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Accurate depictions of the tropopause and its changes are important for studies on stratosphere-troposphere exchange and climate change. Here, the fidelity of primary lapse-rate tropopause altitudes and double tropopause frequencies in four modern reanalyses (ERA-Interim, JRA-55, MERRA-2, and CFSR) is examined using global radiosonde observations. In addition, long-term trends (1981-2015) in these tropopause properties are diagnosed in both the reanalyses and radiosondes. It is found that reanalyses reproduce observed tropopause altitudes with little bias (typically less than +/- 150 m) and error comparable to the model vertical resolution. All reanalyses underestimate the double tropopause frequency (up to 30% lower than observed), with the largest biases found in JRA-55 and the smallest in CFSR. The underestimates in double tropopause frequency are primarily attributable to the coarse vertical resolution of the reanalyses. Significant increasing trends in both tropopause altitude (40-120 m per decade) and double tropopause frequency (>= 3% per decade) were found in both the radiosonde observations and the reanalyses over the 35-year analysis period (1981-2015). ERA-Interim, JRA-55, and MERRA-2 broadly reproduce the patterns and signs of observed significant trends, while CFSR is inconsistent with the remaining datasets. Trends were diagnosed in both the native Eulerian coordinate system of the reanalyses (fixed longitude and latitude) and in a coordinate system where latitude is defined relative to the mean latitude of the tropopause break (the discontinuity in tropopause altitude between the tropics and extratropics) in each hemisphere. The coordinate relative to the tropopause break facilitates the evaluation of tropopause behavior within the tropical and extratropical reservoirs and revealed significant differences in trend estimates compared to the traditional Eulerian analysis. Notably, increasing tropopause altitude trends were found to be of greater magnitude in coordinates relative to the tropopause break, and increasing double tropopause frequency trends were found to occur primarily poleward of the tropopause break in each hemisphere.