Glacier Mass Balance Simulation Based On Energy Balance

Alpine glaciers have been shrinking and showing an increasing trend of retreat under the background of global warming since the Little Ice Age.The retreat exhibits strong spatial heterogeneity which is attributed to differential supply schemes for glaciers due to the varied climatic conditions and rough topography in the mountain areas.In some mountain areas,such as the Karakoram and East Pamir Plateau,a large number of glaciers was observed to remain the balanced mass budget,and some glacier even showed expansion,which was defined as"Karakoram Anomaly".As a key factor affecting glacier mass budget and an important link between glacier change and climate change,energy balance can be used to quantitatively explore the interactions between glacier and atmosphere.It is helpful to give a comprehensive understanding for the formation of the"Karakoram Anomaly"from the angle of glacier energy balance.The Hunza river basin,as an important sub-basin of Upper Indus Basin（UIB）,is located in the Karakoram,where was observed to be a typical region of the"Karakoram Anomaly".Glacier is the main source of runoff in the UIB and its change has a significant impact on the construction of China Pakistan Economic Corridor,especially on the local production and life in the Hunza basin.Therefore,it is of great practical significance to study the glacier mass budget process and its impact on glacier change,water resource supply and glacial disasters under the influence of climate change.The geodetic method is a major approach evaluating the glacier changes in Hunza basin for existing studies,and there is a lack of studies on systematically analyzing the interannual change,seasonal cycles,altitude effects,and energy budget background of glacier mass balance.Considering that the glaciers in Hunza basin have the characteristics of high accumulation rate and the significant impact of supraglacial debris cover on the mass budget process,which can not be effectively recognized with the average status of glacier mass budget.Thus,the current knowledge shows some gaps in revealing the essence of the“Karakoram Anomaly”in mass change from the perspective of mass and energy exchange process on glacier surface.This study simulated the energy and mass budget on glaciers in Hunza basin from the perspectives of point-scale,glacier-scale,and basin-scale by using a distributed energy balance model that coupled the heat conduction process in snow layers and supraglacial debris layers.The climatic variables derived from statistical downscaled HAR dataset were used to drive the model.Based on the outputs of simulation,this study systematically analyzed the following points including（1）the characteristics of altitude gradient of mass and energy balance,（2）the influence mechanism and intensity of supraglacial debris on energy and mass balance,（3）the spatiotemporal heterogeneity of mass budget and its evolution,and（4）the impact of energy budget and climate change on mass balance.The main conclusions of this study are shown as follows.（1）The established energy and mass balance model can effectively describe the mass budget processes of glaciers at a regional scale,which is mainly reflected in three aspects.Firstly,the interannual variation and annual cycle of the simulated energy terms are highly correlated with the observations.Secondly,the mass balance obtained by simulation is consistent with that derived from remote sensing products based on geodetic methods at glacier-scale and basin-scale.Thirdly,the simulated ablation in summer is basically the same as the observed ablation.The mass balance is the most sensitive to temperature,followed by incoming shortwave radiation.When temperature rises by 1℃,the mass balance changes by-310%.Incoming shortwave radiation decreases by 10%leads to an increase of+29%on mass balance.Mass balance changes by-26%while precipitation decreases by 10%.Due to there is high correlation between precipitation and mass balance in interannual and annual cycles,the low sensitivity of precipitation on mass change become a key to maintain a relative conservation status of glacier mass budget.