the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 Sep 2024
Observations of creep of polar firn at different temperatures
Abstract. To improve our understanding of firn compaction and deformation processes, constant-load compressive creep tests were performed on specimens from a Summit, Greenland (72°35’ N, 38°25’ W) firn core that was extracted in June, 2017. Cylindrical specimens were tested at temperatures of −5 °C, −18 °C and −30 °C from depths of 20 m, 40 m and 60 m at stresses of 0.21 MPa, 0.32 MPa and 0.43 MPa, respectively. The microstructures were characterized before and after creep using both X-ray micro-computed tomography (micro-CT) and thin sections viewed between optical crossed polarizers. Examining the resulting strain vs. time and strain vs. strain rate curves from the creep tests revealed the following notable features. First, the time exponent k was found to be 0.34–0.69 during transient creep, which is greater than the 0.33 usually observed in fully-dense ice. Second, the strain rate minimum (SRMin) in secondary creep occurred at a greater strain from specimens with lower density and at higher temperature. Third, tertiary creep occurred more easily for the lower-density specimens at greater effective stresses and higher temperatures, where strain softening is primarily due to recrystallization. Fourth, the SRMin is a function of the temperature for a given firn density. Lastly, we developed empirical equations for inferring the SRMin, as it is difficult to measure during creep at low temperatures. The creep behaviors of polar firn, being essentially different from full-density ice, imply that firn densification is an indispensable process within the snow-to-ice transition, particularly firn deformation at different temperatures connected to a changing climate.
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RC1: 'Comment on egusphere-2024-2337', Louis Védrine, 21 Oct 2024
The authors introduce a method to quantify the influence of temperature on firn creep. Through laboratory creep tests conducted at various temperatures and with different initial microstructures, they investigate how firn responds under these conditions. The microstructure of the samples is assessed before and after the tests using microtomography and thin-section analysis. Subsequently, the activation energy is determined and compared with the activation energy for grain-boundary sliding, which is estimated based on the observed grain growth rates.
This study represents a notable advancement in modelling the mechanical behaviour of firn, enhancing our understanding of ice material properties and informing the interpretation of ice-core data relevant to paleoclimatology.
However, the methodology used to determine the activation energies is not sufficiently detailed (lines 385–390). Specifically, the authors assume a fixed value for the stress exponent (without providing the actual value) and neglect to mention that the pre-factor A is considered constant across different microstructures and test temperatures. These omissions represent significant methodological shortcomings. I have serious concerns about the validity and applicability of the methodology, raising doubts about the reliability of the results. Therefore, I recommend major revisions.
General comments:
To determine the activation energy, the authors use the Glen-type power law (line 386). This equation introduces the activation energy (Qc), the stress exponent (n), and the pre-factor (A). Thus, to identify the value of Qc, assumptions about A and n must be made
- Prefactor: The authors assume that the pre-factor in the power law remains constant across the different temperatures tested. However, the sample densities vary from 589 kg/m³ to 615 kg/m³ at 20 m depth. This approximation is not mentioned by the authors and must be acknowledged as a limitation of the method.
- Stress exponent: The stress exponent is only mentioned toward the end of the section (lines 462-470), where the values 0.1 and -1.2 are considered. However, the method for determining these values is not explained. Moreover, these exponents are inconsistent with those reported in the literature and in Li and Baker (2022), and they do not align with any known physical behaviour of materials.
A “post-calibration” method is then introduced, which imposes a fixed stress exponent but fails to account for density dependence. This approach leads to variable results, depending on the chosen reference sample. These inconsistencies arise from the identification of the power law using data in which both stress and density vary simultaneously. As demonstrated in Li and Baker (2022a), the strain-rate minimum (SRMin) is dependent on density, with the strain rate decreasing by a factor of 12 when the density increases from 756 to 861 kg/m³. However, the effect of microstructure is overlooked in this study, as it treats samples with densities ranging from 589 to 790 kg/m³ as identical.
The authors need to improve the methodology and clearly outline the assumptions made, particularly regarding the density dependence of viscoplastic behaviour. This could be based on their previous work (Li and Baker, 2022) or by considering other models from the literature. Finally, the discussion in the “activation energy” section should be revisited in light of these methodological assumptions.
Specific Comments:
- Lines 43-48: What about the study of Burr et al., (2019) for the in-situ compression test ? Does it relate or include relevant data to evaluate the results of this study?
