# Global Sensitivity Analysis for Canopy Reflectance and Vegetation Indices of Mangroves

^{*}

## Abstract

**:**

## 1. Introduction

_{ab}) and average leaf inclination angle (θ

_{l}), and evaluating the uncertainties caused by these factors. This study found that leaf parameters such as C

_{ab}and leaf dry matter content (C

_{m}) had an increasing impact on the uncertainty of estimated LAI towards higher LAI and θ

_{l}was the most critical factor for LAI estimation if an ellipsoidal distribution [18] was used. Xiao et al. [19] also adopted EFAST and model simulations to investigate the sensitivities of reflectance and VIs to biophysical and biochemical parameters at the leaf, canopy and regional levels. The importance of leaf parameters reduced at the canopy level, especially for a LAI value of 0–3, where LAI dominated except for the absorption bands of C

_{ab}and leaf water content (C

_{w}). Although the contributions of LAI and soil were still evident for a sparse canopy, the fractional cover of vegetation (fCv) dominated at the regional level. The importance of LAI and soil dropped significantly for LAI > 3 at both the canopy and regional levels. Mousivand et al. [20] proposed an improved design and sampling for SA to identify influential and non-influential factors on canopy reflectance based on the SLC model [12], in which soil moisture (SM) and fCv were explicitly considered. fCv, LAI, θ

_{l}and SM were recognised as the most influential factors for a LAI range of 0–6.

_{ab}and θ

_{l}. Both radiative transfer simulations and linear spectral mixture simulations based on real endmembers were applied. The new VIs were found to have a higher sensitivity to LAI and θ

_{l}and better capacity in separating aquatic and terrestrial vegetation compared with previous VIs for terrestrial vegetation such as NDVI. Unfortunately, the fCv in 4SAIL2 was fixed to 1, and thus its impact was not discussed. Zhou et al. [22] conducted EFAST for emergent and submerged vegetation based on a CRM model for aquatic vegetation [23]. Four scenarios were adopted according to the combinations of shallow or deep water and sparse or dense canopies. Canopy reflectance spectra and four VIs, including NDAVI and WAVI for Sentinel-2A (S2A) images, were simulated. The most influential factors were found to be different for two vegetation types, with leaf and canopy parameters being dominant for emergent vegetation while water components accounted for most variability in canopy reflectance of submerged vegetation. For emergent vegetation, the total order sensitivity indices of all four VIs to LAI were high for a sparse canopy but dropped notably for a dense canopy. NDAVI outperformed the other three VIs for a dense emergent canopy in terms of their sensitivities to LAI.

## 2. Methodology

#### 2.1. Overview

#### 2.2. Canopy Reflectance Model of Mangroves

_{ab}, PAI, fCv, L2T ratio, inclination distributions of leaves and woody material and environmental factors such as the water body. It could be regarded as an extension of a previous CRM for aquatic vegetation [23], which was a revision of the PROSAIL model. Mangroves were divided into three layers as in [28]: the understory (L1), the stem (L2) and the crown (L3) layers (Figure 2). The layer index would be added to the variable names in the following to distinguish them from each other, e.g., PAI(3) for the PAI of the crown layer. The height of the understory was assumed to be the same as water depth (H

_{w}), and water was not allowed to immerse the crown as that could change canopy reflectance significantly [29]. Stems were assumed to be covered by the crowns and hence only had a minor contribution to canopy reflectance. Thus, the stem layer was assigned a low PAI value of 0.5 and a low fCv value of 0.15, according to [28]. Similarly, most factors with regard to the optically active components in the water body and other environmental factors such as bottom reflectance were also fixed as their impact on canopy reflectance was minor when covered by the canopy. For example, the contribution of suspended particles in the background water on canopy reflectance was around 10% or lower and mainly in the visible region [22,28]. Therefore, more attention was paid to the crown, the understory and H

_{w}, and other factors were beyond the scope of this study. H

_{w}corresponded to the changing tidal height. PAI(1) and fCv(1) were employed to explore if there were any potential contributions from the understory to the observed canopy reflectance, especially for a sparse canopy.

