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![Page 1: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/1.jpg)
Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal
Systems
Kerry J. Ritter, SCCWRPMolly Leecaster, SCCWRP
N. Scott Urquhart, CSUKen Schiff , SCCWRP
Dawn Olsen, City of San DiegoTim Stebbins, City of San Diego
![Page 2: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/2.jpg)
Project Funding
• The work reported here was developed under the STAR Research Assistance Agreement CR-829095 awarded by the U.S. Environmental Protection Agency (EPA) to Colorado State University. This presentation has not been formally reviewed by EPA. The views expressed here are solely those of the presenter and STARMAP, the Program they represent. EPA does not endorse any products or commercial services mentioned in this presentation.
• Southern Californian Coastal Water Research Project (SSCWRP)
![Page 3: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/3.jpg)
Background• Maps of sediment condition are important for
making decisions regarding pollutant discharge• Maps in marine systems are rare• Special study by San Diego Municipal Wastewater
Treatment Plant• Objective: To build statistically defensible maps
of chemical constituents and biological indices around two sewage outfalls– Point Loma
– South Bay
![Page 4: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/4.jpg)
Point Loma and
South Bay Outfalls
![Page 5: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/5.jpg)
TYPICAL DESIGN SITUATION
• Many features of the real situation are unknown.– Here: The nature of the semivariogram
• Multiple Responses What is a good solution for one response
may not be a good design for another!
• Time constraint– Answer was required by June 14, 2004
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Two-Phase Approach• Phase I: Model spatial variability at various
spatial scales (eg. Variogram) – This summer
• Phase II: Use information from Phase I to design survey that meets accuracy requirements – next summer = 2005
• Current focus is on Phase I
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Variogram
distance
ga
mm
a
0 10 20 30 40 50
0.0
0.5
1.0
1.5
2.0
2.5
VARIOGRAM
}NUGGET=>
SILL=>
RANGE
![Page 8: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/8.jpg)
Design Considerations for Modeling the Variogram
• Sufficient replication at various spatial scales– Variogram model
– Parameter estimates
• Adequate spatial coverage to support investigating– Stationarity
– Isotropy vs. Anisotropy
– Strata
• Allow for multiple responses
![Page 9: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/9.jpg)
Empirical Variograms(Point Loma 2000 Regional Survey)
distance
gam
ma
0 2 4 6 8
010
2030
4050
60
CHROMIUM
R=5.09 S=36.27 N =0.00distance
gam
ma
0 2 4 6 8
0.0
0.05
0.10
0.15
TOC
R=8.8 S=.077 N =0.0242distance
gam
ma
0 2 4 6 8
05
1015
2025
30
COPPER
R=2.75 S=22.53 N =0.00
distance
gam
ma
0 2 4 6 8
050
100
150
200
250
300
ZINC
R=6.14 S=218.55 N =0.00
Lag Distribution Variogram
lag distance (km)
No.
of p
airs
2 4 6 8
1020
3040
50
![Page 10: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/10.jpg)
Multi-Lag Cluster (MCL) Enhancements to Fixed Grids
• Clusters of sites, spaced at various lag distances, are placed around fixed locations on an existing grid.
• Allows current monitoring grid to remain “in tact”.
• Provides replication at multiple spatial-scales
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There are many ways to allocate resources within the
MLC• Economic constraints: limit total number of
samples– ( eg. 100 in Point Loma)
• More clusters with fewer sites within a cluster?• or less clusters with fewer sites?• Shorter sample spacing or larger sample spacing?• What is best (decent!) design configuration?
