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Irrigation water requirements are commonly estimated based on the estimated crop evapotranspiration (ETc) as determined by the reference evapotranspiration (ETr) and crop coefficient (Kc). Recent studies show that, at high evaporative demand (high ETr), Kc tends to decrease, creating an inverse ETr-Kc relationship. The focus of this long-term study is to, if at high atmosphere demand, there is the same inverse ETr-Kc relationship in Nebraska, USA, one of the most intensely irrigated regions in the world, and as a result, propose an adjustment to the Kc–ETr approach. The study was carried out in eastern Nebraska for maize-soybean rotation fields for the period 2002–2012. The Kc was estimated based on energy balance data from eddy covariance flux towers installed in the field and a nearby automated weather station throughout the growing seasons. We found that average Kc values varied depending on the year under high ETr; measured ETc agreed reasonably well with the FAO-56 manual predicted values, but in years with high ETr such as 2012 and 2002 affecting ETc values over the growing season. It was observed that Kc decreased as ETr increased, mainly when ETr reaches values greater than 6 mm d−1 (P values < 0.001). This most likely was due to internal plant stomatal resistance to vapor release from the leaves diffusing to the atmosphere at high atmospheric demands. So, the time-based Kc curves described by FAO 56 manual should be adjusted for the analyzed crops considering different ranges of ETr to improve the required irrigation depth and irrigation management. [ABSTRACT FROM AUTHOR]