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 not only describes a nonlinear dependence on ice thickness but also reveals its relation with the dependence on frequency. This nonlinear dependence on ice thickness can have more 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.