Summertime surface mass balance and energy balance of Urumqi Glacier No. 1, Chinese Tien Shan, modeled by linking COSIMA and in-situ measured meteorological records

doi:10.21203/rs.3.rs-1010764/v2

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Summertime surface mass balance and energy balance of Urumqi Glacier No. 1, Chinese Tien Shan, modeled by linking COSIMA and in-situ measured meteorological records

https://doi.org/10.21203/rs.3.rs-1010764/v2

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To get a better overview of atmosphere-driven mass changes at Urumqi Glacier No.1, Chinese Tien Shan, the surface energy balance and mass balance is modeled by linking the COupled Snowpack and Ice surface energy and MAss balance model (COSIMA) with in-situ measured meteorological records for the ablation period in 2018. The COSIMA is calibrated by manual optimization and the modeled results agree well with the in-situ surface temperature, snow height and seasonal mass balance. Our results reveal that Urumqi Glacier No.1 experienced a significant mass loss, with an average value of -0.77 m w.e. over the ablation period 2018. The main components in energy balance were two radiation components, i.e. net shortwave radiation and net longwave radiation, and turbulent fluxes. Surface melt and solid precipitation were dominated components of mass balance. The COSIMA can reproduce the glaciological mass balance compared with other models. Sensitivity analysis showed that the mass balance was more sensitive to the temperature than precipitation, and mass loss caused by temperature increase of 1 K needed to be compensated by at least 40% precipitation increase. Air temperature during the ablation period was more important than annual precipitation in controlling mass balance changes on Urumqi Glacier No.1. These findings will enhance our understanding of the mechanisms underlying mass balance processes of ablation period and their contribution to the acceleration of glacier retreat in Tien Shan.

ablation period

energy balance

mass balance

sensitivity analysis

Urumqi Glacier No. 1

Tien Shan

The glaciers in the Tien Shan provide the sources of rivers that supply water to billions of people (Farinotti et al., 2015). Several studies have found the glaciers in Tien Shan represented an accelerated melting tendency recently (Wang et al., 2019; Miles et al., 2021). The majority of glaciers have been receding and shrinking (Yao et al., 2012), which could endanger the water resource in the downstream region (Immerzeel et al., 2010).

Given the importance of glaciers in the Tien Shan, the quantitative understanding of the physical relationship between glaciers and climate is necessary to help predicting the responses of glaciers to climate change and its potential impacts. Most of previous studies on the response of glacier mass balance to climate change in the Tien Shan have focused on the effect of annual air temperature change (Farinotti et al., 2015; Pieczonka et al., 2015; Sakai and Fujita, 2017; Wang et al., 2017, 2016). However, the air temperature in the Tien Shan shows a large spatial discrepancy in seasonal variations (Wang et al., 2020). Few studies on the Tien Shan quantify the effects of seasonal air temperature changes on changes in glacier mass balance. Furthermore, glaciers in the western and eastern Tien Shan exhibit strong heterogeneous changes due to their different climatic settings (Wang et al., 2015).

Due to the lack of in-situ glacio-meteorological observations in different regions of the Tien Shan, our understanding of the relationship between glaciers and climate change and glacier melt water runoff patterns are limited. The relationship between glaciers and climate change can be resolved by studying glacier energy and mass balance, which has been conducted in detail on many mountain glaciers and ice sheets around the world (Bintanja et al., 1997; Oerlemans and Klok, 2002; Kaser et al., 2004). The glacier energy and mass balance modeling has been systematically studied on the individual Tibetan Plateau glaciers (Fujita and Ageta, 2000; Yang et al., 2011; Mölg et al., 2012; Huintjes et al., 2015a, b; Sun et al., 2018; Li et al., 2018; Zhu et al., 2020). These studies mainly focus on the impact of meteorological factors or regional-scale atmospheric circulation on the mass balance, the reconstruction of the glacier mass balance has also accomplished using an energy and mass balance model. Few systematic studies have been conducted on Tien Shan glaciers (Kang et al., 1992; Han et al., 2005), and glacier mass balance and meteorological data are currently only available from the Urumqi Glacier No.1.

Compared with the previous studies in the Urumqi Glacier No.1, hourly high-resolution surface mass balance modeling was only available until 2012 (Che et al., 2019; Li, 2020), but the parameterizations of subsurface energy and mass fluxes were not incorporated or poorly resolved by these commonly models. Huintjes et al. (2015a, b) has applied COupled Snowpack and Ice surface energy and MAss balance model (COSIMA) with observations from Automatic Weather Station (AWS) or High Asia Refined (HAR) reanalysis data as atmospheric input to investigate glacier-wide surface energy balance and mass balance processes. Subsurface processes can be well resolved by COSIMA. In general, parameterization scheme within COSIMA makes the calculation of mass balance more reasonable. However, as yet, COSIMA has not been tested in the Tien Shan using hourly AWS observation data as input.

Taking this into account, COSIMA was applied to the Urumqi Glacier No. 1, Chinese Tien Shan, forcing by hourly meteorological data collected at an AWS on the glacier surface. The energy fluxes and mass balance at the glacier surface and in the subsurface layers are calculated and a comparison with different types of field in-situ measurements was conducted to validate model performance. Our specific aims were: (1) to understand the temporal variability of meteorological conditions and characteristics of glacier-wide energy balance; (2) to quantitatively characterize the glacier-wide mass balance components and their profiles; and (3) to analyze the climate sensitivity of the Urumqi Glacier No.1 and to identify the control of atmospheric variables on the mass balance of Urumqi Glacier No.1.

Urumqi Glacier No.1 (43°06′N, 86°49′E) is a typical continental, valley-type glacier, covering an area of 1.52 km² (Li et al., 2021). It consists of two independent small glaciers: the east branch (EB) and the west branch (WB), and its altitude ranges between 3743 to 4267 m a.s.l. Urumqi Glacier No.1 is situated on the northern slope of Tianger Summit II in the eastern Tien Shan (Fig. 1). It is situated in the continental climate zone. According to Liu et al. (1997), this glacier is therefore a typical summer-accumulation-type glacier because both accumulation and ablation take place simultaneously between June and September. The region is mainly controlled by three dynamical factors: A westerly jet in the upper troposphere, Siberian anticyclonic circulation, and westerly cyclonic disturbance. According to the observation data of the Daxigou Meteorological Station (3539 m), 3 km southeast of Urumqi Glacier No.1, the average annual temperature is approximately − 4.9°C, and the annual precipitation was 465 mm during 1959–2018. The average annual temperature increased by a rate of 0.29°C (10a)⁻¹ and the annual precipitation increased gradually at a rate of 20 mm (10a)⁻¹ based on the linear analyses shown in Fig. 2. The main ablation period is from May to August, and the precipitation mainly comes from the water vapor carried by the west wind. The precipitation from May to August accounts for 78% of the annual amount, with the main type of solid fall, such as snow, hail and sleet.

3.1 COSIMA descriptions

COSIMA is a physical surface energy and mass balance model that assumes mass conservation in the snowpack. Thus, COSIMA couples a surface energy balance to a multi-level subsurface model, and it can calculate energy and mass balance for different components, including energy balance, meltwater percolation, refreezing and densification (Huintjes et al., 2015a). Now, COSIMA is available online as an open-source software and used for this study (https://bitbucket.org/glaciermodel/cosima; last accessed on 17 June 2021; Huintjes et al., 2015a). It is in detail presented by Huintjes et al. (2015a, b) and Wang et al. (2020). COSIMA calculates the mass balance of the surface melt, subsurface melt, sublimation, deposition, solid precipitation, and refreezing at hourly time step. The surface energy balance equation governs the calculation of the mass fluxes:

F = SW_in (1-α) + LW_in + LW_out + Q_sens +Q_lat + Q_G…………………….(1)

Where SW_in, LW_in and LW_out represents incoming shortwave radiation, incoming longwave radiation and outgoing longwave radiation, respectively. SW_in (1-α) is net incoming shortwave radiation (SW_net). α is the surface albedo. Q_sens and Q_lat are turbulent sensible and latent heat flux, respectively. Q_G is the ground heat flux which consists of fluxes of heat conduction (Q_C) and penetrating shortwave radiation (Q_PS). Q_PS is equal to SW_net (1-ζ). For ζ we take the values of 0.8 for ice, and 0.9 for snow, respectively, as determined by Bintanja and van den Broeke (1995). The heat flux from liquid precipitation is neglected within COSIMA according to Huintjes et al. (2015a, b). The flux towards the surface is considered positive, while the flux from the surface has a negative sign. Only sublimation causes mass loss when the surface temperature is below 273.16 K. It is set to 273.16 K when surface temperature exceeds the melting point, and the excess energy is converted into the heat flux for snow/ice melting (Huintjes et al., 2015a).

