# Response to Variations in River Flowrate by a Spaceborne GNSS-R River Width Estimator

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. CYGNSS Background

#### 2.2. Theoretical Basis of the High-Spatial-Resolution Land/Water Mapping Capability

- (τ, f) = delay and Doppler coordinates in the delay Doppler map (DDM)
- P
_{T}= transmitted power - G
_{R}= receive antenna gain - G
_{T}= transmit antenna gain - Λ = lag correlation function due to the correlation with a local replica of the GPS pseudorandom noise (PRN) code
- S = Doppler filter response due to selective filtering of the Doppler-shifted received signal
- $\overline{{r}_{T}},\overline{{r}_{R}}$ = vector distances from the specular point to the transmitter and receiver, respectively
- σ
_{0}= normalized scattering cross section of the rough surface (BRCS) - λ = signal wavelength (19 cm)
- $\overline{r}$ = vector distance from a point on the Earth’s surface to the specular point
- Z
_{f}= term to account for area/shape of smooth surface region affecting first Fresnel zone - $\mathsf{\Re}$ = surface Fresnel reflectivity for incidence angle $\theta $
- ${k}_{0}=2\pi /\lambda $; electromagnetic wavenumber
- h = surface rms height

_{inc}is the scattering area of the incoherent region bounded by the lag correlation and Doppler filter response functions. For the GPS L1 C/A signal used by CYGNSS, A

_{inc}is ~ 15 × 15 km

^{2}. Variations in both $\overline{{r}_{R}}$ and $\overline{{r}_{T}}$ are well parameterized by the incidence angle of the propagating signal at the specular reflection point. This is illustrated in Figure 2a,b, which respectively plot the incidence angle vs. $\overline{{r}_{R}}$ and vs. the relative signal strength between coherent and incoherent scatterers for the same 24-h collection of data. The greatest number of samples occurs near an incidence angle of ~30° and $\overline{{r}_{R}}$ = 600 km. An incidence angle of ~30° corresponds to the angle of maximum gain in the receive antenna pattern.

#### 2.3. Case Study: Pascagoula River

## 3. Results

^{2}coefficient of the regression is 0.97.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Histogram of propagation distances: (

**a**) $\overline{{r}_{R}}$ (from specular point to CYGNSS receiver); (

**b**) $\overline{{r}_{T}}$ (from GPS transmitter to specular point) for a full day of samples on 9 June 2017.

**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.

**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 4.**April 2019 raw IF data collections over the Pascagoula River: (

**a**) track locations; (

**b**) corresponding flowrates at the time of each overpass (color coded to match the track locations plotted on the left), plotted over the USGS flowrates over the time period spanning the data collections.

**Figure 5.**Fitted power series for each of the five April 2019 Pascagoula overpasses, using a threshold of 22% of the peak as the cutoff for the portion of the waveform to be fitted.

**Figure 6.**Linear regression between the river AGW derived from CYGNSS observations and the river flow rate measured by the USGS stream gauge. The R

^{2}coefficient is 0.97. Marker colors correspond to the tracks and flowrates shown in Figure 4.

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**MDPI and ACS Style**

Warnock, A.; Ruf, C. Response to Variations in River Flowrate by a Spaceborne GNSS-R River Width Estimator. *Remote Sens.* **2019**, *11*, 2450.
https://doi.org/10.3390/rs11202450

**AMA Style**

Warnock A, Ruf C. Response to Variations in River Flowrate by a Spaceborne GNSS-R River Width Estimator. *Remote Sensing*. 2019; 11(20):2450.
https://doi.org/10.3390/rs11202450

**Chicago/Turabian Style**

Warnock, April, and Christopher Ruf. 2019. "Response to Variations in River Flowrate by a Spaceborne GNSS-R River Width Estimator" *Remote Sensing* 11, no. 20: 2450.
https://doi.org/10.3390/rs11202450