Water Isotope Diffusion Rates from the Northgrip Ice Core for The

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arXiv:1404.4201v4 [physics.geo-ph] 19 Dec 2017 tlwadhg frequencies. high signals and temperature resolve low time at same the in can It method. itr setmtdb h pcrlcaatrsisof diffusion characteristics isotope spectral water the the by into estimated the look as we history study this In susaprn nteueo h classical the of use the the overcoming to in by able apparent is estimates technique issues temperature reconstruction past new 4000 provide The approximately scales at b2k. over centennial occurring years cooling variability and profound millennial climatic a with spanning a Holocene presents the fractionation record isotopic the conditio This glacial gas for Finally, b2k. reduction recent similar ky thinning a 8 by proposing studies at ice supported 10% overestimates is the about model result, by of flow rates ice accumulation adjustment the past that necessary indicating Our a function thereafter. 9 optimum, trend to climatic and Holocene cooling 7 points the apparent for between estimate an seen temperature with is b2k optimum ky climatic Holocene transitions. Dryas Younger A and magni- temperature Bølling–Allerød and the The of timing tude the model. site, as captures flow accurately history the reconstruction ice and rate from Dansgaard–Johnsen chronology counted strain a layer signal GICC05 and the in temperature using accumulation estimated model the the densification infer assuming steady-state a to as diffusion a used isotope order to be water can coupled a signal model use the We thus paleothermometer. higher of and firn induce components smoothing temperatures frequency of Higher rates high spectrum. the power on predominantl the signal, impact firn the isotopic an of initial having medium the porous the attenuates in pack vapor water of diffusion eod( record c oefrtels 600yas-gailgcland glaciological - years 16,000 last the for core ice 2 1 a e stp ifso ae rmteNorthGRIP the from rates diffusion isotope Water Abstract nttt o lieadAci eerh nvriyo Col of University Research, Arctic and Alpine for Institute etefrIeadCiae il orIsiue Universit Institute, Bohr Niels Climate, and Ice for Centre 3 δ i.o ednmc,DUsaeNtoa pc nttt,El Institute, Space National space DTU Geodynamics, of Div. 18 O δ 18 iesre oeigtels 600yas The years. 16,000 last the covering series time Ahg eouin(.5m ae isotopic water m) (0.05 resolution high —A .Gkinis V. O saalbefo h otGI c core. ice NorthGRIP the from available is ) 1,2 .B Simonsen B. S. , aeciai implications. paleoclimatic K20 oehgn Denmark Copenhagen, DK-2100 1,3 .L Buchardt L. S. , δ 18 O O833USA 80303 CO slope Denmark ns. y sdalna eainhpbtentema annual value mean as: isotopic described the annual snow mean of between the and (2001) relationship temperature al. linear surface et Johnsen a conditions, Green- used present For and site. precipitation sites rela- the land linear at temperature a precipitatio the polar reported and of al., signal have isotopic et the 1969) (Johnsen between tionship al., 1997; studies et al., Previous Lorius et conden- 1989; 2001). Jouzel of al., time 1984; et the Merlivat, Johnsen proxy at and a cloud (Jouzel as the used sation of site been temperature far condensation the gra- so for and has temperature and evaporation the 1964) (Dansgaard, to the related between is dient 2000) the Mook, through 1953; expressed changes. monly and climate system future climate predict Earth’s to within of possibility high study the is the thus archive of data context paleoclimate the of and relevance type continuity The this resolution. their of temporal is high archives, for climate potential data the as features proxy cores important embedded most ice via and the of composition of part One isotopic large impurities. water chemical a the in as such present, 800,000 before to up years changes environmental past of views tailed apesiooi ai eaiet hto eeec wate reference a of the that through expressed to VSMOW) relative ratio isotopic sample’s where 1 h stpcsgaueo oa rcptto,com- precipitation, polar of signature isotopic The de- most the of some provide records core ice Polar 1 stpcaudne r yial eotda eitoso deviations as reported typically are abundances Isotopic .W .White C. W. J. , 2 R = rd,Budr 503t tetBoulder, Street 30th 1560 Boulder, orado, fCpnae,JlaeMre e 30, Vej Maries Juliane Copenhagen, of y 2 1 H H δ 18 and krvj ul.37 g.Lyngby, Kgs. 327, Build. ektrovej, 0 = O 18 .I I. R = . 2 67 NTRODUCTION n .M Vinther M. B. and , 18 16 · O O T δ ( ◦ notation: C) δ − notation 13 δ . i 7 = h i i R R . SMOW sample 1 1 (Epstein, − (e.g. r [ 1 (1) h a f n 1 ] 2

