Spatial interpolation for expansive area predictive modeling

1. Numerically Optimized Empirical ModelingNumerically Optimized Empirical Modeling
of Highly Dynamic, Spatially Expansive,of Highly Dynamic, Spatially Expansive,
and Behaviorally Heterogeneousand Behaviorally Heterogeneous
Hydrologic Systems – Part 2Hydrologic Systems – Part 2
Jana Stewart, U.S. Geological Survey, Middleton, WI
Matthew Mitro, Wisconsin DNR, Madison, WI
Ed Roehl, Advanced Data Mining, LLC, Greer, SC
John Risley, U.S. Geological Survey, Portland, OR

2. Part 1Part 1
International EnvironmentalInternational Environmental
Modelling and SoftwareModelling and Software
Society 2006, Burlington VTSociety 2006, Burlington VT

3. Well Locations
(100x100 miles)
16-year hydrographs Upper Floridan Aquifer,Upper Floridan Aquifer,
Suwannee River Valley, FloridaSuwannee River Valley, Florida
• Research – MLP ANNs to spatially interpolate
• Highly spatially discontinuous
– MLP ANNs – continuous functions
– Optimally segment well behaviors?
• High temporal variability

4. Western Oregon Stream Temperature ModelingWestern Oregon Stream Temperature Modeling
• Thermal TMDL
• Modeled Output - ST
hourly time series
Jun-Oct 1999 at 146
“pristine” sites
• Potential Inputs
– STATIC - 34 variables,
including stream
shading and basin
forestation
– CLIMATE TIME
SERIES - 65 hourly air
temperature, dew-
point, solar radiation,
barometric pressure,
snowpack, and
precipitation from 25
locations.
ST sites
Climatic sites
CoastRangeEcoregion
CascadesEcoregion
Klamath
Mountains
Ecoregion
Willamette
Valley
Eco-
region
Portland
Corvallis
Eugene
Ashland
PacificOcean

5. ObjectivesObjectives
• Model Highly Dynamic, Spatially Expansive,
and Behaviorally Heterogeneous Hydrologic
Systems
• Divide and conquer – big problem
transformed into multiple small problems
• Use a sequence of numerically optimized
algorithms
– minimize subjectivity

6. Steps (divide and conquer)Steps (divide and conquer)
1. SEGMENT DATA - into behavioral classes
• Cluster time series - k-means, SOM
– Intermediate cross correlation matrix
• Bonus – identifies redundant/unique sites for network
optimization
1. MODEL EACH BEHAVIORAL CLASS separately
• Process signals to separate low and high frequency
components
• “Stacked” data set for training
• Decorrelate input variables as needed
• ANNs – multivariate, non-linear curve fitting
• Sub-models of low and high frequency components,
combine predictions = “super model”
• Sensitivity analysis determines which static and time
series variables are predictive

7. Steps – cont.Steps – cont.
3. BUILD CLASSIFIER – to link static site
characteristics to dynamic behaviors (classes)
• static inputs ⇒ mapping function ⇒ class id
• krigging in Floridan Aquifer (x,y,class id)
• classification model
– Nearest neighbor classifier (linear)
– ANN-classifier (non-linear)
4. RUN MODEL
i. Input new site vector of static inputs
ii. Run classifier to select behavioral model
iii. Run behavioral model
iv. Write output

8. Clustering Results – Floridan AquiferClustering Results – Floridan Aquifer
12 classes – probably more12 classes – probably more
than necessarythan necessary
indicates well redundancyindicates well redundancy

9. Accuracy by ClusterAccuracy by Cluster
Actual
Prediction
C1C1
History from Apr 1982 to Oct 1998
NormalizedWaterLevel
aboveSeaLevel
C3C3
C6C6
C10C10

10. Super Model PredictionSuper Model Prediction
Gulf of Mexico
Max elevation above
sea level ~ 180 feet
Suw
annee
River
⇑⇑ run timerun time
applicationapplication
displaydisplay

11. Western Oregon – 1 of 6 validationWestern Oregon – 1 of 6 validation
sites not used for trainingsites not used for training
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20
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15
14
13
12
11
25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15
JUNE JULY AUGUST SEPTEMBER

12. Western Oregon – another validation siteWestern Oregon – another validation site
• Good dynamics
• Static inputs primary source of error
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25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15
JUNE JULY AUGUST SEPTEMBER

13. Part 2Part 2
HIC06HIC06

14. Wisconsin Temperature ModelingWisconsin Temperature Modeling
• Fisheries management
• Modeled Output
– 254 ST daily time series
measured Jun-Aug, 1990-2002
• temporally discontinuous –
different sites measured
different years
• Potential Inputs
– STATIC - 42 variables including
land cover, drainage area, and
streambed characteristics
– CLIMATE TIME SERIES- 353
daily air temperature, dew-point,
solar radiation, barometric
pressure and precipitation from
25 locations.

15. Asynchronous Site MonitoringAsynchronous Site Monitoring
• Modified time series clustering method
• Steps
a) Compile populations having overlapping signals
• 1998 to 2002 made up 241 of the 254 sites
a) Estimate # classes per population, then choose same k
for all populations. k=3 for Wisconsin model
b) Apply the standard time series clustering algorithm to
each population using k
c) Perform sensitivity analyses with prototype ANN
classification models - determine best static variables
d) Determine overall best static variables
e) Cluster all sites using best static variables
f) ANN dynamic models of each behavioral class as before.
g) ANN classification models as before for “new sites”

16. Best Static VariablesBest Static Variables
Top variables
Variable description 6 10 14
Land cover–agriculture (W) * * *
Area–drainage area (W) * * *
Land cover–forest (W) * * *
Bedrock depth–depth to bedrock (0?50 feet) (W) * * *
Surficial deposit texture–medium (W) * * *
Stream network–downstream link (S) * * *
Stream network–gradient (S) * *
Land cover–wetland (W) * *
Darcy value–darcy (W) * *
Bedrock depth–depth to bedrock (51?100 feet) (W) * *
Land cover–urban (W) *
Surficial deposit texture–fine (W) *
Bedrock type–sandstone (W) *
Bedrock depth–depth to bedrock (101?200 feet) (W) *

17. Measured & Predicted Class 1 Stream TempsMeasured & Predicted Class 1 Stream Temps
• 14 “test” sites not used to train ANNs
– concatenated
– June – August
• R2
=0.66
• Dynamically good
• Offsets (high or low) from static variables
measured predicted

18. ConclusionsConclusions
• Numerical methods
1. Signal processing, e.g., spectral filtering
2. Clustering, e.g., k-means
3. ANN non-linear, dynamic sub-models of behavioral
components assembled into super-model
4. Classification, e.g., ANN non-linear classifier
• Approach uses all available static and time series
data
• Divide and conquer makes big problems tractable
• Near optimal results – limited by data quality
• Compact finished model

19. Florida Everglades Water LevelsFlorida Everglades Water Levels
• In progress
• Water management
• Modeled Output - 260
real-time WL gages
• Potential Inputs
– STATIC - 6 variables –
x,y + 4 vegetation
– WL TIME SERIES - 260
real-time WL gages
• autoregressive