A mid-Holocene case study Investigating the consistency between proxies and between proxies and models using data assimilation: a mid-Holocene case study

The mid-Holocene (6 thousand years before present) is a key period to study the consistency between model results and proxy data as it corresponds to a standard test for models and a reasonable number of proxy records are available. Taking advantage of this relatively large amount of information, we have ﬁrst compared a compilation of 5 50 air and sea surface temperature reconstructions with the results of three simulations performed with general circulation models and one carried out with LOVECLIM, a model of intermediate complexity. The conclusions derived from this analysis con-ﬁrm that models and data agree on the large-scale spatial pattern but underestimate the magnitude of some observed changes and that large discrepancies are observed 10 at the local scale. To further investigate the origin of those inconsistencies, we have constrained LOVECLIM to follow the signal recorded by the proxies selected in the compilation using a data assimilation method based on a particle ﬁlter. In one simulation, all the 50 proxies are used while in the other two, only the continental or oceanic proxies constrains the model results. This assimilation improves the consistency be- 15 tween model results and the reconstructions. In particular, this is achieved in a robust way in all the experiments through a strengthening of the westerlies at mid-latitude that warms up the Northern Europe. Furthermore, the comparison of the LOVECLIM simulations with and without data assimilation has also objectively identiﬁed 16 proxies whose reconstructed signal is either incompatible with the one recorded by some other 20 proxies or with model physics.


Introduction
The Holocene, our current interglacial, has been the subject of a large number of studies based on reconstructions derived from proxy records (e.g., Bartlein et al., 2011;Davis et al., 2003;Leduc et al., 2010;Marcott et al., 2013;Viau and Gajewski, 2009; In particular, the mid-Holocene, corresponding to 6 ky BP (thousand years before present), is a standard period in the Paleoclimate Modelling Intercomparison Project (PMIP) for which boundary conditions have been specified to facilitate the comparison between models results and with reconstructions. One of the most robust conclusions of those model studies is that the summer of the mid to high latitudes of the Northern Hemisphere is warmer during the mid-Holocene compared to the pre-industrial conditions (Braconnot et al., 2007a). This is consistent with the trends of the pollen-based reconstructions of Bartlein et al. (2011) and Davis et al. (2003) for Northern Europe and with several other proxy records (e.g., Andreev et al., 2003;Clegg et al., 2010;Marcott et al., 2013;Birks, 2002, 2001;Vinther et al., 2009). 15 The model-data comparisons have nonetheless underlined some major differences between reconstructions and simulation results. Brewer et al. (2007b) have highlighted that PMIP2 models are able to capture the large-scale surface temperature patterns over Europe reconstructed from pollen records, but they tend to underestimate the magnitude of the observed changes, which is also in agreement with the conclusion 20 of Braconnot et al. (2007a). Lohmann et al. (2012) have found similar results when analyzing the trends of annual mean sea surface temperature of the last 6000 yr obtained from alkenone data: the large-scale spatial pattern derived from the proxies is consistent with the ones of models, while the latter underestimate the magnitude of the changes.
of information, derived here from a climate model, the forcing and the proxy records. By performing different experiments, driven by different subsets of proxies, we plan to identify the ones that are compatible with model physics, the ones that are not, and those that are incompatible with other proxy records.
We focus on the mid-Holocene as this is a well-documented period. LOVECLIM1.2 10 (Goosse et al., 2010), a three-dimensional Earth Model of Intermediate Complexity, is constrained to follow a compilation of 50 air and sea surface temperature reconstructions located in the Northern Hemisphere by means of a particle filter with resampling (Dubinkina et al., 2011). These simulations with data assimilation will be compared with a simulation performed with LOVECLIM without data assimilation and with three GCMs 15 (General Circulation Models) simulations following the PMIP3-CMIP5 framework (Paleoclimate Models Intercomparison Project phase 3 -Coupled Model Inter-comparison Project phase 5) in order to assess the dependance of model-data differences on the model selected.