Assuming that the isotope sensitivity of 0.67 hK−1 in from the water isotopic signal, is to look into its spectral Eq.(1) (hereafter “spatial slope” ζs) holds for different properties. Inherently noisy at the beginning and affected climatic regimes (as glacial conditions and inter-stadial by a number of post depositional effects, the isotopic events) one can reconstruct the temperature history of an signal experiences attenuation via a molecular diffusion ice core site based on the measured δ18O profile. process during the stage of firn densification. The diffu- The validity of the temperature reconstruction sion process eliminates the power of the high frequency based on ζs was questioned when studies based on components of the spectrum and often results in a more borehole temperature inversion (Cuffey et al., 1994; common δ18O signal between ice cores whose upper Johnsen et al., 1995; Dahl Jensen et al., 1998) and parts show a very low cross-correlation of their δ18O gas isotopic fractionation studies (Severinghaus et al., time series (Fisher et al., 1985). Information on this 1998; Severinghaus and Brook, 1999; Lang et al., 1999; process is contained in the spectral characteristics of the Schwander et al., 1997; Landais et al., 2004) were de- δ18O signal. We work here along the lines of previously veloped. The aforementioned studies drew the following published work by Johnsen (1977), Johnsen et al. (2000) conclusions regarding the isotopic thermometer. First, and Simonsen et al. (2011) presenting a technique that the isotopic slope is not constant with time. Second, is based on the spectral analysis of the δ18O signal during glacial conditions the spatial slope presents an only, thus not requiring dual isotope measurements isotopic sensitivity higher than the sensitivity suggested of both δ18O and δD as in Simonsen et al. (2011). by the borehole inversion and gas isotopic studies. As a An estimate of the densification process is vital for result, reconstructions of past temperatures based on the this type of study and can be carried out in various water isotope signal, should assess the sensitivity of the ways (Herron and Langway, 1980; Alley et al., 1982; δ18O to temperature for different climatic regimes, thus Schwander et al., 1997; Goujon et al., 2003), with each inferring the “temporal slope” ζt. approach posing its own uncertainty levels, implementa- The main reasons that drive the fluctuations of ζt tion characteristics and challenges. The technique yields with time are not precisely determined yet. Changes of actual firn temperatures and thus overcomes many of the the vapor source location and temperature, the possible issues of the traditional δ18O thermometer based on the presence of an atmospheric inversion over the precipita- “temporal slope” ζt. tion site, microphysical cloud processes affecting the in– cloud phase changes, as well as effects related to the sea- II. THE WATER ISOTOPE DIFFUSION - DENSIFICATION sonality of the precipitation, have previously been pro- MODEL posed as possible causes of this behavior (Jouzel et al., We will outline here the theory of water isotope 1997). Furthermore, Vinther et al. (2009) showed how diffusion in firn and ice. Almost exclusively, the for- changes of the ice sheet geometry affect the elevation mulations used here are based on the work presented of ice core sites and can create isotopic artifacts, thus in Johnsen (1977) and Johnsen et al. (2000) and the “masking” the Holocene climatic optimum signal from experimental work of Jean-Baptiste et al. (1998) and ice core records. The complications emerging from the Van der Wel et al. (2011). variable nature of ζt, have possibly also resulted in the isotopic signal pointing towards a climatically stable Holocene epoch. A very low signal to noise ratio is A. Firn diffusion 18 observed in the δ O signal of almost every deep ice The diffusion of water isotopes in firn is a process core from the Greenland ice divide. This observation that occurs after the deposition of precipitation. It is a contradicts with studies that indicate that the Holocene molecular exchange process taking place in the vapor epoch has not been as stable as previously thought and phase and it is driven by isotopic gradients existing along likely significant climatic changes have occurred at high the firn column. As the densification of firn continues, the latitude sites (Denton and Karlen, 1973; Bond et al., diffusion process slows down until it ceases at pore close 15 2001). More recently, and based on combined δ N and off. Assuming a coordinate system fixed on a sinking 40 δ Ar gas analysis on the GISP2 ice core Kobashi et al. layer of firn, the process can be described mathematically (2011) suggested temperature variations up to 3 K during by Fick’s second law accounting for layer thinning as: the last 4,000 years. The impacts of these changes are 2 believed to have been significant for the evolution of ∂δ ∂ δ ∂δ = D (t) ε˙z (t) z . (2) past human civilizations (Dalfes et al., 1997; deMenocal, ∂t ∂z2 − ∂z 2001; Weiss and Bradley, 2001). Here, D (t) is the diffusivity coefficient and ε˙z (t) the An alternative way to extract temperature information vertical strain rate. Use of Fourier integrals yields the 3 solution to Eq.(2) as the convolution of the initial iso- the top firn layer. Pressure gradients caused by wind topic signal δ (z, 0) with a Gaussian filter of standard flowing over the surface topography (Colbeck, 1989; deviation σ: Waddington et al., 2002) or by diurnal temperature fluc- 1 −z2 = e 2σ2 , (3) tuations (Hindmarsh et al., 1998) can cause Darcian va- G σ√2π por fluxes penetrating the firn. These fluxes can alter the The isotopic signal δ (z,t) will then be given by isotopic composition of the upper firn. The importance ∞ of these effects depends on parameters like temperature, 1 + (z u)2 δ (z,t)= (t) δ (z, 0) exp − − duaccumulation, . wind and surface topography. Considering S σ√2π −∞ 2σ2 Z ( ) the relatively high accumulation rates at the NorthGRIP (4) site, it is likely that the surface snow is not exposed to Here (t) is the total thinning the layer has experienced the overlying vapor at times sufficiently long to result S ′ during the time interval t = 0 t = t due to the ice → in isotopic changes that will have a major impact in our flow and equal to: reconstruction. We acknowledge that diffusion models t′ ′ εz t t that take these effects into account are likely to give a t = eR0 ˙ ( )d . (5) S more accurate reconstruction of past temperatures. For The standard deviation term σ of the Gaussian filter, the very low accumulation sites of the East Antarctic commonly referred to as diffusion length, represents the plateau these affects can be significant and should be mean displacement of a water molecule along the z-axis taken into account. and can be calculated as (Johnsen, 1977): 2 B. Diffusion below the close–off depth dσ 2 2ε ˙z(t) σ = 2D(t) . (6) dt − At the close–off depth, the process of diffusion in the In the firn the simple strain rate can be assumed vapor phase ceases. After ρ ρice, self diffusion takes place in the solid phase. For the≥ temperature dependence dρ 1 ε˙z (t)= . (7) of the diffusivity we use an Arrhenius type equation as − dt ρ (Ramseier, 1967; Johnsen et al., 2000): Combining Eq.(6) and Eq.(7) and substituting the inde- −4 7186 2 −1 pendent variable t with the density ρ, we can calculate Dice = 9.2 10 exp m s . (10) · · − T the quantity σ2 provided an expression of the diffusivity D (ρ) (see SOM), a density profile for the site and its In order to calculate the quantity σice we start from adjoint age are estimated. The expression we finally get Eq.(6) and use Dice as the diffusivity parameter, for the diffusion length is (see SOM for a more detailed 2 dσice 2 2ε ˙z(t) σ = 2Dice(t) . (11) derivation): dt − ice − 1 ρ dρ 1 The solution for Eq.(11) yields (see SOM): σ2 (ρ)= 2ρ2 D(ρ) dρ, (8) ρ2 dt t′ Zρo 2 ′ ′ 2 −2 σice t = S t 2Dice(t) S(t) dt (12) where with ρ we symbolize the surface density. In o Z0 this study we used the empirical steady-state densifica- For a further discussion on the ice diffusion coefficient tion model by Herron and Langway (1980) (H–L model the reader is referred to the SOM. hereafter), according to which: dρ(z) C. The total diffusion signal at depth z = K(T )Aϑ (ρ ρ (z)) . (9) i dt ice − 2 If with σfirn we symbolize the firn diffusion length as Here K(T ) is a temperature dependent Arrhenius–type estimated by performing the integration in Eq.(8) from densification rate coefficient, A is the annual accumu- the surface density ρo to the close–off density ρco and − lation rate (here in kgm 2yr−1) and ϑ is a factor that expressed in ice equivalent length, then the total diffusion determines the effect of the accumulation rate during length at a depth zi will be: the different stages of the densification. For a better σ2 (z) = [S(z)σ (z)]2 + σ2 (z) (13) insight on those parameters the reader is referred to i firn ice 2 Herron and Langway (1980). In this study, for the estimation of σice we use the The mathematical treatment of the diffusion pro- temperature profile from the borehole of the NorthGRIP cess presented in this section does not take into ac- core (Dahl-Jensen et al., 2003) and assume a steady state count possible effects of barometric wind pumping in condition. 4

