Climate change induces rapid growth of dead ice in Asian glaciers

Climate change induces rapid growth of dead ice in Asian glaciers | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Short Report Climate change induces rapid growth of dead ice in Asian glaciers Qiong Wang, Xin Wang, Keqin Duan, Shiyin Liu, Yongsheng Yin, Qiao Liu, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5301165/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Dead ice in High Mountain Asia (HMA) varies responsive to dramatic glacier loss, profoundly impacting alpine water cycle patterns. We find significant dead ice increase over this century, additional area exceeds 3,000 km2, with mass 44.3 ± 2.0 ~ 64.1 ± 5.2 Gt. Debris coverage dominates dead ice spatial pattern. Dead ice expansion would significantly alter spatio-temporal patterns of glacier ablation and impact water supply sustainability in World's Water Towers. Figures Figure 1 Figure 2 Main Dead ice is a large ice body that has detached from the main glacier as a result of ice avalanches, glacier surges, or retreats. This type of ice body can no longer be recharged by glacier system and movement almost ceases 1 . Dead ice mostly forms as glacier experiences negative mass balance and the surface is covered by thick debris (as thick debris coverage isolates heat transfer to glacier surface) 2 . With present rapid retreat of glaciers worldwide, while thin debris may enhance glacier ablation and accelerate glacier water resource loss, thick debris insulates heat and retains significant ice storage 3 , which would lead to richer dead ice distribution 2 . Dead ice retains a considerable glacier water resource in a new form, which will be a potentially available future water source in alpine region that cannot be ignored. However, quantitative studies of dead ice are scarce, and there are still gaps in how dead ice evolution respond to rapid global climate change. High Mountain Asia (HMA) hosts the most extensive glacier coverage except for two poles. Warming rate of the area is significantly higher than global mean level 4 , which induces rapid thinning and retreat of HMA glaciers 5 , 6 . Even though debris-covered glaciers are distributed in glacierized regions worldwide, there is a particularly large concentration in HMA (especially in the subregions of Karakoram, Central Tien Shan, Western Himalaya, etc.) 7 , 8 . Drastic negative mass balance in HMA may cause massive development of dead ice 9 . Dead ice ablation is less influenced by intra-annual temperature fluctuations, since heat exchange between ice body and atmosphere is inhibited by debris coverage. Dead ice meltwater runoff contributes to the alleviation of seasonal water scarcity 10 and profoundly impacts the ecological environment, and social and productive activities in alpine region 11 . In this study, we employ a full-distributed mass balance gradient model coupled with glacier dynamics to simulate glacier evolution process for HMA glaciers with areas no less than 1 km² in Randolph Glacier Inventory version 6.0 (RGI6.0) (n = 15970, over 97% of total glacier mass in HMA). The distribution of potential dead ice and its evolutionary dynamics are identified by determining whether the various parts of the glacier fractal satisfy the definition of dead ice, i.e., whether detached from the main body of the glacier, whether recharged by the glacier, and whether glacier flow is ceased. A collection of four Shared Socio-economic Pathways (SSPs) from 28 General Circulation Models (GCMs) from Phase 6 of the Coupled Model Intercomparison Project (CMIP6) is utilized to drive the glacier evolution model, which is bias-corrected and downscaled with a baseline of ERA5 Land historical reference period (1950–2021). This study could contribute to advancing the understanding of glacier evolution in response to climate change and support regional water resource sustainability. Significant amounts of dead ice develop in HMA under different SSPs and increase with radiative forcing intensification. Additional dead ice area reached 3000–4000 km 2 by the end of this century, with additional ice mass of 44.3 ± 2.0 ~ 64.1 ± 5.2 Gt (Fig. 1 – 2 ). Dead ice development is controlled by debris coverage, with subregions of dead ice mass demonstrating a significant correlation (r = 0.94, p < 0.01) with debris coverage area (Fig. 1 E). Central Himalaya, Karakoram, Western Himalaya, and Western Pamir covered by the most extensive debris, develop more than 300 km 2 of new dead ice area with new ice mass exceeding 5 Gt under different SSPs (Fig. 1 ). The spatial distribution of debris in Central Tien Shan, Nyainqentangla, and Eastern Hindu Kush is significantly larger than the other subregions, and the development of dead ice is also considerably higher (Fig. 1 ). Western Himalaya is the most developed subregion of dead ice in HMA, with more than 700 km 2 of new dead ice under the high-emission scenario (SSP5-8.5), and ~ 30% of total new dead ice mass in HMA (Fig. 1 E). Apart from extensive debris coverage, the sharp glacier loss in Western Himalaya also contributed to the development of dead ice (~ 300 Gt of glacier mass loss and ~ 4000 km 2 of area shrink under the high-emission scenario (SSP5-8.5), both accounting for ~ 10% of total glacier loss in HMA) (Fig. 1 ). The existence of dead ice depends on lower temperatures. As heat transfer due to higher absolute temperatures reaches the ice layer through the thick debris, the dead ice melts. Despite increasing glacier recession with intensifying radiative forcing, causing an overall expansion of dead ice, warmer subregions present a moderate shrinkage in the future (Fig. 1 , Fig. 2 ). For instance, Central Himalaya increases dead ice mass by more than 8.5 Gt under the low-emission scenario (SSP1-2.6), while it shrinks under higher radiative forcing scenarios as temperatures continue to rise with less than 7 Gt of