Equilibrium Line Research Articles

The 21st-century fate of the Mocho-Choshuenco ice cap in southern Chile

Abstract. Glaciers and ice caps are thinning and retreating along the entire Andes ridge, and drivers of this mass loss vary between the different climate zones. The southern part of the Andes (Wet Andes) has the highest abundance of glaciers in number and size, and a proper understanding of ice dynamics is important to assess their evolution. In this contribution, we apply the ice-sheet model SICOPOLIS (SImulation COde for POLythermal Ice Sheets) to the Mocho-Choshuenco ice cap in the Chilean Lake District (40∘ S, 72∘ W; Wet Andes) to reproduce its current state and to project its evolution until the end of the 21st century under different global warming scenarios. First, we create a model spin-up using observed surface mass balance data on the south-eastern catchment, extrapolating them to the whole ice cap using an aspect-dependent parameterization. This spin-up is able to reproduce the most important present-day glacier features. Based on the spin-up, we then run the model 80 years into the future, forced by projected surface temperature anomalies from different global climate models under different radiative pathway scenarios to obtain estimates of the ice cap's state by the end of the 21st century. The mean projected ice volume losses are 56±16 % (RCP2.6), 81±6 % (RCP4.5), and 97±2 % (RCP8.5) with respect to the ice volume estimated by radio-echo sounding data from 2013. We estimate the uncertainty of our projections based on the spread of the results when forcing with different global climate models and on the uncertainty associated with the variation of the equilibrium line altitude with temperature change. Considering our results, we project a considerable deglaciation of the Chilean Lake District by the end of the 21st century.

The form, distribution and palaeoclimatic implications of cirques in southwest Turkey (Western Taurus)

The Taurus Mountains of southwest Turkey are split into numerous separated ranges, of which eleven supported former glaciers. We describe cirques and related moraines in four new locations, as well as those in seven ranges where glaciation was previously known. This gives a complete inventory of the 85 cirques in southwest Turkey. These are comparable in size to those elsewhere, but narrower and often less developed. Lengths averaging 672 m are high relative to widths of 542 m. Overall axial gradients average 22.4°. Cirque floor altitudes are controlled largely by altitudes of the mountains above, but they also vary in relation to precipitation, in sympathy with ELAs (Equilibrium Line Altitudes) of former glaciers. In most ranges where glaciers were short (extending little beyond cirques), ELA can be predicted from mean mid-floor altitude. Our observations demonstrate lower ELAs than in previous literature. Both ELAs and cirque floors rise eastward in the west, and northward inland from the coast. This supports the importance of winds from the west and southwest, off the Mediterranean Sea, bringing LGM (Last Glacial Maximum) conditions wetter than present to mountains near the coast. Cirques face on average a little east of north, showing the effects of shade and differential solar radiation receipt.

Climatic controls on mountain glacier basal thermal regimes dictate spatial patterns of glacial erosion

Abstract. Climate has been viewed as a primary control on the rates and patterns of glacial erosion, yet our understanding of the mechanisms by which climate influences glacial erosion is limited. We hypothesize that climate controls the patterns of glacial erosion by altering the basal thermal regime of glaciers. The basal thermal regime is a first-order control on the spatial patterns of glacial erosion. Polythermal glaciers contain both cold-based portions that protect bedrock from erosion and warm-based portions that actively erode bedrock. In this study, we model the impact of various climatic conditions on glacier basal thermal regimes and patterns of glacial erosion in mountainous regions. We couple a sliding-dependent glacial erosion model with the Parallel Ice Sheet Model (PISM) to simulate the evolution of the glacier basal thermal regime and glacial erosion in a synthetic landscape. We find that both basal thermal regimes and glacial erosion patterns are sensitive to climatic conditions, and glacial erosion patterns follow the patterns of the basal thermal regime. Cold temperature leads to limited glacial erosion at high elevations due to cold-based conditions. Increasing precipitation can overcome the impact of cold temperature on the basal thermal regime by accumulating thick ice and lowering the melting point of ice at the base of glaciers. High precipitation rates, therefore, tend to cause warm-based conditions at high elevations, resulting in intensive erosion near the peak of the mountain range. Previous studies often assessed the impact of climate on the spatial patterns of glacial erosion by integrating climatic conditions into the equilibrium line altitudes (ELAs) of glaciers, and glacial erosion is suggested to be maximal around the ELA. However, our results show that different climatic conditions produce glaciers with similar ELAs but different patterns of basal thermal regime and glacial erosion, suggesting that there might not be any direct correlation between ELAs and glacial erosion patterns.