![Page 12: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/12.jpg)
Choosing the Best DesignCase Study: Point Loma
• Three design configurations– S, STAR, and S with satellites
• Two sets of lag classes– Shorter vs. larger sample spacing
• Compare lag distributions• Simulation study
– Simulate response– Consider different models of spatial variability
• Compare relative performance of designs for estimating parameters
![Page 13: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/13.jpg)
“STAR” and “S” Cluster Designs
S DESIGN
Xkm
Ykm
0 20 40 60 80 100
020
4060
8010
0
STAR DESIGN
Xkm
Ykm
0 20 40 60 80 100
020
4060
8010
0
![Page 14: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/14.jpg)
“S” and “S with Satellites” Design
S DESIGN
Xkm
Ykm
0 20 40 60 80 100
020
4060
8010
0
S with SATELLITES DESIGN
Xkm
Ykm
0 20 40 60 80 100
020
4060
8010
0
![Page 15: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/15.jpg)
STAR DESIGN
Xkm
Ykm
0 20 40 60 80 100
020
4060
8010
0
![Page 16: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/16.jpg)
S DESIGN
Xkm
Ykm
0 20 40 60 80 100
020
4060
8010
0
![Page 17: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/17.jpg)
S with SATELLITES DESIGN
Xkm
Ykm
0 20 40 60 80 100
020
4060
8010
0
![Page 18: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/18.jpg)
Sample AllocationStar S S with Satellites
Grid Stations =12 Grid Stations =12 Grid Stations =12
5 “STAR” Clusters of Size 17
3 grid station
2 sites of interest
1 “S” Cluster of Size 9
11 “S” Clusters of Size 9
5 grid stations
6 sites of interest
8 “S” Clusters of Size 9
8 Satellites added to 3 S”
4 grid stations
4 sites of interest
Field duplicates=9 Field duplicates=6 Field duplicates=8
Total Samples =
12+3*(17-1) +2*(17)+9+9=112
Total Samples =
12+5*(9-1)+6*(9)+6=112
Total Samples =
12+4*(9-1) +6*(9)+6=112
![Page 19: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/19.jpg)
“Star” Cluster Design
Point Loma 5 Star + 1 S Cluster
Xkm
Ykm
466 468 470 472 474
3610
3615
3620
3625
Point Loma 5 Star + 1 S Cluster
Xkm
Ykm
466 468 470 472 474
3610
3615
3620
3625
![Page 20: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/20.jpg)
“S” Cluster Design
S DESIGN
Xkm
Ykm
466 468 470 472 474
3610
3615
3620
3625
S DESIGN
Xkm
Ykm
466 468 470 472
3610
3615
3620
3625
Lag = 0.05, 0.10, 0.20, 0.50 Lag = 0.05, 0.25, 1.00, 3.00
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“S” Cluster with SatellitesS with SATELLITES DESIGN
Xkm
Ykm
466 468 470 472 474
3610
3615
3620
3625
S with SATELLITES DESIGN
Xkm
Ykm
466 468 470 472
3610
3615
3620
3625
![Page 22: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/22.jpg)
Omnidirectional Lag Dist.
Ominidirectional Lag Dist
Pairwise Lag distances
No. o
f pair
s
0 2 4 6 8
010
020
030
040
0
SD3StarD5SSATD3
Ominidirectional Lag Dist
Pairwise Lag distances
No. o
f pair
s
0 2 4 6 8
010
020
030
040
0
SStarSSAT
Lag = 0.05, 0.10, 0.20, 0.50 Lag = 0.05, 0.25, 1.00, 3.00
![Page 23: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/23.jpg)
Directional Lag DistLag = 0.05, 0.10, 0.20, 0.50
{ Lag = 0.05, 0.25, 1.00, 3.00 is similar}
Direction = 0
Pairwise Lag distances
No
. o
f p
air
s
0 2 4 6 8
02
04
06
08
01
00
12
0
S0STAR0SSAT0
Direction = 45
Pairwise Lag distances
No
. o
f p
air
s
0 2 4 6 8
02
04
06
08
01
00
12
0
S45STAR45SSAT45
Direction = 90
Pairwise Lag distances
No
. o
f p
air
s
0 2 4 6 8
02
04
06
08
01
00
12
0
S90STAR90SSAT90
Direction = 135
Pairwise Lag distances
No
. o
f p
air
s
0 2 4 6 8
02
04
06
08
01
00
12
0
S135STAR135SSAT135
![Page 24: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/24.jpg)
Simulation Study• 3 Grid Enhancements: S, STAR, S with Satellites• Two sets of lag classes of size 4
– 0.05, 0.10, 0.20, 0.50 (km)– 0.05, 0.25, 1, 3 (km)
• Spherical variogram– Range = 1, 2, 4, 6– Nugget = 0.00, 0.10– Sill = 1