dead ice under the high-emission scenario (SSP5-8.5) (Fig. 1 , Fig. 2 ). Similar phenomena are also observed in Dzhungarsky Alatau, Eastern Tibetan Mountains, Hengduan Shan, Northern/Western Tien Shan, and Pamir Alay, which are generally at lower elevations (Fig. 1 , Fig. 2 ). In terms of time-series evolution dynamics, the development of dead ice is not monotonically increasing and there is a mismatch between area and mass trends (Fig. 2 ). It is attributed to the accelerated ablation of dead ice after a rapid expansion phase, as the continued warming of the mid- to late-century temperatures conducts more heat than the limitations of thermal resistance capacity of thick debris. Especially for the high-emission scenario (SSP5-8.5), this phenomenon is most pronounced (Fig. 2 ). In terms of subregions, Karakoram, Western Himalaya, Pamir, Kunlun Shan and other higher altitude regions demonstrate a clear monotonically increasing trend in overall dead ice scale (Fig. 2 ). Whereas, there are fluctuations of dead ice scale in mid- to late-century in low-elevation areas along HMA margins such as Pamir Alay, Qilian Shan, Northern/Western Tien Shan, Hengduan Shan and Eastern Tibetan Mountains (Fig. 2 ). In this study, we conducted extensive modeling of the HMA glacier to quantify the evolution of dead ice dynamics, and our results suggest a dramatic expansion of dead ice in this century. Under continuous warming, dead ice runoff covered by thick debris peaks significantly later than glacier runoff (Fig. S1 ), enhancing the sustainability of runoff from glacierized zone and downstream basin. Lower sensitivity of dead ice to intra-annual temperature fluctuations narrows seasonal meltwater runoff variability, which contributes to alleviating ecological and irrigation water scarcity during the dry season. Meanwhile, the presence and demise of dead ice shapes diverse glaciated landscapes 13 and contributes to the formation of thermokarst lakes. As the dead ice covered by thick surface moraine becomes partial moraine lake dams in form of buried ice 14 , its extremely high instability would exacerbate the frequency of glacial lake outburst flood events. We set the 90th quantile of surface velocity within a glacier fractal not exceeding 1 m yr − 1 as one of the thresholds to identify extent of dead ice. Because of the conceptual similarity between dead ice and rock glacier, the identification results may include part of rock glaciers. This leads to certain uncertainties in model results, but also provides a reference for future evolution dynamics simulation of rock glaciers. Multiple sources of uncertainty are present in this study due to limitations in knowledge of glacier evolution and driving data precision. To cope with potentially complex fluctuations in climate drivers and model parameters, we employ Monte Carlo frameworks to increase model stochasticity. Constrained by computational performance, our glacier dynamics scheme utilizes a simplified 3D model, which leads to uncertainties in glacier dynamics. As the mechanism of debris evolution is still unclear, debris dynamics are neglected in this study, and related studies have illustrated that it may lead to ~ 3% error 15 . Comparisons with observations demonstrate that our model exhibits good performance, with glacier mass loss errors of 4.6% ± 2.8%, 6.5% ± 2.8%, 3.4% ± 2.8% and 8.1% ± 2.7% under different SSPs. We emphasize the necessity of mapping dead ice zones with InSAR/LiDAR to more accurately quantify and monitor dead ice change and to enhance integrated management of dead ice water resources. Methods 2.1 Climatology implement We used the ensemble member r1i1p1f1 of each of the 28 CMIP6 GCMs for four common SSPs (SSP1–3 and 5 resulting in a total of 112 datasets) to quantify future climate change and drive the glacier evolution model (Table. S1). Observation data and CMIP6 GCM output differ in spatial resolution and initial conditions; therefore, we used ERA5-Land from the European Centre for Medium-Range Weather Forecasts (ECMRWF) for bias correction and downscaling of GCM output. The ERA5 dataset has inherent uncertainties but it offers long time series and complete coverage of the study region, and allows consistent characterization of the climate of HMA over the long term. Monthly ERA5-Land (1950–2021) and CMIP6 (1850–2100) time series data were decomposed into long-term trend, seasonal trend, and residuals as follows 16 : $$\:\begin{array}{c}{GCM}_{decompose}={GCM}_{trend}+{GCM}^{{\prime\:}}={GCM}_{trend}+{GCM}_{season}+{GCM}_{resid}\:\#\left(1\right)\end{array}$$ $$\:\begin{array}{c}{ERA}_{decompose}={ERA}_{trend}+{ERA}^{{\prime\:}}={ERA}_{trend}+{ERA}_{season}+{ERA}_{resid}\:\#\left(2\right)\end{array}$$ where \(\:{GCM}_{decompose}\) is the decomposed GCM time series, \(\:{ERA}_{decompose}\) is the decomposed ERA5-Land time series, \(\:{GCM}_{trend}\) and \(\:{ERA}_{trend}\) are the long-term nonlinear trends of the GCM and ERA5-Land time series, respectively, and \(\:{GCM}^{{\prime\:}}\) and \(\:{ERA}^{{\prime\:}}\) are the perturbation factors, which are composed of their respective seasonal trends ( \(\:{GCM}_{season}\) and \(\:{ERA}_{season}\) ) and residuals ( \(\:{GCM}_{resid}\) and \(\:{ERA}_{resid}\) ). Climate model output was adjusted to match ERA5-Land observation data pixel by pixel on the ERA5-Land reanalysis data grid and downscaled to 0.1° resolution by matching two sequences to the closest spatial location. Moreover, we calculated environmental lapse rate distribution and trend using temperature and geopotential height between 300 and 1000 hPa at 100 hPa intervals from ERA5 data on pressure levels from 1950 to 2021. 2.2 Glacier evolution simulation To track glacier evolution under different climate scenarios, glaciers in HMA with areas no less than 1 km 2 in RGI6.0 were selected. Mass balance was calculated using a retrofit of mass balance gradient model (MBGR) that captures the spatial differences of mass balance with a high-resolution 2D grid combined with a continuity-equation-based 3D glacier dynamics model component for mass redistribution. 