In Fig. 1 the quantities σi, σice, σfirn and S(z)σfirn is supported by synthetic data tests described in section 6 are illustrated for typical modern day conditions at of the SOM where additional information on the spectral NorthGRIP. These parameters are only approximately and σ2 estimation can also be found. representative of the modern NorthGRIP conditions and It is worth noting that the spectral estimation does not chosen as such, solely for the purpose of illustration. require that the δ18O record is corrected for changes in elevation or the δ18O content of sea water. III. ESTIMATION OF THE DIFFUSION LENGTH BASED IV. INFERRINGTEMPERATURESFROMTHE ON HIGH RESOLUTION δ18O DATASETS ESTIMATEDDIFFUSIONLENGTHS The transfer function for the Gaussian filter in Eq. (3) Let us assume that the total diffusion length value σ2 will be given by its Fourier transform, which is itself i at depth z is estimated from the power spectral density a Gaussian and equal to i and a combination of firn densification and flow modelb −k2σ2 parameters as well as an estimate of past accumulation F[ (z)] = ˆ = e 2 , (14) Gcfa Gcfa rates is known. The first step towards obtaining a tem- where k = 2π/∆ and ∆ is the sampling resolution of perature Ti is to account for the artifactual diffusion that the δ18O time series (Abramowitz and Stegun, 1964). occurs due to the finite sampling scheme. We require Harmonics with an initial amplitude Γ0 and wavenumber that the transfer function of a rectangular filter with width k will be attenuated to a final amplitude Γs as described equal to ∆, is equal to the transfer function of a Gaussian 2 in Eq.(15): filter with diffusion length σdis. This results in: −k2σ2 2 Γ =Γ e 2 (15) 2∆ π s 0 σ2 = log . (18) dis π2 2 Based on the latter, one can describe the behavior of Then, the sampling diffusion length is subtracted from the power spectrum of the isotopic time series that has σˆ2 in the Gaussian sense as: been subjected to the firn diffusion process, assuming i that at the time of deposition the power spectral density σ2 = σ2 σ2 . (19) i i − dis shows a white noise behavior. For a time series that is Combining Eq.(13, 19) we get sampled at resolution equal to ∆ and presenting a noise 2b 2 2 2 σi σdis σice level described by η (k), the power spectral density will σfirn = − −2 . (20) be described as: S(z) The result of this calculationb describes the data based 2 Ps = Pσ + ηˆ(k) (16) | | diffusion length of the layer under consideration at the −k2σ2 1 close–off depth in m ice eq. where Pσ = P e , k = 2πf and f 0, 0 ∈ 2∆ A model based calculation of the diffusion length (17) at the close–off depth can be obtained that will allow the calculation of the temperature . Central to this From Eq.(16, 17) one can see that the estimation of the T calculation is Eq.(8) where and the integration diffusion length σ benefits from time series sampled at a ρ = ρco takes place from the surface density to the close–off high resolution ∆ and presenting a low noise level η (k). ρo density ρco. The primed notation is used for the model We obtain an estimate Pˆs of the power spectral density based diffusion length estimate as σ′2 . Additional to density Ps by using Burg’s spectral estimation method firn the temperature T , the model also requires a value for and assuming a µ-order autoregressive (AR-µ) process the accumulation rate parameter . Our accumulation (Kay and Marple, 1981; Hayes, 1996). On a sliding A rate estimates are based on the combined information window with a length of 500 points (25 m), we apply the from the ice flow model and the estimate of the annual algorithm described in Andersen (1974). We calculate layer thickness, available from the GICC05 chronology a value for the diffusion length σ2, by minimizing the (see section V-B). The temperature estimation uses the misfit between P and Pˆ in the least squares sense. An s s Newton-Raphson method in order to find the roots of the example of an estimated spectrum and the inferred model term: is given in Fig. 2. ρ The key assumption underpinning the diffusion length co σ2 (ρ = ρ , T (z), A(z)) σ2 . (21) ρ co − firn estimation is that variations in the frequency content of ice 18 ′2 the primary record (i.e., the δ O of snowfall before σfirn diffusive smoothing) through time are small compared to The computation| is summarized{z in the} block diagram in the imprint of isotopic diffusion itself. This assumption Fig. 3. 5

V. THE NORTHGRIP DIFFUSION LENGTH BASED described in section III and section 4 in the SOM. In TEMPERATURE HISTORY order to investigate the stability of the spectral estimation A. The high resolution δ18O NorthGRIP record technique we vary the value of the order µ of the AR ◦ filter in the interval [40, 80]. This results in 41 estimates The NorthGRIP ice core was drilled at 75.10 N, of the diffusion length for every depth, providing an 42.32 ◦W at an elevation of 2,917 m, to a depth estimate of the stability of the power spectral estimation of 3,085 m and extending back to 123,000 years as well as the variance of the diffusion length estimation. (NGRIP members, 2004). A high resolution record of In Fig. 5, we present the result of the this estimation δ18O is available from this ice core with a resolution representing the value of σ2 together with its adjoint of ∆ = 0.05 m. Stable isotope δ18O analysis were i variance (top panel in Fig. 5). We also show the result of performed at the stable isotope laboratory of the Uni- the discrete sampling, ice flow thinning and ice diffusion versity of Copenhagen using a SIRA10 isotope ratio b correction representing the value of σ2 . This is the data- mass spectrometer with an adjacent CO H O isotopic firn 2 2 based diffusion length value we use in order to infer the equilibration system. The analytical uncertainty− of the temperature of the record using the computation scheme system is 0.06 h. This number refers to the analytical described in section IV and illustrated in Fig. 3. Based performance of the mass spectrometry system alone and on a sensitivity study described in detail in section 5, does not necessarily describe the variance of the δ18O 6 and 8 of the SOM we estimate the uncertainty of the time series. The latter is largely affected by the accu- reconstruction to be approximately 2.7 K (1σ). mulation patterns at the site as well as effects occurring after deposition of the snow (Fisher et al., 1985) The high resolution δ18O record down to 1700 m is presented VI. DISCUSSION in Fig. 2. A. General picture Based on a diffusion length estimation for the last B. Dating - accumulation and strain rate history 16,000 years we reconstructed a temperature history for The NorthGRIP ice core has been dated by man- the NorthGRIP site. In Fig. 6 we present the temperature ual counting of annual layers down to 60 ka, as reconstruction after applying two sharp low–pass filters a part of the Greenland Ice Core Chronology 2005 with a cut–offs at 200 and 1000 y. By perturbing the (GICC05) (Vinther et al., 2006; Rasmussen et al., 2006; diffusivity model parameters with varying atmospheric Andersen et al., 2006; Svensson et al., 2008). In this pressure values, we have found our temperature inversion study, a combination of the GICC05 estimated annual to be insensitive to ice sheet elevation changes within the layer thickness λ(z) and a thinning function S(z) in- range estimated in Vinther et al. (2009). The estimation ferred by an ice flow model provides an accumulation of the temperature signal presented here does not include rate history A(z) for the site. We use a Dansgaard- any lapse rate corrections. The temperature at every Johnsen (hereafter D–J model) type 1–D ice flow model point in time is the temperature at the surface of the (Dansgaard and Johnsen, 1969) with basal melting and NorthGRIP site. sliding. The model is inverted in a Monte–Carlo fashion The reconstruction stops at 225y b2k, a time that cor- allowing estimation of the ice flow parameters and responds approximately to the present close–off depth. constrained by measured depth–age horizons. The values The diffusion based reconstruction, results in a mean inferred from the model for the present day accumulation temperature between 250 and 350 y b2k of 241.4 K (- rate, basal melting and the kink height are Amodern = 31.7 C). This is a reasonable estimate within the pre- −1 −3 −1 0.189 m y (ice equiv.), b = 7.5 10 my and scribed error bars, considering the modern temperature = 1620 m respectively. In Fig. 4, we present ◦ H at the NorthGRIP site of 31.5 C (NGRIP members, the annual layer thickness together with the estimated 2004). Additionally the temperature− history presents an thinning function and the accumulation rate. Note how obvious Holocene optimum at 8ky b2k. However, the S(z) varies linearly with depth. This is a result of a temperature gradient of 10 K≈ between the Holocene the D–J flow model that requires the horizontal velocity optimum and the present time is not supported by any to be constant from the surface until the kink height of previous study and is likely unrealistic. We assess this = 1620m (1465 m depth). H issue in more detail in section VI-B The record shows two prominent transitions from C. The diffusion length record for NorthGRIP colder to warmer climatic conditions at 14.7ky For the calculation of the diffusion length profile and 11.7ky respectively resembling the Bølling–Allerød≈ we follow the power spectral estimation approach as (BA) and Younger Dryas (YD) oscillations. Based 6 on our reconstruction, the amplitudes of those events the variable nature of the isotope temperature sensitivity are found to be 10.7 2.7K and 7 2.7 K re- with time. ± ± spectively. These results are in line with δ15N stud- With that in mind, we hereby propose that the ob- ies from the summit of Greenland as presented in served Holocene optimum discrepancy is due to an Severinghaus et al. (1998); Grachev and Severinghaus inaccurate correction for the ice thinning S (z) as de- (2005) and Severinghaus and Brook (1999). In our re- scribed in Eq.(13) and illustrated in Fig. 5. In order to 2 construction, the absolute temperature right before the account for this effect we correct σi with a modified beginning of the warming of the YD termination is thinning function S′ (z). We tune S′ (z) such that the calculated to be 232 2.7K, a temperature that is higher obtained temperature at 8ky b2k is 3 K higher than the than the suggested 227± K in Severinghaus et al. (1998). temperature at 225y b2k, in line with≈ Dahl Jensen et al. When calculated using the “classical” isotope ther- (1998); Johnsen et al. (1995, 2001) and Vinther et al. mometer and assuming a constant sensitivity of (2009). The first three studies are based on the borehole 0.67 hK−1, the magnitudes of these oscillations are un- temperature reconstruction while in Vinther et al. (2009) derestimated by almost a factor of two. To overcome this the δ18O signal of the NorthGRIP site is corrected problem, Johnsen et al. (1995) tuned the isotope sensi- for elevation effects assuming a common climate signal tivity using the low resolution borehole inferred tem- between NorthGRIP and the Renland icecap - the latter perature history (Cuffey et al., 1995; Dahl Jensen et al., proposed to have experienced minimal changes in eleva- 1998) and assuming a quadratic relationship between tion throughout the Holocene. A 3 K Holocene optimum temperature and the δ18O signal. With this in mind and signal is in a broad sense consistent with terrestrial considering that our result is based on the δ18O signal and marine proxy reconstructions of temperature for itself, we find our conclusions to be relevant within the Greenland (Table 3 in Kaufman et al. (2004)). discussion regarding the overall validity and eventually In order to obtain a 3 K Holocene optimum signal we the importance of the isotope thermometer. assume a linearly varying thinning function with respect ′ At approximately 8.5 ky b2k we observe a strong to depth and set S (z = 2100) = 0.28. The temperature cooling event ( 5 K) that lasts about 500 years. Similar reconstruction that utilizes the proposed modified thin- paleoclimatic signals≈ indicating widespread cooler/drier ning function is presented in Fig. 6. By adopting this conditions have been reported from regions of the North correction we do not impose any change in the higher Atlantic (Andrews et al., 1999; Risebrobakken et al., frequencies of the temperature signal. As a result the 2003; Rohling and Palike, 2005) as well as monsoon ar- magnitudes of the BA and the YD transitions remain eas (Gasse, 2000; Haug et al., 2001; Gupta et al., 2003; unaltered. The same applies for the 8.5k cooling event Wang et al., 2005). The magnitude and age of the event as well as the rest of the observed Holocene variability. resemble those of the 8.2k event observed in the δ18O Additionally, the thinning correction has an impact on signal of Greenland ice cores (Alley et al., 1997). Even the inferred temperature of the Younger – Dryas stadial, though the 8.2k event could possibly be seen as part of a resulting in a temperature of 227.5 2.7 K. With this ± more general climate instability (Ellison et al., 2006), it updated estimate, we achieve an agreement well within would be speculative to propose that the North Atlantic the 1σ uncertainty when compared to Severinghaus et al. freshening mechanism that likely triggered the 8.2k event (1998). is related to the longer cooling event we observe here. Here we assume that the use of the modified thinning function S′(z) should not imply a change on the layer counted GICC05 chronology and the profile of annual B. Proposed thinning function correction layer thickness λ(z). Hence, the proposed change re- Considering the above features of our temperature quires a reduction of the inferred accumulation rates. In reconstruction, we can comment that apart from the Fig. 7, we present the old and proposed scenarios for Holocene optimum discrepancy and warm glacial, the the thinning function and accumulation rates. We use general characteristics of the signal are in line with the the primed notation for the proposed scenarios as S′(z) synthesized picture we have for the Greenland summit for the thinning function and A′(z) for the accumulation temperature history over the last 16ky years. This picture rate. The required reduction of the accumulation rate is based on a variety of methods and proxies, most is 10% at 8ky b2k and 15% at the time of the ≈ ≈ prominently the gas isotopic fractionation δ15N studies Younger–Dryas stadial. and the borehole inversion technique. Additionally, our A similar correction in accumulation rate for the technique seems to overcome some of the problems of NorthGRIP site has been proposed for Marine Isotope the classical interpretation of the δ18O signal, caused by Stage 3 (MIS–3) by Huber et al. (2006). A reduction by 7

