Proton count rate measurements were obtained from the polar orbiting environmental satellites POES15 and POES16 during three solar proton events in 2001. From these data the invariant latitude of the cutoff in proton flux was determined at four local times. The satellites sample the edge of the northern polar cap at approximately 0300, 0830, 1230, and 1800 hours local time, covering the early morning, late morning, noon, and evening. During the event of 2 April the cutoff latitude for 35--70 MeV protons was almost constant, showing no more than 1.5¿ variation with local time. CME impacts occurred during the 24 September and 4 November events, the effects of which were to reduce the cutoff latitudes by between 5¿ and 8¿. The equatorward displacement of the cutoff latitude was found to be strongly correlated with the magnetic storm indices (Dst and SYM-H). Cutoff latitude prediction formulae are defined. Simulations using the Tsyganenko (2002) model of the magnetosphere are consistent with observations to within 2σ during quiet conditions and weak disturbances.