2.2.1 Retrofit of Mass Balance Gradient model (MBGR) The mass balance gradient (MBG) model of Kraaijenbrink et al. 17 assumes a linear relationship between temperature and glacier mass balance, and expresses mass balance as a function of elevation. A mathematical relationship between annual ablation at the terminus and the mass balance of different elevation bands is used to derive the mass balance distribution. The MBG model over-smoothes spatial differences in mass balance because it uses elevation bands as its unit. We transformed the semi-distributed MBG model into a full-distributed model with grid cells as its unit. The MBGR model retains the role of nonlinear ablation factors and is described by: $$\:\begin{array}{c}{MB}_{ij}=\sum\:_{k}(({MB}_{init}+\left({z}_{ij}-{z}_{min}\right)\frac{\partial\:MB}{\partial\:z})\times\:\frac{\partial\:MB}{\partial\:{Red}_{k}}),k=debris,\:\dots\:\:\#\left(3\right)\end{array}$$ where \(\:{MB}_{ij}\) and \(\:{z}_{ij}\) are mass balance and elevation, at the grid coordinate \(\:(i,\:\:j)\) , respectively, \(\:{MB}_{init}\) and \(\:{z}_{min}\) are ablation and elevation at the terminus, respectively, \(\:\partial\:MB/\partial\:z\) is the mass balance gradient, which is the relationship between mass balance \(\:MB\) and elevation \(\:z\) , and \(\:{Red}_{k}\) includes any factors that are clearly related to glacier ablation (e.g., debris, supraglacial pond, ice cliff). Mean annual sum of positive degree–days at the terminus and mean annual precipitation at the centroid (location where annual accumulation is maximum) from the ERA5-Land reanalysis dataset for the reference period of 2000–2014 are used to initialize the MBGR model. Coupling debris coverage is used to calculate mass balance for all grid cells (Eq. (3), refer to Østrem curve 3 ). Following the MBG model, ablation at the terminus is simply defined as a function of cumulative positive degree–days. 2.2.2 Glacier Dynamics Components In the MBGR model, the statistics-based mass redistribution component that is part of the MBG model was replaced with a 3D ice flow dynamics model that is widely used in polar ice sheet simulations. Because of the special Stokes flow (creeping flow) of glaciers, we used the Stokes equation as a simplified version of the momentum Eq. 1 8–20 : $$\:\begin{array}{c}\nabla\:·\sigma\:+\rho\:g=0\:\#\left(4\right)\end{array}$$ where \(\:\varvec{\sigma\:}\) is stress tensor, \(\:\rho\:\) is ice density (916.7 kg‧m − 3 ), and \(\:\varvec{g}=(0,\:0,\:-g)\) is gravitational acceleration. The Shallow Shelf Approximation (SSA) further ignores vertical shear, decouples the vertical component \(\:z\) from initial equations, and has been used to simulate basal slide, surge, and other situations where the critical state is reached 18 . The Shallow Ice Approximation (SIA) is based on the Blatter–Pattyn approximation; it ignores the horizontal gradient of vertical velocity and has been used to model glaciers with a dominant plastic flow 19 . The SSA + SIA hybrid flow greatly improves the performance of glacier dynamics models. Basal velocity of grounded ice is \(\:{\varvec{v}}_{b}={\varvec{v}}_{SSA}\) , overall glacier velocity is \(\:\varvec{v}={\varvec{v}}_{SSA}+{\varvec{v}}_{SIA}\) 19 – 21 , and accuracy of model output is high. In the ice flow dynamics model, the energy balance is based on enthalpy conservation. It takes into account dissipation heating rate \(\:Q\) , advective enthalpy flux \(\:\rho\:H\varvec{v}\) , and non-advective enthalpy flux and \(\:\varvec{q}\) , and avoids the latent heat of phase transformation in polythermal glaciers 22 : $$\:\begin{array}{c}\rho\:\frac{dH}{dt}=-\nabla\:·q+Q\:\#\left(5\right)\end{array}$$ where \(\:\varvec{q}\) and \(\:Q\) are made up of their respective components of water and ice, i.e., \(\:\varvec{q}={\varvec{q}}_{ice}+{\varvec{q}}_{water}\) , and \(\:Q={Q}_{ice}+{Q}_{water}\) . 2.3 Extraction of dead ice We used image-connected domain algorithms to separate glacier sections, identified dead ice according to various criteria (absence of connection with the main body of glacier, glacial recharge, and surface velocity), and mapped the distribution and recorded the properties of the dead ice. Given the small interannual variability, a decadal time step was used. Declarations Acknowledgments This work was funded by the National Natural Science Foundation of China (No. 42171137, No. U23A2011, and No. 42171134) and National Cryosphere Desert Data Center (No. E01Z790201). The authors acknowledge the Beijing Super Cloud Computing Center (BSCC) for providing HPC resources that have contributed to the research results reported within this paper. URL: http://www.blsc.cn/. Data and code availability The statistics, results and media files of this study are provided in supplementary materials. All data and code will be open source upon publication. During the review process, support data is temporarily available via https://doi.org/10.5281/zenodo.13759486. Conflict of interest The authors declare no competing interests. Author Contributions Q.W. and X.W. designed the study and wrote the manuscript; Q.W. developed the model and performed all analyses with additional support from Y.Y. and J.H. All authors contributed to the final form of the study. