Spectral analysis of the tropospheric wet refractivity field with ERA5: a case study in Tahiti

The spectral behavior of the wet refractivity in the troposphere has not yet been studied, contrary to air temperature, specific humidity, and wind field. As wet refractivity is directly linked to air moisture, it causes highly variable tropospheric delays in geodetic observations using radio wave signals. Knowing the spectral behavior of the wet refractivity thus provides scientists with an important constraint or source of data for both tropospheric delays modeling and numerical weather/climate modeling. To fill this gap, in this work, we present a new toolset to analyze the spectral properties of the tropospheric wet refractivity field. As an example, using fifth-generation European center for medium-range weather forecasts re-analysis (ERA5) hourly products, the three-dimensional (3D) wet refractivity fields overhead Tahiti Island during 2019–2020 are derived as a case study, where the perturbations of the wet refractivity field are modeled with 3D Zernike functions and a corresponding power spectrum w.r.t a radial index n and a space index l is derived. Results show that the power spectrum w.r.t the power index n×l is almost flat at low n×l but progressively transitions to a power-law decline with an index of −2.9 (approximately −3) at higher n×l. The flat pattern indicates large-scale atmospheric processes considered in ERA5, and the −3-scaling law conforms to the two-dimensional (2D) atmospheric turbulence theory as found in other atmospheric variables. This −3-scaling law is also similar to the well-known Kaula’s rule in geodesy works, allowing us to derive a Kaula-like rule as an additional a priori information for modeling the wet refractivity field with 3D Zernike functions.