Minnesota Forestry Research Notes Published by the Department of Forest Resources, University of Minnesota, St. Paul

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1 Minnesota Forestry Research Notes Published by the Department of Forest Resources, University of Minnesota, St. Paul May 2017 No. 302 Automating the Creation of Stem Maps for Permanent Forest Inventory Plots Using R (Revised) David C. Wilson, John M. Zobel, and Alan R. Ek 1 Abstract A method is presented and documented for constructing tree location maps for permanent field plots to aid remeasurement and usage of the tree and plot data. Keywords: continuous forest inventory, plot map, tree map, R Introduction Documenting change on permanent forest monitoring plots presents several challenges, especially for the specific trees over many observation cycles. Difficulties associated with identifying individual trees, and maintaining continuity in records over time can be greatly reduced through the use of tree location data, e.g., coordinates. Given such coordinates, plot maps provide an easily understood record of the position of each tree, along with various identifying characteristics (e.g. species, tree number, Dbh, tree class, etc.). Tree maps were developed for the 2014, 2000 and earlier remeasurements of the Cloquet Forestry Center (CFC) Continuous Forest Inventory (CFI) to help with the inventory process (see Shrestha et al. 2015; Dieser and Ek 2011). These maps have proved especially helpful in identifying trees which have been removed or lost through harvesting, competition, weather events, etc. In this case they were also a key tool for finding plot centers and for ensuring the accuracy of tree detail. This note describes the coded process and technical aspects of producing these tree maps. Methods and Results Maps for the above remeasurement, as illustrated in Figure 1, were created using the recorded distance and azimuth of each tree with respect to plot center as data inputs to an R (R Core Team 2015) script automating the production of tree maps for each inventory plot. Additional functions were also implemented to provide useful symbology indicating the species, tree number, and relative Dbh of each tree (linked to tree Dbh class), along with tree position on the plot. Summary statistics for trees per acre (TPA), basal area (BA), timber volume, and total biomass are also printed to the tree map for each inventory plot. Individual tree locations were also calculated as the tree locations were assigned (Figure 2). These tree locations were then output in Universal Transverse Mercator (UTM) coordinates consistent with UTM zone 15N. The R code shown in Appendix A was used to create the plot and tree maps. An initial set of maps was produced prior to the 2014 remeasurement to assist field crews with finding plot centers and identifying specific trees on the plots. A second set of maps and tree coordinates was also produced immediately following the re-measurement to create an updated product for analysis in subsequent studies. Three R functions were written and used together to create the tree maps. An initial function used to draw the plot circles was adapted from code presented by Madouasse (2011). This circle function depends only on the {base R package, which comes standard with the installation of R, and will overlay as many circles as desired on a plot using the add=true parameter of the plot function. A second function interprets the tree data (e.g. azimuth, distance, species, Dbh, tree class) 1 David Wilson is a Research Associate, Department of Forest Resources, University of Minnesota; John Zobel is an Assistant Professor, Department of Forestry, Wildlife & Fisheries, University of Tennessee; Alan Ek is Professor Emeritus, Department of Forest Resources, University of Minnesota. This work was supported by the Department of Forest Resources, the Interagency Information Cooperative, the Minnesota Agricultural Experiment Station, and the USDA NIFA McIntire-Stennis Cooperative Forest Research Program. 1

2 associated with a given plot, and adds a point for each tree to the map. Symbology is then adjusted based on tree species, Dbh, and tree class (e.g. live/dead, harvested, missing, etc.). A third wrapper function loops through a table of plot level data, reads summarized biometric statistics, and calls the tree mapping function for each plot. Biometric statistics were produced using the relationships and analytical techniques described by Walters and Ek (1993), Hahn (1984), Hahn and Carmean (1982), and Ek et al. (1984), and summarized by Shrestha et al. (2015) and Dieser and Ek (2011). Figure 1. A plot level map of all trees observed in the 2014 inventory. Trees present in the 2000 inventory, but missing or dead in 2014 are indicated by an X through the marker symbol. 2

3 c ɵ b a Trigonometric Relationships sin(ɵ) = opposite(a) / hypotenuse(c) cos(ɵ) = adjacent(b) / hypotenuse(c) tan(ɵ) = opposite(a) / adjacent(b) Pythagorean Theorem a 2 + b 2 = c 2, for any right triangle Figure 2: Schematic illustration of the trigonometric relationships used to calculate UTM coordinates for each tree observed in the 2014 CFC-CFI re-measurement. 3

4 Literature Cited and References Dieser, Peter J., and Alan R. Ek Cloquet Forestry Center continuous forest inventory for 2000: Analysis and integration with the historical database. Staff Paper Series No St. Paul, MN: University of Minnesota, Department of Forest Resources. Ek, Alan R.; Birdsall, Earl T.; Spears, Rebecca J A Simple Model for Estimating Total and Merchantable Tree Heights. Research Note NC-309. St. Paul, MN: U.S. Dept. of Agriculture, Forest Service, North Central Forest Experiment Station Hahn, Jerold T Tree volume and biomass equations for the Lake States. Research Paper NC-250. St. Paul, MN: USDA Forest Service, North Central Forest Experiment Station. Hahn, Jerold T., and Willard H. Carmean Lake States site index curves formulated. General Technical Report NC-88. St. Paul, MN: USDA Forest Service, North Central Forest Experiment Station. Hatch, Charles R., and Hugo H. John Cloquet Forest Center forest stand structure and growth estimates derived from permanent plots and a multiple random start sampling design. Sci. Jour. Ser. Paper No St. Paul, MN: University of Minnesota, Agriculture Experiment Station. Madouasse, A Shrestha, M., D.C. Wilson, J.M. Zobel, and A.R. Ek Cloquet Forestry Center continuous forest inventory Update for Staff Paper Series No St. Paul, MN: University of Minnesota, Department of Forest Resources R Core Team (2015). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL 4