The double critical temperature index method is used to separate solid and liquid precipitation in COSIMA. The precipitation is liquid precipitation when the air temperature is higher than 6 ℃, whilst it is solid precipitation when lower than 0 ℃ in our study region. The air temperature between the two critical air temperatures is calculated by linear interpolation (Jia et al., 2020). In COSIMA, the albedo is calculated using the parameterization of Oerlemans and Knap (1998). The ice albedo variation in the Urumqi Glacier No.1 has a range from 0.06 to 0.44 due to topographic effects and light-absorbing impurities (Yue et al., 2017). Manual tests and inspection of albedo in Landsat-8 data showed that the albedo decreased from a fresh snow of 0.83 to a firn albedo of 0.58, with an aging factor of 1.1 day after the snowfall events. The albedo drops to 0.35 when glacier surface is without snow layer (Yue et al., 2017). The depth scaling factor of the albedo is 3 cm after manual tests (Table 2). The vertical profiles of subsurface temperature and density are key for Q_G. The subsurface temperature is solved by the thermodynamic thermal equation (Anderson, 1976). And subsurface density is calculated through an empirical relation following Herron and Langway (1980). The initial temperature profile is defined by the available subsurface measurements and linear interpolation with depth. The initial snow density profile is calculated from a linear interpolation between 250 kg m^− 3 of the uppermost snow layer and 550 kg m^− 3 from the bottom snow layer.

The distributed SW_in including effects from both terrain shading and cloud cover were calculated based on the radiation model in COSIMA and the detailed information about the parameters are given in Kumar et al. (1997). LW_in and LW_out are obtained by the Stefan-Boltzmann law. For LW_in, atmospheric emission rates ε is calculated following Klok and Oerlemans (2002). To calculate the turbulent heat fluxes, COSIMA assumes that the surface roughness length varies with the duration of the fresh snow to firn snow (Mölg et al. 2009). Surface roughness length ranged from a fresh snow value of 0.24 mm (Gromke et al., 2011) increases linearly to a firn snow value of 4 mm (Brock et al., 2006). If the glacier surface is without snow, the bare ice is assumed to be 1.7 mm (Cullen et al., 2007). The correction of turbulent fluxes under stable conditions is based on the Richardson number (Braithwaite,1995). The Q_C is determined by the temperature difference between the surface layer and the two top subsurface layers, depending on the thermal conductivity of the medium (ice or snow). The thermal conductivity is calculated from the subsurface density (ρ, in kg m^− 3) (Anderson, 1976). The Q_PS is calculated according to Bintanja and van den Broeke (1995). At the top level of the model, the proportion of SW_net absorbed in surface layer reaches an exponentially decreasing flux to the bottom layer and increases the subsurface temperature. For the fraction of the SW_net absorption and extinction coefficients, we take the values of 0.8 and 2.5 for ice, and 0.9 and 17.1 for snow, respectively, as determined by Bintanja and van den Broeke (1995). The detailed information of the COSIMA is presented in the appendix A.

3.2. COSIMA configuration

The final COSIMA run was initiated from 00:00 a.m. 1 May 2018. The analyzed COSIMA output also started from this time. At this time there was a little fresh snow observed at the glacier surface facilitating the initialization process of the model. The input meteorological series of hourly air temperature, relative humidity, precipitation and incoming shortwave radiation were used for the timespan between 00:00 a.m. 1 May and 00:00 a.m. 31 August 2018. The input meteorological data and their processing were shown in section 4. For the COSIMA modeling, the bottom temperature was 266.15 K as mean value for the ablation period at the AWS1. Therefore, the surface energy balance and mass balance from AWS1 is conducted for hourly values.

3.3 Mass changes assessment

In this paper, by analyzing the interannual changes of temperature (σ_T) and annual precipitation (C_v) during the ablation period, the meteorological factors that control the mass balance of glaciers can be quantitatively determined. This method has been successfully applied to the Chhota Shigri glacier in the western Himalayas, Parlung Glacier No. 94 in the southeast Tibetan Plateau, Muji Glacier in the northeastern Pamir (Azam et al.,2014, Yang et al., 2013, Li et al., 2020). σ_T refers to the standard deviation of air temperature during ablation period, C_v is the ratio of the standard deviation to the annual precipitation. σ_T or C_v has been used to indicate interannual changes in ablation period air temperature and annual precipitation, respectively. Then COSIMA was run by virtue of modifying air temperature or precipitation to obtain respective mass balance change. In this study, the forcing data include the air temperature and annual precipitation of Daxigou meteorological station and the detailed information has been described in section 4.1.

4.1 Input meteorological data

An automatic weather station (AWS1; Table 1) was set up on a relatively flat surface (slope < 5°) near the equilibrium line altitude (ELA) of the Urumqi Glacier No.1 from 29 April 2018 (43°06′22″N, 86°48′23″E; 4025 m a.s.l.; Fig. 1a, c, d). AWS2 was installed on the glacier terminal moraine in 2011 at an altitude of 3,835 m a.s.l. providing the same meteorological datasets as AWS1 and stored in the Campbell CR1000 data logger as 30-min mean values. Table 1 shows the technical specifications of all sensors in AWS1 and AWS2. Detailed information of both AWSs can be found in Wang et al. (2020). The air temperature (T), relative humidity (RH), precipitation (P_r) and incoming shortwave radiation (SW_in) recorded by AWS1 and AWS2, are required for this study. Surface temperature recorded by AWS1 for evaluation model performance. Unfortunately, there was a data gap spanning from 12:00 p.m. 20 August to 12:00 p.m. 22 August 2018 due to harsh environmental conditions. The following part will offer the process for filling in data gap. The annual precipitation and the mean air temperature in the ablation period of the Daxigou meteorological station (43°06'N, 86°50'E) during 1959–2018, located at an altitude of 3539 m a.s.l., were used to assess how climate factors control the change in mass balance.

Table 1

Information and parameters of AWSs sensor and precipitation gauge used in this study
Instrument	Sensors	Company	Parameter*	Accuracy	Height
AWS1; AWS2	HC2-S3	Rotronic	T (℃)	± 0.1℃ (23℃)	2 m
	HC2-S3	Rotronic	RH (%)	± 0.8% (23℃)	2 m
	Young 05103	RMYoung	u (m s^− 1)	± 0.3 m s^− 1	2 m
	PTB110	Campbell	P (hPa)	± 0.3 hPa (20℃)	2 m
	CNR4	Kipp&Zonen	SW_in and SW_out (W m^− 2) LW_in and LW_out(W m^− 2)	± 10%	1.5 m
	CNR4	Kipp&Zonen	SW_in and SW_out (W m^− 2) LW_in and LW_out(W m^− 2)	(T: -40℃~80℃; RH: 0%~100%)	1.5 m
Precipitation gauge (AWS1; AWS2)	T-200B	Geonor	P_r (mm)	± 0.1 mm (-40℃~60℃)	1.7 m
Surface temperature (AWS1)	SI-111	Apogee	T_S	± 0.5 ◦C (T: −40 ℃~70 ℃)	1.5 m
*T = air temperature; P_r= precipitation; P = air pressure; RH = relative humidity; u = wind speed; SW_in and SW_out= incoming and outgoing shortwave radiation; LW_in and LW_out= incoming and outgoing longwave radiation; T_s= surface temperature.

Due to frequent snowfall events, the top of the radiation sensor often forms snow and frost, which may affect SW_in measurements, causing defects in the data. Correction for SW_in must be carried out and the method was proposed by Van den Broeke et al. (2004). Since the SW_in correlation coefficients of AWS1 and AWS2 reached 0.95, the gap in the SW_in was filled by establishing the linear regression between AWS1 and AWS2.

Both forms of rain and snow were recorded using a Geonor T-200B weighing bucket precipitation gauge. Considering the impact of wind speed on solid precipitation, the raw precipitation data was corrected by He et al. (2009). To prepare the continuous precipitation for the 2018 ablation period, the precipitation recorded by AWS1 and AWS2 were used to fill the data gap and obtain a vertical gradient of precipitation. And the air temperature data gap has also been filled by lapse rate for air temperature. The vertical gradient of precipitation and the lapse rate of air temperature were 1.6 mm (100 m)⁻¹ and − 1.1 ℃ (100 m)⁻¹, respectively. Cloud cover (N) is a forcing variable but cannot be observed directly and is estimated using a method described by Favier et al. (2004).

N = 1.3 − 1.4 × (SW_in/SW_TOA) (2)

where SW_TOA represents the solar radiation at the top of atmosphere with the unit of W m^− 2, which can be calculated according to the method of Duffie et al. (1991).

Hock et al. (2005) found that the wind speed depends on the meteorological station location, and it is impossible to get a general scheme to quantitatively analyze the wind speed on the glacier. Linear regression analysis of wind speed from AWS1 and AWS2 yielded hourly regression parameters that could then be used to reconstruct wind speed during ablation period at the AWS1. This method was previously applied by Yang et al. (2016). The interpolation of relative humidity was also based on the method described by Hock et al. (2005), and the relative humidity varies relatively little between AWS1 and AWS2. Therefore, the linear regression analysis of relative humidity between AWS1 and AWS2 was also conducted and the relative humidity in the same period have similar change trend (R = 0.85, RMSE = 0.23%), so that it can be extended to the overall glacier surface. Moreover, the isothermal atmospheric pressure formula was used to obtain continuous air pressure (Zhou et al., 1997). Anyway, the gap time is just a short period and the effect on modeled results adopted by the methods mentioned above is limited.

