# Remotely Sensed Monitoring of Small Reservoir Dynamics: A Bayesian Approach

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Datasets

#### 2.1. Ground Truth

#### 2.2. Precipitation Data

#### 2.3. Radarsat-2 SAR Data

## 3. Methods

#### 3.1. Pre-Processing SAR Imagery

#### 3.2. Growing Bayesian Classifier

#### 3.2.1. Basic Growing Bayesian Classifier

_{k}is the class with k ∈ l, w, u for the land, water and unclassified classes, respectively, and ${\Phi}_{k}^{*}\left({\mathbf{x}}_{i}\right)$ the likelihood, Φ

_{k}(

**x**

_{i}), based on the pixel intensity vector,

**x**

_{i}, for pixel i multiplied with the growing prior, P(ω

_{k}|ν

_{j}), which is proportional to the posterior probability, according to:

_{j}is a conditional variable of the growing prior with state j, which is based on the classification of neighboring pixels; see Table 2. Here, the assumption is made that the likelihood function is independent of the state of the conditional variable, ν. Note that a pixel is only classified if its probability of being a member of a class is larger than the probability of remaining unclassified. The likelihood, Φ

_{u}(

**x**

_{i}), for a pixel to remain unclassified is defined as the minimum of the land and water likelihood for that pixel. The classification is therefore not governed by the priors alone, but based on the likelihood computed from the pixel intensity vector.

#### 3.2.2. Extended Growing Bayesian Classifier

## 4. Results and Discussion

#### 4.1. Polarimetric SAR Remote Sensing of Small Reservoirs for Different Backscatter Scenarios

#### 4.1.1. Smooth Open Water

#### 4.1.2. Water With Vegetation

#### 4.1.3. Wind-Induced Bragg Scatter

#### 4.1.4. Rain Event

#### 4.2. Comparison with Ground Truth

#### 4.3. Image Quality

#### 4.4. Time Series Analysis

^{t}

^{+1}change as well as from the 14 March acquisition; see Table 4.

^{t−}

^{1}). Additional updating based on the subsequent classification (prior τ

^{t+}

^{1}) only improves the classification in some cases. An extreme case of Bragg scatter is found in the 7 April image for SR120, where the full reservoir is affected and the contrast with the surrounding land significantly deteriorates. Here, the classification is mostly governed by the temporal priors, as can be seen from the large difference in the delineations with and without temporal priors. The classification at the previous time step is affected by rainfall; see the next paragraph. In the case that the delineation is updated with the classification from this time step, the small reservoir area is still overestimated. When updated with the classification from the subsequent time step, the overestimation is further limited. The discrepancy between the normal and the filtered time series (the 28 March acquisition is filtered out) of small reservoir areas for 7 April shows that the temporal priors are less effective when two low quality images follow each other (Figure 8).

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The study area in the Upper East Region of Ghana, overlaid with a base map of small reservoirs in the region.

**Figure 2.**Flow diagram for the growing Bayesian classifier: first, the seeds are initialized (

**top right**) for which a SAR reservoir image is required (

**top left**); then, the iterative Bayesian classification is performed (

**right middle**); finally, a growing filter is applied (

**right bottom**); the algorithm can readily be extended with additional information (

**left middle**).

**Figure 3.**Backscatter intensity distributions and scatter plots for the land and water classes from the samples of four distinct small reservoir backscatter scenarios, i. e., smooth open water, water with vegetation, Bragg scattering and backscatter during a rain event.

**Figure 4.**Jeffries-Matusita (JM) distances for the samples of three distinct backscatter scenarios from small reservoirs, where the error bars show the mean, minimum and maximum JM distances from the different samples.

**Figure 5.**Ground truth (yellow line) and delineation (red line) based on the ‘HH, HV’ polarization combination overlaid on Pauli RGB-images, with red colors for double bounce, green for volume scatter and blue for single bounce; note that the different color scales are used for the different Pauli components to enhance the image contrast.

**Figure 6.**Comparison between classified and ground truth areas of all 29 small reservoir from November 2012, based on the Differential Area Index (DAI) and the Jeffries Matusita (JM) distance.

**Figure 7.**Rainfall time senes (

**top**), the quality of an acquisition based on the Jeffries Matusita (JM) distance (

**middle**) and the mean backscatter intensity of the minimum delineated small reservoir area (

**bottom**), where the boxplots show the median, first and second quartile boundaries and the red crosses are outliers; the error bars show the mean and one standard deviation boundaries.

**Figure 8.**Time series of small reservoir delineation based on the ‘HH, HV’ polarization combination and the basic gBC (red line), the gBC updated with temporal prior τ

^{t−}

^{1}(blue line) and the gBC updated with both priors τ

^{t−}

^{1}and τ

^{t+}

^{1}(green line) overlaid on HH backscatter intensity images; the bottom graphs show the areal variation in time for the same reservoirs, where the crosses show the filtered time series without the rain-affected March 28 acquisition.

