基于多源遥感数据的玛纳斯河流域冰川物质平衡变化

doi:10.11821/dlxb202001008

摘要/Abstract

摘要：

冰川物质平衡变化是连接气候和水资源的重要纽带,对河川径流有重要的调节功能。本文采用MOD11C3和TRMM 3B43等多源遥感数据驱动度日模型,模拟了2000—2016年玛纳斯河（简称玛河）流域冰川物质平衡过程,并分析了冰川融水对径流的补给规律。结果表明： ① 通过构建气温及降水反演模型能有效校正气象遥感原数据的精度,且经降尺度后能较精细刻画冰川区气候变化特征。冰川区年均气温和降水量分别为-7.57 ℃和410.71 mm,海拔4200 m处为气候变化剧烈地带,气温直减率以其为界上下分别为-0.03 ℃/100 m和-0.57 ℃/100 m,降水梯度分别为-2.66 mm/100 m和4.8 mm/100 m,海拔大于4700 m后降水又以5.17 mm/100 m递增。② 研究期内流域冰川持续呈负平衡状态,累积物质平衡达-9811.19 mm w.e.,年均物质平衡介于-464.85~-632.19 mm w.e.之间。垂向物质平衡在消融区和积累区分别以244.83 mm w.e./100 m、18.77 mm w.e./100 m递增。2000—2002年、2008—2010年冰川消融减缓,2002—2008年、2010—2016年消融加剧,其中2005—2009年期间冰川亏损最为强烈。③ 年内河川径流对冰川物质平衡变化响应强烈,尤以7月、8月物质平衡亏损最为严重占全年总量的75.4%,使得同期河川径流量占全年径流总量的55.1%。年际冰川融水补给率波动于19%~31%之间,可能是不同年份降水和积雪融水补给率差异较大所致。玛河与天山北坡其他河流冰川融水贡献率非常接近,也进一步证实了本研究物质平衡估算结果的可靠性。本研究可为其他流域冰川物质平衡研究提供借鉴和参考。

关键词: 多源遥感数据, 度日模型, 物质平衡, 冰川融水, 玛纳斯河流域

Abstract:

The glacier mass balance (GMB) is an important link between climate and water resources, which has remarkable regulation functions for river runoff. The research, using MOD11C3, TRMM 3B43 and other multi-source remote sensing data to drive the degree-day model, simulates the GMB processes and analyzes the recharge of glacial meltwater to runoff in the Manas River Basin (MRB) during 2000-2016. The results show that: (1) By constructing the temperature and precipitation inversion model, the accuracy of the meteorological remote sensing data can be effectively corrected, and the characteristics of climate change in the glacial region can be well described after downscaling. The annual average temperature and precipitation in the glacier area were -7.57 ℃ and 410.71 mm, respectively. The place at an altitude of 4200 m is a severe climate change zone. Above 4200 m, the temperature drop rates and precipitation gradients were -0.03 ℃/100 m and -2.66 mm/100 m, respectively; while below 4200 m, they were -0.57 ℃/100 m and 4.8 mm/100 m, respectively. Besides, at a higher altitude of 4700 m, the precipitation increased by 5.17 mm/100 m. (2) During the study period, the glaciers in the basin continued to be in a negative state, with a cumulative GMB of -9811.19 mm w.e. and an average annual GMB between -464.85 mm w.e. and -632.19 mm w.e. The vertical GMB increased by 244.83 w.e./100 m and 18.77 w.e./100 m in the ablation zone and the accumulation zone, respectively. From 2000 to 2002 and 2008 to 2010, the melting of glaciers slowed down, and the ablation was intensified from 2002 to 2008 and from 2010 to 2016. Strikingly, the loss of glaciers was most serious during the period 2005-2009. (3) The river runoff responded strongly to the change of GMB within the year, especially in July and August, namely, the GMB loss accounted for 75.4% of the total amount of the whole year, and the river runoff accounted for 55.1% of the annual total. The inter-annual glacial meltwater recharge rate fluctuated between 19% and 31%, which may be due to the differences of precipitation and snow melt water recharge rates in different years. The contribution rate of glacial meltwater of the MRB is close to that of other river basins on the northern slope of the Tianshan Mountains, which can further confirm the reliability of the GMB estimation results. Above all, the research can provide reference for the study of GMB in other river basins.

