# Identifying Hydro-Geomorphological Conditions for State Shifts from Bare Tidal Flats to Vegetated Tidal Marshes

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## Abstract

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## 1. Introduction

^{2}-10³ km), and high temporal resolutions (sec) but large simulated periods (~decades). Therefore, a synthetic statistical assessment, including these factors, is expected to improve our understanding of the mechanisms that cause shifts between bare and vegetated ecosystem states and the predictability of such state shifts. The overall objective of this study is to develop the knowledge of where state shifts from the bare to vegetated state are likely to occur on a large spatial scale of an estuary (~326 km²), Western Scheldt estuary (SW Netherlands). To achieve this, a spatial statistical modeling approach that enables us to identify the locations of the shifts occurring in the intertidal zone is built. The model combines data on spatially-distributed elevation, tidal currents, and wind waves. Specifically, we use the model to address the following three questions:

- (1)
- Do stable states in vegetation biomass and elevation co-occur? To answer this question, we tested (1a) whether both vegetation biomass and elevation have a bimodal frequency distribution in intertidal zones; (1b) whether the spatial variation in vegetation biomass as a function of elevation shows an abrupt change from a bare to vegetated state (above a threshold elevation); and (1c) whether the temporal change in vegetation biomass is the largest in areas with an unstable intermediate elevation state;
- (2)
- Does hydrodynamics abruptly change between different states? We tested whether spatial variations in (2a) tidal currents and (2b) waves change abruptly between different biomass and elevation states, in order to identify potential mechanisms causing the two stable states, i.e., the biogeomorphic interactions between elevation, biomass, tidal currents, and waves;
- (3)
- Can we identify the location of state shifts? We examined whether we can identify the locations where shifts from bare state to vegetated state occur, based on integrating the spatially explicit data on elevation, tidal currents, and waves.

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Materials and Data Preprocessing

#### 2.2.1. Aerial Images and Vegetation Maps

#### 2.2.2. Elevation Data and Intertidal Zones

#### 2.2.3. Tidal Current Velocity from a TELEMAC 2D Model

#### 2.2.4. Wave Orbital Velocity from a SWAN Model

_{peak,bed}, which was given by the following equation, assuming linear sine theory and Rayleigh distributed wave heights,

#### 2.3. Data Analysis

#### 2.3.1. Spatial Distribution of Vegetation and Intertidal Elevation

#### 2.3.2. Spatial Variation of Currents and Waves

#### 2.3.3. Identification of the State Shift

^{2}, correct percentage for new marshes, the correct percentage for stable bare flats, and the overall correct percentage. The threshold p-level was determined as 50%. We also assessed the accuracy of the analysis by comparing the observed percentage of new vegetation with the quantified probability. In addition, the coverage of new vegetation was mapped for the new grids to validate the analysis spatially. The new vegetation coverage was calculated as the absolute number of newly vegetated pixels in a certain grid divided by the total number of pixels in the grid.

## 3. Results

#### 3.1. Spatial Distribution of Biomass and Elevation

#### 3.1.1. Bimodality in Biomass Distribution and Elevation Distribution

#### 3.1.2. Relations between Variations in Elevation and NDVI

#### 3.1.3. Abrupt Temporal Increase in Biomass in Intermediate Unstable Elevations

#### 3.2. Spatial Variation of Hydrodynamics in between the Different States

#### 3.2.1. Variation of Tidal Current and Wave Orbital Velocity in Relation with NDVI

#### 3.2.2. Variation of Tidal Current and Wave Orbital Velocity in Relation with Elevation

#### 3.3. Identification of State Shift

^{2}, the overall percentage of correctly identified pixels, and the percentage of correctly identified pixels that stay bare. In contrast, the percentage of correctly identified pixels that shift to new marsh vegetation increases with increasing pixel size, i.e., a reduction in spatial resolution. The correct percentage for new marshes rises rapidly, from 30% to 50% when the pixel size increases from 2 to 30 m. With a further increase in pixel size, the increase in the correct percentage slows down. See below for further details on the logistic regression of the 30 m resolution data.

^{2}= 0.320), with slightly better performance than elevation (Model 1; Nagelkerke R

^{2}= 0.304) and much better performance than wave orbital velocity (Model 3; Nagelkerke R

^{2}= 0.168). The Nagelkerke R

^{2}increased considerably when including both elevation and tidal current velocity in the model (Model 4; Nagelkerke R

^{2}= 0.435). Adding wave velocity to the model further raised the Nagelkerke R

^{2}value to 0.475 (Model 7). The overall percentage of correctly identified pixels varied between 84% and 89%. The percentage of correctly identified stable bare pixels varied between 96% and 99%. The percentage of correctly identified new marsh pixels increased from 23% to 50% when using more explanatory variables.

