Stefan Solution Research Articles

Phase change in a one-dimensional functionally graded material

Functionally graded materials (FGMs) are a class of materials with engineered microstructure to achieve spatial variation in properties so as to serve a desired function. While FGMs have been well-researched for their structural properties, there is a lack of investigation of FGMs in solid-liquid phase change heat transfer processes. A well-designed functionally graded phase change material (FG-PCM) may overcome some of the well-known limitations of the phase change process. In order to investigate this possibility, this work presents a theoretical model to predict phase change propagation in a one-dimensional FG-PCM containing an arbitrary spatial variation in thermal conductivity, thermal diffusivity and latent heat. The problem is solved using the method of eigenfunction expansion to determine the temperature distribution, wherein, spatial variation in thermophysical properties listed above is accounted for by deriving a first-order matrix ordinary differential equation in the coefficients of the series solution. Results are found to correctly reduce to the well-known Stefan solution under special conditions. The impact of variation in thermophysical properties is investigated in detail. It is found that while spatial variation in thermal conductivity and latent heat has a significant effect on the rate of phase change, the impact of the thermal diffusivity function is negligible for realistic values of the Stefan number. The effect of the Stefan number governing this problem on the rate of melting is investigated. The nature of phase change under linear (1+aξ), polynomial (1+aξn) and exponential (eaξ) functional forms of thermophysical properties is investigated. It is shown that an appropriate choice of these spatial functions may help overcome the well-known self-limiting nature of phase change and produce a nearly-linear phase change propagation curve. For example, results show 33% increase in phase change propagation for a linear (1+5ξ) variation in thermal conductivity compared to baseline. The theoretical tools developed here may help design and optimize functionally graded PCMs towards improved phase change heat transfer in applications of practical interest.

Thermal photogrammetry on a permafrost rock wall for the active layer monitoring

Permafrost and active layer models often cannot explain the high spatial variability, especially in heterogeneous environments like the mountainous regions due to their scarce resolution, paucity of climatic data and topographic details. In this study, we want to introduce a new application of the unmanned aerial vehicle (UAV) in thermal photogrammetry to model the active layer thickness (ALT) of an alpine rock wall through the computation of the thermal inertia and compare the results with a widespread ALT model. On the Gran Zebrù South rock wall, 8 thermal UAV surveys has been conducted in 4 different summer days during 2021-2022 in order to have two 3D thermal models per day at different solar radiation inputs. By analyzing topographic data, visible imagery and the thermal models, the apparent thermal inertias (ATIs) have been converted into heat transfer coefficients (HTCs) and then into ALT of 2021 and 2022. These maps have been validated through the placement of thermistors at different elevations and with variable depths (2, 15 and 40 cm from the rock surface).The resulting ALT has been compared with the Stefan's solution and the alpine permafrost index map (APIM), which showed large underestimations and a noncorrespondence with permafrost occurrence. The average ALT increase of 29.3 cm from 2021 to 2022 has been discussed regarding permafrost formation/degradation future trend under the climatic change and potential risks of alpine areas.

Analytical modeling of phase change in a composite wall comprising two distinct phase change materials in series

Most of the past literature on solid-liquid phase change heat transfer modeling focuses on a single phase change material (PCM), whereas, a sandwich of two or more PCMs arranged in series may be of interest in several applications. The modeling of heat transfer and phase change in such a system is complicated by the presence of multiple phase change fronts propagating at the same time. This work presents a theoretical analysis of the problem of melting of a two-PCM stack being heated from one end. Depending on whether the lower-melting PCM is located next to or away from the heat source, two distinct cases are considered. The propagation of the phase change fronts in each case is divided into several stages, each of which is characterized by a distinct phase change and/or sensible heating processes. The transient temperature field in each stage is determined in the form of infinite series solutions, and the propagation of phase change front over time is then determined using energy conservation at the phase change interface. In this manner, explicit expressions are derived for the time taken for each layer to completely melt. Results are shown to be in good agreement with finite-element simulations, and with the exact Stefan solution under special conditions. Key non-dimensional parameters that influence the nature of the two-PCM phase change process are identified, and their impact on phase change performance is analyzed. Quantitative predictions are presented for the conditions under which both PCMs finish melting at the same time, which is a favorable outcome for efficient energy storage.