4.2 Topography and glacier mask

A Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model Version 3 (GDEM 003) with a 30 m spatial resolution, provided by the National Aeronautics and Space Administration (NASA) Land Processes Distributed Active Archive Center (LPDAAC, http://www.usgs.gov), has been arranged for the model experiments. Resulting elevations range from 3700 m a.s.l to 4600 m a.s.l. The UAV survey (MATRICE 200) made by DJI Technology Co, Ltd. on 28 August 2018 has conducted on the Urumqi Glacier No. 1 (Wang et al., 2021). Two flights were carried out with the flying height of 120 m for each flight. The overlap of each flight was 80%, and the camera pitch angle was 70°. The UAV-DEM was generated with a spatial resolution of 0.36 m based on Pix4D Mapper software. Glacier outlines were extracted from the UAV-DEM and used to split the terrain into glacier and non-glaciated area (Fig. 1a), which was used to modeling energy and mass balance for the Urumqi Glacier No. 1.

4.3 Mass balance measurement

Glacier mass balance of the Urumqi Glacier No. 1 was measured following the glaciological method using ablation stakes or snow pits. Thirty-six stakes were evenly distributed on the glacier at different elevation bands by a steam drill (Fig. 1a). The ablation stakes were measured at 29 April 2018 and 1 September 2018, respectively. The measurement items include the vertical height of stakes above the glacier surface, superimposed ice thickness and the density and thickness of each snow/firn layer at an individual ablation stake. Then all the measurement items were converted to water equivalent (w.e.) using the single-point density values from in-situ measurements. The summer mass balance at each stake was then calculated based on these data. Point values were calculated for individual elevation intervals. The mean specific mass balance, expressed as a function of elevation, was calculated by the interpolation and extrapolation of the point results to the whole glacier surface in order to compare with modeled mass balance.

5.1 Meteorological conditions during ablation period

The daily mean air temperature was approximately − 3.2 ℃ throughout the ablation period 2018. Daily mean air temperature fluctuated dramatically for the first few days of ablation period (1 May-8 June) and stayed comparatively low. The daily mean air temperature almost remained above the melting point between 9 June and 28 August (Fig. 3a). The daily mean relative humidity and air temperature exhibited similar variations. Daily mean relative humidity was about 69% during ablation period indicating a fairly humid condition (Fig. 3b). Daily mean relative humidity in May was relatively low. High moisture was particularly evident in the mature period of the rainy season (June to August). The daily mean wind speed typically fell between 0.6 m s^− 1 and 5.3 m s^− 1, with an average of 2.3 m s^− 1 (Fig. 3c). Relatively high wind speed occurred before 27 June and then it became lower. The pressure during the ablation period was relatively stable, with an average of 625 hPa (Fig. 3d). Moreover, the cloud cover declined until 22 May and then increased (Fig. 3e). The total precipitation during our observation period was approximately 692 mm, and mostly occurred from June to August (Fig. 3f). The incoming shortwave radiation (SW_in) is the important model forcing. SW_in exhibited obvious diurnal variation (Fig. 3g) and the average value of SW_in during the ablation period was 224.3 W m^− 2.

5.2 Model optimization and evaluation

The parameter combinations of COSIMA should be carefully selected to obtain an optimal model performance. Since the modeling period is ablation period 2018, a manual trial and error method outperforms an automated Monte Carlo method for long-term documented modeled mass balance (Mölg et al., 2012; Cullen et al., 2014). A manual tuning of model parameters provides a better understanding of the simulation results in response to configuration changes. A list of parameterization options available in COSIMA is presented in Table 5 in Appendix B. The range of values tested and optimized values for COSIMA run is shown in Table 2. Input data from the AWS1 during the period 00:00 a.m. 1 May to 00:00 a.m. 31 August were used for optimization. In the next step, the model is applied to Urumqi Glacier No.1 and the results are also evaluated.

Table 2

List of key parameters, the range of values tested and optimized values for COSIMA run.
Parameters	Lower bound	Upper bound	Optimized values	Unit	References
Albedo fresh snow	0.82	0.88	0.83	-	Measurement; Mölg et al. (2012)
Albedo firn snow	0.5	0.6	0.58	-	Measurement; Mölg et al. (2012)
Albedo ice	0.2	0.4	0.35	-	Measurement; Mölg et al. (2012)
Albedo time scale	1	3	1.1	day	Measurement; Mölg et al. (2012)
Albedo depth scale	2	4	3	cm	Measurement; Mölg et al. (2012)
Surface roughness length fresh snow	0.19	0.29	0.24	mm	Gromke et al. (2011)
Surface roughness length firn	1.5	6.5	4	mm	Brock et al. (2006); Mölg et al. (2012)
Surface roughness length ice	0.7	2.7	1.7	mm	Cullen et al. (2007); Brock et al. (2006)

Given the possible range of COSIMA parameters in Table 2, a manual trial and error approach was used to obtain the optimal value of the COSIMA modeling. Afterwards, the model evaluation of COSIMA is conducted for the ablation period (from 1 May to 31 August 2018). The visual comparison is presented in Fig. 4 for AWS1. The comparison against the observation from AWS1 reveals a good agreement of COSIMA with the measured surface temperature (R = 0.71, RMSE = 2.61 K). In terms of snow height change, there is a significant offset in the AWS1. Especially the modeled snow height not captured is after 7 August. This is partly attributed to the measurement error during the strongly ablation period. The sensor used to measure the distance between the surface and it also has a membrane, which is affected by the weather conditions of the ice surface causing this membrane to fail and produce false values for snow height. This was a generally problem for these instruments (Mölg et al., 2020). Otherwise the mistakes of the measured snow height could be existed during this period. The effect of snowdrift on the snow height has been reported by Li et al. (2018) for Qiangtang Glacier No.1. As strong ablation usually occurs on Urumqi Glacier No.1 during this period (Li et al., 2021), there are few effects of snowdrift on the snow height. COSIMA overestimates the snow height at the location of AWS1. The RMSE between the daily measured and modeled snow height was 0.15 m over the observation period and R was 0.94.

This study carried out the comparison between the measured and modeled summer cumulative mass balance in order to validate the robustness of COSIMA performance (Fig. 5). Negative values point to ablation and decreasing surface height, while the positive values indicate accumulation and increasing surface height. During the ablation period, summer cumulative mass balance calculated using the glaciological method and COSIMA was − 0.85 m w.e. and − 0.77 m w.e., respectively. This difference (i.e., 0.08 m w.e) is acceptable given the measured mass balance uncertainty. The modeled mass balance agreed well with the measured mass balance (R_total=0.70; RMSE_total = 0.43 m w.e.). The R is 0.75 and the RMSE is 0.35 m w.e. for the WB, while the R is 0.70 and RMSE is 0.49 for the EB. Such a good performance regarding the mass balance simulations makes us confident in the COSIMA’s ability to capture the mass balance on Urumqi Glacier No. 1. Therefore, COSIMA in its current configuration can offer a good estimate of surface energy and mass balance of Urumqi Glacier No. 1 and is therefore analyzed further in the following parts.

5.3 Glacier-wide energy balance

Figure 6 depicts the daily heat flux for snow/ice melting (Q_melt), net shortwave radiation (SW_net), incoming longwave radiation (LW_in), outgoing longwave radiation (LW_out), sensible heat flux (Q_sens), latent heat flux (Q_lat) and ground heat flux (Q_G). The main energy component causing the glacier ablation were SW_net (148.18 W m^− 2), LW_in (241.84 W m^− 2) and Q_sens (10.08 W m^− 2). The main energy expenditure were the LW_out (-283.11 W m^− 2), Q_lat (-5.93 W m^− 2) and Q_G (-3.41 W m^− 2).

Generally, SW_net dominated the the heat flux for snow/ice melting throughout the ablation period. SW_net tended to increase before early June and then decrease, which may be related to increased precipitation. This can increase surface albedo, and finally result in the decreasing SW_net. Due to the small air and surface temperatures, LW_net was negative and acted as a heat sink. The record of LW_net indicated three separate phases. Relatively larger negative LW_net occurred before the early June and after the late August. Between these two periods, LW_net was less negative. Q_sens constantly provided energy gain for glacier melt, because relative humidity, wind speed, and air temperature are always higher than glacier surface’s. Q_lat was negative throughout the ablation period, mainly affected by the specific humidity gradient and the relative humidity gradient, indicating that the sublimation process also existed throughout the ablation period and led to mass loss. This is because relatively lower temperatures and relative humidity led to specific humidity gradients signing from the glacier surface to the atmosphere. Q_G provided a more minor heat sink compared with other heat fluxes depending on SW_in and glacier surface temperature.