Key words: multi-source remote sensing data, degree-day model, glacier mass balance (GMB), glacial meltwater, Manas river basin (MRB)

赵贵宁, 张正勇, 刘琳, 徐丽萍, 王璞玉, 李丽, 宁珊. 基于多源遥感数据的玛纳斯河流域冰川物质平衡变化[J]. 地理学报, 2020, 75(1): 98-112.

ZHAO Guining, ZHANG Zhengyong, LIU Lin, XU Liping, WANG Puyu, LI Li, NING Shan. Changes of glacier mass balance in Manas river basin based on multi-source remote sensing data[J]. Acta Geographica Sinica, 2020, 75(1): 98-112.

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参考文献 48

[1]	Chen Yaning, Fang Gong Huan, Wang Huaijun , et al. Research progress on the impact of climate change on water resources in the arid region of Northwest China. Acta Geographica Sinica, 2014,69(9):1295-1304.
	[ 陈亚宁, 方功焕, 王怀军 , 等. 西北干旱区气候变化对水文水资源影响研究进展. 地理学报, 2014,69(9):1295-1304.]
[2]	Gao H, Ding Y, Zhao Q , et al. The importance of aspect for modelling the hydrological response in a glacier catchment in Central Asia. Hydrological Processes, 2017,31(16):2842-2859.
[3]	Qing Wenwu, Liu Junfeng, Yang Yuquan , et al. Uncertainty analysis of the parameters of the temperature-index method: A case study of Shiyi Glacier in Qilian Mountains. Advance in Earth Sciences, 2016,31(9):937-945.
	[ 卿文武, 刘俊峰, 杨钰泉 , 等. 基于气温的物质平衡模型的参数不确定性分析: 以祁连山十一冰川为例. 地球科学进展, 2016,31(9):937-945.]
[4]	Yin Zhenliang, Feng Qi, Liu Shiyin , et al. The application progress of hydrological model in quantifying the contribution of glacier runoff to total watershed runoff. Journal of Glaciology and Geocryology, 2016,38(1):248-258.
	[ 尹振良, 冯起, 刘时银 , 等. 水文模型在估算冰川径流研究中的应用现状. 冰川冻土, 2016,38(1):248-258.]
[5]	Fang Xiaoyu, Li Zhongqin, Wuennemann B , et al. Physical energy-balance and statistical glacier melting models comparison and testing for Shiyi Glacier, Heihe River Basin, Qilian Mountains, China. Journal of Glaciology and Geocryology, 2015,37(2):336-350.
	[ 方潇雨, 李忠勤, Wuennemann B , 等. 冰川物质平衡模式及其对比研究: 以祁连山黑河流域十一冰川研究为例. 冰川冻土, 2015,37(2):336-350.]
[6]	Yang Min . Comparison and application of space-time fusion methods for scale-down of surface temperature [D]. Xi'an: Xi'an University of Science and Technology, 2017.
	[ 杨敏 . 地表温度降尺度时空融合方法对比及其应用[D]. 西安: 西安科技大学, 2017.]
[7]	Jin Xiaolong, Shao Hua, Qiu Yuan , et al. Correction method of TRMM satellite precipitation data in Tianshan Mountains. Meteorological Monthly, 2018,44(7):882-891.
	[ 金晓龙, 邵华, 邱源 , 等. TRMM卫星降水数据在天山山区的校正方法研究. 气象, 2018,44(7):882-891.]
[8]	Fan Xuewei, Liu Hailong . Downscaling method of TRMM satellite precipitation data over the Tianshan Mountains. Journal of Natural Resources, 2018,33(3):478-488.
	[ 范雪薇, 刘海隆 . 天山山区TRMM降水数据的空间降尺度研究. 自然资源学报, 2018,33(3):478-488.]
[9]	Zhang Zhengyong, He Xinlin, Liu Lin , et al. Ecological service functions and value estimation of glaciers in the Tianshan Mountains, China. Acta Geographica Sinica, 2018,73(5):856-867.
	[ 张正勇, 何新林, 刘琳 , 等. 中国天山冰川生态服务功能及价值评估. 地理学报, 2018,73(5):856-867.]
[10]	Chen Wuhua . Study on glacier change in Tomur Area of Tianshan Mountains based on RS and GIS[D]. Lanzhou: Northwest Normal University, 2016.
	[ 陈物华 . 基于RS和GIS的天山托木尔地区冰川变化研究[D]. 兰州: 西北师范大学, 2016.]
[11]	Xinjiang Institute of Ecology and Geography. Progress in the monitoring and reconstruction of the material balance of the BatySook glacier in the Xier River Basin, Tianshan Mountains, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences. Arid Land Geography, 2017,40(2):354.