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5301165","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Short Report","associatedPublications":[],"authors":[{"id":370906154,"identity":"bdffa3c8-38b6-4ac5-bc91-376da772c68a","order_by":0,"name":"Qiong Wang","email":"","orcid":"","institution":"Hunan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Qiong","middleName":"","lastName":"Wang","suffix":""},{"id":370906157,"identity":"28eb0b10-df70-41e9-97c1-622063bcd7ce","order_by":1,"name":"Xin Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYNCCigNQBhvRWs6AtDCTooWxjRQtBsfPHn7NO+9OnsH58wcYPpQdZuCf3UBAy5m8NMuZ254VG9xIZmCcce4wg8SdA/i1mB3IMTP4uO1w4oYbzAzMvG2HGQwkEghoOf/GzCBxDlDL+cMMzH+J0nIjx/jBxwaglgPJDMyMxGixv/HGjHHGscOJM28kGxzsOZfOI3GDgBbJ/hzjzzw1hxP7zh98+OBHmbUc/wwCWoCATQLGOgDEPATVAwHzB2JUjYJRMApGwQgGAHNMSygMwqQPAAAAAElFTkSuQmCC","orcid":"","institution":"Hunan University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Xin","middleName":"","lastName":"Wang","suffix":""},{"id":370906159,"identity":"52856fd6-4c1c-46e5-b46e-1a3bdea66a5d","order_by":2,"name":"Keqin Duan","email":"","orcid":"","institution":"Shaanxi Normal University","correspondingAuthor":false,"prefix":"","firstName":"Keqin","middleName":"","lastName":"Duan","suffix":""},{"id":370906160,"identity":"ef7ac3e4-05f7-427f-84e6-1bc640d92db3","order_by":3,"name":"Shiyin Liu","email":"","orcid":"","institution":"Yunnan University","correspondingAuthor":false,"prefix":"","firstName":"Shiyin","middleName":"","lastName":"Liu","suffix":""},{"id":370906161,"identity":"8cc23f94-8c1e-4e8c-a470-caf833ca1850","order_by":4,"name":"Yongsheng Yin","email":"","orcid":"","institution":"Institute of Mountain Hazards and Environment","correspondingAuthor":false,"prefix":"","firstName":"Yongsheng","middleName":"","lastName":"Yin","suffix":""},{"id":370906162,"identity":"81147f3f-2ebb-4336-8e76-488aef1a358c","order_by":5,"name":"Qiao Liu","email":"","orcid":"","institution":"Institute of Mountain Hazards and Environment","correspondingAuthor":false,"prefix":"","firstName":"Qiao","middleName":"","lastName":"Liu","suffix":""},{"id":370906163,"identity":"d0cb34a3-c3ee-40be-a05f-35db20128b44","order_by":6,"name":"Jinping He","email":"","orcid":"","institution":"Shaanxi Normal University","correspondingAuthor":false,"prefix":"","firstName":"Jinping","middleName":"","lastName":"He","suffix":""},{"id":370906164,"identity":"781d25c6-b5ff-4e86-aecb-10c245599cd8","order_by":7,"name":"Yong Zhang","email":"","orcid":"","institution":"Hunan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Yong","middleName":"","lastName":"Zhang","suffix":""},{"id":370906165,"identity":"20ce0fea-ef12-47fa-a7f8-26de402642f6","order_by":8,"name":"Junfeng Wei","email":"","orcid":"","institution":"Hunan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Junfeng","middleName":"","lastName":"Wei","suffix":""},{"id":370906166,"identity":"893f813d-38d1-4435-b9f6-f280d402984c","order_by":9,"name":"Zongli Jiang","email":"","orcid":"","institution":"Hunan University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Zongli","middleName":"","lastName":"Jiang","suffix":""}],"badges":[],"createdAt":"2024-10-21 04:53:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5301165/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5301165/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":67631975,"identity":"7ab7328a-adba-456f-8deb-3a18d3573766","added_by":"auto","created_at":"2024-10-28 08:56:07","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":398604,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial patterns of HMA dead ice in 2100 under different SSPs. (A) Spatial distribution of 1° × 1° gridded dead ice in 2100 under SSP5-8.5 and subregional debris conditions. (B-D) Spatial distribution of 1° × 1° gridded dead ice in 2100 under SSP1-2.6, SSP2-4.5 and SSP3-7.0. (E) Relationship between the area of debris coverage and dead ice mass in 2100 under SSP5-8.5, and the subplot show that the relationship after Western Himalaya has been removed from the data. HMA subregions are according to Bolch et al. 12. The corresponding full names of the subregion abbreviations are below: AS (Altun Shan), CH (Central Himalaya), CT (Central Tien Shan), DA (Dzhungarsky Alatau), EH (Eastern Himalaya), HK (Eastern Hindu Kush), EK (Eastern Kunlun Shan), EP (Eastern Pamir), ETP (Eastern Tibetan Plateau), ET (Eastern Tien Shan), GD (Gangdise Mountains), HS (Hengduan Shan), ITP (Inner Tibetan Plateau), KK (Karakoram), NWT (Northern/Western Tien Shan), NQ (Nyainqentanglha), PA (Pamir Alay), QS (Qilian Shan), TG (Tanggula Shan), WH (Western Himalaya), WK (Western Kunlun Shan), WP (Western Pamir).\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5301165/v1/9e2f1229c82f119979c3e18f.png"},{"id":67631974,"identity":"b8621759-2642-4051-a33e-d2ad6046c500","added_by":"auto","created_at":"2024-10-28 08:56:07","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":489743,"visible":true,"origin":"","legend":"\u003cp\u003eTime series of decadal dead ice evolution in HMA under different SSPs (cyan: SSP1-2.6, green: SSP2-4.5, orange: SSP3-7.0, red: SSP5-8.5). The black axis (bar) is the mass of dead ice (unit: Gt), and the red axis (line) is the area of dead ice (unit: km\u003csup\u003e2\u003c/sup\u003e).\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5301165/v1/4fdcb157de9fa41aebcc2675.png"},{"id":68533201,"identity":"7d19df60-5792-4d11-b15b-770abe591dbb","added_by":"auto","created_at":"2024-11-08 09:32:14","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1158633,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5301165/v1/ad1bd06a-85ad-4359-85c9-2b8f858fcad0.pdf"},{"id":67631976,"identity":"d130acc6-1e50-40da-8662-c46addc9782d","added_by":"auto","created_at":"2024-10-28 08:56:07","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":560115,"visible":true,"origin":"","legend":"","description":"","filename":"SIAppendixnpj.docx","url":"https://assets-eu.researchsquare.com/files/rs-5301165/v1/f03ffe93ba115667f30dc46c.