Annual average of reconstructed modulation potential Φ since 1937 (gray line and dots with units on the left axis) and estimated annual dose equivalent rate derived from different models (with units on the right axis). Cyan/green line shows the dose equivalent values derived from the nonlinear model (Eq. (3)) based on detector B/E measurements. Magenta/red line represents the dose equivalent values derived from the linear model (Eq. (2)) based on detector B/E measurements. Black, yellow, and blue dots represent the data within the range of modulation Φ between 550 and 810 MV which the RAD cruise measurements covered.