Table 3

Seasonal change of modeled energy fluxes during the ablation period of 2018.
Month	Location	SW_net	LW_in	LW_out	LW_net	Q_sens		Q_lat		Q_G	Q_melt
May	Urumqi Glacier No. 1	90.23	216.43	-279.21	-62.78	6.48		-17.59		-5.62	-12.78
	EB	92.86	218.25	-281.06	-62.81	6.77		-17.95		-5.43	-14.48
	WB	85.66	213.23	-275.96	-62.73	5.97		-16.96		-5.95	-9.80
June	Urumqi Glacier No. 1	52.40	268.01	-290.15	-22.14	8.20		-3.89		1.39	-29.28
	EB	55.57	270.22	-291.51	-21.29	8.47		-3.78		1.38	-32.93
	WB	46.93	264.14	-287.77	-23.63	7.73		-4.07		1.40	-22.86
July	Urumqi Glacier No. 1	52.94	262.04	-288.29	-26.26	9.37		-3.17		-1.34	-30.76
	EB	56.27	264.20	-289.55	-25.35	9.44		-3.06		-1.20	-34.28
	WB	47.18	258.24	-286.1	-27.85	9.25		-3.38		-1.58	-24.58
August	Urumqi Glacier No. 1	50.84	220.9	-274.82	-53.92		16.27		0.92	-8.07	-18.56
	EB	54.42	222.75	-276.68	-53.93		15.87		0.85	-7.84	-20.69
	WB	44.65	217.64	-271.54	-53.90		16.96		1.06	-8.46	-14.83

5.4 Spatial changes in modeled mass balance

Figure 7 shows the spatial distribution of the modeled cumulative mass balance derived from COSIMA during the ablation period 2018. Spatially, the glacier mass balance ranged from 0.23 to -2.12 m w.e. The significant mass loss was at the lower elevations, while mass loss decreased at higher elevations. The glacier ablation and accumulation were affected by the glacial topography. Spatial distributions of modeled mass balance were in line with the observation (Fig. 5). The spatial variation of the mass balance was influenced by slope and aspect. The cumulative mass balance was − 0.77 m w.e. during the ablation period, mass loss is mainly in the southeast of EB and WB. For the EB, the glacier melting in the western part was stronger than that in eastern part with the higher elevation and steeper, because of the mountain shadow covered. In the same time, the cumulative mass balance of the EB and WB was − 0.86 m w.e. and − 0.52 m w.e., respectively, showing mass loss of EB was more obvious than that of WB.

5.5 Seasonal specific mass balance components

Urumqi Glacier No. 1 is a typical summer-accumulation type glacier and the ablation and accumulation mainly take place simultaneously in the ablation period. The annual mass balance is significantly related to the summer mass balance (Liu and Han, 1992; Li et al., 2011; Wang et al., 2016), therefore it is necessary and important to study the modeled mass balance over Urumqi Glacier No.1 during the ablation period. Moreover, the individual components of the glacier mass gain and loss were also derived from COSIMA. As formulated by COSIMA, the mass balance is composed of solid precipitation, sublimation, refreezing, surface melt, subsurface melt and deposition. Figure 8 shows the glacier-wide daily mass balance components. Modeled mass balance continued to decrease until August 17. In general, the mass loss was significantly dominated by the surface melt with a value of -0.73 m w.e., and then subsurface melt with a value of -0.17 m w.e. (Table 4). The melting showed an increasing trend during May to July. Sublimation resulted in mass loss of 0.03 m w.e. during ablation period and mainly occurred in May. Although several studies have shown that the sublimation in the ablation period was smaller than in the cold season because of the dry environment, our result about sublimation was significantly smaller compared with other continental glaciers (Yang et al., 2013; Zhu et al., 2018). Mass gain was derived from solid precipitation with a contribution of 0.19 m w.e., which mainly occurred from June to August. Refreezing contributed to mass gain could be neglected during the ablation period. Whether refreezing leads to mass gain during cold season provides an important internal mass storage component, needs to be further studied.

Table 4

Seasonal change of mass balance components during the ablation period of 2018.
Month	Location	Solid precipitation	Refreezing	Surface melt	Subsurface melt	Sublimation	Deposition
Month	Location	(m w.e.)	(m w.e.)	(m w.e.)	(m w.e.)	(m w.e.)	(m w.e.)
May	Urumqi Glacier No. 1	0.04120	0.00002	-0.10665	-0.05355	-0.01742	-0.00026
	EB	0.04384	0.00002	-0.12124	-0.05922	-0.01777	-0.00025
	WB	0.03742	0.00002	-0.08134	-0.04361	-0.01679	-0.00024
June	Urumqi Glacier No. 1	0.04727	0.00019	-0.22723	-0.04102	-0.00464	-0.00109
	EB	0.04591	0.00018	-0.25621	-0.04604	-0.00456	-0.00109
	WB	0.05077	0.00021	-0.17743	-0.03220	-0.00480	-0.00108
July	Urumqi Glacier No. 1	0.05371	0.00038	-0.24716	-0.04102	-0.00399	-0.00099
	EB	0.05150	0.00038	-0.27535	-0.04572	-0.00387	-0.00098
	WB	0.05792	0.00039	-0.19787	-0.03277	-0.00421	-0.00102
August	Urumqi Glacier No. 1	0.04811	0.00023	-0.14989	-0.03198	-0.00191	-0.00278
	EB	0.04281	0.00026	-0.16647	-0.03603	-0.00188	-0.00268
	WB	0.05763	0.00019	-0.11986	-0.02487	-0.00196	-0.00296
From May to August	Urumqi Glacier No. 1	0.19029	0.00082	-0.73093	-0.16757	-0.02796	-0.00512
	EB	0.18406	0.00084	-0.81927	-0.18701	-0.02808	-0.00500
	WB	0.20374	0.00081	-0.57650	-0.13345	-0.02776	-0.00530

5.6 Altitudinal distribution of modeled mass balance

Figure 9 compares the modeled and measured summer mass balance during the ablation period of 2018 as a function of elevation. The modeled mass balance well agreed with the measured mass balance, except for a discernible underestimation at the glacier terminus ranging from 3800 m a.s.l to 3900 m a.s.l. The change in the modeled mass balance with altitude during the ablation period can be divided into three stages (Fig. 9a): mass balance tended to decrease and then increased in the altitude range 3800–3900 m a.s.l.; mass balance decreased gradually above 3900 m a.s.l.; mass balance was more positive in the altitude range 4150–4500 m a.s.l. The ELA was at 4150 m a.s.l. The absolute values of surface melt decreased with increasing altitude (Fig. 9a), and ranged from − 1.6 m w.e. at the glacier terminus (3800 m a.s.l.) to 0.1 m w.e. at the top of the glacier (4250 m a.s.l.). Mass balance of EB and WB as a function of elevation in-depth analysis should be helpful to shed light on the details of mass balance. Glacier melt mainly occurred below 4150 m a.s.l. and the mass balance of EB was more negative than that of WB (Fig. 9b, c).

Figure 9d shows the altitudinal distribution of the averaged mass balance components. Obviously, solid precipitation and glacier melt (including surface melt and subsurface melt) during the ablation period were prominent components of mass balance, whereas refreezing, deposition and sublimation were less dominant. On average, surface melt significantly dominated the glacier mass loss, and then subsurface melt. Mass loss by way of sublimation could be negligible. On the other hand, the mass gain was mainly due to solid precipitation. Meanwhile, refreezing and deposition were especially close to zero with little variations.

6.1 Error analysis for COSIMA

The uncertainties of input parameters in the process of energy mass balance calculation can influence COSIMA results, which need to be considered. At Urumqi Glacier No. 1, uncertainties of input parameters are associated with the albedo, surface roughness length, vertical gradient for precipitation and lapse rate for air temperature (Table 6 in Appendix B). 10 scenarios for parameter sensitivity tests are set by perturbing one parameter and keeping other parameters unchanged.

Figure 10 shows the evaluation of parameter uncertainty in COSIMA. Mass balance is less sensitive to the vertical gradient of precipitation than the lapse rate of air temperature. When the lapse rate for air temperature increased (or decreased) by 10%, a mass gain (or loss) of 0.012 (or 0.010) m w.e. was achieved, and the vertical gradient for precipitation ± 10% was produced less than 1 mm w.e. of mass loss. The highest parameter sensitivity was related to ice albedo. The sensitivity for fresh snow albedo was higher than the firn snow albedo. When ice albedo increased (or decreased) by 10%, a mass loss (or gain) of -0.50 (or 0.41) m w.e. occurred on Urumqi Glacier No. 1, which was similar with the results on the Zhadang Glacier (Mölg et al., 2012). Changes in the albedo depth scale also have significant effects on mass balance compared with albedo time scale. When the albedo depth scale increased (or decreased) by 10%, the modeled mass gain (or loss) was 0.013 (or -0.015) m w.e. The albedo time scale increased (or decreased) by 10% results in mass balance change of -0.003 (or 0.004) m w.e. Moreover, we also evaluated sensitivity of surface roughness length, such as surface roughness length ice, firn snow and fresh snow, indicating that the effect of surface roughness length on mass balance can be neglected.

6.2 Parametrization of the surface energy fluxes

The SW_net is an important source of energy for glaciers. It is determined by SW_in and albedo of the glacier surface within the COSIMA. The albedo values for snow and ice are variable due to grain size and form, liquid water content, topographic effects, impurities, etc. (Cuffey and Paterson, 2010; Yue et al., 2017). Albedo parameterization scheme in COSIMA tries to reproduce albedo by introducing albedo of fresh snow, firn snow and ice, albedo time scale and albedo depth scale, which can solve exponentially decreases from fresh snow albedo to ice albedo (Oerlemans and Knap, 1998). In Fig. 11 we show the comparison between the measured and modeled albedo during the ablation period 2018. In generally, this albedo parametrizations in COSIMA were able to capture increases except early ablation period, and several studies had also used similar albedo parametrizations (e.g. Mölg et al., 2012; Huintjes et al., 2015b), nevertheless the measured albedo was much more variable than modeled albedo. The modeled albedo as shown in Fig. 11 was small in the early ablation period, which was probably related to the small solid precipitation in the same period. However, measured albedo has a slight fluctuation compared with modeled albedo. Measured albedo values were calculated as a ratio of the outcoming shortwave radiation to the incoming shortwave radiation. Because the CNR4 radiation sensor has poor cosine response quality at solar zenith angles larger than 80◦, the outcoming shortwave radiation flux was greater than the incoming shortwave radiation at certain moments early in the ablation period, Therefore, we deduced that the measured albedo at AWS1 site may be wrong, and the possible reason was the failure of the CNR4 radiation sensor. Most of the measured albedo increases are associated with snowfall events (as shown in Fig. 3f), but the double critical temperature index method is adopted to deduce it from total precipitation measured at AWS1 (see section 3.1). Additionally, the faster the albedo decreases after snowfall events and the lower albedo time scale (1.1 day), indicating the faster snow metamorphism during the ablation period and may be associated with increased ambient temperature.