The methodology is presented in Sect. 2, including a description of LOVECLIM, the similation can be performed at a reasonable cost. This model includes three main components named ECBilt2, CLIO3 and VECODE, which represent the development of the atmosphere, the ocean and the vegetation, respectively. ECBilt2 is a spectral T21 (corresponding to about 5.625 • in latitude and longitude) global 3-level quasi-geostrophic model (Opsteegh et al., 1998). CLIO3 is an ocean general circulation model coupled 10 to a comprehensive sea-ice model (Goosse and Fichefet, 1999). It has a horizontal resolution of 3 • × 3 • and 20 unequally spaced vertical levels ranging from 10 m near surface to 500 m at 5500 m depth. VECODE is the continental biosphere component that describes the distribution of trees, grass and desert at the same resolution as EC-Bilt2 (Brovkin et al., 1997). For a complete description of LOVECLIM1.2, please refer to Goosse et al. (2010).

Assimilation method
The particle filter with resampling applied here is identical to the one described in Dubinkina et al. (2011) and used in several recent studies (e.g., Goosse et al., 2012;Mathiot et al., 2013). An ensemble of 96 simulations, also referred to as particles or 20 ensemble members, is first initiated from slightly different states obtained by perturbing the surface temperature of an equilibrium experiment under the same conditions as the simulation without data assimilation (Dubinkina and Goosse, 2013). Due to the chaotic nature of the climatic system, each particle evolves in a different way. After the assimilation step, which is six months here, the likelihood of each member of the difference between mid-Holocene (the period 5500-5000 y BP) and modern conditions (the period 950-450 y BP). This function is computed for all the locations and months for which paleodata is available. The particles that have the largest likelihood are retained. The other ensemble members are rejected. The remaining particles are resampled a number of times proportional to their likelihood in order to keep the num-10 ber of particles constant and avoid a degenerative issue. For more details about the resampling method please refer to Dubinkina et al. (2011). A small perturbation of surface temperature is then added to the initial conditions of the members that have been sampled more than once, and the particles are propagated forward in time using the climate model. The whole procedure is repeated until the end of the simulated period 15 (which corresponds to 400 yr here).

The proxy dataset
Numerous surface and sea surface temperature reconstructions derived from proxies are available for the Holocene. These reconstructions are derived from marine, continental and ice archives using different methods such as, among others, the Alkenone 20 Paleothermometry (Grimalt and Lopez, 2007;Herbert, 2003), the modern Analog Technique (Brewer et al., 2007a) or the Stable Isotopes Analysis (Brook, 2007). Each quantitative reconstruction has its strengths and weaknesses (Birks et al., 2010;Juggins, 2013;Telford and Birks, 2005). For instance, almost all of them are influenced by the confounding effects, which means that environmental variables other than the climate 25 variable of interest influence the reconstruction (Birks et al., 2010;Ortiz, 2007). For instance, a summer temperature derived from pollen records could include a signal related to winter temperature or precipitation (Birks et al., 2010). Furthermore, attributing 3958 pretation proposed in the original studies describing the proxies. For instance, if the reconstructed signal represents the summer surface air temperature according to the authors of those studies, this is also the case for us. The proxy dataset used in the simulations with data assimilation results from a selection among more than 300 Holocene records according to the following criteria: (i) the 10 record represents the air or the sea surface temperature, (ii) comes from archives located between 20 • N and 90 • N, (iii) has a mean temporal resolution of at least 250 yr for the mid-Holocene time-slice (6 ± 0.5 ky BP) and for the reference period (950 to 450 yr BP), as we work with anomalies related to this period (Sect. 2.2). (iv) If multiple reconstructions with different temporal interpretations are located within the same 15 model grid, the seasonal reconstructions are retained, as we consider that it provides more information on the system. On the basis of these criteria, we have selected 50 records of air and sea surface temperature for the mid-Holocene (Table 1). For each selected record, an anomaly is calculated between the mean value of the period of interest (6 ± 0.5 ky BP) and the mean value of the reference period (500 yr) (Fig. 1). As 20 we perform averages over periods that are longer than the dating uncertainties of the records, we neglect any potential biases related to those dating uncertainties.
