In this paper, we study the variations of the solar-wind parameters (solar wind velocity, plasma density, and IMF-B_z component) and the Earth’s disturbance storm-time index (D_st), in relation to cosmic ray flux measurements from 8 neutron monitor stations distributed over Canada, Russia, Finland, and Greenland, during 3 intense geomagnetic storms occurred during the 24^th solar cycle (March 16-18, 2015, June 21-23, 2015, and September 7-9, 2017). The wavelet analysis of the Forbush decrease seen in the cosmic ray intensity reveals the clear evolution of the classical two-step process, and with a peak period of approximately 2.1 h. The correlation-delay analyses show a very strong correlation (~0.9) between the relative count rate changes cosmic ray intensity and the indices of solar wind velocity and D_st. We obtain similar time-delay responses to the solar wind velocity for all the cases (~4 hours), but large discrepancies are seen for the D_st index between the storms. We therefore recommend not using the D_st index for predicting Forbush decreases. Finally, we employ the resulting delay-times to parameterize the Forbush decreases in terms of solar wind, and we obtain a predictive model with R² parameter of an approximate value of 0.8. Moreover, we observe a possible dependence on solar wind proton density which modulates the magnitude of Forbush decreases under similar solar wind velocity conditions. Our results verify the suitability of using solar wind parameters to predict Forbush decreases in the cosmic ray flux.