scholarly journals Glacier subsurface heat-flux characterizations for energy-balance modelling in the Donjek Range, southwest Yukon, Canada

2011 ◽  
Vol 57 (201) ◽  
pp. 121-133 ◽  
Author(s):  
Brett A. Wheler ◽  
Gwenn E. Flowers
Keyword(s):  
Heat Flux ◽  
Energy Balance ◽  
Surface Temperature ◽  
Energy Balance Equation ◽  
Shortwave Radiation ◽  
Balance Model ◽  
Glacier Surface ◽  
Sophisticated Model ◽  
The Mean ◽  
Polythermal Glacier

AbstractWe apply a point-scale energy-balance model to a small polythermal glacier in the St Elias Mountains of Canada in order to investigate the applicability and limitations of different treatments of the glacier surface temperature and subsurface heat flux. These treatments range in complexity from a multilayer subsurface model that simulates snowpack evolution, to the assumption of a constant glacier surface temperature equal to 0°C. The most sophisticated model includes dry densification of the snowpack, penetration of shortwave radiation into the subsurface, internal melting, refreezing of percolating meltwater and generation of slush layers. Measurements of subsurface temperature and surface lowering are used for model validation, and highlight the importance of including subsurface penetration of shortwave radiation in the model. Using an iterative scheme to solve for the subsurface heat flux as the residual of the energy-balance equation results in an overestimation of total ablation by 18%, while the multilayer subsurface model underestimates ablation by 6%. By comparison, the 0°C surface assumption leads to an overestimation of ablation of 29% in this study where the mean annual air temperature is about −8°C.

scholarly journals Application of an improved surface energy balance model to two large valley glaciers in the St. Elias Mountains, Yukon

2020 ◽  
pp. 1-16
Author(s):  
Tim Hill ◽  
Christine F. Dow ◽  
Eleanor A. Bash ◽  
Luke Copland
Keyword(s):  
Energy Balance ◽  
Surface Energy ◽  
Surface Energy Balance ◽  
Shortwave Radiation ◽  
Balance Model ◽  
Landsat 8 ◽  
Glacier Surface ◽  
Ice Dynamics ◽  
Surface Melt

Abstract Glacier surficial melt rates are commonly modelled using surface energy balance (SEB) models, with outputs applied to extend point-based mass-balance measurements to regional scales, assess water resource availability, examine supraglacial hydrology and to investigate the relationship between surface melt and ice dynamics. We present an improved SEB model that addresses the primary limitations of existing models by: (1) deriving high-resolution (30 m) surface albedo from Landsat 8 imagery, (2) calculating shadows cast onto the glacier surface by high-relief topography to model incident shortwave radiation, (3) developing an algorithm to map debris sufficiently thick to insulate the glacier surface and (4) presenting a formulation of the SEB model coupled to a subsurface heat conduction model. We drive the model with 6 years of in situ meteorological data from Kaskawulsh Glacier and Nàłùdäy (Lowell) Glacier in the St. Elias Mountains, Yukon, Canada, and validate outputs against in situ measurements. Modelled seasonal melt agrees with observations within 9% across a range of elevations on both glaciers in years with high-quality in situ observations. We recommend applying the model to investigate the impacts of surface melt for individual glaciers when sufficient input data are available.

scholarly journals A Test Study of an Energy and Mass Balance Model Application to a Site on Urumqi Glacier No. 1, Chinese Tian Shan

Water ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2865
Author(s):  
Puyu Wang ◽  
Zhongqin Li ◽  
Christoph Schneider ◽  
Hongliang Li ◽  
Alexandra Hamm ◽  
...  
Keyword(s):  
Heat Flux ◽  
Mass Balance ◽  
Sensible Heat Flux ◽  
Shortwave Radiation ◽  
Balance Model ◽  
Mass Balance Model ◽  
Sensitivity Testing ◽  
Glacier Surface ◽  
Precipitation Decrease ◽  
Tian Shan

