We report about the early implementation of a Swarm-based S4 index which models the amplitude scintillation strength on Global Navigation Satellite System (GNSS) signals recorded at ground level. We leverage: (i) the plasma density data provided by the high-resolution faceplate measurements at a 16 Hz sampling rate made by the Electric Field Instrument (EFI) onboard Swarm satellites; (ii) Rino’s theory for weak scattering regime, which adopts a power law phase screen to enable modelling of amplitude scintillations; and (iii) the reconstruction of the irregularity layer based on the application of the NeQuick2 model, in a data ingestion scheme. This procedure is inspired by the Wernik-Alfonsi-Materassi (WAM) scintillation model approach for high-latitudes and for low-latitudes. The plasma density estimates made by Swarm are used to reconstruct the one-dimensional spectral slope p of the power spectrum of the plasma density irregularities measured in situ. The 16 Hz sampling rate, combined with the Swarm orbital features, allow modelling the effect of spatial scales having a typical scale size of about 500 m along the Swarm flight direction (roughly North-South), which causes L-band scintillations and affect the quality of GNSS-based positioning. The use of the Swarm-based proxy for S4 is potentially of great use for the community involved in studying, monitoring, and modelling the impact of small-scale irregularities on GNSS signals in the space weather context as it complements and extends the information based on ground-based observations, also by covering ionospheric sectors scarcely covered by ground scintillation data, including remote areas and over the oceans, being not easily accessible. We report about its formulation and early validation against S4 data from L-band Ionospheric Scintillation Monitor Receivers.