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Estimation of Above
Ground Biomass in the
Bonanza Creek
Experimental Forest
Richard Groenewald, Mehmet Hatip, Katrina Lewis, Astride Tchakoua,
Sylvester Wiebeck
Bonanza Creek
Experimental Forest
● Long-Term Ecological
Research (LTER) site within
Tanana Valley Alaska.
● Consists of vegetation and
landforms typical of interior
Alaska.
Project Goal
Create a continuous map of predicted
Above Ground Biomass (AGB) with
uncertainty quantification for the
Bonanza Creek Experimental Forest in
interior Alaska.
Data
● Forest Inventory Plots data
● G-LiHT LiDAR Plane Data
● LandSat Data
Steps Taken
1. Finding and exploring the data
2. Looking for relationships among the variables (AGB, TD and BA) and
covariates (the BGW tasseled cap indices)
3. Coming up with simpler models for a rough estimate, which takes less time.
4. Designing and implementing more complex models
5. Visualizing our model into a continuous map
All Relevant Variables
● P10..P100 values
● Tree Density (TD)
● Basal Area (BA)
● Brightness
● Greenness
● Wetness
● Land Cover Type (open water,
deciduous forest, etc.)
● Percent Tree Cover (Hansen)
● Location
Predictor Variables of AGB
● TD, BA measured along with AGB, only
on plot land
● Not relevant to measuring AGB on any
point in the map
● P90 and P100 have strong correlation
with AGB, and are measured in a
larger area with the LiDAR sensor
● Likewise, brightness, greenness,
wetness, and percent tree cover
measured everywhere in forest with
satellites
Simplified Models
● By basis of comparison, prevents skewed results
● Shows why we need a more complex model
○ They vary in answer because not all the data is considered
○ Instead, approximations are made
The simplest model: Add up the AGB of the 71 plots, multiply that out to
reflect the full forest size.
Simplified Model
● Based on simple spatial
model used in Colorado
data tutorial
● Inconsistent, but early
indicator of trends
● Proved necessity for a
more complex model, one
based on multiple
variables
Methodology
Let denote AGB and denote a vector of observed
explanatory variables. We model our response as follows:
where and
*Note: assume two error terms are independent.
- Mean function f may be any function of the explanatory variables. Note matrix
of transposed f vectors is our design matrix F
Conditioning as if we know R, we choose a vector c(x) which at unobserved x:
Correlation Structure
Maximum Likelihood Estimation
Denote
We assume (symmetric) is positive definite and thus invertible
with a Cholesky decomposition (i.e.
for some lower triangular and invertible L)
In this case, the MLE for , assuming R is KNOWN, is:
Maximum Likelihood Estimation (Cont.)
We maximize the profile likelihood function:
with respect to the parameters in the covariance matrix [1].
Results (Model 1)
Initially fit ordinary least squares stepwise regression to help guess at
covariates to use.
Settled on basic linear combination of P90, brightness, greenness, wetness,
and hansen (% of tree cover)
Imputed 51/284 missing values for P90 using initial spatial regression model.
Used imputations to construct final spatial regression model for AGB.
Results (Model 1)
Fitted Model:
Problem:
Note the negative AGB values: this
is an error in the model, possibly
due to imputation issues in P90.
Visualization http://rpubs.com/katlewis15/391861
Results (Model 2)
Refit without P90 values, this time for entirely
available satellite data:
Fitted model:
Model Verification
● We know the exact AGB for the plots, so if our model can predict that
number when we plug in the coordinates, then we are successful
● The satellite covariates give us a low-quality full map, which we can
compare to the map constructed by our model to validate results
Challenges faced
● How to account for missing data
● Observed AGB without consideration of tree species, due to limited time
● Large amounts of data caused technological difficulties with laptop
running time
Ideas for future work
Cross validation (dividing data into one used to learn or train a model and the
other used to validate the model) to estimate how accurately the predictive model
will perform in practice.
Incorporate uncertainty into the model predictions.
Fitting the Puzzle Together
Katrina - Powerpoint design, visualization of data using Leaflet
Richard - Model selection, choosing a covariance structure, obtaining resources
from papers/literature, coding, implementation
Mehmet- Discovering preliminary correlations through R, compiling full data set,
applying R tutorial knowledge in project
Astride - Document the challenges, and ideas for future work on the project.
Implement finishing touches to powerpoint.
