al (2012) for instance whose work was motivated by theconstruction of a gridded climate reconstruction from spa-tially sparsely distributed proxy series under considerationsof long-range teleconnections (Jones et al 1997) For thelarger search radius we introduced the condition that at least

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 441

one chronology must be within 200 km of a grid cell suchthat both search radii result in the same spatial coverage

In contrast to modelling individual chronologies mod-elling aggregated chronologies requires a first-order sepa-ration of the climatic influences on growth into ldquomoisture-limitedrdquo and ldquotemperature-limitedrdquo chronologies to enhancethe signal-to-noise ratio Note that this aggregation approachmeans that changes in the limitations over time cannot beaccounted for as might apply to the debate over the so-called ldquodivergence phenomenardquo (DrsquoArrigo et al 2008 Es-per and Frank 2009) Yet site aggregation is particularlyimportant in mountainous terrain with more complex cli-matic conditions and rapidly changing conditions withinsmall spatial scales that locally impact tree growth (Salzerand Kipfmueller 2005) Accordingly we differentiated thesites based upon their principal climatic drivers and thusseparately aggregated all temperature- and moisture-limitedchronologies located within each grid cell nodersquos search ra-dius Specifically we classified temperature- and moisture-sensitive chronologies using the long-term averaged monthlygrowth responsesgT and gM from the VSL model forall months whereg gt 0 Temperature-sensitive chronolo-gies were defined as sites that have more temperature- thanmoisture-limited months (ie a greater number of monthswheregT gt gM) All other series are moisture-limited (equalor more months withgT gt gM) Aggregated tree-ring width(ATRW) series for temperature- and moisture-limited se-ries were computed for every grid cell with one or moretemperature andor moisture-limited tree-ring chronologieslocated within the given search radius For the 200 km(600 km) search radii 10 (7 ) of all land grid cellscontain only temperature-limited series 7 (5 ) are onlymoisture-limited and 11 (37 ) of the cells include bothtemperature- and moisture-limited chronologies

After identifying the series to be aggregated we definedthe aggregated tree-ring width ATRWITRDB as weightedmeans of the corresponding TRWITRDB series Weights wereassigned according to four factors (Eqs 6ndash9) and multipli-cation of the four relative weights gives the weight value weapply to each individual tree-ring series within the searchradius The weighting factors are (a) mean Rbar of eachchronology (b) mean EPS of each chronology (c) distancesd between the site location and the grid node and (d) thesmaller p value of two correlations between CRUTS31temperature or precipitation and TRWITRDB for 12-monthaverages (JanuaryndashDecember in the Northern HemisphereJulyndashJune in the Southern Hemisphere respectively) andfor 5-month averages for growing season interval (MayndashSeptember and NovemberndashMarch respectively) These twoseasonal windows consider the summer months when cli-mate generally dominates tree growth (Briffa et al 2002a)and also possibilities that growth is driven by a much widerseasonal window

Weights are determined by to following functions (seeFig S1) which vary between 0 and 1

wRbar= eminus2(1minusRbar)5(6)

wEPS= eminus2(1minusEPS) (7)

wd = eminus2d2

R2 (8)

wp = eminus2p (9)

There is no a priori reason to choose any particular weigh-ing function but we determined the functions based on the-oretical considerations (eg see Ljungqvist et al 2012 whoused the Gaussian distance) and the parameter distribution asshown in Table 1 We re-calibrated the VSL simulations forall grid cells containing at least one aggregated tree-ring se-ries The calibration was performed using monthly temper-ature and precipitation series from CRU and with the sameVSL model parameter set-up described in Table 1

25 Experimental and analysis design

The following experimental design is used in our studyFirst we modelled (following Sect 22) each individual ob-served chronology with data from the closest CRU grid cellas climatic input These simulated chronologies are termedTRWVSL In addition we also modelled the aggregatedchronologies using climate data from the centre of the searchradius (closest grid cell) but calibrated using the aggregatedobserved chronologies ATRWITRDB These chronologies aretermed ATRWVSL All observed and modelled chronologieswere normalised (ie given a mean of zero and standard de-viation of unity) over the 1901ndash1970 period

For both TRWVSL and ATRWVSL we utilised 1901ndash1970as the main calibration period for the growth parametersHowever for assessing result consistency we also performedsplit-sample validation experiments in which we used the1901ndash1935 period for calibration and the 1936ndash1970 periodfor validation and vice versa

3 Results

31 Quality indicators for tree-ring chronologies

In order to assess the chronology or site attributes that mayaffect the robustness of the climate signal in TRWITRDBwe computed various characteristics of all 2287 ring-widthchronologies for the 1901ndash1970 common period (Fig 2 seeFig 1 for locations) The average inter-series correlation be-tween all series in a chronology (Rbar) indicates commonvariance (Cook et al 1990) while the expressed popula-tion signal (EPS) quantifies the degree to which a chronol-ogy matches a hypothetical population chronology (Wigley

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

442 P Breitenmoser et al Forward modelling of tree-ring width

Fig 2 Binned chronology characteristics for 1901ndash1970 Rbar isthe average inter-series correlation between all series from differenttrees (Cook et al 1990) EPS is the expressed population signaland the vertical dashed line denotes the commonly cited 085 EPScriterion (Wigley et al 1984 Cook et al 1990) Mean 1901ndash1970Rbar and EPS values were calculated using a 30 yr window that lags15 yr MSL is the mean segment length and ASD is the averagesample depth (48 bins were distinguished in each variable)

et al 1984 a threshold value of 085 is routinely but ar-bitrarily cited in dendrochronological literature) Rbar andEPS statistics were calculated over moving 30 yr windowswith 15 yr overlap A total of 93 of all mean EPS valuesin our network are above 085 over the 1901ndash1970 time pe-riod Rbar values roughly follow a normal distribution witha mean of 039 These statistics suggest that the vast major-ity of chronologies have a relatively robust signal that shouldallow climatic drivers to be inferred On average tree-ringchronologies are composed of 30 series with a mean segmentlength of 170 yr However these distributions have relativelylong tails reflecting sites that are exceptionally well repli-cated or composed of long-lived tree species (eg Bristleconepine) The mean segment length and our detrending approachsuggest that we should be able to test inter-annual to (at least)multi-decadal variability in our modelling efforts The geo-graphical distribution of the sites is dominated by low alti-tudes and the mid-latitudes but there are also a considerablenumber of high-latitude and high-elevation sites particularlyin the Northern Hemisphere

32 Site-specific Bayesian parameter estimation

The Bayesian approach provides estimates of the optimalparametersT1T2M1 andM2 for each site with descrip-tive statistics of the parameter estimation for split-samplevalidation given in Table 2 Notably we find great consis-tency among the temperature and moisture parameters thatwere calculated independently and separately for the 1901ndash1935 and 1936ndash1970 periods We find for example that themean temperature for growth onset is 46 and 48C for theearly and late calibration periods Similarly temperature nolonger limited growth above 163 and 165C again for theindependent early and late calibration periods Figure 3 fur-

Fig 3 Histogram of the Bayesian estimated VSL growth responseparameters(a) T1 lowest threshold temperature(b) T2 lowerbound for optimal temperature(c) M1 lowest threshold for mois-ture (d) M2 lower bound for optimal moisture parameters cal-culated during 1911ndash1970 for different tree genera pine (pinusn = 821) spruce (picean = 407) fir (abiesn = 286) hemlock(tsugan = 124) larch (larixn = 126) cedar (cedrusn = 107)juniper (juniperusn = 40) oak (quercusn = 253) and south-ern beech (nothofagusn = 62) Histogram ofT1 threshold tem-perature for different pine species(e) Scots pine (Pinus sylvat-ica n = 172) Austrian pine (Pinus negra n = 45) ponderosa pine(Pinus ponderosa n = 181) pinyon pine (Pinus edulis n = 73)bristlecone pine (Pinus aristata Pinus longaeva and Pinus bal-fouriana n = 34) stone pine (Pinus pinea n = 7) and jack pine(Pinus banksiana n = 15) Numbers in brackets give the series con-tributing in each group of tree genera The number of bins for eachparameter is determined through the square root of its length

ther illustrates the estimated temperature and moisture pa-rametersT1T2M1 andM2 for each site and different treegenera In terms of the currently debated (see Discussion)growth-onset threshold temperature (T1) we find most esti-mates fall within 4ndash6C with values for all sites and speciesbetween 180 and 841C (see also Table 2) Despite thegenerally narrow range of the parameters for all study sitessome evidence for species-dependent values also exists Forspruce our estimates ofT1 andT2 are generally higher thanfor pine trees whileM2 is lower We also find differencesamong the pine species For ponderosa and pinyon pinesT1is about 1 to 2C lower than for other pine species (Fig 3ecompare also to Fig 3a in which these two species clearlyinfluence the shape of the pine histogram towards coolerthreshold temperatures)

Although these parameter values were computed indepen-dently we found clear associations among the four growthparameters For instanceT1 andT2 values andM1 andM2

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P Breitenmoser et al Forward modelling of tree-ring width 443

Table 2 Statistics of the Bayesian estimation of the site-by-site tuned VSL growth response parametersT1 T2 M1 andM2 for the 1901ndash1935 and 1936ndash1970 calibration intervals

Calib 1 1901ndash1935 Calib 2 1936ndash1970

Mean Min Max SD Mean Min Max SD

T1 (C) 464 180 841 093 475 174 797 089T2 (C) 1634 1014 2280 162 1652 1036 2187 159M1 (vv) 0023 002 0025 0001 0023 0019 0025 0001M2 (vv) 044 011 064 009 043 011 064 009

values are significantly correlated with each other (r = 060and r = 047 bothp lt 001) The often negative correla-tion between temperature and precipitation at inter-annualtime scales is expressed by the inversely related tempera-ture and moisture growth parameters with the relationshipbetweenT2 andM2 (r = minus063 p lt 001) being the mostnoteworthy Moreover temperature-limited sites tend to havehigher T1 and T2 values in comparison to the moisture-limited sites whereas higherM1 andM2 values are charac-teristic of moisture-limited sites (please refer to Sect 24 forthe definition of temperature- and moisture-limited sites)

33 Relationships between actual and simulatedtree-ring growth

The VSL model was able to simulate tree-ring series for 2271out of the 2287 sites suggesting general applicability to di-verse environments and species Of the remaining 16 sitesnine were high-latitude or high-elevation sites in Nepal (3)Siberia (1) and CanadaAlaska (5) for which no growth wassimulated because temperatures never reached the thresholdtemperatureT1 for growth initiation (hencegT = 0) The re-maining seven sites were (sub-)tropical sites in Florida (1)Mexico (4) Argentina (1) and Indonesia (1) for which nei-ther temperature- nor moisture-limited growth (hencegT = 1andgM = 1)

Similarity between the 2271 actual TRWITRDB and thecorresponding modelled TRWVSL chronologies was assessedby Pearsonrsquos correlation coefficients during the 1901ndash1970period (Fig 1) The average of Pearsonrsquos correlation coeffi-cients between all TRWITRDB and TRWVSL is 029 (standarddeviation= 022) Approximately 41 of the correlation co-efficients between TRWVSL and TRWITRDB are statisticallysignificant at the 95 confidence level (r gt 035) takinginto account the reduction of degrees of freedom due to au-tocorrelation (Mitchell Jr et al 1966) Note however thatthe 1901ndash1970 period includes the calibration interval Thusanalysing the correlation coefficients between TRWITRDBand TRWVSL in the split-sample validation we find signif-icant (p = 005 r gtsim 044) correlations during all four cali-brationvalidation intervals (calibration 1901ndash1935 and vali-dation 1936ndash1970 and vice versa) for 133 of all the series

Fig 4 Simulated monthly growth response curves for each year(1911ndash1970) for temperature (gT magenta lines) and moisture(gM cyan lines) for two sites in Switzerland(a) Berguumln Val TuorsEuropean larch 2065 m and(b) Krauchthal Scots pine 550 m Thelong-term (1911ndash1970) mean value is overlaid in red for tempera-ture and in blue for moisture(c) TRWITRDB and TRWVSL (dashedlines) for Berguumln Val Tuors (black lines)r = 069 p lt 001 andKrauchthal (green lines)r = 044p lt 001

Significant pairwise relationships between the TRWITRDBand TRWVSL series are found across the globe on all con-tinents In particular geographic areas with tendencies forhigher modelndashdata agreement are found in central EuropeScandinavia easterncentral Siberia and in the United Stateswith a cluster of high correlations in California wherer gt

08 Weak relationships are characteristic of the Africa sitesbut are also evident in New Zealand Tasmania Alaska aNWSE band from central Canada to NE USA the northernpart of the British Isles and parts of southern Europe (Fig 1)

To illustrate the monthly growth response valuesgT andgM we plot both the year-to-year variability and mean valuesover all simulated years (1911ndash1970) for one high-altitude(Fig 4a) and one low-altitude site (Fig 4b) in SwitzerlandSimulations (TRWVSL) as well as the observed chronolo-gies (VSLITRDB) for both sites are shown in Fig 4c Be-cause the simulated growth response is controlled by the

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

444 P Breitenmoser et al Forward modelling of tree-ring width

month-wise minimum of either temperature or precipitationFig 4a clearly shows that growth at the high-altitude siteis temperature-limited (gT lt gM) The lower-elevation site(Fig 4b) on the other hand is temperature-limited onlybriefly at the beginning and at the end of the growing sea-son while precipitation limits growth during the summermonths (gM lt gT ) Importantly tree growth at the high-elevation site is negatively correlated with growth at thelower-elevation site This negative correlation holds for boththe observed and modelled chronologies with coefficients ofminus013 andminus044 respectively These relationships demon-strate the VSL modelrsquos ability to incorporate joint influencesof temperature and precipitation on growth and simulta-neously suggest care is required when developing regionaltree-ring time series (see Sect 342 below) Our simulatedgrowth responses for two selected sites in Switzerland ap-pears to be widely applicable across mountainous forest re-gions with large climatic gradients such as the southwest-ern USA (Salzer and Kipfmueller 2005 Tolwinski-Wardet al 2011a) and Mongolia (Poulter et al 2013) One-year lagged autocorrelation coefficients (AR1) were assessedfrom TRWITRDBand TRWVSLseries at all sites Mean coeffi-cients of 046 and 042 respectively over all series clearlyreveal persistence ie 21 and 18 respectively of the vari-ance in the width of the ring in the current year can be pre-dicted based upon simulated growth during the past year

331 VSL simulations for aggregated TRW series

The aggregation generally enhances the correlation betweenATRWVSL and ATRWITRDB For instance the average ofall coefficients forR = 200 km during the common 1901ndash1970 interval is 034 for the temperature-limited series and038 for the moisture-limited series compared with a meanof 029 for the non-aggregated tree-ring series The spa-tial patterns of correlation coefficients for temperature- andmoisture-limited ATRW for both search radii are shown inFig 5 Notably ATRWVSL and ATRWITRDB show spatialcoherency and capture the main climate signals and arethus suitable for data assimilation approaches (see Discus-sion) The 600 km search radius improves the relationshipsfor both temperature and precipitation Coherent regional-scale correlation patterns for temperature-limited series canbe found in Scandinavia westerncentral Siberia and alongthe western and eastern United States (Fig 5a and c) Re-gional correlation patterns for moisture-sensitive series en-compass the United States and central Canada (Fig 5b andd) Regions such as central Europe Turkey central Asia andthe Andes are characterised by both temperature and mois-ture limitations which is an expression of a complex terrainwith small-scale climatic features and large climatic gradi-ents High correlation coefficients between ATRWVSL andATRWITRDB are present in all those regions with a cleartendency towards temperature-limited high-elevation sitesPoor agreement for the temperature-limited series can be

Fig 5 World map displaying Pearsonrsquos correlation coefficients be-tween ATRWVSL and ATRWITRDB for a search radius of 200 km(a b) and 600 km(c d) at temperature-limited(a c)and moisture-limited (b d) grid cells Note that in panels(c) and(d) at least onechronology has to be within the 200 km search radius to make thecorrelations comparable

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 445

31

Fig 5 World map displaying Pearson correlation coefficients between ATRWVSL and 1

ATRWITRDB for a search radius of 200 km (ab) and 600 km (cd) at temperature-limited (ac) 2

and moisture-limited (bd) grid cells Note that in panels c) and d) at least one chronology has 3

to be within the 200km search radius to make the correlations comparable 4

5

6

7

8

9

10

11

Fig 6 Scatter plot of correlation coefficients between each ATRWVSL and ATRWITRDB (200 km 12

search radius) series for the 1901-1935 and 1936-1970 independent time periods Results are 13

shown for a) the early 1901-1935 calibration interval and b) the late 1936-1970 calibration 14

interval 15

-1 -05 0 05 1-1

-08-06-04-02

002040608

1a) b)

-1-08-06

002040608

1

-04-02

-1 -0 0 05 15 r during calibration 1901-35 r during calibration 1936-70

r dur

ing

valid

atio

n 19

36-7

0

r dur

ing

valid

atio

n 19

01-3

5

Fig 6 Scatterplot of correlation coefficients between eachATRWVSL and ATRWITRDB (200 km search radius) series for the1901ndash1935 and 1936ndash1970 independent time periods Results areshown for(a) the early 1901ndash1935 calibration interval and(b) thelate 1936ndash1970 calibration interval

found in Tasmania New Zealand western-central Canadaand in the eastern-central US while moisture characteristicsare poorly captured in Patagonia northern Canada and in theEuropean Alps