#### 2.3. Mangrove Scenarios

#### 2.3.1. Factors, Their Ranges and Distributions

#### 2.3.2. Correlated PAI(3) and fCv(3)

#### 2.4. Vegetation Indices

_{w}. These indices were either widely applied for terrestrial vegetation such as NDVI [34] and EVI [35] or in particular, proposed for aquatic vegetation such as NDAVI [36]. Some of the VIs for aquatic vegetation included shortwave infrared (SWIR) bands to address the existence of background water, e.g., RGVI [37] and WFI [38].

#### 2.5. Sensitivity Analysis Methods

#### 2.5.1. Variance-Based Sensitivity Analysis

_{1}, X

_{2}, …, X

_{k}), the variance (V(·)) of Y can be decomposed as [14,15]:

_{i}could be represented by the expected reduction in output variance if X

_{i}could be fixed [15]:

_{i}or

**X**

_{~i}indicated that the operation (E(·) or V(·)) was taken over X

_{i}or all factors but X

_{i}. The total order indices ${S}_{i}^{\mathrm{T}}$ could be written as [15]:

_{i}could be fixed. Other partial variances in Equation (1) corresponded to the interactions among input factors, and more details could be found in [15]. Both first and total order indices were broadly used, but this study only focused on total order indices. Due to numerical errors, this approach might produce negative sensitivity indices, usually corresponding to noninfluential factors [7]. Hence, negative values were reset to zero.

^{®}was employed in this study as it also provided a DBSA method. Trial tests showed that the computed sensitivity indices in VBSA could be affected by the number of samples, especially for NRM. Multiple sample sizes from 16,000 (1000 × 16) to 128,000 (8000 × 16) with an increment of 16,000 were tested for SPS_NRM and DEN_NRM. Finally, 112,000 samples were generated for each VBSA case as the computed sensitivity indices of reflectance spectra were consistent and stable.

#### 2.5.2. Density-Based Sensitivity Analysis

_{u}samples were randomly generated for a model of k input factors Y = f(X

_{1}, X

_{2}, … X

_{k}), to evaluate the empirical unconditional CDF of output F

_{Y}(Y). Second, n samples were generated for each input factor X

_{i}and acted as conditional points. At each conditional point, N

_{c}random samples were generated over

**X**

_{~i}to obtain the empirical conditional CDF of output ${F}_{Y|{X}_{i}}\left(Y\right)$. The Kolmogorov–Smirnov (KS) statistic was applied as a measure of the distance between unconditional and conditional CDFs (as cited in [25]):

_{i}. Considering all the conditional points of an input factor X

_{i}, another statistic, e.g., the maximum or the median, was computed over all conditional points of X

_{i}to obtain the PAWN sensitivity index ${P}_{i}^{\mathrm{T}}$ [25]:

## 3. Results

#### 3.1. General Scenario

_{ab}rose and fell abruptly and the NIR bands where the influence of L2T(3) dropped. WIDFa(3) was the next most influential factor, especially in the SWIR, followed by PAI(3) across NIR and SWIR bands. Comparatively, PAWN NSIs were slightly different from VBSA NSIs in that PAI(3) had higher NSI values while the NSI values of L2T(3) and fCv(3) were lower, especially in SWIR (Figure 5f). It is worth noting that H

_{w}had higher NSI values in visible bands compared with its NSI values in other regions.

_{w}, their KS values only grew noticeably if their values decreased to zero, e.g., lower than 1 for PAI(3). This implied that PAI(3) was more influential when its value was low.

#### 3.2. Sparse Mangroves—Uniform Input Probability Distributions

_{w}in visible bands (Figure 5b,g). In the NIR region, the NSI values of PAI(1) and fCv(1) slightly increased in PAWN, but only the NSI values of fCv(1) increased in VBSA. This implied that the understory and water background had a larger impact on SPS, which was intuitive. Therefore, more attention was paid to H

_{w}in this section.

