# Spectral Characteristics of the Dynamic World Land Cover Classification

^{1}

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^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data

**Laguna Mountains–Sonoran Desert:**The Laguna-Sonoran hotspot in southern California spans the near-coastal western slope of the Laguna mountains, the forested range top, and the Anza-Borrego section of the Sonoran Desert in the rain shadow to the east. Upslope from the near-coastal suburban developments, the land cover transitions from chaparral to open woodland at the 1200 m range top. Woodland rapidly grades into desert scrub in the rain shadow downslope to the Salton Trough below sea level.

**San Joaquin Valley:**The San Joaquin hotspot in the southern part of the Great Central Valley of California is one of most diverse and productive agricultural basins on Earth. The broad, flat valley bottom hosts rich soils supportive of industrial-scale production of diverse, high-value crops. This cropland-dominated landscape is interspersed with human settlements, most notably the city of Fresno in the north-central portion of the tile. The distinct southwest portion of the scene is reflective of soil and crop differences linked to the northern end of the now-dry Tulare Lake and associated drainages.

**Coast Ranges–Transverse Ranges:**The Coast-Transverse hotspot at the southern end of the California Riviera spans the intersection of the Coast Ranges trending northward and the Transverse ranges trending eastward. The agriculturally dominated Santa Ynez valley occupies the space between the Coast and Transverse ranges in the northwest corner of this scene. Notably, the abrupt reorientation of the coastline from N-S to E-W orientation (at Point Conception) occurs at the transition between the Southwestern and Central Coastal floristic regions of California, and the Northern California Current and Southern California Current marine ecoregions. The complex convergence of multiple biogeographic factors establishing this spectral diversity hotspot gives this site global significance for biodiversity and conservation [14].

**Andean Altiplano–Amazon Basin:**The Andes-Amazon hotspot spans a climatic gradient encompassing 5 biomes ranging from >5500 to <500 m elevation. The Altiplano is composed of ice-capped mountains and semi-arid scrubland descending into the Amazon basin, primarily composed of biodiverse, closed canopy, humid tropical forest.

**Mauna Kea–Kohala watersheds:**The Mauna Kea-Kohala hotspot on the island of Hawaii spans multiple biomes along multiple elevation gradients along a ridge extending from Mauna Kea summit (~4500 m) to sea level. A rain shadow extends southeastward from the humid tropical forests and farms on the northeast slopes over extensive grassland flanking the ridge down to the arid scrublands and lava flows on the southwestern slope of the volcano. The forest preserves in the Kohala watershed on the northern slope of the ridge are considered a biodiversity hotspot.

**Nilgiri Mountains, Western Ghats:**The Western Ghats hotspot is near the southernmost extent of the west coast of India. From the semi-arid 1000 m Deccan Plateau in the northeast, over the 3000 m Nilgiri Mountains, down to near sea level on the west coastal plain, this hotspot spans at least 4 biomes and contains the Nilgiri biosphere reserve.

**New York City–Hudson River Valley and Highlands:**The NYC-Hudson hotspot in the northeastern USA contains a diversity of urban, suburban, peri-urban, and rural development amid temperate deciduous forest. Climatically and ecologically, it is the least diverse of the hotspots, but the most diverse in terms of developed land cover.

**Ganges–Brahmaputra Delta:**The G-B Delta hotspot in Bangladesh spans a variety of terrains and hydrologic settings on the largest, most populous delta on Earth. The tropical megacity of Dhaka is surrounded by a diverse agricultural mosaic interspersed with anthropogenically forested embankments, villages, and agricultural fields supporting one to three crops per year, with an agricultural diversity approaching that of the San Joaquin Valley hotspot.

**Transvaal Drakensberg:**The Drakensberg hotspot spans the Southern African Central Plateau and the westernmost section of the Great African Escarpment. Highveld and bushveld environments on the plateau at ~1000 m elevation rise to >1500 m forests on the escarpment before plummeting to <50 m on the lowveld savannah to the east.

`Export.image.toDrive()`function in Earth Engine.

#### 2.2. Methods

_{S}E

_{1}+ F

_{V}E

_{1}+ F

_{D}E

_{1}R

_{1}

. . . = .

. . . .

