Radar Beam Tracing Methods Based on Atmospheric Refractive Index

Abstract

Simulation of radar beam propagation is an important component of numerous radar applications in meteorology, including height assignment, quality control, and especially the so-called radar forward operator. Although beam propagation in the atmosphere depends on the refractive index and its vertical variation, which themselves depend on the actual state of the atmosphere, the most common method is to apply the 4 /3 earth radius model, based on climatological standard conditions. Serious deviations from the climatological value can occur under so-called ducting conditions, where radar beams at low elevations can be trapped or propagate in a waveguide-like fashion, such that this model is unsuitable in this case. To account for the actual atmospheric conditions, sophisticated methods have been developed in literature. However, concerning the practical implementation of these methods, it was determined that the description in the literature is not always complete with respect to possible pitfalls for practical implementations.In this paper, a revised version of an existing method (one example for the above-mentioned ''pitfall'' statement) is introduced that exploits Snell's law for spherically stratified media. From Snell's law, the correct sign of the local elevation is a priori ambiguous, and the revised method explicitly applies (i) a total reflection criterion and (ii) another ad hoc criterion to solve the problem.Additionally, a new method, based on an ordinary differential equation with respect to range, is proposed in this paper that has no ambiguity.Sensitivity experiments are conducted to investigate the properties of these three methods. The results show that both the revised and new methods are robust under nonstandard conditions. But considering the need to catch an elevation sign ambiguity in the revised method (which cannot be excluded to fail in rare instances), the new method is regarded as more robust and unproblematic, for example, for applications in radar forward operators.

From model to radar variables: a new forward polarimetric radar operator for COSMO

“…Atmospheric refraction model (Zeng et al, 2014) In case of non-standard temperature profiles, such as a temperature inversion, the profile of n can vary significantly from the one assumed by the Equivalent Earth Model, which can lead to strong underestimation of the beam refraction. Fortunately Zeng et al (2014) proposed a more generic and accurate model that is based on the vertical profile of atmospheric refractivity derived from the model data.…”

“…Fortunately Zeng et al (2014) proposed a more generic and accurate model that is based on the vertical profile of atmospheric refractivity derived from the model data. This vertical profile can be approximated from the temperature T , the partial pressure of water vapor P w , and the total pressure P ( Doviak and Zrnić, 2006).…”

“…The whole evaluation of the radar operator presented in Sect. 4 was performed with the more advanced model of Zeng et al (2014).…”

Estimation of Surface Duct Using Ground-Based GPS Phase Delay and Propagation Loss

“…The methods of sounding refractivity profiles-such as radiosondes, microwave refractometers, and evaporation duct sensors-have been developed [10][11][12][13][14]. However, these methods are direct sensing techniques and have lower sparse sampling rates.…”

Observational operators for dual polarimetric radars in variational data assimilation systems

“…In this study, the bending is determined by considering the climatological vertical gradient of the refractive index of the atmosphere in accordance with the effective earth radius model (Doviak and Zrnić, 1993), following Haase and Crewell (2000), who showed statistically that the climatological refractive index is close to the actual refractive index at elevation angles higher than 1°, instead of by considering the actual atmospheric conditions, although Zeng et al (2014) Remote sensing observations usually have higher spatial resolutions than the model grid spacings. To avoid correlations of the observational errors in such high-resolution data, it is necessary either to thin the data or to use "super observations".…”