Dual-sided melting of a one-dimensional composite wall comprising two distinct phase change material (PCM) layers

Past literature on theoretical modeling of solid-liquid phase change heat transfer mostly addresses a single phase change material (PCM), whereas, a series combination of two or more PCMs is often used in practical applications. This work presents an approximate analytical model for the melting/freezing of a one-dimensional composite of two PCMs being heated/cooled from both ends. It is shown that up to three phase change fronts may simultaneously exist in this problem. In addition to direct melting/freezing from the respective walls, it is shown that each PCM may also melt/freeze due to heat transfer through the other PCM. Using a quasi-stationary assumption, temperature field during the multi-stage phase change process is approximated by solving a multilayer transient thermal conduction problem using eigenfunction expansion. Good agreement with numerical simulations, and with the Stefan solution for a special case is demonstrated. The impact of key non-dimensional parameters on performance metrics including total time for phase change is determined. A quantitative prediction of conditions leading to the thermodynamically favorable situation of simultaneous completion of phase change of two commonly used PCMs is carried out. This work improves the theoretical understanding of phase change in composite PCMs, leading to optimization of practical thermal systems.

Ultrafast Axial Freezing in a Liquid-Filled Capillary Tube.

Liquid-filled capillary tubes are a kind of standard component in life science (e.g., blood vessels, interstitial pores, and plant vessels) and engineering (e.g., MEMS microchannel resonators, heat pipe wicks, and water-saturated soils). Under sufficiently low temperatures, the liquid in a capillary tube undergoes phase transition, forming an ice nucleus randomly on its inner wall. However, how an ice layer forms from the nucleus and then expands, either axially or radially to the tube inner wall, remains obscure. We demonstrated, both experimentally and theoretically, that axial freezing along the inner wall of a water-filled capillary tube occurs way ahead of radial freezing, at a nearly constant velocity 3 orders in magnitude faster than the latter. Rapid release of latent heat during axial freezing was identified as the determining factor for the short duration of recalescence, resulting in an exponential rise of the supercooling temperature from ice nucleation via axial freezing to radial freezing. The profile of the ice-water interface is strongly dependent upon the length-to-radius ratio of the capillary tube and the supercooling degree at ice nucleation. The results obtained in this study bridge the knowledge gap between the classical nucleation theory and the Stefan solution of phase transition.

Projected changes in soil freeze depth and their eco-hydrological impacts over the Tibetan Plateau during the 21st century

In the context of global warming, the soil freeze depth (SFD) over the Tibetan Plateau (TP) has undergone significant changes, with a series of profound impacts on the hydrological cycle and ecosystem. The complex terrains and high elevations of the TP pose great challenges in data acquisition, presenting difficulties for studying SFD in this region. This study employs Stefan's solution and downscaled datasets from the Coupled Model Intercomparison Project Phase 6 (CMIP6) to simulate the future SFDs over the TP. The changing trends of the projected SFDs under different Shared Socio-economic Pathways (SSP) scenarios are investigated, and; the responses of SFDs to potential climatic factors, such as temperature and precipitation, are analyzed. The potential impacts of SFD changes on eco-hydrological processes are analyzed based on the relationships between SFDs, the distribution of frozen ground, soil moisture, and the Normalized Difference Vegetation Index (NDVI). Results show that the projected SFDs of the TP are estimated to decrease at rates of 0.100 cm/yr under the SSP126, 0.330 cm/yr under the SSP245, 0.565 cm/yr under the SSP370, and 0.750 cm/yr under the SSP585. Additionally, the SFD decreased at a rate of 0.160 cm/yr during the historical period from 1950 to 2014, which was between the decreasing rates of the SSP126 and SSP245 scenarios. The projected SFDs are negatively correlated with air temperature and precipitation, more significant under the higher emissions scenario. The projected decrease in SFDs will significantly impact eco-hydrological processes. A rapid decrease in SFD may lead to a decline in soil moisture content and have adverse impacts on vegetation growth. This research provides valuable insights into the future changes in SFD on the TP and their impacts on eco-hydrological processes.