F

_{S}E

_{10}+ F

_{V}E

_{10}+ F

_{D}E

_{10}R

_{10}

**E**+ ε

**E**is the 3-column matrix of 10-band endmember vectors, R is the observed reflectance vector to be modeled, F

_{S|V|D}is the vector of endmember fractions to be estimated, and ε is the model misfit to be minimized by the inversion. In addition, a unit sum constraint equation was added to the model to urge the fractions to sum to 1. As in earlier such analyses using Landsat [8,9,10] and MODIS [11], the least squares solution, F = (

**E**

^{T}

**E**)

^{−}

^{1}

**E**

^{T}R [15], for the SVD endmember fraction estimates, yielded a stable result with fractions well-bounded [0, 1]. Model validity was assessed by multiplying the estimated SVD fractions with the SVD endmember spectra to forward model the observed mixed spectra. The distribution of root mean square (RMS) misfit between the observed and modeled spectra for the 80-hotspot composite had <6% misfit for >99% of 80,000,000 Sentinel 2 spectra (and <4% for 95%). The same global SVD endmembers were used to unmix the 9-hotspot composite. All subsequent comparisons used the SVD fractions estimated from inversion of the SVD mixture model for the 9-hotspot composite. The misfit distribution of the 9-hotspot composite was virtually identical to that of the 80-hotspot composite.

## 3. Results

## 4. Discussion

#### 4.1. The SVD Model: Why It Works

#### 4.2. The Dynamic World Class Probability Continuum

#### 4.3. Spectral Characteristics and Physical Properties of the Dynamic World Classes

#### 4.4. Information Content and Spatial Context

## 5. Conclusions

- We used a continuous, pixelwise, physical land cover model to characterize a discrete, spatially convolved, statistical land cover classification.
- SVD land cover fractions provided simple, physically meaningful quantification of Dynamic World class similarity and difference.
- Continuous tetrahedral simplices consistently emerged in the Dynamic World class probability space.
- Topology-preserving UMAP manifolds embedded from the Dynamic World probability space revealed further topological structure not obvious from PC feature spaces.
- SVD land cover fractions provided interpretable physical context to the spatio-spectral information used by FCNN-based models.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Sentinel 2 reflectance, continuous land cover fraction, and Dynamic World land cover classification for three spectral diversity hotspots spanning multiple biomes and climatic zones. Reflectance (top) and land cover fraction (center) composites are each displayed with a 1% linear stretch. The land cover classification (bottom) shows the discrete class with the highest probability for each pixel. Each Sentinel 2 tile is 109.8 × 109.8 km. (

**b**) Sentinel 2 reflectance, continuous land cover fraction, and Dynamic World land cover classification for three spectral diversity hotspots spanning multiple biomes and climatic zones. Reflectance (top) and land cover fraction (center) composites are each displayed with a 1% linear stretch. The land cover classification (bottom) shows the discrete class with the highest probability for each pixel. Each full Sentinel 2 tile is 109.8 × 109.8 km, but Mauna Kea-Kohala is 55 × 55 km and Western Ghats is 55 × 109.8 km, rescaled N-S. (

**c**) Sentinel 2 reflectance, continuous land cover fraction, and Dynamic World land cover classification for three spectral diversity hotspots spanning multiple biomes and climatic zones. Reflectance (top) and land cover fraction (center) composites are each displayed with a 1% linear stretch. The land cover classification (bottom) shows the discrete class with the highest probability for each pixel. Each full Sentinel 2 tile is 109.8 × 109.8 km. NYC-Hudson and Drakensberg are swath edge tiles, 55 × 109.8 km, rescaled N-S. Mauna Kea-Kohala is ¼ tile to reduce open ocean area.

**Figure 2.**Sentinel 2 spectral feature spaces for spectral diversity hotspot mosaics. Orthogonal projections of three low-order principal component distributions are bounded by substrate, vegetation, and dark spectral endmembers at apices spanning spectral mixtures within the triangular space. The 9X larger, more diverse global mosaic has a more distinct internal structure with multiple clusters and mixing continua denoting different types of land cover. Both spaces are effectively 2D, with >95% of variance on the PC1-2 plane. Axes of rotation are indicated by arrows.

**Figure 3.**Spectral feature spaces for 9 spectral diversity hotspots. Each Sentinel 2 tile has been projected onto the silhouette of the 9-site composite space in Figure 2 using the composite rotation parameters. In each space, the trajectory of the vegetation limb is determined by background substrate albedo and vegetation canopy shadow.

**Figure 4.**Variance partition of Dynamic World class probability feature spaces for 9 spectral diversity hotspots. Note logarithmic scaling on % variance plot. All but NYC-Hudson are effectively 5D, requiring 5 dimensions to represent >95% of the total feature space variance.