25% is required in order to eliminate the discrepancy 1999; Cuffey et al., 2000). Additionally a concern can between≈ the output of a firn densification/gas fraction- be raised regarding the validity of the assumption of ation model and δ15N measurements over the sequence the constant horizontal velocity from the kink height to of Interstadials 9–17. Similarly, Guillevic et al. (2013) the surface. We believe that implementations of ice flow require a 30% reduction of past accumulation rates as models that take into account the aforementioned issues derived by a D–J ice flow model for the NEEM site tuned can likely provide better estimates of the ice thinning to the GICC05 chronology on a gas fractionation study function and consequently past accumulation rates. focusing on Interstadials 8–10. In combination with these Furthermore, an additional effect that may have an results, our study indicates an inadequacy of the D–J impact on the accuracy of the thinning function esti- ice flow model in accurately reconstructing the strain mation by means of a D–J model concerns possible and accumulation rate histories of the NorthGRIP and migrations of the ice divide in the past. Previous studies NEEM sites. In a synthesis of their results with the study have demonstrated that such effects have occurred at the of Landais et al. (2004, 2005) , Guillevic et al. (2013) Siple Dome (Nereson et al., 1998) and the Greenland propose that this possible inadequacy applies only for summit (Marshall and Cuffey, 2000) ice core sites. De- glacial conditions, but not for interglacial periods as well spite the uncertainty involved in the modeling efforts as glacial inceptions. In contrast, our study demonstrates addressing the problem of migrating ice divides, it is how the D–J model fails to accurately estimate the accu- safe to assume that the Greenland Ice Sheet was very mulation rate history for the time span of the Holocene different during glacial times. For that reason one can epoch with an error that is increasing as one approaches expect that a simple ice flow model is very likely to glacial conditions. Preliminary results, indicate that this present inaccuracies regarding the calculated strain rate error converges to a value of approximately 25% at a history of the NorthGRIP site. depth of 2100 m ( 40.2ky b2k). However, due to the ice diffusion length≈ increasing with depth, inference of C. On the Holocene climate variability past temperatures below the depth of 2000m comes with much greater uncertainty. ≈ An interesting feature of the diffusion derived temper- One of the possible explanations for the observed ature history is the observed Holocene variability. The error is the use of a constant value used for the kink 200y and 1ky low–pass filtered temperature signals in height in the D–J ice flow model. This is the height Fig. 6 reveal a climate variability on both millennial that definesH the shape of the ice horizontal velocity and centennial time scales. It can be seen in the 1 ky vx (z). Above , vx is assumed to be constant and filtered curve (dark blue in Fig. 6), that the cooling H independent of z. Below , vx is assumed to lin- trend that started after the Holocene optimum persists early decrease until the valueH of basal sliding veloc- through the Holocene and it intensifies at around 4 ky ity (Dansgaard and Johnsen, 1969). The choice of a b2k, signifying a shift to cooler temperatures. In fact, a constant value for constitutes an oversimplification. look into the 200 y low-pass filtered curve (light blue Measurements of inclinationH in the bore–holes of the in Fig. 6) reveals a warm event preceding the shift to Dye–3 and Camp Century sites, reveal an enhanced de- cooler temperatures and giving rise to a mid-Holocene formation of the ice below (Hansen and Gundestrup, optimum. The climatic shift at around 4ky b2k is of 1988; Gundestrup et al., 1993).H The estimated horizontal particular interest. It possibly indicates that traces of velocity profiles from those measurements demonstrate the 4.2ky climatic event, observed in a wide range of two things. First, an apparent kink in the estimated sites (Staubwasser and Weiss, 2006; Fisher et al., 2008; vx profile is observed at the transition between the Berkelhammer et al., 2012; Walker et al., 2012) at low Holocene and glacial ice. Second, vx deviates from the mid and high latitudes, can also be found on the Green- assumed constant value already above (Fig. 7 and 8 land Ice Sheet. in Hansen and Gundestrup (1988) and GundestrupH et al. An analysis of the derived Holocene climate vari- (1993)) respectively. These two observations support ability based on the firn diffusion reconstruction is not the theory of a moving kink as also suggested by a goal of this study. The several observable features Guillevic et al. (2013). It is possible that the kink moves of the temperature history possibly resemble climatic along with the interface between Holocene and glacial events documented by other proxies. The reconstruction ice owing to the strong gradient in shear strain rates is broadly similar to the borehole temperature reconstruc- between the two materials. The latter is shown to be tion from GRIP (Dahl Jensen et al., 1998). On the other dependent on the ice fabric, impurity content and grain hand features of the inferred millennial and especially size of the ice (Paterson, 1991; Thorsteinsson et al., centennial temperature variability are inconsistent with 8 the elevation corrected δ18O temperature reconstruction core respectively. We also proposed possible reasons for from Vinther et al. (2009) with parts of the record this discrepancy related to the constant value of the kink presenting high magnitude and changes that are fast. height in the D–J model as well as probable past ice This calls for more work on the diffusion reconstruction divide migrations. technique and points to the necessity for replication of We believe that the climate variability of our record, the results on samples from neighboring ice coring sites. spanning millennial to centennial scales, is of particular The recently drilled and currently analyzed at a high interest and therefore requires further analysis, possi- resolution NEEM ice core (NEEM members, 2013) can bly additional evidence from other ice cores from the constitute an excellent dataset for such a study. Dual Greenland Ice Sheet and obviously careful comparisons δ18O and δD measurements on this high resolution with reconstructions based on other proxies from low, sample set will also allow for a further investigation mid and especially high latitudes. The NEEM ice core and application of the differential diffusion method as can potentially provide an excellent record, especially introduced in Johnsen et al. (2000) and applied in the when considering the application of recently developed works of Simonsen et al. (2011) and Gkinis (2011). continuous infrared techniques (Gkinis et al., 2011) that provide high resolution and precision δD and δ18O VII. CONCLUSIONS AND OUTLOOK datasets. Extending the diffusion reconstructions to the Based on a high resolution δ18O record from North- sections of the ice core shallower than the close–off GRIP, Greenland we estimated the diffusion length his- depth will also allow for a very useful comparison with tory for the site. By using a coupled water isotope the instrumental temperature record. Such an attempt diffusion and firn densification model, in combination will require slight modifications to the diffusion model with the GICC05 chronology and an estimate of the in order for it to deal with the firn layers in which the total thinning function obtained with a D–J ice flow diffusion process is still under way. model, we reconstructed a temperature history for the Our future study objectives will revolve around these period 400–16,000y b2k. We outlined the technicalities topics, not only within the scope of studying the past regarding the implementation of the model as well as the climate during the Holocene epoch, but also within the spectral based estimation of the diffusion length from scope of understanding the mechanisms that affect the the high resolution record. Based on a sensitivity study responsivity of the δ18O signal to a set of input climatic we estimated the 1σ uncertainty of the reconstructed parameters, most notably temperature and furthermore temperature to be approximately 2.7 K. result in a low (almost absent) signal to noise ratio during The inferred temperature history shows the climatic a period that has likely seen sizable climatic variations. transition from the Last Glacial to the Holocene Op- timum and the Holocene cooling trend thereafter. The ACKNOWLEDGEMENTS BA and YD climatic transitions are present in the IRMS analysis was performed by Anita Boas. We record, with a timing and amplitude that is broadly would like to thank Eric Steig, Christo Buizert, Takuro consistent with previous estimates obtained with gas Kobashi, Bradley Markle and Spruce Schoenemann for isotopic fractionation methods. A cooling event with a fruitful discussions. We acknowledge funding through duration of approximately 500 years and an amplitude NSF Award ARC 0806387 and the Lundbek foundation. of 5 K is observed in the early Holocene. It marks a The NorthGRIP project is directed and organized by the possible relationship with signals of similar nature from Department of Geophysics at the Niels Bohr Institute other north high latitude as well as monsoon sites at for Astronomy, Physics and Geophysics, University of approximately 8.5 ky b2k. Copenhagen. It was being supported by the National An overestimation of the temperature of the Holocene Science Foundations of Denmark, Belgium, France, Climatic Optimum points to the necessity for a correction Germany, Iceland, Japan, Sweden, Switzerland and the of the total thinning function. Assuming that the layer United States of America. We would like to thank three counted chronology is accurate, this correction would anonymous reviewers for looking into our work in detail require a reduction of the accumulation rate of the order and providing thoughtful comments and corrections. This of 10% at 8ky b2k with respect to the level estimated work would not have been possible without the insight with the D–J ice flow model. We discussed this result and innovative mind of Sigfus J. Johnsen. with respect to recent (Guillevic et al., 2013) as well as earlier (Huber et al., 2006) findings based on δ15N studies that propose a similar reduction for Interstadials 9–17 and MIS–3 from the NEEM and NorthGRIP ice 9

