A rigorous approach to the specific surface area evolution in snow during temperature gradient metamorphism
<p>Despite being one of the most fundamental microstructural parameters of snow, the specific surface area (SSA) dynamics during temperature gradient metamorphism (TGM) have so far been addressed only within empirical modeling. To surpass this limitation, we propose a rigorous modeling of SSA...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2024-04-01
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| Series: | The Cryosphere |
| Online Access: | https://tc.copernicus.org/articles/18/1653/2024/tc-18-1653-2024.pdf |
| _version_ | 1797216346840236032 |
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| author | A. Braun A. Braun K. Fourteau K. Fourteau H. Löwe |
| author_facet | A. Braun A. Braun K. Fourteau K. Fourteau H. Löwe |
| author_sort | A. Braun |
| collection | DOAJ |
| description | <p>Despite being one of the most fundamental microstructural parameters of snow, the specific surface area (SSA) dynamics during temperature gradient metamorphism (TGM) have so far been addressed only within empirical modeling. To surpass this limitation, we propose a rigorous modeling of SSA dynamics using an exact equation for the temporal evolution of the surface area, fed by pore-scale finite-element simulations of the water vapor field coupled with the temperature field on X-ray computed tomography images. The proposed methodology is derived from the first principles of physics and thus does not rely on any empirical parameter. Since the calculated evolution of the SSA is highly sensitive to fluctuations in the experimental data, we quantify the impact of these fluctuations within a stochastic error model. In our simulations, the only poorly constrained physical parameter is the condensation coefficient <span class="inline-formula"><i>α</i></span>. We address this problem by simulating the SSA evolution for a wide range of <span class="inline-formula"><i>α</i></span> values and estimate optimal values by minimizing the differences between simulations and experiments. This methodology suggests that <span class="inline-formula"><i>α</i></span> lies in the intermediate range <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">3</mn></mrow></msup><mo><</mo><mi mathvariant="italic">α</mi><mo><</mo><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="80pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="d0947cd230d9bb35acfd3a4929760db7"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tc-18-1653-2024-ie00001.svg" width="80pt" height="13pt" src="tc-18-1653-2024-ie00001.png"/></svg:svg></span></span> and slightly varies between experiments. Also, our results suggest a transition of the value of <span class="inline-formula"><i>α</i></span> in one TGM experiment, which can be explained by a transition in the underlying surface morphology. Overall, we are able to reproduce very subtle variations in the SSA evolution with correlations of <span class="inline-formula"><i>R</i><sup>2</sup>=0.95</span> and <span class="inline-formula">0.99</span>, respectively, for the two TGM time series considered. Finally, our work highlights the necessity of including kinetic effects and of using realistic microstructures to comprehend the evolution of SSA during TGM.</p> |
| first_indexed | 2024-04-24T11:44:30Z |
| format | Article |
| id | doaj.art-17960491c4a54abaa614dd5261e2bde6 |
| institution | Directory Open Access Journal |
| issn | 1994-0416 1994-0424 |
| language | English |
| last_indexed | 2024-04-24T11:44:30Z |
| publishDate | 2024-04-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | The Cryosphere |
| spelling | doaj.art-17960491c4a54abaa614dd5261e2bde62024-04-09T11:50:07ZengCopernicus PublicationsThe Cryosphere1994-04161994-04242024-04-01181653166810.5194/tc-18-1653-2024A rigorous approach to the specific surface area evolution in snow during temperature gradient metamorphismA. Braun0A. Braun1K. Fourteau2K. Fourteau3H. Löwe4Group Snow Physics, Research Unit Snow and Atmosphere, WSL Institute for Snow and Avalanche Research SLF, 7260 Davos Dorf, SwitzerlandLaboratory of Cryospheric Sciences, School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, SwitzerlandGroup Snow Physics, Research Unit Snow and Atmosphere, WSL Institute for Snow and Avalanche Research SLF, 7260 Davos Dorf, SwitzerlandUniversité Grenoble Alpes, Université de Toulouse, Météo-France, CNRS, CNRM, Centre d'Études de la Neige, Grenoble, FranceGroup Snow Physics, Research Unit Snow and Atmosphere, WSL Institute for Snow and Avalanche Research SLF, 7260 Davos Dorf, Switzerland<p>Despite being one of the most fundamental microstructural parameters of snow, the specific surface area (SSA) dynamics during temperature gradient metamorphism (TGM) have so far been addressed only within empirical modeling. To surpass this limitation, we propose a rigorous modeling of SSA dynamics using an exact equation for the temporal evolution of the surface area, fed by pore-scale finite-element simulations of the water vapor field coupled with the temperature field on X-ray computed tomography images. The proposed methodology is derived from the first principles of physics and thus does not rely on any empirical parameter. Since the calculated evolution of the SSA is highly sensitive to fluctuations in the experimental data, we quantify the impact of these fluctuations within a stochastic error model. In our simulations, the only poorly constrained physical parameter is the condensation coefficient <span class="inline-formula"><i>α</i></span>. We address this problem by simulating the SSA evolution for a wide range of <span class="inline-formula"><i>α</i></span> values and estimate optimal values by minimizing the differences between simulations and experiments. This methodology suggests that <span class="inline-formula"><i>α</i></span> lies in the intermediate range <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M4" display="inline" overflow="scroll" dspmath="mathml"><mrow><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">3</mn></mrow></msup><mo><</mo><mi mathvariant="italic">α</mi><mo><</mo><msup><mn mathvariant="normal">10</mn><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="80pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="d0947cd230d9bb35acfd3a4929760db7"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tc-18-1653-2024-ie00001.svg" width="80pt" height="13pt" src="tc-18-1653-2024-ie00001.png"/></svg:svg></span></span> and slightly varies between experiments. Also, our results suggest a transition of the value of <span class="inline-formula"><i>α</i></span> in one TGM experiment, which can be explained by a transition in the underlying surface morphology. Overall, we are able to reproduce very subtle variations in the SSA evolution with correlations of <span class="inline-formula"><i>R</i><sup>2</sup>=0.95</span> and <span class="inline-formula">0.99</span>, respectively, for the two TGM time series considered. Finally, our work highlights the necessity of including kinetic effects and of using realistic microstructures to comprehend the evolution of SSA during TGM.</p>https://tc.copernicus.org/articles/18/1653/2024/tc-18-1653-2024.pdf |
| spellingShingle | A. Braun A. Braun K. Fourteau K. Fourteau H. Löwe A rigorous approach to the specific surface area evolution in snow during temperature gradient metamorphism The Cryosphere |
| title | A rigorous approach to the specific surface area evolution in snow during temperature gradient metamorphism |
| title_full | A rigorous approach to the specific surface area evolution in snow during temperature gradient metamorphism |
| title_fullStr | A rigorous approach to the specific surface area evolution in snow during temperature gradient metamorphism |
| title_full_unstemmed | A rigorous approach to the specific surface area evolution in snow during temperature gradient metamorphism |
| title_short | A rigorous approach to the specific surface area evolution in snow during temperature gradient metamorphism |
| title_sort | rigorous approach to the specific surface area evolution in snow during temperature gradient metamorphism |
| url | https://tc.copernicus.org/articles/18/1653/2024/tc-18-1653-2024.pdf |
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