Magnetic confinement in the wind of low mass stars

AbstractMagnetic confinement of material is observed on both high and low mass stars. On low mass stars, this confinement can be seen as slingshot prominences, in which condensations are supported several stellar radii above the surface by strong magnetic fields. We present a model for generating cooled field lines in equilibrium with the background corona, which we use to populate a model corona. We find prominence masses on the order of observationally derived values. We find two types of solutions: footpoint heavy “solar-like prominences” and summit heavy “slingshot prominences” which are centrifugally supported. These can form within the open field region i.e. embedded in the wind. We generate Hα spectra from different field structures and show that all display behaviour that is consistent with observations. This implies that the features seen in observations could be supported by a range of conditions, suggesting they would be common across rapidly rotating stars.

Geomorphological record and equilibrium line altitude of glaciers during the last glacial maximum in the Rodna Mountains (eastern Carpathians) – Corrigendum

Geomorphological record and equilibrium line altitude of glaciers during the last glacial maximum in the Rodna Mountains (eastern Carpathians) – Corrigendum

Surface Mass-Balance Gradients From Elevation and Ice Flux Data in the Columbia Basin, Canada

The mass-balance—elevation relation for a given glacier is required for many numerical models of ice flow. Direct measurements of this relation using remotely-sensed methods are complicated by ice dynamics, so observations are currently limited to glaciers where surface mass-balance measurements are routinely made. We test the viability of using the continuity equation to estimate annual surface mass balance between flux-gates in the absence of in situ measurements, on five glaciers in the Columbia Mountains of British Columbia, Canada. Repeat airborne laser scanning surveys of glacier surface elevation, ice penetrating radar surveys and publicly available maps of ice thickness are used to estimate changes in surface elevation and ice flux. We evaluate this approach by comparing modeled to observed mass balance. Modeled mass-balance gradients well-approximate those obtained from direct measurement of surface mass balance, with a mean difference of +6.6 ± 4%. Regressing modeled mass balance, equilibrium line altitudes are on average 15 m higher than satellite-observations of the transient snow line. Estimates of mass balance over flux bins compare less favorably than the gradients. Average mean error (+0.03 ± 0.07 m w.e.) between observed and modeled mass balance over flux bins is relatively small, yet mean absolute error (0.55 ± 0.18 m w.e.) and average modeled mass-balance uncertainty (0.57 m w.e.) are large. Mass conservation, assessed with glaciological data, is respected (when estimates are within 1σ uncertainties) for 84% of flux bins representing 86% of total glacier area. Uncertainty on ice velocity, especially for areas where surface velocity is low (<10 m a−1) contributes the greatest error in estimating ice flux. We find that using modeled ice thicknesses yields comparable modeled mass-balance gradients relative to using observations of ice thickness, but we caution against over-interpreting individual flux-bin mass balances due to large mass-balance residuals. Given the performance of modeled ice thickness and the increasing availability of ice velocity and surface topography data, we suggest that similar efforts to produce mass-balance gradients using modern high-resolution datasets are feasible on larger scales.

Climatological analysis of freezing level height over China and its implications using homogenized in‐situ data

