Impact of Radar Data Sampling on the Accuracy of Atmospheric Refractivity Inversions Over Marine Surfaces

Abstract

The turbulent nature of the marine atmospheric boundary layer and interactions across the air‐sea interface cause ever‐changing environmental conditions, including atmospheric properties that affect the index of refraction, or atmospheric refractivity. Variations in atmospheric refractivity lead to many types of anomalous propagation phenomena of electromagnetic (EM) signals; thus, improving performance of EM systems requires in situ knowledge of the refractivity. Inversion approaches to estimate refractivity rely on measured EM data; however, despite its importance, few studies have examined the influence of data density on the accuracy of refractivity inversions. This study applies a bistatic radar data inversion process to estimate atmospheric refractivity parameters in evaporative ducting conditions and examines the impacts of the sampling density of radar propagation loss data, and its source location, on accuracy of refractivity inversions. Genetic algorithms and a radar propagation model are used to perform the inversions. Numerical experiments examine various randomly distributed amounts of synthetic data from a 100‐m (altitude) by 60‐km (range) area. Three domains within this area are examined from which data were sourced. A data density of approximately 1% of the prediction domain yielded the smallest errors of refractivity parameters, and root mean square errors of refractivity and propagation loss. These error reductions are attributed to avoidance of nonunique solutions that likely impact lower data densities, supported by their classification as a misleading or difficult inverse problem. Generally, data sourced from long range result in lower refractivity and propagation loss root mean square errors compared to data sourced from other domains.

Refractivity Inversions From Point‐To‐Point X‐Band Radar Propagation Measurements

“…To evaluate the inversion-based environment, refractivity for the forward models that resulted in lowest PL MSE are compared to the (refractivity) inverse solutions in Figure 9, where it should be noted that forward model cases with range dependent refractivity are averaged over range to improve legibility of the figure (e.g., COAMPS refractivity profile in Figure 9a). The most striking differences occur with respect to the mixed layer slope (e.g., Figures 9A, 9I or 9L); however, it has been shown that differences in the mixed layer slope do not affect propagation as significantly as other refractive parameters in the near surface (Lentini & Hackett, 2015;Matsko & Hackett, 2019;Pastore et al, 2021;Penton & Hackett, 2018), resulting in a relative insensitivity of the GA optimization to this parameter. Much more important is the duct height and the shape below the duct height (Cherrett, 2015;Pastore et al, 2021).…”

“…Although the lower average $${{\Phi}}_{\text{MSE}}$$ for inversion PL confirms more accurate PL predictions, the better propagation predictions do not necessarily imply improved environmental predictions. The inversion approach may converge on an environment that only predicts the propagation accurately at the receiver heights and not necessarily everywhere, in other words, there can be nonunique solutions with a limited RF data set (Matsko & Hackett, 2019; Wang et al., 2019).…”

“…In this study we apply a GA to optimize parameters of a refractivity model that best represent the atmospheric conditions in which the RF data were collected. The parametric model is a piecewise modified refractivity model consisting of two layers, an evaporation layer and a mixed layer (Gerstoft, 2003;Matsko & Hackett, 2019;Penton & Hackett, 2018;Saeger et al, 2015):…”

“…In this study we apply a GA to optimize parameters of a refractivity model that best represent the atmospheric conditions in which the RF data were collected. The parametric model is a piecewise modified refractivity model consisting of two layers, an evaporation layer and a mixed layer (Gerstoft, 2003; Matsko & Hackett, 2019; Penton & Hackett, 2018; Saeger et al., 2015): $$$\begin{array}{l}M(z)={M}_{0}+\left\{\begin{array}{rl}\hfill {c}_{0}\left(z-{z}_{d}\hspace*{.5em}\mathrm{ln}\left(\frac{z+0.00015}{0.00015}\right)\right),& z\le {z}_{L}\hfill \\ {m}_{1}z-{M}_{1},\hfill & z > {z}_{L}\hfill \end{array}\right.\hfill \end{array}$$$ where $$M$$ is modified refractivity, the surface refractivity is $${M}_{0}=333$$ M ‐units, $${z}_{d}$$ is evaporation duct height (EDH), $$\hspace*{.5em}{m}_{1}$$ is mixed layer slope, and $$\hspace*{.5em}{M}_{1}$$ is a term defined by other parameters ($${c}_{0}$$, $${z}_{d},$$ and $${m}_{1}$$) ensuring a continuous profile between layers. The potential refractivity gradient (Paulus,…”

“…Propagation predictions are generated by the Variable Terrain Radio‐Wave Parabolic Equation (VTRPE) simulation; VTRPE simulates radio wave propagation in a variety of environmental conditions (Ryan, 1991). The full‐wave solution of the EM field is computed via a split step rotated Green's function parabolic equation (Matsko & Hackett, 2019; Pastore et al., 2021; Penton & Hackett, 2018; Ryan, 1991; Saeger et al., 2015; Sirkova, 2012). PL data are simulated matching the antenna characteristics of the measured RF data (Table 1), including the Gaussian antenna pattern with two side lobes emulating the horn antennae.…”