Sylvester- Keep team spirits up, simplified models, ideas for future work, and
powerpoint work
Special Thanks to
● Statistical and Applied Mathematical Sciences Institute.
● Elvan Ceyhan, Doug Nychka, Chris Jones and Thomas Gehrmann for
organizing and supervising the workshop.
● Andrew Finley for giving us more insight about spatial models as well as
overview of the forest project.
● Huang Huang, our project leader.
Citations
1. Sacks, Jerome; Welch, William J.; Mitchell, Toby J.; Wynn, Henry P. Design and Analysis of Computer
Experiments. Statist. Sci. 4 (1989), no. 4, 409--423. doi:10.1214/ss/1177012413.
https://projecteuclid.org/euclid.ss/1177012413
2. Nychka, D., Furrer, R. & Sain, S. 2015. Package “fields.” CRAN.
3. Finley AO, Banerjee S, Carlin BP (2007). “spBayes: An R Package for Univariate and Multivariate Hierarchical
Point-Referenced Spatial Models.” Journal of Statistical Software, 19(4), 1–24. URL
http://www.jstatsoft.org/v19/i04/.
4. Bechtold, W.A. and Patterson, P.L. (2005). The Enhanced Forest Inventory and Analysis Program: National
Sampling Design and Estimation Procedures. US Department of Agriculture Forest Service, Southern Research
Station Asheville, North Carolina.
5. Jakubowski, M.K., Guo, Q., and Kelly, M. (2013). Tradeoffs between lidar pulse density and forest measurement
accuracy. Remote Sensing of Environment, 130, 245-253.
6. White, J.C., Wulder, M.A., Varhola, A., Vastaranta, M., Coops Nicholas, C., Cook, B.D., Pitt, D., and Woods, M.
(2013). A best practices guide for generating forest inventory attributes from airborne laser scanning data
using an area-based approach. The Forestry Chronicle, 89, 722-723.

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Undergraduate Modeling Workshop - Forest Cover Working Group Final Presentation, May 25, 2018

  • 1. Estimation of Above Ground Biomass in the Bonanza Creek Experimental Forest Richard Groenewald, Mehmet Hatip, Katrina Lewis, Astride Tchakoua, Sylvester Wiebeck
  • 2. Bonanza Creek Experimental Forest ● Long-Term Ecological Research (LTER) site within Tanana Valley Alaska. ● Consists of vegetation and landforms typical of interior Alaska.
  • 3. Project Goal Create a continuous map of predicted Above Ground Biomass (AGB) with uncertainty quantification for the Bonanza Creek Experimental Forest in interior Alaska.
  • 4. Data ● Forest Inventory Plots data ● G-LiHT LiDAR Plane Data ● LandSat Data
  • 5. Steps Taken 1. Finding and exploring the data 2. Looking for relationships among the variables (AGB, TD and BA) and covariates (the BGW tasseled cap indices) 3. Coming up with simpler models for a rough estimate, which takes less time. 4. Designing and implementing more complex models 5. Visualizing our model into a continuous map
  • 6. All Relevant Variables ● P10..P100 values ● Tree Density (TD) ● Basal Area (BA) ● Brightness ● Greenness ● Wetness ● Land Cover Type (open water, deciduous forest, etc.) ● Percent Tree Cover (Hansen) ● Location
  • 7. Predictor Variables of AGB ● TD, BA measured along with AGB, only on plot land ● Not relevant to measuring AGB on any point in the map ● P90 and P100 have strong correlation with AGB, and are measured in a larger area with the LiDAR sensor ● Likewise, brightness, greenness, wetness, and percent tree cover measured everywhere in forest with satellites
  • 8. Simplified Models ● By basis of comparison, prevents skewed results ● Shows why we need a more complex model ○ They vary in answer because not all the data is considered ○ Instead, approximations are made The simplest model: Add up the AGB of the 71 plots, multiply that out to reflect the full forest size.
  • 9. Simplified Model ● Based on simple spatial model used in Colorado data tutorial ● Inconsistent, but early indicator of trends ● Proved necessity for a more complex model, one based on multiple variables
  • 10. Methodology Let denote AGB and denote a vector of observed explanatory variables. We model our response as follows: where and *Note: assume two error terms are independent. - Mean function f may be any function of the explanatory variables. Note matrix of transposed f vectors is our design matrix F Conditioning as if we know R, we choose a vector c(x) which at unobserved x:
  • 12. Maximum Likelihood Estimation Denote We assume (symmetric) is positive definite and thus invertible with a Cholesky decomposition (i.e. for some lower triangular and invertible L) In this case, the MLE for , assuming R is KNOWN, is:
  • 13. Maximum Likelihood Estimation (Cont.) We maximize the profile likelihood function: with respect to the parameters in the covariance matrix [1].
