Predicting Median Substrate

1
Predicting Median Substrate

• for Oregon and Washington EMAP sites
• Utilizing GIS data

Julia J. Smith December 12, 2005
2
Why Predict Median Substrate?

• Indicator of overall stream health
• Bed load transport
• Stream Power
• Microinvertebrate habitat
• Fish habitat
• How is human development affecting a stream

3
What is LD50?

• LD50 is a measure of median substrate.
• Geometric mean of class boundaries
• Log10 of the geometric means
• Several samples at each site
• LD50 is the median value of
• log10(geometric mean of class)

4
Substrate Classifications
5
(No Transcript)
6
(No Transcript)
7
Geomorphic Metrics

• ? is the total bank-full shear stress
• ?s is the density of sediment
• ? is fluid density
• g is gravitational acceleration
• h is bank-full depth
• S is channel slope

8
Geomorphic Metrics
Distance-weighted Stream Power versus LD50 r
0.327, p-value 2.63 x 10 -12
9
Geomorphic Metrics
Outlet link mean slope versus LD50 r 0.214,
p-value 3.78 x 10-6
10
Geologic Metrics

• Percent Unconsolidated Geologic type versus LD50
• r -0.246, p-value 1.18 x 10-7

11
Climatic Metrics
Annual average precipitation versus LD50 r
0.199, p-value 1.56 x 10-6
12
Climatic Metrics

• Average annual potential evapotranspiration (mm)
  versus LD50
• r -0.046, p-value 0.342

13
Land Cover Metrics

• 1. Developed
• 2. Barren
• 3. Forest
• 4. Grasses
• 5. Agriculture
• 6. Wetlands
• 7. Open water/perennial ice and snow
• 8. Shrubland

14
Land Cover Metrics
Percentage of watershed that is forest versus
LD50 r 0.19, p-value 3.516 x 10-5
15
Distance-Weighted metrics

• j represents the land cover type of concern,
• Aj represents the total area for land cover type
  j in the watershed,
• represents the coefficient of exponential decay,
  
• represents average distance from outlet for
  land cover of type j
• n represents the total number of the land cover
  types

16
Additional Land Cover Metrics

• Buffered Metrics Buffered within a measure of
  the stream (30 meters, 100 meters, 300 meters)
• Buffered and Distance-weighted metrics

17
Goals

• Predict LD50 without visiting sites
• Small number of predictors for scientifically
  sensible model

18
Methods-Stepwise Variable Selection

• Multiple Linear Regression
• Top-in-tier models
• Top geomorphic models plus one from each of the
  remaining tiers

19
Akaikes Information Criterion
N observations p predictors RSS is the sum of
squared residuals
20
AIC in stepwise variable selection

• Forward Stepwise Selection -
• Method for choosing the top predictor from each
  tier
• Start with the intercept model
• Choose the variable that reduces AIC the most and
  include in model.
• Stepwise selection in both directions-
• Method chosen for choosing all top Geomorphic
  predictors
• Start with full model.
• Add and subtract variables until the model with
  minimum AIC is found or iteration stops.

21
Methods CART Classification and Regression
Trees
22
Methods CART Classification and Regression
Trees

• Predicted Response

23
Hybrid of Multiple Linear Regression and CART

• Utilize CART on the residuals
• Add indicator variables to the multiple linear
  regression equation for one minus the number of
  terminal nodes in the tree
• Create new multiple regression model with
  variables and indicator variables

24
Predictive-ability Statistics

25
Analysis Comparison Top 4-tier Models

• Problems with top 4-tier models
• Low Adjusted R2
• Low Predictive Ability
• Over-prediction and under-prediction of fine and
  bedrock substrate
• Non-normal residuals
• Benefit of top 4-tier models
• Small number of predictors

26
Example of Non-normality of ResidualsTop 4-Tier
Model
27
Analysis Comparison Geomorphic plus Top 3-Tier
Models

• Problems with top geomorphic plus top 3-tier
  model
• Increase in number of variables
• Predictive ability still low
• Over-prediction and under-prediction of fine and
  bedrock substrate
• Some collinearity between variables

28
Analysis Comparison Geomorphic plus Top 3-Tier
Models

• Benefits with top geomorphic plus top 3-tier
  model
• Improved predictions
• Improved normality of residuals

29
Comparison of Analysis - CART

• Problems with CART
• Low predictive-ability
• Predicts several observed substrate sizes in one
  node
• Over-prediction and under-prediction of fines and
  bedrock substrate
• Omitting one site creates different tree
• Benefits of CART
• Simple analysis
• Missing variables not an issue

30
CART Predictions
31
Comparison of Analysis-Hybrids

• Problems with hybrid models
• Increased number of variables
• Collinearity with introduction of node indicator
  variables
• Non-normal residuals

32
Comparison of Analysis-Hybrids

• Benefit of hybrid models
• Residuals closer to normal
• Increased predictive-ability
• Explains some of the variation created by fitting
  a linear model to ordinal data

33
One example Residual Tree forHybrid Geomorphic
plus Top 3-Tier Model

• Most promising multiple regression prediction
  model Geomorphic plus top 3-tier

34
One example Residual Tree forHybrid Geomorphic
plus Top 3-Tier Model
35
One example Observed vs. Predicted forHybrid
Geomorphic plus Top 3-Tier Model

• Plot of predictions against observed LD50

36
QQ-Plot of Residuals for Hybrid Model
37
Coast Range Ecoregion

• Less skewed distribution of LD50
• No measurements are outliers
• Similar ecosystem throughout region

38
Ecoregion Distributions
39
Coast Range EMAP Sites
40
Top 4-Tier Coast Range Model

• Predictors
• Average aspect (climatic)
• Average watershed elevation (geomorphic)
• watershed as volcanic geologic type (geologic)
• wetlands (distance weighted and buffered)

41
QQ-Plot Top 4-Tier Coast Range
42
Observed versus Predicted Top 4-Tier Coast
Range Model
43
Coast Range ModelTop Geomorphic Variables

• Average watershed elevation (m)
• Drainage density
• Mean slope within a 300-meter buffer
• Ratio of width of stream to width of floodplain
• Coefficient of average hill connectivity
• Distance to the first tributary (m)
• Percent of landscape with less than 4 slope
• Percent of landscape with less than 7 slope
• Measure of size and complexity of river
• Percent of stream as cascade
• Distance-weighted stream power
• Watershed relief divided by its length

44
QQ-Plot Coast Range Geomorphic plus Top 3-Tier
model
45
Observed versus Predicted Coast Range
Geomorphic Top 3-Tier
46
CART - Coast Range Ecoregion
Predictions versus Observed LD50
47
Coast Range Hybrid Models

• Benefits of hybrid
• Improved prediction
• Improved fit
• Improved normality of residuals
• Problems with hybrid
• Increased number of predictors
• Collinearity with node indicator variables

48
QQ-PlotCoast Range Hybrid Top 4-Tier
49
Observed versus PredictedCoast Range Hybrid Top
4-Tier
50
QQ-Plot Coast Range Hybrid Geomorphic plus Top
3-Tier
51
Observed versus Predicted Coast Hybrid
Geomorphic plus Top 3-Tier
52
Comparison of Coast Models
53
Conclusions

• LD50 is difficult to predict
• Additional geomorphic predictors increases
  prediction ability
• Hybrid models increase prediction ability
• More success in Coast Range Ecoregion

54
Future Work

• Logistic Regression
• Ordinal data treated as continuous in this study
• 12 categories might require more sophisticated
  methods
• Spatial Analysis
• Appears to be spatial correlation in distribution
  of LD50