A number of physical or data-driven models have been proposed to evaluate stream water temperatures based on hydrological and meteorological observations. However, physical models require a large amount of information that is frequently unavailable, while data-based models ignore the physical processes. Recently the air2stream model has been proposed as an intermediate alternative that is based on physical heat budget processes, but it is so simplified that the model may be applied like data-driven ones. However, the price for simplicity is the need to calibrate eight parameters that, although have some physical meaning, cannot be measured or evaluated a-priori. As a result, applicability and performance of the air2stream model for a particular stream relies on the efficiency of the calibration method. The original air2stream model uses an inefficient 20-year old approach called Particle Swarm Optimization with inertia weight.

This study aims at finding an effective and robust calibration method for the air2stream model. Twelve different optimization algorithms are examined on six different streams from northern USA (states of Washington, Oregon and New York), Poland and Switzerland, located in both high mountains, hilly and lowland areas. It is found that the performance of the air2stream model depends significantly on the calibration method. Two algorithms lead to the best results for each considered stream. The air2stream model, calibrated with the chosen optimization methods, performs favorably against classical streamwater temperature models. The MATLAB code of the air2stream model and the chosen calibration procedure (CoBiDE) are available as Supplementary Material on the Journal of Hydrology web page.

已经提出了许多物理或数据驱动的模型，以基于水文和气象观测来评估溪流水温。但是，物理模型需要大量经常不可用的信息，而基于数据的模型则忽略了物理过程。最近，已经提出了air2stream模型作为基于物理热量收支过程的中间替代方案，但由于简化了模型，因此可以像数据驱动模型一样应用该模型。然而，为简单起见，价格是需要校准八个参数，尽管这些参数具有某些物理意义，但无法先验或评估。结果，气流模型对特定气流的适用性和性能取决于校准方法的效率。原始的气流模型使用了一种效率低下的20年方法，称为惯性权重的粒子群优化方法。

这项研究旨在为air2stream模型找到一种有效而强大的校准方法。在来自美国北部（华盛顿州，俄勒冈州和纽约州），波兰和瑞士的六条不同河流上研究了十二种不同的优化算法，这些河流分别位于高山，丘陵和低地地区。发现气流模型的性能在很大程度上取决于校准方法。对于每种考虑的流，两种算法都能得出最佳结果。使用选定的优化方法进行校准的air2stream模型相对于经典的溪水温度模型具有良好的性能。air2stream模型的MATLAB代码和所选的校准程序（CoBiDE）可在《水文学杂志》网页上作为补充材料获得。