A new method of resolving annual precipitation for the past millennia from Tibetan ice cores

Net accumulation records derived from ice cores provide the most direct measurement of past precipitation. However, quantitative reconstruction of accumulation for past millennia remains challenging due to the difficulty in identifying annual layers in the deeper sections of ice cores. In this study, we propose a new method to quantify annual accumulation from ice cores for past millennia, using 20 as an example an ice core drilled at the Chongce ice cap in the northwestern Tibetan Plateau (TP). First, we used the Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS) technology to develop an ultra-high-resolution trace element records in three sections of the ice core and identified annual layers in each section based on seasonality of these elements. Second, based on nine C ages determined for this ice core, we applied a two-parameter flow model to established the thinning 25 parameter of this ice core. Finally, we converted the thickness of annual layers in the three sample sections to past accumulation rates based on the thinning parameter derived from the ice-flow model. Our results show that the mean annual accumulation rate for the three sample sections are 102 mm/year (2511-2541 a B.P.), 76 mm/year (1682-1697 a B.P.) and 84 mm/year (781-789 a B.P.). For comparison, the Holocene mean precipitation is 103 mm/year. This method has the potential to reconstruct continuous 30 high-resolution precipitation records covering millennia or even longer time periods. 1 https://doi.org/10.5194/tc-2021-115 Preprint. Discussion started: 26 May 2021 c © Author(s) 2021. CC BY 4.0 License.


General Comments
Zhang et al. "A new method of resolving annual precipitation for the past millennia from Tibetan ice cores" presents a detailed study on the average accumulation rate for 3 epochs in the last 2500 years for an ice core site on the Chongce ice cap, northwestern Tibetan Plateau. The paper combines annual layer thickness data (from ultra-high resolution ice core elemental chemistry) with a flow thinning model (constrained by water-insoluble organic carbon 14 C ages) to determine local net accumulation over 3 disjoint epochs. The paper is well written and structured and generally presents sufficient supporting evidence. I recommend minor alterations and corrections detailed below.

Major specific comment
The most significant problem with the manuscript as it stands is the data fit to the flow model presented in Figure  2 and associated text on P8 L228-229. In particular, it appears that all of the 14 C ages are above the nonlinear least squares data fit. This raises questions about the validity of the data fit and if the solution has converged. I would have expected at least some of the 14 C ages to be below the data fit. Specially, the data fit line can be moved upward and this would reduce the error at every observational data point, and hence the overall error of the fit. The authors need to verify that the data fit presented is indeed a (near) optimal fit, and redo the accumulation analysis if the data fit needs to be revised and improved. Response: In this study, the depth-age relationship of the Chongce 135.81 m Core 2 was established by using a twoparameter (2p) model. The 2p model was first constrained by the 14 C calibrated ages, together with the β-activity reference horizon of the Chongce 58.82 m Core 3, located only ~ 2 meters apart (Hou et al., 2018;Pang et al., 2020). We found that by using these data only, the 2p model is poorly constrained at the deep section, and giving an estimate bottom age much older than the bottom age (8.3 ± 3.6 6.2 ka B.P.) estimated for Core 4 (Hou et al., 2018). Therefore, we included the Core 4 bottom age to constrain the final 2p model. Due to its mathematical configuration to account for ice flow dynamics, the 2p model gives more weight to points at deeper sections. Therefore, the inclusion of the Core 4 bottom age (relatively younger than otherwise derived bottom age) pushes the curve towards the left (younger) of most 14 C dates. However, we believe this model gives the most reasonable results, compared with several other model fit based on different data combinations ( Figure 1). The details of these model fits are provided as follows.
(1) all data (including β-activity peak of Core 3 and nine 14 C ages) (Fig. 1a). Results: The derived annual accumulation rate of 137 ± 54 mm w.e./year is in good agreement with the value of 140 mm w.e./year based on the tritium horizon. But the model is poorly constrained in deeper sections: the derived age estimate at the depth of the deepest 14 C sample is 9.1 ± 4.0 7.2 ka B.P.. This is much older than the actual measured 14 C age of 6.3 ± 0.2 ka B.P. at that depth (Fig. 1a).
Results: The derived ice age at the bedrock is 30.7 ± 18.4 44.8 ka B.P., which is much older than the bottom age (8.3 ± 3.6 6.2 ka B.P.) estimated for Core 4. In addition, the derived age estimate at the depth of the deepest 14 C sample is 9.2 ± 3.6 6.0 ka B.P.. This is much older than the 14 C age of 6.3 ± 0.2 ka B.P. at that depth. (Fig. 1b).
Results: The derived ice age at the bedrock is 50.1 ± 35.6 118.4 ka B.P., which is much older than the bottom age (8.3 ± 3.6 6.2 ka B.P.) estimated for Core 4. In addition, the derived age estimate at the depth of the deepest 14 C sample is 9.6 ± 4.1 7.3 ka B.P.. This is much older than the 14 C age of 6.3 ± 0.2 ka B.P. at that depth ( Fig. 1d).
(5) all data (including β-activity peak of Core 3 and nine 14 C ages) plus bedrock estimate from Core 4 (Hou et al., 2018) as an additional model input point (the method used in this manuscript) (Fig. 1e).
Results: The derived ice age at the bedrock is 9.0 ± 3.6 7.9 ka B.P., which is roughly consistent with the bottom age (8.3 ± 3.6 6.2 ka B.P.) estimated for Core 4. The derived accumulation rate (103 ± 34 mm w.e./year) is in relative agreement with the β-activity based estimate (140 mm w.e./year). In addition, the modeled age at the depth of the deepest 14 C sample is now 5.2 ± 1.2 1.9 ka B.P. which, with the uncertainty range, is similar to the 14 C age of 6.3 ± 0.2 ka B.P. (Fig. 1e). We believe this model provides most reasonable results, and is therefore adopted for this paper.

