Revisiting the light time correction in gravimetric missions like GRACE and GRACE follow-on

Abstract

The gravity field maps of the satellite gravimetry missions Gravity Recovery and Climate Experiment (GRACE ) and GRACE Follow-On are derived by means of precise orbit determination. The key observation is the biased inter-satellite range, which is measured primarily by a K-Band Ranging system (KBR) in GRACE and GRACE Follow-On. The GRACE Follow-On satellites are additionally equipped with a Laser Ranging Interferometer (LRI), which provides measurements with lower noise compared to the KBR. The biased range of KBR and LRI needs to be converted for gravity field recovery into an instantaneous range, i.e. the biased Euclidean distance between the satellites’ center-of-mass at the same time. One contributor to the difference between measured and instantaneous range arises due to the nonzero travel time of electro-magnetic waves between the spacecraft. We revisit the calculation of the light time correction (LTC) from first principles considering general relativistic effects and state-of-the-art models of Earth’s potential field. The novel analytical expressions for the LTC of KBR and LRI can circumvent numerical limitations of the classical approach. The dependency of the LTC on geopotential models and on the parameterization is studied, and afterwards the results are compared against the LTC provided in the official datasets of GRACE and GRACE Follow-On. It is shown that the new approach has a significantly lower noise, well below the instrument noise of current instruments, especially relevant for the LRI, and even if used with kinematic orbit products. This allows calculating the LTC accurate enough even for the next generation of gravimetric missions.

Comparing GRACE-FO KBR and LRI ranging data with focus on carrier frequency variations

“…( 52) can be obtained from the GPS orbit products and are also used for the light-time correction computation. The quantities differ by c 0 |∆t AB − ∆t BA | ≈ 10 m in GRACE-FO due to the finite speed of light and the relative velocity between satellites [20]. Note that the USO frequencies f A/B,USO in eq.…”

“…On the reference satellite, the laser is stabilized using an optical cavity and the phase meter output ϕ R contains both the ranging information and the transponder phase ramp. Since the same phase ramp is present on both satellites, it cancels out in the differential measurement ϕ TWR and one can write the TWR phase as [20]…”

“…from GPS orbit data of the satellites and using formulas for the light time propagation time (∆t GPS RTR ) that depend on the orbit data [20]. The magnitude of ρ LTC,TWR is below a millimeter such that the GPS accuracy of a few millimeter over the inter-satellite baseline of approx.…”

“…where the second correction term on the right-hand side in line ( 22) is usually much smaller than the first ranging term, as the expression in the bracket is close to zero due to the introduced constant −1/2. The round-trip propagation time at the initial epoch received the superscript GPS (c 0 ∆τ GPS RTR (0)) in order to indicate that the value can be derived from GPS orbit data and algorithms to compute the light propagation time [20]. The millimeter to centimeter precision of GPS is sufficient to derive the absolute distance c 0 ∆t GPS RTR (0) ≈ 440 km without spoiling the high precision from LRI in ρ TWR,1corr , since the correction term is small due to ν R (0)/ν R (t) ≈ 1.…”

“…where the first term mainly describes the effect of the ionosphere on the propagation time, which is proportional to the squared frequency (∆t K/Ka media,AB ∝ 1/ν 2 A ). The second term on the right-hand side is the light-time correction [20] ∆t LTC,AB (t…”