	[ 中国科学院新疆生态与地理研究所. 中国科学院新疆生态与地理研究所在天山锡尔河流域BatySook冰川物质平衡监测与重建中获进展. 干旱区地理, 2017,40(2):354.]
[12]	Liu Q, Liu S . Response of glacier mass balance to climate change in the Tianshan Mountains during the second half of the twentieth century. Climate Dynamics, 2016,46(1/2):303-316.
[13]	Li Jia . Monitoring the glacier mass balance variations in the Central Tien Shan using remote sensing techniques. Geography and Geo-Information Science, 2018,34(1):128.
	[ 李佳 . 利用遥感技术监测天山中部冰川物质平衡变化. 地理与地理信息科学, 2018,34(1):128.]
[14]	Li Junli, Jiang Liangliang, Bao Anming , et al. Spatio-temporal change analysis of cultivated land in Manas drainage basin during 1962-2010. Transactions of the Chinese Society of Agricultural Engineering, 2015,31(4):277-285.
	[ 李均力, 姜亮亮, 包安明 , 等. 1962—2010年玛纳斯流域耕地景观的时空变化分析. 农业工程学报, 2015,31(4):277-285.]
[15]	Xu Chunhai, Wang Feiteng, Li Zhongqin , et al. Glacier variation in the Manas River Basin during the Period from 1972 to 2013. Arid Zone Research, 2016,33(3):628-635.
	[ 徐春海, 王飞腾, 李忠勤 , 等. 1972—2013年新疆玛纳斯河流域冰川变化. 干旱区研究, 2016,33(3):628-635.]
[16]	Fan Xiaobing, Yan Lili, Xu Jinghua , et al. Analysis of glacier change in Manas River basin in the last 50 years based on multi-source data. Journal of Glaciology and Geocryology, 2015,37(5):1188-1198.
	[ 樊晓兵, 彦立利, 徐京华 , 等. 基于多源数据的近50 a玛纳斯河流域冰川变化分析. 冰川冻土, 2015,37(5):1188-1198.]
[17]	Cheng Weiming, Zhou Chenghu, Liu Haijiang , et al. Oasis expansion and eco-environmental evolution in Manas River Basin in the past 50 years. Science in China: Earth Sciences, 2005,35(11):1074-1086.
	[ 程维明, 周成虎, 刘海江 , 等. 玛纳斯河流域50年绿洲扩张及生态环境演变研究. 中国科学: 地球科学, 2005,35(11):1074-1086.]
[18]	Zheng Wenlong, Du Jinkang, Zhou Xiaobing , et al. Vertical distribution of snow cover and its relation to temperature over the Manasi River Basin of Tianshan Mountains, Northwest China. Acta Geographica Sinica, 2017,72(4):403-419.
	[ 郑文龙, 都金康, 周小兵 , 等. 中国天山玛纳斯河流域积雪垂直分布及其与温度的关系. 地理学报, 2017,72(4):403-419.]
[19]	Shi Yafeng. Concise Glacier Inventory of China. Shanghai Science Popularization Press, 2005: 1-158.
	[ 施雅风 . 简明中国冰川目录. 上海科学普及出版社, 2005: 1-158.]
[20]	Chen Ni, Feng Xuezhi, Xiao Pengfeng , et al. Analysis of snow layer parameters in Manasi River Basin. Journal of Nanjing University (Natural Sciences), 2015,51(5):936-943.
	[ 陈妮, 冯学智, 肖鹏峰 , 等. 玛纳斯河流域春季雪层参数特性分析. 南京大学学报(自然科学), 2015,51(5):936-943.]
[21]	Li Xiaojun, Jiang Tao, Xin Xiaozhou , et al. Spatial downscaling of land surface temperature based on MODIS data. Chinese Journal of Ecology, 2016,35(12):3443-3450.
	[ 李小军, 江涛, 辛晓洲 , 等. 基于MODIS的地表温度空间降尺度方法. 生态学杂志, 2016,35(12):3443-3450.]
[22]	Zhang Yiran . Spatial scaling method of surface temperature and its application based on domestic high-score image[D]. Hangzhou: Zhejiang University, 2017.
	[ 张逸然 . 地表温度空间降尺度方法及其基于国产高分影像的应用研究[D]. 杭州: 浙江大学, 2017.]
[23]	Wang Wanrui . Temporal and spatial variation of precipitation in Northwest China based on TRMM data[D]. Lanzhou: Lanzhou University, 2018.
	[ 王万瑞 . 基于TRMM数据的中国西北降水时空变化研究[D]. 兰州: 兰州大学, 2018.]
