Types of Spatial Models
Purely statistical
(driven by statistical models of
correlations and structures
inferred from data)
Descriptive spatial and spatio-temporal
statistics
Examples: Geostatistics (Variogram analysis), Point-pattern
analysis, Moran’s I, Spectral/Wavelet analysis, etc.
Regression & machine-learning models that
link: data, environmental process variables, and
statistical models of process/observation error
Examples: GLM, GAM, GLMM, RandomForest, MaxEnt,
Geostatistics (Regression-Kriging)
Purely mechanstic
(driven by equations whose
parameters and functional
forms are taken from prior
process-studies or first
principles)
Coupled Dynamic Physical-Biological Models
Examples: ROMS-NPZD, Atlantis, HAB forecast models,
spawning habitat models
Overview of spatial statistics tools for
pelagic habitat characterization
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Spatial statistics and spatial modeling is a vast and rapidly developing field; would
be impossible to cover everything here
What specific types of problems do we have to address for pelagic habitat
characterization?
– Generating gap-free gridded maps from scattered survey data
– Filling gaps in satellite data
– Characterize scales of environmental and biological correlation and coherence
– Predictive modeling of species distribution and abundance and/or ecosystem
properties
• Spatial
• Spatio-temporal
Not covered here…
– Predicting/simulating coupled physical-biological processes
– Assimilating data into hindcast ocean models (e.g., 4DVAR)
Some handy techniques for
marine/ecological spatial modeling
Descriptive analysis of pattern
• Variography (auto-correlation, cross-correlation)
• Point-pattern techniques (e.g., detecting clusters)
• Wavelet analysis (scale-dependent coupling)
• Empirical Orthogonal Function analysis (EOF)
Interpolation
• Geostatistical models (Optimal Interpolation)
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Ordinary Kriging
Indicator Kriging
Universal Kriging, Kriging with external drift
Modeling distribition and abundance
• Spatial Generalized Linear Models (GLM’s)
• Spatial Generalized Additive Models (GAM’s)
• Spatial Generalized Linear Mixed Models (GLMM’s)
• Geostatistics: Regression-Kriging, Universal Kriging, Kriging with external drift
• ‘Machine learning’ techniques: Regression Trees (e.g., TreeNet, RandomForest), MaxEnt (for
presence-only data), Neural nets
• Hierarchical Bayesian Spatial Models (Markov Random Fields, CAR models)
Challenges to ocean habitat
characterization
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Ocean is dynamic
Multiscale
Complex interactions
Coupling to human systems
Threshold behavior; need to identify and
validate indicators
Example: geostatistical interpolation
Predicted Mean
Prediction Error
Method: Ordinary Kriging with external drift
Source: Poti et al. 2012 (Ch. 3 in NOAA NOS Tech Memo 141)
A BIOGEOGRAPHIC ASSESSMENT OF SEABIRDS, DEEP-SEA CORALS AND OCEAN HABITATS
OF THE NEW YORK BIGHT: SCIENCE TO SUPPORT OFFSHORE SPATIAL PLANNING
Example: Quantifying hierarchical
habitat structures with variography
Text-book spatial variogram
•Results from a single, spatially-varying
process
•Fits a theoretical model well
•Informative for understanding spatial scaling
and sampling precision.
Actual spatial variogram for sea scallop
density on Georges from HabCam data
(50m resolution).
• Evidence of spatial patchiness
•Evidence of hierarchical habitat
structures.
Parallel evidence for hierarchical habitat structure from scallop fishing behavior (VMS data).
HabCam
VMS Mid Atlantic
VMS Georges Bank
Example: Delineating regions with distinct phytoplankton dynamics
Methodology:
•Merge SeaWiFS and MODIS Chl A datasets for 1998 – 2010
•Transform, scale and center data for each pixel / day of the year
•Perform Empirical Orthogonal Function (EOF) analysis
•Run cluster analysis on EOF scores to delineate regions
Example: Juvenile salmon habitat in the NCC
• H0: Alongshore transport links
PDO to regional ocean conditions
• Results
– Cold phase: more water from north,
more cold water copepods, and
more habitat
– Bi et al. (2011) GRL
– Habitat based on presence: Bi et al.
MEPS (2007), Bi et al. FO (2008)
– Habitat with spatial structure:
GLMMS (Bi et al. FO 2011), GAM (Yu
et al. in revision)
Software overview
(not a comprehensive list)
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R packages
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Matlab toolboxes
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mGstat
EasyKrig
BMElib
Wavelets
others…google search recommended
ArcGIS extensions/toolboxes
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Gstat
RandomFields
others…see CRAN spatial task view
Geostatistical Analyst, Spatial Analyst, Spatial Statistics extensions
Marine Geospatial Ecology Tools (MGET)
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Hybrid of R, ArcGIS, Python
Free standalone programs
• SGeMS
• Gstat
• GSLIB
• Many others…see AI-geostats list on next page
A few links for more information
AI Geostats: Forum that has compiled lists of free and commercial geostatistical software w/detailed
capabilities; excellent resource:
http://www.ai-geostats.org/bin/view/AI_GEOSTATS/WebHome
CRAN Task View: Analysis of Spatial Data
http://cran.r-project.org/web/views/Spatial.html
ESRI Geostatistical Analyst http://www.esri.com/software/arcgis/extensions/geostatistical/index.html
Marine Geospatial Ecology Tools (MGET)
http://code.env.duke.edu/projects/mget
http://www.spatialanalysisonline.com
http://en.wikipedia.org/wiki/Kriging