Deriving a global troposphere model for space geodetic simulations based on an ML ensemble featuring uncertainty quantification

Abstract This work presents a global, three-dimensional (latitude–longitude–time) model of the refractive index structure constant ( $$C_n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> ), enabling the spatiotemporally correlated simulation of tropospheric delays for space geodetic observations at radio frequencies. The model is based on an ensemble of 100 XGBoost models trained on 21 years of observations from 18,500 GNSS stations, using meteorological variables from ERA5 as features. It effectively captures high-frequency spatial and temporal variations, achieving a mean absolute error of $$0.52\,\hbox {m}^{-1/3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0.52</mml:mn> <mml:mspace/> <mml:msup> <mml:mtext>m</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . To simplify the use of the model, monthly average $$C_n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> values are computed on a regular $$2.5\times 2.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2.5</mml:mn> <mml:mo>×</mml:mo> <mml:mn>2.5</mml:mn> </mml:mrow> </mml:math> degree grid, which are sufficiently accurate for most simulation studies. Besides, the model provides a Monte Carlo-based measure for the prediction uncertainty based on the XGBoost ensemble spread, which is revealed to be primarily driven by feature augmentation using ensemble spread information from ERA5. The model is validated both independently on 2500 GNSS stations over 3 years and externally through very long baseline interferometry simulations. The results demonstrate a significant improvement over current state-of-the-art simulation approaches.