Furthermore, if two reconstructions which represent the same physical variable at the same period of the year are located in the same model grid, they are merged. This is the case for the proxies number 2 (hereafter N2) and N2 which are merged 25 under the identifier N2. In the evaluation of the likelihood, we assume that the proxies represent the climate of the scale of the model grid, except for the reconstructions of Davis et al. (2003) and Viau and Gajewski (2009)  Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | before computing the model-data difference. Therefore, the signal reconstructed from the proxies is representative on a 3 • grid box for CLIO3 and a 5.625 • grid box for ECBilt2. Finally, an estimation of the uncertainty for each reconstruction derived from proxies is required for data assimilation. This information is frequently not available, and when it is, these uncertainties are often very large and thus sometimes of the same order as the signal itself (Ohlwein and Wahl, 2011). As in Mathiot et al. (2013), we have thus deliberately selected here lower bounds for those uncertainties in order to provide a strong constraint on the model during the data assimilation process. By simplicity, we have also chosen only one error for each proxy type (Table 1) based on values provided in previous studies (e.g., Heikkilä and Seppä, 2003;Martrat et al., 2007;Mathiot et al., 2013;Müller et al., 1998;Seppä and Birks, 2001). Those values of the uncertainties affect weakly the spatial patterns but influence the magnitude of the changes induced by the data assimilation processes (Goosse et al., 2012). This will be taken into account in the interpretation of our results.

Experimental design
Three mid-Holocene simulations with data assimilation are performed and compared to a mid-Holocene reference simulation realized with LOVECLIM, named NODATA (Table 2). In two simulations either the continental or the oceanic proxies are assimilated and in one simulation these proxies are assimilated together. They are named CON, 20 OCE and ALL, respectively. The objective is to propose two extreme cases in which we either constrain the model by only the continental archives or by only the signal inferred from oceanic proxies in order to identify the signal brought by each subset as well as the compatibility between model physics and the proxies, and between the proxies themselves. In addition, a simulation spanning the reference period (950 to 450 yr BP) 25 is required as the likelihood in the data assimilation process compares proxy anomalies with modeled anomalies (Sect. 2.2). This simulation is driven by both natural and anthropogenic forcings as in Crespin et al. (2013) We also analyse simulations performed with GCMs to allow the comparison of the LOVECLIM results with the ones from three state-of-the-art models: BCC-CSM1-1, CSIRO-Mk3L-1-2 and MPI-ESM-P. For details about these models, please refer to the references listed in Table 2. These models were chosen because at the time of our analysis they were the only ones on the CMIP5 data portal that provide the variables 5 needed for our diagnostics over the period 950-450 yr BP and the mid-Holocene.
The four mid-Holocene simulations performed with LOVECLIM are either 200 yr (NO-DATA) or 400 yr long (ALL, CON and OCE). The lenght of the simulation NODATA is smaller because it is the prolongation of an equilibrium simulation in the same conditions. The four simulations are driven by the same constant forcing which is identical 10 to the one used by Mathiot et al. (2013). The orbital parameters follow Berger (1978). The greenhouse gas concentrations are based on the data of Flückiger et al. (2002). The Laurentide ice sheet topography and surface albedo have been adapted for LOVE-CLIM by Renssen et al. (2009) from the reconstruction of Peltier (2004). In comparison to the present, the changes in topography and surface albedo are extremely small. As  Renssen et al., 2009). This design is slightly different from the PMIP3 protocol 20 used in GCMs as the latter assumed a similar ice sheet topography as the present one and no additional freshwater fluxes from ice sheet melting. But this has only a very marginal effect on our results at 6 ky BP. 3961 3 Results and discussion

Simulations without data assimilation
The climate anomalies simulated by LOVECLIM and the selected GCMs for mid-Holocene conditions display similar large-scale patterns (Fig. 2) and are consistent with previous modeling studies (e.g., Braconnot et al., 2007a). They all depict warmer 5 air and sea surface temperature during the mid-Holocene summer and cooler air surface temperature during the winter, except in the Arctic. The mid-Holocene seasonal cycle amplitude is then more pronounced than the one of the reference period for most of the location in the Northern Hemisphere. This signal is mainly caused by the higher (lower) summer (winter) insolation for mid-Holocene (Braconnot et al., 2007a;Wanner et al., 2008). The winter Arctic warming is due to a memory effect associated with the summer insolation as the latter induces a decrease in ice thickness which leads to larger oceanic heat fluxes during the autumn and the winter, and then to a surface temperature increase during these seasons (Renssen et al., 2005).