REFERENCES Research-solid Earth 105 (B12), 27889–27894. Dahl-Jensen, D., Gundestrup, N., Gogineni, S. P., Miller, Abramowitz, M., Stegun, I. A., 1964. Handbook of H., 2003. Basal melt at NorthGRIP modeled from Mathematical Functions with Formulas, Graphs, and borehole, ice-core and radio-echo sounder observa- Mathematical Tables, ninth dover printing, tenth gpo tions. Annals of Glaciology, Vol 37 37, 207–212. printing Edition. Dover, New York. Dahl Jensen, D., Mosegaard, K., Gundestrup, N., Clow, Alley, R. B., Bolzan, J. F., Whillans, I., 1982. Polar firn G. D., Johnsen, S. J., Hansen, A. W., Balling, N., Oct. densification and grain growth. Annals Of Glaciology 1998. Past temperatures directly from the Greenland 3, 7–11. ice sheet. Science 282 (5387), 268–271. Alley, R. B., Mayewski, P. A., Sowers, T., Stuiver, M., Dalfes, H., Kukla, G., Weiss, H. (Eds.), 1997. Third Taylor, K. C., Clark, P. U., Jun. 1997. Holocene millennium BC climate change and old world collapse. climatic instability: A prominent, widespread event Vol. 49. NATO ASI Ser. 1, Springer, New York. 8200 yr ago. Geology 25 (6), 483–486. Dansgaard, W., 1964. Stable isotopes in precipitation. Andersen, K. K., Ditlevsen, P. D., Rasmussen, S. O., Tellus 16 (4), 436–468. Clausen, H. B., Vinther, B. M., Johnsen, S. J., Stef- Dansgaard, W., Johnsen, S. J., 1969. A flow model and fensen, J. P., Aug. 2006. Retrieving a common ac- a time scale for the ice core from Camp Century, cumulation record from greenland ice cores for the Greenland. Journal of Glaciology 8 (53), 215–223. past 1800 years. Journal Of Geophysical Research- deMenocal, P. B., Apr. 2001. Cultural responses to Atmospheres 111 (D15), D15106. climate change during the late holocene. Science Andersen, N., 1974. Calculation of filter coefficients 292 (5517), 667–673. for maximum entropy spectral analysis. Geophysics Denton, G. H., Karlen, W., 1973. Holocene climatic 39 (1), 69–72. variations. their pattern and possible cause. Quaternary Andrews, J. T., Keigwin, L., Hall, F., Jennings, Research 3 (2), 155 – 205. A. E., Aug. 1999. Abrupt deglaciation events and Ellison, C. R. W., Chapman, M. R., Hall, I. R., Jun. 2006. Holocene palaeoceanography from high-resolution Surface and deep ocean interactions during the cold cores, Cartwright Saddle, Labrador Shelf, Canada. climate event 8200 years ago. Science 312 (5782), Journal of Quaternary Science 14 (5), 383–397. 1929–1932. Berkelhammer, M., Sinha, A., Stott, L., Cheng, H., Epstein, S. Mayeda, T., 1953. Variations of 18O content Pausata, F. S. R., Yoshimura, K., 2012. An abrupt shift of waters from natural sources. Geochimica Cos- in the Indian Monsoon 4000 years ago. In: Geophys. mochimica Acta 4, 213?224. Monogr. Ser. Vol. 198. AGU, Washington, DC, pp. Fisher, D., Osterberg, E., Dyke, A., Dahl-Jensen, D., 75–87. Demuth, M., Zdanowicz, C., Bourgeois, J., Koerner, Bond, G., Kromer, B., Beer, J., Muscheler, R., Evans, R. M., Mayewski, P., Wake, C., Kreutz, K., Steig, E., M. N., Showers, W., Hoffmann, S., Lotti-Bond, R., Zheng, J., Yalcin, K., Goto-Azuma, K., Luckman, B., Hajdas, I., Bonani, G., Dec. 2001. Persistent solar in- Rupper, S., Aug. 2008. The Mt Logan Holocene-late fluence on north Atlantic climate during the Holocene. Wisconsinan isotope record: Tropical pacific-yukon Science 294 (5549), 2130–2136. connections. Holocene 18 (5), 667–677. Colbeck, S. C., 1989. Air movement in snow due to Fisher, D., Reeh, N., Clausen, H. B., 1985. Stratigraphic windpumping. Journal of Glaciology 35 (120), 209– noise in the time series derived from ice cores. Annals 213. Of Glaciology 7, 76–83. Cuffey, K. M., Alley, R. B., Grootes, P. M., Bolzan, J. M., Gasse, F., Jan. 2000. Hydrological changes in the african Anandakrishnan, S., 1994. Calibration of the delta-o- tropics since the last glacial maximum. Quaternary 18 isotopic paleothermometer for central Greenland, Science Reviews 19 (1-5), 189–211. using borehole temperatures. Journal Of Glaciology Gkinis, V., 2011. High resolution water isotope data from 40 (135), 341–349. ice cores. Ph.D. thesis, Niels Bohr Institute, University Cuffey, K. M., Clow, G. D., Alley, R. B., Stuiver, M., of Copenhagen. Waddington, E., Saltrus, R. W., Oct. 1995. Large arctic Gkinis, V., Popp, T. J., Blunier, T., Bigler, M., Schup- temperature-change at the Wisconsin-Holocene glacial bach, S., Kettner, E., Johnsen, S. J., 2011. Water transition. Science 270 (5235), 455–458. isotopic ratios from a continuously melted ice core Cuffey, K. M., Thorsteinsson, T., Waddington, E. D., sample. Atmospheric Measurement Techniques 4 (11), Dec. 2000. A renewed argument for crystal size con- 2531–2542. trol of ice sheet strain rates. Journal of Geophysical Goujon, C., Barnola, J. M., Ritz, C., Dec. 2003. Model- 10