[24]	Liu Shiyin, Ding Yongjian, Wang Ninglian , et al. Mass balance sensitivity to climate change of the Glacier No. 1 at the Urumqi River Head, Tianshan Mts. Journal of Glaciology and Geocryology, 1998,20(1):9-13.
	[ 刘时银, 丁永建, 王宁练 , 等. 天山乌鲁木齐河源1号冰川物质平衡对气候变化的敏感性研究. 冰川冻土, 1998,20(1):9-13.]
[25]	Zhang Yong, Liu Shiyin, Ding Yongjian . Spatial variation of degree-day factors on the observed glaciers in western China. Acta Geographica Sinica, 2006,61(1):89-98.
	[ 张勇, 刘时银, 丁永建 . 中国西部冰川度日因子的空间变化特征. 地理学报, 2006,61(1):89-98.]
[26]	Gao Xin, Ye Baisheng, Zhang Shiqiang , et al. The change of glacial meltwater in the Tarim River Basin from 1961 to 2006 and its impact on runoff. Chinese Science: Earth Science, 2010,40(5):654-665.
	[ 高鑫, 叶柏生, 张世强 , 等. 1961—2006年塔里木河流域冰川融水变化及其对径流的影响. 中国科学: 地球科学, 2010,40(5):654-665.]
[27]	Muattar Saydi, Ding Jianli, Abudu Shalamus , et al. Simulation of snowmelt runoff in the catchments on northern slope of the Tianshan Mountains. Arid Zone Research, 2016,33(3):636-642.
	[ 穆艾塔尔·赛地, 丁建丽, 阿不都·沙拉木 , 等. 天山北坡山区流域融雪径流模拟研究. 干旱区研究, 2016,33(3):636-642.]
[28]	Chen Rensheng, Kang Ersi, Ding Yongjian . Some knowledge on and parameters of China's alpine hydrology. Advances in Water Science, 2014,25(3):307-317.
	[ 陈仁升, 康尔泗, 丁永建 . 中国高寒区水文学中的一些认识和参数. 水科学进展, 2014,25(3):307-317.]
[29]	Liang Pengbin, Li Zhongqin, Zhang Hui , et al. Temporal and spatial variation characteristics of mass balance of global reference glaciers from 1984 through 2016. Journal of Glaciology and Geocryology, 2018,40(3):415-425.
	[ 梁鹏斌, 李忠勤, 张慧 , 等. 1984-2016年全球参照冰川物质平衡时空变化特征. 冰川冻土, 2018,40(3):415-425.]
[30]	Zhang Guofei, Li Xiangfei, Li Zhongqin . Analysis of the changes of glacier mass balances in different parts of the world from 1980 to 2011. Journal of Glaciology and Geocryology, 2018,40(2):214-222.
	[ 张国飞, 李祥飞, 李忠勤 . 1980—2011年全球不同地区冰川物质平衡变化分析. 冰川冻土, 2018,40(2):214-222.]
[31]	Wu Lihua, Li Huilin, Wang Lin . Application of a degree-day model for determination of mass balance of Urumqi Glacier No. 1, Eastern Tianshan, China. Journal of Earth Science, 2011,22(4):470-481.
[32]	Mu Jianxin, Li Zhongqin, Zhang Hui , et al. Mass balance variation of continental glacier and temperate glacier and their response to climate change in western China: Taking Urumqi Glacier No. 1 and Parlung No. 94 Glacier as examples. Arid Land Geography, 2019,42(1):20-28.
	[ 牟建新, 李忠勤, 张慧 , 等. 中国西部大陆性冰川与海洋性冰川物质平衡变化及其对气候响应: 以乌源1号冰川和帕隆94号冰川为例. 干旱区地理, 2019,42(1):20-28.]
[33]	Zhang Hui, Li Zhongqin, Zhou Pin , et al. Mass-balance observations and reconstruction for Haxilegen Glacier No. 51, eastern Tien Shan, from 1999 to 2015. Journal of Glaciology, 2018,64(247):689-699.
[34]	Yao Tandong, Li Zhiguo, Yang Wei , et al. Characteristics of glacial distribution and material balance in the Yarlung Zangbo River Basin and its impact on lakes. Chinese Science Bulletin, 2010,55(18):1750-1756.
	[ 姚檀栋, 李治国, 杨威 , 等. 雅鲁藏布江流域冰川分布和物质平衡特征及其对湖泊的影响. 科学通报, 2010,55(18):1750-1756.]
[35]	Lan Yongchao, Shen Yongping, Wu Sufen , et al. Changes of the glaciers and the glacier water resources in the typical river basins on the north and south slopes of the Tianshan Mountains since 1960s. Journal of Arid Land Resources and Environment, 2007,21(11):1-8.
	[ 蓝永超, 沈永平, 吴素芬 , 等. 近50年来新疆天山南北坡典型流域冰川与冰川水资源的变化. 干旱区资源与环境, 2007,21(11):1-8.]