In comparison with the first half of the last millennium, the westerlies are slightly 15 weakened during the mid-Holocene in LOVECLIM in winter (Fig. 3). This appears consistent with smaller meridional gradient in temperature due to the Arctic warming and leads to a tendency towards more negative NAO state in the model for that period. BCC-CSM1-1 also shows a weakening of the westerlies in the Pacific during the mid-Holocene while MPI-ESM-P and CSIRO-Mk3L-1-2 show a slight strengthening. These 20 results are consistent with an analysis of PMIP2 simulations realized by Gladstone et al. (2005) showing that many models display anomalies similar to either positive or negative NAO phases during the mid-Holocene compared to present day but without a clear and robust signal common between the different models. The mid-Holocene reconstruction based on proxies (Fig. 2)  Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | proxies for the same seasons, in contrast to model results. Risebrobakken et al. (2003) argue that this reconstructed cooling in the Norwegian sea may rather represent a subsurface signal, explaining the discrepancy with other estimates of surface temperature in the region. Over Europe, the northern part is warmer during the mid-Holocene and the southern one is colder all year long in the proxy-based reconstruction. Those ica, surface temperature is slightly warmer in the reconstructions over the western part while it is colder over the eastern part, a signal that appears thus weaker than the one simulated by models. A more quantitative model-data comparison shows that the magnitude of the signal (estimated here by the standard deviation of the anomalies) is much weaker in models, with a mean value of 0.9 • C, than in reconstructions based on proxies which reach a value of 1.6 • C (Fig. 4). The difference is seen both for continental and oceanic proxies but is more marked over the ocean where the signal in the proxies is 4.5 times greater than one of models, a result consistent with the recent findings of Lohmann et al. (2012). According to Fig. 4, the mean signal recorded by the selected proxies 20 is larger over the ocean that over land by about 0.5 • C. This might appear surprising as the oceanic response to many forcings is expected to be smaller than the one over continents because of the larger thermal inertia of the ocean and of various feedbacks (e.g., Boer, 2011). Investigating in detail this issue is out of the scope of this study but it might be related to the too small number of proxies used here to estimate precisely the 25 mean over oceans and continents or to the location of oceanic proxies that represent relatively local-regional phenomena in coastal areas or close to fronts and thus not the mean open ocean conditions. Additional information on the local agreement between model results and proxy reconstructions can be obtained by computing the Root Mean Square Error (RMSE) defined as where n is the number of proxies, ∆T obs i is one particular mid-Holocene air or sea sur-5 face temperature anomaly derived from a proxy record and ∆T mod i is the corresponding modeled value. The minimum RMSE value for the different models is 1.7 • C (Fig. 4).
This is larger than the mean signal, showing that the models have nearly no skill at the local scale as discussed in Hargreaves et al. (2013). Furthermore, the RMSE is larger for the oceanic proxies than for continental proxies in all the models. Actually, models 10 results are in much better agreement between themselves than with the proxies as the root mean square difference between different models, at locations for which proxies are available, is close to 0.6 • C on average (i.e. about a third of the RMSE shown in Fig. 4). Nevertheless, this quantitative evaluation of model performance based on results at 15 the grid scale could be considered as a too strong test on several aspects. First, it does not take into account proxies uncertainties. Second, any small spatial shift in the model response compared to data would lead to large errors (e.g., Guiot et al., 1999). Third, model results and proxy records do not necessarily represent the climate at the same scale, leading to difference in the recorded signal, in particular on its magnitude.

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As a consequence, we have divided for Fig. 5a all the proxies into three categories: (i) LOVECLIM agrees with the proxies with error bars, (ii) LOVECLIM agrees only with the sign of the proxy record anomaly, (iii) it does not agree with the sign of the proxy record anomaly. This is displayed for the LOVECLIM model but the results are similar for the three GCMs (not shown). This leads to much more encouraging results than the 25 conclusions derived from the analysis of the RMSE since LOVECLIM mid-Holocene 3964 Introduction simulation agrees with the sign of the anomaly of about two thirds of the proxies. This agreement displays no clear dependance on the season, on the location of the proxies or on the type of the proxies.