Based on the split-sample validation experiment Fig 6shows a scatterplot of the correlation coefficients between theATRWVSL and ATRWITRDB 200 km search radius duringdifferent calibrationvalidation intervals (1901ndash19351936ndash1970 and 1936ndash19701901ndash1935) Points along the 1 1 lineare sites for which VSL produces simulations that are sta-ble in time whereas points below this line represent sitesfor which the model yields a higher correlation during thecalibration period We find model skill (r gt 044) in Pear-sonrsquos correlation coefficients in 36 of the series duringthe calibration period of which 54 are also significant inthe validation period Correlations are stable for moisture-limited sites in large areas of the United States and cen-tral Canada the lower-elevation sites in west-central Eu-rope Turkey Mongolia the western Himalayas and in mid-Chile whereas temperature-limited sites dominate Scandi-navia Siberia the eastern Himalayas central Europe south-ern South America and parts of the western United StatesCorrelations are not particularly skilful for New ZealandTasmania and Patagonia

4 Discussion

41 Growth parameters

The site-by-site parameterisation for the moisture and tem-perature thresholds revealed interesting global-scale patternsNotably the parameter estimation of the VSL model pro-vides novel insights into the currently debated temperaturethreshold below which growth may no longer take place Ourestimations of growth-onset temperature (ca 4ndash6C) is inagreement with the temperature range found by Tolwinski-Ward et al (2013) who used a four-parameter beta distribu-tion to calibrate the model parameters on a subset of 277 se-

ries in the United States More striking is the convergence offindings with assessments of growing season temperatures attree line based upon in situ loggers or remote sensing and in-terpolated climatic data (Koumlrner and Paulsen 2004 Koumlrner2012) as well as observational studies of wood formation(Rossi et al 2007) The wide range (1ndash9C) of the priorsconsidered in our approach allowed ample room for devia-tion from the previous literature so we interpret the agree-ment from these various lines of evidence as strong supportfor growth onset thresholds near 5C

At the level of individual species or individual sites ourresults compare well with findings of Vaganov et al (2006)who based on the VS model reported minimum and opti-mal temperatures in the northern Taiga of 4 and 16C forlarch 6 and 18C for spruce and 5 and 18C for Scots pinerespectively The differences in growth thresholds might re-flect the better adaption of pines to lower-temperature con-ditions and drought A comparison of the site values of thethreshold temperatureT1 at the corresponding elevations fordifferent tree genera is shown in Fig S2 in the SupplementSpecies-related difference in moisture parameters may bedue to needle structure as well as frequency and density ofstomata which influence water loss due to evapotranspira-tion (Vaganov et al 2006) Our results contribute to under-standing species specific growth responses as recently docu-mented in an analysis of 36 species from across the Europeancontinent (Babst et al 2013)

At the same time uncertainties arise from the parameter-isation of M and estimation ofM1 and from the missingrepresentation of winter precipitation stored as snowpack inthe CPC Leaky Bucket model and its impact on the timingof snowmelt (Tolwinski-Ward et al 2011a) Temperature-limited sites tend to have higherT1 andT2 than moisture-limited sites and vice versa forM1 and M2 This may bean expression of different climatic conditions but may alsobe related to edaphic conditions and plant physiological dif-ferences Figure S3 of the Supplement shows scatterplots ofjoint posterior relationships at each site between parameters(a)T1 andT2 (b) M1 andM2 (c) T2 andM2 and (d)T1 andM1 Application of the VSL model in more controlled frame-works such as in stands with mixed species compositionswill be useful to isolate and define species-specific growthcharacteristics while simultaneously excluding the possibili-ties that non-uniform species distributions along elevationalgradients contribute to systemic differences in the obtainedmodel parameters

42 Relationships between actual and simulated growth

The comparison between observed (ATRWVSL) and mod-elled (ATRWITRDB) tree-ring width series showed generallygood agreement and robust calibrationvalidation statisticsWe found significant model skill in independent verificationsacross all forested continents ndash tendencies that increasedwhen aggregating the tree-ring sites

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

446 P Breitenmoser et al Forward modelling of tree-ring width

The broad-scale pattern of temperature-limited growth forhigh latitudes (eg Taymyr Peninsula Russia) and high al-titudes (eg the European Alps) extends previous analysesof subsets of the ITRDB network (eg Briffa et al 2002aWettstein et al 2011 Babst et al 2013) Our findings fur-thermore largely match the distribution of potential climaticconstraints to plant growth in Nemani et al (2003) and Beeret al (2010) as well as the climate classification based onKoumlppen-Geiger by Kottek et al (2006)

However also prominent in our analysis were locations(eg Tasmania and New Zealand) where VSL simulationsrevealed little skill To explore possible reasons for this weconducted initial simulations where climate variability wasforced from a reanalysis product (20CR Compo et al 2011)and from the individual climate stations themselves Wefound some evidence for improved skill which suggests that(a) the quality of the instrumental data sets and (b) strongorographic effects can affect our simulations Caution is par-ticularly warranted where the quality and quantity of instru-mental stations rapidly decreases back in time (eg muchof the Mediterranean Asia and Southern Hemisphere loca-tions with low population density andor strong orographiceffects)

The fact that VSL reproduces first-order autocorrelationstructures (AR1) similar to the actual tree-ring chronologieshighlights the importance of including last yearrsquos growingseason for growth simulation in the VSL model in orderto retain potentially useful climate information contained intree rings (see Table 1) Similarly Wettstein et al (2011) re-port median first-order autocorrelation coefficients of 047for 762 ITRDB-derived tree-ring width series located pole-ward of roughly 30 to 40 northern latitude while Tingley etal (2012) found first-order autocorrelation coefficients of ap-proximately 06 for the tree-ring width series used in Mannet al (2008) This reasonable agreement between the auto-correlation structure in actual versus simulated tree-ring datasuggests that mechanistic modelling may help to reduce theeffect of biases in the spectral characteristics of tree-ringchronologies on climate reconstructions (Meko 1981 Cooket al 1999 Franke et al 2013) The global applicability ofa 16-month seasonal window as applied herein will requirefurther assessments for individual regions and species (forinstance as in Wu et al 2013) It is also conceivable to ap-ply differential weighting to previous yearsrsquo growth but suchschemes would be best implemented when understanding oflagged physiological processes and the roles of carbon re-serves are further advanced (eg Babst et al 2013 Zielis etal 2013)

43 Use of VSL in data assimilation

The favourable calibrationndashvalidation statistics of the VSLmodel and its ability to skilfully simulate growth for a widerange of environments suggest that the model could possi-bly be used for data assimilation approaches In the follow-

ing section several pathways are briefly outlined (see alsoBroumlnnimann et al 2013) and connections are made to howsuch assimilation approaches could be implemented usingthe VSL model

Data assimilation in general combines information fromobservations (here tree-ring width termedy) with a numeri-cal model simulation (termedxb) to obtain a physically con-sistent estimate of the climate statex It can be formulatedas a cost function problem of the form

J (x) = (x minus xb)T Bminus1(x minus xb) + (y minus H [x])T Rminus1(y minus H [x]) (10)

whereB and R represent the error covariance matrices ofthe model simulation and of the tree-ring widths respec-tively H is the observation operator which simulates the treerings from the model state Provided that the model stateencompasses all required climatic variables this could bethe VSL model How VSL is used in the approach then de-pends on how Eq (10) is minimised Following Broumlnnimannet al (2013) we distinguish ldquocovariance-based approachesrdquoldquoanalogue approachesrdquo and ldquonudging approachesrdquo

Covariance-based approaches use observations (here treerings) to correct the model simulations based on the modelerror covariance matrix Formally these approaches (eg en-semble Kalman filter 4D-VAR) require the matrixH whichis the Jacobian ofH (requiring slight adaptations to VSL)A further constraint of this family of approaches is the statevector which easily becomes excessively large Bhend etal (2012) proposed an off-line assimilation approach whichdoes not require the entire model state to be analysed

Analogue approaches minimise the cost function by se-lecting among existing simulations rather than by correctingthem Hence the cost function becomes

J (x) = (y minus H [x])T Rminus1(y minus H [x]) for xε x1x2 xn (11)

It is minimised by evaluating it for all availablex which canbe an ensemble of simulations (eg particle filter Goosse etal 2010) or different slices of a long control simulation (egproxy surrogate reconstruction Franke et al 2011) The ana-logue approach does not pose any restrictions on the size ofthe state vector or on the observation operator Hence VSLor also its parent model VS (provided again that all relevantclimate variables are in the model state) can directly be usedeither in the form of individual chronologies (an example isgiven in Broumlnnimann et al 2013) or aggregated chronolo-gies Moreover in contrast to many implementations of theensemble Kalman filterR can be non-diagonal The resultsfrom our study ie the comparison of observed and mod-elled tree-ring width can directly be used to estimateR Fur-thermore our results can be used to assess biases relative toobservations which need to be accounted for eg as an ad-ditional term in the observation operator

In the third approach nudging the cost function is notsolved explicitly Rather small increments are added to thetendency equations These increments depend on a targetwhich might be a ldquoclassicalrdquo climate reconstruction In this

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 447

case VSL may guide the aggregation of tree rings in order toincrease the signal-to-noise ratio in classical reconstructionapproaches

Our analysis has advanced the notion that the VSL modelhas the potential to be used as an observation operator inpalaeoclimatic data assimilation albeit in different form de-pending on the approach chosen

The VSL model within data assimilation approaches moti-vates future analyses on the ldquodivergence problemrdquo by explic-itly being able to take changes of limitations over time intoaccount

5 Conclusions

We investigated relationships between climate and tree-ringdata on a global scale using the non-linear process-basedVaganovndashShashkin Lite (VSL) forward model of tree-ringwidth formation (Tolwinski-Ward et al 2011a) We inves-tigated relations between actual tree-ring growth and growthsimulated based on climatic influences A network of 2287globally distributed tree-width chronologies has shown toprovide a large and high-quality sample space for these anal-yses Bayesian estimation of the VSL growth response pa-rameters yielded values that are stable with respect to thechoice of calibration interval for a wide range of speciesenvironmental conditions and time intervals showing themodelrsquos general applicability for worldwide studies usingCRU climate input data A benefit from this parameterisa-tion approach was also a novel global assessment of thegrowth-onset threshold temperature of approximately 4ndash6Cfor most sites and species thus providing new evidence foron-going debates regarding the lower temperatures at whichgrowth may take place (Anchukaitis et al 2012 Mann etal 2012 Koumlrner 2012) Moreover our results demonstratethe VSL model skill across a wide range of environmentsspecies and different time intervals Spatial aggregation oftree-ring chronologies based upon chronology quality cli-mate response and proximity reduced non-climatic noisecontained in the tree-ring data and resulted in an improvedrelationship between actual and modelled tree growth Wefurther demonstrate that the potential of the VSL model canbe exploited for instance in data assimilation approaches toreconstruct the climate of the past

Supplementary material related to this article isavailable online athttpwwwclim-pastnet104372014cp-10-437-2014-supplementpdf

AcknowledgementsThis work was funded by the Swiss Na-tional Science Foundation through the NCCR Climate (projectsPALAVAREXIII and DETREE) and Sinergia project FUPSOL Wethank Susan Tolwinski-Ward for providing the MATLAB codes forthe VSL model We also greatly thank the numerous researchers

involved in sharing their tree-ring measurements through theInternational Tree Ring Data Bank (ITRDB) maintained by theNOAA Paleoclimatology Program and the World Data Center forPaleoclimatology and Bruce Bauer for supporting our queries Wealso thank the anonymous reviewers for their valuable comments

Edited by J Guiot

References

Anchukaitis K J Evans M N Kaplan A Vaganov EA Hughes M K Grissino-Mayer H D and CaneM A Forward modeling of regional scale tree-ring pat-terns in the southeastern United States and the recent influ-ence of summer drought Geophys Res Lett 33 L04705doi1010292005GL025050 2006

Anchukaitis K J Breitenmoser P Briffa K R Buchwal ABuumlntgen U Cook E R DrsquoArrigo R D Esper J EvansM N Frank D Grudds H Gunnarson B Hughes M KKirdyanov A V Koumlrner C Krusic P J Luckman B MelvinT M Salzer M W Shashkin A V Timmreck C VaganovE A and Wilson R J S Tree rings and volcanic cooling NatGeosci 5 836ndash837 doi101038ngeo1645 2012

Babst F Poulter B Trouet V Tan K Neuwirth B WilsonR Carrer M Grabner M Tegel W Levanic T PanayotovM Urbinati C Bouriaud O Ciais P and Frank D Site- andspecies-specific responses of forest growth to climate across theEuropean continent Global Ecol Biogeogr 22 706ndash717 2013

Beer C Reichstein M Tomelleri E Ciais P Jung M BonanG B Bondeau A Cescatti A Lasslop G Lindroth A Lo-mas M Luyssaert S Margolis H Oleson K W RoupsardO Veenendaal E Viovy N Williams C Woodward F I andPapale D Terrestrial gross carbon dioxide uptake global dis-tribution and covariation with climate Science 329 834ndash8382010

Bhend J Franke J Folini D Wild M and Broumlnnimann S Anensemble-based approach to climate reconstructions Clim Past8 963ndash976 doi105194cp-8-963-2012 2012

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 1 local and regional cli-mate signals Holocene 12 737ndash757 2002a

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 2 spatio-temporal vari-ability and associated climate patterns Holocene 12 759ndash7892002b

Broumlnnimann S Franke J Breitenmoser P Hakim G GoosseH Widmann M Crucifix M Gebbie G Annan J and vander Schrier G Transient state estimation in paleoclimatologyusing data assimilation PAGES News 212 74ndash75 2013

Compo G P Whitaker J S Sardeshmukh PD Matsui N Al-lan R J Yin X Gleason B E Vose R S Rutledge GBessemoulin P Broumlnnimann S Brunet M Crouthamel R IGrant A N Groisman P Y Jones P D Kruk M C KrugerA C Marshall G J Maugeri M Mok H Y Nordli Oslash RossT F Trigo R M Wang X L Woodruff S D and Worley SJ The Twentieth Century Reanalysis Project Q J Roy Meteo-rol Soc 137 1ndash28 2011

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

442 P Breitenmoser et al Forward modelling of tree-ring width

Fig 2 Binned chronology characteristics for 1901ndash1970 Rbar isthe average inter-series correlation between all series from differenttrees (Cook et al 1990) EPS is the expressed population signaland the vertical dashed line denotes the commonly cited 085 EPScriterion (Wigley et al 1984 Cook et al 1990) Mean 1901ndash1970Rbar and EPS values were calculated using a 30 yr window that lags15 yr MSL is the mean segment length and ASD is the averagesample depth (48 bins were distinguished in each variable)

et al 1984 a threshold value of 085 is routinely but ar-bitrarily cited in dendrochronological literature) Rbar andEPS statistics were calculated over moving 30 yr windowswith 15 yr overlap A total of 93 of all mean EPS valuesin our network are above 085 over the 1901ndash1970 time pe-riod Rbar values roughly follow a normal distribution witha mean of 039 These statistics suggest that the vast major-ity of chronologies have a relatively robust signal that shouldallow climatic drivers to be inferred On average tree-ringchronologies are composed of 30 series with a mean segmentlength of 170 yr However these distributions have relativelylong tails reflecting sites that are exceptionally well repli-cated or composed of long-lived tree species (eg Bristleconepine) The mean segment length and our detrending approachsuggest that we should be able to test inter-annual to (at least)multi-decadal variability in our modelling efforts The geo-graphical distribution of the sites is dominated by low alti-tudes and the mid-latitudes but there are also a considerablenumber of high-latitude and high-elevation sites particularlyin the Northern Hemisphere

32 Site-specific Bayesian parameter estimation

The Bayesian approach provides estimates of the optimalparametersT1T2M1 andM2 for each site with descrip-tive statistics of the parameter estimation for split-samplevalidation given in Table 2 Notably we find great consis-tency among the temperature and moisture parameters thatwere calculated independently and separately for the 1901ndash1935 and 1936ndash1970 periods We find for example that themean temperature for growth onset is 46 and 48C for theearly and late calibration periods Similarly temperature nolonger limited growth above 163 and 165C again for theindependent early and late calibration periods Figure 3 fur-

Fig 3 Histogram of the Bayesian estimated VSL growth responseparameters(a) T1 lowest threshold temperature(b) T2 lowerbound for optimal temperature(c) M1 lowest threshold for mois-ture (d) M2 lower bound for optimal moisture parameters cal-culated during 1911ndash1970 for different tree genera pine (pinusn = 821) spruce (picean = 407) fir (abiesn = 286) hemlock(tsugan = 124) larch (larixn = 126) cedar (cedrusn = 107)juniper (juniperusn = 40) oak (quercusn = 253) and south-ern beech (nothofagusn = 62) Histogram ofT1 threshold tem-perature for different pine species(e) Scots pine (Pinus sylvat-ica n = 172) Austrian pine (Pinus negra n = 45) ponderosa pine(Pinus ponderosa n = 181) pinyon pine (Pinus edulis n = 73)bristlecone pine (Pinus aristata Pinus longaeva and Pinus bal-fouriana n = 34) stone pine (Pinus pinea n = 7) and jack pine(Pinus banksiana n = 15) Numbers in brackets give the series con-tributing in each group of tree genera The number of bins for eachparameter is determined through the square root of its length

ther illustrates the estimated temperature and moisture pa-rametersT1T2M1 andM2 for each site and different treegenera In terms of the currently debated (see Discussion)growth-onset threshold temperature (T1) we find most esti-mates fall within 4ndash6C with values for all sites and speciesbetween 180 and 841C (see also Table 2) Despite thegenerally narrow range of the parameters for all study sitessome evidence for species-dependent values also exists Forspruce our estimates ofT1 andT2 are generally higher thanfor pine trees whileM2 is lower We also find differencesamong the pine species For ponderosa and pinyon pinesT1is about 1 to 2C lower than for other pine species (Fig 3ecompare also to Fig 3a in which these two species clearlyinfluence the shape of the pine histogram towards coolerthreshold temperatures)

