6.1 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. (Yue et al., 2017; Cuffey and Paterson, 2010). 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. 10 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. Most of the measured albedo increases are associated with snowfall events (as shown in Fig. 2f). However, the drawback is that the exact amount of solid precipitation does not know, 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 metamorphic of snow 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. 5), the resulted sublimation was also evident in the mass balance record (Fig. 7). 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. 2a, 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).
6.2 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 11a shows a comparison between the modeled results using COSIMA within this study and the geodetic results from Wang et al. (2021) based on repeated high-resolution UAV photogrammetries. 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. Wang et al. (2021) used in-situ measured densities of firn-snow data (change in ice thickness) to estimate the single-point density conversion of 752±34 kg m−3 during the ablation period of 2018. The accuracy was within decimeter accuracy, with a mean value of 0.14 m for the ablation period. Such decimeter-scale uncertainty supports the acquisition of the glacier elevation changes derived from COSIMA. Figure 11b 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).
6.3 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 air temperature change scenarios were established by perturbing air temperatures adjusted in 0.5 K steps from -2 K to 2 K while keeping other variables and COSIMA parameters unchanged. In the same way, eight independent precipitation change scenarios were also designed with the change of precipitation within 10%, ranging from -40–40%. The COSIMA was run under the background of these sixteen scenarios as a sensitivity analysis and the results are presented in Figure 12. 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. Compared with Che et al. (2019), our sensitivity analysis has significant advantages. On the one hand, it is forced by AWS1 on the glacier surface and can accurately show glacio-meteorological conditions. On the other hand it can more accurately reflect sensitivity analysis using detailed COSIMA coupled surface and subsurface mass balance process together.
For the continental Haxilegen Glacier No.51, mass balance was more sensitive to 1 K air temperature change than to a 65% precipitation change (Zhang et al., 2018). When air temperature of the Qiyi Glacier increased by 1 K, the equilibrium line altitude (ELA) increased by 172 m, while the precipitation increased by 10%, the ELA decreased by 62 m (Wang et al., 2011). After air temperature increased by 1 K, the mass loss of the extreme continental glaciers such as Abramov, Shumskiy, Tsentralniy, Tuyuksuyskiy and Golubina glacier was similar to a 23% increase of precipitation (Liu and Liu, 2015). 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). The Parlung Glacier No. 94 as one of the maritime glaciers, its mass balance was approximately 2~3 times more sensitive to 1K temperature change than to 30% precipitation change (Yang et al., 2013). 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.
6.4 Using sensitivity to assess how climatic factors control the mass balance change
Based on the method, 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.). 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 studies about the control of air temperature or precipitation on mass balance in the western China together with our results in Figure. 13. The difference between mass balance changes at single glacier strongly underlines the controlling of climatic on mass balance, and presents the response of glaciers to climate. We calculate more negative mass balances corresponding with controlling of air temperature in the Zhadang Glacier and Palung Glacier No.94, which was mainly influenced by the stronger monsoon. 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 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, however, theses physical mechanisms could also be suitable for the Haxilegen Glacier No.51, because the two glaciers are situated in the eastern Tien Shan with a relatively dry continental climate. 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.
6.5 Comparison to previous studies of mass balance in Urumqi Glacier No. 1
Figure 14 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. (2011) 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. 14, 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 of these, such as wind speed or shortwave radiation, are difficult to model at glacier surface, and extrapolation methods also fail, especially wind speed, because this cannot be identified due to 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).
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. 3), and similar with annual glaciological mass balance (Fig. 14). 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.