Minor specific comment
P2 L40 Is Christiansen and Ljungqvist (2017) the correct citation? This paper is about temperature reconstruction, and only mentions precipitation because of its influence on temperature reconstructions. Response: We replaced this citation with Sun et al., 2018, which presented a comprehensive review of the data sources and estimation methods of 30 currently available global precipitation data sets, including gauge-based, satelliterelated, and reanalysis data sets.
P2 2 nd paragraph. This needs a restructure, at the moment, the sentence topics are annual layers, thinning, annual layers then thinning again. Suggest you move the sentence starting "In addition, the nonlinear" to after the sentence starting "The most common approach". Then change "The thinning parameter" → "This thinning parameter".
Response: We agree with the reviewer, and have revised the sentence accordingly. The revised sentence is as follows; The most common approach is to obtain annual-layer thickness based on the seasonal cycles of ice core parameters such as stable isotope ratio of oxygen in the water (δ 18 O), the concentration of major ions (e.g. Ca 2+ , Mg 2+ , NH 4 + , SO 4 2-), and the presence of melt layers (Thompson et al., 2018). In addition, the nonlinear thinning of annual layers caused by ice flow must be suitably constrained (Bolzan, 1985;Henderson et al., 2006;Roberts et al., 2015).
P3 L80 I think the location map (Fig. S1) should be moved into the main manuscript, as this is key information.
Response: We agree with the reviewer, and have included the location map (Fig. S1) in the main text of the manuscript.
P5 Section 2.3 You do not give the vertical size of the samples required to give the 1kg sample, this is key information for the depth uncertainty estimate of the β-activity dating.
Response: We have given details on ice samples for β-activity measurements (Table S1) in the supporting information. P5 L130 Was the Argon gas flow purged or was the system purged using Argon gas? If the later, suggest changing "whilst the Argon (Ar) gas flow was purged for two minutes" → "whilst the system was purged with Argon (Ar) gas for two minutes".
Response: We thank the reviewer for clarification, and have revised this sentence accordingly, as "whilst the system was purged with Argon (Ar) gas for two minutes".
P5 Section 2.4 you do not give the vertical size of the samples used for the 14 C extraction, this is key information for the uncertainty estimate of the 14 C dating, as there is uncertainty in both the age and depth.
Response: We have given the vertical size of the samples used for the 14 C extraction in the supporting information.
P6 L188-189 These grouped peaks could also be from independent snow events with dry wind blown dust deposition between these snow events.
Response: We agree with the reviewer, and have revised the text accordingly. The revised sentence is as follows; These grouped peaks are interpreted as independent snow events with elevated element concentrations or with windblown dust deposition between these snow events.
P9 L241-242 Make it clear that you are using the values of "b" and "p" that you found in Section 3.2.
Response: We have revised this sentence as "where ( ) is the modeled annual layer thickness (mm w.e.) for the average accumulation rate (b, i.e., 103 ± 34 mm w.e.) at the depth of z given the thinning parameter of p (i.e., 0.008).". P10 L257 Change "can be securely stored" → "is preserved". In fact your density profiles (Fig. S6) suggest this for Core 2 and 3, which both lack the lower densities near the surface indicative of snow. I suggest you add a sentence at Line 258 making this point.
Response: Following the reviewer's comment, we have revised this sentence as "However, not all snowfall is preserved in high-elevation glaciers, due to wind scouring, snow drifting, and sublimation (Hardy et al., 2003). Moreover, firnification process might develop rapidly as indicated from the lack the lower density layers (indicative of snow) near the glacier surface (Fig. S6) Response: We agree with the reviewer, but because the density profile of the Guliya ice core is not available (Thompson et al., 1995), we are not able to calculate the accumulation rate of the Guliya ice core as mm w.e./yr, but this comparison is still reasonable given the similar density for the periods of 1950-1989 A.D. and 1160-1169 A.D. P10 L284-286 This statement is not correct. For example, an error in either the 14 C dating, or the flow model fit (see main points above) will introduce an error in the flow thinning model, which due to its non-linear nature will result in different relative average accumulations over various epochs.
Response: We agree with the reviewer. For this reason, we deleted this statement in the revision. P11 L295-299 In fact you already have 9 such markers from the 14 C age ties, which allow you to calculate the average accumulation rate over the 8 epochs these 9 makers define.
Response: This suggestion is theoretically possible, but we are not able to calculate the average accumulation rates over the 8 epochs between the 9 14 C age ties because the errors of the 14 C ages cause overlaps of some ages.
Supp info, Figure 1b give details of where the remote sensing data is from, what is the instrument (e.g. optical, SAR) and give a data citation.
Response: We have included details about the remote sensing data, and provided a citation in the supporting information.
Supp info, Figure S8 Give details of which core (or cores) are being compared here.
Response: We have included details of the ice cores in the supporting information.
Supp info, Table S1 is the depth in meters water equivalent? Explain the difference between " 14 C age" and "cal age".
Response: The depth in Table S2 is the measured depth in the field. For convenience of the readers, we also included the depth in meters water equivalent in the revision after taking account of the density profile.
Regarding " 14 C age" and "cal age", " 14 C age" denotes conventional radiocarbon age, which is calculated from the formula below: t = -8033 × ln (Fs) where t is conventional radiocarbon age, Fs is the 14 C / 12 C ratio of the sample divided by the same ratio of the modern standard. "cal age" denotes the calibrated age using OxCal v4.3 (Ramsey and Lee, 2013) with the Northern (IntCal13) calibration curve. P2 L34 Kidd and Hoffman 2011 do not say "most important" only "variable parameter associated with atmospheric circulation". Delete "most important".
Response: Correction has been made accordingly.