Accurate modeling of tropospheric delay is important for high-precision data analysis of space geodetic techniques, such as the Global Navigation Satellite System (GNSS). Empirical tropospheric delay models provide zenith delays with an accuracy of 3 to 4 cm globally and do not rely on external meteorological input. They are thus important for providing a priori delays and serving as constraint information to improve the convergence of real-time GNSS positioning, and in the latter case proper weighting is critical. Currently, empirical tropospheric delay models only provide delay values but not the uncertainty of delays. For the first time, we present a global empirical tropospheric delay model, which provides both the zenith delay and the corresponding uncertainty, based on 10 years of tropospheric delays from numerical weather models (NWMs). The model is based on a global grid and, at each grid point, a set of parameters that describes the delay and uncertainty in the constant, annual, and semiannual terms. The empirically modeled zenith delay has agreements of 36 and 38 mm compared to 3-year delay values from the NWM and 4-year estimates from GNSS stations, which is comparable to previous models such as Global Pressure and Temperature 3 (GPT3). The modeled zenith tropospheric delay (ZTD) uncertainty shows a correlation of 96 % with the accuracy of the empirical ZTD model over 380 GNSS stations over the 4 years. For GNSS stations where the uncertainty annual amplitude is larger than 20 mm , the temporal correlation between the formal error and smoothed accuracy reaches 85 %. Using GPS observations from ∼ 200 globally distributed IGS stations processed in kinematic precise point positioning (PPP) mode over 4 months in 2020, we demonstrate that using proper constraints can improve the convergence speed. The formal error modeling is based on a similar dataset to that of the GPT series, and thus it is also applicable for these empirical models. [ABSTRACT FROM AUTHOR]

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