[36]	Yang Zhenniang . Glacier water resources in China. Natural Resources, 1987(1):46-55, 68.
	[ 杨针娘 . 中国冰川水资源. 自然资源, 1987(1):46-55, 68.]
[37]	Shen Yongping, Su Hongchao, Wang Guoya , et al. The responses of glaciers and snow cover to climate change in Xinjiang (Ⅰ): Hydrological effects. Journal of Glaciology and Geocryology, 2013,35(3):513-527.
	[ 沈永平, 苏宏超, 王国亚 , 等. 新疆冰川、积雪对气候变化的响应(Ⅰ): 水文效应. 冰川冻土, 2013,35(3):513-527.]
[38]	Sun Congjian, Chen Wei . Streamflow components in inland rivers in the Tianshan Mountains, Northwest China. Arid Land Geography, 2017,40(1):37-44.
	[ 孙从建, 陈伟 . 天山山区典型内陆河流域径流组分特征分析. 干旱区地理, 2017,40(1):37-44.]
[39]	Sun Meiping, Li Zhongqin, Yao Xiaojun , et al. Analysis on runoff variation of Glacier No. 1 at the Headwaters of the Urumqi River from 1959 to 2008. Journal of Natural Resources, 2012,27(4):650-660.
	[ 孙美平, 李忠勤, 姚晓军 , 等. 1959—2008年乌鲁木齐河源1号冰川融水径流变化及其原因. 自然资源学报, 2012,27(4):650-660.]
[40]	He Haidi, Li Zhongqin, Wang Puyu , et al. Variation characteristics of glacier mass balance in Svalbard, Arctic, in recent 50 years. Journal of Glaciology and Geocryology, 2017,39(4):701-709.
	[ 何海迪, 李忠勤, 王璞玉 , 等. 近50年来北极斯瓦尔巴地区冰川物质平衡变化特征. 冰川冻土, 2017,39(4):701-709.]
[41]	Zhang Guofei, Li Zhongqin, Wang Wenbin , et al. A positive mass balance appeared at Urumuqi Glacier No. 1 in 2009. Arid Land Geography, 2013,36(2):263-268.
	[ 张国飞, 李忠勤, 王文彬 , 等. 乌鲁木齐河源1号冰川2009年出现物质正平衡. 干旱区地理, 2013,36(2):263-268.]
[42]	Cui Hang, Wang Jie . The methods for estimating the equilibrium line altitudes of a glacier. Journal of Glaciology and Geocryology, 2013,35(2):345-354.
	[ 崔航, 王杰 . 冰川物质平衡线的估算方法. 冰川冻土, 2013,35(2):345-354.]
[43]	Zheng Jintao . Research on runoff evolution in mountainous area under climate change in Manas River[D]. Shihezi: Shihezi University, 2018.
	[ 郑锦涛 . 气候变化驱动下玛纳斯河山区径流演变规律研究[D]. 石河子: 石河子大学, 2018.]
[44]	Zhang Guofei . Glacier matter balance and its relation to climate change at the source of Urumqi River, Tianshan, China[D]. Lanzhou: Northwest Normal University, 2014.
	[ 张国飞 . 中国天山乌鲁木齐河源1号冰川物质平衡及其与气候变化关系研究. 兰州: 西北师范大学, 2014.]
[45]	Zhang Guofei, Li Zhongqin, Wang Weidong , et al. Mass balance change in east and west branches of Glacier No. 1 at Urumqi riverhead, China, during last 20 years. Chinese Journal of Ecology, 2013,32(9):2412-2417.
	[ 张国飞, 李忠勤, 王卫东 , 等. 近20年乌鲁木齐河源1号冰川东支和西支物质平衡变化. 生态学杂志, 2013,32(9):2412-2417.]
[46]	Zhang Wei, Dong Yingwei, Yu Zhilong , et al. Discussion of the difference of the timing and extent of glaciers in the late Quaternary controlled by the westerly and East Asia monsoon as well as the tectonic movement. Acta Geographica Sinica, 2013,68(7):909-920.
	[ 张威, 董应巍, 于治龙 , 等. 气候和地貌对晚第四纪冰川发育差异性的影响. 地理学报, 2013,68(7):909-920.]
[47]	Li Kaiming, Li Zhongqin, Gao Wenyu , et al. Recent retreat of glaciers in the East Tianshan Mountains of Xinjiang and its impact on water resources. Chinese Science Bulletin, 2011,56(32):2708-2716.
	[ 李开明, 李忠勤, 高闻宇 , 等. 近期新疆东天山冰川退缩及其对水资源影响. 科学通报, 2011,56(32):2708-2716.]
[48]	Wang Guoya, Shen Yongping . The effect of change in glacierized area on the calculation of mass balance in the Glacier No. 1 at the Headwaters of Urumqi River. Journal of Glacilogy and Geocryology, 2011,33(1):1-7.
	[ 王国亚, 沈永平 . 天山乌鲁木齐河源1号冰川面积变化对物质平衡计算的影响. 冰川冻土, 2011,33(1):1-7.]

