Hydrologic research and operations make extensive use of streamflow time series. In most applications, these time series are estimated from rating curves, which relate flow to some easy-to-measure surrogate, typically stage. The conventional stage-discharge rating takes the form of a segmented power law, with one segment for each hydrologic control at the stream gauge. However, these ratings are difficult to estimate with numerical methods, such that most are still developed manually. A few automated algorithms have emerged, but their use is sporadic, and their relative merits have not been rigorously assessed. One recently developed approach, the generalized power-law, avoids the segmenting problem by representing the power-law exponent as a Gaussian process. On one hand, this representation is more flexible and easier to fit, but that flexibility might also allow unrealistic solutions. This study evaluates the operational viability of the generalized power-law rating curve model under a range of conditions, using observations from 180 streams in Iceland, Sweden, and the United States. Overall, the model proved flexible and computationally robust, generating convincing rating curves across a range of geographic settings and was comparable to curves generated by a segmented rating model. Lastly, we propose a model-selection algorithm based on information theory to help identify the best rating curve model for a particular stream gauge.

中文翻译：

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评估广义幂律评级曲线模型的适用性：应用于冰岛、瑞典和美国的配对放电阶段数据


水文研究和运营广泛使用径流时间序列。在大多数应用程序中，这些时间序列是根据评级曲线估计的，评级曲线将流量与一些易于测量的替代项（通常是阶段）相关联。传统的阶段-排放额定值采用分段幂律的形式，流量计上的每个水文控制都有一个段。但是，这些评级很难用数值方法估计，因此大多数仍然是手动开发的。已经出现了一些自动化算法，但它们的使用是零星的，而且它们的相对优点尚未得到严格评估。最近开发的一种方法，广义幂律，通过将幂律指数表示为高斯过程来避免分割问题。一方面，这种表示形式更灵活，更容易适应，但这种灵活性也可能允许不切实际的解决方案。本研究使用来自冰岛、瑞典和美国的 180 条溪流的观测结果，评估了广义幂律评级曲线模型在一系列条件下的可操作可行性。总体而言，该模型被证明是灵活的，并且计算稳健，在一系列地理设置中生成了令人信服的评级曲线，并且与分段评级模型生成的曲线相当。最后，我们提出了一种基于信息论的模型选择算法，以帮助确定特定流量计的最佳评级曲线模型。