In this study, energy and mass balance is quantified using an energy balance model to represent the glacier melt of Urumqi Glacier No. 1, Chinese Tian Shan. Based on data from an Automatic Weather Station (4025 m a.s.l) and the mass balance field survey data nearby on the East Branch of the glacier, the “COupled Snowpack and Ice surface energy and Mass balance model” (COSIMA) was used to derive energy and mass balance simulations during the ablation season of 2018. Results show that the modeled cumulative mass balance (−0.67 ± 0.03 m w.e.) agrees well with the in-situ measurements (−0.64 ± 0.16 m w.e.) (r2 = 0.96) with the relative difference within 5% during the study period. The correlation coefficient between modeled and observed surface temperatures is 0.88 for daily means. The main source of melt energy at the glacier surface is net shortwave radiation (84%) and sensible heat flux (16%). The energy expenditures are from net longwave radiation (55%), heat flux for snow/ice melting (32%), latent heat flux of sublimation and evaporation (7%), and subsurface heat flux (6%). The sensitivity testing of mass balance shows that mass balance is more sensitive to temperature increase and precipitation decrease than temperature decrease and precipitation increase.

scholarly journals Reconnaissance Study of glacier energy balance in North Greenland, 1993–94

1998 ◽  
Vol 44 (147) ◽  
pp. 239-247 ◽  
Author(s):  
Roger J. Braithwaite ◽  
Thomas Konzelmann ◽  
Christoph Marty ◽  
Ole B. Olesen
Keyword(s):  
Energy Balance ◽  
Field Experiments ◽  
Longwave Radiation ◽  
Heat Fluxes ◽  
Shortwave Radiation ◽  
Balance Model ◽  
Conductive Heat ◽  
Glacier Surface ◽  
West Greenland ◽  
North Greenland

AbstractReconnaissance energy-balance studies were made for the first time at two sites in North Greenland to compare with conditions in West Greenland. The field experiments were planned to save weight because it is expensive to operate in North Greenland. The larger energy components (incoming radiation and ablation) were measured for 55 days altogether, and the smaller components were evaluated by indirect methods, e.g. turbulent fluxes are calculated from air temperature, humidity and wind speed, to save the weight of instruments. The energy-balance model is “tuned" by choosing surface roughness and albedo to reduce the mean error between measured ablation and modelled daily melting. The error standard deviation for ablation is only ± 5 kg m−2d−1’, which is much lower than found in West Greenland, due to better instruments and modelling in the present study. Net radiation is the main energy source for melting in North Greenland but ablation is relatively low because sublimation and conductive-heat fluxes use energy that would otherwise be available for melting. There is a strong diurnal variation in ablation, mainly forced by variations in shortwave radiation and reinforced by nocturnal cooling of the ice surface by outgoing longwave radiation and sublimation. The model frequently predicts a frozen glacier surface at night even when air temperatures are positive.

scholarly journals Analysis of a 3 year meteorological record from the ablation zone of Morteratschgletscher, Switzerland: energy and mass balance

2000 ◽  
Vol 46 (155) ◽  
pp. 571-579 ◽  
Author(s):  
J. Oerlemans
Keyword(s):  
Heat Flux ◽  
Sensible Heat Flux ◽  
Longwave Radiation ◽  
Solar Radiation Pressure ◽  
Turbulent Energy ◽  
Snow Accumulation ◽  
Shortwave Radiation ◽  
Glacier Surface ◽  
The Mean ◽  
Snow Temperature