数据类型	时间	分辨率	数据来源
DEM	-	30 m×30 m	地理空间数据云(http://www.gscloud.cn/)
NDVI	2000—2016年	250 m×250 m	地理空间数据云(http://www.gscloud.cn/)
MOD11C3		0.05°×0.05°	美国国家航空航天局(https://www.nasa.gov/)
TRMM 3B43		0.25°×0.25°	美国国家航空航天局(https://www.nasa.gov/)
气温		逐月	国家气象信息中心(http://data.cma.cn/)
降水			国家气象信息中心(http://data.cma.cn/)
径流量			肯斯瓦特水文站
冰川面积	2009年	-	寒区旱区科学数据中心(http://westdc.westgis.ac.cn/)
积雪密度	2014年	-	文献[20]

月份	回归因子系数								精度验证
月份	λ	a	b	c	d	e	f	g	RMSE	R²
1	5.41	1.12	-0.64	-0.0020	0.210	0.0110	3.89	1.57	3.06	0.89
2	56.48	-0.47	-0.41	-0.0040	0.260	0.0101	8.97	1.38	1.78	0.94
3	121.38	-2.05	-0.26	-0.0070	0.220	0.0130	15.43	1.22	2.88	0.95
4	143.06	-2.54	-0.11	-0.0120	0.170	0.0060	6.88	0.84	1.82	0.94
5	140.79	-2.31	-0.05	-0.0100	0.170	0.0043	-1.61	0.76	1.16	0.95
6	127.95	-1.80	-0.04	-0.0130	0.136	0.0080	-4.57	0.63	1.16	0.96
7	108.19	-1.36	-0.04	-0.0130	0.120	0.0120	-5.25	0.66	1.42	0.96
8	109.65	-1.40	-0.05	-0.0130	0.120	0.0110	-5.25	0.63	1.16	0.94
9	111.77	-1.70	-0.04	-0.0090	0.160	0.0101	-3.00	0.72	1.30	0.92
10	81.19	-1.35	-0.10	-0.0058	0.208	0.0058	6.03	1.06	1.15	0.89
11	48.80	-0.57	-0.25	-0.0034	0.240	0.0110	9.49	1.18	1.27	0.90
12	51.62	0.26	-0.71	-0.0030	0.280	0.0120	-14.49	0.62	1.52	0.90

