Estimating Changes in the Observed Relationship Between Humidity and Temperature Using Noncrossing Quantile Smoothing Splines

The impacts of warm season heat extremes are dependent on both temperature and humidity, so it is critical to properly model their relationship, including how it may be changing. This presents statistical challenges because the bivariate temperature–humidity (measured here by dew point) distribution is complex and spatially variable. Here, we develop a flexible, semiparametric model based on quantile smoothing splines to summarize the distributional dependence of dew point on temperature, including how the dependence is changing with increasing global mean temperature. Noncrossing constraints enforce both the validity of the modeled distributions and the physical constraint that dew point cannot exceed temperature. The proposed method is first demonstrated with four synthetic, representative case studies. We then apply it to data from 2416 weather stations spanning the globe, with a focus on analyzing dew point trends during hot days. In general, dew point is increasing on both hot, humid and hot, dry days in the tropics and high latitudes, but decreasing in the subtropics, especially on hot, dry days. These changes appear to be mostly explained by changes in the temperature–dew point relationship, rather than by increases in temperature with a fixed temperature–dew point relationship.