Although these parameter values were computed indepen-dently we found clear associations among the four growthparameters For instanceT1 andT2 values andM1 andM2

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 443

Table 2 Statistics of the Bayesian estimation of the site-by-site tuned VSL growth response parametersT1 T2 M1 andM2 for the 1901ndash1935 and 1936ndash1970 calibration intervals

Calib 1 1901ndash1935 Calib 2 1936ndash1970

Mean Min Max SD Mean Min Max SD

T1 (C) 464 180 841 093 475 174 797 089T2 (C) 1634 1014 2280 162 1652 1036 2187 159M1 (vv) 0023 002 0025 0001 0023 0019 0025 0001M2 (vv) 044 011 064 009 043 011 064 009

values are significantly correlated with each other (r = 060and r = 047 bothp lt 001) The often negative correla-tion between temperature and precipitation at inter-annualtime scales is expressed by the inversely related tempera-ture and moisture growth parameters with the relationshipbetweenT2 andM2 (r = minus063 p lt 001) being the mostnoteworthy Moreover temperature-limited sites tend to havehigher T1 and T2 values in comparison to the moisture-limited sites whereas higherM1 andM2 values are charac-teristic of moisture-limited sites (please refer to Sect 24 forthe definition of temperature- and moisture-limited sites)

33 Relationships between actual and simulatedtree-ring growth

The VSL model was able to simulate tree-ring series for 2271out of the 2287 sites suggesting general applicability to di-verse environments and species Of the remaining 16 sitesnine were high-latitude or high-elevation sites in Nepal (3)Siberia (1) and CanadaAlaska (5) for which no growth wassimulated because temperatures never reached the thresholdtemperatureT1 for growth initiation (hencegT = 0) The re-maining seven sites were (sub-)tropical sites in Florida (1)Mexico (4) Argentina (1) and Indonesia (1) for which nei-ther temperature- nor moisture-limited growth (hencegT = 1andgM = 1)

Similarity between the 2271 actual TRWITRDB and thecorresponding modelled TRWVSL chronologies was assessedby Pearsonrsquos correlation coefficients during the 1901ndash1970period (Fig 1) The average of Pearsonrsquos correlation coeffi-cients between all TRWITRDB and TRWVSL is 029 (standarddeviation= 022) Approximately 41 of the correlation co-efficients between TRWVSL and TRWITRDB are statisticallysignificant at the 95 confidence level (r gt 035) takinginto account the reduction of degrees of freedom due to au-tocorrelation (Mitchell Jr et al 1966) Note however thatthe 1901ndash1970 period includes the calibration interval Thusanalysing the correlation coefficients between TRWITRDBand TRWVSL in the split-sample validation we find signif-icant (p = 005 r gtsim 044) correlations during all four cali-brationvalidation intervals (calibration 1901ndash1935 and vali-dation 1936ndash1970 and vice versa) for 133 of all the series

Fig 4 Simulated monthly growth response curves for each year(1911ndash1970) for temperature (gT magenta lines) and moisture(gM cyan lines) for two sites in Switzerland(a) Berguumln Val TuorsEuropean larch 2065 m and(b) Krauchthal Scots pine 550 m Thelong-term (1911ndash1970) mean value is overlaid in red for tempera-ture and in blue for moisture(c) TRWITRDB and TRWVSL (dashedlines) for Berguumln Val Tuors (black lines)r = 069 p lt 001 andKrauchthal (green lines)r = 044p lt 001

Significant pairwise relationships between the TRWITRDBand TRWVSL series are found across the globe on all con-tinents In particular geographic areas with tendencies forhigher modelndashdata agreement are found in central EuropeScandinavia easterncentral Siberia and in the United Stateswith a cluster of high correlations in California wherer gt

08 Weak relationships are characteristic of the Africa sitesbut are also evident in New Zealand Tasmania Alaska aNWSE band from central Canada to NE USA the northernpart of the British Isles and parts of southern Europe (Fig 1)

To illustrate the monthly growth response valuesgT andgM we plot both the year-to-year variability and mean valuesover all simulated years (1911ndash1970) for one high-altitude(Fig 4a) and one low-altitude site (Fig 4b) in SwitzerlandSimulations (TRWVSL) as well as the observed chronolo-gies (VSLITRDB) for both sites are shown in Fig 4c Be-cause the simulated growth response is controlled by the

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

444 P Breitenmoser et al Forward modelling of tree-ring width

month-wise minimum of either temperature or precipitationFig 4a clearly shows that growth at the high-altitude siteis temperature-limited (gT lt gM) The lower-elevation site(Fig 4b) on the other hand is temperature-limited onlybriefly at the beginning and at the end of the growing sea-son while precipitation limits growth during the summermonths (gM lt gT ) Importantly tree growth at the high-elevation site is negatively correlated with growth at thelower-elevation site This negative correlation holds for boththe observed and modelled chronologies with coefficients ofminus013 andminus044 respectively These relationships demon-strate the VSL modelrsquos ability to incorporate joint influencesof temperature and precipitation on growth and simulta-neously suggest care is required when developing regionaltree-ring time series (see Sect 342 below) Our simulatedgrowth responses for two selected sites in Switzerland ap-pears to be widely applicable across mountainous forest re-gions with large climatic gradients such as the southwest-ern USA (Salzer and Kipfmueller 2005 Tolwinski-Wardet al 2011a) and Mongolia (Poulter et al 2013) One-year lagged autocorrelation coefficients (AR1) were assessedfrom TRWITRDBand TRWVSLseries at all sites Mean coeffi-cients of 046 and 042 respectively over all series clearlyreveal persistence ie 21 and 18 respectively of the vari-ance in the width of the ring in the current year can be pre-dicted based upon simulated growth during the past year

331 VSL simulations for aggregated TRW series

The aggregation generally enhances the correlation betweenATRWVSL and ATRWITRDB For instance the average ofall coefficients forR = 200 km during the common 1901ndash1970 interval is 034 for the temperature-limited series and038 for the moisture-limited series compared with a meanof 029 for the non-aggregated tree-ring series The spa-tial patterns of correlation coefficients for temperature- andmoisture-limited ATRW for both search radii are shown inFig 5 Notably ATRWVSL and ATRWITRDB show spatialcoherency and capture the main climate signals and arethus suitable for data assimilation approaches (see Discus-sion) The 600 km search radius improves the relationshipsfor both temperature and precipitation Coherent regional-scale correlation patterns for temperature-limited series canbe found in Scandinavia westerncentral Siberia and alongthe western and eastern United States (Fig 5a and c) Re-gional correlation patterns for moisture-sensitive series en-compass the United States and central Canada (Fig 5b andd) Regions such as central Europe Turkey central Asia andthe Andes are characterised by both temperature and mois-ture limitations which is an expression of a complex terrainwith small-scale climatic features and large climatic gradi-ents High correlation coefficients between ATRWVSL andATRWITRDB are present in all those regions with a cleartendency towards temperature-limited high-elevation sitesPoor agreement for the temperature-limited series can be

Fig 5 World map displaying Pearsonrsquos correlation coefficients be-tween ATRWVSL and ATRWITRDB for a search radius of 200 km(a b) and 600 km(c d) at temperature-limited(a c)and moisture-limited (b d) grid cells Note that in panels(c) and(d) at least onechronology has to be within the 200 km search radius to make thecorrelations comparable

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 445

31

Fig 5 World map displaying Pearson correlation coefficients between ATRWVSL and 1

ATRWITRDB for a search radius of 200 km (ab) and 600 km (cd) at temperature-limited (ac) 2

and moisture-limited (bd) grid cells Note that in panels c) and d) at least one chronology has 3

to be within the 200km search radius to make the correlations comparable 4

5

6

7

8

9

10

11

Fig 6 Scatter plot of correlation coefficients between each ATRWVSL and ATRWITRDB (200 km 12

search radius) series for the 1901-1935 and 1936-1970 independent time periods Results are 13

shown for a) the early 1901-1935 calibration interval and b) the late 1936-1970 calibration 14

interval 15

-1 -05 0 05 1-1

-08-06-04-02

002040608

1a) b)

-1-08-06

002040608

1

-04-02

-1 -0 0 05 15 r during calibration 1901-35 r during calibration 1936-70

r dur

ing

valid

atio

n 19

36-7

0

r dur

ing

valid

atio

n 19

01-3

5

Fig 6 Scatterplot of correlation coefficients between eachATRWVSL and ATRWITRDB (200 km search radius) series for the1901ndash1935 and 1936ndash1970 independent time periods Results areshown for(a) the early 1901ndash1935 calibration interval and(b) thelate 1936ndash1970 calibration interval

found in Tasmania New Zealand western-central Canadaand in the eastern-central US while moisture characteristicsare poorly captured in Patagonia northern Canada and in theEuropean Alps

Based on the split-sample validation experiment Fig 6shows a scatterplot of the correlation coefficients between theATRWVSL and ATRWITRDB 200 km search radius duringdifferent calibrationvalidation intervals (1901ndash19351936ndash1970 and 1936ndash19701901ndash1935) Points along the 1 1 lineare sites for which VSL produces simulations that are sta-ble in time whereas points below this line represent sitesfor which the model yields a higher correlation during thecalibration period We find model skill (r gt 044) in Pear-sonrsquos correlation coefficients in 36 of the series duringthe calibration period of which 54 are also significant inthe validation period Correlations are stable for moisture-limited sites in large areas of the United States and cen-tral Canada the lower-elevation sites in west-central Eu-rope Turkey Mongolia the western Himalayas and in mid-Chile whereas temperature-limited sites dominate Scandi-navia Siberia the eastern Himalayas central Europe south-ern South America and parts of the western United StatesCorrelations are not particularly skilful for New ZealandTasmania and Patagonia

4 Discussion

41 Growth parameters

The site-by-site parameterisation for the moisture and tem-perature thresholds revealed interesting global-scale patternsNotably the parameter estimation of the VSL model pro-vides novel insights into the currently debated temperaturethreshold below which growth may no longer take place Ourestimations of growth-onset temperature (ca 4ndash6C) is inagreement with the temperature range found by Tolwinski-Ward et al (2013) who used a four-parameter beta distribu-tion to calibrate the model parameters on a subset of 277 se-

ries in the United States More striking is the convergence offindings with assessments of growing season temperatures attree line based upon in situ loggers or remote sensing and in-terpolated climatic data (Koumlrner and Paulsen 2004 Koumlrner2012) as well as observational studies of wood formation(Rossi et al 2007) The wide range (1ndash9C) of the priorsconsidered in our approach allowed ample room for devia-tion from the previous literature so we interpret the agree-ment from these various lines of evidence as strong supportfor growth onset thresholds near 5C

At the level of individual species or individual sites ourresults compare well with findings of Vaganov et al (2006)who based on the VS model reported minimum and opti-mal temperatures in the northern Taiga of 4 and 16C forlarch 6 and 18C for spruce and 5 and 18C for Scots pinerespectively The differences in growth thresholds might re-flect the better adaption of pines to lower-temperature con-ditions and drought A comparison of the site values of thethreshold temperatureT1 at the corresponding elevations fordifferent tree genera is shown in Fig S2 in the SupplementSpecies-related difference in moisture parameters may bedue to needle structure as well as frequency and density ofstomata which influence water loss due to evapotranspira-tion (Vaganov et al 2006) Our results contribute to under-standing species specific growth responses as recently docu-mented in an analysis of 36 species from across the Europeancontinent (Babst et al 2013)

At the same time uncertainties arise from the parameter-isation of M and estimation ofM1 and from the missingrepresentation of winter precipitation stored as snowpack inthe CPC Leaky Bucket model and its impact on the timingof snowmelt (Tolwinski-Ward et al 2011a) Temperature-limited sites tend to have higherT1 andT2 than moisture-limited sites and vice versa forM1 and M2 This may bean expression of different climatic conditions but may alsobe related to edaphic conditions and plant physiological dif-ferences Figure S3 of the Supplement shows scatterplots ofjoint posterior relationships at each site between parameters(a)T1 andT2 (b) M1 andM2 (c) T2 andM2 and (d)T1 andM1 Application of the VSL model in more controlled frame-works such as in stands with mixed species compositionswill be useful to isolate and define species-specific growthcharacteristics while simultaneously excluding the possibili-ties that non-uniform species distributions along elevationalgradients contribute to systemic differences in the obtainedmodel parameters

42 Relationships between actual and simulated growth

The comparison between observed (ATRWVSL) and mod-elled (ATRWITRDB) tree-ring width series showed generallygood agreement and robust calibrationvalidation statisticsWe found significant model skill in independent verificationsacross all forested continents ndash tendencies that increasedwhen aggregating the tree-ring sites

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

446 P Breitenmoser et al Forward modelling of tree-ring width

The broad-scale pattern of temperature-limited growth forhigh latitudes (eg Taymyr Peninsula Russia) and high al-titudes (eg the European Alps) extends previous analysesof subsets of the ITRDB network (eg Briffa et al 2002aWettstein et al 2011 Babst et al 2013) Our findings fur-thermore largely match the distribution of potential climaticconstraints to plant growth in Nemani et al (2003) and Beeret al (2010) as well as the climate classification based onKoumlppen-Geiger by Kottek et al (2006)

However also prominent in our analysis were locations(eg Tasmania and New Zealand) where VSL simulationsrevealed little skill To explore possible reasons for this weconducted initial simulations where climate variability wasforced from a reanalysis product (20CR Compo et al 2011)and from the individual climate stations themselves Wefound some evidence for improved skill which suggests that(a) the quality of the instrumental data sets and (b) strongorographic effects can affect our simulations Caution is par-ticularly warranted where the quality and quantity of instru-mental stations rapidly decreases back in time (eg muchof the Mediterranean Asia and Southern Hemisphere loca-tions with low population density andor strong orographiceffects)

The fact that VSL reproduces first-order autocorrelationstructures (AR1) similar to the actual tree-ring chronologieshighlights the importance of including last yearrsquos growingseason for growth simulation in the VSL model in orderto retain potentially useful climate information contained intree rings (see Table 1) Similarly Wettstein et al (2011) re-port median first-order autocorrelation coefficients of 047for 762 ITRDB-derived tree-ring width series located pole-ward of roughly 30 to 40 northern latitude while Tingley etal (2012) found first-order autocorrelation coefficients of ap-proximately 06 for the tree-ring width series used in Mannet al (2008) This reasonable agreement between the auto-correlation structure in actual versus simulated tree-ring datasuggests that mechanistic modelling may help to reduce theeffect of biases in the spectral characteristics of tree-ringchronologies on climate reconstructions (Meko 1981 Cooket al 1999 Franke et al 2013) The global applicability ofa 16-month seasonal window as applied herein will requirefurther assessments for individual regions and species (forinstance as in Wu et al 2013) It is also conceivable to ap-ply differential weighting to previous yearsrsquo growth but suchschemes would be best implemented when understanding oflagged physiological processes and the roles of carbon re-serves are further advanced (eg Babst et al 2013 Zielis etal 2013)

43 Use of VSL in data assimilation

The favourable calibrationndashvalidation statistics of the VSLmodel and its ability to skilfully simulate growth for a widerange of environments suggest that the model could possi-bly be used for data assimilation approaches In the follow-

ing section several pathways are briefly outlined (see alsoBroumlnnimann et al 2013) and connections are made to howsuch assimilation approaches could be implemented usingthe VSL model

Data assimilation in general combines information fromobservations (here tree-ring width termedy) with a numeri-cal model simulation (termedxb) to obtain a physically con-sistent estimate of the climate statex It can be formulatedas a cost function problem of the form

J (x) = (x minus xb)T Bminus1(x minus xb) + (y minus H [x])T Rminus1(y minus H [x]) (10)

whereB and R represent the error covariance matrices ofthe model simulation and of the tree-ring widths respec-tively H is the observation operator which simulates the treerings from the model state Provided that the model stateencompasses all required climatic variables this could bethe VSL model How VSL is used in the approach then de-pends on how Eq (10) is minimised Following Broumlnnimannet al (2013) we distinguish ldquocovariance-based approachesrdquoldquoanalogue approachesrdquo and ldquonudging approachesrdquo

Covariance-based approaches use observations (here treerings) to correct the model simulations based on the modelerror covariance matrix Formally these approaches (eg en-semble Kalman filter 4D-VAR) require the matrixH whichis the Jacobian ofH (requiring slight adaptations to VSL)A further constraint of this family of approaches is the statevector which easily becomes excessively large Bhend etal (2012) proposed an off-line assimilation approach whichdoes not require the entire model state to be analysed

Analogue approaches minimise the cost function by se-lecting among existing simulations rather than by correctingthem Hence the cost function becomes

J (x) = (y minus H [x])T Rminus1(y minus H [x]) for xε x1x2 xn (11)

It is minimised by evaluating it for all availablex which canbe an ensemble of simulations (eg particle filter Goosse etal 2010) or different slices of a long control simulation (egproxy surrogate reconstruction Franke et al 2011) The ana-logue approach does not pose any restrictions on the size ofthe state vector or on the observation operator Hence VSLor also its parent model VS (provided again that all relevantclimate variables are in the model state) can directly be usedeither in the form of individual chronologies (an example isgiven in Broumlnnimann et al 2013) or aggregated chronolo-gies Moreover in contrast to many implementations of theensemble Kalman filterR can be non-diagonal The resultsfrom our study ie the comparison of observed and mod-elled tree-ring width can directly be used to estimateR Fur-thermore our results can be used to assess biases relative toobservations which need to be accounted for eg as an ad-ditional term in the observation operator

In the third approach nudging the cost function is notsolved explicitly Rather small increments are added to thetendency equations These increments depend on a targetwhich might be a ldquoclassicalrdquo climate reconstruction In this

