Precise mapping of relative surface elevation using spaceborne GNSS-R phase altimetry with crossover adjustment: A case study of Lake Ladoga

Abstract

This paper investigates a crossover adjustment method for spaceborne GNSS Reflectometry (GNSS-R) phase altimetry and demonstrates its capability for precise surface elevation mapping through a case study of Lake Ladoga, which is the largest lake in Europe and exhibits unmodeled gravitational effects on its water surface. GNSS-R phase altimetry measures relative surface height with a constant but unknown offset and may also include errors in the retrieved surface gradients due to factors such as the residual atmospheric propagation error after model correction. The crossover adjustment method estimates the offsets between multiple GNSS-R tracks and each track’s surface gradient errors by formulating and solving a constrained least-squares problem to minimize differences at intersections. Additionally, this method evaluates the accuracy of GNSS-R altimetry retrievals by comparing the consistency of each track with others, enabling the identification of measurement outliers with respect to stable geophysical features. In the case study, we utilize 871 sets of Spire grazing-angle GNSS-R data collected from 2020 to 2023, containing signals coherently reflected off Lake Ladoga, to map the unmodeled gravitational effects on the lake’s water surface. The mapping results are validated using 16 ICESat-2 altimetry datasets, demonstrating a high accuracy with a root-mean-square (RMS) difference of about 3 cm.