  • 14. Results (Model 1) Initially fit ordinary least squares stepwise regression to help guess at covariates to use. Settled on basic linear combination of P90, brightness, greenness, wetness, and hansen (% of tree cover) Imputed 51/284 missing values for P90 using initial spatial regression model. Used imputations to construct final spatial regression model for AGB.
  • 15. Results (Model 1) Fitted Model: Problem: Note the negative AGB values: this is an error in the model, possibly due to imputation issues in P90.
  • 17. Results (Model 2) Refit without P90 values, this time for entirely available satellite data: Fitted model:
  • 18. Model Verification ● We know the exact AGB for the plots, so if our model can predict that number when we plug in the coordinates, then we are successful ● The satellite covariates give us a low-quality full map, which we can compare to the map constructed by our model to validate results
  • 19. Challenges faced ● How to account for missing data ● Observed AGB without consideration of tree species, due to limited time ● Large amounts of data caused technological difficulties with laptop running time
  • 20. Ideas for future work Cross validation (dividing data into one used to learn or train a model and the other used to validate the model) to estimate how accurately the predictive model will perform in practice. Incorporate uncertainty into the model predictions.
  • 21. Fitting the Puzzle Together Katrina - Powerpoint design, visualization of data using Leaflet Richard - Model selection, choosing a covariance structure, obtaining resources from papers/literature, coding, implementation Mehmet- Discovering preliminary correlations through R, compiling full data set, applying R tutorial knowledge in project Astride - Document the challenges, and ideas for future work on the project. Implement finishing touches to powerpoint. Sylvester- Keep team spirits up, simplified models, ideas for future work, and powerpoint work
  • 22. Special Thanks to ● Statistical and Applied Mathematical Sciences Institute. ● Elvan Ceyhan, Doug Nychka, Chris Jones and Thomas Gehrmann for organizing and supervising the workshop. ● Andrew Finley for giving us more insight about spatial models as well as overview of the forest project. ● Huang Huang, our project leader.
  • 23. Citations 1. Sacks, Jerome; Welch, William J.; Mitchell, Toby J.; Wynn, Henry P. Design and Analysis of Computer Experiments. Statist. Sci. 4 (1989), no. 4, 409--423. doi:10.1214/ss/1177012413. https://projecteuclid.org/euclid.ss/1177012413 2. Nychka, D., Furrer, R. & Sain, S. 2015. Package “fields.” CRAN. 3. Finley AO, Banerjee S, Carlin BP (2007). “spBayes: An R Package for Univariate and Multivariate Hierarchical Point-Referenced Spatial Models.” Journal of Statistical Software, 19(4), 1–24. URL http://www.jstatsoft.org/v19/i04/. 4. Bechtold, W.A. and Patterson, P.L. (2005). The Enhanced Forest Inventory and Analysis Program: National Sampling Design and Estimation Procedures. US Department of Agriculture Forest Service, Southern Research Station Asheville, North Carolina. 5. Jakubowski, M.K., Guo, Q., and Kelly, M. (2013). Tradeoffs between lidar pulse density and forest measurement accuracy. Remote Sensing of Environment, 130, 245-253. 6. White, J.C., Wulder, M.A., Varhola, A., Vastaranta, M., Coops Nicholas, C., Cook, B.D., Pitt, D., and Woods, M. (2013). A best practices guide for generating forest inventory attributes from airborne laser scanning data using an area-based approach. The Forestry Chronicle, 89, 722-723.

Hinweis der Redaktion

  1. AGB- Tree above ground biomass (AGB) includes stem, branches, and leaves is ~52 carbon
  2. After compiling the full data set and going over the documentation outlining what variables we were given, these variables were selected as the ones most relevant to AGB. P10..100 were taken on site along with TD, BA, and the type of land cover, while brightness, greenness, wetness, and percent tree cover were taken on a satellite.
  3. Link to Share: https://docs.google.com/presentation/d/1MiwqEH6eu8xioQ4w-BN76F6jpZes2smUcNBivaSIJ8o/edit?usp=sharing