# Prospects for Imaging Terrestrial Water Storage in South America Using Daily GPS Observations

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

#### 2.1. Hydrology

#### 2.2. Geodynamics

## 3. Material and Methods

#### 3.1. Datasets

#### 3.1.1. GPS Time Series

#### 3.1.2. Model for Continental Hydrology

#### 3.1.3. TRMM Rainfall Fields

#### 3.1.4. GRACE TWS Solutions

#### 3.2. Methods

#### 3.2.1. Forward Modeling: From Mass Loadings to Radial Displacements

#### 3.2.2. Inverse Modeling: From Radial Displacements to Mass Loadings

#### 3.2.3. Checkerboard Test: Model Resolution

## 4. Results

#### 4.1. Experiment 1: What Is the Potential Spatial Resolution of GPS-Imaged TWS over South America?

#### 4.2. Experiment 2: How About the Impact of the Varied Number of Daily GPS Data?

#### 4.3. Experiment 3: What Is the Result of Considering the Actual GPS Data?

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**(

**a**) The maximum correlations (circles) between GPS-observed radial displacements and GLDAS-TWS; the color bar depicts their respective lags (circles’ colors). Positive lag values mean GLDAS-TWS leads GPS radial displacements, and conversely, negative lag values mean GLDAS-TWS lags GPS radial displacements. (

**b**) The maximum correlations (circles) between GPS-observed radial displacements and precipitation (TRMM), and the respective lags (circles’ colors) in days. (

**c**) The maximum correlations (circles) between GLDAS-TWS and precipitation (TRMM) and the respective lags (circles’ colors) in days.

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**Figure 1.**Distribution of GPS stations (circles) over South America. The colors of the circles depict the number of years of observations, as shown in the color bar (within the map’s frame) for each GPS station. The colored surface shows the long-term changes in terrestrial water storage (TWS) for the period between April 2002 and June 2017 using GRACE data [51]. The plate boundaries were provided by Bird [52]. The arrows indicate horizontal plate motions [46]. The scale refers to the parallel 20${}^{\circ}$S in Albers projection.

**Figure 2.**(

**a**) The time series of radial displacements of each GPS station sorted by latitude from north to south. The right y-axis shows the approximated values of the latitude ranges. (

**b**) The number of stations available at each epoch (day) available for the inversion.

**Figure 3.**(

**a**) Recharged groundwater and the Earth’s surface; (

**b**) subsidence induced by groundwater drop (e.g., pumpage); (

**c**) shows the uplift due to the groundwater recharge; (

**d**) permanent subsidence due to the irreversible deformation caused by the compaction of aquitards. Source: Adapted from Galloway et al. [69].

**Figure 4.**Schematic of the experimental design using a closed-loop simulation. The top shows the arbitrary model used for the computation of synthetic loading data with a pattern of alternate high (+250 kg/m${}^{2}$) and low (−250 kg/m${}^{2}$) attenuation elementary squares, which is the pattern used in the so-called “checkerboard test”. The middle panel shows the displacements due to the loading induced by the synthetic loading patterns at each GPS station. The bottom panel shows the inverted model obtained from the synthetic data corresponding to the model on top, which is identical to the initial model.

**Figure 5.**Flowchart presenting the main steps of the experiments based on the methods and datasets described in Section 3.1 and Section 3.2, respectively. Comparisons are presented in the following sections accordingly.

**Figure 6.**Top panels show (

**a**) synthetic checkerboard patterns with positive and negative mass loadings, (

**b**) inverted checkerboard patterns, and (

**c**) residuals of the differences between “observed” and inverted mass loadings at a spatial resolution of $1.{0}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}1.{0}^{\circ}$. Middle Panels (

**d**,

**e**,

**f**) show the same results as Panels (a–c), respectively, but for a spatial resolution of $2.{0}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}2.{0}^{\circ}$. Bottom Panels (

**g**–

**i**) show the same results as Panels (a–c), respectively, but for a spatial resolution of $3.{0}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}3.{0}^{\circ}$. The dashed lines indicate a buffer zone of 5.0${}^{\circ}$ w.r.t. the boundary of South America.

