We develop a climatological model for the Northern Hemisphere based on a long-term dataset (2010-2021) of the rate of change of the total electron content (TEC) index (ROTI) maps from the International GNSS Service (IGS). The IGS ROTI maps are daily averaged in magnetic latitude and local time coordinates. To develop a climatological model, the ROTI maps are decomposed into a few base functions and coefficients using the empirical orthogonal function (EOF) method. The EOF method converges very quickly, and the first four EOFs reflect the majority (96%) of the total data variability. Furthermore, different EOF components can reflect different drivers of ionospheric irregularities. The first EOF reflects the averaged ROTI activity and the impact of the solar radiation and geomagnetic activity; the 2nd EOF reflects the impact of the interplanetary magnetic field (IMF) Bz and electric field; the 3rd and 4th EOFs reflect the dawn-dusk asymmetry around the auroral oval and polar cap, and they can be related to the IMF By. To build an empirical model, we fit the EOF coefficients using helio-geophysical indices from four different categories (solar activity; geomagnetic indices; IMF; the solar wind coupling function). The final EOF model is dependent on seven selected indices (F10.7P, Kp, Dst, Bt, By, Bz and Ekl). The statistical data-model comparisons show satisfactory results with a good correlation coefficient. However, the model cannot capture the significant expansion of the dayside ROTI activity during strong geomagnetic storms. Future effort is needed to provide corrections to the model for severe storms.