• 1000 sims• Fit using automated procedure in Splus
– This may have introduced artifacts
![Page 25: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/25.jpg)
Percent Difference from Target Range(Median Range) S=1, N= 0.10
True Range
Perc
ent o
f Tar
get
1 2 3 4 5 6
-10
010
2030
40
SStarSSAT
Lag = 0.05, 0.25, 1.00, 3.00
True Range
Perc
ent o
f Tar
get
1 2 3 4 5 6
-10
010
2030
40
SStarSSAT
Lag = 0.05, 0.10, 0.20, 0.50
![Page 26: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/26.jpg)
Percent Difference from Target Sill(Median Sill) S=1, N= 0.10
True Range
Perc
ent o
f Tar
get
1 2 3 4 5 6
-10
-50
510
1520
SStarSSAT
Lag = 0.05, 0.25, 1.00, 3.00
True Range
Per
cent
of T
arge
t
1 2 3 4 5 6
-10
-50
510
1520
SStarSSAT
Lag = 0.05, 0.10, 0.20, 0.50
![Page 27: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/27.jpg)
Percent Difference from Target Nugget(Median Nugget)
S=1, N= 0.10
True Range
Med
ian
1 2 3 4 5 6
-100
-50
050
100
SSTARSSAT
Lag = 0.05, 0.25, 1.00, 3.00
True Range
Med
ian
1 2 3 4 5 6
-100
-50
050
100
SSTARSSAT
Lag = 0.05, 0.10, 0.20, 0.50
![Page 28: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/28.jpg)
Summary
STAR- performed better than S and S with Satellites for estimating variogram parameters- robust to different lag classes
Multiple lag distances better than increased replication at fewer lag distances
Larger lag classes generally did better than shorter lag classes (eliminates “holes”)
![Page 29: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/29.jpg)
Final Design
Five “S” clusters and includes10 duplicates: five at star centers & five elsewhere)
![Page 30: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/30.jpg)
Further Research
• Choose another variogram model– Exponential
• Choose another variogram fitting algorithm– REML
• Simulate anisotropy• Investigate robustness to model misspecification• Explore other designs
![Page 31: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/31.jpg)
STARMAP and CITY OF SAN DIEGO?
• Outreach to a member of the EPA affiliates
• Research opportunity – real problem– Mapping consequences– Apparently no other US data exists which is
• spatially intense and
• near coastal
– This mapping requirement resulted from SD’s permit renewal
– Similar repeats are very likely
![Page 32: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/32.jpg)
MORE GENERAL QUESTION
• How much spatial correlation is there in aquatic systems, after accounting for habitat features?– I am trying to assemble spatially intense
relevant data sets in a number of settings– Ask for such data sets at EMAP 2004
Symposium in May• Have located a few
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SPATIALLY INTENSE DATA SETS
OF ENVIRONMENTAL RESPONSES
• Ohio River– Have 400+ sites
• Josh French is looking at this data
• Have about 60 Virginia stream sites• On two streams
• Access to a northeast estuary study 100+ points• Some spatial correlation demonstrated
• Detroit River – fairly short segment 60+ points
• San Diego study = near coastal
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SPATIALLY INTENSE DATA SETS
OF ENVIRONMENTAL RESPONSES
• Have nothing on wetlands• Other possibilities
– San Francisco Bay
• Preliminary observation – SD data shows greater range in the semivariogram than I had expected– Even after accounting for depth or particle size– Why had I expected that? Effluent is fresh water; it
rises fast from outfall. Coastal and tidal currents are strong there.
![Page 35: Multi-Lag Cluster Enhancement of Fixed Grids for Variogram Estimation for Near Coastal Systems Kerry J. Ritter, SCCWRP Molly Leecaster, SCCWRP N. Scott.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b5e91/html5/thumbnails/35.jpg)
END OF PLANNED PRESENTATION
• Questions and suggestions are welcome