_{w}, but all factors had large confidence intervals (around 0.4 or higher, Figure 9a). Although H

_{w}could still be distinguished, its bounds were already overlapped with those of other factors. This was somewhat unexpected as the S2A-B3 values were quite normally distributed and far from skewed (Figure 7c). Moreover, a larger sample size of up to 128,000 did not significantly reduce the confidence intervals. For RGVI and NDAVI, H

_{w}, fCv(3) and PAI(3) were all identified as influential, but their SI values slightly varied and their confidence intervals might overlap. For NDWI, the SI of fCv(3) was slightly higher than that of H

_{w}, i.e., 0.360 vs. 0.348. Their confidence intervals were narrow (lower than 0.1) but still overlapping. Ranking them further might not be reliable because of the overlapping confidence intervals [8,45]. Therefore, a high SI itself in VBSA might not guarantee a solid link between the output and an input factor. It was better to check the output distributions and confidence intervals as well, as suggested by [32].

_{w}higher than 0.6 and those of other factors lower than 0.3, but the confidence intervals of all factors were much narrower (around 0.1 or lower). For NDWI, H

_{w}, fCv(3) and PAI(3) had SI values of 0.685, 0.414 and 0.404, separately. All factors had narrow confidence intervals (lower than 0.1) in PAWN, and there was no overlapping between them and other factors. As for the KS plot Figure 9b, PAI(3) and fCv(3) presented similar patterns with those in Figure 8b, except that the KS values of fCv(3) continued rising with increasing fCv(3) since its maximum value was 0.7 rather than 1 in GEN. H

_{w}had a two-way impact on NDWI and S2A-B3. This might be attributed to the different contributions of absorption and scattering by the water body and its components, both of which could vary with water depth. In contrast, only low H

_{w}values could make a difference for VIs based on SWIR bands, e.g., MNDWI in Figure 8b, as the absorption of water in SWIR was strong.

#### 3.3. Sparse Mangroves—Normal Input Probability Distributions

#### 3.4. Dense Mangroves—Uniform Input Probability Distributions

_{w}barely made a difference in this case. In the meanwhile, the influences of LIDFa(3) increased in NIR and C

_{w}in SWIR. Moreover, the impact of L2T(3) and WIDFa(3) grew significantly, especially in SWIR. L2T(3) had the highest SI values over other factors for multiple VIs such as MDI2, LSWI, NDAVI and WFI (Figure 6d,i). This might be attributed to the distinct spectral responses of leaves and woody material, and the adopted reflectance values of woody material were higher than the reflectance of leaves in SWIR.

_{ab}also had outstanding PAWN SI values for multiple VIs such as NDVI, EVI and S2A-B4 (Figure 6i). Comparatively, this was less significant for NDVI and EVI in VBSA (Figure 6d). The KS plots for NDVI in PAWN were presented in Figure 11b. L2T(3) had a two-way impact while the KS values of C

_{ab}increased dramatically only when its values were lower than 20 μg·cm

^{−2}. This was because low C

_{ab}values close to zero could remarkably increase the canopy reflectance in chlorophyll absorption bands [46]. The SI values of C

_{ab}and L2T(3) for NDVI in PAWN were 0.879 and 0.771, respectively, with SI values of other factors lower than 0.4. The confidence intervals of all factors were within 0.1 in PAWN. In contrast, L2T(3) was the most influential factor (SI = 0.544) for NDVI in VBSA, followed by C

_{ab}(SI = 0.207, Figure 11a). However, the confidence intervals were wide (around 0.3 or higher) and overlapping.

#### 3.5. Dense Mangroves—Normal Input Probability Distributions

_{l}= 67°) than they were when LIDFa(3) was close to 0 (θ

_{l}= 45°), which implied that canopy reflectance in NIR changed more significantly if leaves were vertically distributed.

#### 3.6. General Scenario with Correlated PAI(3) and fCv(3)

#### 3.7. A Brief Summary

_{w}for a sparse mangrove canopy and inclination distributions of plant material and C

_{ab}for a dense canopy might also be noteworthy. VIs with SWIR bands such as MNDWI and RGVI also had potential for mapping the fCv(3) and PAI(3) of mangroves and traditional VIs like EVI. Several VIs such as LSWI, MDI and WFI were sensitive to the L2T(3) of mangroves and might be helpful for estimating the LAI of mangroves from multispectral satellite images.

## 4. Discussion

#### 4.1. Global Sensitivity Analysis Methods and Interpretations of the Results

#### 4.2. Differences between Sparse and Dense Mangrove Canopies

_{w}and fCv(1) in visible and NIR bands were identified by both methods. If the inputs were turned into normal distributions (SPS_NRM), the computed NSIs of reflectance spectra also changed remarkably. As shown in Figure 5c,h, PAI(3) became less influential while the impact of fCv(3) and L2T(3) increased in NIR and SWIR, respectively.

