# Geolocation, Calibration and Surface Resolution of CYGNSS GNSS-R Land Observations
## 4 Analysis of Coherent Surface Resolution Using Ancillary River Width Data  
To assess CYGNSS's spatial resolution under the conditions of coherent reflection quantitatively, we have performed a statistical study using the North American River Width Data Set (NARWidth) [21]. This dataset provides a reference for locations with greater expectation of generating a coherent reflection. The RMS error of the NARWidth river data set, compared to in-situ measured river widths, is estimated to be approximately 38 m [21]. a detailed coherency analysis using raw sampled data from CYGNSS (from which coherent phase information can be estimated) was previously presented in [22]. However, this work presents CYGNSS results in its normal processing mode (including the non-coherent instrument integration which eliminates all phase information in the observable). Using the available CYGNSS measurements together with reported river widths, the mean Level-1 power ratio \(PR\) coherence metric with respect to varying river widths is examined in Figure 7. The \(PR\) is an estimate of the ratio of the amount of received power near the peak to the integrated power away from the peak, derived in [13]. Increasing river widths were found to be associated with a steady increase in the Level-1 coherence metric and the probability of detecting the river, with the detection probability approaching 100% for rivers with widths exceeding \(\approx\) 1.2 km. This is to be expected as rivers with larger widths present a target more conducive to result in identifiable coherence characterized by a significant concentration of power about the DDM peak. They are also less susceptible to ambiguities introduced by the L1 integration time(s) as well as perturbations associated with more heterogeneous scenes. It is also noted that operationally, a DDM measurement is declared as being the result of a dominantly coherent reflection process if its power ratio exceeds the detection threshold \(\rho_{0}\) = 2.0. From the analysis presented in Figure 7 it is observed that this occurs, on average, for rivers with a minimum width exceeding 250 m and 200 m for 1 Hz and 2 Hz CYGNSS data, respectively. This places a minimum bound on the finest spatial features CYGNSS measurements are able to resolve, on average, suggesting that this is on the order of a first Fresnel zone and provides empirical support for previous theoretical treatments of this question [23]. However, there are several caveats to this analysis which assumes that rivers will generally satisfy the conditions to produce coherent CYGNSS forward reflections:  
1. River widths are known to change dynamically, seasonally and during flooding events. The NARWidth data set provides an estimate of the river width at mean discharge, thus it does not account for natural seasonal variations. The analysis undertaken here focuses on using CYGNSS data over two eight month periods, the first starting with July 2018 and ending with February  
Figure 6: **(left)** Mean surface reflectivity from 12-days of CYGNSS observations. (middle) Mean surface peak bistatic radar cross section (BRCS) over the same 12-days of CYGNSS observations. (right) Estimated mean reflected signal coherency estimate over same 12-day interval (1 = coherent, 0 = non-coherent) for the Indian Peninsula and the Gulf of Mexico regions. 2019 and the second starting with July 2019 and ending with February 2020. This included a total of 50 million measured CYGNSS specular points, within the NARWidth dataset's coverage, providing ample data to generate statistically significant results. While variations in the size of the coherent reflection surface due to natural fluctuations in river widths will contribute errors into the analysis, the mean correspondence of measures of interest to varying river widths is expected to remain indicative of CYGNSS's spatial resolution under conditions of coherent reflection. 2. Previous analysis of CYGNSS data has shown that river surfaces are generally smooth enough to result in coherent forward reflections [6].