**Figure 9.**Time series of the cumulative classified area for 26 small reservoirs, based on the growing Bayesian classifier (gBC) with and without temporal priors (

**top**) and the gBC without temporal priors for different polarization combinations (

**bottom**).

Date | Year | Time/Pass | Beam Mode | Incidence Angle (degree) | Pixel Spacing (rg× ax) (m) |
---|---|---|---|---|---|

18 November | 2012 | 05:44:13/desc | FQ31 | 48.3–49.4 | 5.14 × 6.28 |

21 November | 2012 | 05:56:37/desc | FQ10 | 29.1–30.9 | 5.19 × 9.26 |

15 January | 2013 | 05:52:27/desc | FQ17W | 35.7–8.6 | 5.6 × 7.83 |

25 January | 2013 | 06:00:44/desc | FQ4W | 21.3–24.8 | 4.6 × 11.94 |

8 February | 2013 | 05:52:27/desc | FQ17W | 35.7–38.6 | 5.6 × 7.83 |

18 February | 2013 | 06:00:43/desc | FQ4W | 21.3–24.8 | 4.6 × 11.94 |

4 March | 2013 | 05:52:27/desc | FQ17W | 35.7–38.6 | 5.6 × 7.83 |

14 March | 2013 | 06:00:43/desc | FQ4W | 21.3–24.8 | 4.6 × 11.94 |

28 March | 2013 | 05:52:27/desc | FQ17W | 35.7–38.6 | 5.6 × 7.83 |

7 April | 2013 | 06:00:44/desc | FQ4W | 21.3–24.8 | 4.6 × 11.94 |

21 April | 2013 | 05:52:27/desc | FQ17W | 35.7–38.6 | 5.6 × 7.83 |

Growing Prior | v_{1} | v_{2} | v_{3} | v_{4} |
---|---|---|---|---|

land pixels | >=1 | >=1 | 0 | 0 |

water pixels | 0 | >=1 | >=1 | 0 |

P(ω_{land}) | 0.5 | 0.5 | 0 | 0 |

P(ω_{water}) | 0 | 0.5 | 0.5 | 0 |

P(ω_{unclassified}) | 0.5 | 0 | 0.5 | l.0 |

**Table 3.**Temporal conditional prior probabilities based on the classification of a pixel in the previous time step.

Prior τ^{t−1} | ${\tau}_{\mathbf{1}}^{\mathbf{t}-\mathbf{1}}$ | ${\tau}_{\mathbf{2}}^{\mathbf{t}-\mathbf{1}}$ | ${\tau}_{\mathbf{3}}^{\mathbf{t}-\mathbf{1}}$ |
---|---|---|---|

Classification in Time Step t-l | Land | Water | Unclassified |

P(ω_{land}) | 0.6 | 0.25 | 1/3 |

P(ω_{water}) | 0.2 | 0.5 | 1/3 |

P(ω_{unclassified}) | 0.2 | 0.25 | 1/3 |

**Table 4.**Temporal conditional prior probabilities based on the classification of a pixel in the subsequent time step.

Prior τ^{t+1} | ${\tau}_{\mathbf{1}}^{\mathbf{t}+\mathbf{1}}$ | ${\tau}_{\mathbf{2}}^{\mathbf{t}+\mathbf{1}}$ | ${\tau}_{\mathbf{3}}^{\mathbf{t}+\mathbf{1}}$ |
---|---|---|---|

Classification in time step t + 1 | Land | Water | Unclassified |

prior τ^{t+}^{1} dry season | |||

P(ω_{land}) | 0.5 | 0 | 1/3 |

P(ω_{water}) | 0.25 | 1 | 1/3 |

P(ω_{unclassified}) | 0.25 | 0 | 1/3 |

prior τ^{t+}^{1} rainy season/after rain | |||

P(ω_{land)} | 0.5 | 0.25 | 1/3 |

P(ω_{water}_{)} | 0.25 | 0.5 | 1/3 |

P(ω_{unclassified}) | 0.25 | 0.25 | 1/3 |

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**MDPI and ACS Style**

Eilander, D.; Annor, F.O.; Iannini, L.; Van de Giesen, N.
Remotely Sensed Monitoring of Small Reservoir Dynamics: A Bayesian Approach. *Remote Sens.* **2014**, *6*, 1191-1210.
https://doi.org/10.3390/rs6021191

**AMA Style**

Eilander D, Annor FO, Iannini L, Van de Giesen N.
Remotely Sensed Monitoring of Small Reservoir Dynamics: A Bayesian Approach. *Remote Sensing*. 2014; 6(2):1191-1210.
https://doi.org/10.3390/rs6021191

**Chicago/Turabian Style**

Eilander, Dirk, Frank O. Annor, Lorenzo Iannini, and Nick Van de Giesen.
2014. "Remotely Sensed Monitoring of Small Reservoir Dynamics: A Bayesian Approach" *Remote Sensing* 6, no. 2: 1191-1210.
https://doi.org/10.3390/rs6021191