Active Layer Thickness and Permafrost Area Projections for the 21st Century

AbstractPermafrost warming leads to greenhouse gas release to the atmosphere, resulting in a positive feedback to climate change. Earth system models indicate that more than 80% of the near‐surface permafrost is projected to disappear by the end of this century, but with a high degree of uncertainty. Here, we apply the Stefan solution to estimate permafrost degradation under future emission scenarios. We find that the most severe future scenario is likely to lead to only a 14% decrease in area extent of the near‐surface permafrost at 3.5 m depth, and an area extent decrease of 1.3% at a depth of 6.0 m. Relative to active layer thickness increases from historical simulations, we find a less than 30% deepening for most permafrost regions by the end of this century. These results imply that the Stefan solution provides near‐surface permafrost area extent degradation estimates that are substantially lower than directly projected by models.

Observation of spatial and temporal patterns of seasonal ground deformation in central Yakutia using time series InSAR data in the freezing season

The seasonal freeze/thaw variations of the active layer cause seasonal ground deformation, such as thaw subsidence in summer and frost heave in winter due to the cyclic phase changes of soil water. The Synthetic Aperture Radar (SAR) remote sensing, especially interferometric SAR (InSAR) techniques, has been proven to be a very useful tool for observing surface displacements of permafrost environments. Most previous studies on seasonal InSAR displacement have been concentrated in several study sites in the Arctic tundra regions. The objective of this study is to extend the InSAR analysis of seasonal ground deformations to boreal forest regions, where monitoring ground deformation is particularly important in terms of better understanding active layer dynamics under various ecological and geological conditions. In this study, we presented a strategy to analyze the time series SAR data in the freezing season to estimate the differential phase for seasonal ground deformation while overcoming the problem of coherence losses due to the rapid growth of vegetation during the short growing season. We applied the SBAS-based InSAR processing method to Sentinel-1 SAR in the central Yakutian lowlands, where boreal forests and thermokarst landforms are widely distributed, and retrieved frost-related displacement signals successfully. In addition to the magnitude of ground deformation in the freezing season, we further examined the temporal deformation pattern related to the progression of the freezing front in the soil during active freezing. Based on the Stefan solution, we proposed a piecewise linear model for the time series deformation. The proposed model divides the time series displacement according to the progression of freezing into three linear segments, and the slope parameter of each linear model can be interpreted as indicating the hydrological characteristics of the upper, middle, and lower parts of the soil. The results for the Yakutian lowlands illustrated the potential of SAR remote sensing to observe and quantify spatial details of the thermal and hydrological properties inside the active layer soil even in highly vegetated subarctic boreal forest areas.

Estimation of Soil Freeze Depth in Typical Snowy Regions Using Reanalysis Dataset: A Case Study in Heilongjiang Province, China

Soil freeze depth variations greatly affect energy exchange, carbon exchange, ecosystem diversity, and the water cycle. Given the importance of these processes, obtaining freeze depth data over large scales is an important focus of research. This paper presents a simple empirical algorithm to estimate the maximum seasonally frozen depth (MSFD) of seasonally frozen ground (SFG) in snowy regions. First, the potential influences of driving factors on the MSFD variations were quantified in the baseline period (1981–2010) based on the 26 meteorological stations within and around the SFG region of Heilongjiang province. The three variables that contributed more than 10% to MSFD variations (i.e., air freezing index, annual mean snow depth, and snow cover days) were considered in the analysis. A simple multiple linear regression to estimate soil freeze depth was fitted (1981–2010) and verified (1975–1980 and 2011–2014) using ground station observations. Compared with the commonly used simplified Stefan solution, this multiple linear regression produced superior freeze depth estimations, with the mean absolute error and root mean square error of the station average reduced by over 20%. By utilizing this empirical algorithm and the ERA5-Land reanalysis dataset, the multi-year average MSFD (1981–2010) was 132 cm, ranging from 52 cm to 186 cm, and MSFD anomaly exhibited a significant decreasing trend, at a rate of −0.38 cm/decade or a net change of −28.14 cm from 1950–2021. This study provided a practical approach to model the soil freeze depth of SFG over a large scale in snowy regions and emphasized the importance of considering snow cover variables in analyzing and estimating soil freeze depth.

