Magnetic perturbations on ground at high latitudes are directly associated only with the divergence-free component of the height-integrated horizontal ionospheric current, $\textbf{J}_{\perp,df}$. Here we show how $\textbf{J}_{\perp,df}$ can be expressed as the total horizontal current $\textbf{J}_\perp$ minus its curl-free component, the latter being completely determined by the global Birkeland current pattern. Thus in regions where $\textbf{J}_\perp = 0$, the global Birkeland current distribution alone determines the local magnetic perturbation. We show with observations from ground and space that in the polar cap, the ground magnetic field perturbations tend to align with the Birkeland current contribution in darkness but not in sunlight. We also show that in sunlight, the magnetic perturbations are typically such that the equivalent overhead current is anti-parallel to the convection, indicating that the Hall current system dominates. Thus the ground magnetic field in the polar cap relates to different current systems in sunlight and in darkness.