_{w}had negligible influence now. In the meanwhile, biophysical properties related to woody material, such as L2T(3) and WIDFa(3), had a dominant impact in SWIR. The impact of LIDFa(3) also grew remarkably in NIR. In addition, the influences of leaf parameters, including C

_{ab}, C

_{w}and C

_{m}, increased by various degrees in different spectral regions. For the DEN_NRM case, the NSI patterns in PAWN (Figure 5j) were similar but slightly different from Figure 5i for DEN_UNI. The impact of fCv(3), L2T(3) and LIDFa(3) increased while that of WIDFa(3) decreased. In VBSA, fCv(3) and L2T(3) became the most influential factors, and the influences of LIDFa(3) and WIDFa(3) both decreased (Figure 5e).

_{w}mainly affected the reflectance of sparse canopies, but it was worth noting that the water body was not allowed to immerse the crown in this study. Otherwise, the infrared reflectance of submerged mangroves would reduce dramatically, which had been used to identify them from satellite images [4,48].

#### 4.3. Potential Limitations and Suggestions

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Illustrations of the understory (L1), stem (L2) and crown (L3) layers for mangroves. H

_{w}is the water depth and is assumed to be the same as the height of the understory for simplicity (The symbols are courtesy of the Integration and Application Network, University of Maryland Center for Environmental Science (ian.umces.edu/symbols/, accessed on 14 June 2018)).

**Figure 3.**Illustrations of generated samples (N = 1000) if the crown plant area index (PAI(3)) and fractional cover (fCv(3)) are assumed to be independent (using Latin hypercube sampling) (

**a**) or linearly correlated (

**b**).

**Figure 4.**Unconditional (red) and conditional (grey) cumulative distribution functions (

**a**) and corresponding Kolmogorov–Smirnov (KS) statistics (

**b**) of the normalised difference vegetation index with regard to the fractional cover of the mangrove crown (fCv(3)). The PAWN index can be different if the maximum (blue) or the median (green) metric is adopted (

**b**).

**Figure 5.**Stacked bar plots for normalised sensitivity indices (NSIs) of reflectance spectra in VBSA (

**a**–

**e**) and PAWN (

**f**–

**j**) for a general (GEN) canopy with uniformly sampled inputs (UNI) (

**a**,

**f**), a sparse (SPS) canopy with UNI (

**b**,

**g**), SPS with normally sampled inputs (NRM) (

**c**,

**h**), a dense (DEN) canopy with UNI (

**d**,

**i**) and DEN with NRM (

**e**,

**j**). Each x value corresponds to a wavelength. The NSI value is represented by the height of a bar and marked in the y-axis. Each colour corresponds to a factor defined in Table 1.

**Figure 6.**Stacked bar plots for sensitivity indices (SIs) of Sentinel-2A (S2A) band reflectance and vegetation indices (VIs) in VBSA (

**a**–

**e**) and PAWN (

**f**–

**j**) for a general (GEN) canopy with uniformly sampled inputs (UNI) (

**a**,

**f**), a sparse (SPS) canopy with UNI (

**b**,

**g**), SPS with normally sampled inputs (NRM) (

**c**,

**h**), a dense (DEN) canopy with UNI (

**d**,

**i**) and DEN with NRM (

**e**,

**j**). Each x value corresponds to a S2A band reflectance or a VI. The SI value is represented by the height of a bar and marked in the y-axis. The scale of the y-axis is restricted from 0 to 3.8 to show sufficient details. Each colour corresponds to a factor defined in Table 1.

**Figure 7.**Probability density function (PDF) of Sentinel-2A (S2A) band reflectance and vegetation indices for a general (GEN) canopy with uniformly sampled inputs (UNI) (blue curves), a sparse (SPS) canopy with UNI (red curves) and SPS with normally sampled inputs (NRM) (yellow curves). The bin size for SPS_NRM is one-third of that for GEN_UNI and SPS_UNI to show details of the latter two.

