<p>A super geomagnetic storm is one of the most significant natural phenomenon that has the potential to produce electromagnetic disturbances in the solar system. The paper presents to the reader the new modeling of some space climate monitoring instruments (the TEC (TECU) map, Dst (nT), ap (nT), and IMF (nT)) throughout the <i>Saint Patrick's Day</i> superstorm (Dst =  − 234nT) period. The prototype of the <i>Bézier</i> family's curves in Euclidean topology and the <i>artificial neural network</i> are used to construct the instruments' models. The problem lies in establishing a well-posed model of space instruments under consideration. The aim is to be able to support potential hybrid prediction approaches through the proposed model. The model is compared with a neural network, a linear interpolated line model, and cubic splines. While the network model governs the preparation and training processes through the solar wind parameters, the Bézier generates its segmented model starting from class C⁰ without any preliminary procedure. Pearson's correlation coefficient and mean squared error are used to evaluate the models. The results show that the curve and the neural network prototype are acceptable. The results indicate a correlation of around 98.8% and 99.5% for the Bézier and network models, respectively. Their mean squared errors are reduced to 0.990 TECU, 1.722 nT, and 0.699 TECU, 0.294 nT for the Bézier and the network model, respectively. The paper's unique contribution is demonstrating that the segmented curve model may support hybrid models for the neural network in the upper atmosphere research. The paper hopes to support future hybrid approaches by transforming complex and nonlinear space weather parameters into segmented continuous differential geometric forms with as small error as possible.</p>