ABSTRACTFreezing level height (FLH) is the altitude of a location where the air temperature is 0°C. The FLH denotes the approximate position for water phase transitions from liquid (or vapour) to solid but not vapour to liquid. Based on temperature and height data on the ground surface to heights with an atmospheric pressure of 400 hPa, the monthly FLH at 118 radiosonde stations located in China are derived for the 1958–2017 period. The monthly and annual climatology during 1981–2010 and the seasonal, intra‐annual and decadal variabilities of the FLH during 1958–2017, along with its long‐term trends, were quantitatively evaluated at the regional scale and for individual stations. FLH climatology is generally related to season, zone and topography. The annual FLH anomalies decline initially, followed by a rise, with synchronous changes in the temperature in the lower and middle troposphere; the anomalies in south‐eastern China are partly associated with El Niño–Southern Oscillation events. The increasing trends of FLH are closely associated with tropospheric warming and show evident regional and seasonal differences. Stronger increasing trends are observed in northern and western China in autumn or winter (particularly in recent decades). The changes in FLH have implications on long‐term trends in equilibrium line altitude (ELA) of glaciers in Tianshan Mountains, snow cover extent in melt season and hail frequency in China especially in high‐elevations. During recent decades, the evolution of the FLH and major composition in the cryosphere has accelerated as a response to tropospheric warming. The study on FLH change can provide valuable information for the evaluation of glaciers, snow cover extent and hail frequency in China from a new perspective; which is helpful for understanding regional hydrological processes and climate changes better. Further application of FLH in cryosphere monitoring can improve water management and flood forecasting in headwater regions in China.

A novel hybrid method for the calculation of methane hydrate-water interfacial tension along the three-phase (hydrate-liquid water-vapor) equilibrium line.

We use a novel hybrid method to explore the temperature dependence of the solid-liquid interfacial tension of a system that consists of solid methane hydrate and liquid water. The calculated values along the three-phase (hydrate-liquid water-vapor) equilibrium line are obtained through the combination of available experimental measurements and computational results that are based on approaches at the atomistic scale, including molecular dynamics and Monte Carlo. An extensive comparison with available experimental and computational studies is performed, and a critical assessment and re-evaluation of previously reported data is presented.

Helheim Glacier diurnal velocity fluctuations driven by surface melt forcing

AbstractThe influence of surface melt on the flow of Greenland's largest outlet glaciers remains poorly known and in situ observations are few. We use field observations to link surface meltwater forcing to glacier-wide diurnal velocity variations on East Greenland's Helheim Glacier over two summer melt seasons. We observe diurnal variations in glacier speed that peak ~6.5 h after daily maximum insolation and extend from the terminus region to the equilibrium line. Both the amplitude of the diurnal speed variation and its sensitivity to daily melt are largest at the glacier terminus and decrease up-glacier, suggesting that the magnitude of the response is controlled not only by melt input volume and temporal variability, but also by background effective pressure, which approaches zero at the terminus. Our results provide evidence that basal lubrication by meltwater drives diurnal velocity variations at Greenland's marine-terminating glaciers in a similar manner to alpine glaciers and Greenland's land-terminating outlet glaciers.

Subcritical Andronov-Hopf scenario for systems with a line of equilibria.

Using numerical simulation methods and analytical approaches, we demonstrate hard self-oscillation excitation in systems with infinitely many equilibrium points forming a line of equilibria in the phase space. The studied bifurcation phenomena are equivalent to the excitation scenario via the subcritical Andronov-Hopf bifurcation observed in classical self-oscillators with isolated equilibrium points. The hysteresis and bistability accompanying the discussed processes are shown and explained. The research is carried out on an example of a nonlinear memristor-based self-oscillator model. First, a simpler model including Chua's memristor with a piecewise-smooth characteristic is explored. Then, the memristor characteristic is changed to a function being smooth everywhere. Finally, the action of the memristor forgetting effect is taken into consideration.