ing the densification of polar firn including heat diffu- Earth And Planetary Science Letters 158 (1-2), 81–90. sion: Application to close-off characteristics and gas Johnsen, S. J., 1977. Stable isotope homogenization of isotopic fractionation for Antarctica and Greenland polar firn and ice. Isotopes and impurities in snow and sites. Journal Of Geophysical Research-Atmospheres ice, 210–219. 108 (D24), 4792. Johnsen, S. J., Clausen, H. B., Cuffey, K. M., Hoffmann, Grachev, A. M., Severinghaus, J. P., Mar. 2005. A revised G., Schwander, J., Creyts, T., 2000. Diffusion of stable +10 +/- 4 degrees c magnitude of the abrupt change isotopes in polar firn and ice. the isotope effect in in Greenland temperature at the Younger Dryas ter- firn diffusion. In: Hondoh, T. (Ed.), Physics of Ice mination using published GISP2 gas isotope data and Core Records. Hokkaido University Press, Sapporo, air thermal diffusion constants. Quaternary Science pp. 121–140. Reviews 24 (5-6), 513–519. Johnsen, S. J., Dahl Jensen, D., Dansgaard, W., Gun- Guillevic, M., Bazin, L., Landais, A., Kindler, P., Orsi, destrup, N., Nov. 1995. Greenland paleotemperatures A., Masson-Delmotte, V., Blunier, T., Buchardt, S. L., derived from GRIP borehole temperature and ice Capron, E., Leuenberger, M., Martinerie, P., Prié, F., core isotope profiles. Tellus Series B-Chemical And Vinther, B. M., 2013. Spatial gradients of temperature, Physical Meteorology 47 (5), 624–629. accumulation and δ18O-ice in Greenland over a series Johnsen, S. J., DahlJensen, D., Gundestrup, N., Stef- of Dansgaard–Oeschger events. Climate of the Past fensen, J. P., Clausen, H. B., Miller, H., Masson- 9 (3), 1029–1051. Delmotte, V., Sveinbjornsdottir, A. E., White, J., 2001. Gundestrup, N. S., Dahl-Jensen, D., Hansen, B. L., Kelty, Oxygen isotope and palaeotemperature records from J., Jan. 1993. Bore-hole survey at Camp Century, six Greenland ice-core stations: Camp Century, Dye- 1989. Cold Regions Science and Technology 21 (2), 3, GRIP, GISP2, Renland and NorthGRIP. Journal Of 187–193. Quaternary Science 16 (4), 299–307. Gupta, A. K., Anderson, D. M., Overpeck, J. T., Jan. Johnsen, S. J., Dansgaard, W., White, J. W. C., 1989. 2003. Abrupt changes in the Asian southwest mon- The origin of Arctic precipitation under present and soon during the Holocene and their links to the North glacial conditions. Tellus 41B, 452–468. Atlantic Ocean. Nature 421 (6921), 354–357. Jouzel, J., Alley, R. B., Cuffey, K. M., Dansgaard, W., Hansen, B. L., Gundestrup, N. S., 1988. Resurvey of bore Grootes, P., Hoffmann, G., Johnsen, S. J., Koster, hole at Dye-3, South Greenland. Journal of Glaciology R. D., Peel, D., Shuman, C. A., Stievenard, M., 34 (117), 178–182. Stuiver, M., White, J., Nov. 1997. Validity of the Haug, G. H., Hughen, K. A., Sigman, D. M., Peterson, temperature reconstruction from water isotopes in L. C., Rohl, U., Aug. 2001. Southward migration ice cores. Journal Of Geophysical Research-Oceans of the intertropical convergence zone through the 102 (C12), 26471–26487. Holocene. Science 293 (5533), 1304–1308. Jouzel, J., Merlivat, L., 1984. Deuterium and oxygen 18 Hayes, M. H., 1996. Statistical digital signal processing in precipitation: modeling of the isotopic effects dur- and modeling. John Wiley & Sons. ing snow formation. Journal of Geophysical Research- Herron, M. M., Langway, C., 1980. Firn densification Atmospheres 89 (D7), 11749 – 11759. - an empirical-model. Journal Of Glaciology 25 (93), Kaufman, D. S., Ager, T. A., Anderson, N. J., Anderson, 373–385. P. M., Andrews, J. T., Bartlein, P. J., Brubaker, L. B., Hindmarsh, R. C. A., Van der Wateren, F. M., Verbers, A. Coats, L. L., Cwynar, L. C., Duvall, M. L., Dyke, L. L. M., 1998. Sublimation of ice through sediment in A. S., Edwards, M. E., Eisner, W. R., Gajewski, K., Beacon Valley, Antarctica. Geografiska Annaler Series Geirsdottir, A., Hu, F. S., Jennings, A. E., Kaplan, A-physical Geography 80A (3-4), 209–219. M. R., Kerwin, M. N., Lozhkin, A. V., MacDonald, Huber, C., Leuenberger, M., Spahni, R., Fluckiger, J., G. M., Miller, G. H., Mock, C. J., Oswald, W. W., Schwander, J., Stocker, T. F., Johnsen, S., Landals, Otto-Bliesner, B. L., Porinchu, D. F., Ruhland, K., A., Jouzel, J., Mar. 2006. Isotope calibrated Greenland Smol, J. P., Steig, E. J., Wolfe, B. B., Mar. 2004. temperature record over Marine Isotope Stage 3 and its Holocene thermal maximum in the western arctic (0- relation to CH4. Earth and Planetary Science Letters 180 degrees w) rid e-4643-2011 rid d-4720-2011. 243 (3-4), 504–519. Quaternary Science Reviews 23 (5-6), 529–560. Jean-Baptiste, P., Jouzel, J., Stievenard, M., Ciais, P., Kay, S. M., Marple, S. L., 1981. Spectrum analysis - a May 1998. Experimental determination of the diffu- modern perspective. Proceedings Of The Ieee 69 (11), sion rate of deuterated water vapor in ice and appli- 1380–1419. cation to the stable isotopes smoothing of ice cores. Kobashi, T., Kawamura, K., Severinghaus, J. P., Barnola, 11

