# Estimating River Depth from SWOT-Type Observables Obtained by Satellite Altimetry and Imagery

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Case Study

- The Po River with its narrow width (150–650 m) highlights the limitations of both altimetry and imagery.
- We have access to a variety of in situ data for the validation purposes.

## 3. Data

#### 3.1. In Situ Data

#### 3.2. Water Level from Satellite Altimetry

- Normalization of the data between zero and one: The measurements are merged by normalizing the time series according to their statistical characteristics. This step helps to make the range for the distribution of water level variations at different virtual stations consistent. For the merging process, the data of each virtual station is normalized by assigning the third percentile to zero and the 85th percentile to one.
- Confidence limit definition of 99% of a Student’s t-test for a sliding time window: The length of the time window can be experimented with to achieve the best performance. Here, a time window of one month (15 days before and 15 days after the selected measurement) is chosen as it leads to optimal results in terms of time series behavior and the number of identified outliers.
- Outlier identification and rejection: The identification and the rejection of the outliers is carried out by an iterative data snooping method and by iteratively updating the confidence limits. The data snooping method searches for the observation (always one observation) with the largest gross error [42].
- Rescaling of normalized values to their corresponding river water level heights: After removing the outliers, the combined normalized altimetric values are ready to be rescaled back to their true water level values.
- Constructing the time series: After rescaling, we now have a cloud of measurements with their corresponding uncertainty for the selected location along the river, which is free from outliers. The dense time series of water level can then be obtained by connecting the measurements using a three-point distance weighted moving averaging.

#### 3.3. River Width from Satellite Imagery

## 4. Methodology to Estimate River Depth

## 5. Results, Validation and Discussion

## 6. Perspective for the SWOT Mission

- Satellite altimetry is put on an operational footing through the Sentinel 3 series of the European Copernicus program. At the same time, research satellites such as CryoSat-2, SARAL/AltiKa or Jason-3 remain in orbit and provide complementary space-time sampling. This constellation addresses many current limitations and opens a significant area of investigation into the operational use of altimetry missions for hydrological purposes. Developing methods to generate dense time series of water level using altimetry data, demonstrated in this study, raise the hope of using operational altimetry together with SWOT data in the future for a better monitoring of temporal dynamics in many rivers around the world.
- Remote sensing techniques have been introduced as viable choices to monitor surface water variations [5]. Optical and SAR satellite imagery missions provide the opportunity to monitor surface water extent repeatedly at appropriate time intervals. Recent missions provide images with better spatial and temporal resolution. Different Landsat missions have been gathering images in various multispectral bands from the Earth since 1980. Recently, Landsat 8 with 30 m spatial resolution has provided monthly images of the Earth’s surface. Applications that demand a high temporal resolution preferably make use of the daily snapshots of MODIS imagery with 250-m resolution. Since 2015, Sentinel-2 has provided images with better resolution (10 m, 20 m, 60 m) and also a high revisit time (five days). On the other hand, SAR missions with images from ERS-1, ERS-2 and ENVISAT in C-band are the main sources for spatial water area monitoring in the tropical area, which is cloudy and rainy most of the year [12]. TerraSAR-X in X-band provides high resolution images with 1-, 2- and-3 meter pixel size every two days. From 2014 onwards, Sentinel-1A has provided continuous imagery (day, night and all weather) in C-band, expanding our understanding of surface water. Therefore, developing reliable algorithms to obtain reliable dynamic river masks, as developed by [38] and implemented in this study, gives the perspective of the SWOT mission that the results from different imagery sensors could be combined with the results from SWOT for a better monitoring of river masks in the future.
- In terms of river depth estimation, our results in Figure 11, Figure 12 and Figure 13 highlight the weaker dependency of error in river depth estimation to the error of river width and river discharge. This means that a preliminary result of river width and a coarse river discharge would be enough to estimate river depth. This is especially important for discharge algorithms, which work based on Manning’s flow resistance equation, and the initial values of variables play an important role in the fast and precise estimation of discharge. Moreover, this result would mean that one could use a rough estimation of river discharge instead of in situ data and still receive acceptable results for river depth.

## 7. Summary and Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Comparison of Water Level and Effective River Width with Discharge

**Figure A1.**Comparison of water level time series and discharge at nearby gauging stations for 16 reaches along the Po River.

**Figure A2.**Comparison of effective river width and discharge at close-by gauging stations for 16 reaches along the Po River.

**Figure A3.**Sections along Reach 4. The red straight line represents the average water level obtained from altimetry.

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**Figure 1.**Available stations (updated in March 2017) with discharge data according to the Global Runoff Data Centre (GRDC) database (http://www.bafg.de/GRDC) for different years from 1970–2013.

**Figure 2.**A schematic representation of a river with observable parameters (black) and unobservable ones (red, orange) from space. ${H}_{0}$ is the average riverbed’s height that does not correspond to the height of the deepest location in the channel section.

**Figure 3.**The Po River flowing eastward in Italy. The red triangles indicate the location of virtual stations and the white ones the location of gauging stations from west to east: Piacenza, Cremona, Borgoforte, Sermide and Pontelagoscuro.