Machine learning initialization to accelerate Stokes profile inversions

Context. At present, an exponential growth in scientific data from current and upcoming solar observatories is expected. Most of the data consist of high spatial and temporal resolution cubes of Stokes profiles taken in both local thermodynamic equilibrium (LTE) and non-LTE spectral lines. The analysis of such solar observations requires complex inversion codes. Hence, it is necessary to develop new tools to boost the speed and efficiency of inversions and reduce computation times and costs. Aims. In this work we discuss the application of convolutional neural networks (CNNs) as a tool to advantageously initialize Stokes profile inversions. Methods. To demonstrate the usefulness of CNNs, we concentrate in this paper on the inversion of LTE Stokes profiles. We use observations taken with the spectropolarimeter on board the Hinode spacecraft as a test bench mark. First, we carefully analyse the data with the SIR inversion code using a given initial atmospheric model. The code provides a set of atmospheric models that reproduce the observations well. These models are then used to train a CNN. Afterwards, the same data are again inverted with SIR but using the trained CNN to provide the initial guess atmospheric models for SIR. Results. The CNNs allow us to significantly reduce the number of inversion cycles when used to compute initial guess model atmospheres (‘assisted inversions’), therefore decreasing the computational time for LTE inversions by a factor of two to four. CNNs alone are much faster than assisted inversions, but the latter are more robust and accurate. CNNs also help to automatically cluster pixels with similar physical properties, allowing the association with different solar features on the solar surface, which is useful when inverting huge datasets where completely different regimes are present. The advantages and limitations of machine learning techniques for estimating optimum initial atmospheric models for spectral line inversions are discussed. Finally, we describe a python wrapper for the SIR and DeSIRe codes that allows for the easy setup of parallel inversions. The tool implements the assisted inversion method described in this paper. The parallel wrapper can also be used to synthesize Stokes profiles with the RH code. Conclusions. The assisted inversions can speed up the inversion process, but the efficiency and accuracy of the inversion results depend strongly on the solar scene and the data used for the CNN training. This method (assisted inversions) will not obviate the need for analysing individual events with the utmost care but will provide solar scientists with a much better opportunity to sample large amounts of inverted data, which will undoubtedly broaden the physical discovery space.

A model for freeze-thaw-induced plastic volume changes in saturated clays

A new model is proposed for describing freeze-thaw-induced plastic volume changes in saturated clays based on microscopic inhomogeneities inherent in the soil structure and the pore water transfer between them. It is shown through a simple inhomogeneous mesostructure model that the equilibrium state reached after freezing serves as an important reference state for interpreting the volumetric behaviour. The soil state evolution towards this freeze equilibrium state describes many features seen in the experimentally observed freeze-thaw behaviour, such as the existence of a limiting stress level above which no plastic volume change occurs. The process of freezing/thawing is modelled as a rate process approaching the freeze equilibrium line (FEL) and representing the eventual equilibrium states at a particular sub-freezing temperature, exploiting a newly defined state parameter, ψfe. The model offers a mesoscopic three-dimensional yield surface in the specific volume – effective stress – temperature space, expressed by a simple equation. Although the model’s essence is encapsulated in only two simple equations, it can simulate well the experimentally observed volume change accumulation with freeze-thaw cycles under different stress levels and densities (or over-consolidation ratios). As the model is formulated in an incremental rate form, it can be applied to general freeze-thaw problems, even those with irregular temperature and stress history – a feature not seen in existing models.

DISTRIBUTION AND EVOLUTION OF ICE APRONS IN A CHANGING CLIMATE IN THE MONT-BLANC MASSIF (WESTERN EUROPEAN ALPS)

Abstract. Ice Apron (IA) is a poorly studied ice feature, commonly existing in all the world’s major mountain regions. This study aims to map the locations of the IAs in the Mont Blanc massif (MBM), making use of the very high-resolution optical satellite images from 2001, 2012 and 2019. 423 IAs were identified and accurately delineated in the MBM on the images from 2019, and their topographic characteristics were studied. We generated our own Digital Elevation Model (DEM) at 4 m resolution since the freely available products predominantly suffer from significant inconsistencies, especially in steep mountain areas. Results show that most IAs exist at elevations above the regional Equilibrium Line Altitude (ELA), on steep slopes, on concave surfaces, on northern and southern aspects and on the most rugged terrains. They are also commonly associated with steep slope glaciers as 85% of them occur on these glaciers’ headwalls. A comparison between 2001 and 2019 shows that IAs have lost around 29% of their area over a period of 18 years. This is significant and the rate of area loss is very alarming in comparison with the larger glacier bodies. We also studied the effect of topographic parameters on the area loss. We found that topographic factors like slope, aspect, curvature, elevation and Terrain Ruggedness Index (TRI) strongly influence the rate of area loss of IAs.

Alpine relief limited by glacial occupation time

AbstractGlaciers exert a major control on the shape of mountain topography. They tend to reduce relief above and scour troughs below the equilibrium line altitude (ELA). While many studies report this dichotomy, relief-limiting effects are controversial due to difficulties in quantifying key factors such as the initial topography, the timing of glacial occupancy, or rock uplift counteracting glacial erosion. Consequently, effectivity and degree of glacial erosion remain ambiguous. In geologically and climatically well-investigated parts of the European Central Alps, our calculation of glacial occupation time (GOT) from Quaternary ELA variations allows the quantification of gradual topographic modifications generated by the cumulative impact of cirque erosion over the Quaternary. We show that under low uplift, relief is effectively limited by glacial and periglacial headwall retreat, leading to a decline in topographic relief as GOT increases. Conversely, higher uplift rates seem to induce more persistent valley glaciation, triggering a positive feedback loop in which steep slopes are protected against erosion and relief increases.

