-This paper aims to introduce a new model for the short-term forecast of the vertical Total Electron Content (vTEC). The basic idea of the proposed model lies on the concept of the Solar Wind driven autoregressive model for Ionospheric short-term Forecast (SWIF). In its original version, the model is operationally implemented in the DIAS system (http://dias.space.noa.gr) and provides alerts and warnings for upcoming ionospheric disturbances, as well as single site and regional forecasts of the foF2 critical frequency over Europe up to 24 h in advance. The forecasts are driven by the real time assessment of the solar wind conditions at ACE location. The comparative analysis of the variations in foF2 and vTEC during eleven geomagnetic storm events that occurred in the present solar cycle 24 reveals similarities but also differences in the storm-time response of the two characteristics with respect to the local time and the latitude of the observation point. Since the aforementioned dependences drive the storm-time forecasts of the SWIF model, the results obtained here support the upgrade of the SWIF's modeling technique in forecasting the storm-time vTEC variation from its onset to full development and recovery. According to the proposed approach, the vTEC storm-time response can be forecasted from 1 to 12-13 h before its onset, depending on the local time of the observation point at storm onset at L1. Preliminary results on the assessment of the performance of the proposed model and further considerations on its potential implementation in operational mode are also discussed.