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 447

case VSL may guide the aggregation of tree rings in order toincrease the signal-to-noise ratio in classical reconstructionapproaches

Our analysis has advanced the notion that the VSL modelhas the potential to be used as an observation operator inpalaeoclimatic data assimilation albeit in different form de-pending on the approach chosen

The VSL model within data assimilation approaches moti-vates future analyses on the ldquodivergence problemrdquo by explic-itly being able to take changes of limitations over time intoaccount

5 Conclusions

We investigated relationships between climate and tree-ringdata on a global scale using the non-linear process-basedVaganovndashShashkin Lite (VSL) forward model of tree-ringwidth formation (Tolwinski-Ward et al 2011a) We inves-tigated relations between actual tree-ring growth and growthsimulated based on climatic influences A network of 2287globally distributed tree-width chronologies has shown toprovide a large and high-quality sample space for these anal-yses Bayesian estimation of the VSL growth response pa-rameters yielded values that are stable with respect to thechoice of calibration interval for a wide range of speciesenvironmental conditions and time intervals showing themodelrsquos general applicability for worldwide studies usingCRU climate input data A benefit from this parameterisa-tion approach was also a novel global assessment of thegrowth-onset threshold temperature of approximately 4ndash6Cfor most sites and species thus providing new evidence foron-going debates regarding the lower temperatures at whichgrowth may take place (Anchukaitis et al 2012 Mann etal 2012 Koumlrner 2012) Moreover our results demonstratethe VSL model skill across a wide range of environmentsspecies and different time intervals Spatial aggregation oftree-ring chronologies based upon chronology quality cli-mate response and proximity reduced non-climatic noisecontained in the tree-ring data and resulted in an improvedrelationship between actual and modelled tree growth Wefurther demonstrate that the potential of the VSL model canbe exploited for instance in data assimilation approaches toreconstruct the climate of the past

Supplementary material related to this article isavailable online athttpwwwclim-pastnet104372014cp-10-437-2014-supplementpdf

AcknowledgementsThis work was funded by the Swiss Na-tional Science Foundation through the NCCR Climate (projectsPALAVAREXIII and DETREE) and Sinergia project FUPSOL Wethank Susan Tolwinski-Ward for providing the MATLAB codes forthe VSL model We also greatly thank the numerous researchers

involved in sharing their tree-ring measurements through theInternational Tree Ring Data Bank (ITRDB) maintained by theNOAA Paleoclimatology Program and the World Data Center forPaleoclimatology and Bruce Bauer for supporting our queries Wealso thank the anonymous reviewers for their valuable comments

Edited by J Guiot

References

Anchukaitis K J Evans M N Kaplan A Vaganov EA Hughes M K Grissino-Mayer H D and CaneM A Forward modeling of regional scale tree-ring pat-terns in the southeastern United States and the recent influ-ence of summer drought Geophys Res Lett 33 L04705doi1010292005GL025050 2006

Anchukaitis K J Breitenmoser P Briffa K R Buchwal ABuumlntgen U Cook E R DrsquoArrigo R D Esper J EvansM N Frank D Grudds H Gunnarson B Hughes M KKirdyanov A V Koumlrner C Krusic P J Luckman B MelvinT M Salzer M W Shashkin A V Timmreck C VaganovE A and Wilson R J S Tree rings and volcanic cooling NatGeosci 5 836ndash837 doi101038ngeo1645 2012

Babst F Poulter B Trouet V Tan K Neuwirth B WilsonR Carrer M Grabner M Tegel W Levanic T PanayotovM Urbinati C Bouriaud O Ciais P and Frank D Site- andspecies-specific responses of forest growth to climate across theEuropean continent Global Ecol Biogeogr 22 706ndash717 2013

Beer C Reichstein M Tomelleri E Ciais P Jung M BonanG B Bondeau A Cescatti A Lasslop G Lindroth A Lo-mas M Luyssaert S Margolis H Oleson K W RoupsardO Veenendaal E Viovy N Williams C Woodward F I andPapale D Terrestrial gross carbon dioxide uptake global dis-tribution and covariation with climate Science 329 834ndash8382010

Bhend J Franke J Folini D Wild M and Broumlnnimann S Anensemble-based approach to climate reconstructions Clim Past8 963ndash976 doi105194cp-8-963-2012 2012

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 1 local and regional cli-mate signals Holocene 12 737ndash757 2002a

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 2 spatio-temporal vari-ability and associated climate patterns Holocene 12 759ndash7892002b

Broumlnnimann S Franke J Breitenmoser P Hakim G GoosseH Widmann M Crucifix M Gebbie G Annan J and vander Schrier G Transient state estimation in paleoclimatologyusing data assimilation PAGES News 212 74ndash75 2013

Compo G P Whitaker J S Sardeshmukh PD Matsui N Al-lan R J Yin X Gleason B E Vose R S Rutledge GBessemoulin P Broumlnnimann S Brunet M Crouthamel R IGrant A N Groisman P Y Jones P D Kruk M C KrugerA C Marshall G J Maugeri M Mok H Y Nordli Oslash RossT F Trigo R M Wang X L Woodruff S D and Worley SJ The Twentieth Century Reanalysis Project Q J Roy Meteo-rol Soc 137 1ndash28 2011

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

P Breitenmoser et al Forward modelling of tree-ring width 443

Table 2 Statistics of the Bayesian estimation of the site-by-site tuned VSL growth response parametersT1 T2 M1 andM2 for the 1901ndash1935 and 1936ndash1970 calibration intervals

Calib 1 1901ndash1935 Calib 2 1936ndash1970

Mean Min Max SD Mean Min Max SD

T1 (C) 464 180 841 093 475 174 797 089T2 (C) 1634 1014 2280 162 1652 1036 2187 159M1 (vv) 0023 002 0025 0001 0023 0019 0025 0001M2 (vv) 044 011 064 009 043 011 064 009

values are significantly correlated with each other (r = 060and r = 047 bothp lt 001) The often negative correla-tion between temperature and precipitation at inter-annualtime scales is expressed by the inversely related tempera-ture and moisture growth parameters with the relationshipbetweenT2 andM2 (r = minus063 p lt 001) being the mostnoteworthy Moreover temperature-limited sites tend to havehigher T1 and T2 values in comparison to the moisture-limited sites whereas higherM1 andM2 values are charac-teristic of moisture-limited sites (please refer to Sect 24 forthe definition of temperature- and moisture-limited sites)

33 Relationships between actual and simulatedtree-ring growth

The VSL model was able to simulate tree-ring series for 2271out of the 2287 sites suggesting general applicability to di-verse environments and species Of the remaining 16 sitesnine were high-latitude or high-elevation sites in Nepal (3)Siberia (1) and CanadaAlaska (5) for which no growth wassimulated because temperatures never reached the thresholdtemperatureT1 for growth initiation (hencegT = 0) The re-maining seven sites were (sub-)tropical sites in Florida (1)Mexico (4) Argentina (1) and Indonesia (1) for which nei-ther temperature- nor moisture-limited growth (hencegT = 1andgM = 1)

Similarity between the 2271 actual TRWITRDB and thecorresponding modelled TRWVSL chronologies was assessedby Pearsonrsquos correlation coefficients during the 1901ndash1970period (Fig 1) The average of Pearsonrsquos correlation coeffi-cients between all TRWITRDB and TRWVSL is 029 (standarddeviation= 022) Approximately 41 of the correlation co-efficients between TRWVSL and TRWITRDB are statisticallysignificant at the 95 confidence level (r gt 035) takinginto account the reduction of degrees of freedom due to au-tocorrelation (Mitchell Jr et al 1966) Note however thatthe 1901ndash1970 period includes the calibration interval Thusanalysing the correlation coefficients between TRWITRDBand TRWVSL in the split-sample validation we find signif-icant (p = 005 r gtsim 044) correlations during all four cali-brationvalidation intervals (calibration 1901ndash1935 and vali-dation 1936ndash1970 and vice versa) for 133 of all the series

Fig 4 Simulated monthly growth response curves for each year(1911ndash1970) for temperature (gT magenta lines) and moisture(gM cyan lines) for two sites in Switzerland(a) Berguumln Val TuorsEuropean larch 2065 m and(b) Krauchthal Scots pine 550 m Thelong-term (1911ndash1970) mean value is overlaid in red for tempera-ture and in blue for moisture(c) TRWITRDB and TRWVSL (dashedlines) for Berguumln Val Tuors (black lines)r = 069 p lt 001 andKrauchthal (green lines)r = 044p lt 001

Significant pairwise relationships between the TRWITRDBand TRWVSL series are found across the globe on all con-tinents In particular geographic areas with tendencies forhigher modelndashdata agreement are found in central EuropeScandinavia easterncentral Siberia and in the United Stateswith a cluster of high correlations in California wherer gt

08 Weak relationships are characteristic of the Africa sitesbut are also evident in New Zealand Tasmania Alaska aNWSE band from central Canada to NE USA the northernpart of the British Isles and parts of southern Europe (Fig 1)

To illustrate the monthly growth response valuesgT andgM we plot both the year-to-year variability and mean valuesover all simulated years (1911ndash1970) for one high-altitude(Fig 4a) and one low-altitude site (Fig 4b) in SwitzerlandSimulations (TRWVSL) as well as the observed chronolo-gies (VSLITRDB) for both sites are shown in Fig 4c Be-cause the simulated growth response is controlled by the

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

444 P Breitenmoser et al Forward modelling of tree-ring width

month-wise minimum of either temperature or precipitationFig 4a clearly shows that growth at the high-altitude siteis temperature-limited (gT lt gM) The lower-elevation site(Fig 4b) on the other hand is temperature-limited onlybriefly at the beginning and at the end of the growing sea-son while precipitation limits growth during the summermonths (gM lt gT ) Importantly tree growth at the high-elevation site is negatively correlated with growth at thelower-elevation site This negative correlation holds for boththe observed and modelled chronologies with coefficients ofminus013 andminus044 respectively These relationships demon-strate the VSL modelrsquos ability to incorporate joint influencesof temperature and precipitation on growth and simulta-neously suggest care is required when developing regionaltree-ring time series (see Sect 342 below) Our simulatedgrowth responses for two selected sites in Switzerland ap-pears to be widely applicable across mountainous forest re-gions with large climatic gradients such as the southwest-ern USA (Salzer and Kipfmueller 2005 Tolwinski-Wardet al 2011a) and Mongolia (Poulter et al 2013) One-year lagged autocorrelation coefficients (AR1) were assessedfrom TRWITRDBand TRWVSLseries at all sites Mean coeffi-cients of 046 and 042 respectively over all series clearlyreveal persistence ie 21 and 18 respectively of the vari-ance in the width of the ring in the current year can be pre-dicted based upon simulated growth during the past year

331 VSL simulations for aggregated TRW series

The aggregation generally enhances the correlation betweenATRWVSL and ATRWITRDB For instance the average ofall coefficients forR = 200 km during the common 1901ndash1970 interval is 034 for the temperature-limited series and038 for the moisture-limited series compared with a meanof 029 for the non-aggregated tree-ring series The spa-tial patterns of correlation coefficients for temperature- andmoisture-limited ATRW for both search radii are shown inFig 5 Notably ATRWVSL and ATRWITRDB show spatialcoherency and capture the main climate signals and arethus suitable for data assimilation approaches (see Discus-sion) The 600 km search radius improves the relationshipsfor both temperature and precipitation Coherent regional-scale correlation patterns for temperature-limited series canbe found in Scandinavia westerncentral Siberia and alongthe western and eastern United States (Fig 5a and c) Re-gional correlation patterns for moisture-sensitive series en-compass the United States and central Canada (Fig 5b andd) Regions such as central Europe Turkey central Asia andthe Andes are characterised by both temperature and mois-ture limitations which is an expression of a complex terrainwith small-scale climatic features and large climatic gradi-ents High correlation coefficients between ATRWVSL andATRWITRDB are present in all those regions with a cleartendency towards temperature-limited high-elevation sitesPoor agreement for the temperature-limited series can be

Fig 5 World map displaying Pearsonrsquos correlation coefficients be-tween ATRWVSL and ATRWITRDB for a search radius of 200 km(a b) and 600 km(c d) at temperature-limited(a c)and moisture-limited (b d) grid cells Note that in panels(c) and(d) at least onechronology has to be within the 200 km search radius to make thecorrelations comparable

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 445

31

Fig 5 World map displaying Pearson correlation coefficients between ATRWVSL and 1

ATRWITRDB for a search radius of 200 km (ab) and 600 km (cd) at temperature-limited (ac) 2

and moisture-limited (bd) grid cells Note that in panels c) and d) at least one chronology has 3

to be within the 200km search radius to make the correlations comparable 4

5

6

7

8

9

10

11

Fig 6 Scatter plot of correlation coefficients between each ATRWVSL and ATRWITRDB (200 km 12

search radius) series for the 1901-1935 and 1936-1970 independent time periods Results are 13

shown for a) the early 1901-1935 calibration interval and b) the late 1936-1970 calibration 14

interval 15

-1 -05 0 05 1-1

-08-06-04-02

002040608

1a) b)

-1-08-06

002040608

1

-04-02

-1 -0 0 05 15 r during calibration 1901-35 r during calibration 1936-70

r dur

ing

valid

atio

n 19

36-7

0

r dur

ing

valid

atio

n 19

01-3

5

Fig 6 Scatterplot of correlation coefficients between eachATRWVSL and ATRWITRDB (200 km search radius) series for the1901ndash1935 and 1936ndash1970 independent time periods Results areshown for(a) the early 1901ndash1935 calibration interval and(b) thelate 1936ndash1970 calibration interval

found in Tasmania New Zealand western-central Canadaand in the eastern-central US while moisture characteristicsare poorly captured in Patagonia northern Canada and in theEuropean Alps

Based on the split-sample validation experiment Fig 6shows a scatterplot of the correlation coefficients between theATRWVSL and ATRWITRDB 200 km search radius duringdifferent calibrationvalidation intervals (1901ndash19351936ndash1970 and 1936ndash19701901ndash1935) Points along the 1 1 lineare sites for which VSL produces simulations that are sta-ble in time whereas points below this line represent sitesfor which the model yields a higher correlation during thecalibration period We find model skill (r gt 044) in Pear-sonrsquos correlation coefficients in 36 of the series duringthe calibration period of which 54 are also significant inthe validation period Correlations are stable for moisture-limited sites in large areas of the United States and cen-tral Canada the lower-elevation sites in west-central Eu-rope Turkey Mongolia the western Himalayas and in mid-Chile whereas temperature-limited sites dominate Scandi-navia Siberia the eastern Himalayas central Europe south-ern South America and parts of the western United StatesCorrelations are not particularly skilful for New ZealandTasmania and Patagonia

4 Discussion

41 Growth parameters

The site-by-site parameterisation for the moisture and tem-perature thresholds revealed interesting global-scale patternsNotably the parameter estimation of the VSL model pro-vides novel insights into the currently debated temperaturethreshold below which growth may no longer take place Ourestimations of growth-onset temperature (ca 4ndash6C) is inagreement with the temperature range found by Tolwinski-Ward et al (2013) who used a four-parameter beta distribu-tion to calibrate the model parameters on a subset of 277 se-

ries in the United States More striking is the convergence offindings with assessments of growing season temperatures attree line based upon in situ loggers or remote sensing and in-terpolated climatic data (Koumlrner and Paulsen 2004 Koumlrner2012) as well as observational studies of wood formation(Rossi et al 2007) The wide range (1ndash9C) of the priorsconsidered in our approach allowed ample room for devia-tion from the previous literature so we interpret the agree-ment from these various lines of evidence as strong supportfor growth onset thresholds near 5C

At the level of individual species or individual sites ourresults compare well with findings of Vaganov et al (2006)who based on the VS model reported minimum and opti-mal temperatures in the northern Taiga of 4 and 16C forlarch 6 and 18C for spruce and 5 and 18C for Scots pinerespectively The differences in growth thresholds might re-flect the better adaption of pines to lower-temperature con-ditions and drought A comparison of the site values of thethreshold temperatureT1 at the corresponding elevations fordifferent tree genera is shown in Fig S2 in the SupplementSpecies-related difference in moisture parameters may bedue to needle structure as well as frequency and density ofstomata which influence water loss due to evapotranspira-tion (Vaganov et al 2006) Our results contribute to under-standing species specific growth responses as recently docu-mented in an analysis of 36 species from across the Europeancontinent (Babst et al 2013)

At the same time uncertainties arise from the parameter-isation of M and estimation ofM1 and from the missingrepresentation of winter precipitation stored as snowpack inthe CPC Leaky Bucket model and its impact on the timingof snowmelt (Tolwinski-Ward et al 2011a) Temperature-limited sites tend to have higherT1 andT2 than moisture-limited sites and vice versa forM1 and M2 This may bean expression of different climatic conditions but may alsobe related to edaphic conditions and plant physiological dif-ferences Figure S3 of the Supplement shows scatterplots ofjoint posterior relationships at each site between parameters(a)T1 andT2 (b) M1 andM2 (c) T2 andM2 and (d)T1 andM1 Application of the VSL model in more controlled frame-works such as in stands with mixed species compositionswill be useful to isolate and define species-specific growthcharacteristics while simultaneously excluding the possibili-ties that non-uniform species distributions along elevationalgradients contribute to systemic differences in the obtainedmodel parameters

42 Relationships between actual and simulated growth

The comparison between observed (ATRWVSL) and mod-elled (ATRWITRDB) tree-ring width series showed generallygood agreement and robust calibrationvalidation statisticsWe found significant model skill in independent verificationsacross all forested continents ndash tendencies that increasedwhen aggregating the tree-ring sites