Usually the LW_net makes an important contribution to the energy exchange on the glacier surface. The LW_net is often negative, this is because glacier surface is like as blackbody within COSIMA and atmosphere emissivity is often smaller than 1. Schaefer et al. (2020) has reported that the variability in emissivity cannot only be explained by the variability in the cloudiness and the relative humidity may influence emissivity. The uncertainties in the change of the cloud cover might result in the large emissivity. Cloud cover as input data in COSIMA was obtained from a parametrization described by Favier et al. (2004). However, this parametrization is not unique (for instant Oerlemans, 2001). Additionally, temperature of atmosphere often emits LW_in, however, in this study, whether the 2 m air temperature measured at AWS1over the glacier surface can represent the temperature of atmosphere is still to be proved.

The turbulent fluxes are often affected by local meteorological conditions. Due to the negative Q _lat discussed in section 5.3 which peaked in the months prior to 8 June (Fig. 6), the resulted sublimation was also evident in the mass balance record (Fig. 8). But the air temperature remained rather low, which favored a large surface-air vapor pressure gradient, and the lower relative humidity and higher wind speeds also drive turbulence (Fig. 3a, b, c). Generally, monthly means of Q_sens and Q_lat were of opposite sign, but absolute values of Q_sens were larger than Q_lat when air temperature rose, especially after 8 June, increasing the importance of Q_sens for surface melt (Table 3).

6.3 Geodetic v.s. modeled melt rates

In this study, glacier mass balance of Urumqi Glacier No.1 was modeled using the AWS1-driven COSIMA during the ablation period in 2018. The mean surface velocity in the same investigative period was 0.026 m d^− 1 corresponds to 3.3 m yr^− 1, which was derived by the comparison of two high-resolution UAV photogrammetries (Wang et al. 2021). Assuming no significant speed up during the ablation period and considering the 30 m spatial resolution of COSIMA, the dynamical change can be neglected for modeling at seasonal timescales due to derived small surface velocities. Figure 12a illustrated the spatial differences of surface elevation changes between COSIMA and UAV. Modeled results using COSIMA within this study and the geodetic results referred to Wang et al. (2021) based on repeated high-resolution UAV photogrammetries, respectively. Since different densities for snow, firn, and ice were used within COSIMA, we employed an average ice density of 900 ± 17 kg m^− 3 for the conversion from surface elevation changes to mass changes in COSIMA. The in-situ measured densities of firn-snow data (change in ice thickness) was used to estimate the single-point density conversion of 752 ± 34 kg m^− 3 during the ablation period of 2018. Differences between both datasets at the tongues are small, while high differences occur at the middle part. The accuracy was within decimeter accuracy, with a mean value of 0.14 m for the ablation period (Fig. 12b). Such decimeter-scale uncertainty supports the acquisition of the glacier elevation changes derived from COSIMA. Figure 12c shows that profiles of differences between surface elevation changes derived using COSIMA and repeated UAV surveys. Overall, both agreed well with each other, but the difference still existed (R = 0.56; Std dev = 0.54). Repeated UAV surveys observed glacier thinning even in the upper-elevation areas, while COSIMA estimated a gain of mass in the upper-elevation areas and a loss of mass in the ablation area. Differences between both datasets at the middle part are small, while high differences occur at the glacier tongues. The latter is caused by a constant ice flow into this branch over time. Surface velocity is larger in the middle-lower part than in upper stream (Wang et al., 2018). By comparison, the geodetic results of Wang et al. (2021) indicated a stronger thickening in some upper parts, which might be compensated by stronger thinning in the lowest regions compared to this study. The modeled melt rates in this study ranged from 0.2 to 1.7 cm w.e. d^− 1 in the ablation period of 2018 with the mean value of 0.6 cm w.e. d^− 1. According to Xu et al. (2019), the melt rates of 0.9 and 0.8 cm w.e. d^− 1 were derived from long-range terrestrial laser scanning measurements in the ablation periods of 2015 and 2016 on Urumqi Glacier No.1, respectively, indicating the slightly reduced mass loss in recent year together with our modeled results. This phenomenon was also founded in Li et al. (2021).

6.4 Sensitivity of mass balance to air temperature and precipitation

To assess the sensitivity of the mass balance of the Urumqi Glacier No.1 to climatic factors, various air temperature or precipitation changes as input data were applied to run COSIMA over the ablation period of 2018. Eight independent temperature change scenarios were designed with air temperatures adjusted in 0.5 K steps from − 2 to 2 K while other variables and model parameters were held constant. Eight independent precipitation change scenarios were also established in the same way by perturbing the precipitation in 10% steps from − 40 to 40%. The COSIMA was run under the background of these sixteen scenarios as a sensitivity analysis and the results are presented in Fig. 13. The sensitivity of mass balance to increasing air temperature was higher than that to increasing precipitation on Urumqi Glacier No.1, and the dependence of mass balance on changes in air temperature and precipitation was close to linear. However, this does not mean that air temperature is more important than precipitation for controlling changes in mass balance. It only shows that the mass balance will change accordingly when the air temperature changes by 1 K or the precipitation changes by 10%. To roughly keep the mass balance on the Urumqi Glacier No.1, 1 K increase in air temperature would have to be compensated by at least 40% precipitation change in our study.

For Urumqi Glacier No.1, Che et al. (2019) found that 23% increase of the precipitation could justly compensate to the mass loss caused by 1 K increasing in air temperature (Che et al. 2019). By comparison, the sensitivity result in this study with higher accuracy is larger than Che et al. (2019). There are two probable reasons. Firstly, the forcing data is from AWS1 on the glacier surface, which can accurately show glacio-meteorological conditions. Secondly, COSIMA coupled surface and subsurface mass balance process together, which can account for meltwater percolation, retention, and refreezing. For the continental Haxilegen Glacier No.51 located close to Urumqi Glacier No.1, the mass balance was more sensitive to 1 K air temperature change than to a 65% precipitation change (Zhang et al., 2018). The mass balance of the Guliya ice cap was more sensitive to the changes in moisture related variables than that in temperature (Li et al., 2018). When the air temperature of Qiyi Glacier increased by 1 K, the ELA increased by 172 m, while the precipitation increased by 10%, the ELA decreased by 62 m (Wang et al., 2011). However, the mass loss after a 1 K change temperature in Muji glacier needs to be compensated for by increasing precipitation by approximately 39% (Zhu et al., 2020). To roughly maintain the mass balance of the Shiyi Glacier, a 1 K increase in air temperature must be compensated by at least 35% of the precipitation changes (Zhang et al., 2020). As one of the maritime glaciers, the mass balance of Parlung Glacier No. 94 was approximately 2 ~ 3 times more sensitive to 1K temperature change than to 30% precipitation change (Yang et al., 2013). The sensitivities of glacier mass balance in response to climate change were different in various mountain ranges, which were mainly resulted from the discrepancies in the ratio of snowfall to precipitation during ablation period, the amount of melt energy during ablation period, and precipitation seasonality in the different local regions. Although there are significant differences in the sensitivity of different types of glaciers to air temperature and precipitation, extreme continental glaciers have a lower percentage increase than precipitation required for maritime glaciers in order to balance the effects of a 1 K temperature increase.

6.5 Climatic factors controlling mass changes

Summer mass balance on Urumqi Glacier No.1 plays a dominant role for the annual mass balance (Li et al., 2011; Wang et al., 2016). So the modeled summer mass balance was used to assess how climatic factors controlling the mass changes. However, it should be noted, this result is inevitably subject to uncertainties when compared with other studies, which referred to annual mass balance change. Based on the method used in this study by analyzing interannual variability of ablation period air temperature and annual precipitation, mass balance on Urumqi Glacier No.1 is considered to be more strongly controlled by ablation period air temperature than by annual precipitation, because the sensitivity of air temperature on mass balance change (149 mm w.e.) is larger than annual precipitation on mass balance (91 mm w.e.) (Fig. 14). Similar results found that the mass loss from increasing in air temperature was significantly higher than that from compensating in precipitation in Urumqi Glacier No.1 based on air temperature and annual precipitation during the period of 1958–2015 (Che et al., 2019). Therefore, it is deduced that the glacier mass loss in Urumqi Glacier No.1 was mostly resulted from increasing in air temperature.

