Development 

of the 

Gulf of Mexic

Marine Debris

Model 

Zachary Nixon and Nir Barnea 

US Department of Commerce 

National Oceanic and Atmospheric Administration 

National Ocean Service 

Office of Response and Restoration 

Marine Debris Division 

Silver Spring, MD 20910 

National Oceanic and Atmospheric Administration 

Technical Memorandum NOS-OR&R-35 

January 2010 

o 
Mention of trade names or commercial products does not constitute endorsement or recommendation 

for their use by the National Oceanic and Atmospheric Administration. 
DEVELOPMENT OF THE GULF OF MEXICO MARINE 

DEBRIS MODEL 

Zachary Nixon1 and Nir Barnea2 

1 Research Planning, Inc.

 Columbia, SC 29201, USA

2 National Oceanic and Atmospheric Administration

 Office of Response & Restoration

 NOAA Marine Debris Division

 Silver Spring, MD 20910, USA 

National Oceanic and Atmospheric Administration 

Technical Memorandum NOS-OR&R-35 

January 2010 

This document should be cited as follows: 

Nixon, Z., and N. Barnea. 2010. Development of the Gulf of Mexico Marine Debris Model. 

January 2010. NOAA Technical Memorandum NOS-OR&R-35. 

For copies of this document, please contact: 

NOAA Marine Debris Division 

N/ORR, SSMC-4 

1305 East-West Highway 

Silver Spring, MD 20910 

www.MarineDebris.noaa.gov 
   

Development of the Gulf of Mexico Marine Debris Model  2010

ACKNOWLEDGMENTS

The development of this model benefited greatly from the support and guidance of a 

number of people who worked on survey, assessment, and removal of marine debris after 

hurricanes Katrina and Rita:

 Steve Heath, Mark Clark, and Nyle Trimble: Alabama Marine Resources Division, 

Dauphin Island, AL

 Irvin Jackson Grant Larsen, and Kim Denz: Mississippi Department of Marine 

 Resources, Biloxi, MS 

 Marty Bourgeois, Harry Blanchet, and Jim Hanifen,: Louisiana

 Department of Wildlife and Fisheries, Baton Rouge, LA 

 Garrett Broussard, and Sam Martin: Louisiana Department of Natural Resources, 

Lafayette and Baton Rouge, LA 

 Robert Travis: U.S. Coast Guard, New Orleans, LA 

 Mark Nickelson: FEMA Inshore Lead, Mandeville, LA 

Christopher Barker, Holly Bamford, Debra Simecek‐Beatty, Brendan Bray, George 

Graettinger, Neal Parry, and Glen Watabayashi of NOAA’s Office of Response and 

Restoration, and Michael Carron, of the Northern Gulf Institute at Stennis Space Center 

reviewed earlier drafts, and their comments greatly improved the document. 

Carey Morishige of NOAA’s Marine Debris Program edited the final version of the document 

and turned it into a Technical Memorandum.  

We welcome any comments or suggestions you may have to improve the current version of 

the document. Please send your comments to: 

Marine Debris ERP

NOAA OR&R 

7600 Sand Point Way N.E. 

Seattle, WA 98115 

Fax: (206)526‐6329

Email: mderp@noaa.gov
   

Development of the Gulf of Mexico Marine Debris Model  2010

Table of Contents

Identified Problem and Opportunity ............................................................................................ 1 

Goal.............................................................................................................................................................. 1 

Previous Efforts...................................................................................................................................... 1 

Model Overview and Limitations ................................................................................................... 2 

Predictor Data ......................................................................................................................................... 2 

................................................................................................................. 9 

Methodology ............................................................................................................................................ 8 

Exploratory Data Analysis

Model Construction ............................................................................................................................ 13 

Results...................................................................................................................................................... 15 

Uncertainty............................................................................................................................................. 17 

Model Validation.................................................................................................................................. 17 

Generalization....................................................................................................................................... 18 

References .............................................................................................................................................. 19 

Appendix A – Additional Model Results .................................................................................. A‐1 
     

   

  

   

Development of the Gulf of Mexico Marine Debris Model  2010

Identified Problem and Opportunity

During the 2005 hurricane season, Hurricane Katrina inflicted severe damage on the 

Gulf of Mexico (GOM) coastal region and deposited huge amounts of debris over 

large areas of the Gulf coast.  Submerged marine debris poses a hazard to vessel 

traffic, can cause snags and hang‐ups during fishing and can adversely affect viable 

fishing grounds.  To address the submerged debris problem, Congress appropriated 

funds to survey areas potentially affected by submerged marine debris, tasking the 

National Oceanic and Atmospheric (NOAA) Office of Coast Survey and Office of 

Response and Restoration to conduct the surveys, compile and disseminate data to 

the public and stakeholders in an effective and useable format, carry out outreach 

activities, and otherwise coordinate for removal of marine debris, identifying both 

present and future needs.  This project, lasting over three and a half years, came to 

be known as the Gulf of Mexico Marine Debris Project (GOMMDP). 