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Climate change induces rapid growth of dead ice in Asian glaciers","fulltext":[{"header":"Main","content":"\u003cp\u003eDead ice is a large ice body that has detached from the main glacier as a result of ice avalanches, glacier surges, or retreats. This type of ice body can no longer be recharged by glacier system and movement almost ceases \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Dead ice mostly forms as glacier experiences negative mass balance and the surface is covered by thick debris (as thick debris coverage isolates heat transfer to glacier surface) \u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. With present rapid retreat of glaciers worldwide, while thin debris may enhance glacier ablation and accelerate glacier water resource loss, thick debris insulates heat and retains significant ice storage \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, which would lead to richer dead ice distribution \u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Dead ice retains a considerable glacier water resource in a new form, which will be a potentially available future water source in alpine region that cannot be ignored. However, quantitative studies of dead ice are scarce, and there are still gaps in how dead ice evolution respond to rapid global climate change.\u003c/p\u003e \u003cp\u003eHigh Mountain Asia (HMA) hosts the most extensive glacier coverage except for two poles. Warming rate of the area is significantly higher than global mean level \u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e, which induces rapid thinning and retreat of HMA glaciers \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. Even though debris-covered glaciers are distributed in glacierized regions worldwide, there is a particularly large concentration in HMA (especially in the subregions of Karakoram, Central Tien Shan, Western Himalaya, etc.) \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. Drastic negative mass balance in HMA may cause massive development of dead ice \u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. Dead ice ablation is less influenced by intra-annual temperature fluctuations, since heat exchange between ice body and atmosphere is inhibited by debris coverage. Dead ice meltwater runoff contributes to the alleviation of seasonal water scarcity \u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e and profoundly impacts the ecological environment, and social and productive activities in alpine region \u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn this study, we employ a full-distributed mass balance gradient model coupled with glacier dynamics to simulate glacier evolution process for HMA glaciers with areas no less than 1 km\u0026sup2; in Randolph Glacier Inventory version 6.0 (RGI6.0) (n\u0026thinsp;=\u0026thinsp;15970, over 97% of total glacier mass in HMA). The distribution of potential dead ice and its evolutionary dynamics are identified by determining whether the various parts of the glacier fractal satisfy the definition of dead ice, i.e., whether detached from the main body of the glacier, whether recharged by the glacier, and whether glacier flow is ceased. A collection of four Shared Socio-economic Pathways (SSPs) from 28 General Circulation Models (GCMs) from Phase 6 of the Coupled Model Intercomparison Project (CMIP6) is utilized to drive the glacier evolution model, which is bias-corrected and downscaled with a baseline of ERA5 Land historical reference period (1950\u0026ndash;2021). This study could contribute to advancing the understanding of glacier evolution in response to climate change and support regional water resource sustainability.\u003c/p\u003e \u003cp\u003eSignificant amounts of dead ice develop in HMA under different SSPs and increase with radiative forcing intensification. Additional dead ice area reached 3000\u0026ndash;4000 km\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e by the end of this century, with additional ice mass of 44.3\u0026thinsp;\u0026plusmn;\u0026thinsp;2.0\u0026thinsp;~\u0026thinsp;64.1\u0026thinsp;\u0026plusmn;\u0026thinsp;5.2 Gt (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Dead ice development is controlled by debris coverage, with subregions of dead ice mass demonstrating a significant correlation (r\u0026thinsp;=\u0026thinsp;0.94, p\u0026thinsp;\u0026lt;\u0026thinsp;0.01) with debris coverage area (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eE). Central Himalaya, Karakoram, Western Himalaya, and Western Pamir covered by the most extensive debris, develop more than 300 km\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e of new dead ice area with new ice mass exceeding 5 Gt under different SSPs (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The spatial distribution of debris in Central Tien Shan, Nyainqentangla, and Eastern Hindu Kush is significantly larger than the other subregions, and the development of dead ice is also considerably higher (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Western Himalaya is the most developed subregion of dead ice in HMA, with more than 700 km\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e of new dead ice under the high-emission scenario (SSP5-8.5), and ~\u0026thinsp;30% of total new dead ice mass in HMA (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eE). Apart from extensive debris coverage, the sharp glacier loss in Western Himalaya also contributed to the development of dead ice (~\u0026thinsp;300 Gt of glacier mass loss and ~\u0026thinsp;4000 km\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e of area shrink under the high-emission scenario (SSP5-8.5), both accounting for ~\u0026thinsp;10% of total glacier loss in HMA) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe existence of dead ice depends on lower temperatures. As heat transfer due to higher absolute temperatures reaches the ice layer through the thick debris, the dead ice melts. Despite increasing glacier recession with intensifying radiative forcing, causing an overall expansion of dead ice, warmer subregions present a moderate shrinkage in the future (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). For instance, Central Himalaya increases