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

446 P Breitenmoser et al Forward modelling of tree-ring width

The broad-scale pattern of temperature-limited growth forhigh latitudes (eg Taymyr Peninsula Russia) and high al-titudes (eg the European Alps) extends previous analysesof subsets of the ITRDB network (eg Briffa et al 2002aWettstein et al 2011 Babst et al 2013) Our findings fur-thermore largely match the distribution of potential climaticconstraints to plant growth in Nemani et al (2003) and Beeret al (2010) as well as the climate classification based onKoumlppen-Geiger by Kottek et al (2006)

However also prominent in our analysis were locations(eg Tasmania and New Zealand) where VSL simulationsrevealed little skill To explore possible reasons for this weconducted initial simulations where climate variability wasforced from a reanalysis product (20CR Compo et al 2011)and from the individual climate stations themselves Wefound some evidence for improved skill which suggests that(a) the quality of the instrumental data sets and (b) strongorographic effects can affect our simulations Caution is par-ticularly warranted where the quality and quantity of instru-mental stations rapidly decreases back in time (eg muchof the Mediterranean Asia and Southern Hemisphere loca-tions with low population density andor strong orographiceffects)

The fact that VSL reproduces first-order autocorrelationstructures (AR1) similar to the actual tree-ring chronologieshighlights the importance of including last yearrsquos growingseason for growth simulation in the VSL model in orderto retain potentially useful climate information contained intree rings (see Table 1) Similarly Wettstein et al (2011) re-port median first-order autocorrelation coefficients of 047for 762 ITRDB-derived tree-ring width series located pole-ward of roughly 30 to 40 northern latitude while Tingley etal (2012) found first-order autocorrelation coefficients of ap-proximately 06 for the tree-ring width series used in Mannet al (2008) This reasonable agreement between the auto-correlation structure in actual versus simulated tree-ring datasuggests that mechanistic modelling may help to reduce theeffect of biases in the spectral characteristics of tree-ringchronologies on climate reconstructions (Meko 1981 Cooket al 1999 Franke et al 2013) The global applicability ofa 16-month seasonal window as applied herein will requirefurther assessments for individual regions and species (forinstance as in Wu et al 2013) It is also conceivable to ap-ply differential weighting to previous yearsrsquo growth but suchschemes would be best implemented when understanding oflagged physiological processes and the roles of carbon re-serves are further advanced (eg Babst et al 2013 Zielis etal 2013)

43 Use of VSL in data assimilation

The favourable calibrationndashvalidation statistics of the VSLmodel and its ability to skilfully simulate growth for a widerange of environments suggest that the model could possi-bly be used for data assimilation approaches In the follow-

ing section several pathways are briefly outlined (see alsoBroumlnnimann et al 2013) and connections are made to howsuch assimilation approaches could be implemented usingthe VSL model

Data assimilation in general combines information fromobservations (here tree-ring width termedy) with a numeri-cal model simulation (termedxb) to obtain a physically con-sistent estimate of the climate statex It can be formulatedas a cost function problem of the form

J (x) = (x minus xb)T Bminus1(x minus xb) + (y minus H [x])T Rminus1(y minus H [x]) (10)

whereB and R represent the error covariance matrices ofthe model simulation and of the tree-ring widths respec-tively H is the observation operator which simulates the treerings from the model state Provided that the model stateencompasses all required climatic variables this could bethe VSL model How VSL is used in the approach then de-pends on how Eq (10) is minimised Following Broumlnnimannet al (2013) we distinguish ldquocovariance-based approachesrdquoldquoanalogue approachesrdquo and ldquonudging approachesrdquo

Covariance-based approaches use observations (here treerings) to correct the model simulations based on the modelerror covariance matrix Formally these approaches (eg en-semble Kalman filter 4D-VAR) require the matrixH whichis the Jacobian ofH (requiring slight adaptations to VSL)A further constraint of this family of approaches is the statevector which easily becomes excessively large Bhend etal (2012) proposed an off-line assimilation approach whichdoes not require the entire model state to be analysed

Analogue approaches minimise the cost function by se-lecting among existing simulations rather than by correctingthem Hence the cost function becomes

J (x) = (y minus H [x])T Rminus1(y minus H [x]) for xε x1x2 xn (11)

It is minimised by evaluating it for all availablex which canbe an ensemble of simulations (eg particle filter Goosse etal 2010) or different slices of a long control simulation (egproxy surrogate reconstruction Franke et al 2011) The ana-logue approach does not pose any restrictions on the size ofthe state vector or on the observation operator Hence VSLor also its parent model VS (provided again that all relevantclimate variables are in the model state) can directly be usedeither in the form of individual chronologies (an example isgiven in Broumlnnimann et al 2013) or aggregated chronolo-gies Moreover in contrast to many implementations of theensemble Kalman filterR can be non-diagonal The resultsfrom our study ie the comparison of observed and mod-elled tree-ring width can directly be used to estimateR Fur-thermore our results can be used to assess biases relative toobservations which need to be accounted for eg as an ad-ditional term in the observation operator

In the third approach nudging the cost function is notsolved explicitly Rather small increments are added to thetendency equations These increments depend on a targetwhich might be a ldquoclassicalrdquo climate reconstruction In this

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 447

case VSL may guide the aggregation of tree rings in order toincrease the signal-to-noise ratio in classical reconstructionapproaches

Our analysis has advanced the notion that the VSL modelhas the potential to be used as an observation operator inpalaeoclimatic data assimilation albeit in different form de-pending on the approach chosen

The VSL model within data assimilation approaches moti-vates future analyses on the ldquodivergence problemrdquo by explic-itly being able to take changes of limitations over time intoaccount

5 Conclusions

We investigated relationships between climate and tree-ringdata on a global scale using the non-linear process-basedVaganovndashShashkin Lite (VSL) forward model of tree-ringwidth formation (Tolwinski-Ward et al 2011a) We inves-tigated relations between actual tree-ring growth and growthsimulated based on climatic influences A network of 2287globally distributed tree-width chronologies has shown toprovide a large and high-quality sample space for these anal-yses Bayesian estimation of the VSL growth response pa-rameters yielded values that are stable with respect to thechoice of calibration interval for a wide range of speciesenvironmental conditions and time intervals showing themodelrsquos general applicability for worldwide studies usingCRU climate input data A benefit from this parameterisa-tion approach was also a novel global assessment of thegrowth-onset threshold temperature of approximately 4ndash6Cfor most sites and species thus providing new evidence foron-going debates regarding the lower temperatures at whichgrowth may take place (Anchukaitis et al 2012 Mann etal 2012 Koumlrner 2012) Moreover our results demonstratethe VSL model skill across a wide range of environmentsspecies and different time intervals Spatial aggregation oftree-ring chronologies based upon chronology quality cli-mate response and proximity reduced non-climatic noisecontained in the tree-ring data and resulted in an improvedrelationship between actual and modelled tree growth Wefurther demonstrate that the potential of the VSL model canbe exploited for instance in data assimilation approaches toreconstruct the climate of the past

Supplementary material related to this article isavailable online athttpwwwclim-pastnet104372014cp-10-437-2014-supplementpdf

AcknowledgementsThis work was funded by the Swiss Na-tional Science Foundation through the NCCR Climate (projectsPALAVAREXIII and DETREE) and Sinergia project FUPSOL Wethank Susan Tolwinski-Ward for providing the MATLAB codes forthe VSL model We also greatly thank the numerous researchers

involved in sharing their tree-ring measurements through theInternational Tree Ring Data Bank (ITRDB) maintained by theNOAA Paleoclimatology Program and the World Data Center forPaleoclimatology and Bruce Bauer for supporting our queries Wealso thank the anonymous reviewers for their valuable comments

Edited by J Guiot

References

Anchukaitis K J Evans M N Kaplan A Vaganov EA Hughes M K Grissino-Mayer H D and CaneM A Forward modeling of regional scale tree-ring pat-terns in the southeastern United States and the recent influ-ence of summer drought Geophys Res Lett 33 L04705doi1010292005GL025050 2006

Anchukaitis K J Breitenmoser P Briffa K R Buchwal ABuumlntgen U Cook E R DrsquoArrigo R D Esper J EvansM N Frank D Grudds H Gunnarson B Hughes M KKirdyanov A V Koumlrner C Krusic P J Luckman B MelvinT M Salzer M W Shashkin A V Timmreck C VaganovE A and Wilson R J S Tree rings and volcanic cooling NatGeosci 5 836ndash837 doi101038ngeo1645 2012

Babst F Poulter B Trouet V Tan K Neuwirth B WilsonR Carrer M Grabner M Tegel W Levanic T PanayotovM Urbinati C Bouriaud O Ciais P and Frank D Site- andspecies-specific responses of forest growth to climate across theEuropean continent Global Ecol Biogeogr 22 706ndash717 2013

Beer C Reichstein M Tomelleri E Ciais P Jung M BonanG B Bondeau A Cescatti A Lasslop G Lindroth A Lo-mas M Luyssaert S Margolis H Oleson K W RoupsardO Veenendaal E Viovy N Williams C Woodward F I andPapale D Terrestrial gross carbon dioxide uptake global dis-tribution and covariation with climate Science 329 834ndash8382010

Bhend J Franke J Folini D Wild M and Broumlnnimann S Anensemble-based approach to climate reconstructions Clim Past8 963ndash976 doi105194cp-8-963-2012 2012

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 1 local and regional cli-mate signals Holocene 12 737ndash757 2002a

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 2 spatio-temporal vari-ability and associated climate patterns Holocene 12 759ndash7892002b

Broumlnnimann S Franke J Breitenmoser P Hakim G GoosseH Widmann M Crucifix M Gebbie G Annan J and vander Schrier G Transient state estimation in paleoclimatologyusing data assimilation PAGES News 212 74ndash75 2013

Compo G P Whitaker J S Sardeshmukh PD Matsui N Al-lan R J Yin X Gleason B E Vose R S Rutledge GBessemoulin P Broumlnnimann S Brunet M Crouthamel R IGrant A N Groisman P Y Jones P D Kruk M C KrugerA C Marshall G J Maugeri M Mok H Y Nordli Oslash RossT F Trigo R M Wang X L Woodruff S D and Worley SJ The Twentieth Century Reanalysis Project Q J Roy Meteo-rol Soc 137 1ndash28 2011

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

444 P Breitenmoser et al Forward modelling of tree-ring width

month-wise minimum of either temperature or precipitationFig 4a clearly shows that growth at the high-altitude siteis temperature-limited (gT lt gM) The lower-elevation site(Fig 4b) on the other hand is temperature-limited onlybriefly at the beginning and at the end of the growing sea-son while precipitation limits growth during the summermonths (gM lt gT ) Importantly tree growth at the high-elevation site is negatively correlated with growth at thelower-elevation site This negative correlation holds for boththe observed and modelled chronologies with coefficients ofminus013 andminus044 respectively These relationships demon-strate the VSL modelrsquos ability to incorporate joint influencesof temperature and precipitation on growth and simulta-neously suggest care is required when developing regionaltree-ring time series (see Sect 342 below) Our simulatedgrowth responses for two selected sites in Switzerland ap-pears to be widely applicable across mountainous forest re-gions with large climatic gradients such as the southwest-ern USA (Salzer and Kipfmueller 2005 Tolwinski-Wardet al 2011a) and Mongolia (Poulter et al 2013) One-year lagged autocorrelation coefficients (AR1) were assessedfrom TRWITRDBand TRWVSLseries at all sites Mean coeffi-cients of 046 and 042 respectively over all series clearlyreveal persistence ie 21 and 18 respectively of the vari-ance in the width of the ring in the current year can be pre-dicted based upon simulated growth during the past year

331 VSL simulations for aggregated TRW series

The aggregation generally enhances the correlation betweenATRWVSL and ATRWITRDB For instance the average ofall coefficients forR = 200 km during the common 1901ndash1970 interval is 034 for the temperature-limited series and038 for the moisture-limited series compared with a meanof 029 for the non-aggregated tree-ring series The spa-tial patterns of correlation coefficients for temperature- andmoisture-limited ATRW for both search radii are shown inFig 5 Notably ATRWVSL and ATRWITRDB show spatialcoherency and capture the main climate signals and arethus suitable for data assimilation approaches (see Discus-sion) The 600 km search radius improves the relationshipsfor both temperature and precipitation Coherent regional-scale correlation patterns for temperature-limited series canbe found in Scandinavia westerncentral Siberia and alongthe western and eastern United States (Fig 5a and c) Re-gional correlation patterns for moisture-sensitive series en-compass the United States and central Canada (Fig 5b andd) Regions such as central Europe Turkey central Asia andthe Andes are characterised by both temperature and mois-ture limitations which is an expression of a complex terrainwith small-scale climatic features and large climatic gradi-ents High correlation coefficients between ATRWVSL andATRWITRDB are present in all those regions with a cleartendency towards temperature-limited high-elevation sitesPoor agreement for the temperature-limited series can be

Fig 5 World map displaying Pearsonrsquos correlation coefficients be-tween ATRWVSL and ATRWITRDB for a search radius of 200 km(a b) and 600 km(c d) at temperature-limited(a c)and moisture-limited (b d) grid cells Note that in panels(c) and(d) at least onechronology has to be within the 200 km search radius to make thecorrelations comparable

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 445

31

Fig 5 World map displaying Pearson correlation coefficients between ATRWVSL and 1

ATRWITRDB for a search radius of 200 km (ab) and 600 km (cd) at temperature-limited (ac) 2

and moisture-limited (bd) grid cells Note that in panels c) and d) at least one chronology has 3

to be within the 200km search radius to make the correlations comparable 4

5

6

7

8

9

10

11

Fig 6 Scatter plot of correlation coefficients between each ATRWVSL and ATRWITRDB (200 km 12

search radius) series for the 1901-1935 and 1936-1970 independent time periods Results are 13

shown for a) the early 1901-1935 calibration interval and b) the late 1936-1970 calibration 14

interval 15

-1 -05 0 05 1-1

-08-06-04-02

002040608

1a) b)

-1-08-06

002040608

1

-04-02

-1 -0 0 05 15 r during calibration 1901-35 r during calibration 1936-70

r dur

ing

valid

atio

n 19

36-7

0

r dur

ing

valid

atio

n 19

01-3

5

Fig 6 Scatterplot of correlation coefficients between eachATRWVSL and ATRWITRDB (200 km search radius) series for the1901ndash1935 and 1936ndash1970 independent time periods Results areshown for(a) the early 1901ndash1935 calibration interval and(b) thelate 1936ndash1970 calibration interval

found in Tasmania New Zealand western-central Canadaand in the eastern-central US while moisture characteristicsare poorly captured in Patagonia northern Canada and in theEuropean Alps

Based on the split-sample validation experiment Fig 6shows a scatterplot of the correlation coefficients between theATRWVSL and ATRWITRDB 200 km search radius duringdifferent calibrationvalidation intervals (1901ndash19351936ndash1970 and 1936ndash19701901ndash1935) Points along the 1 1 lineare sites for which VSL produces simulations that are sta-ble in time whereas points below this line represent sitesfor which the model yields a higher correlation during thecalibration period We find model skill (r gt 044) in Pear-sonrsquos correlation coefficients in 36 of the series duringthe calibration period of which 54 are also significant inthe validation period Correlations are stable for moisture-limited sites in large areas of the United States and cen-tral Canada the lower-elevation sites in west-central Eu-rope Turkey Mongolia the western Himalayas and in mid-Chile whereas temperature-limited sites dominate Scandi-navia Siberia the eastern Himalayas central Europe south-ern South America and parts of the western United StatesCorrelations are not particularly skilful for New ZealandTasmania and Patagonia

4 Discussion

41 Growth parameters

The site-by-site parameterisation for the moisture and tem-perature thresholds revealed interesting global-scale patternsNotably the parameter estimation of the VSL model pro-vides novel insights into the currently debated temperaturethreshold below which growth may no longer take place Ourestimations of growth-onset temperature (ca 4ndash6C) is inagreement with the temperature range found by Tolwinski-Ward et al (2013) who used a four-parameter beta distribu-tion to calibrate the model parameters on a subset of 277 se-

ries in the United States More striking is the convergence offindings with assessments of growing season temperatures attree line based upon in situ loggers or remote sensing and in-terpolated climatic data (Koumlrner and Paulsen 2004 Koumlrner2012) as well as observational studies of wood formation(Rossi et al 2007) The wide range (1ndash9C) of the priorsconsidered in our approach allowed ample room for devia-tion from the previous literature so we interpret the agree-ment from these various lines of evidence as strong supportfor growth onset thresholds near 5C

At the level of individual species or individual sites ourresults compare well with findings of Vaganov et al (2006)who based on the VS model reported minimum and opti-mal temperatures in the northern Taiga of 4 and 16C forlarch 6 and 18C for spruce and 5 and 18C for Scots pinerespectively The differences in growth thresholds might re-flect the better adaption of pines to lower-temperature con-ditions and drought A comparison of the site values of thethreshold temperatureT1 at the corresponding elevations fordifferent tree genera is shown in Fig S2 in the SupplementSpecies-related difference in moisture parameters may bedue to needle structure as well as frequency and density ofstomata which influence water loss due to evapotranspira-tion (Vaganov et al 2006) Our results contribute to under-standing species specific growth responses as recently docu-mented in an analysis of 36 species from across the Europeancontinent (Babst et al 2013)