One of the most pressing needs when addressing marine debris dispersion caused 

by a major storm is to assess and verify debris locations.  Knowing where high 

densities of marine debris are likely to be found could greatly assist in developing 

survey priorities and in planning for debris removal.  Moreover, a simple, 

inexpensive, rapid, and verifiable model to predict marine debris densities could be 

very useful to Federal and State managers dealing with marine debris.  The data

collected by this project comprise one of the largest systematically collected, post‐

storm investigations of marine debris in existence, and provide the building blocks 

for assembling such a model.  This document describes model construction and 

performance. 

Goal

The purpose of the model is to characterize spatial differences in the distribution of 

relatively large, storm‐mobilized and deposited, anthropogenic marine debris 

objects across the nearshore seafloor so as to help prioritize these areas for survey.

The guidance for developing the model was that it should be conceptually and 

statistically robust and based upon the data collected by the GOMMDP.  In addition,

the model should be as applicable as possible to a generic storm event, or a storm 

event to occur in the future. 

Previous Efforts

Previous efforts at quantitatively modeling debris generated by hurricanes have

largely focused on terrestrial debris.  Notable efforts include the HAZUS‐MH family 

of models maintained by the Federal Emergency Management Agency (FEMA, 

2008).  The commercially developed HurDET model (Umpierre and Margolies, 

2005) is another example.  These efforts, while robust and based upon actual data 

derived from multiple storm events, are limited to the spatial support of existing 

terrestrial boundaries – municipalities, census blocks, or traffic analysis zones.  As 

1 
     

   

   

such, they are incompatible with the goal of estimating spatial differences in the

distribution of marine debris.

Model Overview and Limitations

This effort models gross relative differences in the spatial distribution of all types of 

non‐floating anthropogenic marine debris objects across the nearshore seafloor by 

statistical correlations via logistic regression.  The model focus is limited to debris 

objects generated from coastal inhabited areas, and mobilized and deposited during 

a hurricane‐level storm event.  This model does not attempt to mechanistically 

describe the sources, movement, and deposition of marine debris, nor will it be able 

to predict actual concentrations or volumes of debris.  Instead, the model attempts 

to relate spatial data describing the relative densities of observed marine debris to 

spatial data describing potential influencing factors, and to identify potential 

hotspots based upon actual data.

The data used to construct the model are the locations of marine debris items 

related to Hurricanes Katrina and Rita identified via side scan sonar in surveys 

conducted in 2006 by the GOMMDP.  These data do not distinguish between natural 

or anthropogenic debris, or between storm‐generated and non‐storm‐generated 

debris.  The model, however, will be confined to predicting concentrations of post‐

storm, anthropogenic debris, which is usually of greatest concern.  It is assumed that

the data collected by this project represent a realistic picture of storm‐mobilized 

and deposited subsurface anthropogenic marine debris objects.

It is difficult to quantify the time and length scales of the model in the sense used for 

physical deterministic models.  The model itself examines correlations only, and has 

no inherent time scale, however some generalizations are possible.  This model

examines trends in the essentially static distribution of marine debris objects at 

timescales of months to years after the originating storm event.  As such, it is

intended to provide a snapshot of this distribution after a storm, but before another 

event capable of mobilizing substantial amounts of debris.  All predictor data have 

been discretized to a common grid of 100 meter (m) by 100m square cells.  This can

be considered the minimum length scale of the model.  The model was constructed 

using data from a raster grid at this resolution that spans approximately 250 

kilometers (km).  As such, the maximum length scale of the model can be considered 

to be hundreds of kilometers.   The output of the model is an estimated probability 

of encountering one or more debris items within that grid cell, given the values of 

the predictor data in that cell.     

