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

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

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We have two sources for forest variables, from direct measurements, which are always expensive and
would be sparse in space, and correlated LiDAR data that has complete coverage. The Bonanza Creek Experimental Forest (BCEF) is a Long-Term Ecological Research (LTER) site consisting of vegetation and landforms typical of interior Alaska. People are interested in three forest variables: above-ground biomass (AGB); tree density (TD); basal area (BA). The brightness, greenness, and wetness tasseled cap indices can be used as covariates to explain the forest variables. In the undergraduate workshop project, students can brainstorm from the easiest regression models to more sophisticated spatial models and compare the differences
of inferences from different ideas.

Group members: Richard Groenwald, Mehmut Hatip, Katrina Lewis, Jennifer Soter, Astride Tchkaoua, Sylvester Wieb

We have two sources for forest variables, from direct measurements, which are always expensive and
would be sparse in space, and correlated LiDAR data that has complete coverage. The Bonanza Creek Experimental Forest (BCEF) is a Long-Term Ecological Research (LTER) site consisting of vegetation and landforms typical of interior Alaska. People are interested in three forest variables: above-ground biomass (AGB); tree density (TD); basal area (BA). The brightness, greenness, and wetness tasseled cap indices can be used as covariates to explain the forest variables. In the undergraduate workshop project, students can brainstorm from the easiest regression models to more sophisticated spatial models and compare the differences
of inferences from different ideas.

Group members: Richard Groenwald, Mehmut Hatip, Katrina Lewis, Jennifer Soter, Astride Tchkaoua, Sylvester Wieb

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

  1. 1. Estimation of Above Ground Biomass in the Bonanza Creek Experimental Forest Richard Groenewald, Mehmet Hatip, Katrina Lewis, Astride Tchakoua, Sylvester Wiebeck
  2. 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. 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. 4. Data ● Forest Inventory Plots data ● G-LiHT LiDAR Plane Data ● LandSat Data
  5. 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. 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. 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. 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. 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. 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:
  11. 11. Correlation Structure
  12. 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. 13. Maximum Likelihood Estimation (Cont.) We maximize the profile likelihood function: with respect to the parameters in the covariance matrix [1].
  14. 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. 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.
  16. 16. Visualization http://rpubs.com/katlewis15/391861
  17. 17. Results (Model 2) Refit without P90 values, this time for entirely available satellite data: Fitted model:
  18. 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. 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. 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. 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. 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. 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

  • AGB- Tree above ground biomass (AGB) includes stem, branches, and leaves is ~52 carbon
  • 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.
  • Link to Share: https://docs.google.com/presentation/d/1MiwqEH6eu8xioQ4w-BN76F6jpZes2smUcNBivaSIJ8o/edit?usp=sharing

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