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 SWnet is an important source of energy for glaciers. It is determined by SWin 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 LWnet makes an important contribution to the energy exchange on the glacier surface. The LWnet 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 LWin, 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 Qsens and Qlat were of opposite sign, but absolute values of Qsens were larger than Qlat when air temperature rose, especially after 8 June, increasing the importance of Qsens 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.