月份	回归因子系数								精度验证
月份	λ	a	b	c	d	e	f	g	RMSE	R²
1	19.27	-1.15	0.34	-0.0021	0.049	0.0036	-1.86	1.15	3.69	0.74
2	42.42	-2.33	0.68	-0.0030	0.136	-0.0020	-38.85	1.18	9.31	0.76
3	-60.87	1.32	0.04	-0.0018	-0.006	0.0105	4.37	1.03	6.75	0.81
4	158.81	-4.82	0.65	-0.0113	0.108	0.0011	-29.90	1.64	10.33	0.85
5	63.84	-2.64	0.66	-0.0053	0.065	-0.0054	-24.15	1.31	13.20	0.85
6	-149.02	2.60	0.44	0.0095	-0.014	-0.0289	-19.10	1.01	14.41	0.88
7	-174.73	2.97	0.47	0.0145	0.106	-0.0261	-11.22	0.97	14.33	0.83
8	-83.76	1.29	0.26	0.0113	0.072	-0.0201	-11.61	1.11	19.69	0.84
9	-25.69	1.09	-0.27	0.0001	-0.027	0.0172	-20.52	1.51	8.43	0.82
10	38.29	0.60	-0.72	-0.0034	0.038	0.0143	-8.00	0.91	8.42	0.85
11	60.39	-1.92	0.28	-0.0047	0.035	-0.0002	-5.51	1.12	9.08	0.78
12	-4.97	-0.06	0.10	-0.0024	0.001	0.0007	-6.95	0.93	4.29	0.71

年份	零物质平衡线高度(m)	物质平衡(mm w.e.)	冰川融水(10⁸ m³)	纯冰消融(10⁸ m³)	纯冰消融比率	河川径流(10⁸ m³)	冰川融水比率
2000	4538	-545.86	3.29	2.72	0.83	16.29	0.20
2001	4550	-566.88	2.99	2.60	0.87	14.43	0.21
2002	4530	-551.41	3.51	2.82	0.80	18.74	0.19
2003	4558	-584.20	3.22	2.72	0.85	11.05	0.29
2004	4560	-620.49	3.47	2.90	0.83	12.28	0.28
2005	4532	-575.59	3.37	2.71	0.81	13.39	0.25
2006	4588	-632.19	3.63	2.99	0.82	13.18	0.28
2007	4537	-602.90	3.68	2.81	0.76	15.47	0.24
2008	4569	-624.72	3.27	2.82	0.86	13.77	0.24
2009	4507	-464.85	2.91	2.56	0.88	11.00	0.26
2010	4533	-527.05	3.36	2.84	0.85	16.62	0.20
2011	4560	-602.95	3.65	2.90	0.79	11.74	0.31
2012	4555	-597.01	3.46	2.79	0.81	12.54	0.28
2013	4553	-587.42	3.41	2.79	0.82	13.37	0.25
2014	4556	-563.95	3.21	2.75	0.86	10.65	0.30
2015	4573	-605.61	4.01	3.20	0.80	18.35	0.22
2016	4528	-558.11	3.48	2.82	0.81	15.45	0.23
均值	4549	-577.13	3.41	2.81	0.83	14.02	0.25

区域	拟合方程	相关性
消融区	y₁ = 2.4483x-10729	R² = 0.927
积累区	y₂ = 0.1877x-788.3	R² = 0.073
冰川区(整体)	y₃ = 1.7909x-2522.5(线性)	R² = 0.873
冰川区(整体)	y₄= -0.0014x²+13.75x-32691(非线性)	R² = 0.993