Predictor Data

The factors influencing the distribution of anthropogenic marine debris following a 

storm event are largely intuitive.  In general, higher storm energy in the form of 

wind, waves, and storm surge in the vicinity of concentrations of human structures

leads to larger amounts of anthropogenic debris.  If these debris sources are close to 

open water, then there is a higher potential for mobilization of debris from sources 

2 
Development of the Gulf of Mexico Marine Debris Model  2010

and deposition in the nearby marine environment.  Thus, selecting candidate 

predictor data sets for marine debris seems equally intuitive.  The critical part in

building a model that will be useful in the future, however, is selecting and 

evaluating candidate predictor data sets that one might reasonably anticipate being 

available in a consistent format soon after a storm event.  Here, we evaluate only 

data that are spatial in nature and that either exist for the entire country or would 

be produced in a consistent format after a storm event.  Table 1 lists the evaluated 

predictor data sets.

Storm surge, wind speed, and bathymetric data were evaluated as proxies for

debris‐generating storm energy.  Distance to shoreline, distance to waterways, and 

nearby onshore structure damage, and offshore oil and gas infrastructure density 

were measured as proxies for relative potential debris sources.  Note that all spatial

data analysis, including processing of the predictor data, was carried out using the 

ArcGIS 9.2 software package (ESRI, 2007a).

TABLE 1. Evaluated debris probability predictor raw data sets.  

Source Title Format

NOAA  H*Wind Surface Wind Analysis data  ESRI shapefile 

NOAA  Experimental probabilistic hurricane storm surge 

data  GRIB2 grid

NOAA  NGDC 3‐Arc second coastal relief model data  ASCII grid 

ESRI  Shoreline data  ESRI shapefile

USACE National waterways network data  BTS text file

LOSCO  Navigated waterways of Louisiana ESRI Shapefile 

FEMA  Remote sensing data ESRI shapefile 

MMS  Oil and gas platforms in federal waters ESRI Shapefile 

GSA  Oil and gas platforms in Alabama State Waters  ESRI Shapefile 

MARIS  Oil and gas platforms in Mississippi State Waters  ESRI Shapefile 

LDNR  Oil and gas platforms in Louisiana State Waters  ESRI Shapefile

NOAA’s H* Wind Surface Wind Analysis products (NOAA, 2007b) describe hurricane 

surface wind fields by summarizing data from a variety of observation platforms.  

Powell et al. (1998) provide more background on these data products.  While

multiple datasets representing snapshots representing various time intervals are 

available, a single dataset consisting of a lattice of vector points representing the

peak surficial wind speed was obtained.  These data were imported to ArcGIS and 

interpolated to the project grid spacing of 100 m by 100 m using an inverse distance 

weighting method.  Figure 1 depicts the final maximum wind speed grid. 

3 
   

FIGURE 1.	 100 m grid of maximum surface wind speeds in meters per second for hurricane 

Katrina.  Dotted line indicates storm eye track.

NOAA’s Experimental Probabilistic Hurricane Storm Surge data (NOAA, 2007a) 

describe the 10 percent chance storm surge exceedance height above normal high 

tide based upon an ensemble of Sea, Lake, and Overland Surge from Hurricanes 

(SLOSH) model runs using the last posted National Hurricane Center (NHC) official 

hurricane advisory.  These data were converted from the GRIB2 format to vector 

points, imported to ArcGIS, and interpolated to the project grid spacing using an 

inverse distance weighting method.  Figure 2 depicts the final storm surge height

grid for hurricane Katrina.   

We will later note that wind speed as described above and the predicted 

probabilistic storm surge data are strongly correlated, largely because the SLOSH 

model ensembles used to generate surge estimates rely mainly upon wind speed as 

an input.  True, independent measures of storm surge (from post‐landfall ground 

surveys; USGS sensors; or remote sensing techniques) or hindcast SLOSH model 

output from after storm landfall would be better variables to include a part of this 

model.  Currently, however, such products are not generated in consistent or timely 

manner after all storm events, and so, are not proposed as candidates for inclusion 

in this effort, which is intended to produce a “nowcast” product. 

NOAA NGDC’s 3‐Arc Second Coastal Relief Model data (Divins and Metzger, 2007) 

describe integrated bathymetric and topographic information for the coastal zone 

derived from all of applicable data sources, including topographic maps, 

hydrographic soundings, and sonar and LIDAR data.  These data were converted 

from the ASCII format to a raster in ArcGIS and resampled to the project grid 

spacing using a cubic convolution method.  Figure 3 depicts the final bathymetric‐

topographic grid.

4 
Development of the Gulf of Mexico Marine Debris Model  2010

FIGURE 2. 100 m grid of 10 percent chance storm surge exceedance heights in meters for 

hurricane Katrina.   

FIGURE 3. 100 m grid of bathymetric/topographic elevation in meters.  

The Environmental Systems Research Institute (ESRI) high resolution shoreline 

(ESRI, 2007b) was converted to a land‐water grid using the project grid cell spacing.  

