The upper troposphere and lower stratosphere (UTLS) plays an important role in climate and atmospheric chemistry. Despite its importance on the point of causing deep intrusions of tropics originated air into the midlatitudes, the quasi-horizontal transport process in the UTLS, represented by global chemistry-transport models (CTMs) or chemistry-climate models (CCMs), cannot easily be diagnosed with conventional analyses on isobaric surfaces. We use improved diagnostic tools to better evaluate CTMs and CCMs relative to satellite observations in the region of UTLS. Using the Hellinger distance, vertical profiles of probability density functions (PDFs) of chemical tracers simulated by the Model for OZone And Related chemical Tracers 3.1 (MOZART-3.1) are quantitatively compared with satellite data from the Microwave Limb Sounder (MLS) instrument in the tropopause relative altitude coordinate to characterize features of tracer distributions near the tropopause. Overall, the comparison of PDFs between MLS and MOZART-3.1 did not satisfy the same population assumption. Conditional PDFs are used to understand the meteorological differences between global climate models and the real atmosphere and the conditional PDFs between MOZART-3.1 and MLS showed better agreement compared to the original PDFs. The low static stability during high tropopause heights at midlatitudes suggests that the variation of tropopause height is related to transport processes from the tropics to midlatitudes. MOZART-3.1 with the GEOS4 GCM winds reproduces episodes of the tropical air intrusions. However, our diagnostic analyses show that the GEOS4 GCM did not properly reproduce the high tropopause cases at midlatitudes especially in spring.