We present the past studies about the control of air temperature or precipitation on mass balance in the western China together with our results in Figure. 14. The difference between mass balance changes at a single glacier strongly underlines the controlling of climate on mass balance, and presents the response of glaciers to climate change. The Urumqi Glacier No.1 and Haxilegen Glacier No.51 located in the eastern Tien Shan are continental glaciers. The mass loss of the Urumqi Glacier No.1 was similar to that of the Haxilegen Glacier No.51, and a statistically significant relationship in mass balance has also been identified (Zhang et al., 2018). Mass loss of them could be attributed to air temperature rise during the ablation period. For Urumqi Glacier No.1, the former combined with ice temperature increase and albedo reduction on the glacier surface must be considered together. The physical mechanisms could also be suitable for the Haxilegen Glacier No.51, because both of the glaciers are situated in the eastern Tien Shan with a relatively dry continental climate. More negative mass balances occurred in Zhadang Glacier as a continental glacier, located in the Nam Co basin, south Tibetan Plateau, air temperature can contribute to this mass loss. In summer, positive incoming shortwave radiation as the most significant heat flux, together with sensible heat flux, contributed to positive heat flux for melting for glacier surface melting. As a result, strong summertime melting occurred on the glacier surface (Zhang et al., 2015). The Muztag Ata Glacier No.15 and Muji Glacier are extreme continental glaciers. The smallest mass loss is observed at the Muztag Ata Glacier No.15 and Muji Glacier in the eastern and northeastern Pamir regions due to the strengthening westerlies with controlling of precipitation. The mass balance change of the Palung Glacier No.94, which is a maritime glacier, is also controlled by air temperature. In conclusion, the intensity of air temperature and precipitation controlling mass balance is various in different regions. The mass loss of these glaciers is mainly controlled by air temperature except the Muztag Ata No.15 Glacier and Muji Glacier, the mass balance of which are mainly dominated by the annual precipitation.

6.6 Comparison with previous studies

Figure 15 shows the comparison of our results with the glaciological mass balance, Degree-day model and geodetic method results on Urumqi Glacier No.1. The mass balance obtained by different methods compares with glaciological mass balance to clearly present the optimal model performance. The energy balance model is usually regarded as reference model in calculating mass balance. Che et al. (2019) conducted an energy balance modeling experiment forcing by AWS2 datasets and the result was in line with actual observation. The relative coefficient between the modeled and measured cumulative mass balance was 0.86, and the coefficient of determination was 0.75 (Che et al., 2019). The Degree-day model was more suitable for long-term mass balance estimates, because overall mass balance estimates were in a good agreement with glaciological mass balance for the long term (Wu et al., 2011). In term of the enhanced Degree-day model, the spatial distribution of mass balance in Urumqi Glacier No.1 showed that the performance was less performed compared with the glaciological mass balance (Huintjes et al., 2010).

There was actual phenomenon that annual mass balance was mainly related to summer mass balance (mass balance in the ablation period) in Urumqi Glacier No.1 (Li et al., 2011; Wang et al., 2016). As shown in Fig. 15, our result was more consistent with annual glaciological mass balance compared with Che et al. (2019). The hourly meteorological records and COSIMA combined with surface and subsurface processes together produce this optimal result. It is therefore regarded as more accurately reflect energy and mass balance process on glacier surface. Geodetic mass balance in ablation period of 2015 and 2016 was more negative compared with annual glaciological mass balance, while our estimate with the value of -0.77 m w.e. was also more consistent with the annual glaciological mass balance. The performance of the simplified energy balance model is better than that of the Degree-day model in the short time, but the Degree-day model performed better than the simplified energy balance model in the same zone (e.g. the zone around the ELA) (Li, 2020).

We collect the model comparison studies during ablation period and assess their difference in space and time. Some studies reveal the enhanced Degree-day model offering significant improvements over the classical Degree-day model at the point scale, nevertheless the improvement was limited (Pellicciotti et al., 2005). However, at the glacier scale, the result is less clear. Pellicciotti et al. (2013) showed that there were obvious differences in performance between the enhanced Degree-day model and an energy balance model. MacDougall et al. (2011) also applied an energy balance model and four empirical models, and similar conclusions were obtained. The two models can be demonstrated to be clearly superior to others, and their performance strongly depends on input data and temporal and spatial resolution of the application. For the enhanced Degree-day model, the input meteorological variables need to be extrapolated from point observations to the grid cells of the glacier, as the energy mass balance require a number of input meteorological variables. Some meteorological data, such as wind speed or shortwave radiation, are difficult to model on the glacier surface. On the other hand, interpolation methods also cannot accurately obtain these meteorological data changes on the glacier surface, especially the wind speed, because there is no clear elevation or spatial dependency. It is not clear which is superior at whole glacier and larger scales between the two models. At Urumqi Glacier No.1, the both performances have not compared with glaciological mass balance as yet. The results presented here are important, since some studies have shown that the modeled mass balance affects runoff projections (Gabbi et al., 2014).

Compared with previous studies, we have clarified the connection between glacier change and the atmospheric conditions. Through the forcing of hourly-scale value for each meteorological variable, this paper has revealed the melting process and mechanism of the Urumqi Glacier No.1 during the ablation period. The spatial and temporal changes of the energy fluxes and mass balance components are well demonstrated, and the meteorological factors controlling the mass balance of the glacier can also be quantitatively determined. Our study is the first attempt to evaluate the performance of mass balance at Urumqi Glacier No.1 by linking COSIMA with the in-situ measured meteorological records and to understand glacier energy and mass balance process. Our estimate result is consistent with glaciological mass balance (Fig. 4), and similar with annual glaciological mass balance (Fig. 15). However, our study is limited in time scale and the insight into for model performance, such as parameter instability. In future, we plan to extend the input data time series using the ERA-5 reanalysis data, particularly with regard to glacier projections.

Based on the meteorological measurements in AWS1 on the surface of Urumqi Glacier No.1 in the Chinese Tien Shan during the ablation period 2018, the temporal variations in energy and mass balance and the response of mass balance to climate variations, were investigated using COSIMA. The optimization of our modeled results is not suitable for traditional optimization method (e.g. Monte-Carlo approach) because of the short-term investigated period. Therefore, we attempted to find the best parameter selection for AWS1. The manual model optimization conducted to meet the climatic observations from AWS1, afterwards, the model evaluation of COSIMA was conducted using surface temperature, snow height and glacier-wide mass balance measurements.

Relative humidity was small while wind speed was high prior to 8 June, but air temperature remained rather low and surface temperature rose. These meteorological conditions will drive turbulence. The main components in energy balance were radiation components (SW_net and LW_net) and turbulent fluxes during ablation period. Albedo as a key parameter could affect SW_net, and most of the measured increases in albedo can be associated with precipitation events. Surface melt and solid precipitation were two dominant components of mass balance. Most surface melt and solid precipitation occurred simultaneously in June-August with the strongest mass losses in July. Urumqi Glacier No.1 experienced a significant mass loss, with an average value of -0.77 m w.e. corresponds to 0.6 cm w.e. d^− 1 over ablation period 2018. Comparing with the UAV results at Urumqi Glacier No.1 during the same period showed that the modeled surface elevation change agreed well with surface elevation change determined by repeated UAV surveys. By comparing this result with the geodetic mass balance observations of Urumqi Glacier No.1 for ablation periods of 2015 and 2016, it is indicated the slightly reduced mass loss was experienced in recent year.

Sensitivity analysis showed that the sensitivity of temperature is greater than precipitation, and mass loss caused by temperature increase of 1 K needed to be compensated by at least 40% precipitation. The air temperature during ablation period was more important than annual precipitation in controlling mass balance changes on Urumqi Glacier No.1. The key of performance of the energy balance model depended on the accurate of meteorological records and optimization of parameters. In general, the COSIMA can reproduce the glaciological mass balance compared with geodetic method and other energy balance model. The Degree-day model was more suitable for long-term mass balance estimates, and the performance of the simplified energy balance model was better than that of the Degree-day model in the short time. However, at the glacier-wide scale, it is difficult to identify which is better between the enhanced Degree-day model and energy balance models, that is because it strongly depends on input data.

Acknowledgements. This research was jointly funded by the National Natural Science Foundation of China (grant no. 41771077), the Youth Innovation Promotion Association of CAS, the Third Xinjiang Scientific Expedition Program (Grant No. 2021xjkk0801), National Natural Science Foundation of China (grant no. 42001067), and the State Key Laboratory of Cryospheric Science (grant no. SKLCS-ZZ-2021).

Data availability. Glaciological mass balance data related to this study are submitted to the WGMS and be available at the following website: https://doi.org/10.5904/wgms-fog-2019-12 (WGMS, 2019). COSIMA is available online as an open-source software and used for this study (https://bitbucket.org/glaciermodel/cosima; Huintjes et al., 2015a). The meteorological data are available upon request by email to the corresponding author ([email protected]).