These same grid dimensions were used for all predictor grids.  For each cell, 

Euclidean distance to land was calculated in meters in ArcGIS.  Figure 4 depicts the 

final distance to land grid.

The United States Army Corps of Engineers (USACE) National Waterways Network 

Data (USACE, 2007) and Louisiana waterway data (LOSCO, 1999) describe linear 

waterway routes for the intra‐coastal and near‐coastal waters of the nation.  These

data were obtained, imported into ArcGIS and merged to a single dataset of vector

lines.  For each cell, Euclidean distance to linear waterway was calculated in meters.

Figure 5 depicts the final distance to waterway grid. 

5 
FIGURE 4. 100 m grid of Euclidean distance to shoreline in meters.  

FIGURE 5. 100 m grid of Euclidean distance to waterways in meters.  

FEMA damage assessment polygons (FEMA, 2007) describe areas damaged by 

storm events and are generated by interpretation of remote sensing data after a 

storm.  Polygons are digitized by analysts and assigned one of several damage 

descriptors.  These damage descriptors are qualitative.  To assist in using such 

descriptors in a quantitative model, these descriptors were converted to a set of

damage indices ranging from 10 to 80.  These indices are an estimate of the 

percentage of destroyed structures within areas with that descriptor, as per Table 2.  

These polygon data were imported to ArcGIS and converted to a damage index grid 

at the project grid spacing.  It is anticipated that marine debris will be more likely to 

be located proximal to areas with significant storm damage, but it is not known 

what degree of proximity will be significant.  A series of derivative grids were 

generated to represent local damage indices at three different spatial scales.  These

derivative grids represent summations of the damage index values at each location 

within four different distances – 10 km, 5 km, 2.5 km, and 1 km ‐ from that location.  

These sums serve as proxy variables for the potential amount of debris derived from 

nearby onshore structures.  These three distances were selected as representative

of what “nearby” means, in the context of debris mobilization and deposition.  

Figure 6 depicts the damage index grid and three focal sum grids.

6 
   

   

Development of the Gulf of Mexico Marine Debris Model  2010

TABLE 2. FEMA hurricane damage descriptors, definitions and assigned damage index values.
 

Descriptor Definition Damage

Index

Flood Area No explicit definition of damage; assumed similar to the 

Limited Damage category defined below.  10

Limited Damage

Generally superficial damage to solid structures (e.g., loss 

of tiles or roof shingles); some mobile homes and light 

structures are damaged or displaced. 

10

Moderate Damage 

Solid structures sustain exterior damage (e.g., missing

roofs or roof segments); some mobile homes and light

structures are destroyed, many are damaged or displaced.

25

Extensive Damage

Some solid structures are destroyed; most sustain exterior 

and interior damage (e.g., roofs missing, interior walls 

exposed), most mobile homes and light structures are 

destroyed.

50

Catastrophic Damage Most solid and all light or mobile structures destroyed.  80

Multiple datasets exist that describe the locations of offshore oil and gas 

infrastructure in the Gulf of Mexico.  Data describing wells and oil and gas platforms 

in federal waters (MMS, 1998) as well as state waters (GSA, 2008; LDNR, 2007; 

MARIS, 2004) were obtained and merged into a single dataset of vector points.  It is

anticipated that marine debris will be more likely to be located proximal to oil and 

gas infrastructure, but, similar to the onshore damage data, it is not known what 

degree of proximity will be significant. Again, derivative grids were created at 

different spatial scales to explore these relationships.  These derivative grids 

represent point densities in counts per square kilometer of oil and gas 

infrastructure at each location within four different distances – 10 km, 5 km, 2.5 km 

and 1 km ‐ from that location.  These densities serve as proxy variables for the 

potential amount of debris derived from nearby oil and gas infrastructure.  Figure 7

depicts the three density grids.

FIGURE 6. 100 m grid of 5 km focal sum of damage index derived from FEMA damage 

polygons.   

7 
   

FIGURE 7.	 100 m grid of oil and gas infrastructure density evaluated at 5 km kernel size in 

counts per square km.  

Methodology

The goal of the model is to relate some measure of marine debris density or

likelihood after a storm event to spatially distributed predictor variables.  Maps of

these predictor variables can be used in the future to estimate the locations of 

debris concentration areas for survey prioritization.  There are a number of 

statistical methodologies that might be used to construct such a model.  The logistic

regression variant of Generalized Linear Modeling (GLM) was selected because it is 

a relatively simple, robust modeling strategy implementable in a number of 

software packages that yields a relatively easily understandable output.  Venables 

and Ripley (2003) provide a review of modern logistic regression techniques.  The

coupling of logistic regression models with spatially distributed predictors derived 

from data sets stored in Geographical Information System (GIS) is widespread

across a number of disciplines, including ecology and hazard modeling.