**Figure 5.**Class probability feature spaces for nine spectral diversity hotspots. Orthogonal projections of low-order principal component distributions form 3D feature spaces illustrating continuous probability distributions among discrete classes. Maximum probability distributions (class histograms) show a combination of strongly skewed classes with modes near 0.7 with long lower tails (e.g., Trees) and less skewed distributions with modes <0.5 (e.g., Shrub). The NYC-Hudson and G-B Delta hotspots illustrate the extremes between more clustered and more continuous feature spaces, respectively. Density-shading of the feature spaces uses the same cool to warm color table as Figure 2 and Figure 3. Probability histograms range from 0 to 0.8 in probability and 0 to 10

^{6}pixels in area.

**Figure 6.**Land cover class SVD fraction distributions and spectral separability matrices for nine spectral diversity hotspots. Trivariate distributions in ternary diagrams all show spectral mixing continua tapering from a range of substrate albedos to increasing vegetation fraction. Most are displaced toward the dark endmember because of shadow and soil moisture darkening. Spectral separability of class pairs, quantified as transformed divergence of reflectance spectra distributions of each class pair, is displayed in spectral separability matrices with a linear stretch between 1.5 (black) and 2.0 (white). Class pairs with lighter shades are more spectrally separable within the corresponding hotspot. For example, the Built (U), Bare (B), and Water (W) classes are much more separable than the other classes in the NYC-Hudson and Laguna-Sonoran hotspots, while only the Tree (T), Grass (G), and Crop (C) classes show low separability for the Mauna Kea–Kohala hotspot. In hotspots where both occur, water (W) and flooded vegetation (F) have low separability. Density-shading of the SVD ternaries uses the same cool to warm color table as Figure 2 and Figure 3.

**Figure 7.**Aggregate spectral separability and maximum probability of classes. The generally more spatially homogeneous Water and Bare classes have high mean (m) separability (more red) with low variability (s) among the nine sites. Each has more variable separability (more cyan) with one other class. The Built class (U) also has high mean separability with all classes except Crops. The aggregate maximum probability histogram (right) shows similar distributions to those in Figure 5.

**Figure 8.**Class probability feature spaces for the nine-site composite. Low-order principal components form a tetrahedral space with continua spanning Trees, Shrub, Crops, Bare, and Built, while Water is more distinct. Density-shaded distributions (top) illustrate the land cover continuum as distinct from Water, while the maximum probability class distribution shows the decision boundaries at intermediate probabilities. Density-shading uses the same cool to warm color table as Figure 2 and Figure 3. The Tree class was omitted for clarity on PC3–PC2 class projection, lower right.

**Figure 9.**Class probability feature space for the nine-site composite. In contrast to the 3D projection of the PCs in Figure 8, the 2D UMAP manifold preserves the local structure, with continua spanning Trees, Crops, and Shrub, and more distinct limbs for Bare, Built, and Water. Grass forms a separate cluster in the UMAP projection but is relegated to higher PC dimensions because it contributes much less variance than the other classes. Density-shading of the feature space uses the same cool to warm color table as Figure 2 and Figure 3.

Hotspot | Date | TileID |
---|---|---|

Laguna-Sonoran | 5 April 2022 | L1C_T11SNS_A035445_20220405T182333 |

San Joaquin | 31 May 2022 | L1C_T11SKA_A036246_20220531T185113 |

Coast-Transverse | 25 February 2022 | L1C_T10SGD_A025979_20220225T184402 |

Andes-Amazon | 23 July 2021 | L1C_T18LZL_A031782_20210723T150514 |

Mauna Kea-Kohala | 12 December 2017 | L1C_T04QHH_A012924_20171212T210918 |

Western Ghats | 18 February 2020 | L1C_T43PFN_A024326_20200218T051826 |

NYC-Hudson | 23 July 2021 | L1C_T18TWL_A033041_20211019T154735 |

G-B Delta | 15 February 2022 | L1C_T46QBM_A034736_20220215T042852 |

Drakensberg | 16 August 2020 | L1C_T35JRN_A017993_20200816T080232 |

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Small, C.; Sousa, D.
Spectral Characteristics of the Dynamic World Land Cover Classification. *Remote Sens.* **2023**, *15*, 575.
https://doi.org/10.3390/rs15030575

**AMA Style**

Small C, Sousa D.
Spectral Characteristics of the Dynamic World Land Cover Classification. *Remote Sensing*. 2023; 15(3):575.
https://doi.org/10.3390/rs15030575

**Chicago/Turabian Style**

Small, Christopher, and Daniel Sousa.
2023. "Spectral Characteristics of the Dynamic World Land Cover Classification" *Remote Sensing* 15, no. 3: 575.
https://doi.org/10.3390/rs15030575