**Figure 8.**Mean sensitivity indices and confidence intervals estimated via bootstrapping for S2A-B8a in VBSA (

**a**). Kolmogorov–Smirnov (KS) statistics for MNDWI with regard to input factors in PAWN (

**b**).

**Figure 9.**Mean sensitivity indices and confidence intervals estimated via bootstrapping for S2A-B3 in VBSA (

**a**). Kolmogorov–Smirnov (KS) statistics for NDWI with regard to input factors in PAWN (

**b**).

**Figure 10.**Mean sensitivity indices and confidence intervals estimated via bootstrapping for MNDWI in VBSA (

**a**) and PAWN (

**b**).

**Figure 11.**Mean sensitivity indices and confidence intervals estimated via bootstrapping for NDVI in VBSA (

**a**). Kolmogorov–Smirnov (KS) statistics for NDVI with regard to input factors in PAWN (

**b**).

**Figure 12.**Mean sensitivity indices and confidence intervals estimated via bootstrapping for S2A-B8 (

**a**) and Kolmogorov–Smirnov (KS) statistics for S2A-B8 with regard to input factors (

**b**) in PAWN.

**Figure 13.**Stacked bar plots for normalised sensitivity indices of reflectance spectra in VBSA (

**a**) and PAWN (

**b**) for a general canopy with correlated PAI(3) and fCv(3). Each x value corresponds to an output, e.g., reflectance or VI, and each colour represents an input factor. The SI value is represented by the height of a bar and marked in the y-axis.

Factors | Unit | Definitions | General Uniform | Sparse Uniform | Sparse Normal | Dense Uniform | Dense Normal | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Min | Max | Min | Max | Mean | STD | Min | Max | Mean | STD | |||

Leaf | ||||||||||||

N | - | Leaf structural properties | 1 | 4 | 1 | 4 | 3 | 0.3 | 1 | 4 | 3 | 0.3 |

C_{ab} | μg∙cm^{−2} | Leaf chlorophyll content | 0 | 100 | 0 | 100 | 35 | 3.5 | 0 | 100 | 35 | 3.5 |

C_{w} | μg∙cm^{−2} | Leaf water content | 0 | 0.2 | 0 | 0.2 | 0.07 | 0.007 | 0 | 0.2 | 0.07 | 0.007 |

C_{m} | g∙cm^{−2} | Leaf dry matter content | 0 | 0.05 | 0 | 0.05 | 0.01 | 0.001 | 0 | 0.05 | 0.01 | 0.001 |

Canopy | ||||||||||||

PAI(1) | - | Plant area index (PAI) of Layer 1 (L1, understory) | 0 | 3 | 0 | 3 | 1 | 0.1 | 0 | 3 | 1 | 0.1 |

PAI(3) | - | PAI of Layer 3 (L3, crown) | 0 | 6 | 0 | 3 | 2 | 0.2 | 3 | 6 | 4.5 | 0.45 |

L2T(1) | - | Leaf-to-total area ratio of L1 | 0 | 1 | 0 | 1 | 0.5 | 0.05 | 0 | 1 | 0.5 | 0.05 |

L2T(3) | - | Leaf-to-total area ratio of L3 | 0 | 1 | 0 | 1 | 0.75 | 0.075 | 0 | 1 | 0.75 | 0.075 |

fCv(1) | - | Fractional cover of L1 | 0 | 1 | 0 | 1 | 0.5 | 0.05 | 0 | 1 | 0.5 | 0.05 |

fCv(3) | - | Fractional cover of L3 | 0 | 1 | 0 | 0.7 | 0.3 | 0.03 | 0.5 | 1 | 0.8 | 0.08 |

LIDFa(3) | - | Leaf inclination distribution function parameter a of L3 ^{a} | −1 | 1 | −1 | 1 | −0.2 | 0.1 | −1 | 1 | −0.2 | 0.1 |

WIDFa(3) | - | Wood inclination distribution function parameter a of L3 | −1 | 1 | −1 | 1 | −0.2 | 0.1 | −1 | 1 | −0.2 | 0.1 |

HSl(3) | - | Hot spot size parameter of L3 | 0 | 0.1 | 0 | 0.1 | 0.05 | 0.005 | 0 | 0.1 | 0.05 | 0.005 |

zeta(3) | - | Tree shape factor of L3 | 0 | 2 | 0 | 2 | 1 | 0.1 | 0 | 2 | 1 | 0.1 |

