1.兰州大学资源环境学院西部环境教育部重点实验室,甘肃 兰州 730000
2.中国科学院寒区旱区环境与工程研究所黑河上游生态—水文试验研究站,甘肃 兰州 730000

Uncertainty Analysis of the Parameters of the Temperature-index Method: A Case Study of Shiyi Glacier in Qilian Mountains
Qing Wenwu1,2, Liu Junfeng2, Yang Yuquan1, Chen Rensheng2, Han Chuntan2
1.Key Laboratory of Western China's Environmental Systems(Ministry of Education), College of Earth and Environmental Sciences, Lanzhou University, Lanzhou 730000, China
2.Qilian Alpine Ecology and Hydrology Research Station, Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000,China

First author:Qing Wenwu(1982-), male, Loudi City, Hu’nan Province,Lecturer. Research areas include the hydrology and water resources in cold area.E-mail:qingww@lzu.edu.cn

Abstract

In order to assess the performance of the common temperature-index melt model at both spatial and temporal scale in Qilian Mountains, we performed the sensitivity and uncertainty analysis on the parameters of a common temperature-index method and evaluated the glacier mass balance on a small alpine glacier, which is separated into two relatively independent branches, with the daily mass balance and the meteorological data in the summer of 2011 and 2012. Sensitivity analysis was conducted by perturbation analysis and uncertainty analysis was carried out by Generalized Likelihood Uncertainty Estimation (GLUE) for different conditions. The results showed that the temperature-index method could properly capture the diurnal variability of the glacier mass balance. But strong equifinality of model parameter existsed in model calibration due to the uncertainty in the parameters. The model was very sensitive to changes in the value of Kice, followed by the Ksnow and Ts. It was also found that the GLUE approaches could estimate and derive the posterior distributions of 3 parameters properly. Moreover, there existed an acceptable range, which ensured high precision under different conditions.

Keyword: Glacier mass balance; The snow/rain threshold temperature; Temperature-index glacier melt model; Uncertainty analysis.
1 引言

2 研究区与资料

 Figure Option 图1 研究冰川及物质平衡观测点分布图(图中照片拍摄于2012年10月)Fig.1 The map of the study glacier and the distribution of stakes (the above photo was taken in October 2012)

3 方法
3.1 物质平衡计算

M =c+a+f (1)

Ps= $0 T≥TsP T< Ts$(2)

M= $Ksnow/ice×T T> 00 T≤0$(3)

3.2 参数不确定分析

$NSE=∑i=1n(Mi-Mi'2∑i=1i(Mi-M̅)24$

4 结果与分析
4.1 冰川物质平衡模拟

Table 1 Parameters and results of the model
4.2 参数敏感性分析

4.3 参数的不确定性分析

 Figure Option 图2 十一冰川日物质平衡量实测值和模拟值对比Fig.2 Contrast between the measured daily mass balance and the calculated with the method

 Figure Option 图3 模型参数对评价系数NSE的敏感性分析Fig.3 Sensitivity analysis of the model parameters to NSE

 Figure Option 图4 参数与似然值散点图(随机选取的5 000组后验参数)Fig.4 Scatter plot of likelihood values for parameters(5 000 sets of random data)

 Figure Option 图5 NSE在Ksnow和Kice不同组合下的分布Fig.5 The NSE index for different combinations of calibration parameters

 Figure Option 图6 Ksnow和Kice组合最优参数范围Fig.6 The optimum parameter range of parameters

5 结论

(1) 在时空尺度上, 基于气温的物质平衡经验模型能较好地模拟十一冰川夏季物质平衡量, 模型具有较好的适用性, 但不能完全保证模型预测精度。

(2) 强消融期, Kice是影响模型精度的最敏感参数, Ksnow的敏感性与下垫面特性有关系, Ts不敏感。

(3) 参数优化结果存在明显“ 异参同效” 现象, 但GLUE方法能较好去掉不合理的参数组, 得到更加合理的预测区间。

(4) 对4种情况下参数区间进行重叠, 可得到模型“ 最佳参数区间” , 能较好地保证模型预测的精度。

The authors have declared that no competing interests exist.