^{1}

^{2}

^{1}

^{2}

<p>Nitrogen and argon stable-isotope data extracted from ancient air in ice cores provides the possibility to reconstruct Greenland past temperatures when inverting firn-densification and heat-diffusion models (firn-models) to fit the gas-isotope data (δ<sup>15</sup>N, δ<sup>40</sup>Ar, δ<sup>15</sup>N<sub>excess</sub>). This study uses the Döring and Leuenberger (2018) fitting-algorithm coupled on two state of the art firn-models to fit multiple Holocene gas-isotope data measured on the GISP2 ice core. We present for the first time the resulting temperature estimates when fitting δ<sup>15</sup>N, δ<sup>40</sup>Ar and δ<sup>15</sup>N<sub>excess</sub> as single targets with misfits generally in the low permeg level. Whereas the comparison between the reconstructions using δ<sup>15</sup>N and δ<sup>40</sup>Ar shows a high agreement, the use of δ<sup>15</sup>N<sub>excess</sub> for reconstructing temperature is problematic, due to higher statistical and systematic data uncertainty influencing especially multi-decadal to multi-centennial signals, and results in an unrealistic temperature estimate that differs significantly from the two other reconstructions. We find evidence for systematic too high δ<sup>40</sup>Ar data in the early- and late-Holocene potentially caused by post coring gas-loss or an insufficient correction of this mechanism. Next, we compare the performance of the Goujon et al. (2003) firn-model and the Schwander et al. (1997) firn-model for Holocene temperature reconstructions. Besides small differences of the reconstructed temperature anomalies – potentially caused by slightly different implementation of firn physics and parameters in the two models – the reconstructed temperature anomalies are highly comparable. We were able to quantify the contribution of the firn-model difference to the uncertainty budget of our reconstruction. Furthermore, the fractions of uncertainty on the reconstructed temperatures, arising from the non-perfect reproducibility of the fitting algorithm and from the remaining final misfits (low permeg level), were quantified. Together with the published measurement uncertainty of the gas-isotope data and the analysis of the impact of accumulation-rate uncertainty on the reconstruction, we were able to calculate the mean uncertainty (2σ) for the nitrogen and the argon based temperature estimates with 2σ<sub>T</sub> = 0.80 ... 0.88 K for T(δ<sup>15</sup>N), and 2σ<sub>T</sub> = 0.87 ... 1.81 K for T(δ<sup>40</sup>Ar), respectively. Finally, we compare our reconstructed temperatures to two recent reconstructions based on the same gas-isotope data as used here, but following different reconstruction strategies: first the study of Buizert et al. (2018), which uses a combination of δ<sup>18</sup>O<sub>ice</sub>-calibration and δ<sup>15</sup>N-fitting, and second the study of Kobashi et al. (2017), where δ<sup>15</sup>N<sub>excess</sub> was fitted in order to conduct the temperature reconstruction. We find generally higher agreement between our T(δ<sup>15</sup>N) estimate and the Buizert et al. (2018) temperature – in terms of variability and correlation in three investigated periodic-time bands (multi-decadal, multi-centennial and multi-millennial) – as if our T(δ<sup>15</sup>N) reconstruction is compared to the Kobashi et al. (2017) temperature. However, all three reconstruction strategies lead to distinct temperature realizations.</p>