- Lines 57-59: Using homogenization approaches, considering the behaviour of ice, is common for studying the physical properties of firn and snow.
- Lines 233-235: Please provide more details on how the thermal gradient was evaluated during your experiments.
- Lines 285-289: As deformation mechanisms are not directly measured in this study, please add references to the literature in this discussion.
- Line 336: Unclear, it is the temperature which is a state variable of the strain-rate.
- Lines 410-411: The word “methods” can be misleading. Using 2 or 3 data points to identify a parameter is not a separate method. Either remove the word “method” or include the data point at -10 °C in the overall dataset.
- Lines 453-455: The statement about the activation energy of firn should be nuanced. While older studies show lower values than those of ice, you have already discussed that values of Qc are highly scattered and debated (as mentioned in lines 416-426 of your manuscript).
- Lines 475-480: It's not clear that each brace corresponds to a depth. Please clarify it.
Technicals Comments:
- Figure 6: Please specify in the title of the y-axis in Figure 6 that this is the logarithm of SRmin, to ensure consistency in the names used.
- Figure 6: The text and colours in the caption do not appear to correspond to the figure. Please check.
References:
- Alexis Burr, Pierre Lhuissier, Armelle Philip, Christophe L. Martin. In situ X-ray tomography densification of firn: The role of mechanics and diffusion processes. Acta Materialia, 2019, 167, pp.210-220. 10.1016/j.actamat.2019.01.053.
Citation: https://doi.org/10.5194/egusphere-2024-2337-RC1 -
RC2: 'Comment on egusphere-2024-2337', Anonymous Referee #2, 31 Oct 2024
Review of manuscript entitled “Observations of creep of polar firn at different temperatures” submitted to EGUsphere by Yuan Li.
General comments
This manuscript investigates the metamorphism and deformation mechanism using natural firn samples recovered at Greenland summit by mechanical tests and microstructure observations. Based on the experimental results, activation energy for creep deformation and grain boundary diffusion is estimated. The authors compare the results with previous studies on activation energy and discuss the firn deformation, and differences between firn and solid ice, and argued that the minimum strain rate is determined by temperature. Microstructures of firn samples before and after creep experiments are analyzed by X-ray micro computed tomography. Changes in geometric structure during creep deformation are investigated in detail.
This manuscript provides interesting results in mechanical behavior of firn samples (strain rate vs strain) and extensive 3D data on geometric structures before and after creep experiments. They are important data for discussion the deformation mechanisms and microstructural evolution of firn.
However, I have some significant concerns in the methodology, interpretation and references. In particular, experimental samples and conditions should be verified. Cited references are biased toward the author’s paper. Please cite the references widely. Reconstruction of the manuscript is required. Therefore, I recommend major revisions.
Specific comments:
Abstract and Introduction:
- It is difficult to understand the new findings of this study. In the field of ice and snow deformation, it is widely recognized that temperature is an important factor, and that tertiary creep is driven by recrystallization (Cuffey and Paterson, 2010; Faria et al., 2014). Compression deformation of firn, accompanied by an increase in density, differs from that of ice. Different creep behaviors between firn and ice could be expected.
- The Introduction Section includes few references to previous research on firn deformation and metamorphism, making it unclear how this study fits within the context of current research and its problems. In addition to prior studies on ice deformation experiments, please also cite prior studies on firn deformation experiments.
- In the Discussion section, there are many comparisons with the authors' own related papers, and the discussion with other studies is not sufficient. Please specify how the findings of this study advance our current understanding of firn deformation.
2. Sample and measurements
- Please provide a schematic diagram of experimental setup even if it is shown in supporting paper (Li and Baker, 2022a).
- Differences in initial conditions of each sample may significantly impact the results. For example, factors like fabric and impurity concentration may vary with depth. In the case of EastGRIP, it has been reported that fabric develops even in near-surface snow (Montagnat et al., 2022). Although geometric structure is discussed in the text and Table 1, it is also necessary to examine other elements of the initial samples, such as fabric, impurity concentration, and grain size. Not only is there a difference in the initial microstructure depending on the depth, but there is also a heterogeneity unique to the natural sample at the same depth. Otherwise, direct comparisons between different samples may not be valid. I have question about the reproducibility of the experiment, in particular, strain rate vs strain.
