Abstract. In this paper we show how multiple data sets, including observations and models, can be combined using the “three-cornered hat” (3CH) method to estimate vertical profiles of the errors of each system. Using data from 2007, we estimate the error variances of radio occultation (RO), radiosondes, ERA-Interim, and Global Forecast System (GFS) model data sets at four radiosonde locations in the tropics and subtropics. A key assumption is the neglect of error covariances among the different data sets, and we examine the consequences of this assumption on the resulting error estimates. Our results show that different combinations of the four data sets yield similar relative and specific humidity, temperature, and refractivity error variance profiles at the four stations, and these estimates are consistent with previous estimates where available. These results thus indicate that the correlations of the errors among all data sets are small and the 3CH method yields realistic error variance profiles. The estimated error variances of the ERA-Interim data set are smallest, a reasonable result considering the excellent model and data assimilation system and assimilation of high-quality observations. For the four locations studied, RO has smaller error variances than radiosondes, in agreement with previous studies. Part of the larger error variance of the radiosondes is associated with representativeness differences because radiosondes are point measurements, while the other data sets represent horizontal averages over scales of ∼ 100 km.

Abstract. Characteristics of the lapse rate tropopause are analyzed globally for tropopause altitude and temperature using global positioning system (GPS) radio occultation (RO) data from late 2001 to the end of 2013. RO profiles feature high vertical resolution and excellent quality in the upper troposphere and lower stratosphere, which are key factors for tropopause determination, including multiple ones. RO data provide measurements globally and allow examination of both temporal and spatial tropopause characteristics based entirely on observational measurements. To investigate latitudinal and longitudinal tropopause characteristics, the mean annual cycle, and inter-annual variability, we use tropopauses from individual profiles as well as their statistical measures for zonal bands and 5 • × 10 • bins. The latitudinal structure of first tropopauses shows the well-known distribution with high (cold) tropical tropopauses and low (warm) extra-tropical tropopauses. In the transition zones (20 to 40 • N/S), individual profiles reveal varying tropopause altitudes from less than 7 km to more than 17 km due to variability in the subtropical tropopause break. In this region, we also find multiple tropopauses throughout the year. Longitudinal variability is strongest at northern hemispheric mid latitudes and in the Asian monsoon region. The mean annual cycle features changes in amplitude and phase, depending on latitude. This is caused by different underlying physical processes (such as the Brewer-Dobson circulation -BDC) and atmospheric dynamics (such as the strong polar vortex in the southern hemispheric winter). Inter-annual anomalies of tropopause parameters show signatures of El Niño-Southern Oscillation (ENSO), the quasi-biennial oscillation (QBO), and the varying strength of the polar vortex, including sudden stratospheric warming (SSW) events. These results are in good agreement with previous studies and underpin the high utility of the entire RO record for investigating latitudinal, longitudinal, and temporal tropopause characteristics globally.

The three-cornered hat (3CH) method, which was originally developed to assess the random errors of atomic clocks, is a means for estimating the error variances of three different data sets. Here we give an overview of the historical development of the 3CH and select other methods for estimating error variances that use either two or three data sets. We discuss similarities and differences between these methods and the 3CH method.This study assesses the sensitivity of the 3CH method to the factors that limit its accuracy, including sample size, outliers, different magnitudes of errors between the data sets, biases, and unknown error correlations. Using simulated data sets for which the errors and their correlations among the data sets are known, this analysis shows the conditions under which the 3CH method provides the most and least accurate estimates. The effect of representativeness errors caused by differences in vertical resolution of data sets is investigated. These representativeness errors are generally small relative to the magnitude of the random errors in the data sets, and the impact of this source of errors can be reduced by appropriate filtering.

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