Modeling Heat Transfer through Permafrost Soil Subjected to Seasonal Freeze-Thaw

The present paper proposes an iterative implicit numerical method for simulating the thaw depth of permafrost soil. For this purpose, the enthalpy-porosity model was used for the phase change process, and the finite difference scheme FTCS (Forward Time Centered Space) was used for discretization. An artificial mushy zone was maintained with the same thickness by keeping the regularization parameter proportional to the temperature gradient. In doing so, we made the scheme more stable and convergence occurred faster. The model accuracy was validated by comparing the numerical results with the analytical Stefan solution and with the results of a derived numerical model, based on an explicit scheme. The model performance was also tested against observation data collected on four different landscapes with different soil profiles and located on a basin underlain by continuous permafrost. It was found that the proposed model matched noticeably well the analytical solution for a volumetric liquid fraction (phi) equal to 0.5 regardless of the grid resolution. Furthermore, compared with the observation data, the model reproduced the annual maximum thaw depth with an absolute error lying between 0.7 and 7.7%. In addition, the designed algorithm allowed the model to converge after a maximum of eight iterations, reducing the computational time by around 75% compared to the explicit model. The results were so encouraging that the model can be included in a hydrological modeling of permafrost watersheds or cold regions in general.

Active Layer Thickness Variation on the Qinghai‐Tibetan Plateau: Historical and Projected Trends

AbstractAs the buffer layer between the atmosphere and permafrost, the active layer is vulnerable to climate change. The variation in the active layer thickness (ALT) has important effects on surface energy balance, ecosystem, hydrological cycle, vegetation cover, and engineering construction in permafrost regions. The goal of this study is to discuss the active layer variation under different shared socioeconomic pathways (SSPs) for specific warming levels and to reveal the potential interactions between the ALT and the associated driving factors in typical hydrological basins. We revised the Stefan solution using the edaphic factor and the thawing index calculated by multimodel data from the Coupled Model Intercomparison Project Phase 6 to estimate the variation in the ALT. During 2015 to 2100, the ALT will increase by 14 cm (SSP1‐2.6), 43 cm (SSP2‐4.5), and 1.44 m (SSP5‐8.5), with average increase rates of 2.5 cm/decade, 5.8 cm/decade, and 17.5 cm/decade, respectively. The rates of increase of the ALT in the Hexi basin, Inner basin, Mekong basin, Yangtze basin, and Yellow basin are 12.6 cm/decade, 6.7 cm/decade, 5.2 cm/decade, 8.0 cm/decade, and 5 cm/decade, respectively. These results illustrate that air temperature is the primary determinant of ALT variation and normalized difference vegetation index (NDVI) and snow depth may influence the ALT change. The most significant correlations are between the ALT and NDVI in the Yangtze basin. In different seasons, the spring snow depth has the greatest impact on the ALT in the Hexi basin.

A Semianalytical Interface Model of Soil Freeze/Thaw and Permafrost Evolution

AbstractA physically based one‐dimensional sharp‐interface model of active layer evolution and permafrost thaw is presented. This computationally efficient, semianalytical, nonequilibrium solution to soil freeze‐thaw problems in partially saturated media is proposed as a component of hydrological models to describe seasonal ground ice, active layer evolution, and changes in permafrost temperature and extent. The model is developed and validated against the analytical Stefan solution and a finite volume coupled heat and mass transfer model of freeze‐thaw in unsaturated porous media. Unlike analytic models, the interface model provides a nonequilibrium solution to the heat equation while permitting a wide range of temporally variable boundary conditions and supporting the simulation of multiple interfaces between frozen and unfrozen soils. The model is implemented for use in discontinuous permafrost peatlands where soil properties are highly dependent on soil ice content and infiltration capacity is high. It is demonstrated that the model is suitable for the representation of variably saturated active layer and permafrost evolution in cases both with and without a talik.

