A simplification of rigorous atmospheric raytracing based on judicious rectilinear paths for near-surface GNSS reflectometry

Earth, Planets and Space

Table 3 Definition of rectilinear propagation quantities

	Rectilinear geometric (RG)		Rectilinear apparent (RA)
	Vacuum distance	Radio length	Vacuum distance	Radio length
Direct	\( \bar{D}_{d} = \left\\| {\varvec{r}_{\text{ant}} - \varvec{r}_{\text{sat}} } \right\\| \)	\( \bar{L}_{d} = \int_{{r}_{\text{ant}}}^{{r}_{\text{sat}}} {n~ds} \)	\( {\bar{D}}^{\prime}_{d} = \left\\| {{\varvec{r}}_{\text{ant}} - {\varvec{r}}^{\prime}_{\text{sat}} } \right\\| \)	\( {\bar{L}}^{\prime}_{d} = \int_{{\user2{r}}_{\text{ant}} }^{{\user2{r}}^{\prime}_{\text{sat}} } {n~ds} \)
Reflection	\( \bar{D}_{r} = \left\\| {\varvec{r}_{\text{ant}} - \varvec{r}_{\text{sfc}} } \right\\| + \left\\| {\varvec{r}_{\text{sfc}} - \varvec{r}_{\text{sat}} } \right\\| \)	\( \bar{L}_{r} = \int_{{\user2{r}_{\text{sfc}} }}^{{\user2{r}_{\text{sat}}}} {n\,ds} + \int_{{\user2{r}_{\text{ant}}}}^{{\user2{r}_{\text{sfc}} }} {n\,ds} \)	\( \bar{D}^{\prime}_{r} = \left\\| {{\varvec{r}}_{\text{ant}} - {\varvec{r}}^{\prime}_{\text{sfc}} } \right\\| + \left\\| {{\varvec{r}}^{\prime}_{\text{sfc}} - {\varvec{r}}^{\prime}_{\text{sat}} } \right\\| \)	\( \bar{L}_{r} = \int_{{\user2{r}}^{\prime}_{\text{sfc}} }^{{\user2{r}}^{\prime}_{\text{sat}} } {n~ds} + \int_{{\user2{r}}_{\text{ant}} }^{{\user2{r}}^{\prime}_{\text{sfc}} } {n~ds} \)
Interferometric	\( \bar{D}_{i} = \bar{D}_{r} - \bar{D}_{d} \)	\( \bar{L}_{i} = \bar{L}_{r} - \bar{L}_{d} \)	\( \bar{D}^{\prime}_{i} = \bar{D}^{\prime}_{r} - \bar{D}^{\prime}_{d} \)	\( \bar{L}^{\prime}_{i} = \bar{L}^{\prime}_{r} - \bar{L}^{\prime}_{d} \)