AbstractSince 1 October 1995, an automatic weather station has been operated on the tongue of Morteratschgletscher, Switzerland. The station stands freely on the ice, and sinks with the melting glacier surface. It is located at 2100 m a.s.l., and measures air temperature, wind speed and direction, incoming and reflected solar radiation, pressure and snow temperature. A sonic ranger, mounted to stakes drilled into the ice, measures surface height from which melt rates and snow accumulation can be derived. In this paper the data for the period 1 October 1995 to 30 September 1998 are used to evaluate the surface energy balance. The turbulent energy fluxes are calculated with the bulk method. The turbulent exchange coefficient Ch is used as a control parameter. With Ch = 0.00127 the calculated melt equals the observed melt, which is 17.70 m w.e. over the 3 years. When averaged over the time when melting occurs (i.e. 35% of the time), the mean surface heat flux equals 191 W m−2. Net shortwave radiation contributes 177 W m−2, net longwave radiation −25 W m−2, the sensible-heat flux 31 W m−2 and the latent-heat flux 8 W m−2.

scholarly journals On the role of subsurface heat conduction in glacier energy-balance modelling

2009 ◽  
Vol 50 (50) ◽  
pp. 16-24 ◽  
Author(s):  
Francesca Pellicciotti ◽  
Marco Carenzo ◽  
Jakob Helbing ◽  
Stefan Rimkus ◽  
Paolo Burlando
Keyword(s):  
Heat Conduction ◽  
Energy Balance ◽  
Shortwave Radiation ◽  
Balance Model ◽  
Glacier Surface ◽  
Central Chile ◽  
Air Temperatures ◽  
Weather Stations ◽  
The Difference

AbstractWe discuss the inclusion of the subsurface heat-conduction flux into the calculation of the energy balance and ablation at the glacier–atmosphere interface. Data from automatic weather stations are used to force an energy-balance model at several locations on alpine glaciers and at one site in the dry Andes of central Chile. The heat-conduction flux is computed using a two-layer scheme, assuming that 36% of the net shortwave radiation is absorbed by the surface layer and that the rest penetrates into the snowpack. We compare simulations conducted with and without subsurface heat flux. Results show that assuming a surface temperature of zero degrees leads to a larger overestimation of melt at the sites in the accumulation area (10.4–13.3%) than in the ablation area (0.5–2.8%), due to lower air temperatures and the presence of snow. The difference between simulations with and without heat conduction is also high at the beginning and end of the ablation season (up to 29% for the first 15 days of the season), when air temperatures are lower and snow covers the glacier surface, while they are of little importance during periods of sustained melt at all the locations investigated.

scholarly journals Debris-covered energy balance model for Imja-Lhotse Shar Glacier in the Everest region of Nepal

2015 ◽  
Vol 9 (3) ◽  
pp. 3503-3540 ◽  
Author(s):  
D. R. Rounce ◽  
D. J. Quincey ◽  
D. C. McKinney
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Surface Roughness ◽  
Energy Balance ◽  
Latent Heat ◽  
Latent Heat Flux ◽  
Energy Balance Model ◽  
Balance Model ◽  
Glacier Surface ◽  
Supraglacial Lakes

Abstract. Debris thickness plays an important role in regulating ablation rates on debris-covered glaciers as well as controlling the likely size and location of supraglacial lakes. Despite its importance, lack of knowledge about debris properties and associated energy fluxes prevents the robust inclusion of the effects of a debris layer into most glacier surface energy balance models. This study combines fieldwork with a debris-covered energy balance model to estimate debris temperatures and ablation rates on Imja-Lhotse Shar glacier located in the Everest region of Nepal. The debris properties that significantly influence the energy balance model are thermal conductivity, albedo, and surface roughness. Fieldwork was conducted to measure thermal conductivity and a method was developed using Structure from Motion to estimate surface roughness. Debris temperatures measured during the 2014 melt season were used to calibrate and validate a debris-covered energy balance model by optimizing the albedo, thermal conductivity, and surface roughness at 10 debris-covered sites. Furthermore, three methods for estimating the latent heat flux were investigated. Model calibration and validation found the three methods had similar performance; however, comparison of modeled and measured ablation rates revealed that assuming a zero latent heat flux may overestimate ablation. Results also suggest that where debris moisture is unknown, measurements of the relative humidity or precipitation may be used to estimate wet debris periods, i.e., the latent heat flux is non-zero. The effect of temporal resolution on the model was also assessed and results showed that both 6 h data and daily average data slightly underestimate debris temperatures and ablation rates, thus these should only be used to estimate rough ablation rates when no other data are available.