At the same time uncertainties arise from the parameter-isation of M and estimation ofM1 and from the missingrepresentation of winter precipitation stored as snowpack inthe CPC Leaky Bucket model and its impact on the timingof snowmelt (Tolwinski-Ward et al 2011a) Temperature-limited sites tend to have higherT1 andT2 than moisture-limited sites and vice versa forM1 and M2 This may bean expression of different climatic conditions but may alsobe related to edaphic conditions and plant physiological dif-ferences Figure S3 of the Supplement shows scatterplots ofjoint posterior relationships at each site between parameters(a)T1 andT2 (b) M1 andM2 (c) T2 andM2 and (d)T1 andM1 Application of the VSL model in more controlled frame-works such as in stands with mixed species compositionswill be useful to isolate and define species-specific growthcharacteristics while simultaneously excluding the possibili-ties that non-uniform species distributions along elevationalgradients contribute to systemic differences in the obtainedmodel parameters

42 Relationships between actual and simulated growth

The comparison between observed (ATRWVSL) and mod-elled (ATRWITRDB) tree-ring width series showed generallygood agreement and robust calibrationvalidation statisticsWe found significant model skill in independent verificationsacross all forested continents ndash tendencies that increasedwhen aggregating the tree-ring sites

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

446 P Breitenmoser et al Forward modelling of tree-ring width

The broad-scale pattern of temperature-limited growth forhigh latitudes (eg Taymyr Peninsula Russia) and high al-titudes (eg the European Alps) extends previous analysesof subsets of the ITRDB network (eg Briffa et al 2002aWettstein et al 2011 Babst et al 2013) Our findings fur-thermore largely match the distribution of potential climaticconstraints to plant growth in Nemani et al (2003) and Beeret al (2010) as well as the climate classification based onKoumlppen-Geiger by Kottek et al (2006)

However also prominent in our analysis were locations(eg Tasmania and New Zealand) where VSL simulationsrevealed little skill To explore possible reasons for this weconducted initial simulations where climate variability wasforced from a reanalysis product (20CR Compo et al 2011)and from the individual climate stations themselves Wefound some evidence for improved skill which suggests that(a) the quality of the instrumental data sets and (b) strongorographic effects can affect our simulations Caution is par-ticularly warranted where the quality and quantity of instru-mental stations rapidly decreases back in time (eg muchof the Mediterranean Asia and Southern Hemisphere loca-tions with low population density andor strong orographiceffects)

The fact that VSL reproduces first-order autocorrelationstructures (AR1) similar to the actual tree-ring chronologieshighlights the importance of including last yearrsquos growingseason for growth simulation in the VSL model in orderto retain potentially useful climate information contained intree rings (see Table 1) Similarly Wettstein et al (2011) re-port median first-order autocorrelation coefficients of 047for 762 ITRDB-derived tree-ring width series located pole-ward of roughly 30 to 40 northern latitude while Tingley etal (2012) found first-order autocorrelation coefficients of ap-proximately 06 for the tree-ring width series used in Mannet al (2008) This reasonable agreement between the auto-correlation structure in actual versus simulated tree-ring datasuggests that mechanistic modelling may help to reduce theeffect of biases in the spectral characteristics of tree-ringchronologies on climate reconstructions (Meko 1981 Cooket al 1999 Franke et al 2013) The global applicability ofa 16-month seasonal window as applied herein will requirefurther assessments for individual regions and species (forinstance as in Wu et al 2013) It is also conceivable to ap-ply differential weighting to previous yearsrsquo growth but suchschemes would be best implemented when understanding oflagged physiological processes and the roles of carbon re-serves are further advanced (eg Babst et al 2013 Zielis etal 2013)

43 Use of VSL in data assimilation

The favourable calibrationndashvalidation statistics of the VSLmodel and its ability to skilfully simulate growth for a widerange of environments suggest that the model could possi-bly be used for data assimilation approaches In the follow-

ing section several pathways are briefly outlined (see alsoBroumlnnimann et al 2013) and connections are made to howsuch assimilation approaches could be implemented usingthe VSL model

Data assimilation in general combines information fromobservations (here tree-ring width termedy) with a numeri-cal model simulation (termedxb) to obtain a physically con-sistent estimate of the climate statex It can be formulatedas a cost function problem of the form

J (x) = (x minus xb)T Bminus1(x minus xb) + (y minus H [x])T Rminus1(y minus H [x]) (10)

whereB and R represent the error covariance matrices ofthe model simulation and of the tree-ring widths respec-tively H is the observation operator which simulates the treerings from the model state Provided that the model stateencompasses all required climatic variables this could bethe VSL model How VSL is used in the approach then de-pends on how Eq (10) is minimised Following Broumlnnimannet al (2013) we distinguish ldquocovariance-based approachesrdquoldquoanalogue approachesrdquo and ldquonudging approachesrdquo

Covariance-based approaches use observations (here treerings) to correct the model simulations based on the modelerror covariance matrix Formally these approaches (eg en-semble Kalman filter 4D-VAR) require the matrixH whichis the Jacobian ofH (requiring slight adaptations to VSL)A further constraint of this family of approaches is the statevector which easily becomes excessively large Bhend etal (2012) proposed an off-line assimilation approach whichdoes not require the entire model state to be analysed

Analogue approaches minimise the cost function by se-lecting among existing simulations rather than by correctingthem Hence the cost function becomes

J (x) = (y minus H [x])T Rminus1(y minus H [x]) for xε x1x2 xn (11)

It is minimised by evaluating it for all availablex which canbe an ensemble of simulations (eg particle filter Goosse etal 2010) or different slices of a long control simulation (egproxy surrogate reconstruction Franke et al 2011) The ana-logue approach does not pose any restrictions on the size ofthe state vector or on the observation operator Hence VSLor also its parent model VS (provided again that all relevantclimate variables are in the model state) can directly be usedeither in the form of individual chronologies (an example isgiven in Broumlnnimann et al 2013) or aggregated chronolo-gies Moreover in contrast to many implementations of theensemble Kalman filterR can be non-diagonal The resultsfrom our study ie the comparison of observed and mod-elled tree-ring width can directly be used to estimateR Fur-thermore our results can be used to assess biases relative toobservations which need to be accounted for eg as an ad-ditional term in the observation operator

In the third approach nudging the cost function is notsolved explicitly Rather small increments are added to thetendency equations These increments depend on a targetwhich might be a ldquoclassicalrdquo climate reconstruction In this

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 447

case VSL may guide the aggregation of tree rings in order toincrease the signal-to-noise ratio in classical reconstructionapproaches

Our analysis has advanced the notion that the VSL modelhas the potential to be used as an observation operator inpalaeoclimatic data assimilation albeit in different form de-pending on the approach chosen

The VSL model within data assimilation approaches moti-vates future analyses on the ldquodivergence problemrdquo by explic-itly being able to take changes of limitations over time intoaccount

5 Conclusions

We investigated relationships between climate and tree-ringdata on a global scale using the non-linear process-basedVaganovndashShashkin Lite (VSL) forward model of tree-ringwidth formation (Tolwinski-Ward et al 2011a) We inves-tigated relations between actual tree-ring growth and growthsimulated based on climatic influences A network of 2287globally distributed tree-width chronologies has shown toprovide a large and high-quality sample space for these anal-yses Bayesian estimation of the VSL growth response pa-rameters yielded values that are stable with respect to thechoice of calibration interval for a wide range of speciesenvironmental conditions and time intervals showing themodelrsquos general applicability for worldwide studies usingCRU climate input data A benefit from this parameterisa-tion approach was also a novel global assessment of thegrowth-onset threshold temperature of approximately 4ndash6Cfor most sites and species thus providing new evidence foron-going debates regarding the lower temperatures at whichgrowth may take place (Anchukaitis et al 2012 Mann etal 2012 Koumlrner 2012) Moreover our results demonstratethe VSL model skill across a wide range of environmentsspecies and different time intervals Spatial aggregation oftree-ring chronologies based upon chronology quality cli-mate response and proximity reduced non-climatic noisecontained in the tree-ring data and resulted in an improvedrelationship between actual and modelled tree growth Wefurther demonstrate that the potential of the VSL model canbe exploited for instance in data assimilation approaches toreconstruct the climate of the past

Supplementary material related to this article isavailable online athttpwwwclim-pastnet104372014cp-10-437-2014-supplementpdf

AcknowledgementsThis work was funded by the Swiss Na-tional Science Foundation through the NCCR Climate (projectsPALAVAREXIII and DETREE) and Sinergia project FUPSOL Wethank Susan Tolwinski-Ward for providing the MATLAB codes forthe VSL model We also greatly thank the numerous researchers

involved in sharing their tree-ring measurements through theInternational Tree Ring Data Bank (ITRDB) maintained by theNOAA Paleoclimatology Program and the World Data Center forPaleoclimatology and Bruce Bauer for supporting our queries Wealso thank the anonymous reviewers for their valuable comments

Edited by J Guiot

References

Anchukaitis K J Evans M N Kaplan A Vaganov EA Hughes M K Grissino-Mayer H D and CaneM A Forward modeling of regional scale tree-ring pat-terns in the southeastern United States and the recent influ-ence of summer drought Geophys Res Lett 33 L04705doi1010292005GL025050 2006

Anchukaitis K J Breitenmoser P Briffa K R Buchwal ABuumlntgen U Cook E R DrsquoArrigo R D Esper J EvansM N Frank D Grudds H Gunnarson B Hughes M KKirdyanov A V Koumlrner C Krusic P J Luckman B MelvinT M Salzer M W Shashkin A V Timmreck C VaganovE A and Wilson R J S Tree rings and volcanic cooling NatGeosci 5 836ndash837 doi101038ngeo1645 2012

Babst F Poulter B Trouet V Tan K Neuwirth B WilsonR Carrer M Grabner M Tegel W Levanic T PanayotovM Urbinati C Bouriaud O Ciais P and Frank D Site- andspecies-specific responses of forest growth to climate across theEuropean continent Global Ecol Biogeogr 22 706ndash717 2013

Beer C Reichstein M Tomelleri E Ciais P Jung M BonanG B Bondeau A Cescatti A Lasslop G Lindroth A Lo-mas M Luyssaert S Margolis H Oleson K W RoupsardO Veenendaal E Viovy N Williams C Woodward F I andPapale D Terrestrial gross carbon dioxide uptake global dis-tribution and covariation with climate Science 329 834ndash8382010

Bhend J Franke J Folini D Wild M and Broumlnnimann S Anensemble-based approach to climate reconstructions Clim Past8 963ndash976 doi105194cp-8-963-2012 2012

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 1 local and regional cli-mate signals Holocene 12 737ndash757 2002a

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 2 spatio-temporal vari-ability and associated climate patterns Holocene 12 759ndash7892002b

Broumlnnimann S Franke J Breitenmoser P Hakim G GoosseH Widmann M Crucifix M Gebbie G Annan J and vander Schrier G Transient state estimation in paleoclimatologyusing data assimilation PAGES News 212 74ndash75 2013

Compo G P Whitaker J S Sardeshmukh PD Matsui N Al-lan R J Yin X Gleason B E Vose R S Rutledge GBessemoulin P Broumlnnimann S Brunet M Crouthamel R IGrant A N Groisman P Y Jones P D Kruk M C KrugerA C Marshall G J Maugeri M Mok H Y Nordli Oslash RossT F Trigo R M Wang X L Woodruff S D and Worley SJ The Twentieth Century Reanalysis Project Q J Roy Meteo-rol Soc 137 1ndash28 2011

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

P Breitenmoser et al Forward modelling of tree-ring width 445

31

Fig 5 World map displaying Pearson correlation coefficients between ATRWVSL and 1

ATRWITRDB for a search radius of 200 km (ab) and 600 km (cd) at temperature-limited (ac) 2

and moisture-limited (bd) grid cells Note that in panels c) and d) at least one chronology has 3

to be within the 200km search radius to make the correlations comparable 4

5

6

7

8

9

10

11

Fig 6 Scatter plot of correlation coefficients between each ATRWVSL and ATRWITRDB (200 km 12

search radius) series for the 1901-1935 and 1936-1970 independent time periods Results are 13

shown for a) the early 1901-1935 calibration interval and b) the late 1936-1970 calibration 14

interval 15

-1 -05 0 05 1-1

-08-06-04-02

002040608

1a) b)

-1-08-06

002040608

1

-04-02

-1 -0 0 05 15 r during calibration 1901-35 r during calibration 1936-70

r dur

ing

valid

atio

n 19

36-7

0

r dur

ing

valid

atio

n 19

01-3

5

Fig 6 Scatterplot of correlation coefficients between eachATRWVSL and ATRWITRDB (200 km search radius) series for the1901ndash1935 and 1936ndash1970 independent time periods Results areshown for(a) the early 1901ndash1935 calibration interval and(b) thelate 1936ndash1970 calibration interval

found in Tasmania New Zealand western-central Canadaand in the eastern-central US while moisture characteristicsare poorly captured in Patagonia northern Canada and in theEuropean Alps

Based on the split-sample validation experiment Fig 6shows a scatterplot of the correlation coefficients between theATRWVSL and ATRWITRDB 200 km search radius duringdifferent calibrationvalidation intervals (1901ndash19351936ndash1970 and 1936ndash19701901ndash1935) Points along the 1 1 lineare sites for which VSL produces simulations that are sta-ble in time whereas points below this line represent sitesfor which the model yields a higher correlation during thecalibration period We find model skill (r gt 044) in Pear-sonrsquos correlation coefficients in 36 of the series duringthe calibration period of which 54 are also significant inthe validation period Correlations are stable for moisture-limited sites in large areas of the United States and cen-tral Canada the lower-elevation sites in west-central Eu-rope Turkey Mongolia the western Himalayas and in mid-Chile whereas temperature-limited sites dominate Scandi-navia Siberia the eastern Himalayas central Europe south-ern South America and parts of the western United StatesCorrelations are not particularly skilful for New ZealandTasmania and Patagonia

4 Discussion

41 Growth parameters

The site-by-site parameterisation for the moisture and tem-perature thresholds revealed interesting global-scale patternsNotably the parameter estimation of the VSL model pro-vides novel insights into the currently debated temperaturethreshold below which growth may no longer take place Ourestimations of growth-onset temperature (ca 4ndash6C) is inagreement with the temperature range found by Tolwinski-Ward et al (2013) who used a four-parameter beta distribu-tion to calibrate the model parameters on a subset of 277 se-

ries in the United States More striking is the convergence offindings with assessments of growing season temperatures attree line based upon in situ loggers or remote sensing and in-terpolated climatic data (Koumlrner and Paulsen 2004 Koumlrner2012) as well as observational studies of wood formation(Rossi et al 2007) The wide range (1ndash9C) of the priorsconsidered in our approach allowed ample room for devia-tion from the previous literature so we interpret the agree-ment from these various lines of evidence as strong supportfor growth onset thresholds near 5C

At the level of individual species or individual sites ourresults compare well with findings of Vaganov et al (2006)who based on the VS model reported minimum and opti-mal temperatures in the northern Taiga of 4 and 16C forlarch 6 and 18C for spruce and 5 and 18C for Scots pinerespectively The differences in growth thresholds might re-flect the better adaption of pines to lower-temperature con-ditions and drought A comparison of the site values of thethreshold temperatureT1 at the corresponding elevations fordifferent tree genera is shown in Fig S2 in the SupplementSpecies-related difference in moisture parameters may bedue to needle structure as well as frequency and density ofstomata which influence water loss due to evapotranspira-tion (Vaganov et al 2006) Our results contribute to under-standing species specific growth responses as recently docu-mented in an analysis of 36 species from across the Europeancontinent (Babst et al 2013)

At the same time uncertainties arise from the parameter-isation of M and estimation ofM1 and from the missingrepresentation of winter precipitation stored as snowpack inthe CPC Leaky Bucket model and its impact on the timingof snowmelt (Tolwinski-Ward et al 2011a) Temperature-limited sites tend to have higherT1 andT2 than moisture-limited sites and vice versa forM1 and M2 This may bean expression of different climatic conditions but may alsobe related to edaphic conditions and plant physiological dif-ferences Figure S3 of the Supplement shows scatterplots ofjoint posterior relationships at each site between parameters(a)T1 andT2 (b) M1 andM2 (c) T2 andM2 and (d)T1 andM1 Application of the VSL model in more controlled frame-works such as in stands with mixed species compositionswill be useful to isolate and define species-specific growthcharacteristics while simultaneously excluding the possibili-ties that non-uniform species distributions along elevationalgradients contribute to systemic differences in the obtainedmodel parameters

42 Relationships between actual and simulated growth

The comparison between observed (ATRWVSL) and mod-elled (ATRWITRDB) tree-ring width series showed generallygood agreement and robust calibrationvalidation statisticsWe found significant model skill in independent verificationsacross all forested continents ndash tendencies that increasedwhen aggregating the tree-ring sites

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

446 P Breitenmoser et al Forward modelling of tree-ring width

The broad-scale pattern of temperature-limited growth forhigh latitudes (eg Taymyr Peninsula Russia) and high al-titudes (eg the European Alps) extends previous analysesof subsets of the ITRDB network (eg Briffa et al 2002aWettstein et al 2011 Babst et al 2013) Our findings fur-thermore largely match the distribution of potential climaticconstraints to plant growth in Nemani et al (2003) and Beeret al (2010) as well as the climate classification based onKoumlppen-Geiger by Kottek et al (2006)

However also prominent in our analysis were locations(eg Tasmania and New Zealand) where VSL simulationsrevealed little skill To explore possible reasons for this weconducted initial simulations where climate variability wasforced from a reanalysis product (20CR Compo et al 2011)and from the individual climate stations themselves Wefound some evidence for improved skill which suggests that(a) the quality of the instrumental data sets and (b) strongorographic effects can affect our simulations Caution is par-ticularly warranted where the quality and quantity of instru-mental stations rapidly decreases back in time (eg muchof the Mediterranean Asia and Southern Hemisphere loca-tions with low population density andor strong orographiceffects)