J. M., Nakaegawa, T., Vinther, B. M., Johnsen, S. J., R., Fischer, H., Goto-Azuma, K., Hansson, M. E., Box, J. E., Nov. 2011. High variability of Greenland Ruth, U., Mar. 2006. A new Greenland ice core surface temperature over the past 4000 years estimated chronology for the last glacial termination. Jour- from trapped air in an ice core. Geophysical Research nal Of Geophysical Research-Atmospheres 111 (D6), Letters 38, L21501. 10.1029/2005JD006079. Landais, A., Barnola, J. M., Masson-Delmotte, V., Risebrobakken, B., Jansen, E., Andersson, C., Mjelde, Jouzel, J., Chappellaz, J., Caillon, N., Huber, C., E., Hevroy, K., Mar. 2003. A high-resolution study Leuenberger, M., Johnsen, S. J., Nov. 2004. A contin- of Holocene paleoclimatic and paleoceanographic uous record of temperature evolution over a sequence changes in the Nordic seas. Paleoceanography 18 (1), of Dansgaard-Oeschger events during Marine Isotopic 1017. Stage 4 (76 to 62 kyr bp). Geophysical Research Rohling, E. J., Palike, H., Apr. 2005. Centennial-scale Letters 31 (22), L22211. climate cooling with a sudden cold event around 8,200 Landais, A., Jouzel, J., Masson-Delmotte, V., Caillon, years ago. Nature 434 (7036), 975–979. N., Aug. 2005. Large temperature variations over rapid Schwander, J., Sowers, T., Barnola, J. M., Blunier, T., climatic events in Greenland: a method based on air Fuchs, A., Malaize, B., Aug. 1997. Age scale of isotopic measurements. Comptes Rendus Geoscience the air in the summit ice: Implication for glacial- 337 (10-11), 947–956. interglacial temperature change. Journal Of Geophys- Lang, C., Leuenberger, M., Schwander, J., Johnsen, ical Research-Atmospheres 102 (D16), 19483–19493. S., 1999. 16C rapid temperature variation in central Severinghaus, J. P., Brook, E. J., Oct. 1999. Abrupt Greenland 70,000 years ago. Science 286 (5441), 934– climate change at the end of the last glacial pe- 937. riod inferred from trapped air in polar ice. Science Lorius, C., Merlivat, L., Hagenmann, R., 1969. Varia- 286 (5441), 930–934. tion in mean deuterium content of precipitations in Severinghaus, J. P., Sowers, T., Brook, E. J., Alley, R. B., Antarctica. Journal of Geophysical Research 74 (28), Bender, M. L., Jan. 1998. Timing of abrupt climate 7027–7030. change at the end of the Younger Dryas interval Marshall, S. J., Cuffey, K. M., Jun. 2000. Peregrinations from thermally fractionated gases in polar ice. Nature of the Greenland ice sheet divide in the last glacial 391 (6663), 141–146. cycle: implications for central Greenland ice cores. Simonsen, S. B., Johnsen, S. J., Popp, T. J., Vinther, Earth and Planetary Science Letters 179 (1), 73–90. B. M., Gkinis, V., Steen-Larsen, H. C., 2011. Past Mook, W., 2000. Environmental Isotopes in the Hy- surface temperatures at the NorthGRIP drill site from drological Cycle: Principles and Applications, vol. I, the difference in ﬁrn diffusion of water isotopes. IAEA. Unesco and IAEA. Climate of the Past 7 (4), 1327–1335. NEEM members, Jan. 2013. Eemian interglacial recon- Staubwasser, M., Weiss, H., Nov. 2006. Holocene cli- structed from a Greenland folded ice core. Nature mate and cultural evolution in late prehistoric-early 493 (7433), 489–494. historic West Asia - introduction. Quaternary Research Nereson, N. A., Raymond, C. F., Waddington, E. D., 66 (3), 372–387. Jacobel, R. W., 1998. Migration of the Siple Dome Svensson, A., Andersen, K. K., Bigler, M., Clausen, ice divide, West Antarctica. Journal of Glaciology H. B., Dahl-Jensen, D., Davies, S. M., Johnsen, S. J., 44 (148), 643–652. Muscheler, R., Parrenin, F., Rasmussen, S. O., Roeth- NGRIP members, 2004. High-resolution record of lisberger, R., Seierstad, I., Steffensen, J. P., Vinther, Northern Hemisphere climate extending into the last B. M., 2008. A 60 000 year Greenland stratigraphic interglacial period. Nature 431 (7005), 147–151. ice core chronology rid a-2643-2010 rid b-5560-2008. Paterson, W. S. B., Nov. 1991. Why ice-age ice is Climate of the Past 4 (1), 47–57. sometimes soft. Cold Regions Science and Technology Thorsteinsson, T., Waddington, E. D., Taylor, K. C., 20 (1), 75–98. Alley, R. B., Blankenship, D. D., 1999. Strain-rate en- Ramseier, R. O., 1967. Self-diffusion of tritium in natural hancement at Dye 3, Greenland. Journal of Glaciology and synthetic ice monocrystals. Journal Of Applied 45 (150), 338–345. Physics 38 (6), 2553–2556. Van der Wel, L. G., Gkinis, V., Pohjola, V. A., Meijer, H. Rasmussen, S. O., Andersen, K. K., Svensson, A. M., A. J., 2011. Snow isotope diffusion rates measured in a Steffensen, J. P., Vinther, B. M., Clausen, H. B., laboratory experiment. Journal of Glaciology 57 (201), Siggaard-Andersen, M. L., Johnsen, S. J., Larsen, 30–38. L. B., Dahl-Jensen, D., Bigler, M., Rothlisberger, Vinther, B. M., Buchardt, S. L., Clausen, H. B., Dahl- 12