Soil freeze depth variability across Eurasia during 1850–2100

Soil freeze depth (SFD) is an important indicator of cryospheric and climate change. Changes in SFD have important effects on hydrology, the energy balance, carbon exchange, and ecosystem diversity. However, quantifying and predicting SFD at large scales remains a challenge due to sparse long-term observations. This study employs the Stefan solution combined with 16 of the coupled model inter-comparison project phase 5 (CMIP5) models over the historical period (1850–2005) and three representative concentration pathways (RCP 2.6, 4.5, and 8.5) for 2006–2100, the Climatic Research Unit dataset (1901–2013), and hundreds of soil temperature, air temperature, precipitation, and snow depth sites to analyze the spatiotemporal variability of SFD in Eurasia under historical and projected climate change. During 1850–2005, a statistically significant SFD decrease of 0.49 ± 0.04 cm/decade is observed. Spatially, the biggest decreases are generally in Siberia and on the Tibetan Plateau. There is a projected decrease in 2006–2100 SFD of 4.58 ± 0.26, 1.85 ± 0.21, and 0.45 ± 0.18 cm/decade for RCP 8.5, 4.5, 2.6, respectively. These variations in SFD provide key insights into spatiotemporal changes in climate, and facilitate improved understanding of variation in frozen ground across Eurasia.

Urban Geocryology: Mapping Urban–Rural Contrasts in Active-Layer Thickness, Barrow Peninsula, Northern Alaska

The maximum depth of seasonal thaw is a critical design factor for civil infrastructure in permafrost regions. Although maps of active-layer thickness (ALT) have been created for localized areas in undisturbed terrain, this has rarely been done within urbanized areas. The modified Berggren solution was used to map ALT at a resolution of 30 × 30 m over the 150-km2 Barrow Peninsula in northern Alaska. Emphasis was placed on analyzing differences in accuracy obtained in urbanized and relatively undisturbed tundra. Although the modified Berggren solution is known to provide more accurate estimates of frost and thaw depth than the Stefan solution, it has not been used previously in mapping applications. As part of the Barrow Urban Heat Island Study, seventy-one miniature data loggers were installed in and surrounding the City of Utqiaġvik (formerly Barrow) to measure air and soil temperature. The resulting data were used to calculate air and soil surface temperature fields, as well as summer n-factors, based on nine urban and rural land-cover classes. Regional soil and land-cover maps were used to obtain additional input data. Validation was performed by comparing probed ALT measurements with predicted pixel values. Model results confirm that the presence of urban infrastructure increases both the magnitude and the geographic variability of ALT relative to surrounding undisturbed tundra. The Berggren solution performed well for estimating mean values for land-cover classes in both rural and urban areas and has considerable potential as a tool for mapping ALT in other applications. Key Words: active layer, Alaska, Barrow, frozen ground, geocryology, mapping, permafrost, urban, Utqiaġvik.

Estimating Seasonally Frozen Ground Depth From Historical Climate Data and Site Measurements Using a Bayesian Model

AbstractWe develop a Bayesian model to predict the maximum thickness of seasonally frozen ground (MTSFG) using historical air temperature and precipitation observations. We use the Stefan solution and meteorological data from 11 stations to estimate the MTSFG changes from 1961 to 2016 in the Yellow River source region of northwestern China. We employ an antecedent precipitation index model to estimate changes in the liquid soil water content. The marginal posterior probability distributions of the antecedent precipitation index parameters are estimated using Markov chain Monte Carlo sampling methods. We compare the results of our stochastic method with those obtained from the traditional deterministic method and find that they are consistent in general. The stochastic approach is effective for estimating the historical changes in the frozen ground depth (root‐mean‐square errors = 0.13–0.35 m), and it provides more information on model uncertainty regarding soil moisture variations. Additionally, simulation shows that the MTSFG has decreased by 0.31 cm per year over the last 56 years on the northeastern Qinghai‐Tibet Plateau. This decrease in frost depth accelerated in the 1990s and 2000s. Considering the lack of data on seasonally frozen soil monitoring, the Bayesian method provides a pragmatic approach to statistically model frozen ground changes using available meteorological data.

