Hic06 spatial interpolation
Download as PPT, PDF1 like223 views
This document describes a methodology for numerically optimizing empirical models of highly dynamic, spatially expansive, and behaviorally heterogeneous hydrologic systems. The key steps are: 1) Segmenting data into behavioral classes using clustering algorithms. 2) Modeling each behavioral class separately with artificial neural networks (ANNs) to capture nonlinear dynamics. 3) Building ANN classifiers to link static site characteristics to dynamic behaviors. 4) Running the full model by classifying new sites and running the appropriate behavioral model. The approach is demonstrated on stream temperature, Floridan aquifer, and Wisconsin stream temperature modeling cases.
Hic06 spatial interpolation
- 1. Numerically Optimized Empirical Modeling of Highly Dynamic, Spatially Expansive, and Behaviorally Heterogeneous Hydrologic 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 1 International Environmental Modelling and Software Society 2006, Burlington VT
- 3. 16-year hydrographs Upper Floridan Aquifer, Suwannee River Valley, Florida • Research – MLP ANNs to spatially interpolate • Highly spatially discontinuous – MLP ANNs – continuous functions – Optimally segment well behaviors? • High temporal variability Well Locations (100x100 miles)
- 4. Western Oregon Stream Temperature Modeling ST sites Climatic sites • Thermal TMDL • Modeled Output - ST Portland hourly time series Pacific Ocean Willamette Jun-Oct 1999 at 146 egion “pristine” sites Valley Eco- region • Potential Inputs or des Ec Corvallis egion – STATIC - 34 variables, including stream cor shading and basin Casca ange E forestation Eugene – CLIMATE TIME SERIES - 65 hourly air R temperature, dew- Coast point, solar radiation, barometric pressure, Klamath snowpack, and Mountains precipitation from 25 Ecoregion locations. Ashland
- 5. Objectives • 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) 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. 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 Aquifer indicates well redundancy 12 classes – probably more than necessary
- 9. Normalized Water Level Accuracy by Cluster C1 Actual C3 Prediction above Sea Level History from Apr 1982 to Oct 1998 C10 C6
- 10. Super Model Prediction Max elevation above sea level ~ 180 feet ⇑ run time application Su w an display n ee River Gulf of Mexico
- 11. Western Oregon – 1 of 6 validation sites not used for training 21 20 19 18 17 16 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 site 14 13 12 11 10 9 8 7 6 5 25 30 5 10 15 20 25 31 5 10 15 20 25 31 5 10 15 JUNE JULY AUGUST SEPTEMBER • Good dynamics • Static inputs primary source of error
- 13. Part 2 HIC06
- 14. Wisconsin 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 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 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 Temps measured predicted • 14 “test” sites not used to train ANNs – concatenated – June – August • R2=0.66 • Dynamically good • Offsets (high or low) from static variables
- 18. Conclusions • 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 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