**Figure 7.**Top panels show (

**a**) gridded mass loadings expressed by the RMS of the TWS series from GLDAS-Noah, (

**b**) inverted TWS recovered from the 397 forward displacements, and (

**c**) errors quantified as the difference between the input (a) and inverted loads (b) at a spatial resolution of $1.{0}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}1.{0}^{\circ}$. Bottom Panels (

**d**,

**e**,

**f**) show the same results as Panels (a–c), respectively, but for a spatial resolution of $3.{0}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}3.{0}^{\circ}$. The dashed lines in Panels (a,b,d,e) indicate a buffer zone of 5.0${}^{\circ}$ with respect to (w.r.t.) the boundary of South America, and the dot-marks in Panels (c) and (f) show the distribution of GPS sites.

**Figure 8.**(

**a**) Daily errors in terms of the RMSE for the GPS-imaged TWS w.r.t. the input model of the RMSs of the GLDAS-Noah TWS series. (

**b**) The same as (a), but the input model is the GLDAS-Noah TWS series for each day corresponding to the available GPS solutions.

**Figure 9.**(

**a**) Daily errors in terms of the RMSE for the GPS-imaged TWS w.r.t. GLDAS-Noah “TWS”. (

**b**) The GPS-imaged TWS over South America for 12 February 2017, equivalent to the inversion with the minimum RMSE as shown in (

**a**). (

**c**) GLDAS-Noah TWS for 12 February 2017. (

**d**) Residuals as the differences between GPS-imaged TWS and GLDAS-Noah TWS. The black dots indicate the distribution of the GPS sites used for the inversion.

**Figure 10.**(

**a**) Daily differences between GPS-imaged TWS and GLDAS-Noah TWS at each GPS site. (

**b**) The coefficient correlations (circles) and the RMSEs (colored circles with amplitudes depicted by the color bar) between the GPS-imaged TWS and GLDAS-Noah TWS at each GPS site.

**Table 1.**Summary of the results presented in Section 4.1, Section 4.2 and Section 4.3. The check marks (ticks) ✓ and ✗ stand for “yes” and “no”, respectively.

Synthetic Experiments | |||||||||
---|---|---|---|---|---|---|---|---|---|

Summary | Checkerboard | GLDAS-TWS | Daily GPS Data | ||||||

RMS of TWS | Daily TWS | ||||||||

Resolution | ${1}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}{1}^{\circ}$ | ${2}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}{2}^{\circ}$ | ${3}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}{3}^{\circ}$ | ${1}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}{1}^{\circ}$ | ${3}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}{3}^{\circ}$ | ${3}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}{3}^{\circ}$ | ${3}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}{3}^{\circ}$ | ${3}^{\circ}\phantom{\rule{0.166667em}{0ex}}\times \phantom{\rule{0.166667em}{0ex}}{3}^{\circ}$ | site |

No. of observ. | 397 | 397 | 397 | 397 | 397 | varied | varied | varied | - |

RMSE (kg/m${}^{2}$) | 233.88 | 163.00 | 3.90 | 38.34 | 1.10 | 3.29 | 4.50 | 80.49 | 53.48 |

Bias (kg/m${}^{2}$) | −0.85 | −0.76 | −0.02 | 12.86 | 0.13 | 0.50 | 0.11 | 3.36 | −0.29 |

Is it feasible? | ✗ | ✗ | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ * | ✓ |

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Ferreira, V.G.; Ndehedehe, C.E.; Montecino, H.C.; Yong, B.; Yuan, P.; Abdalla, A.; Mohammed, A.S.
Prospects for Imaging Terrestrial Water Storage in South America Using Daily GPS Observations. *Remote Sens.* **2019**, *11*, 679.
https://doi.org/10.3390/rs11060679

**AMA Style**

Ferreira VG, Ndehedehe CE, Montecino HC, Yong B, Yuan P, Abdalla A, Mohammed AS.
Prospects for Imaging Terrestrial Water Storage in South America Using Daily GPS Observations. *Remote Sensing*. 2019; 11(6):679.
https://doi.org/10.3390/rs11060679

**Chicago/Turabian Style**

Ferreira, Vagner G., Christopher E. Ndehedehe, Henry C. Montecino, Bin Yong, Peng Yuan, Ahmed Abdalla, and Abubakar S. Mohammed.
2019. "Prospects for Imaging Terrestrial Water Storage in South America Using Daily GPS Observations" *Remote Sensing* 11, no. 6: 679.
https://doi.org/10.3390/rs11060679