scholarly journals Reconnaissance Study of glacier energy balance in North Greenland, 1993–94

1998 ◽  
Vol 44 (147) ◽  
pp. 239-247 ◽  
Author(s):  
Roger J. Braithwaite ◽  
Thomas Konzelmann ◽  
Christoph Marty ◽  
Ole B. Olesen
Keyword(s):  
Energy Balance ◽  
Field Experiments ◽  
Longwave Radiation ◽  
Heat Fluxes ◽  
Shortwave Radiation ◽  
Balance Model ◽  
Conductive Heat ◽  
Glacier Surface ◽  
West Greenland ◽  
North Greenland

AbstractReconnaissance energy-balance studies were made for the first time at two sites in North Greenland to compare with conditions in West Greenland. The field experiments were planned to save weight because it is expensive to operate in North Greenland. The larger energy components (incoming radiation and ablation) were measured for 55 days altogether, and the smaller components were evaluated by indirect methods, e.g. turbulent fluxes are calculated from air temperature, humidity and wind speed, to save the weight of instruments. The energy-balance model is “tuned" by choosing surface roughness and albedo to reduce the mean error between measured ablation and modelled daily melting. The error standard deviation for ablation is only ± 5 kg m −2 d−1’, which is much lower than found in West Greenland, due to better instruments and modelling in the present study. Net radiation is the main energy source for melting in North Greenland but ablation is relatively low because sublimation and conductive-heat fluxes use energy that would otherwise be available for melting. There is a strong diurnal variation in ablation, mainly forced by variations in shortwave radiation and reinforced by nocturnal cooling of the ice surface by outgoing longwave radiation and sublimation. The model frequently predicts a frozen glacier surface at night even when air temperatures are positive.

scholarly journals The secret life of ice sails

2017 ◽  
Vol 63 (242) ◽  
pp. 1049-1062 ◽  
Author(s):  
GEOFFREY W. EVATT ◽  
CHRISTOPH MAYER ◽  
AMY MALLINSON ◽  
I. DAVID ABRAHAMS ◽  
MATTHIAS HEIL ◽  
...  
Keyword(s):  
Heat Flux ◽  
Sensitivity Analysis ◽  
Steady State ◽  
Energy Balance ◽  
Surface Energy ◽  
Surface Energy Balance ◽  
Sensible Heat Flux ◽  
Balance Model ◽  
Sensible Heat ◽  
Glacier Surface

ABSTRACTWe present the first dedicated study into the phenomenon of ice sails. These are clean ice structures that protrude from the surface of a small number of debris-covered glaciers and can grow to heights of over 25 m. We draw together what is known about them from the academic/exploration literature and then analyse imagery. We show here that ice sails can develop by one of two mechanisms, both of which require clean ice to become surrounded by debris-covered ice, where the debris layer is shallow enough for the ice beneath it to melt faster than the clean ice. Once formed, ice sails can persist for decades, in an apparently steady state, before debris layer thickening eventually causes a reversal in the relative melt rates and the ice sails decay to merge back with the surrounding glacier surface. We support our image-based analysis with a surface energy-balance model and show that it compares well with available observations from Baltoro Glacier in the Karakoram. A sensitivity analysis of the model is performed and confirms the results from our empirical study that ice sails require a relatively high evaporative heat flux and/or a relatively low sensible heat flux in order to exist.

scholarly journals The Half-order Energy Balance Equation, Part 1: The homogeneous HEBE and long memories

