# The Use of SMAP-Reflectometry in Science Applications: Calibration and Capabilities
## 2 Capabilities
### SMAP-R Spatial Resolution  
In order to determine the capabilities of SMAP-R for science applications, there is a need to determine the footprint of the SMAP-R measurements. The spatial resolution of GNSS-R observations is variable and depends on the scattering surface, the incidence angle, and the integration time. The following methodology applies to SMAP-R, CYGNSS, and TDS-1 measurements, regardless of the scattering surface and incidence angle. The measurement obtained from a GNSS-R receiver is a delay-Doppler map (DDM), [34; 35; 36] which represents the power scattering of the GPS signal over the Earth surface collected at different values of delay and Doppler. We present a general approach to map the DDM information to its native spatial resolution [37; 38; 39; 40]:  
1. A power threshold is applied to the DDM in order to estimate the area from where the scattering signal is coming from. In order to set a threshold, most of the area representing the total power needs to be accounted for. We select a threshold that gathers the N% of the total power, N being an arbitrary number. N% in our studies has been selected to at least 80%. This threshold defines a delay and a Doppler value for the area under consideration. 2. Map the delay and Doppler values into the surface, drawing the iso-delay and Doppler lines. Both delay and Doppler provide the exact area of the scattering considered. For the sake of simplicity, we use the delay value alone, which translates to an ellipse in the surface. 3. The ellipse is centered in the specular point and is rotated to the scattering plane formed by the receiver and transmitter geometries, with the semi-major ellipse axis aligned with the scattering plane and the semi-minor axis perpendicular to it. 4. The ellipse is then elongated by the distance obtained by multiplying the integration time by the velocity of the satellite in the along-track direction. 5. The final elongated ellipse is mapped into the surface, with a fine enough grid that allows the delineation of the shape of such ellipse. 6. Steps 1 to 5 are repeated for all measurements. We have applied the described methodology to SMAP-R measurements (Table 1). Similar studies could be done for the other GNSS-R missions (TDS-1 and CYGNSS). The methodology is therefore general, but results are mission-dependent. Table 1 shows the mean and the standard deviation of the size of the scattering area computed for a number of scenes and N% threshold values. Explored scenarios are sea ice, lakes, wetlands, arid land, low vegetation, high vegetation, and ocean. The N value ranges from 80% to 60%, in steps of 5%. When a threshold N = 80% is used, the DDM signals  
Figure 4: Peak signal to noise ratio (SNR) of the GPS reflections captured by (**a**) SMAP-R at V-polarization 25 ms integration time and (**b**) TDS-1 for 1 day of measurements with 1000 ms integration time. Peak SNR plotted in dB. from land, vegetated, and ocean scenes, overflow to the system noise instead of staying in the actual scattering power, which erroneously increases the value the mean and standard deviation. The thresholds N = 65% and N = 60% are not accounting for all the scattering power from the scene, missing important contribution and hence the threshold tends to underestimate the size of the footprint. The range within N = 70% and N = 75% show all the scenarios with similar stable behavior. For N = 75% we observe an averaged spatial resolution of 2.4 km for sea ice scenarios. A spatial resolution of 2.6 km is observed for the lakes and 3.3 km for wetlands, even in cases where there is vegetation. The spatial resolution decreases over arid land with 6.4 km and is even lower when there is vegetation, starting at 12.5 km for low vegetation volume and up to 38.9 km on high vegetation areas. Notice that when N = 75% for high vegetation scenes, the DDM noise might still prevail due to the lower power of the high vegetation scenes. The true spatial resolution may be found when N = 70%, giving an averaged spatial resolution of a circle 26.6 km diameter.