Since the time scale of weak storms is about half the time scale of intense storms, it is troublesome and important to examine the solar wind parameters/interplanetary magnetic field (IMF) (E, v, P, T, N, and B-z) to evolve and affect to zonal geomagnetic indices (Kp, Dst, AE, and ap). In a severe storm, which usually has two main phases, solar parameters have enough time to react, but weak storms cannot find this time. They have to yield their reaction in a short time. One can find a weak storm in order to reveal and discuss the consistency of models that have proven themselves in severe and moderate storms in this study. I discuss weak storm (Dst = -46) on May 8, 2014, via solar wind parameters and zonal geomagnetic indices. The goal of the work is to realize the models applicable to the moderate and the strong storms for a weak storm. Hereby, all possible correlations between solar parameters and zonal indices are discussed in depth. I tried to obey the cause-effect relationship while creating mathematical models while not ignoring the physical principles. Therefore, the physical principles govern the study. The results are visualized with tables and graphs for the understanding of the dynamic structure of the storm.