The cool tropics paradox is the apparent difference between modeled estimates of tropical temperatures during warm, ice-free periods of the Cretaceous and Eocene, and the colder temperatures which proxies suggested were present. The long-standing paradox was resolved when novel proxy derived temperatures showed significantly warmer tropics during past greenhouse climates. The low-gradient problem, i.e. the very warm polar regions with respect to present day, is still an issue for state-of-the-art climate models. Origin of the paradox Proxy-based reconstructions of paleotemperature appeared to predict a low temperature gradient between the tropics and poles. Data from surface-dwelling foramanifera suggested that during the late Cretaceous, an unusually warm period, sea surface temperatures were cooler than today's. The term was later applied to similar situations, for example during the Eocene. Climate models which worked during the Tertiary failed to produce this low temperature gradient; in order to match the observed data, they predicted that the tropics should be 40 °C or more - much hotter than the proxies said they were, and much hotter than the tropical surface temperatures observed today, which average around 25 °C (77 °F). To attempt to match the data, bizarre models involving unreasonable eddies were required. Models Models were developed to predict and explain the lack of ice during the warm periods of the Cretaceous and Eocene. Models are developed according to the fundamental principle that they should be kept as simple as possible. Consequently, the first models attempted to explain the lack of ice using solely the different continental configuration. These could not produce an ice-free state without using an increased atmospheric concentration of ; this assumption was checked against the evidence and found to be valid. This introduced a new difficulty: more would produce warmer tropical sea temperatures, and the evidence suggested they were the same or even colder than today's. Data supporting cool tropical oceans Foraminiferal data, suggesting tropical temperatures cooler than today's, disagreed with terrestrial proxies, which spoke of warmer temperatures - although most of the terrestrial figures are based on extrapolation of data from outside the tropics. Sources of error Analytical error is around 2−3 °C for individual specimens, but this drops to 0.5−1.0 °C when a sample is analysed - not enough to explain the discrepancy. Other factors mean that any pristine sample can be considered to have an associated error of up to 3 °C. Changes in salinity, kinetic and diagenesis, can