# Latest Advances in the Global Navigation Satellite System--Reflectometry (GNSS-R) Field
The world maps describe the color code for the central chart. The number of publications is indicated for each colored part of the chart. Note that world maps have been adapted from Wikipedia images—licensed through CC BY-SA 4.0.  
can penetrate vegetation, the water content of the plants, as well as the density and height, impacts the signal due to volume scattering. GNSS signals are sensitive to standing water, such as lakes, rivers, or wetlands, and also to water in a frozen state, such as frozen soil (during winter) or sea ice. Reflections on calm water and ice produce coherent reflections as compared to reflections from bare soil or vegetated soil. The ability to detect inland water is valuable for mapping in wetlands or other floods. GNSS reflections can also be used for frozen soil detection, which allows for studies of the freeze/thaw characteristics of land surfaces. Thanks to its sensitivity to different surfaces, GNSS-R signals can be used in many different applications. Figure 4 shows an image relating the GNSS-R applications to the essential climate variables (ECV) described by the global climate observing system (GCOS), providing a clear idea as to the relevance of the GNSS-R field to improving our knowledge of Earth and its processes. The power collected by a GNSS receiver after the GNSS signal scatters over the Earth's surface is known as a delay-Doppler map (DDM). The mathematical equation was defined in [2; 3] and can easily be found in the literature. We provide the equations for the general understanding of the different studies that are explained here and for the completeness of this review article. Equation (1) describes the reflected GNSS signal that would be received from a surface dominated by incoherent scattering. \[P_{incoh}(\tau,f_{d})=T_{i}^{2}\int\frac{P_{tx}G_{tx}G_{rx}(\overrightarrow{\rho} )\lambda^{2}\Lambda^{2}\left(\tau-\tau_{s}(\overrightarrow{\rho})\right)}{ \left(4\pi\right)^{3}R_{rx}^{2}\left(\overrightarrow{\rho}\right)R_{tx}^{2} \left(\overrightarrow{\rho}\right)}\times\left|S\left(f_{d}\left(\overrightarrow {\rho}\right)-f\right)\right|^{2}\sigma_{0}\left(\overrightarrow{\rho} \right)d^{2}\rho \tag{1}\]  
where:  
* \(\overrightarrow{\rho}\) identifies the various surface pixels in the scattering area;
* T\({}_{i}\) represents the coherent integration time;
* P\({}_{tx}\) stands for GPS transmitted power;
* G\({}_{tx}\) and G\({}_{rx}\) denote the transmitter and receiver antenna gain, respectively;
* \(\lambda\) is the wavelength of the GPS signal (which is 24.42 cm at GPS-L2C);  
Figure 4: Environmental climate variables that can be measured by GNSS-R: (from left to right) Sea state, surface stress, sea ice, surface currents, sea level, plankton, ice sheets, snow, glaciers, permafrost, above-ground biomass, land cover, leaf area index, river discharge, lakes, soil moisture, and terrestrial water storage. Adapted from the global climate observing system (GCOS) [[[https://gcos.wmo.int/copyright](https://gcos.wmo.int/copyright)]([https://gcos.wmo.int/copyright](https://gcos.wmo.int/copyright)) accessed on 16 April 2023] under CC-BY-4.0. * \(\mathrm{R_{rx}}\) and \(\mathrm{R_{rx}}\) represent the distance from the transmitter to the particular surface pixel \(\overrightarrow{\rho}\), and the distance between the receiver and the particular surface pixel \(\overrightarrow{\rho}\), respectively;
* The sinc(S) function characterizes the signal spread in Doppler;
* The delta \(\Lambda\) function characterizes the spread of the signal in time;
* The bistatic radar cross section of a rough surface \(\sigma_{0}\!\left(\overrightarrow{\rho}\right)\) is given by the following equation: \(\sigma_{0}\!\left(\overrightarrow{\rho}\right)=\pi\Big{|}\mathcal{R}\!