3.4 Relationship of strain rate to strain and 3.5 Apparent activation energy for creep:
- I have questions about the calibration of experimental data. If the number of experiments is increased or experimental conditions are changed, then no calibration would be necessary. Or is it common practice to make calibration in firn deformation experiments? Looking at Table 2 and Figure 6, 7, it appears that the results vary greatly depending on the type of calibration. The discussion of strain rate (creep curve) and activation energy does not seem robust because of the large influence of the calibration. Please explain clarify, as it is difficult to understand the necessity and appropriateness of the calibration.
Appendix A:
- The authors determine the loading stress during deformation experiments from the hydrostatic pressure at the point where the sample was taken, but is this reasonable? Hydrostatic pressure is considered to have no effect on strain rate in ice (Rigsby, 1958; Cuffey and Paterson, 2010), and in ice it is the deviatoric stress that determines strain rate.
- It is understandable that a high stress is necessary to make the experiment (deformation) proceed quickly and that the ratio of effective stress to hydrostatic pressure should be considered to approximate actual ice sheet conditions (set so that the effective stress becomes smaller as the depth increases). However, the strain rates obtained in this experiment are on the order of 10-5 to 10-6 s-1, which is several orders of magnitude larger than actual ice sheet firn. As an example, Faria et al. (2014) estimated the vertical strain rate of EDML firn at 50 m depth as order of 10-11 - 10-12 s-1. Furthermore, they concluded that EDML firn at 50-m depth is determing in the tertiary creep with dynamic recrystallization.
- The high stresses (or high strain rate) will also cause dislocation accumulation and tangle, and recrystallization to be more active than it actually is.
Others
- L233-235: Could a decrease in density associated with deformational compression occur in a real ice sheet firn?
- L239-241: Does the fact that the ratio of effective stress to hydrostatic pressure in the experiments (discussed in Appendix A) varies from sample to sample (depth to depth) not affect the differences in density increase?
- L250-255: Only one example of grain size change before and after creep experiment is shown (40-m sample at -5oC). In the manuscript, it just says, refer to Li and Fu (2024) (L401) for other samples, but it needs to mention in the present paper. Please provide other measurement results in grain size changes before and after deformation.
- L285-294: The strain rate transition (creep curve) in deformation and recrystallization have been described by numerous papers and textbooks (e.g., Budd and Jacka, 1989; Cuffey and Paterson, 2010; Faria et al. 2014). Please cite references widely as well as the authors' papers.
- L306-309: What is the reason why the 20m and 60m samples with large density differences are close to each other and the 40m sample is greater than that?
- L309-310: I did not understand this logic (These k values imply that the more the constraints from the grain-boundaries, the slower the deformation rate will be,..). Please explain in detail.
- L327-329: I did not understand this logic (likely suggesting that the effect of temperature overwhelmed the effect of impurities during creep of polar firn.). Please explain in detail.
- L369-370: Why does the strain at which the minimum strain rate is achieved vary with density and temperature?
- L462-464: Why does the stress exponent obtained in this experiment differ from previous studies? The value of 0.1 obtained in this study seems quite low. The difference may be too large to address with calibration alone. Please also cite previous studies other than Li and Baker (2022a) that estimated the stress exponent.
- Also, is it possible for the stress exponent to be negative? There may be large fluctuations in the strain rate obtained in the deformation experiments, which could hinder accurate estimation. If these values are correct, what deformation mechanism do they correspond to?
- I question the practice of determining the stress exponent from experimental results of different samples. If the initial conditions of the samples differ, the deformation characteristics will also change, making it impossible to accurately determine the stress exponent.
- Table 1: Please provide the explanation of each parameter (e.g., S.Th, TP…) in the caption.
- Figure 4 (L317-318): “-30oC (blue lines)” is correct?
References:
Budd, W. D. and T. H. Jacka (1989). "A Review of Ice Rheology for Ice Sheet Modelling." Cold Regions Science and Technology 16: 107-144.
Cuffey, K.M., Paterson, W.S.B., 2010. The Physics of Glaciers, 4th edited. Elsevier Inc.
Faria, S. H., et al. (2014). "The microstructure of polar ice. Part II: State of the art." Journal of Structural Geology 61: 21-49.
Montagnat, M., et al. (2020). "On the birth of structural and crystallographic fabric signals in polar snow: A case study from the EastGRIP snowpack." Frontiers in Earth Science 8: 365.
Rigsby, G. P., 1958: Effect of hydrostatic pressure on velocity of shear deformation of single ice crystals. J. Glaciol., 3, 273-278.
Citation: https://doi.org/10.5194/egusphere-2024-2337-RC2
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