（2）The mass budget of Passu glacier keep basically balance(-0.030±0.546 m w.e.yr^-1,2000～2020).Snowfall and refreezing accounts for 89%and 11%of glacier mass gain.Snow/ice melting accounts for 90%of the mass expenditure and consumes 7%（8W/m²）of energy income.Sublimation accounts for 10%of the mass expenditure and consumes 11%（13 W/m²）of energy income.The mass balance of Batura glacier is-0.262±0.561 m w.e.yr^-1 and supraglacial debris coverage reduces 45%of amount on mass balance.The glacier mass balance in Hunza basin was 0.02±0.34 m w.e.yr^-1from 2000 to 2020.The mass balance in the accumulation period is 1.64±0.65 m w.e.yr^-1,which is mainly controlled by snowfall.In the ablation period,it is-1.62±0.60 m w.e.yr^-1,which is mainly affected by energy budget.The elevation of equilibrium line,generally varying from 4300 m to 4550 m,change progressively with fluctuation of mass balance.Since 2010,this line slightly retreated to high altitude.（3）Above the equilibrium line,the outgoing longwave radiation dominates the net radiation flux.Glacier obtains the heat from the atmosphere through the turbulent heat exchange process to keep energy conservation.Snow accumulation dominates the mass balance since sublimation is the only way for mass loss.Below the equilibrium line,when there is no supraglacial debris,the incoming shortwave radiation dominates the radiation flux,and the turbulent flux has little contribution to the energy balance.Therefore,glacier surface maintains the energy balance through melting snow/ice.In this situation,mass balance is controlled by net radiation,showing a"slope-shaped"structure.Most of incoming net radiation is consumed by the heat conduction between subsurface debris layers when the supraglacial debris is involved.Affected by the thickness distribution of the debris,the mass balance presents a"bow-shaped"distribution.The influence of debris on ablation is mainly reflected in changing the heat transmitted to the ice layer.The thicker the debris,the smaller the temperature lapse rate,the smaller the temperature difference in the contact layer,and the smaller the heat conducted.（4）There is an obvious temporal and spatial heterogeneity on glacier mass budget in the Hunza basin,and the mass budget generally tends to negative balance(the variability is-0.0099 m w.e.yr^-1).The mass basis of"Karakoram Anomaly"is weakening.The positive mass budget is mainly concentrated on the northwest of the basin and the south of the"Batura wall"and generally appears in 2002,2003,2004,2005,2009,and 2010.The region where the mass budget tends to be in negative balance generally displays the decrease in snow accumulation and refreezing and the enhancement in surface ablation.Snowfall presents a decrease trend at all altitude zones.The weaken（3200～3800 m）and enhancement（<3200 m）of ablation determined the positive（3200～3800 m）and negative（<3200 m）tendency of mass budget.（5）The energy background of maintaining the basic balance of glacier mass revenue and expenditure in the Hunza basin is that almost all incoming energy supplied by net shortwave radiation is consumed by net longwave radiation.66%of the melting energy is consumed by sublimation,leading to a small amount of energy for melting snow and ice.The mass basis of the spatio-temporal heterogeneity of mass balance and its change is snow accumulation and differential melting.The energy basis for the differential melting is the revenue and expenditure of net radiation.There is a significant difference in mass balance among glaciers with different types and different aspect,which is largely related to the spatial distribution and altitude gradient effect of precipitation.The region and period with positive glacier mass budget witnessed high snowfall and low net radiation（close to 0 or negative）.Snowfall contributes to the mass accumulation on the one hand,on the other hand,it further affects ablation by affecting surface albedo.The energy drive of interannual fluctuation of mass balance is net shortwave radiation,which is affected by albedo.The climate driving force of the interannual change of mass balance is precipitation.At the same time,the relatively low temperature conditions also have an impact on the summer ablation.The high precipitation in high altitude zones is related to the vertical movement of atmospheric circulation.The decreasing trend of precipitation is mainly affected by the weakening of the Westerly jet,while the low temperature is related to the Karakoram Vortex（KV）.The scheme for building the energy balance model and calibrating and validating the physical parameters from point-scale,glacier-scale,and watershed-scale provide a reference for a large-scale energy balance simulation.The analysis on energy-mass budget processes of glaciers in Hunza basin strengthens the understanding of the mass budget process and mass balance anomaly of the same type of glaciers in the Karakoram mountains.