最小二乘与分位数回归方法在河流水沙研究中的应用——以陕北延河流域为例

基于延河流域1956-2010年气象水沙数据,研究流域降水、径流和输沙量动态变化趋势及时间序列分布特征,并分别采用最小二乘法和分位数回归分析方法研究降水、径流及输沙三者间的相关关系.结果表明：1956-2010年流域年降水量、径流量、输沙量整体呈下降趋势,具有阶段性波动特征,并存在不同程度的异常值;最小二乘回归（OLSR）分析可以描述降水、径流和输沙量三者之间的平均相关关系,但当数据存在偏态、异常值或数据随机误差项为异方差时,最小二乘回归分析受到一定限制;分位数回归（QR）分析更加符合实际的气象、水文数据特征,特别是在分位数τ位于高分位部分,分位数回归拟合的有效性比最小二乘回归更好,可以更真实、准确地反映更多的局部信息.研究结果为河流水沙动态分析提供了一种新方法,可为客观准确地认识河流水沙关系提供参考.

Comparison of ordinary least square regression and quantile regression in the study of hydrological elements of Yanhe River Basin

Based on the 1956-2010 meteorological data of the Yanhe River Basin,the variation tendency and distribution feature of precipitation,runoff and sediment were studied.The relationship among the precipitation,runoff and sediment were also studied with ordinary least square regression （OLSR） and quantile regression （QR）,respectively.The results showed that,from 1956 to 2010,the annual precipitation,runoff and sediment load exhibited a significant downward trend in the study area,the time data had fluctuations in different stages and some outliers existed.The OLSR could describe the average correlation among the precipitation,runoff and sediment.However,when the data are skewed,outliers or data changed greatly,and the OLSR analysis is restricted.QR is more suitable for actual meteorological and hydrological data,and particularly it could better express their relationships in high quantiles and accurately reflect more local information.According to our analysis,the quantile regression as a new method for river runoff and sediment dynamic analysis can reflect the relationship between water and sediment more accurately and objectively.