Forward modeling of bending angles with a two‐dimensional operator for GNSS airborne radio occultations in atmospheric rivers

The Global Navigation Satellite System (GNSS) airborne radio occultation (ARO) technique is used to retrieve profiles of the atmosphere during reconnaissance missions for atmospheric rivers (ARs) on the west coast of the United States. The measurements of refractive bending angle integrate the effects of variations in refractive index over long near‐horizontal ray‐paths from a spaceborne transmitter to a receiver onboard an aircraft. A forward operator is required to assimilate ARO observations, which are sensitive to pressure, temperature, and humidity, into numerical weather prediction models to support forecasting of ARs. A two‐dimensional (2D) bending angle operator is proposed to enable capturing key atmospheric features associated with strong ARs. Comparison to a one‐dimensional (1D) forward model supports the evidence of large bending angle departures within 3–7 km impact heights for observations collected in a region characterized by the integrated water vapor transport (IVT) magnitude above 500 kg . The assessment of the 2D forward model for ARO retrievals is based on a sequence of six flights leading up to a significant AR precipitation event in January 2021. Since the observations often sample regions outside the AR where moisture is low, the significance of horizontal variations is obscured in the average bending angle statistics. Examples from individual flights sampling the cross‐section of an AR support the need for the 2D forward model. Additional simulation experiments are performed to quantify forward modeling errors due to tangent point drift and horizontal gradients suggesting contributions on the order of 5% and 20%, respectively.