An evaluation of the expression of the atmospheric refractivity for GPS signals

An expression is derived from first principles for the refractivity of air at L band frequencies, which includes GPS, as well as other GNSS satellite radionavigation signals. Under conditions of pressure, temperature, and moisture content found in the Earth's atmosphere, the expression has an average relative error of approximately 0.01%. This level of accuracy is required to guarantee that the expression does not introduce bias, when it is used within the context of Numerical Weather Prediction (NWP) applications. The thermodynamic dependences of the air's refractivity N are revisited, and the possible sources of uncertainty are analyzed. A first principles microphysical model is constructed, which relates the refractivity at L band frequencies with several measurable properties of matter. The experimental values that are critical for this purpose are already available in the literature and are of high accuracy. Based on this model, a simple expression suitable for atmospheric and weather applications is proposed: N ≡ (n - 1) · 10⁶ = N₀ · (1 + ?N₀) where N₀ = (222.682 + 0.069 · τ) · ρ_d + (6701.605 + 6385.886 · τ) · ρ_w with ρ_d and ρ_w as the densities of dry air and water vapor in the air (kg/m³), τ = 273.15/T - 1, and T as the absolute temperature in K. The dependence of the coefficients in the expression with respect to the input physical parameters is analyzed. Given the error of the experimental parameters, it is concluded that the proposed expression improves the accuracy to meet the needs of NWP applications.