The fact that VSL reproduces first-order autocorrelationstructures (AR1) similar to the actual tree-ring chronologieshighlights the importance of including last yearrsquos growingseason for growth simulation in the VSL model in orderto retain potentially useful climate information contained intree rings (see Table 1) Similarly Wettstein et al (2011) re-port median first-order autocorrelation coefficients of 047for 762 ITRDB-derived tree-ring width series located pole-ward of roughly 30 to 40 northern latitude while Tingley etal (2012) found first-order autocorrelation coefficients of ap-proximately 06 for the tree-ring width series used in Mannet al (2008) This reasonable agreement between the auto-correlation structure in actual versus simulated tree-ring datasuggests that mechanistic modelling may help to reduce theeffect of biases in the spectral characteristics of tree-ringchronologies on climate reconstructions (Meko 1981 Cooket al 1999 Franke et al 2013) The global applicability ofa 16-month seasonal window as applied herein will requirefurther assessments for individual regions and species (forinstance as in Wu et al 2013) It is also conceivable to ap-ply differential weighting to previous yearsrsquo growth but suchschemes would be best implemented when understanding oflagged physiological processes and the roles of carbon re-serves are further advanced (eg Babst et al 2013 Zielis etal 2013)

43 Use of VSL in data assimilation

The favourable calibrationndashvalidation statistics of the VSLmodel and its ability to skilfully simulate growth for a widerange of environments suggest that the model could possi-bly be used for data assimilation approaches In the follow-

ing section several pathways are briefly outlined (see alsoBroumlnnimann et al 2013) and connections are made to howsuch assimilation approaches could be implemented usingthe VSL model

Data assimilation in general combines information fromobservations (here tree-ring width termedy) with a numeri-cal model simulation (termedxb) to obtain a physically con-sistent estimate of the climate statex It can be formulatedas a cost function problem of the form

J (x) = (x minus xb)T Bminus1(x minus xb) + (y minus H [x])T Rminus1(y minus H [x]) (10)

whereB and R represent the error covariance matrices ofthe model simulation and of the tree-ring widths respec-tively H is the observation operator which simulates the treerings from the model state Provided that the model stateencompasses all required climatic variables this could bethe VSL model How VSL is used in the approach then de-pends on how Eq (10) is minimised Following Broumlnnimannet al (2013) we distinguish ldquocovariance-based approachesrdquoldquoanalogue approachesrdquo and ldquonudging approachesrdquo

Covariance-based approaches use observations (here treerings) to correct the model simulations based on the modelerror covariance matrix Formally these approaches (eg en-semble Kalman filter 4D-VAR) require the matrixH whichis the Jacobian ofH (requiring slight adaptations to VSL)A further constraint of this family of approaches is the statevector which easily becomes excessively large Bhend etal (2012) proposed an off-line assimilation approach whichdoes not require the entire model state to be analysed

Analogue approaches minimise the cost function by se-lecting among existing simulations rather than by correctingthem Hence the cost function becomes

J (x) = (y minus H [x])T Rminus1(y minus H [x]) for xε x1x2 xn (11)

It is minimised by evaluating it for all availablex which canbe an ensemble of simulations (eg particle filter Goosse etal 2010) or different slices of a long control simulation (egproxy surrogate reconstruction Franke et al 2011) The ana-logue approach does not pose any restrictions on the size ofthe state vector or on the observation operator Hence VSLor also its parent model VS (provided again that all relevantclimate variables are in the model state) can directly be usedeither in the form of individual chronologies (an example isgiven in Broumlnnimann et al 2013) or aggregated chronolo-gies Moreover in contrast to many implementations of theensemble Kalman filterR can be non-diagonal The resultsfrom our study ie the comparison of observed and mod-elled tree-ring width can directly be used to estimateR Fur-thermore our results can be used to assess biases relative toobservations which need to be accounted for eg as an ad-ditional term in the observation operator

In the third approach nudging the cost function is notsolved explicitly Rather small increments are added to thetendency equations These increments depend on a targetwhich might be a ldquoclassicalrdquo climate reconstruction In this

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 447

case VSL may guide the aggregation of tree rings in order toincrease the signal-to-noise ratio in classical reconstructionapproaches

Our analysis has advanced the notion that the VSL modelhas the potential to be used as an observation operator inpalaeoclimatic data assimilation albeit in different form de-pending on the approach chosen

The VSL model within data assimilation approaches moti-vates future analyses on the ldquodivergence problemrdquo by explic-itly being able to take changes of limitations over time intoaccount

5 Conclusions

We investigated relationships between climate and tree-ringdata on a global scale using the non-linear process-basedVaganovndashShashkin Lite (VSL) forward model of tree-ringwidth formation (Tolwinski-Ward et al 2011a) We inves-tigated relations between actual tree-ring growth and growthsimulated based on climatic influences A network of 2287globally distributed tree-width chronologies has shown toprovide a large and high-quality sample space for these anal-yses Bayesian estimation of the VSL growth response pa-rameters yielded values that are stable with respect to thechoice of calibration interval for a wide range of speciesenvironmental conditions and time intervals showing themodelrsquos general applicability for worldwide studies usingCRU climate input data A benefit from this parameterisa-tion approach was also a novel global assessment of thegrowth-onset threshold temperature of approximately 4ndash6Cfor most sites and species thus providing new evidence foron-going debates regarding the lower temperatures at whichgrowth may take place (Anchukaitis et al 2012 Mann etal 2012 Koumlrner 2012) Moreover our results demonstratethe VSL model skill across a wide range of environmentsspecies and different time intervals Spatial aggregation oftree-ring chronologies based upon chronology quality cli-mate response and proximity reduced non-climatic noisecontained in the tree-ring data and resulted in an improvedrelationship between actual and modelled tree growth Wefurther demonstrate that the potential of the VSL model canbe exploited for instance in data assimilation approaches toreconstruct the climate of the past

Supplementary material related to this article isavailable online athttpwwwclim-pastnet104372014cp-10-437-2014-supplementpdf

AcknowledgementsThis work was funded by the Swiss Na-tional Science Foundation through the NCCR Climate (projectsPALAVAREXIII and DETREE) and Sinergia project FUPSOL Wethank Susan Tolwinski-Ward for providing the MATLAB codes forthe VSL model We also greatly thank the numerous researchers

involved in sharing their tree-ring measurements through theInternational Tree Ring Data Bank (ITRDB) maintained by theNOAA Paleoclimatology Program and the World Data Center forPaleoclimatology and Bruce Bauer for supporting our queries Wealso thank the anonymous reviewers for their valuable comments

Edited by J Guiot

References

Anchukaitis K J Evans M N Kaplan A Vaganov EA Hughes M K Grissino-Mayer H D and CaneM A Forward modeling of regional scale tree-ring pat-terns in the southeastern United States and the recent influ-ence of summer drought Geophys Res Lett 33 L04705doi1010292005GL025050 2006

Anchukaitis K J Breitenmoser P Briffa K R Buchwal ABuumlntgen U Cook E R DrsquoArrigo R D Esper J EvansM N Frank D Grudds H Gunnarson B Hughes M KKirdyanov A V Koumlrner C Krusic P J Luckman B MelvinT M Salzer M W Shashkin A V Timmreck C VaganovE A and Wilson R J S Tree rings and volcanic cooling NatGeosci 5 836ndash837 doi101038ngeo1645 2012

Babst F Poulter B Trouet V Tan K Neuwirth B WilsonR Carrer M Grabner M Tegel W Levanic T PanayotovM Urbinati C Bouriaud O Ciais P and Frank D Site- andspecies-specific responses of forest growth to climate across theEuropean continent Global Ecol Biogeogr 22 706ndash717 2013

Beer C Reichstein M Tomelleri E Ciais P Jung M BonanG B Bondeau A Cescatti A Lasslop G Lindroth A Lo-mas M Luyssaert S Margolis H Oleson K W RoupsardO Veenendaal E Viovy N Williams C Woodward F I andPapale D Terrestrial gross carbon dioxide uptake global dis-tribution and covariation with climate Science 329 834ndash8382010

Bhend J Franke J Folini D Wild M and Broumlnnimann S Anensemble-based approach to climate reconstructions Clim Past8 963ndash976 doi105194cp-8-963-2012 2012

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 1 local and regional cli-mate signals Holocene 12 737ndash757 2002a

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 2 spatio-temporal vari-ability and associated climate patterns Holocene 12 759ndash7892002b

Broumlnnimann S Franke J Breitenmoser P Hakim G GoosseH Widmann M Crucifix M Gebbie G Annan J and vander Schrier G Transient state estimation in paleoclimatologyusing data assimilation PAGES News 212 74ndash75 2013

Compo G P Whitaker J S Sardeshmukh PD Matsui N Al-lan R J Yin X Gleason B E Vose R S Rutledge GBessemoulin P Broumlnnimann S Brunet M Crouthamel R IGrant A N Groisman P Y Jones P D Kruk M C KrugerA C Marshall G J Maugeri M Mok H Y Nordli Oslash RossT F Trigo R M Wang X L Woodruff S D and Worley SJ The Twentieth Century Reanalysis Project Q J Roy Meteo-rol Soc 137 1ndash28 2011

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

446 P Breitenmoser et al Forward modelling of tree-ring width

The broad-scale pattern of temperature-limited growth forhigh latitudes (eg Taymyr Peninsula Russia) and high al-titudes (eg the European Alps) extends previous analysesof subsets of the ITRDB network (eg Briffa et al 2002aWettstein et al 2011 Babst et al 2013) Our findings fur-thermore largely match the distribution of potential climaticconstraints to plant growth in Nemani et al (2003) and Beeret al (2010) as well as the climate classification based onKoumlppen-Geiger by Kottek et al (2006)

However also prominent in our analysis were locations(eg Tasmania and New Zealand) where VSL simulationsrevealed little skill To explore possible reasons for this weconducted initial simulations where climate variability wasforced from a reanalysis product (20CR Compo et al 2011)and from the individual climate stations themselves Wefound some evidence for improved skill which suggests that(a) the quality of the instrumental data sets and (b) strongorographic effects can affect our simulations Caution is par-ticularly warranted where the quality and quantity of instru-mental stations rapidly decreases back in time (eg muchof the Mediterranean Asia and Southern Hemisphere loca-tions with low population density andor strong orographiceffects)

The fact that VSL reproduces first-order autocorrelationstructures (AR1) similar to the actual tree-ring chronologieshighlights the importance of including last yearrsquos growingseason for growth simulation in the VSL model in orderto retain potentially useful climate information contained intree rings (see Table 1) Similarly Wettstein et al (2011) re-port median first-order autocorrelation coefficients of 047for 762 ITRDB-derived tree-ring width series located pole-ward of roughly 30 to 40 northern latitude while Tingley etal (2012) found first-order autocorrelation coefficients of ap-proximately 06 for the tree-ring width series used in Mannet al (2008) This reasonable agreement between the auto-correlation structure in actual versus simulated tree-ring datasuggests that mechanistic modelling may help to reduce theeffect of biases in the spectral characteristics of tree-ringchronologies on climate reconstructions (Meko 1981 Cooket al 1999 Franke et al 2013) The global applicability ofa 16-month seasonal window as applied herein will requirefurther assessments for individual regions and species (forinstance as in Wu et al 2013) It is also conceivable to ap-ply differential weighting to previous yearsrsquo growth but suchschemes would be best implemented when understanding oflagged physiological processes and the roles of carbon re-serves are further advanced (eg Babst et al 2013 Zielis etal 2013)

43 Use of VSL in data assimilation

The favourable calibrationndashvalidation statistics of the VSLmodel and its ability to skilfully simulate growth for a widerange of environments suggest that the model could possi-bly be used for data assimilation approaches In the follow-

ing section several pathways are briefly outlined (see alsoBroumlnnimann et al 2013) and connections are made to howsuch assimilation approaches could be implemented usingthe VSL model

Data assimilation in general combines information fromobservations (here tree-ring width termedy) with a numeri-cal model simulation (termedxb) to obtain a physically con-sistent estimate of the climate statex It can be formulatedas a cost function problem of the form

J (x) = (x minus xb)T Bminus1(x minus xb) + (y minus H [x])T Rminus1(y minus H [x]) (10)

whereB and R represent the error covariance matrices ofthe model simulation and of the tree-ring widths respec-tively H is the observation operator which simulates the treerings from the model state Provided that the model stateencompasses all required climatic variables this could bethe VSL model How VSL is used in the approach then de-pends on how Eq (10) is minimised Following Broumlnnimannet al (2013) we distinguish ldquocovariance-based approachesrdquoldquoanalogue approachesrdquo and ldquonudging approachesrdquo

Covariance-based approaches use observations (here treerings) to correct the model simulations based on the modelerror covariance matrix Formally these approaches (eg en-semble Kalman filter 4D-VAR) require the matrixH whichis the Jacobian ofH (requiring slight adaptations to VSL)A further constraint of this family of approaches is the statevector which easily becomes excessively large Bhend etal (2012) proposed an off-line assimilation approach whichdoes not require the entire model state to be analysed

Analogue approaches minimise the cost function by se-lecting among existing simulations rather than by correctingthem Hence the cost function becomes

J (x) = (y minus H [x])T Rminus1(y minus H [x]) for xε x1x2 xn (11)

It is minimised by evaluating it for all availablex which canbe an ensemble of simulations (eg particle filter Goosse etal 2010) or different slices of a long control simulation (egproxy surrogate reconstruction Franke et al 2011) The ana-logue approach does not pose any restrictions on the size ofthe state vector or on the observation operator Hence VSLor also its parent model VS (provided again that all relevantclimate variables are in the model state) can directly be usedeither in the form of individual chronologies (an example isgiven in Broumlnnimann et al 2013) or aggregated chronolo-gies Moreover in contrast to many implementations of theensemble Kalman filterR can be non-diagonal The resultsfrom our study ie the comparison of observed and mod-elled tree-ring width can directly be used to estimateR Fur-thermore our results can be used to assess biases relative toobservations which need to be accounted for eg as an ad-ditional term in the observation operator

In the third approach nudging the cost function is notsolved explicitly Rather small increments are added to thetendency equations These increments depend on a targetwhich might be a ldquoclassicalrdquo climate reconstruction In this

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 447

case VSL may guide the aggregation of tree rings in order toincrease the signal-to-noise ratio in classical reconstructionapproaches

Our analysis has advanced the notion that the VSL modelhas the potential to be used as an observation operator inpalaeoclimatic data assimilation albeit in different form de-pending on the approach chosen

The VSL model within data assimilation approaches moti-vates future analyses on the ldquodivergence problemrdquo by explic-itly being able to take changes of limitations over time intoaccount

5 Conclusions

We investigated relationships between climate and tree-ringdata on a global scale using the non-linear process-basedVaganovndashShashkin Lite (VSL) forward model of tree-ringwidth formation (Tolwinski-Ward et al 2011a) We inves-tigated relations between actual tree-ring growth and growthsimulated based on climatic influences A network of 2287globally distributed tree-width chronologies has shown toprovide a large and high-quality sample space for these anal-yses Bayesian estimation of the VSL growth response pa-rameters yielded values that are stable with respect to thechoice of calibration interval for a wide range of speciesenvironmental conditions and time intervals showing themodelrsquos general applicability for worldwide studies usingCRU climate input data A benefit from this parameterisa-tion approach was also a novel global assessment of thegrowth-onset threshold temperature of approximately 4ndash6Cfor most sites and species thus providing new evidence foron-going debates regarding the lower temperatures at whichgrowth may take place (Anchukaitis et al 2012 Mann etal 2012 Koumlrner 2012) Moreover our results demonstratethe VSL model skill across a wide range of environmentsspecies and different time intervals Spatial aggregation oftree-ring chronologies based upon chronology quality cli-mate response and proximity reduced non-climatic noisecontained in the tree-ring data and resulted in an improvedrelationship between actual and modelled tree growth Wefurther demonstrate that the potential of the VSL model canbe exploited for instance in data assimilation approaches toreconstruct the climate of the past

Supplementary material related to this article isavailable online athttpwwwclim-pastnet104372014cp-10-437-2014-supplementpdf

AcknowledgementsThis work was funded by the Swiss Na-tional Science Foundation through the NCCR Climate (projectsPALAVAREXIII and DETREE) and Sinergia project FUPSOL Wethank Susan Tolwinski-Ward for providing the MATLAB codes forthe VSL model We also greatly thank the numerous researchers

involved in sharing their tree-ring measurements through theInternational Tree Ring Data Bank (ITRDB) maintained by theNOAA Paleoclimatology Program and the World Data Center forPaleoclimatology and Bruce Bauer for supporting our queries Wealso thank the anonymous reviewers for their valuable comments

Edited by J Guiot

References

Anchukaitis K J Evans M N Kaplan A Vaganov EA Hughes M K Grissino-Mayer H D and CaneM A Forward modeling of regional scale tree-ring pat-terns in the southeastern United States and the recent influ-ence of summer drought Geophys Res Lett 33 L04705doi1010292005GL025050 2006

Anchukaitis K J Breitenmoser P Briffa K R Buchwal ABuumlntgen U Cook E R DrsquoArrigo R D Esper J EvansM N Frank D Grudds H Gunnarson B Hughes M KKirdyanov A V Koumlrner C Krusic P J Luckman B MelvinT M Salzer M W Shashkin A V Timmreck C VaganovE A and Wilson R J S Tree rings and volcanic cooling NatGeosci 5 836ndash837 doi101038ngeo1645 2012

Babst F Poulter B Trouet V Tan K Neuwirth B WilsonR Carrer M Grabner M Tegel W Levanic T PanayotovM Urbinati C Bouriaud O Ciais P and Frank D Site- andspecies-specific responses of forest growth to climate across theEuropean continent Global Ecol Biogeogr 22 706ndash717 2013