Jensen, D., Johnsen, S. J., Fisher, D. A., Koerner, R. M., Raynaud, D., Lipenkov, V., Andersen, K. K., Blunier, T., Rasmussen, S. O., Steffensen, J. P., Svens- son, A. M., 2009. Holocene thinning of the Greenland ice sheet. Nature 461 (7262), 385–388. Vinther, B. M., Clausen, H. B., Johnsen, S. J., Ras- mussen, S. O., Andersen, K. K., Buchardt, S. L., Dahl- Jensen, D., Seierstad, I. K., Siggaard-Andersen, M. L., Steffensen, J. P., Svensson, A., Olsen, J., Heinemeier, J., 2006. A synchronized dating of three Greenland ice cores throughout the Holocene. Journal Of Geo- physical Research-Atmospheres 111 (D13), D13102. Waddington, E., Steig, E., Neumann, T., 2002. Using characteristic times to assess whether stable isotopes in polar snow can be reversibly deposited. Annals Of Glaciology, Vol 35 35, 118–124. Walker, M. J. C., Berkelhammer, M., Bjorck, S.rck, S., Cwynar, L. C., Fisher, D. A., Long, A. J., Lowe, J. J., Newnham, R. M., Rasmussen, S. O., Weiss, H., 2012. Formal subdivision of the Holocene series/epoch: a discussion paper by a working group of INTIMATE (Integration of ice-core, marine and terrestrial records) and the Subcommission on Quaternary Stratigraphy (International Commission on Stratigraphy). Journal of Quaternary Science 27 (7), 649–659. Wang, Y. J., Cheng, H., Edwards, R. L., He, Y. Q., Kong, X. G., An, Z. S., Wu, J. Y., Kelly, M. J., Dykoski, C. A., Li, X. D., May 2005. The Holocene Asian monsoon: Links to Solar Changes and North Atlantic Climate. Science 308 (5723), 854–857. Weiss, H., Bradley, R. S., Jan. 2001. Archaeology - what drives societal collapse? Science 291 (5504), 609–610. 13

0 σ firn σ 500 S(z) firn σ ice σ i 1000

1500 Depth [m] 2000

2500

3000 -2 0 2 4 6 8x10 Diffusion Length [m]

Fig. 1. Vertical profiles of σfirn, S(z)σfirn, σice and σi For the calculation of σfirn the parameters we used for the H–L model were: P = 0.7 −3 −3 −1 Atm, ρ0 = 330 kgm , ρCO = 804.3 kgm , T = 242.15 K, and A = 0.2 myr ice equivalent.

-30

-35

] Depth Interval 514.4 - 539.35 m οο /

ο -40 window 500 points, µ = 40 Ο [ 18 m] 2 δ

oo -1 /

o 10

-2 -45 10

-3 10

-4 10

Power Spectral Density [ 0 2 4 -1 6 8 10 -50 f [m ]

200 400 600 800 1000 1200 1400 1600 Depth [m]

Fig. 2. NorthGRIP high resolution (0.05 m) δ18O record. The subplot is an example of a power spectral density estimation with the MEM (blue curve). The length of the window is 500 points and the order of the AR model for the spectral estimation is µ = 40. The model for 2 the spectral density Ps is presented in red, |ηˆ(k)| is shown in purple and Pσ in green. 14

2 Fig. 3. Block diagram of the computation scheme for the temperature reconstruction. Data-based estimates of the σfirn parameter are obtained from the spectral estimation procedure and then corrected for discrete sampling, ice diffusion and ice flow thinning effects. A ′2 model based estimate of the diffusion length σfirn using an isothermal firn layer of temperature T and accumulation A is obtained using the ′2 2 densification/diffusion calculation. Finally we compute the roots of the term σfirn − σfirn using T as the independent variable.

0.28 0.9

0.24 0.8

0.20 Total Thinning 0.7 0.16 0.6 0.12 0.5

Accumulation [m ice eq.] 0.08 Annual layer thickness Accumulation 0.04 Total thinning 0.4

400 800 1200 1600 Depth [m]

Fig. 4. Annual layer thickness, total thinning and accumulation rate for NorthGRIP based on the GICC05 chronology and a 1–D Dansgaard– Johnsen ice ﬂow model

-4 10

x10 0 0.12 1.0 0.9 0.10 Total Thinning 0.8 0.08 0.7 0.6 0.06

Diffusion Length [m] 0.5 0.04 0.4 0.02 0.3 400 800 1200 1600 Depth [m]

2 2 Fig. 5. Results of the diffusion length estimation. Bottom plot: raw diffusion length values σi (z) (bottom black curve) and σﬁrn(z) (blue 2 curve) after correcting for total thinning (red curve) and σice Top plot: Standard deviation of the 41 estimates of the diffusion length for every depth in m ice eq. 15

250 -25

240 -30 δ 18 O [

-35 o /

230 oo ]

Temperature [K] Temperature low-pass 200y D-J Temperature low-pass 1000y D-J Temperature low-pass 200 adjusted -40 220 Temperature low-pass 1000 adjusted 18 δ O Low pass 200y 18 δ O Low pass 1000y Temperature Vinther et al. 2009 GRIP Temperature (Dahl Jensen et al. 1998) -45

3 2 4 6 8 10 12 14 16x10 Age [y b2k]

Fig. 6. The old (red) and updated (green) temperature reconstruction using the proposed thinning function S′(z). The signal is filtered by applying a low pass filter with a cut–off at 1ky (thick lines) and 200y (thin lines). In blue we present the low–pass filtered δ18O signal with a cut–off at 1ky (thick line) and 200y (thin line) In purple we plot the temperature reconstruction from Vinther et al. (2009) where an offset of 241K has been added and in black the borehole temperature reconstruction by Dahl Jensen et al. (1998). Accumulation Reduction [%]

] 0.30 -1 20 0.25 15 0.20 10 0.15

0.10 5

0.05 Accumulation Rate [myr 0 1.0 Diffusion Length [m] 0.8 0.10

0.6 Total Thinning 0.4 0.05

200 400 600 800 1000 1200 1400 1600 Depth [m]

Fig. 7. The old (red) and new proposed (blue) accumulation rate (A(z),A′(z)) and thinning history (S(z), S′(z)) for the North GRIP site based on the tuning of the Holocene optimum signal at 8ky b2k to 3 K with respect to the level of 225 y b2k. With the dark gray line we illustrate the % proposed reduction in accumulation rates. At the bottom graph the black curve presents the raw diffusion length signal ′ σi (z). Accounting for the two different scenarios of the thinning function S (z) and S (z) we obtain the red (old) and blue (updated) curve ′ for σﬁrn (z) and σﬁrn (z)