## 4. Discussion

#### 4.1. Do Stable States in Vegetation Biomass and Elevation Co-Occur?

#### 4.2. Does Hydrodynamics Abruptly Change between Different States?

#### 4.3. Can We Predict the Location of State Shifts?

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Location of the Scheldt estuary in Western Europe; (

**b**) Scheldt estuary with indications of tide gauges (red dots), locations of measured discharge transects (red lines), study area Western Scheldt (grey striped box), model boundaries (black line) and bathymetry (the elevations are expressed relative to the Dutch Ordnance Level, NAP, which is close to the mean sea level at the Dutch coast); (

**c**) Detail of measured discharge transects for ebb and flood channel; (

**d**) Locations of Acoustic Doppler Current Profilers (ADCP) measurements on one of the shoals.

**Figure 2.**Wave generation and propagation model grid layout for Grid 0 (

**a**) and Grid 1–11 (

**b**) overlaid with available measurement locations for waves (i.e., WCT1, PVT1, HAN1, HAWI, HFPL, and HFP1) and wind (i.e., HFPL, TNWS, and HAW1).

**Figure 3.**Bimodal frequency distribution of normalized difference vegetation index (NDVI) values (as proxy of vegetation biomass) in (

**a**) 2004 and (

**b**) 2011; intertidal elevations in (

**c**) 2004 and (

**d**) 2011. The elevation is relative to the mean high water level (MHWL). The proportion on the y-axis is computed as the number of pixels in each NDVI class (every 0.01) or relative elevation class (every 0.1 m) to the total number of the pixels for all intertidal pixels (red bold curve), vegetated marsh pixels (green dashed curve), and bare flat pixels (blue dotted curve). NDVI ranges are indicated (with vertical black dashed lines) and denoted as “stable bare” (proportion above threshold), “unstable” (below threshold), and “stable vegetated” (above threshold), based on a threshold proportion of 0.5% (horizontal black dashed line). Elevation ranges are indicated (with vertical black dashed lines) and denoted as “stable low-elevated” (proportion above threshold), “unstable” (below threshold), and “stable high-elevated” (above threshold), based on a threshold proportion of 1.5% (horizontal black dashed line).

**Figure 4.**(

**a**) Variation in NDVI in 2004 as a function of elevation in 2004. Circles denote the mean NDVI value for elevation classes with 0.1 m intervals; error bars denote 25th and 75th percentiles for each elevation class; (

**b**) Variation of elevation in 2004 as a function of NDVI in 2004. Circles denote the mean elevation for NDVI classes of 0.01 interval; error bars denote 25th and 75th percentiles for each NDVI class. Stable and unstable NDVI ranges and elevation ranges are indicated, as determined from Figure 3.

**Figure 5.**NDVI changes between 2004 and 2011 as a function of elevation in 2004. Circles denote the mean NDVI change for elevation classes of 0.1 m interval; error bars denote 25th and 75th percentiles for each elevation class. Stable and unstable elevation ranges are indicated, as determined from Figure 3.

**Figure 6.**Variation of tidal current velocity (

**a**) and wave orbital velocity (

**b**) as a function of NDVI in 2004. Circles denote the mean velocity for NDVI classes of 0.01 interval; error bars denote 25th and 75th percentiles for each elevation class. Stable and unstable NDVI ranges are indicated, as determined from Figure 3.

**Figure 7.**Variation of tidal current velocity (

**a**) and wave orbital velocity (

**b**) as a function of elevation in 2004. Circles denote the mean velocity for elevation classes of 0.1 m interval; error bars denote 25th and 75th percentiles for each elevation class. Stable and unstable elevation ranges are indicated, as determined from Figure 3.

**Figure 8.**Performance of logistic regression model (Equation (7) in Table 2) to identify pixels that stayed bare and pixels that shifted from a bare to vegetated state between 2004 and 2011. (

**a**) Nagelkerke R

^{2}(black solid line) and percentage of correctly identified pixels that stayed bare (blue dotted line), that shifted to new marsh vegetation (green dot–dash line) and the overall percentage of correctly identified pixels (red dashed line), all as a function of increasing pixel size obtained by aggregation; (

**b**) Probability map for a shift from bare to vegetated state based on the Logistic Regression Model No. 7 for a pixel resolution of 30 × 30 m; (

**c**) Observed percentage of pixels that shifted from a bare to vegetated state between 2004 and 2011 within the grids of 30 × 30 m, based on the aerial photograph with a resolution of 0.5 × 0.5 m. The shoals noted are Hooge Platen (A) and Walsoorden (B); (

**d**) Observed percentage of new marshes between 2004 and 2011 in relation to the identified probability of new marshes based on the Logistic Regression Model No. 7.