dead ice mass by more than 8.5 Gt under the low-emission scenario (SSP1-2.6), while it shrinks under higher radiative forcing scenarios as temperatures continue to rise with less than 7 Gt of dead ice under the high-emission scenario (SSP5-8.5) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Similar phenomena are also observed in Dzhungarsky Alatau, Eastern Tibetan Mountains, Hengduan Shan, Northern/Western Tien Shan, and Pamir Alay, which are generally at lower elevations (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn terms of time-series evolution dynamics, the development of dead ice is not monotonically increasing and there is a mismatch between area and mass trends (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). It is attributed to the accelerated ablation of dead ice after a rapid expansion phase, as the continued warming of the mid- to late-century temperatures conducts more heat than the limitations of thermal resistance capacity of thick debris. Especially for the high-emission scenario (SSP5-8.5), this phenomenon is most pronounced (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). In terms of subregions, Karakoram, Western Himalaya, Pamir, Kunlun Shan and other higher altitude regions demonstrate a clear monotonically increasing trend in overall dead ice scale (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Whereas, there are fluctuations of dead ice scale in mid- to late-century in low-elevation areas along HMA margins such as Pamir Alay, Qilian Shan, Northern/Western Tien Shan, Hengduan Shan and Eastern Tibetan Mountains (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn this study, we conducted extensive modeling of the HMA glacier to quantify the evolution of dead ice dynamics, and our results suggest a dramatic expansion of dead ice in this century. Under continuous warming, dead ice runoff covered by thick debris peaks significantly later than glacier runoff (Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e), enhancing the sustainability of runoff from glacierized zone and downstream basin. Lower sensitivity of dead ice to intra-annual temperature fluctuations narrows seasonal meltwater runoff variability, which contributes to alleviating ecological and irrigation water scarcity during the dry season. Meanwhile, the presence and demise of dead ice shapes diverse glaciated landscapes \u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e and contributes to the formation of thermokarst lakes. As the dead ice covered by thick surface moraine becomes partial moraine lake dams in form of buried ice \u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e, its extremely high instability would exacerbate the frequency of glacial lake outburst flood events. We set the 90th quantile of surface velocity within a glacier fractal not exceeding 1 m yr\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e as one of the thresholds to identify extent of dead ice. Because of the conceptual similarity between dead ice and rock glacier, the identification results may include part of rock glaciers. This leads to certain uncertainties in model results, but also provides a reference for future evolution dynamics simulation of rock glaciers.\u003c/p\u003e \u003cp\u003eMultiple sources of uncertainty are present in this study due to limitations in knowledge of glacier evolution and driving data precision. To cope with potentially complex fluctuations in climate drivers and model parameters, we employ Monte Carlo frameworks to increase model stochasticity. Constrained by computational performance, our glacier dynamics scheme utilizes a simplified 3D model, which leads to uncertainties in glacier dynamics. As the mechanism of debris evolution is still unclear, debris dynamics are neglected in this study, and related studies have illustrated that it may lead to ~\u0026thinsp;3% error \u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Comparisons with observations demonstrate that our model exhibits good performance, with glacier mass loss errors of 4.6% \u0026plusmn; 2.8%, 6.5% \u0026plusmn; 2.8%, 3.4% \u0026plusmn; 2.8% and 8.1% \u0026plusmn; 2.7% under different SSPs. We emphasize the necessity of mapping dead ice zones with InSAR/LiDAR to more accurately quantify and monitor dead ice change and to enhance integrated management of dead ice water resources.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Climatology implement\u003c/h2\u003e \u003cp\u003eWe used the ensemble member r1i1p1f1 of each of the 28 CMIP6 GCMs for four common SSPs (SSP1\u0026ndash;3 and 5 resulting in a total of 112 datasets) to quantify future climate change and drive the glacier evolution model (Table. S1). Observation data and CMIP6 GCM output differ in spatial resolution and initial conditions; therefore, we used ERA5-Land from the European Centre for Medium-Range Weather Forecasts (ECMRWF) for bias correction and downscaling of GCM output. The ERA5 dataset has inherent uncertainties but it offers long time series and complete coverage of the study region, and allows consistent characterization of the climate of HMA over the long term. Monthly ERA5-Land (1950\u0026ndash;2021) and CMIP6 (1850\u0026ndash;2100) time series data were decomposed into long-term trend, seasonal trend, and residuals as follows \u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}{GCM}_{decompose}={GCM}_{trend}+{GCM}^{{\\prime\\:}}={GCM}_{trend}+{GCM}_{season}+{GCM}_{resid}\\:\\#\\left(1\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}{ERA}_{decompose}={ERA}_{trend}+{ERA}^{{\\prime\\:}}={ERA}_{trend}+{ERA}_{season}+{ERA}_{resid}\\:\\#\\left(2\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{GCM}_{decompose}\\)\u003c/span\u003e\u003c/span\u003e is the decomposed GCM time series, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{ERA}_{decompose}\\)\u003c/span\u003e\u003c/span\u003e is the decomposed ERA5-Land