1. Worldview-02 offers new capabilities for the monitoring of threatened coral reefs
Jeremy M. Kerr
National Coral Reef Institute
Nova Southeastern University
Khaled bin Sultan Living Oceans Foundation

2. Mapping coral reefs ecosystems
Economically and socially important
Declining health
Marine spatial planning - integrating spatial information into policy
Geospatial information
Benthic habitat maps
Bathymetric maps
Ecological and oceanographic models
Integrating remotely-sensed data:
Bridges gap between regional- and field-scale observations
Constrained by spectral and spatial resolution of the data
Worldview-02 increases the available spatial and spectral
information
Elkhorn coral (Acropora palmata)
Boulder star coral (Montastraea spp.)
QuickBird imagery (True color)
Optically-derived bathymetry
Benthic habitat map

3. Deriving depth from a multispectral image
Important optical properties of water
Beer’s law: light attenuates exponentially with depth
Light attenuation varies across the visible spectrum
Stumpf et al. (2003) estimated depth based on these two properties with the model:
Where
= estimated depth
= reflectance of band i
= constant set to ensure that the logarithm is positive
, = constants estimated by fitting a linear regression of the band-ratio to known depths
Observation:
Increasing the polynomial from first-order to second- or third-order can lead to better depth estimates.
Can the Stumpf model be improved?

4. Data Worldview-02 (WV2) image
10-km by 10-km (100 km2) area in the Florida Keys
Pixel resolution of 2-m by 2-m (4 m2)
Coincides with a pre-existing bathymetric map
Provided the spectral inputs for the expanded depth derivation model
Experimental Advanced Airborne Research LiDAR (EAARL) Digital Elevation Model (DEM)
Created through a combined effort by the USGS, NASA, and NPS (USGS 2008)
Depths values for approximately 129 km2
Depth estimates have error of ±15 cm
Pixel resolution of 1-m by 1-m (1 m2)
Provided the ‘ground-truth’ data for fitting the models and assessing accuracy of predicted depths

5. Data WorldView-2 image (True color):
Reef
Vegetation
Sand
Boats
Optically-
deep water*
WorldView-2 image (True color):
Subset 1 (red box) was used for model comparison.
Subset 2 (orange box) and Transects A, B, C, and D (black lines) were used for accuracy assessments.
Each Subset included 4 million pixels
Transects included between 2000 and 3000 pixels
EAARL DEM:
Subsets and Transects are drawn for reference
* - Optically-deep waters are those in which the sea-floor depth is greater than the detection limit (here: depths > 20 m, approximately).

6. Pre-processing WV2 image:
Sea-surface state between the ‘traditional’ and ‘new’ bands varied
Physical sensor offset
Limited the possible band-ratios
Sun-glint removal (SGR)
Based on the model of Hedley et al. (2003)
Applied to irradiance values
Deep-water correction (DWC)
Applied to apparent reflectance values
EAARL DEM:
Resampled using nearest-neighbor kernal to match the spatial resolution of the Worldview-02 image
Close-up from the a) coastal and b) blue bands demonstrating the observed difference in pixel values between the ‘traditional’ and ‘new’ bands. The top area in the yellow box (rows 1 and 2) is similar in both bands, but the bottom area (rows 3 to 7) has a different pattern in each band.

7. Expanding the Stumpf model
Can the Stumpf model be improved?
Hypothesis: Increasing the spectral information input into the Stumpf model will improve depth estimates.
Increasing the number of band-ratios input into the model results in an expanded model:
Where the n-th band-ratio, , is now:
The constant e is added to ensure that the value inside the logarithm is greater than 0.
What is the optimal set of band-ratios for depth-estimation?

8. The optimal combination of band-ratios
Model selection: Based on Akaike Information Criteria (AIC; Akaike 1973)
Sample size: 1 million pixels
Randomly selected from the 4 million pixels included in Subset 1
Best-fit model:
Full model (containing all 6 band-ratios)
Same model selected for all 4 pre-processing levels
What is the optimal level of pre-processing?
Band i
Band j
Band ratio
Blue
Green
Red
Coastal
Yellow
Red-edge
Limited to the within the ‘traditional’ and ‘new’ sets due to the observed offset
63 candidate models
4 levels of pre-processing