2020 ◽  
Author(s):  
Shaun Lovejoy
Keyword(s):  
Heat Flux ◽  
Energy Balance ◽  
Heat Equation ◽  
Surface Temperature ◽  
Continuum Mechanics ◽  
Balance Equation ◽  
Energy Balance Equation ◽  
Surface Boundary ◽  
The Earth ◽  
The Continuum

Abstract. The original Budyko–Sellers type 1-D energy balance models (EBMs) consider the Earth system averaged over long times and applies the continuum mechanics heat equation. When these and the more phenomenological zero (horizontal) – dimensional box models are extended to include time varying anomalies, they have a key weakness: neither model explicitly nor realistically treats the surface radiative – conductive surface boundary condition that is necessary for a correct treatment of energy storage. In this first of a two part series, we apply standard Laplace and Fourier techniques to the continuum mechanics heat equation, solving it with the correct radiative – conductive BC's obtaining an equation directly for the surface temperature anomalies in terms of the anomalous forcing. Although classical, this equation is half – not integer – ordered: the Half - ordered Energy Balance Equation (HEBE). A quite general consequence is that although Newton's law of cooling holds, that the heat flux across surfaces is proportional to a half (not first) ordered derivative of the surface temperature. This implies that the surface heat flux has a long memory, that it depends on the entire previous history of the forcing, the relationship is no longer instantaneous. We then consider the case where the Earth is periodically forced. The classical case is diurnal heat forcing; we extend this to annual conductive – radiative forcing and show that the surface thermal impedance is a complex valued quantity equal to the (complex) climate sensitivity. Using a simple semi-empirical model, we show how this can account for the phase lag between the summer maximum forcing and maximum surface temperature Earth response. In part II, we extend all these results to spatially inhomogeneous forcing and to the full horizontally inhomogeneous problem with spatially varying specific heats, diffusivities, advection velocities, climate sensitivities. We consider the consequences for macroweather forecasting and climate projections.

scholarly journals Debris-covered glacier energy balance model for Imja–Lhotse Shar Glacier in the Everest region of Nepal

2015 ◽  
Vol 9 (6) ◽  
pp. 2295-2310 ◽  
Author(s):  
D. R. Rounce ◽  
D. J. Quincey ◽  
D. C. McKinney
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Surface Roughness ◽  
Energy Balance ◽  
Latent Heat ◽  
Latent Heat Flux ◽  
Energy Balance Model ◽  
Balance Model ◽  
Glacier Surface ◽  
Supraglacial Lakes

Abstract. Debris thickness plays an important role in regulating ablation rates on debris-covered glaciers as well as controlling the likely size and location of supraglacial lakes. Despite its importance, lack of knowledge about debris properties and associated energy fluxes prevents the robust inclusion of the effects of a debris layer into most glacier surface energy balance models. This study combines fieldwork with a debris-covered glacier energy balance model to estimate debris temperatures and ablation rates on Imja–Lhotse Shar Glacier located in the Everest region of Nepal. The debris properties that significantly influence the energy balance model are the thermal conductivity, albedo, and surface roughness. Fieldwork was conducted to measure thermal conductivity and a method was developed using Structure from Motion to estimate surface roughness. Debris temperatures measured during the 2014 melt season were used to calibrate and validate a debris-covered glacier energy balance model by optimizing the albedo, thermal conductivity, and surface roughness at 10 debris-covered sites. Furthermore, three methods for estimating the latent heat flux were investigated. Model calibration and validation found the three methods had similar performance; however, comparison of modeled and measured ablation rates revealed that assuming the latent heat flux is zero may overestimate ablation. Results also suggest that where debris moisture is unknown, measurements of the relative humidity or precipitation may be used to estimate wet debris periods, i.e., when the latent heat flux is non-zero. The effect of temporal resolution on the model was also assessed and results showed that both 6 h data and daily average data slightly underestimate debris temperatures and ablation rates; thus these should only be used to estimate rough ablation rates when no other data are available.

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