**Figure 4.**(Top panel) Water level time series from satellite altimetry and effective river width from satellite imagery for Reach 12. (Bottom panel) Scatter plot of river discharge against water level (correlation coefficient = 0.73) and effective river width (correlation coefficient = 0.52).

**Figure 5.**(Top panel) A MODIS image of the Po river with the selected river reaches. (Bottom panel) River mask extracted applying the proposed method by [38]. Date: 28 July 2000.

**Figure 6.**Estimated river bed profile along the Po River for 16 defined reaches. VS refers to virtual station.

**Figure 7.**Scatter plot of estimated ${H}_{0}$ using discharge data of different gauging stations along the Po River.

**Figure 8.**Estimated river bed height by considering 20%, 40%, 60%, 80% and 100% of data in the time series of water level, width and discharge along the Po River for 16 defined reaches.

**Figure 9.**Estimated residual for observations of discharge $\widehat{{e}_{\mathrm{Q}}}$, water level $\widehat{{e}_{\mathrm{H}}}$ and effective river width $\widehat{{e}_{\mathrm{W}}}$ for the first reach along the Po River.

**Figure 10.**Bar plot of difference between estimated riverbed’s height $\widehat{{H}_{0}}$ and those from in situ using discharge data of different gauging stations along the Po River.

**Figure 11.**Time series of error in ${H}_{0}$ due to the error in Q, H, W and S for Model (1) over Reach 1.

**Figure 12.**Average error in ${H}_{0}$ due to errors in discharge, water level, effective river width and slope over all 16 reaches.

**Figure 13.**The time variable sensitivity of estimated ${H}_{0}$ to discharge observation $\partial {H}_{0}/\partial Q$.

Reach Number | Starting Point | Ending Point | Reach Length | ||||
---|---|---|---|---|---|---|---|

Lat. | Lon. | Chainage | Lat. | Lon. | Chainage | ||

(${}^{\xb0}$) | (${}^{\xb0}$) | (km) | (${}^{\xb0}$) | (${}^{\xb0}$) | (km) | (km) | |

1 | 45.11 | 9.12 | 250.00 | 45.10 | 9.34 | 270.00 | 20.00 |

2 | 45.10 | 9.34 | 270.00 | 45.11 | 9.55 | 290.00 | 20.00 |

3 | 45.11 | 9.55 | 290.00 | 45.08 | 9.66 | 310.00 | 20.00 |

4 | 45.08 | 9.66 | 310.00 | 45.07 | 9.82 | 329.36 | 19.35 |

5 | 45.07 | 9.82 | 329.36 | 45.09 | 9.90 | 341.16 | 11.80 |

6 | 45.09 | 9.90 | 341.16 | 45.03 | 10.07 | 369.36 | 28.20 |

7 | 45.03 | 10.07 | 369.36 | 45.00 | 10.28 | 389.34 | 19.98 |

8 | 45.00 | 10.28 | 389.34 | 44.94 | 10.46 | 409.37 | 20.02 |

9 | 44.94 | 10.46 | 409.37 | 44.96 | 10.66 | 429.37 | 20.00 |

10 | 44.96 | 10.66 | 429.37 | 45.04 | 10.79 | 449.36 | 20.00 |

11 | 45.04 | 10.79 | 449.36 | 45.07 | 11.00 | 469.33 | 19.97 |

12 | 45.07 | 11.00 | 469.33 | 45.06 | 11.21 | 489.36 | 20.03 |

13 | 45.06 | 11.21 | 489.36 | 44.97 | 11.39 | 509.36 | 20.00 |

14 | 44.97 | 11.39 | 509.36 | 44.92 | 11.57 | 529.34 | 19.98 |

15 | 44.92 | 11.57 | 529.34 | 44.96 | 11.75 | 549.36 | 20.02 |

16 | 44.96 | 11.75 | 549.36 | 44.98 | 11.98 | 569.35 | 19.99 |

Variable | Dataset | Resolution | Time Period | Source | |
---|---|---|---|---|---|

Spatial | Temporal | ||||

Effective river width W | MODIS | 250 m | 8 d | 2000–2014 | [38] |

Variable Surface water level H and slope S | $\underbrace{\mathrm{Multi}-\mathrm{mission}\phantom{\rule{4.pt}{0ex}}\mathrm{altimetry}}$ | – | 3 d | 2000–2014 | [39] |

TOPEX/Poseidon | – | 10 d | 1992–2002 | ||

ENVISAT | – | 35 d | 2002–2010 | ||

TOPEX/Poseidon XT | – | 10 d | 2002–2005 | ||

ENVISAT XT | – | 30 d | 2010–2012 | ||

CryoSat-2 | – | 369 d | 2012–2014 | ||

Jason-2 | – | 10 d | 2008–2016 | ||

River discharge Q | in situ | – | 1 d | 1995–2013 | AIPO |

Channel sections | surveyed | every 250 m | – | – | AIPO |

**Table 3.**The location and height of available in situ data along the Po River. The height refers to the mean water level derived from daily time series.