time series, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{GCM}_{trend}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{ERA}_{trend}\\)\u003c/span\u003e\u003c/span\u003e are the long-term nonlinear trends of the GCM and ERA5-Land time series, respectively, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{GCM}^{{\\prime\\:}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{ERA}^{{\\prime\\:}}\\)\u003c/span\u003e\u003c/span\u003e are the perturbation factors, which are composed of their respective seasonal trends (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{GCM}_{season}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{ERA}_{season}\\)\u003c/span\u003e\u003c/span\u003e) and residuals (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{GCM}_{resid}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{ERA}_{resid}\\)\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eClimate model output was adjusted to match ERA5-Land observation data pixel by pixel on the ERA5-Land reanalysis data grid and downscaled to 0.1\u0026deg; resolution by matching two sequences to the closest spatial location. Moreover, we calculated environmental lapse rate distribution and trend using temperature and geopotential height between 300 and 1000 hPa at 100 hPa intervals from ERA5 data on pressure levels from 1950 to 2021.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003e2.2 Glacier evolution simulation\u003c/h3\u003e\n\u003cp\u003eTo track glacier evolution under different climate scenarios, glaciers in HMA with areas no less than 1 km\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e in RGI6.0 were selected. Mass balance was calculated using a retrofit of mass balance gradient model (MBGR) that captures the spatial differences of mass balance with a high-resolution 2D grid combined with a continuity-equation-based 3D glacier dynamics model component for mass redistribution.\u003c/p\u003e\n\u003ch3\u003e2.2.1 Retrofit of Mass Balance Gradient model (MBGR)\u003c/h3\u003e\n\u003cp\u003eThe mass balance gradient (MBG) model of Kraaijenbrink et al. \u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e assumes a linear relationship between temperature and glacier mass balance, and expresses mass balance as a function of elevation. A mathematical relationship between annual ablation at the terminus and the mass balance of different elevation bands is used to derive the mass balance distribution.\u003c/p\u003e \u003cp\u003eThe MBG model over-smoothes spatial differences in mass balance because it uses elevation bands as its unit. We transformed the semi-distributed MBG model into a full-distributed model with grid cells as its unit. The MBGR model retains the role of nonlinear ablation factors and is described by:\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}{MB}_{ij}=\\sum\\:_{k}(({MB}_{init}+\\left({z}_{ij}-{z}_{min}\\right)\\frac{\\partial\\:MB}{\\partial\\:z})\\times\\:\\frac{\\partial\\:MB}{\\partial\\:{Red}_{k}}),k=debris,\\:\\dots\\:\\:\\#\\left(3\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{MB}_{ij}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{z}_{ij}\\)\u003c/span\u003e\u003c/span\u003e are mass balance and elevation, at the grid coordinate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:(i,\\:\\:j)\\)\u003c/span\u003e\u003c/span\u003e, respectively, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{MB}_{init}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{z}_{min}\\)\u003c/span\u003e\u003c/span\u003eare ablation and elevation at the terminus, respectively, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\partial\\:MB/\\partial\\:z\\)\u003c/span\u003e\u003c/span\u003e is the mass balance gradient, which is the relationship between mass balance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:MB\\)\u003c/span\u003e\u003c/span\u003e and elevation \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:z\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{Red}_{k}\\)\u003c/span\u003e\u003c/span\u003e includes any factors that are clearly related to glacier ablation (e.g., debris, supraglacial pond, ice cliff).\u003c/p\u003e \u003cp\u003eMean annual sum of positive degree\u0026ndash;days at the terminus and mean annual precipitation at the centroid (location where annual accumulation is maximum) from the ERA5-Land reanalysis dataset for the reference period of 2000\u0026ndash;2014 are used to initialize the MBGR model. Coupling debris coverage is used to calculate mass balance for all grid cells (Eq.\u0026nbsp;(3), refer to \u0026Oslash;strem curve \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e). Following the MBG model, ablation at the terminus is simply defined as a function of cumulative positive degree\u0026ndash;days.\u003c/p\u003e\n\u003ch3\u003e2.2.2 Glacier Dynamics Components\u003c/h3\u003e\n\u003cp\u003eIn the MBGR model, the statistics-based mass redistribution component that is part of the MBG model was replaced with a 3D ice flow dynamics model that is widely used in polar ice sheet simulations. Because of the special Stokes flow (creeping flow) of glaciers, we used the Stokes equation as a simplified version of the momentum Eq.\u0026nbsp;1\u003csup\u003e8\u0026ndash;20\u003c/sup\u003e:\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}\\nabla\\:\u0026middot;\\sigma\\:+\\rho\\:g=0\\:\\#\\left(4\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{\\sigma\\:}\\)\u003c/span\u003e\u003c/span\u003e is stress tensor, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\rho\\:\\)\u003c/span\u003e\u003c/span\u003e is ice density (916.7 kg‧m\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e), and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{g}=(0,\\:0,\\:-g)\\)\u003c/span\u003e\u003c/span\u003e is gravitational acceleration.