The model development was based upon the known locations of 5,137 items 

identified via side scan sonar as potential debris items, as in Figure 8.  Of these, 

roughly 10 percent were located in the eastern portion of the study area and were 

thought to have been possibly generated by Hurricane Ivan in 2004.  These items

were removed from the data set, leaving 4,549 debris locations.  Logistic regression

models the binary probability of a given event – in this case, the probability of an

identified item occurring at a given location.  The modeling procedure requires a set 

of locations where items did not occur.  These locations are termed pseudo‐

absences.  Accordingly, a set of 4,549 random locations were generated.  The model

seeks to find differences in the average values of the predictor variables between 

the actual debris item locations and the average values of the entirety of the

surveyed area – as represented by the pseudo‐absence locations.  Note that, while 

there are almost identical numbers of actual and random locations, the actual 

locations appear strongly clustered in certain locations, while the random locations 

are evenly distributed across the study area.

8 
   

     

Development of the Gulf of Mexico Marine Debris Model  2010

All statistical modeling was conducted using the open‐source statistical computing 

language R (R Development Core Team, 2007).  The predictor variable grids were 

sampled at each actual and randomly generated location.  These data were imported 

from the ArcGIS environment to the R environment for exploratory analysis and 

statistical modeling.  After construction of the final model in the R environment, the 

model was implemented as a raster algebra equation in the ArcGIS environment to 

yield a final prediction grid.  The following sections describe the results of the 

exploratory analysis and the details of model construction and results.  

FIGURE 8.	 Identified items (A) and randomly generated pseudo‐locations (B).  The project

study area boundaries outlined.  Debris locations inside the Hurricane Ivan impact 

area in orange.  Note the clustered nature of the actual locations versus the even 

distribution of random locations.

Exploratory Data Analysis

Model construction began with exploratory analysis of the relationships between 

the investigated predictor variables.  Table 3 contains summary statistics for the 

predictor variables at all sampled locations – both debris and pseudo‐absence.  

Figure 9 contains pairs plots for all the predictor variables below the diagonal, and 

absolute correlation coefficients in the upper diagonal.  Note the strong correlations 

between maximum wind speed and maximum storm surge, as well as between the 

damage indices and infrastructure density metrics. 

All potential predictor variables were evaluated for ability to predict the 

distribution of marine debris in several ways.  Figure 10 shows histograms of 

9 
       

   

   

   

   

   

   

  

   

predictor variable values at all locations by presence/absence of an identified

marine debris object.  Univariate logistic regression models were constructed for

each continuous variable.  Parameter significance results via Χ2 tests are reported in 

Table 4.  We note that all the variables are significantly related to the presence of 

debris.  While the strength of these relationships is statistically robust, in some 

cases this is an artifact of the very large sample size.  Often, the effects sizes are not 

very large, implying that there is strong evidence for a relationship, but that 

relationship itself is weak.

TABLE 3.	 Summary statistics and codes for predictor variables 

Variable Code Min 1st Q Med Avg 3rd Q Max.

Max. Wind Speed (m/s)  WSMAX_M 22.5 34.4 42.0 40.8 46.9 50.4

Max. Storm Surge (m)  SURGE_M 1.1 3.0 5.0 4.3 5.4  6.3 

Elevation (m)  BATHY_M ‐17.6 ‐3.6 ‐2.7 ‐3.8 ‐2.1 3.0

Dist. to Land (m)  DLAND_M 0 1000 2341 2842 4272 10782

Dist. To Waterway (m)  DWWAY_M 0 781 2138 2842 4327 14227

Damage Index (10 km)  DAM10 0 50 11410 55136 100975 282145

Damage Index (5 km)  DAM25 0 0 100 18514 21715 112210

Damage Index (2.5 km)  DAM50 0 0 0 4385 2651 47920

Damage Index (1 km)  DAM100 0 0 0 417 0 11520

Infr. Dens. (10 km)  DEN10  0.0 0.0 0.0 0.2 0.1 4.9

Infr. Dens. (5 km)  DEN25  0.0 0.0 0.0 0.1 0.1 4.2

Infr. Dens. (2.5 km)  DEN50  0.0 0.0 0.0 0.2 0.1 8.8

Infr. Dens.(1 km)  DEN100  0.0 0.0 0.0 0.2 0.0 16.0

Note that debris items tend to be located closer to land and waterways in areas with 

higher wind speeds and storm surges, and in areas with higher damage indices.

