Karstic spring discharge is related to the hydraulic head recession through a power function with an exponent <1. In the literature, analytical solutions are available for exponential and non-exponential models based on a set of restrictive physical and mathematical assumptions. The models search for a holistic and deductive solution without basic physical and practical interpretations, simple logical inferences leading to mathematical analytical or empirical formulations. In this paper, an inductive, logical, practical, and instead of holistic modeling, physically plausible piecewise solutions are proposed with detailed inferences and interpretations. In the proposed methodology, the discharge and hydraulic head records are decomposed first into a set of verbal classes and, subsequently, physical meaning for each class is explained leading to simple general but empirical models. For this purpose, Wakula and St. Marks River (Florida) hydrograph records are used for the general solution sinkhole discharge and hydraulic head variations. The solution methodology presented in this paper does not make any distinction between relatively small or large sinkhole heads. The calibration and verification of the methodology is shown with a comparison of the available record values to partial power models. Finally, it is concluded that the proposed methodology is reliable and can be applied to hydraulic head availability with discharge records in any part of the world for karstic aquifer domains.