\u003c/p\u003e \u003cp\u003eThe Shallow Shelf Approximation (SSA) further ignores vertical shear, decouples the vertical component \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:z\\)\u003c/span\u003e\u003c/span\u003e from initial equations, and has been used to simulate basal slide, surge, and other situations where the critical state is reached \u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. The Shallow Ice Approximation (SIA) is based on the Blatter\u0026ndash;Pattyn approximation; it ignores the horizontal gradient of vertical velocity and has been used to model glaciers with a dominant plastic flow \u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. The SSA\u0026thinsp;+\u0026thinsp;SIA hybrid flow greatly improves the performance of glacier dynamics models. Basal velocity of grounded ice is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varvec{v}}_{b}={\\varvec{v}}_{SSA}\\)\u003c/span\u003e\u003c/span\u003e, overall glacier velocity is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{v}={\\varvec{v}}_{SSA}+{\\varvec{v}}_{SIA}\\)\u003c/span\u003e\u003c/span\u003e \u003csup\u003e\u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e, and accuracy of model output is high.\u003c/p\u003e \u003cp\u003eIn the ice flow dynamics model, the energy balance is based on enthalpy conservation. It takes into account dissipation heating rate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Q\\)\u003c/span\u003e\u003c/span\u003e, advective enthalpy flux \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\rho\\:H\\varvec{v}\\)\u003c/span\u003e\u003c/span\u003e, and non-advective enthalpy flux and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{q}\\)\u003c/span\u003e\u003c/span\u003e, and avoids the latent heat of phase transformation in polythermal glaciers \u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e:\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}\\rho\\:\\frac{dH}{dt}=-\\nabla\\:\u0026middot;q+Q\\:\\#\\left(5\\right)\\end{array}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{q}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Q\\)\u003c/span\u003e\u003c/span\u003e are made up of their respective components of water and ice, i.e., \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{q}={\\varvec{q}}_{ice}+{\\varvec{q}}_{water}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:Q={Q}_{ice}+{Q}_{water}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n\u003ch3\u003e2.3 Extraction of dead ice\u003c/h3\u003e\n\u003cp\u003eWe used image-connected domain algorithms to separate glacier sections, identified dead ice according to various criteria (absence of connection with the main body of glacier, glacial recharge, and surface velocity), and mapped the distribution and recorded the properties of the dead ice. Given the small interannual variability, a decadal time step was used.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAcknowledgments\u003c/p\u003e\n\u003cp\u003eThis work was funded by the National Natural Science Foundation of China (No. 42171137, No. U23A2011, and No. 42171134) and National Cryosphere Desert Data Center (No. E01Z790201). The authors acknowledge the Beijing Super Cloud Computing Center (BSCC) for providing HPC resources that have contributed to the research results reported within this paper. URL: http://www.blsc.cn/.\u003c/p\u003e\n\u003cp\u003eData\u0026nbsp;and\u0026nbsp;code\u0026nbsp;availability\u003c/p\u003e\n\u003cp\u003eThe statistics, results and media files of this study are provided in supplementary materials. All data and code will be open source upon publication. During the review process, support data is temporarily available via https://doi.org/10.5281/zenodo.13759486.\u003c/p\u003e\n\u003cp\u003eConflict of interest\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003eAuthor Contributions\u003c/p\u003e\n\u003cp\u003eQ.W. and X.W. designed the study and wrote the manuscript; Q.W. developed the model and performed all analyses with additional support from Y.Y. and J.H. All authors contributed to the final form of the study.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBenn, D. \u0026amp; Evans, D. J. A. \u003cem\u003eGlaciers and Glaciation 2nd edition\u003c/em\u003e. (2014).\u003c/li\u003e\n\u003cli\u003eSchomacker, A. What controls dead-ice melting under different climate conditions? 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An enthalpy formulation for glaciers and ice sheets. \u003cem\u003eJournal of Glaciology\u003c/em\u003e \u003cstrong\u003e58\u003c/strong\u003e, 441-457 (2012). https://doi.org:10.3189/2012JoG11J088\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5301165/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5301165/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDead ice in High Mountain Asia (HMA) varies responsive to dramatic glacier loss, profoundly impacting alpine water cycle patterns. We find significant dead ice increase over this century, additional area exceeds 3,000 km2, with mass 44.3\u0026thinsp;\u0026plusmn;\u0026thinsp;2.0\u0026thinsp;~\u0026thinsp;64.1\u0026thinsp;\u0026plusmn;\u0026thinsp;5.2 Gt. Debris coverage dominates dead ice spatial pattern. Dead ice expansion would significantly alter spatio-temporal patterns of glacier ablation and impact water supply sustainability in World's Water Towers.\u003c/p\u003e","manuscriptTitle":"Climate change induces rapid growth of dead ice in Asian glaciers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-28 08:56:02","doi":"10.21203/rs.3.rs-5301165/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b5b12426-ee3e-4bc4-aca3-2cfe1b2d42df","owner":[],"postedDate":"October 28th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-11-08T09:23:58+00:00","versionOfRecord":[],"versionCreatedAt":"2024-10-28 08:56:02","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5301165","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5301165","identity":"rs-5301165","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}