Anderson EA (1976) A point energy and mass balance model of a snow cover. Technical Report NWS19, NOAA
Bintanja R, Jonsson S, Knap WH (1997) The annual cycle of the surface energy balance of Antarctic blue ice. J Geophys Res 102(D2):1867–1881. doi:10.1029/96JD01801
Bintanja R, van den Broeke M (1995) The surface energy balance of Antarctic snow and blue ice. J Appl Meteorol 34:902–926
Brock BW, Willis IC, Martin MJ (2006) Measurement and parameterization of aerodynamic roughness length variations at Haut Glacier d’Arolla. Switz J Glaciol 52:281–297
Braithwaite RJ (1995) Aerodynamic stability and turbulent sensible heat flux over a melting ice surface, the Greenland ice sheet. J Glaciol 41:562–571
Che YJ, Zhang MJ, Li ZQ, Wei YQ, Nan ZT, Li HL, Wang SJ, Su B (2019) Energy balance model of mass balance and its sensitivity to meteorological variability on Urumqi River Glacier No.1 in the Chinese Tien Shan. Sci Rep 9(1):13958. doi: 10.1038/s41598-019-50398-4
Cullen NJ, Mölg T, Kaser G, Steffen K, Hardy DR (2007) Energy-balance model validation on the top of Kilimanjaro, Tanzania, using eddy covariance data. Ann Glaciol 46:227–233
Cullen NJ, Mölg T, Conway J, Steffen K (2014) Assessing the role of sublimation in the dry snow zone of the Greenland ice sheet in a warming world. J Geophys Res -Atmos 119(11):6563–6577. doi: 10.1002/2014JD021557
Cuffey K, Paterson W (2010) The Physics of Glaciers, Elsevier, 4th Edn
Duffie JA, Beckman WA (1991) Solar Engineering of Thermal Processes, 2nd edn. Wiley, New York, NY, USA
Favier V, Wagnon P, Chazarin JP, Maisincho L, Coudrain A (2004) One year measurements of surface heat budget on the ablation zone of Antizana Glacier 15, Ecuadorian Andes. J Geophys Res 109(D18). https://doi.org/10.1029/2003JD004359
Farinotti D, Longuevergne L, Moholdt G, Duethmann D, Mölg T, Bolch T, Vorogushyn S, Güntner A (2015) Substantial glacier mass loss in the Tien Shan over the past 50 years. Nat. Geosci., 8(9): 716–722, https://doi.org/10.1038/NGEO2513, 2015
Fujita K, Ageta Y (2000) Effect of summer accumulation on glacier mass balance on the tibetan plateau revealed by mass-balance model. J Glaciol 46(153):244–252
Gabbi J, Carenzo M, Pellicciotti F, Bauder A, Funk M (2014) A comparison of empirical and physically based glacier surface melt models for long-term simulations of glacier response. J Glaciol 60(224):1140–1154. doi:10.3189/2014JoG14J011
Gromke C, Manes C, Walter B, Lehning M, Guala M (2011) Aerodynamic roughness length of fresh snow. Bound Layer Meteorol 141:21–34
Han HD, Ding YJ, Liu SY (2005) Estimation and analysis of heat balance parameters in the ablation season of debris-covered kerqikaer glacier, tianshan mountains. J. Glaciol. and Geocryology
He XB, Ye BS, Ding YJ (2009) Bias correction for precipitation mesuament in tanggula mountain tibetan plateau. Adv Water Sci 20(3):403–408
Herron MH, Langway CC (1980) Firn Densification: An Empirical Model. J Glaciol 25:373–385
Huintjes E, Sauter T, Schröter B, Maussion F, Yang W, Kropáček J, Buchroithner M, Scherer D, Kang SC, Schneider C (2015a) Evaluation of a coupled snow and energy balance model for Zhadang glacier, Tibetan Plateau, using glaciological measurements and time-lapse photography. Arct. Antarct. Alp. Res
Huintjes E, Neckel N, Hochschild V, Schneider C (2015b) Surface energy and mass balance at Purogangri Ice Cap, central Tibetan Plateau, 2001–2011. J Glaciol 61(230):1048–1061
Huintjes E, Li HL, Sauter T, Li ZQ, Schneider C (2010) Degree-day modelling of the surface mass balance of Urumqi Glacier No. 1, Tian Shan, China, The Cryosphere Discuss., 4, 207–232, https://doi.org/10.5194/tcd-4-207-2010, 2010
Hock R, Holmgren B (2005) A distributed surface energy-balance model for complex topography and its application to Storglaciren. Swed J Glaciol 51(172):25–36
Immerzeel WW, Beek LPHV, Bierkens MP (2010) Climate change will affect the Asian water towers. Sci (New York N Y) 328(5984):1382–1385. doi: 10.1126/science.1183188
Jiang X, Wang N, He J, Wu X, Song G (2010) A distributed surface energy and mass balance model and its application to a mountain glacier in China. Chin Sci Bull 55(20):2079–2087
Jia YF, Li ZQ, Xu CH, Jin S, Deng HJ (2020) A Comparison of Precipitation Measurements with a PWS100 Laser Sensor and a Geonor T-200B Precipitation Gauge at a Nival Glacial Zone in Eastern Tianshan, Central Asia. Atmosphere 11:1079. https://doi.org/10.3390/atmos11101079
Kaser G, Hardy DR, Mölg T, Bradley RS, Hyera TM (2004) Modern glacier retreat on Kilimanjaro as evidence of climate change: Observations and facts. Int J Climatol 24:329–339. doi:10.1002/joc.1008
Kang ES, Yang DQ, Zhang YS (1992) An experiment study of the water and heat balance in the source area of the Urumqi River in the Tian Shan Moutains.Ann. Glaciol., (16):55–66
Kumar L, Skidmore AK, Knowles E (1997) Modelling topographic variation in solar radiation in a GIS environment. Int J Geogr Inf Sci 11(5):475–497. doi:10.1080/136588197242266)
Klok EJ, Oerlemans J (2002) Model study of the spatial distribution of the energy and mass balance of Morteratschgletscher. Switz J Glaciol 48:505–518
Liu CG, Han TD (1992) Relation between recent glacier variations and climate in the Tien Shan mountains, Central Asia, Ann. Glaciol., 16, 11–16, https://doi.org/10.3189/1992AoG16-1-11-16, 1992
Li SH, Yao TD, Yang W, Yu WS, Zhu ML (2018) Glacier energy and mass balance in the inland Tibetan Plateau: Seasonal and interannual variability in relation to atmospheric changes. J Geophys Res Atmospheres 123:6390–6409. https://doi.org/10.1029/2017JD028120
Li SH, Yao TD, Yu WS, Yang W, Zhu ML (2019) Energy and mass balance characteristics of the Guliya ice cap in the West Kunlun Mountains, Tibetan Plateau. Cold Regions Science and Technology, 2019, 159
Li HL, Wang PY, Li ZQ, Jin S, Xu CH, Liu SS, Zhang ZY, Xu LP (2021) An application of three different field methods to monitor changes in Urumqi Glacier No. 1, Chinese TienShan, during 2012–18. J. Glaciol., 1–13. https://doi.org/10.1017/jog.2021.71
Li HL (2020) Spatial and temporal transferability of Degree-Day Model and Simplified Energy Balance Model: a case study. Sci. Cold Arid Reg., 12(2): 0095 – 0103. Doi: 10.3724/SP.J.1226.2020.00095
Li ZQ, Li HL, Chen YN (2011) Mechanisms and simulation of accelerated shrinkage of continental glaciers: a case study of Urumqi Glacier No. 1 in eastern Tianshan, central Asia. Journal of Earth Science, 22(4): 423 – 430. Doi: 10.1007/s12583-011-0194-5
Liu CH, Xie ZC, Wang CZ (1997) A research on the mass balance process of Glacier No.1 at the headwaters of the Urumqi River, Tianshan Mountains. J Glaciol Geocryol 19:17–24
MacDougall AH, Wheler BA, Flowers GE (2011) A preliminary assessment of glacier melt-model parameter sensitivity and transferability in a dry subarctic environment. The Cryosphere 5(4):1011–1028. doi: 10.5194/tc-5-1011-2011)
Miles E, McCarthy M, Dehecq A, Kneib M, Fugger S, Pellicciotti F (2021) Health and sustainability of glaciers in High Mountain Asia. Nat Commun 12:2868. doi:10.1038/s41467-021-23073-4
Mölg T, Hardy DR, Collier E, Kropac E, Schmid C, Cullen NJ, Kaser G, Prinz R, Winkler M (2020) Mesoscale atmospheric circulation controls of local meteorological elevation gradients on Kersten Glacier near Kilimanjaro summit. Earth Syst Dynam 11(3):653–672. doi: 10.5194/esd-11-653-2020
Mölg T, Maussion F, Yang W, Scherer D (2012) The footprint of Asian monsoon dynamics in the mass and energy balance of a Tibetan glacier. The Cryosphere 6(6):1445–1461. 10.5194/tc- 6-1445-2012
Mölg T, Cullen NJ, Hardy DR, Winkler M, Kaser G (2009) Quantifying climate change in the tropical midtroposphere over East Africa from glacier shrinkage on Kilimanjaro. J Clim 22:4162–4181
Oerlemans J, Knap WH (1998) A 1 year record of global radiation and albedo in the ablation zone of Morteratschgletscher. Switz J Glaciol 44(147):231–238
