Absence of mathematically justified criteria during development of the wind energy input and wave breaking energy dissipation source terms in Hasselmann equation (HE), used as the framework of modern operational wave forecasting models, lead to creation of plethora of parameterizations, having enormous scatter, disconnected from the physical background and obeying dozens of tuning parameters to adjust the HE model to the specific situation. We show that it's possible, based on analytical analysis and experimental observation data, to create the new set of source terms, reproducing experimental observations with minimal number of tuning parameters. We also numerically analyze six historically developed and new wind input source terms for their ability to hold specific invariants, related to HE selfsimilar nature. The degree of preservation of those invariants could be used as their selection tool. We hope that this research is the step toward the creation of physically justified tuning-free operational models.