Beer C Reichstein M Tomelleri E Ciais P Jung M BonanG B Bondeau A Cescatti A Lasslop G Lindroth A Lo-mas M Luyssaert S Margolis H Oleson K W RoupsardO Veenendaal E Viovy N Williams C Woodward F I andPapale D Terrestrial gross carbon dioxide uptake global dis-tribution and covariation with climate Science 329 834ndash8382010

Bhend J Franke J Folini D Wild M and Broumlnnimann S Anensemble-based approach to climate reconstructions Clim Past8 963ndash976 doi105194cp-8-963-2012 2012

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 1 local and regional cli-mate signals Holocene 12 737ndash757 2002a

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 2 spatio-temporal vari-ability and associated climate patterns Holocene 12 759ndash7892002b

Broumlnnimann S Franke J Breitenmoser P Hakim G GoosseH Widmann M Crucifix M Gebbie G Annan J and vander Schrier G Transient state estimation in paleoclimatologyusing data assimilation PAGES News 212 74ndash75 2013

Compo G P Whitaker J S Sardeshmukh PD Matsui N Al-lan R J Yin X Gleason B E Vose R S Rutledge GBessemoulin P Broumlnnimann S Brunet M Crouthamel R IGrant A N Groisman P Y Jones P D Kruk M C KrugerA C Marshall G J Maugeri M Mok H Y Nordli Oslash RossT F Trigo R M Wang X L Woodruff S D and Worley SJ The Twentieth Century Reanalysis Project Q J Roy Meteo-rol Soc 137 1ndash28 2011

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

P Breitenmoser et al Forward modelling of tree-ring width 447

case VSL may guide the aggregation of tree rings in order toincrease the signal-to-noise ratio in classical reconstructionapproaches

Our analysis has advanced the notion that the VSL modelhas the potential to be used as an observation operator inpalaeoclimatic data assimilation albeit in different form de-pending on the approach chosen

The VSL model within data assimilation approaches moti-vates future analyses on the ldquodivergence problemrdquo by explic-itly being able to take changes of limitations over time intoaccount

5 Conclusions

We investigated relationships between climate and tree-ringdata on a global scale using the non-linear process-basedVaganovndashShashkin Lite (VSL) forward model of tree-ringwidth formation (Tolwinski-Ward et al 2011a) We inves-tigated relations between actual tree-ring growth and growthsimulated based on climatic influences A network of 2287globally distributed tree-width chronologies has shown toprovide a large and high-quality sample space for these anal-yses Bayesian estimation of the VSL growth response pa-rameters yielded values that are stable with respect to thechoice of calibration interval for a wide range of speciesenvironmental conditions and time intervals showing themodelrsquos general applicability for worldwide studies usingCRU climate input data A benefit from this parameterisa-tion approach was also a novel global assessment of thegrowth-onset threshold temperature of approximately 4ndash6Cfor most sites and species thus providing new evidence foron-going debates regarding the lower temperatures at whichgrowth may take place (Anchukaitis et al 2012 Mann etal 2012 Koumlrner 2012) Moreover our results demonstratethe VSL model skill across a wide range of environmentsspecies and different time intervals Spatial aggregation oftree-ring chronologies based upon chronology quality cli-mate response and proximity reduced non-climatic noisecontained in the tree-ring data and resulted in an improvedrelationship between actual and modelled tree growth Wefurther demonstrate that the potential of the VSL model canbe exploited for instance in data assimilation approaches toreconstruct the climate of the past

Supplementary material related to this article isavailable online athttpwwwclim-pastnet104372014cp-10-437-2014-supplementpdf

AcknowledgementsThis work was funded by the Swiss Na-tional Science Foundation through the NCCR Climate (projectsPALAVAREXIII and DETREE) and Sinergia project FUPSOL Wethank Susan Tolwinski-Ward for providing the MATLAB codes forthe VSL model We also greatly thank the numerous researchers

involved in sharing their tree-ring measurements through theInternational Tree Ring Data Bank (ITRDB) maintained by theNOAA Paleoclimatology Program and the World Data Center forPaleoclimatology and Bruce Bauer for supporting our queries Wealso thank the anonymous reviewers for their valuable comments

Edited by J Guiot

References

Anchukaitis K J Evans M N Kaplan A Vaganov EA Hughes M K Grissino-Mayer H D and CaneM A Forward modeling of regional scale tree-ring pat-terns in the southeastern United States and the recent influ-ence of summer drought Geophys Res Lett 33 L04705doi1010292005GL025050 2006

Anchukaitis K J Breitenmoser P Briffa K R Buchwal ABuumlntgen U Cook E R DrsquoArrigo R D Esper J EvansM N Frank D Grudds H Gunnarson B Hughes M KKirdyanov A V Koumlrner C Krusic P J Luckman B MelvinT M Salzer M W Shashkin A V Timmreck C VaganovE A and Wilson R J S Tree rings and volcanic cooling NatGeosci 5 836ndash837 doi101038ngeo1645 2012

Babst F Poulter B Trouet V Tan K Neuwirth B WilsonR Carrer M Grabner M Tegel W Levanic T PanayotovM Urbinati C Bouriaud O Ciais P and Frank D Site- andspecies-specific responses of forest growth to climate across theEuropean continent Global Ecol Biogeogr 22 706ndash717 2013

Beer C Reichstein M Tomelleri E Ciais P Jung M BonanG B Bondeau A Cescatti A Lasslop G Lindroth A Lo-mas M Luyssaert S Margolis H Oleson K W RoupsardO Veenendaal E Viovy N Williams C Woodward F I andPapale D Terrestrial gross carbon dioxide uptake global dis-tribution and covariation with climate Science 329 834ndash8382010

Bhend J Franke J Folini D Wild M and Broumlnnimann S Anensemble-based approach to climate reconstructions Clim Past8 963ndash976 doi105194cp-8-963-2012 2012

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 1 local and regional cli-mate signals Holocene 12 737ndash757 2002a

Briffa K R Osborn T J Schweingruber F H Jones P D Shiy-atov S G and Vaganov E A Tree-ring width and density dataaround the Northern Hemisphere Part 2 spatio-temporal vari-ability and associated climate patterns Holocene 12 759ndash7892002b

Broumlnnimann S Franke J Breitenmoser P Hakim G GoosseH Widmann M Crucifix M Gebbie G Annan J and vander Schrier G Transient state estimation in paleoclimatologyusing data assimilation PAGES News 212 74ndash75 2013

Compo G P Whitaker J S Sardeshmukh PD Matsui N Al-lan R J Yin X Gleason B E Vose R S Rutledge GBessemoulin P Broumlnnimann S Brunet M Crouthamel R IGrant A N Groisman P Y Jones P D Kruk M C KrugerA C Marshall G J Maugeri M Mok H Y Nordli Oslash RossT F Trigo R M Wang X L Woodruff S D and Worley SJ The Twentieth Century Reanalysis Project Q J Roy Meteo-rol Soc 137 1ndash28 2011

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014

448 P Breitenmoser et al Forward modelling of tree-ring width

Cook E R A time series approach to tree-ring standardization PhD thesis University of Arizona 1985

Cook E R Briffa K R Shiyatov S Mazepa V and Jones P DData analysis in Methods of dendrochronology applications inthe environmental sciences edited by Cook E R and Kairiuk-stis L A Kluwer Academic Publishers Dordrecht 1990

Cook E R Briffa K R Meko D M Graybill D A andFunkhouser F The ldquosegment length curserdquo in long tree-ringchronology development for palaeoclimatic studies Holocene5 229ndash237 1995

Cook E R Meko D M Stahle D W and Cleaveland M KDrought reconstructions for the continental United States J Cli-mate 12 1145ndash1162 1999

Cook E R Anchukaitis K J Buckley B M DrsquoArrigo R DJacoby G C and Wright W E Asian monsoon failure andmegadrought during the last millennium Science 328 486ndash4892010

Esper J and Frank D Divergence pitfalls in tree-ring researchClim Chang 94 261ndash266 2009

Evans M N Reichert B K Kaplan A Anchukaitis KJ Vaganov E A Hughes M K and Cane M AA forward modeling approach to paleoclimatic interpreta-tion of tree-ring data J Geophys Res 111 G03008doi1010292006JG000166 2006

Fan Y and van den Dool H Climate Prediction Cen-ter global monthly soil moisture data set at 05 resolu-tion for 1948 to present J Geophys Res 109 D10102doi1010292003JD004345 2004

Frank D Esper J and Cook E R Adjustment for proxy numberand coherence in a large-scale temperature reconstruction Geo-phys Res Lett 34 L16709 doi1010292007GL030571 2007

Franke J Gonzaacuteles-Rouco J F Frank D and Graham N E 200years of European temperature variability insights from and testsof the Proxy Surrogate Reconstruction Analog Method ClimDynam 37 133ndash150 2011

Franke J Frank D Raible C Esper J and Broumlnnimann SSpectral biases in tree-ring climate proxies Nat Clim Chang3 360ndash364 2013

Fritts H C Tree rings and climate Academic Press London1976

Goosse H Crespin E de Montety A Mann M E RenssenH and Timmermann A Reconstructing surface temperaturechanges over the past 600 years using climate model simula-tions with data assimilation J Geophys Res 115 D09108doi1010292009JD012737 2010

Grissino-Mayer H D and Fritts H C The International Tree-Ring Data Bank an enhanced global database serving the globalscientific community Holocene 7 235ndash238 1997

Hakim G J Annan J Broumlnnimann S Crucifix M EdwardsT Goosse H Paul A van der Schrier G and Widmann MOverview of data assimilation methods PAGES News 212 72ndash73 2013

Huang J van den Dool H M and Georgankakos K P Analysisof model-calculated soil moisture over the United States (1931ndash1993) and applications to long-range temperature forecasts JClimate 9 1350ndash1362 1996

Hughes M K Dendrochronology in climatology the state of theart Dendrochronologia 20 95ndash116 2002

Hughes M K and Ammann C M The future of the past ndash AnEarth system framework for high resolution paleoclimatologyeditorial essay Clim Change 94 247ndash259 2009

IPCC Climate Change 2007 The physical science basis Contribu-tion of working group I to the Forth Assessment Report of the In-tergovernmental Panel on Climate Change edited by SolomonS Qin D Manning M Chen Z Marquis M Averyt K BTignor M and Miller H L Cambridge University Press Cam-bridge United Kingdom and New York NY USA 2007

Jones P D Osborn T J and Briffa K R Estimating samplingerrors in large-scale temperature averages J Climate 10 2548ndash2568 1997

Jones P D Briffa K R Osborn T J Lough J M van OmmenT D Vinther B M Luterbacher J Wahl E R Zwiers FW Mann M E Schmidt G A Ammann C M Buckley BM Cobb K M Esper J Goosse H Graham N Jansen EKiefer T Kull C Kuumlttel M Mosley-Thompson E OverpeckJ T Riedwyl N Schulz M Tudhope A W Villalba RWanner H Wolff E and Xoplaki E High-resolution palaeo-climatology of the last millennium a review of current status andfuture prospects Holocene 19 3ndash49 2009

Koumlrner C Alpine treelines ndash Functional ecology of the global highelevation tree limits Springer Basel 2012

Koumlrner C and Paulsen J A world-wide study of high altitude tree-line temperatures J Biogeogr 31 713ndash732 2004

Kottek M Grieser J Beck C Rudolf B and Rubel F Worldmap of the Koumlppen-Geiger climate classification updated Mete-orol Z 15 259ndash263 2006

Ljungqvist F C Krusic P J Brattstroumlm G and Sundqvist HS Northern Hemisphere temperature patterns in the last 12centuries Clim Past 8 227ndash249 doi105194cp-8-227-20122012

Mann M E Zhang Z Hughes M K Bradley R S Miller SK Rutherford S and Ni F Proxy-based reconstructions ofhemispheric and global surface temperature variations over thepast two millennia P Natl Acad Sci USA 105 13252ndash132572008

Mann M E Fuentes J D and Rutherford S Underes-timation of volcanic cooling in tree-ring based reconstruc-tions of hemispheric temperatures Nat Geosci 5 202ndash205doi101038ngeo1394 2012

Meko D M Applications of Box-Jenkins methods of time-seriesanalysis to reconstruction of drought from tree rings PhD the-sis University of Arizona 1981

Mitchell Jr J M Dzerdzeevskii B Flohn H Hofmeyr W LLamb H H Rao K N and Wallen C C Climatic changeTechnical Note 79 World Meteorological Organization Geneva1996

Mitchell T D and Jones P D An improved method of construct-ing a database of monthly climate observations and associatedhigh-resolution grids Int J Climatol 25 693ndash712 2005

Nemani R R Keeling C D Hashimoto H Jolly W M PiperS C Tucker C J Myneni R B and Running S W Climate-driven increase in global terrestrial net primary production from1982 to 1999 Science 300 1560ndash1563 2003

Osborn T J Briffa K R and Jones P D Adjusting variancefor sample-size in tree-ring chronologies and other regional timeseries Dendrochronologia 15 89ndash99 1997

Clim Past 10 437ndash449 2014 wwwclim-pastnet104372014

P Breitenmoser et al Forward modelling of tree-ring width 449

Raible C C Casty C Luterbacher J Pauling A Esper JFrank D Buumlntgen U Roesch A C Tschuck P WildM Vidale P-L Schaumlr C and Wanner H Climate variabil-ity ndash observations reconstructions and model simulations forthe Atlantic-European and Alpine region from 1500ndash2100 ADClim Change 79 9ndash29 2006

Rossi S Deslauriers A Anfodillo T and Carraro V Evidenceof threshold temperatures for xylogenesis in conifers at high al-titudes Oecologia 152 1ndash12 2007

Salzer M W and Kipfmueller K F Reconstructed temperatureand precipitation on a millennial timescale from tree-rings in thesouthern Colorado Plateau USA Clim Change 70 465ndash4872005

Shi J Liu Y Vaganov E A Li J and Cai Q Statisticaland process-based modeling analyses of tree growth responseto climate in semi-arid area of north central China A casestudy of Pinus tabulaeformis J Geophys Res 113 G01026doi1010292007JG000547 2008

Steiger N J Hakim G J Steig E J Battisti D S and Roe GH Climate field reconstruction via data assimilation J Climate26 submitted 2014

Tingley M P Craigmile P F Haran M Li B Mannshardt Eand Rajaratnam B Piecing together the past statistical insightsinto paleoclimatic reconstructions Quaternary Sci Rev 35 1ndash22 2012

Tolwinski-Ward S E Evans M N Hughes M K and An-chukaitis K J An efficient forward model of the climate con-trols on interannual variation in tree-ring width Clim Dynam36 2419ndash2439 2011a

Tolwinski-Ward S E Evans M N Hughes M K and An-chukaitis K J Erratum to An efficient forward model of theclimate controls on interannual variation in tree-ring width ClimDynam 36 2441ndash2445 2011b

Tolwinski-Ward S E Anchukaitis K J and Evans M NBayesian parameter estimation and interpretation for an inter-mediate model of tree-ring width Clim Past 9 1481ndash1493doi105194cp-9-1481-2013 2013

Touchan R Shishov V V Meko D M Nouiri I and GrachevA Process based model sheds light on climate sensitivityof Mediterranean tree-ring width Biogeosciences 9 965ndash972doi105194bg-9-965-2012 2012

Trouet V Esper J Graham N E Baker A and Frank D Per-sistent positive North Atlantic Oscillation Mode dominated theMedieval Climate Anomaly Science 324 78ndash80 2009

Vaganov E A Hughes M K and Shashkin A V Growth dy-namics of conifer tree rings in Growth dynamics of tree ringsImages of past and future environments Ecological studies 183Springer New York 2006

Vaganov E A Anchukaitis K J and Evans M N How well un-derstood are the processes that create dendroclimatic recordsA mechanistic model of climatic control on conifer tree-ringgrowth dynamics in Dendroclimatology edited by Hughes MK Swetnam T and Diaz H Developments in Paleoenviron-mental Research 11 Springer New York 2011

van den Dool H Huang J and Fan Y Performance andanalysis of the constructed analogue method applied to USsoil moisture over 1981ndash2001 J Geophys Res 108 8617doi1010292002JD003114 2003

Wahl E and Frank D Evidence of environmental change fromannually-resolved proxies with particular reference to dendrocli-matology and the last millennium in The SAGE handbook ofenvironmental change edited by Matthews J A 1 Sage 320ndash344 2012

Wettstein J J Littell J S Wallace J M and Gedalof Z Co-herent region- species- and frequency-dependent local climatesignals in Northern Hemisphere tree-ring widths J Climate 245998ndash6012 2011

Widmann M Goosse H van der Schrier G Schnur R andBarkmeijer J Using data assimilation to study extratropicalNorthern Hemisphere climate over the last millennium ClimPast 6 627ndash644 doi105194cp-6-627-2010 2010

Wigley T M L Briffa K R and Jones P D On the averagevalue of correlated time series with applications in dendrocli-matology and hydrometeorology J Clim Appl Meteorol 23201ndash213 1984

Wu C Chen J M Black T A Price D T Kurz W A DesaiA R Gonsamo A Jassal R S Gough C M Bohrer GDragoni D Herbst M Gielen B Beminger F Vesala TMammarella I Pilegaard K and Blanken P D Interannualvariability of net ecosystem productivity in forests is explainedby carbon flux phenology in autumn Global Ecol Biogeogr 22994ndash1006 2013

Zhang Y X Shao X M Xu Y and Wilmking M Process-based modelling analyses ofSabina przewalskiigrowth responseto climate factors around the northeastern Qaidam Basin Chi-nese Sci Bull 56 1518ndash1525 2011

wwwclim-pastnet104372014 Clim Past 10 437ndash449 2014