# Response to Variations in River Flowrate by a Spaceborne GNSS-R River Width Estimator
## Materials and Methods
### Case Study: Pascagoula River  
A case study examining the relationship between the river signal width estimated from CYGNSS measurements and river flowrate was carried out using data from five CYGNSS overpasses of a section of the Pascagoula River in southern Mississippi (Figure 3) collected in April 2019. The Pascagoula River was chosen for the case study because of its highly dynamic nature and the availability of streamflow data from a USGS streamflow gauge located at the head of the river. Figure 3: Google Earth imagery of southern Pascagoula River in Mississippi. The location of the USGS streamflow gauge (USGS 02479000) is shown at the head of the river. The mean width along the roughly 40 km span of the river where collections took place is ~100 m.  
Figure 2: Dependence on incidence angle of: (**a**) propagation distances from specular point to receiver; (**b**) relative signal strength received from coherent and incoherent scenes for one full day of samples on 9 June 2017. The red dots indicate the incidence angles at which the greatest number of samples occurs. The standard Level 1 CYGNSS data products are averaged onboard over 1 second increments (equivalent to ~7 km of forward motion), which precludes their use for measuring small water bodies. Hence, we implemented special collections of the raw intermediate frequency (IF) data over 1 second intervals for this study. The raw IF data were post-processed using an incoherent averaging period of 50 ms. The data were collected over the period 18-25 April 2019 over a latitude range of ~30.78\({}^{\circ}\)-30.94\({}^{\circ}\) N. The track locations and the contemporaneous flowrates as measured by USGS gauge 02479000 are shown in Figure 4a,b, respectively. According to the North American River Width data set (NARWidth), a database that provides width measurements based on Landsat imagery corresponding to mean streamflow for rivers in North America greater than 30 m wide [6], the average width along this section of the river under mean flow conditions is 94 m, with a standard deviation of 33 m. The observed flowrates contemporaneous with the raw IF data collections over the river correspond to measured gauge heights ranging from ~6-7 m, with the three highest flowrates exceeding the National Weather Service's flood stage limit of 6.7 m at the gauge location. At these heights, the river should be expanding in width along its banks. For each river overpass, the river width associated with the CYGNSS signal is estimated by fitting a second-order power series to the portion of the waveform corresponding to the river body. The resulting fitted curves are extrapolated to a signal strength of zero before and after the signal peak centered on the river, and the associated width is defined as the distance between the two zero-crossings. This method is illustrated by a number of examples in Figure 5. One complication with this approach is that the CYGNSS signal is very sensitive to nearby waterbodies within a roughly 600 m radius of the specular point on the ground (the first Fresnel zone). Because the Pascagoula is surrounded by many U-shaped (oxbow) lakes, formed by meandering sections of river, the portion of the signal used for the power series fit needs to be limited to exclude the influence of these surrounding water bodies on the waveform corresponding to the river itself. However, using too little of the waveform makes it difficult to discern the true signal width. We find that fitting the power series to the portion of the signal within ~20% of its peak at river center produces the best correlation between the resulting river width and flowrate. This 20% value emphasizes the portion of the waveform nearest the center of the river crossing and least affected by other waterbodies or other sources of clutter nearby the river.