Simulations with data assimilation
Although the results of simulations constrained by data assimilation will be presented 5 in a quantitative way, our interpretation will often be more qualitative for the two following reasons. First, as mentioned in the methodology section, the proxies uncertainty selected here has a potential influence on the amplitude of the difference between the simulations with and without data assimilation. Second, the disagreement between LOVECLIM without data assimilation and proxies is large. Although some improvement 10 are obtained due to data assimilation, it is not expected to have a model state which displays values fully consistent with proxy records. This would for instance require additional perturbations within the ensemble of simulations, for example in model parameters, and thus to develop a specific experimental design. This is out of the scope of this paper, as we would like to focus, in this first study devoted to the mid-Holocene 15 climate, on an estimate of the compatibilities between models and proxies. By construction, the data assimilation method applied in LOVECLIM for the mid-Holocene period provides with results that are locally more consistent with the proxies that are assimilated than with any other simulation performed without data assimilation selected in this study (Fig. 4). Indeed, the simulation constrained by all the proxies, 20 displays the RMSE of 1.6 • C which is 15 % closer to the proxy anomalies compared to the model without data assimilation. The RMSE between this simulation and the proxies is thus of the same magnitude as the mean signal of the proxies from the mid-Holocene (1.6 • C). The assimilation of the continental proxies alone gives the RMSE of 1.5 • C, which corresponds to a reconstruction which is 22 % closer to the proxies 25 that are assimilated compared to the model without data assimilation. Finally, the data assimilation of the oceanic proxies alone provides with a reconstruction that is 15 % 3965 closer to those oceanic proxies, inducing almost a doubling of the simulated oceanic signal compared to the simulation without data assimilation. The Fig. 4 shows also that the assimilation process in ALL leads LOVECLIM to be more consistent with the continental proxies than with the oceanic ones, which is due to the combination of two effects. First, the estimated error of the continental proxies 5 is smaller than the oceanic records (Table 1), which means that in the computation of the likelihood a larger weight is given to the continental archives. Second, the model atmospheric fields and the surface temperature over land have a greater variance than the oceanic ones. Among the ensemble of simulations, it is thus more common to have members that are in agreement with continental proxies. This leads to a larger 10 impact from the continental proxies if both domains are assimilated together and strong similarities between the simulation constrained by all the proxies and the one that is based on the continental proxies only.
Although data assimilation only marginally reduces the RMSE between model and data, the amount of proxies for which LOVECLIM does not agree with the sign of the 15 anomalies decreases by about 20 % in OCE and about 30 % in CON and ALL compared to NODATA (Fig. 5). This is mainly caused in the reconstruction CON and ALL by a slight summer warming over North-East Europe, the Barents sea and the Kara sea and by a summer cooling around Lake Baikal as well as by a winter warming from North-East Europe to Lake Baikal, over North of Greenland and over the central part of 20 North America (Fig. 6). In these simulations, the improvement of sea surface temperature is mainly related to a warming along the coast of North-America at about 40 • N. In the simulation OCE the higher number of proxies that have the same anomalies as the model is mainly due to an annual warming of the North Atlantic and a summer warming in the North Pacific close to the West coast at 45 • N (Fig. 6). Consequently, 25 data assimilation drives the LOVECLIM model to a state which is maybe still not in the range of the anomalies derived from the proxies but that is at least more consistent with the sign of their changes.