These results are consistent with intuition.  We also note that storm surge 

exceedance and wind speed seem to have different coefficient signs, and that all the

infrastructure density variables have negative coefficients 

TABLE 4.	 Univariate model coefficient estimates and parameter p‐values for logistic 

regressions of binary debris item presence versus candidate model variables. 

Code Coefficient Parameter

p­value

WSPMAX_MS  ‐0.03774 <0.0001

SURGE_M  0.5596 <0.0001

BATHY_M  0.3202 <0.0001

DLAND_M  ‐0.0004684 <0.0001

DWWAY_M  ‐0.0002258 <0.0001

DAM10 0.001428 <0.0001

DAM25 0.0001556 <0.0001

DAM50 0.00003891 <0.0001

DAM100 0.00001257 <0.0001

DEN10  ‐0.10679 <0.0001

DEN25  ‐0.54238 <0.0001

DEN50  ‐1.1999 <0.0001

DEN100  ‐2.0856 <0.0001

10
 
   

Development of the Gulf of Mexico Marine Debris Model  2010

FIGURE 9. Pairs plots (below the diagonal) and absolute correlation coefficients (above the 

diagonal) for the evaluated predictor variables. 

11
 
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12
Development of the Gulf of Mexico Marine Debris Model  2010

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is calculated using the 

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ebris 

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13
 
TABLE 5.	 

Coefficient Stepwise Model Stepwise Model (No

Inf. Vars.) BMA Model

Intercept  3.317925209 2.857604815 3.4354686055  

Max. Wind Speed (m/s)  ‐0.122662103 ‐0.098712904 ‐0.1383307294 

Max. Storm Surge (m)  0.380548628  0.273156107 0.4805729010  

Dist. to Land (m)  ‐0.000113435 ‐0.000119084 ‐0.0001046976 

Dist. to Waterway (m)  ‐0.000020349 ‐ ‐

Elevation (m)  0.072490502 0.078413039 0.0726930590 

Damage Index (1 km) 0.000295082 0.000310402 0.0003309315  

Damage Index (2.5 km) 0.000295082 0.000041568 0.0000260500 

Damage Index (5 km) 0.000011030 0.000012413 0.0000191179 

Damage Index (10 km) 0.000002470  0.000001969 0.0000004563 

Infrastructure Density (1 km) 0.619554410 NA  0.5790855283 

Infrastructure Density (2.5 ‐1.165087074 NA  ‐0.9312981047 

Infrastructure Density (5 km) 1.317550611 NA  0.8113536116 

Infrastructure Density (10 ‐0.457476689 NA  ‐

ROC Area Under the Curve 0.82 0.81 0.82

when the infrastructure variables were removed.  It was also not included in any of 

the BMA model ensembles. 

Model coefficients and ROC area under the curve AUC statistics for stepwise, 

stepwise without infrastructure variables, and BMA derived logistic models. 

0 1.8 

e 

0.

tare 

6 

iv

0.

itso

4 

 p eurT

0. 2 0.0 0.

                                               .0 1.8 te 

0

are 

.6 

v

0

tiiso

.4 

 p

0

eurT

.2 0.0 0

.0 1.8 

te 

0

are 

.6 

v

0

tiiso

.4 

 p eurT

0 .2 0.0 0

0.0 

A. 

0.2 0.4 0.6 0.8 1.0 0

B. 

.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 

False positive rate False positive rate	 

C. 

False positive rate 

FIGURE 11.	 Receiver operator characteristic (ROC) curves for stepwise (A), stepwise with no

infrastructure variables, and BMA derived (B) logistic models.

The performance of all three models is good and essentially identical as evaluated 

via the AUC statistic and ROC curves.  The benefits of the BMA method are largely

lost in this 

model selection. 

particular applicat

Also, the inclu

ion, 

sion of the variables yields e

as there seems to be small uncertainty about 

predictive power as measured by AUC (Table 5).  As such, th

ssen

e stepwis

tially 

e

n

 model 

o improved 

without infrastructure density variables was selected as the final model.   