Evolution of Surface Characteristics of Three Debris-Covered Glaciers in the Patagonian Andes From 1958 to 2020

A number of glaciological observations on debris-covered glaciers around the globe have shown a delayed length and mass adjustment in relation to climate variability, a behavior normally attributed to the ice insulation effect of thick debris layers. Dynamic interactions between debris cover, geometry and surface topography of debris-covered glaciers can nevertheless govern glacier velocities and mass changes over time, with many glaciers exhibiting high thinning rates in spite of thick debris cover. Such interactions are progressively being incorporated into glacier evolution research. In this paper we reconstruct changes in debris-covered area, surface velocities and surface features of three glaciers in the Patagonian Andes over the 1958–2020 period, based on satellite and aerial imagery and Digital Elevation Models. Our results show that debris cover has increased from 40 ± 0.6 to 50 ± 6.7% of the total glacier area since 1958, whilst glacier slope has slightly decreased. The gently sloping tongues have allowed surface flow velocities to remain relatively low (<60 m a−1) for the last two decades, preventing evacuation of surface debris, and contributing to the formation and rise of the ice cliff zone upper boundary. In addition, mapping of end of summer snowline altitudes for the last two decades suggests an increase in the Equilibrium Line Altitudes, which promotes earlier melt out of englacial debris and further increases debris-covered ice area. The strongly negative mass budget of the three investigated glaciers throughout the study period, together with the increases in debris cover extent and ice cliff zones up-glacier, and the low velocities, shows a strong linkage between debris cover, mass balance evolution, surface velocities and topography. Interestingly, the presence of thicker debris layers on the lowermost portions of the glaciers has not lowered thinning rates in these ice areas, indicating that the mass budget is mainly driven by climate variability and calving processes, to which the influence of enhanced thinning at ice cliff location can be added.

Geomorphology of the topmost part of the Bistra Mountain, Mavrovo Park, North Macedonia

ABSTRACT Identification of the remnant traces of paleo-glaciers provides important proxies to understand the response of the environment to rapid climate changes. We present a 1:25,000 scale geomorphological map covering ∼12.5 km2 of the upper part of Mount Bistra (North Macedonia) on the basis of remote sensing analyses and geomorphological surveys. Particular attention is given to the description of glacial and periglacial landforms, to the reconstruction of single glacier shapes and to Equilibrium Line Altitude (ELA) value calculation. The results of the survey and the reconstructed ELAs indicate the occurrence of three glacial phases that led to the formation of frontal and lateral moraines. The age of these phases is tentatively attributed to the Late Pleistocene by comparing these ELAs with those of other Balkan mountains. This map is the first step of a wider project aimed at reconstructing the relation between climate change and geomorphic response in this area.

Infinite line of equilibriums in a novel fractional map with coexisting infinitely many attractors and initial offset boosting

Abstract The study of the chaotic dynamics in fractional-order discrete-time systems has received great attention in the past years. In this paper, we propose a new 2D fractional map with the simplest algebraic structure reported to date and with an infinite line of equilibrium. The conceived map possesses an interesting property not explored in literature so far, i.e., it is characterized, for various fractional-order values, by the coexistence of various kinds of periodic, chaotic and hyper-chaotic attractors. Bifurcation diagrams, computation of the maximum Lyapunov exponents, phase plots and 0–1 test are reported, with the aim to analyse the dynamics of the 2D fractional map as well as to highlight the coexistence of initial-boosting chaotic and hyperchaotic attractors in commensurate and incommensurate order. Results show that the 2D fractional map has an infinite number of coexistence symmetrical chaotic and hyper-chaotic attractors. Finally, the complexity of the fractional-order map is investigated in detail via approximate entropy.