Spatiotemporal Changes in Active Layer Thickness under Contemporary and Projected Climate in the Northern Hemisphere

Abstract Variability of active layer thickness (ALT) in permafrost regions is critical for assessments of climate change, water resources, and engineering applications. Detailed knowledge of ALT variations is also important for studies on ecosystem, hydrological, and geomorphological processes in cold regions. The primary objective of this study is therefore to provide a comprehensive 1971–2000 climatology of ALT and its changes across the entire Northern Hemisphere from 1850 through 2100. To accomplish this, in situ observations, the Stefan solution based on a thawing index, and the edaphic factor (E factor) are employed to calculate ALT. The thawing index is derived from (i) the multimodel ensemble mean of 16 models from phase 5 of the Coupled Model Intercomparison Project (CMIP5) over 1850–2005, (ii) three representative concentration pathways (RCP2.6, RCP4.5, and RCP8.5) for 2006–2100, and (iii) Climatic Research Unit (CRU) gridded observations for 1901–2014. The results show significant spatial variability in in situ ALT that generally ranges from 40 to 320 cm, with some extreme values of 900 cm in the Alps. The differences in the ALT climatology between the three RCPs and the historical experiments ranged from 0 to 200 cm. The biggest increases, of 120–200 cm, are on the Qinghai–Tibetan Plateau, while the smallest increases of less than 20 cm are in Alaska. Averaged over all permafrost regions, mean ALT from CMIP5 increased significantly at 0.57 ± 0.04 cm decade−1 during 1850–2005, while 2006–2100 projections show ALT increases of 0.77 ± 0.08 cm decade−1 for RCP2.6, 2.56 ± 0.07 cm decade−1 for RCP4.5, and 6.51 ± 0.07 cm decade−1 for RCP8.5.

Determining Interface Temperature During Rapid Freezing of Supercooled Water

In the classical Stefan solution of solidification in liquids, the solid–liquid interface temperature is considered to be constantly equal to the freezing point. However, if solidification occurred in supercooled liquids, then the interface temperature would be lower than the freezing point due to the nonequilibrium condition. In this study, the interface temperature during rapid freezing of supercooled water is investigated by molecular dynamics simulations. The relationship of interface temperature and velocity is analyzed and fitted into a quadratic function. In most aviation ice accretion situations, the degree of nonequilibrium condition at the ice–water interface falls in a range of interfacial supercooling from 0 to 4 K. Given this condition, the relationship of interface velocity and temperature could be approximated by a constant interfacial kinetic coefficient of . Both regularities are applicable in numerical simulation of dendrite ice growth.

Response of seasonal soil freeze depth to climate change across China

Abstract. The response of seasonal soil freeze depth to climate change has repercussions for the surface energy and water balance, ecosystems, the carbon cycle, and soil nutrient exchange. Despite its importance, the response of soil freeze depth to climate change is largely unknown. This study employs the Stefan solution and observations from 845 meteorological stations to investigate the response of variations in soil freeze depth to climate change across China. Observations include daily air temperatures, daily soil temperatures at various depths, mean monthly gridded air temperatures, and the normalized difference vegetation index. Results show that soil freeze depth decreased significantly at a rate of −0.18 ± 0.03 cm yr−1, resulting in a net decrease of 8.05 ± 1.5 cm over 1967–2012 across China. On the regional scale, soil freeze depth decreases varied between 0.0 and 0.4 cm yr−1 in most parts of China during 1950–2009. By investigating potential climatic and environmental driving factors of soil freeze depth variability, we find that mean annual air temperature and ground surface temperature, air thawing index, ground surface thawing index, and vegetation growth are all negatively associated with soil freeze depth. Changes in snow depth are not correlated with soil freeze depth. Air and ground surface freezing indices are positively correlated with soil freeze depth. Comparing these potential driving factors of soil freeze depth, we find that freezing index and vegetation growth are more strongly correlated with soil freeze depth, while snow depth is not significant. We conclude that air temperature increases are responsible for the decrease in seasonal freeze depth. These results are important for understanding the soil freeze–thaw dynamics and the impacts of soil freeze depth on ecosystem and hydrological process.