14
 
Coefficient Coefficient Std. Error

Intercept  2.857604815 0.220188877

Dist. to Land (m)  ‐0.000119084 0.000015887

Max. Wind Speed (m/s)  ‐0.098712904 0.006942386

Max. Storm Surge (m)  0.273156107 0.042173799

Elevation (m)  0.078413039 0.016030242

Damage Index (1 km) 0.000310401 0.000055248

Damage Index (2.5 km) 0.000041568 0.000041568

Damage Index (5 km) 0.000012413 0.000003820

Development of the Gulf of Mexico Marine Debris Model  2010

The final model can be expressed as an equation that calculates the logit of the 

debris item 

Results

Table 6 lists estimated 

encounter probability as a linear function of the predictor variables. 

final model.  Figure 12 displays t

coefficients 

he fin

and standar

al model as implemented

d errors of those coeffic

algebra.  The coefficients were used to calculate the logit, wh

 in ArcGIS via map 

ients for the

into a prob

unsurprisin

a

gly, the hig

bility ranging from 

hest predic

0 to 1 for each

ted probabilities corres

grid cell.  In 

p

gen

ich was then conver

eral, notice that, 

ted 

Figure 7 with large amounts of debris, and also with areas that

ond 

 sustained high storm 

with areas from

energies and resultant damage.  Thus, the model corresponds well with the intuitive 

and actual knowledge of marine debris distributions in the Gulf of Mexico following 

the passage of Hurricane Katrina. 

TABLE 6. Final model estimated coefficient values and standard errors.

Damage Index (10 km) 0.000001969 0.000000945

It is in this map form that model output following a future storm event will be most 

useful.  This grid of continuous marine debris item encounter probabilities could be 

sliced at so

Alternativel

me arbitrary value t

y, if only a fixed amount of survey effort was avai

o derive hotspot areas of an ar

lable after

bitrary size.  

such data could be used to ensure that the highest probability areas were 

an ev

included

ent, 

in available survey effort – maximizing survey efficiency.

15
 
FIGURE 12. Final model prediction map.  Reds indicate areas of higher predicted likelihood of marine debris concentration

16
Development of the Gulf of Mexico Marine Debris Model  2010

Uncer

Sources of uncerta

tainty

inty in this mod

both spatial and measu

collection of each predictor data

rement.  

 set involves unique assumptio

eling process are manifold.  The in

ns and uncertainty, 

itial data 

described, resulting in statisti

referenced – vector points, grids of various res

Additionally, the way these data are spatially 

predictors used here are indices

cal ch

 (

ange‐of‐support issues. 

olutions, etc. 

densities or focal sums) base

– was modified as 

Finally, many of the 

these issues should be kept in min

datasets, and were derived based u

similar one.  The procedure of logistic regress

d when ev

pon logical but unexamined 

d upon other 

aluating this model 

a

elds as its result a 

or constructing a 

ssumptions.  All of 

ion, however, yi

discrete outcome. 

probability as well as c

As such, the 

onfidenc

mo

e inter

del inherently

vals around that probabi

 accounts for a

lity, r

 large portion of the 

ather than a 

uncertainty of the relationships used to construct it.   

areas 

Finally, note that the m

where data was 

odel output for physical settings very different from the 

reservoirs, 

only be used in ar

is likely to be ex

collected, in

treme a

 particular inland wa

nd not re

ter bodies such as lakes and 

eas similar to those in which 

flective o

these da

f reali

ta were

ty.  Model 

 collect

output should 

near

Model

shore marine and 

ed – 

which were collected somewhat la

Initially, the data from the southern portion o

Validation

estuarine zones.

ter in the process were held as

f the study area in Plaquemines pa

external model validation with independent data.  However, there were few debr

ide to conduct an 

rish 

points in this area, and the area was both remote and homogenous with respect to 

is

predictor data.  As such, this external validation was less than useful. 

Instead, we conducted an internal validation—specifically, a 10

stepwise model procedure was car

of model accuracy.  In this procedure, the da

ried out 10 times, each time us

ta were divided into 10 parts.  The

‐fold cross validation 

data. 

ing 9/10 of the

out.  Summary statis

The model, derived in eac

t

h 

ths 

ics are then generated.  The 10‐fold cross

iteration, is tested using the 1/10

‐validat

th of the dat

ed ROC AUC is 

a held 

depicted 

(95%CI: 0.

in 

and not overfit.  Nonet

80, 0.82).  Th

Figure 13.  The av

is tight 

erag

gro

e AU

uping ind

C of th

icates that th

ese cross‐va

e mo

lidate

del is well‐calibrated 

d runs is 0.81 

heless, validation with data from another storm event would 

be preferable. 

17
 
Average true positive rate 

0.0 0.2 0.4 0.6 0.8 1.0 

0.0 0.2 0.4 0.6 0.8 1.0 

False positive rate 

FIGURE 13.	 Vertical average of 10‐fold cross‐validated ROC curves with box plots for final

logistic model. 