Other | ||||||||||||

H_{w} | m | Water depth | 0 | 2 | 0 | 2 | 0.4 | 0.04 | 0 | 2 | 0.4 | 0.04 |

R_{aw_so} | - | Bidirectional reflectance of water surface | 0 | 0.03 | 0 | 0.03 | 0.02 | 0.002 | 0 | 0.03 | 0.02 | 0.002 |

^{a}Equivalent to average inclination angle (AIA) by a = (45 − AIA)∗π

^{2}/360 [11].

Indices | Descriptions | References |
---|---|---|

NDVI $=\frac{{\rho}_{NIR}-{\rho}_{R}}{{\rho}_{NIR}+{\rho}_{R}}$ | Normalised Difference Vegetation Index | [34] |

SAVI $=\left(1+L\right)\frac{{\rho}_{NIR}-{\rho}_{R}}{{\rho}_{NIR}+{\rho}_{R}+L}$ | Soil Adjusted Vegetation Index (L: 0–1) | [39] |

EVI $=G\frac{{\rho}_{NIR}-{\rho}_{R}}{{\rho}_{NIR}+{C}_{1}{\rho}_{R}-{C}_{2}{\rho}_{B}+L}$ | Enhanced Vegetation Index (G = 2.5, L = 1, C1 = 6, C2 = 7.5) | [35] |

NDWI $=\frac{{\rho}_{G}-{\rho}_{NIR}}{{\rho}_{G}+{\rho}_{NIR}}$ | Normalised Difference Water Index | [40] |

MNDWI $=\frac{{\rho}_{G}-{\rho}_{SWIR1}}{{\rho}_{G}+{\rho}_{SWIR1}}$ | Modified Normalised Difference Water Index | [41] |

NDAVI $=\frac{{\rho}_{NIR}-{\rho}_{B}}{{\rho}_{NIR}+{\rho}_{B}}$ | Normalised Difference Aquatic Vegetation Index | [36] |

WAVI $=\left(1+L\right)\frac{{\rho}_{NIR}-{\rho}_{B}}{{\rho}_{NIR}+{\rho}_{B}+L}$ | Water Adjusted Vegetation Index (L: 0–1) | [21] |

WFI $=\frac{{\rho}_{NIR}-{\rho}_{R}}{{\rho}_{SWIR2}}$ | Wetland Forest Index | [38] |

MDI1 $=\frac{{\rho}_{NIR}-{\rho}_{SWIR1}}{{\rho}_{SWIR1}}$ MDI2 $=\frac{{\rho}_{NIR}-{\rho}_{SWIR2}}{{\rho}_{SWIR2}}$ | Mangrove Discrimination Index using SWIR 1 or SWIR2 | [38] |

LSWI $=\frac{{\rho}_{NIR}-{\rho}_{SWIR1}}{{\rho}_{NIR}+{\rho}_{SWIR1}}$ | Land Surface Water Index | [42] |

RGVI $=1-\frac{{\rho}_{B}+{\rho}_{R}}{{\rho}_{NIR}+{\rho}_{SWIR1}+{\rho}_{SWIR2}}$ | Rice Growth Vegetation Index | [37] |

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## Share and Cite

**MDPI and ACS Style**

Niu, C.; Phinn, S.; Roelfsema, C.
Global Sensitivity Analysis for Canopy Reflectance and Vegetation Indices of Mangroves. *Remote Sens.* **2021**, *13*, 2617.
https://doi.org/10.3390/rs13132617

**AMA Style**

Niu C, Phinn S, Roelfsema C.
Global Sensitivity Analysis for Canopy Reflectance and Vegetation Indices of Mangroves. *Remote Sensing*. 2021; 13(13):2617.
https://doi.org/10.3390/rs13132617

**Chicago/Turabian Style**

Niu, Chunyue, Stuart Phinn, and Chris Roelfsema.
2021. "Global Sensitivity Analysis for Canopy Reflectance and Vegetation Indices of Mangroves" *Remote Sensing* 13, no. 13: 2617.
https://doi.org/10.3390/rs13132617