mapping chemical contaminants in oceanic sediments around point loma’s treated wastewater outfall...
Post on 22-Dec-2015
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Mapping Chemical Contaminants in Oceanic Sediments Around Point
Loma’s Treated Wastewater OutfallKerry Ritter
Ken Schiff
N. Scott Urquhart
Dawn Olson
Ami Groce
Tim Stebbins
Overview
Motivation Problems with current methods Kriging offers a more sophisticated statistical
alternative Provides predictions as well as prediction
errors Allows for a cost-efficiency analyses for any
sampling density or configuration
Maps are useful tools for understanding and managing resources
Spatial patterns are recognized more easily with visual displays
Can quickly locate disturbance, assess its relative magnitude and extent, and weigh risk to neighboring areas
Maps are effective and efficient media for communicating information to the public
How do we design the “optimal” sampling grid?
• Depends on goals of the study
• Samples closer together tend to be more alike than samples farther apart
• Placing samples to far apart may make extrapolation to non-sampled locations suspect
• Placing samples too close together may be redundant and waste resources
Current maps
Often based on sparse data (< 30 sites) Use simple interpolation methods
– Spline smoothing– Triangulation– Linear interpolation
Do not provide measures of uncertainty Cannot determine how dense a sampling grid
is optimal
What is kriging?
A statistical tool used to create maps Predictions = weighted average of neighbors Weights based on the strength of spatial
correlation Provides estimate of confidence Optimal Available in many mapping or statistical
software packages
For kriging understanding the spatial variablity is key
Determines weighting factors for kriging
Provides estimates of kriging errors– Confidence intervals– Cost-efficiency analyses for future studies
How do we model spatial variability?
Variogram= variance of paired sample differences as a function of distance between pairs
Measure of spatial correlation Apply statistical models for fitting variogram
– Spherical– Gaussian– Exponential– Linear
Use method of least squares to fit parameters
Empirical Variogram for Lead (Point Loma)
Log transformed and detrendeddistance
ga
mm
a
0.0 0.02 0.04 0.06
0.0
0.0
50
.10
0.1
50
.20
0.2
5
distance
ga
mm
a
0.0 0.02 0.04 0.06
0.0
0.0
50
.10
0.1
50
.20
0.2
5
objective = 0.0734
2 km 8 km4 km
variogram
Distance b/t sampling sites
Variogram fit for lead (spherical)
Variorgram provides estimates of prediction errors that…
Do not depend on the data
Do not depend on location
*Depend only on distance between sites
Link variogram to cost efficiency
Can determine prediction error for any grid spacing/configuration
Can weigh the cost of increasing sampling effort with benefit of precision
Percent error v. density
1 2 3 4 5
60
70
80
90
10
0
Core 4km 2.5km 1km 0.5km
Per
cent
Cor
e E
rror
Sampling density
Summary
Kriging offers a more sophisticated statistical alternative for creating maps
Provides predictions as well as prediction errors Errors are independent of data, but depend only on
distance between sampling sites Modeling the variogram is key Allows for a cost-efficiency analyses for any sampling
density or configuration– Uneven allocation of resources, targeted sampling