Subduction zone decoupling/retreat modeling explains south Tibet (Xigaze) and other supra-subduction zone ophiolites and their UHP mineral phases

The plate tectonic setting in which proto-ophiolite ‘oceanic’ lithosphere is created remains controversial with a number of environments suggested. Recent opinions tend to coalesce around supra-subduction zone (SSZ) forearc extension, with a popular conceptual model in which the proto-ophiolite forms during foundering of oceanic lithosphere at the time of spontaneous or induced onset of subduction. This mechanism is favored in intra-oceanic settings where the subducting lithosphere is old and the upper plate is young and thin. We investigate an alternative mechanism; namely, decoupling of the subducting oceanic lithosphere in the forearc of an active continental margin, followed by subduction zone (trench) retreat and creation of a forearc oceanic rift basin, containing proto-ophiolite lithosphere, between the continental margin and the retreating subduction zone. A template of 2D numerical model experiments examines the trade-off between strength of viscous coupling in the lithospheric subduction channel and net slab pull of the subducting lithosphere. Three tectonic styles are observed: 1) C, continuous subduction without forearc decoupling; 2) R, forearc decoupling followed by rapid subduction zone retreat; 3) B, breakoff of subducting lithosphere followed by re-initiation of subduction and in some cases, forearc decoupling (B-R). In one case (BA-B-R; where BA denotes backarc) subduction zone retreat follows backarc rifting. Subduction zone decoupling is analyzed using frictional-plastic yield theory and the Stefan solution for the separation of plates containing a viscous fluid. The numerical model results are used to explain the formation of Xigaze group ophiolites, southern Tibet, which formed in the Lhasa terrane forearc, likely following earlier subduction and not necessarily during subduction initiation. Either there was normal coupled subduction before subduction zone decoupling, or precursor slab breakoff, subduction re-initiation and then decoupling. Rapid deep upper-mantle circulation in the models during subduction zone retreat can exhume and emplace material in the forearc proto-ophiolite from as deep as the mantle transition zone, thereby explaining diamonds and other 10–15 GPa UHP phases in Tibetan ophiolites.

Long-term change in the depth of seasonally frozen ground and its ecohydrological impacts in the Qilian Mountains, northeastern Tibetan Plateau

Changes in seasonally frozen ground at high elevations under the effects of global warming and their ecohydrological impacts are important for understanding changes in regional water resources and ecosystems. This study estimates the spatio-temporal variability in the maximum thickness of seasonally frozen ground (MTSFG) in the Qilian Mountains in the northeastern Tibetan Plateau from 1960 to 2014 by using a variant of the Stefan solution. The present study analyzes changes in streamflow and vegetation to reveal the ecohydrological impacts of changes in the MTSFG. Results indicate that the MTSFG shows a mean decreasing trend of 7.4cm/10a in the past 55years in correspondence to the significantly increasing air temperature (0.34°C/10a). The greatest decreasing trend of the MTSFG is at elevations of 3400–3800 m. The annual baseflow has increased significantly in most of the sub-basins for which the increasing precipitation is the main factor. The MTSFG is another major factor for the increase in baseflow during the cold season (from November to April) according to the results of gray relational analysis. The leaf area index (LAI) during the growing season has increased by 0.045/10a since 2000, and the start of growing season has advanced by 1.8–2.1d/10a at elevations of 3000–3800 m, where the vegetation cover is the densest. Furthermore, results of correlation analysis show that the topsoil moisture increases with the MTSFG decreases. Results of gray relational analysis show that the decrease in MTSFG is the main reason for the advancing green-up dates and increasing LAI in the initial period of the growing season. Our results show that the ecohydrological processes are changing along with frozen soil degradation in the northeastern Tibetan Plateau.