Name | Lat. | Lon. | Elevation | Average Width | Average Flow Velocity | Average Discharge |
---|---|---|---|---|---|---|

(${}^{\xb0}$) | (${}^{\xb0}$) | (m) | (km) | (m/s) | (m${}^{3}$/s) | |

Piacenza | 45.06 | 9.70 | 42.37 | 106 | 0.61 | 933 |

Cremona | 45.13 | 9.99 | 29.03 | 157 | 0.82 | 1075 |

Borgoforte | 45.05 | 10.75 | 14.05 | 164 | 0.84 | 1313 |

Sermide | 45.02 | 11.29 | 9.50 | 329 | 0.44 | 1378 |

Pontelagoscuro | 44.89 | 11.61 | 3.48 | 175 | 3.01 | 1477 |

**Table 4.**Estimated river bed height ${H}_{0}$ using the two selected models, for which discharge data of the nearest gauge are used.

Reach | ${\mathit{H}}_{0}^{\mathbf{ins}}$ (m) | Model by Bjerklie et al. [9] | Model by Dingman and Sharma [36] | ||||
---|---|---|---|---|---|---|---|

$\widehat{\mathit{a}}$ | $\widehat{{\mathit{H}}_{0}}$(m) | $\widehat{{\mathit{H}}_{0}}-{\mathit{H}}_{0}^{\mathbf{ins}}$ (m) | $\widehat{\mathit{a}}$ | $\widehat{{\mathit{H}}_{0}}$ (m) | $\widehat{{\mathit{H}}_{0}}-{\mathit{H}}_{0}^{\mathbf{ins}}$ (m) | ||

1 | 50.27 | 0.69 | 50.37 ± 0.15 | 0.10 | 0.39 | 50.66 ± 0.14 | 0.39 |

2 | 45.62 | 0.60 | 44.72 ± 0.15 | 0.89 | 0.30 | 44.96 ± 0.14 | 0.66 |

3 | 40.09 | 1.36 | 41.47 ± 0.10 | 1.38 | 0.67 | 41.69 ± 0.09 | 1.59 |

4 | 35.91 | 2.06 | 40.73 ± 0.03 | 4.83 | 0.88 | 40.85 ± 0.03 | 4.94 |

5 | 32.20 | 29.20 | 32.07 ± 0.01 | 0.12 | 11.95 | 32.13 ± 0.01 | 0.07 |

6 | 24.60 | 0.80 | 24.91 ± 0.09 | 0.31 | 0.40 | 25.16 ± 0.08 | 0.57 |

7 | 20.63 | 0.22 | 16.06 ± 0.31 | 4.56 | 0.13 | 16.53 ± 0.31 | 4.10 |

8 | 17.18 | 0.27 | 13.06 ± 0.26 | 4.12 | 0.16 | 13.58 ± 0.26 | 3.60 |

9 | 12.92 | 0.74 | 12.07 ± 0.14 | 0.85 | 0.42 | 12.48 ± 0.13 | 0.44 |

10 | 11.54 | 0.50 | 9.37 ± 0.16 | 2.17 | 0.27 | 9.77 ± 0.16 | 1.77 |

11 | 7.38 | 0.53 | 7.04 ± 0.16 | 0.34 | 0.29 | 7.48 ± 0.16 | 0.10 |

12 | 2.70 | 1.40 | 5.64 ± 0.07 | 2.94 | 0.73 | 5.91 ± 0.07 | 3.21 |

13 | 2.08 | 1.25 | 3.00 ± 0.10 | 0.92 | 0.66 | 3.31 ± 0.09 | 1.23 |

14 | −0.26 | 0.58 | −1.49 ± 0.20 | 1.23 | 0.34 | −0.87 ± 0.19 | 0.61 |

15 | −3.00 | 4.83 | 1.07 ± 0.04 | 4.07 | 2.28 | 1.23 ± 0.04 | 4.24 |

16 | −6.29 | 4.97 | −1.32 ± 0.08 | 4.97 | 2.64 | −1.07 ± 0.07 | 5.22 |

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## Share and Cite

**MDPI and ACS Style**

Tourian, M.J.; Elmi, O.; Mohammadnejad, A.; Sneeuw, N.
Estimating River Depth from SWOT-Type Observables Obtained by Satellite Altimetry and Imagery. *Water* **2017**, *9*, 753.
https://doi.org/10.3390/w9100753

**AMA Style**

Tourian MJ, Elmi O, Mohammadnejad A, Sneeuw N.
Estimating River Depth from SWOT-Type Observables Obtained by Satellite Altimetry and Imagery. *Water*. 2017; 9(10):753.
https://doi.org/10.3390/w9100753

**Chicago/Turabian Style**

Tourian, Mohammad J., Omid Elmi, Abolfazl Mohammadnejad, and Nico Sneeuw.
2017. "Estimating River Depth from SWOT-Type Observables Obtained by Satellite Altimetry and Imagery" *Water* 9, no. 10: 753.
https://doi.org/10.3390/w9100753