We present a method for predicting wave dissipation by sea ice that is based on the dimensional analysis of data with a scaling defined by ice thickness. Applying the method to an extensive dataset from the measurements during the “Polynyas, Ice Production, and seasonal Evolution in the Ross Sea” (PIPERS) cruise in 2017, we derive a new model of wave dissipation which describes a nonlinear dependence on ice thickness, and reveals the interrelation between the dependences on ice thickness and on wave frequency. This nonlinear dependence on ice thickness can have important implications on predicting low-frequency waves. The root-mean-square error of the prediction is significantly reduced using the new model, compared with other existing parametric models that are also calibrated for the PIPERS dataset. The new model also explicitly describes a condition of similarity between large- and small-scale observations, which is shown to exist when various laboratory datasets collapse onto the prediction. Thus, the new model improves the estimate of wave dissipation by ice across multiple scales.

我们提出了一种预测海冰波浪消散的方法，该方法基于对数据进行维度分析，并具有由冰厚度定义的比例。将该方法应用于 2017 年“罗斯海波利尼亚斯、冰生产和季节性演变”（PIPERS）巡航期间测量的广泛数据集，我们推导出了一种新的波浪耗散模型，该模型描述了对冰厚度的非线性依赖性，并揭示了对冰厚度和波频率的依赖性之间的相互关系。这种对冰厚度的非线性依赖性对预测低频波具有重要意义。与也为 PIPERS 数据集校准的其他现有参数模型相比，使用新模型显着降低了预测的均方根误差。新模型还明确描述了大尺度和小尺度观测之间的相似性条件，当各种实验室数据集崩溃到预测时，这种情况就会出现。因此，新模型改进了对跨多个尺度的冰波耗散的估计。