3966
The three experiments with data assimilation also allow us testing the influence of the data assimilation over the different domains (continent and ocean) on all the proxy by grouping them in three categories (Fig. 7), but on different basis compared to the Fig. 5. The first category consists of proxies for which LOVECLIM results without data assimilation were already consistent with the proxies signal, i.e. the difference between 5 model results and proxy-based reconstruction is smaller than the error assigned here. Moreover, assimilation of these proxies does not deteriorate the consistency between the model results with data assimilation and the signal recorded by the proxies. This category concerns 22 % of all the proxies used in this study. These proxy records can be identified individually on the basis of the numbers on the Fig. 1, using the Table 1. 10 The second category (45 % of all the proxies) deals with the proxies that satisfy the two following criteria: (i) at least in one of the two simulations performed with data assimilation in which these proxies are used, they are more consistent with the results with data assimilation than with the results without data assimilation. (ii) These proxies are not less consistent with the results with data assimilation than with the results 15 without data assimilation if they do not comply with the first rule. This corresponds to all the continental (oceanic) proxies for which the anomaly difference in absolute value decreases by at least 5 % in ALL and/or CON (ALL and/or OCE) and does not increase by more than 5 % in the other(s) simulation(s) with data assimilation. For 66 % of the proxies included in this category (28 % of all the proxies), the anomalies 20 in the three simulations with data assimilation are closer to the proxy record anomaly than in the model without data assimilation. This implies that the model dynamics is able to propagate the signal brought by the assimilated proxies towards the locations where no data is assimilated and also that the information brought by these 28 % of proxies is coherent. The third category (33 % of all the proxies) includes the proxies that 25 are either (i) less consistent (5 % threshold) with at least one of the three simulations with data assimilation compared with the simulation without data assimilation, or that are (ii) not more consistent with any simulation with data assimilation than with the simulation without data assimilation. In the majority of the cases (70 % of the proxies 3967 by the models, in the interpretation of the proxy signal, in the way models and proxies are compared. Our experimental design does not allow us determining which of those is dominant for each proxy record but it indicates that a special attention has to be given to those regions to understand the causes of this disagreement. This is the case, for instance, for the continental proxy N42 whose signal is opposite to the one depicted by the oceanic proxies N4, N7, N9 and N10. Another example is the oceanic proxy N15 whose signal shows a summer negative anomaly opposite to the positive one illustrated by the nearby continental proxies. This incompatibility consolidates the interpretation of Risebrobakken et al. (2003) that this proxy record should not be considered as an estimate of surface temperature. Finally, the proxies that are never more consistent with 15 the simulations performed with data assimilation, indicate a profound disagreement between their information and the model physics. For instance, the model is not able to reproduce the summer (winter) cooling over the Southern-West (Northern-West) Europe depicted by the proxies N43 (N38) with data assimilation as already mentioned for LOVECLIM and the GCMs without data assimilation.

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The improvement brought by data assimilation can be related to modifications of both winds and ocean currents. The atmospheric circulation changes associated with data assimilations in ALL, CON and OCE have a lower magnitude that the one in response to the forcing in NODATA for the summer, while for the winter, these changes are at least of the same magnitude as the model response to forcing (Fig. 8). All the 25 experiments constrained by data assimilation display a decrease in geopotential height at high latitudes and an increase at mid latitudes in winter compared to NODATA, the signal in summer being weaker. This strengthens the westerlies over the North Atlantic inducing a winter warming from the Northern Europe to the Lake Baikal as well as over North America (Fig. 6). This is consistent with the findings of Rimbu et al. (2003), who indicate, using alkenone data, that the NAO was more likely in a positive pattern phase during the mid-Holocene with respect to our reference period. The induced surface temperature changes are more pronounced during the winter since during these months the atmospheric circulation endures the stronger changes. Fur-5 thermore, changes in atmospheric circulation are stronger in the OCE simulation than in the simulations ALL and CON (Fig. 8). This induces stronger westerlies over the Pacific and, therefore, a stronger warming over North America (Fig. 6). In winter the pattern over the North Atlantic is more complex in OCE than in the other experiments, with stronger westerlies northward of 50 • N and weaker ones between 40 • N and 50 • N. 10 The spatial structure of the changes of annual mean sea surface temperature and surface current between each simulation performed with data assimilation and the simulation NODATA are similar, both in the North Atlantic and the North Pacific. Therefore, the figures are shown only for ALL (Fig. 9). In the Pacific, the strengthening of the westerlies produces an intensification of the northern branch of the North Pacific 15 Gyre, which is stronger on the eastern part compared to the western part. This tends (i) to transport the warmer water from the northern extension of the Kuroshio eastward (around 45 • N). It leads to warmer sea surface temperature and a warming of the atmosphere by the ocean. (ii) This also transports the colder western and northern Pacific water (cooled by the Siberian winds) toward the warmer eastern Pacific following the 20 gyre cycle. The pattern is most marked in the simulation OCE than in the others two (Fig. 6) as the westerlies are more intensified in this simulation. Additionally, the northward shift of the westerlies slows down the winds around 30 • N in the western Pacific which induces a reduced heat loss by evaporation and, therefore, a warmer sea surface temperature at this location. These two processes occur also in the Atlantic Ocean. The 25 first is associated with an intensification of the gulf stream current at around 40 • N due to stronger winds at this location (Fig. 8)  results from the ice front shifting. This feature is not robust as it is not present in all our experiments. The meridional overturning circulation is also slightly stronger in the Atlantic in the simulations with data assimilation compared to NODATA. The difference between the maximum in ALL-CON-OCE and the maximum in NODATA is, however, smaller than 1 Sv, which corresponds to an increase of the meridional heat transport at 5 30 • S between 2 % (5 TW) and 8 % (18 TW) compared to the mean value in NODATA, contributing to some extent to the large-scale warming of the North Atlantic.