ОДЕРЖАННЯ ІЗОВАЛЕРІАНОВОЇ КИСЛОТИ МЕТОДОМ ЕКСТРАГУВАННЯ ІЗ РОСЛИННОЇ СИРОВИНИ

The paper presents a mathematical description of the process of obtaining isovaleric acid by the method of extraction of roots and rhizomes of valerian, taking into account its chemical structure and the nature of the extractant. The traditional case of the extraction process, the straight line of equilibrium in the case of using an aqueous alcohol solution as an extractant and the unconventional case of using desalinated water as an extractant, which is represented by a convex equilibrium line, is substantiated. The cause of the unconventional case is the phenomenon of formation of associations between diphilic molecules of isovaleric acid and dipole molecules with water. The possibility of using ion exchange was investigated to isolate isovaleric acid from the extract of biologically active compounds. The identity of isovaleric acid obtained in this way by the gas method was confirmed chromatography.

Topographic signatures of progressive glacial landscape transformation

SummaryThe Pleistocene glaciations left a distinct topographic footprint in mountain ranges worldwide. The geometric signature of glacial topography has been quantified in various ways, but the temporal development of landscape metrics has not been traced in a landscape evolution model so far. However, such information is needed to interpret the degree of glacial imprint in terms of the integrated signal of temporal and spatial variations in erosion as a function of glacial occupation time.We apply a surface process model for cold‐climate conditions to an initially fluvial mountain range. By exploring evolving topographic patterns in model time series, we determine locations where topographic changes reach a maximum and where the initial landscape persists. The signal of glacial erosion, expressed by the overdeepening of valleys and the steepening of valley flanks, develops first at the glacier front and migrates upstream with ongoing glacial erosion. This leads to an increase of mean channel slope and its variance. Above steep flanks and head‐walls, however, the observed mean channel slope remains similar to the mean channel slope of the initial fluvial topography. This leads to a characteristic turning point in the channel slope–elevation distribution above the equilibrium line altitude, where a transition from increasing to decreasing channel slope with elevation occurs. We identify this turning point and a high channel slope variance as diagnostic features to quantify glacial imprint.Such features are abundant in glacially imprinted mid‐latitude mountain ranges such as the Eastern Alps. By analysing differently glaciated parts of the mountain range, we observe a decreasing clarity of this diagnostic morphometric property with decreasing glacial occupation. However, catchments of the unglaciated eastern fringe of the Alps also feature turning points in their channel slope–elevation distributions, but in contrast to the glaciated domain, the variance of channel slope is small at all elevation levels.

Glaciation in the highest parts of the Ukrainian Carpathians (Chornohora and Svydovets massifs) during the local last glacial maximum

The Chornohora and Svydovets massifs represent the highest part of the Ukrainian Carpathians (2061 m a.s.l.) and the north-eastmostmountain area in Europe, which was subject to mountain glaciation during the Quaternary. This region represents one of the least explored areas in terms of glacial geomorphology in Europe, which is crucial for validating the inferred zonal/meridional mode of atmospheric circulation on the continent during glacial stages. Based on new mapping of glacial landforms and sediments, we reconstruct the extent and ice-surface geometry as well as establish equilibrium line altitudes (ELAs) using the Area-Altitude-Balance-Ratio method for 40 palaeo-glaciers in the study area during the local Last Glacial Maximum (LLGM). Additionally, we list the inventory and morphometric characteristics of glacial cirques in the studied massifs (n = 77), which together with the local ELA pattern are discussed in the context of palaeo-wind directions and dominant precipitation patterns during the LGM. ELA values for the Svydovets (1401 m a.s.l.) and Chornohora (1516 m a.s.l.) massifs were much lower than those for the Rodna Mountains (1697 m) in the Northern Romanian Carpathians located 80 km to the southeast, and for the Tatra Mountains (1580 m) located 350 km to the northwest. In the Ukrainian Carpathians both glacier ELA and cirque elevations show a rising trend towards the southeast of 4 m km−1 controlled by preferential moisture transport from the northwest. This suggests that the dominant W-NW precipitation regime in effect during the LGM was similar to present-day conditions. This supports a previous glacial-geomorphologic reconstruction from the Rodna Mountains in Northern Romania and is in line with both model simulations and regional palaeo-wind proxies that show an enhanced mid-latitude North Atlantic zonal circulation pattern over central Europe during the LGM.