Oerlemans J (2001) Glaciers and Climate Change. A.A. Balkema Publishers,Lisse, Abingdon, Exton, Tokyo
Oerlemans J, Klok EJ (2002) Arct Antarct Alp Res 34:477–485. doi:10.2307/1552206. Energy balance of a glacier surface: Analysis of automatic weather station data from the Morteratschgletscher, Switzerland
Pellicciotti F, Ragettli S, Carenzo M, McPhee J (2013) Changes of glaciers in the Andes of Chile and priorities for future work. Sci. Total Environ., 493, 1197–1210 (doi: 10.1016/j.scitotenv. 2013.10.055)
Pellicciotti F, Brock BW, Strasser U, Burlando P, Funk M, Corripio JG (2005) An enhanced temperature-index glacier melt model including shortwave radiation balance: development and testing for Haut Glacier d’Arolla. Switz J Glaciol 51(175):573–587. doi: 10.3189/172756505781829124)
Pieczonka T, Bolch T (2015) Region-wide glacier mass budgets and area changes for the Central Tien Shan between ∼1975 and 1999 using Hexagon KH-9 imagery, Global Planet. Change, 128, 1–13, https://doi.org/10.1016/j.gloplacha.2014.11.014, 2015
Sakai A, Fujita K (2017) Contrasting glacier responses to recent climate change in high-mountain Asia, Sci. Rep., 7, 13717, https://doi.org/10.1038/s41598-017-14256-5, 2017
Schaefer M, Fonseca-Gallardo D, Farías-Barahona D, Casassa G (2020) Surface energy fluxes on Chilean glaciers: measurements and models. The Cryosphere 14:2545–2565. Doi: 10.5194/tc-14-2545-2020)
Sun WJ, Qin X, Wang YT, Chen JZ, Du WT, Zhang T, Huai BJ (2018) The response of surface mass and energy balance of a continental glacier to climate variability, western Qilian Mountains. China Clim Dyn 50(9/10):3557–3570
Broeke MVD, As DV, Reijmer C, Wal R (2004) Assessing and improving the quality of unattended radiation observations in Antarctica. J Atmos Ocean Technol 21(9):1417–1431
Wang PY, Li ZQ, Li HL, Zhang ZY, Xu LP, Yue XY (2020) Glaciers in Xinjiang, China: Past Changes and Current Status. Water 12(9):2367. doi: 10.3390/w12092367
Wang NL, Yao TD, Xu BQ, Chen AA, Wang WC (2019) Spatiotemporal Pattern, Trend, and Influence of Glacier Change in Tibetan Plateau and Surroundings under Global Warming. Bull Chin Acad Sci 34(11):1220–1232. Doi: 10.16418/j.issn.1000-3045.2019.11.005
Wang NL, Wu HB, Wu YW, Chen AA (2015) Variations of the glacier mass balance and lake water storage in the Tarim Basin, northwest China, over the period of 2003–2009 estimated by the ICESat-GLAS data. Environ Earth Sci 74(3):1997–2008. doi: 10.1007/s12665-015-4662-6
Wang PY, Li ZQ, Li HL, Yao HB, Xu CH, Zhou P, Jin S, Wang WB (2016) Analyses of recent observations of Urumqi Glacier No. 1, Chinese Tianshan Mountains. Environ Earth Sci 75(8):720. doi: 10.1007/s12665-016-5551-3
Wang PY, Li ZQ, Schneider C, Li HL, Hamm A, Jin S, Xu CH, Li HL, Yue XY, Yang M (2020) A Test Study of an Energy and Mass Balance Model Application to a Site on Urumqi Glacier No. 1, Chinese Tian Shan. Water 12:2865. https://doi.org/10.3390/w12102865
Wang PY, Li ZQ, Li HL, Wang WB, Zhou P, Wang L (2017) Characteristics of a partially debris-covered glacier and its response to atmospheric warming in Mt. Tomor, Tien Shan, China. Glob Planet Change 159:11–24. doi: 10.1016/j.gloplacha.2017.10.006
Wang PY, Li HL, Li ZQ, Liu YS, Xu CH, Mu JX, Zhang H (2021) Seasonal Surface Change of Urumqi Glacier No. 1, Eastern Tien Shan, China, Revealed by Repeated High-Resolution UAV Photogrammetry. Remote Sens 13(17):3398. doi.org/10.3390/rs13173398
Wang S, Pu JC, Wang NL (2011) Study of mass balance and sensibility to climate change of Qiyi Glacier in Qilian Mountains. J Glaciol and Geocryology 33(06):1214–1221
Wu LH, Li HL, Wang L (2011) Application of a degree-day model for determination of mass balance of Urumqi Glacier No. 1, eastern Tianshan, China. J Earth Sci 22:470–481. https://doi.org/10.1007/s12583-011-0201-x
Xu CH, Li ZQ, Wang PY, Anjum MN, Li HL, Wang FT (2018) Detailed comparison of glaciological and geodetic mass balances for Urumqi Glacier No. 1, eastern Tien Shan, China, from 1981 to 2015. Cold Reg. Sci. Tech, 155, 137–148. https://doi.org/10.1016/j.coldregions.2018.08.006, 2018
Xu CH, Li ZQ, Li HL, Wang FT, Zhou P (2019) Long-range terrestrial laser scanning measurements of annual and intra-annual mass balances for Urumqi Glacier No. 1, eastern Tien Shan, China. The Cryosphere 13:2361–2383. doi: 10.5194/tc-13-2361-2019
Yao TD, Thompson L, Yang W, Yu WS, Gao Y, Guo XJ, Yang XX, Duan KQ, Zhao HB, Xu BQ, Pu JC, Lu AX, Xiang Y, Kattel DB, Joswiak D (2012) Different glacier status with atmospheric circulations in Tibetan Plateau and surroundings. Nat. Clim. Chang, 2012, 2(9): 663–667
Yang W, Guo XF, Yao TD, Yang K, Zhao L, Li SH, Zhu ML (2011) Summertime surface energy budget and ablation modeling in the ablation zone of a maritime Tibetan glacier. J. Geophys. Res., 2011, 116(D14):D14116
Yang W, Yao TD, Guo XF, Zhu ML, Li SH, Kattel DB (2013) Mass balance of a maritime glacier on the southeast Tibetan Plateau and its climatic sensitivity. J Geophys Res : Atmospheres 118(17):9579–9594
Yang W, Guo XF, Yao TD, Zhu ML, Wang YJ (2016) Recent accelerating mass loss of southeast Tibetan glaciers and the relationship with changes in macroscale atmospheric circulations. Clim Dyn 47:805–815. https://doi.org/10.1007/s00382-015-2872-y
Yue XY, Zhao J, Li ZQ, Zhang MJ, Fan J, Wang L, Wang PY (2017) Spatial and temporal variations of the surface albedo and other factors influencing Urumqi Glacier No. 1 in Tien Shan, China, J. Glaciol., 63, 899–911, https://doi.org/10.1017/jog.2017.57, 2017
Zhang H, Li Z, Zhou Q, Zhu P, Wang XF, L (2018) Mass-balance observations and reconstruction for Haxilegen Glacier No.51, eastern Tien Shan, from 1999 to 2015. J Glaciol 64(247):689–699. doi:10.1017/jog.2018.58
Zhang Y, Hirabayashi Y, Liu SY (2012) Catchment-scale reconstruction of glacier mass balance using observations and global climate data: case study of the Hailuogou catchment, south-eastern Tibetan Plateau. J Hydrol 444–445:146–160
Zhu ML, Yao TD, Yang W, Xu BQ, Wu GJ, Wang XJ, Xie Y (2018) Reconstruction of the mass balance of Muztag Ata No. 15 glacier, eastern Pamir, and its climatic drivers. J Glaciol 64(244):259–274
Zhu ML, Yao TD, Yang W, Xu BQ, Wang XJ (2017) Evaluation of parameterizations of incoming longwave radiation in the high-mountain region of the Tibetan Plateau. J Appl Meteorol Clim 56(4):833–848
Zhu ML, Yao TD, Xie Y, Xu BQ, Yang W, Yang S (2020) Mass balance of Muji Glacier, northeastern Pamir, and its controlling climate factors. J. Hydrol., 2020, 590(195):125447. https://doi.org/10.1016/j.jhydrol.2020.125447
Zhou SZ, Zhang RY, Zhang C (1997) Meteorology and climatology. Higher Education Press, Beijing, pp 84–86

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Summertime surface mass balance and energy balance of Urumqi Glacier No. 1, Chinese Tien Shan, modeled by linking COSIMA and in-situ measured meteorological records

Status:

Version 2

Abstract

Figures

1. Introduction

2. Study Site

3. Model Description

3.1 COSIMA descriptions

3.2. COSIMA configuration

3.3 Mass changes assessment

4. Data Sources And Processing

4.1 Input meteorological data

4.2 Topography and glacier mask

4.3 Mass balance measurement

5. Results

5.1 Meteorological conditions during ablation period

5.2 Model optimization and evaluation

5.3 Glacier-wide energy balance

5.4 Spatial changes in modeled mass balance

5.5 Seasonal specific mass balance components

5.6 Altitudinal distribution of modeled mass balance

6. Discussion

6.1 Error analysis for COSIMA

6.2 Parametrization of the surface energy fluxes

6.3 Geodetic v.s. modeled melt rates

6.4 Sensitivity of mass balance to air temperature and precipitation

6.5 Climatic factors controlling mass changes

6.6 Comparison with previous studies

7. Conclusions

Declarations

References

Supplementary Files

Status:

Version 2