Generalization

It is the goal of this effort, as stated above, to construct a model that will be useful in 

future applications.  The key to this process is the ability of the model to generalize

well to future unknown storm events.  Obviously, the data that were used to 

construct this model represent a distribution of marine debris from one particular

storm in one particular region: Hurricane Katrina in the northern Gulf of Mexico.  As

such, the model summarizes trends and correlations particular to this event.   

The only way to either test or improve the generalization of the model is with 

quantitative data from other storm events in other locations.  No information could 

be found for other actual quantitative data describing marine debris distributions 

post‐storm that could be used to directly test the ability of this model to generalize 

at the current time.  However, it is believed that the general trends captured by the 

model – debris  tends to be located close to debris sources and in areas of high 

storm energy – are intuitive and will hold true in other circumstances.  Appendix A

contains model output products for Hurricane Ivan in 2004 and Hurricane Ike in 

2008.  Efforts are currently underway to collect marine debris data in the western 

portion of Louisiana’s coast in the impact area of Hurricane Rita.  These data may

provide valuable insights into how well this model performs for other storm events, 

as well as the raw materials with which to improve its performance.

18
 
Development of the Gulf of Mexico Marine Debris Model  2010

References

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http://www.ngdc.noaa.gov/mgg/coastal/coastal.html. (10/20/06)

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Redlands CA.  Available at: http://www.esri.com.

(8/20/07) 

Environmental Systems Research Institute, Inc. (ESRI).  2007b.  ArcData.  Available

at: http://www.esri.com. (8/20/07) 

Federal Emergency Management Agency (FEMA).  2006.  Hurricane Katrina remote 

sensing data. Available at:

http://www.gismaps.fema.gov/2005pages/rsdrkatrina.shtm. (8/20/07) 

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at:  http://www.fema.gov/plan/prevent/hazus/  (1/20/08). 

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variable and transformation selection in linear regression.  Journal of 

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Louisiana Department of Natural Resources (LDNR).  2007.  Oil, gas, and injection 

wells in Louisiana.  Available at: http://lagic.lsu.edu/data/. (8/20/07) 

Minerals Management Service (MMS).  1998.  Oil and gas producing platforms in the 

Gulf of Mexico. Available at: http://lagic.lsu.edu/data/. (8/20/07)

Mississippi Automated Resource Information System (MARIS).  2004.  Oil and gas

wells.  Available at: http://www.maris.state.ms.us/statewide.html. (1/20/08)

National Oceanic and Atmospheric Administration (NOAA).  2007a.  Experimental

probabilistic storm surge data.  Available at: 

http://www.weather.gov/mdl/psurge/. (8/20/07)

19
 
National Oceanic and Atmospheric Administration (NOAA).  2007b.  H*Wind surface

wind analysis data.  Available at:

http://www.aoml.noaa.gov/hrd/data_sub/wind.html. (8/20/07)

Powell, M., Houston, S., Amat, L., and N. Morisseau‐Leroy.  1998.  The HRD real‐time

hurricane wind analysis system. Journal of Wind Engineering and Industrial 

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R Development Core Team.  2007.  R: A language and environment for statistical 

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http://www.R‐project.org. (8/20/07) 

Raftery, A. E., Madigan, D., and J. A. Hoeting.  1997.  Bayesian model averaging for 

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Umpierre, D and G. Margoles.  2005.  Broward County's web‐based hurricane debris 

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20
 
           

Development of the Gulf of Mexico Marine Debris Model  2010

Appendix A – Additional Model Results

The model described above was used to generate marine debris predictions for 

coastal areas impacted by the following additional storms: 

 Hurricane Ivan on September 16, 2004

 Hurricane Ike on September 13, 2008 

The following maps depict the model output for those storms.  Model output is also 

available as a raster layer for use with GIS software in ESRI® GRID format. Contact

the NOAA Marine Debris Program at www.MarineDebris.noaa.gov or 301.713.2989

for data or information requests.

A-1
 
Development of the Gulf of Mexico Marine Debris Model 2010

A-2
Development of the Gulf of Mexico Marine Debris Model 2010

A-3
United States Department of Commerce 

Gary Locke 

Secretary 

National Oceanic and Atmospheric Administration 

Jane Lubchenco, Ph.D. 

Undersecretary of Commerce for Oceans and Atmosphere 

Administrator, National Oceanic and Atmospheric Administration 

National Ocean Service 

David Kennedy 

Acting Assistant Administrator for Ocean Services and 

Coastal Zone Management