Conclusions
The conclusions derived from our analysis of simulations performed with GCMs and with LOVECLIM with and without data assimilation for the mid-Holocene can be sum-10 marized as follows: 1. In agreement with previous studies, a direct evaluation of the mean error of mid-Holocene simulations performed without data assimilation suggests that models have nearly no skill at the local scale compared to proxy data and that the models agree much better between themselves than with proxies. A comparison of the 15 dominant patterns and of the sign of the changes, taking into account the uncertainties in proxies, leads to a much better consistency between models and data although clear disagreements remain in some regions.
2. The simulations with data assimilation are more consistent with the sign of the proxies anomalies and the spatial pattern of the changes than the simulation with-20 out data assimilation.
3. However, for a third of the proxies, data assimilation does not bring any improvement to the agreement with proxy data. For some proxies, it is due to a fundamental inconsistency with model physics, but for the majority of the proxies in this case, this is due to an incompatibility between the various proxies according  Table 1. Air surface (TS) and sea surface (SST) mid-Holocene temperature proxies used in the simulations with data assimilation. Winter corresponds to December to February (DJF) and summer to June to August (JJA). The anomalies and their error are in • C.  (Pelejero et al., 1999) Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |  Mean air and sea surface temperature anomaly ( • C) for all the proxies available for the mid-Holocene. Each marker type corresponds to a different proxy group. Each anomaly represents a month or a particular period (Table 1). If more than one proxy record is given at the same location, the markers representing the proxies are slightly shifted for improved readability.  Fig. 4. From left to right: RMSE between the mid-Holocene anomalies of each simulation (LOVECLIM with and without data assimilation and the GCMs) and the proxies anomalies for three groups of proxies: all the proxies, the continental proxies only and the oceanic proxies only. The mean mid-Holocene signal (estimated as the standard deviation of the anomalies) for the proxies and the model are the black and the grey horizontal bars, respectively. Introduction  Fig. 5. Agreement between the mid-Holocene anomalies in LOVECLIM and in the proxies. Each marker type corresponds to a different proxy group. It is in green when the model agrees with the proxy record within the error bars; In blue, when the model agrees only with the sign of the anomaly; In red, when the model does not agree on the sign of the anomaly. If more than one proxy record is given at the same location, the markers representing the proxies are slightly shifted for improved readability.  . 6. Mid-Holocene air and sea surface temperature anomaly ( • C) for the proxies and the LOVECLIM simulation performed without data assimilation (NODATA). The reference period is 950 to 450 yr BP. Differences between the three simulations performed with data assimilation (ALL, CON and OCE) and the simulation NODATA ( • C). Winter corresponds to December to February (DJF) and summer to June to August (JJA). Percentage and location of mid-Holocene proxies for which: (i) the modeled anomalies without data assimilation and in the three simulations with data assimilation are always within the estimated uncertainty of a particular proxy record (in blue); (ii) the modeled anomaly of at least one simulation with data assimilation is more consistent with the proxy record at the same location if it is assimilated and is not less consistent in the others simulations with data assimilation (in green); (iii) at least one of the three simulations with data assimilation is less consistent with the proxy records than the simulation without data assimilation or that no improvement is brought when they are assimilated (in red). On the map, if more than one proxy record is given at the same location, the markers representing the proxies are slightly shifted for improved readability. Each marker type corresponds to a different proxy group. ALL-NODATA Fig. 9. Mean annual mid-Holocene difference of sea surface temperature ( • C) and surface oceanic current for the Pacific and the Atlantic Ocean between the simulation ALL and the simulation NODATA. The size of the arrows is not proportional to their velocity to improve the readability of the maps since the objective is to show the current direction and not its strenght.