Grid | Origin | Rotation | Length | Grid Spacing | |||
---|---|---|---|---|---|---|---|

E [m] | N [m] | [°] | x [km] | y [km] | x [km] | y [km] | |

0 | −113,200 | 271,906 | 38.303 | 293 | 148 | 2.9 | 3 |

1 | 16,023 | 376,356 | 352.014 | 62.4 | 19.5 | 0.19 | 0.19 |

2 | 25,226 | 375,297 | 352.014 | 52 | 16.5 | 0.1 | 0.1 |

3 | 35,934 | 376,418 | 326.089 | 5.69 | 2.4 | 0.04 | 0.02 |

4 | 45,632 | 376,523 | 8.787 | 6.84 | 3.45 | 0.05 | 0.02 |

5 | 53,603 | 374,887 | 37.622 | 4.64 | 2.11 | 0.04 | 0.02 |

6 | 29,873 | 378,285 | 347.418 | 8.19 | 4.04 | 0.04 | 0.04 |

7 | 37,522 | 378,999 | 327.858 | 12.4 | 3.3 | 0.04 | 0.04 |

8 | 54,806 | 377,049 | 69.927 | 8.08 | 2.99 | 0.04 | 0.04 |

9 | 55,874 | 380,301 | 350.768 | 4.8 | 3.67 | 0.04 | 0.04 |

10 | 61,203 | 377,403 | 347.418 | 8.2 | 3.33 | 0.04 | 0.04 |

11 | 68,404 | 369,852 | 34.401 | 10.5 | 6.93 | 0.04 | 0.02 |

**Table 2.**Logistic regression models identifying the shift from bare to vegetated state as a function of elevation, tidal current velocity, and wave orbital velocity, with evaluating coefficients.

No. | Parameters | Equations | Nagelkerke R^{2} | Overall Correct Percentage | Correct Percentage for New Marshes | Correct Percentage for Stable Bare Flats |
---|---|---|---|---|---|---|

1 | Elevation (E) | $\mathrm{P}=\frac{{\mathrm{e}}^{0.603+1.4\times \mathrm{E}}}{1+{\mathrm{e}}^{0.603+1.4\times \mathrm{E}}}$ | 0.304 | 85.4 | 22.4 | 97.7 |

2 | Current velocity (C) | $\mathrm{P}=\frac{{\mathrm{e}}^{2.080-18\times \mathrm{C}}}{1+{\mathrm{e}}^{2.080-18\times \mathrm{C}}}$ | 0.320 | 84.2 | 23.1 | 96.1 |

3 | Wave velocity (W) | $\mathrm{P}=\frac{{\mathrm{e}}^{0.304-60\times \mathrm{W}}}{1+{\mathrm{e}}^{0.304-60\times \mathrm{W}}}$ | 0.168 | 84.7 | 11.2 | 99.1 |

4 | Elevation, current velocity | $\mathrm{P}=\frac{{\mathrm{e}}^{3.032+1\times \mathrm{E}-15\times \mathrm{C}}}{1+{\mathrm{e}}^{3.032+1\times \mathrm{E}-15\times \mathrm{C}}}$ | 0.435 | 88.8 | 47.3 | 96.9 |

5 | Elevation, wave velocity | $\mathrm{P}=\frac{{\mathrm{e}}^{1.722+1.1\times \mathrm{E}-50\times \mathrm{W}}}{1+{\mathrm{e}}^{1.722+1.1\times \mathrm{E}-50\times \mathrm{W}}}$ | 0.359 | 86.1 | 34.5 | 96.2 |

6 | Current velocity, wave velocity | $\mathrm{P}=\frac{{\mathrm{e}}^{3.739-17\times \mathrm{C}-60\times \mathrm{W}}}{1+{\mathrm{e}}^{3.739-17\times \mathrm{C}-60\times \mathrm{W}}}$ | 0.412 | 87.1 | 38.4 | 96.6 |

7 | Elevation, current velocity, wave velocity | $\mathrm{P}=\frac{{\mathrm{e}}^{4.055+0.8\times \mathrm{E}-14\times \mathrm{C}-40\times \mathrm{W}}}{1+{\mathrm{e}}^{4.055+0.8\times \mathrm{E}-14\times \mathrm{C}-40\times \mathrm{W}}}$ | 0.475 | 89.0 | 50.1 | 96.6 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, C.; Smolders, S.; Callaghan, D.P.; van Belzen, J.; Bouma, T.J.; Hu, Z.; Wen, Q.; Temmerman, S.
Identifying Hydro-Geomorphological Conditions for State Shifts from Bare Tidal Flats to Vegetated Tidal Marshes. *Remote Sens.* **2020**, *12*, 2316.
https://doi.org/10.3390/rs12142316

**AMA Style**

Wang C, Smolders S, Callaghan DP, van Belzen J, Bouma TJ, Hu Z, Wen Q, Temmerman S.
Identifying Hydro-Geomorphological Conditions for State Shifts from Bare Tidal Flats to Vegetated Tidal Marshes. *Remote Sensing*. 2020; 12(14):2316.
https://doi.org/10.3390/rs12142316

**Chicago/Turabian Style**

Wang, Chen, Sven Smolders, David P. Callaghan, Jim van Belzen, Tjeerd J. Bouma, Zhan Hu, Qingke Wen, and Stijn Temmerman.
2020. "Identifying Hydro-Geomorphological Conditions for State Shifts from Bare Tidal Flats to Vegetated Tidal Marshes" *Remote Sensing* 12, no. 14: 2316.
https://doi.org/10.3390/rs12142316