寒冷区明渠冬季输水结冰是常见的自然现象。南水北调中线工程水面一旦形成冰盖其安全输水流量仅为设计流量的30%~50%,而气温是驱动冰盖形成的主要因子,如何科学评价冬季气温等级是冰期输水面临的关键问题之一。分析了沿线8座气象站1951—2021年冬季日平均气温和日最低气温数据,揭示了总干渠气温沿程和年际变化规律。基于拉格朗日质点跟踪法,结合沿线气温-水温-冰盖生成物理过程,提出了气温链概念并给出通用数学表达式。分别采用国标法、一月平均气温法和气温链法评价冬季气温等级,构建了71 a冬季气温位次。结果表明:①总干渠自南向北气温逐级下降速率为0.48 ℃/(100 km),保定站呈加速下降趋势,对冰盖生成贡献最大。②沿线冬季气温总体呈波动上升趋势,升温速率为0.37 ℃/(10 a),强暖冬出现在最近30 a,强冷冬出现在前30 a,气温的总体上升有利于减缓大范围冰盖生成。③对于冰盖生成预测,气温链法优于一月平均气温法,更优于国标法;不同时间尺度组合评价可获得更优的结果;全球持续变暖背景下,可采用一月平均气温法和北方2站6 d气温链法联合评价。④给出了北方2站6 d气温链法冬季等级的分界阈值,即强暖冬T_C≥-4.0 ℃,弱暖冬-5.7 ℃≤T_C<-4.0 ℃,正常-7.4 ℃<T_C<-5.7 ℃,弱冷冬-9.1 ℃<T_C≤-7.4 ℃,强冷冬T_C≤-9.1 ℃,长系列均值为-6.5 ℃。研究成果可更好地为南水北调中线工程总干渠冰盖生成提供新的参考基准。

The freezing of water-conveying open channel in winter is a common natural phenomenon in cold regions. Once ice carapace appears in the middle route of the South-to-North Water Transfer Project, the safe flow reduces to only 30%-50% of the design flow. As temperature is the main factor driving the formation of ice carapace, the evaluation of air temperature level in winter became a key problem for water conveyance in freezing period. The interannual variations of air temperature along the main canal is revealed according to the daily average temperature and daily minimum temperature data of eight meteorological stations along the line of the Project in winter from 1951 to 2021. A concept of air temperature chain is proposed and the general mathematical expression is given based on the Lagrange particle tracking method in line with the physical process of air temperature affecting water temperature and then further producing ice carapace along the line. The National Standard Method, January’s Average Temperature Method, and the proposed Air Temperature Chain Method are used to evaluate the winter temperature level and construct the temperature order in 71 years. Results manifest that: 1) The air temperature along the main canal decreased gradually from south to north at a rate of 0.48 ℃/(100 km), and in particular, Baoding station displayed an accelerated downward trend, which made the greatest contribution to the formation of ice carapace. 2) The temperature in winter was fluctuating upwardly in general at a rate of 0.37 ℃/10 a. Severe warm winter appeared in the recent three decades and severe cold winter in the first three decades. The rising of air temperature is conducive to alleviating the formation of large-scale ice carappace. 3) The proposed Air Temperature Chain Method is superior to the January’s Average Temperature Method and the National Standard Method in predicting the formation of ice carapace. Better prediction result can be achieved by combining different time scales. Under the background of continuous global warming, the joint evaluation by January’s Average Temperature Method and Air Temperature Chain Method with 6-day data at two north stations can be adopted. 4) The thresholds of winter temperature grade obtained by the Air Temperature Chain Method with 6-day data at two north stations are given as follows. Strong warm winter: T_C≥-4.0 ℃; weak warm winter: -5.7 ℃≤T_C＜-4.0 ℃; normal winter: -7.4 ℃＜T_C＜-5.7 ℃; weak cold winter: -9.1 ℃＜T_C≤-7.4 ℃; strong cold winter: T_C≤-9.1 ℃. The average value of long series T_C is -6.5 ℃. The research finding is expected to offer a new reference for predicting the formation of ice carapace in the main canal.