9. The optimal level of pre-processing
Aggregated and compared all 252 models using AIC
Overall Best-fit model:
Full-model with both SGR and DWC
Other results:
Top 3 models were full models with differing levels of pre-processing.
8 of the top 10 models had both SGR and DWC applied.
The top 10 models all contained 4 or more band-ratios.
How does sample size affect the model selection results?
The top 10 models based on AIC values.
AICc is the AIC value after correction for small samples sizes.
ΔAIC is the difference in AIC values between the model and the best-fit model.
AICw is the weight of evidence within the data-set supporting the model.
Rank
Input variables
Pre-preprocessing
AICc
ΔAIC
AICw 1
SGR, DWC
1.00 2
None
0.00 3
SGR 4 5 6 7 8 9 10
SGR - Sun-glint removal
DWC - Deep-water correction

10. The effect of sample size on the model selection
Method:
Compared top 10 models
Sample sizes: 100, 1000, , and
100 re-samples from Subset 1 selected for each sample size
Results:
Rank 1 model pre-dominantly selected for
all 4 sample sizes
Rank 2 and 3 models occasionally selected
Rank 4 through 10 models rarely or never
selected
How well does this new model perform compared to Stumpf’s original model?
Model (Rank)
Sample size
100
1000
10 000 1
84 %
100 %
94 %
89 % 2
4 %
0 %
2 %
6 % 3
9 %
5 % 4
1 % 5 6 7 8 9 10

11. Data
Note:
Subset 1 (red box) was used for determining optimal model, optimal pre-processing level,
and the effects of sample-size.
Subset 2 (orange box) and Transects A through D (black lines) were used for the accuracy assessment.

12. Assessing the expanded model
Reef top
Depth estimates from the full and blue/green models compared with depths form the EAARL DEM
Overall increase in precision of depth estimates
Blue/green model:
RMSE: 1.03 m
NRMSE: 7.32%
Full model:
RMSE: 0.77 m
NRMSE: 5.49%
Similar increase in precision along the 4 Transects
Increased precision over areas with high albedos
Sand
Reef top
Depth values from the EAARL DEM (black), Full model (blue), and blue/green model (red) along Transects A through D. The full model better estimated depths over reef-top and sand areas.

13. Summary of results Expanded model:
Altered an established model from a linear regression to a multiple linear
regression.
Allowed for increased spectral information to be used for depth estimation.
Full model (with 6 band-ratios) selected as the best-fit model.
Pre-processing:
Sun-glint removal and atmospheric correction improve depth estimates.
Sample size:
Full model feasible even when ground-truth data are limited.
Accuracy:
Full model had more precise depth estimates than the blue/green model.
It also had more precise estimates over seafloor features with high albedos.

14. Future application
Depth is a fundamental environmental parameter in marine systems.
Ecologically important
Resources and disturbances vary with depth.
Benthic community composition varies with depth.
Benthic habitat maps
Depth can improve classification accuracy
Support modelling and analyses
Species distribution models
Hydrodynamic models
Geologic history
Marxan analyses
Fine-scale, detailed bathymetric maps covering large spatial extents improve our knowledge of the distribution of marine resources and the environmental processes shaping these distributions.

15. Future application
Global Reef Expedition: Science Without Borders (
In partnership, the Living Oceans Foundation and host countries will explore, map, and characterize coral reefs in remote locations enabling comparisons with coral reefs located near populated coastlines.
Research activities:
Acquire multispectral satellite imagery
Collect detailed ground-truth and
bathymetric data
Conduct surveys of benthic and fish
communities
Evaluate processes controlling reef
community structure
Targeted sampling and assessment of
resilience indicators
Evaluate connectivity within and
between reef ecosystems
Study sites in the Bahamas (right):
Cay Sal Bank (green box),
Great Inagua (blue box),
Little Inagua (orange box)
Hogsty Reef (red box)

16. Acknowledgements Jeremy M. Kerr National Coral Reef Institute
National Coral Reef Institute at Nova Southeastern University’s Oceanographic Center
Dr. Sam Purkis
Gwilym Rowlands
Alexandra Dempsey
Khaled bin Sultan Living Oceans Foundation
Capt. Phillip Renaud
Dr. Andrew Bruckner
Judges for DigitalGlobe’s “8-band Research Challenge”
Dr. Ing. Anko Börner
Dr. Stuart R. Phinn
Dr. Hrishikesh Samant
Dr. Walter Scott
DigitalGlobe
Ian Gilbert
Brett Thomassie
Jeremy M. Kerr
National Coral Reef Institute
Nova Southeastern University
Khaled bin Sultan Living Oceans Foundation