5 Appendix A: R Code and Functions for creating Tree Maps. #' Load data tree2014 <- read.csv("../fia_rapidforestinventory/tree2014.csv", stringsasfactors=false) plot2014 <- read.csv("../fia_rapidforestinventory/plot2014.csv", stringsasfactors=false) cfc.2014.clean <- subset(tree2014, tree2014$treeclass!=5 & tree2014$treeclass!=7) cfc.2014.clean <- droplevels(cfc.2014.clean) #Function to draw a circle circle <- function(xorig, yorig, radius, add,...){ x <- seq(-radius, radius, length.out = 1000) # Euclidian distance to the origin y <- sapply(x, function(z) sqrt(radius^2 - z^2)) if(add == TRUE){ lines(xorig + c(x, rev(x)), c(yorig + y, yorig + rev(-y)), type = "l",...) else { plot(xorig + c(x, rev(x)), c(yorig + y, yorig + rev(-y)), type = "l",...) ######################################################################################### # Tree level mapping function tree.map2<-function(data,size.large=7,size.small=100,xlim=null,ylim=null,main=null, sub=null){ r<-sqrt(43560/(size.large* )) r2<-sqrt(43560/(size.small* )) plot(0,0,pch=18,xlim=c(-50,50),ylim=c(-50,50),xlab="ft",ylab="ft",main=main,sub=sub,col="grey44") #Draw the 1/7 th acre and 1/100 th acre plots with a North indicator. circle(0,0,r,add=t) circle(0,0,r2,add=t,lty=2) text(0,50,"n") # Add a point for each tree in the data. for(i in 1:length(data$TreeNumber)){ nodbh.flag<-f if(is.na(data$dbh[i])==t) { if(data$treeclass[i]==61 data$treeclass[i]==6){ nodbh.flag<-f else { dbh.exp<-1 nodbh.flag<-t if(data$azimuth[i]>0 & data$azimuth[i]<=90) { theta<-90-data$azimuth[i] A.sign<-1 O.sign<-1 5

6 if(data$azimuth[i]>90 & data$azimuth[i]<=180) { theta<-data$azimuth[i]-90 A.sign<-1 O.sign<--1 if(data$azimuth[i]>180 & data$azimuth[i]<=270) { theta<-270-data$azimuth[i] A.sign<--1 O.sign<--1 if(data$azimuth[i]>270 & data$azimuth[i]<=360) { theta<-data$azimuth[i]-270 A.sign<--1 O.sign<-1 col<-0 pch<-1 lwd<-1.5 if(data$species[i]==7 data$species[i]==8 data$species[i]==9 ) { col<-1 if(data$species[i]==1 data$species[i]==2 data$species[i]==3 data$species[i]==10) { col<-2 if(data$species[i]==4) { col<-3 if(data$species[i]==5) { col<-4 if(data$species[i]==60 data$species[i]==61) { pch<-0; col<-"goldenrod" if(data$species[i]==64){ pch<-0; col<-"purple3" if(col==0) { col<-"brown4"; pch<-5 if(pch==1) { if(data$treeclass[i]==61 data$treeclass[i]==6) { pch<-13; dbh.exp<-1.2 if(pch==0) { if(data$treeclass[i]==61 data$treeclass[i]==6) { pch<-7; dbh.exp<-1.2 if(pch==5) { if(data$treeclass[i]==61 data$treeclass[i]==6) { pch<-9; dbh.exp<-1.2 rad< *theta #convert azimuth angle to radians H<-data$Distance[i] if(data$azimuth[i]==0 & rad==0){ A<-H*sin(rad)*O.sign O<-H*cos(rad)*A.sign if(!data$azimuth[i]==0 & rad==0){ O<-H*sin(rad)*O.sign A<-H*cos(rad)*A.sign if(!rad==0){ O<-H*sin(rad)*O.sign A<-H*cos(rad)*A.sign data$utm.t.north[i]<-data$northing[i]+o* data$utm.t.east[i]<-data$easting[i]+a* if(nodbh.flag==f) points(a,o,cex=dbh.exp,col=col,pch=pch,lwd=lwd) 6

7 if(nodbh.flag==t) points(a,o,cex=dbh.exp,col=col,pch=17,lwd=1) if(dbh.exp<1) pos<-1 else pos<-dbh.exp text(a+pos,o+pos,data$ptn[i],cex=.5) ################################################################################################# # Define top level mapping function tree.map.auto2<-function(data,data.p,file,size.large=7,size.small=100,xlim=null,ylim=null){ pdf(file=file,width=6.7) tree2014.detail<-list() for(i in 1:length(unique(data$PlotNumber))){ data.t<-data[data$plotnumber==sort(unique(data$plotnumber))[i],] plot<-subset(plot2014, plot2014$plot_num==data.t$plotnumber[1] & plot2014$cond_class == 1) data.t$northing<-plot$northing[1] data.t$easting<-plot$easting[1] main<-paste("plot",data.t$plotnumber[1]) sub<-paste("tpa = ", plot$tpa[1], ", BA = ", format(plot$plot_ba[1], digits=5), ", CFVOL = ", format(plot$cfvolacre[1], digits=6), ", Biomass (tons) = ", format(plot$biomass[1], digits=4)) tree2014.detail[[i]]<-tree.map2(data=data.t,size.large=7,size.small=100,xlim=xlim,ylim=ylim,main=main, sub=sub) tree2014.update<-rbind.fill(tree2014.detail) write.csv(tree2014.update,file = "../FIA_RapidForestInventory/tree2014_UTM.csv") dev.off() # Call top level mapping function with necessary inputs tree.map.auto2(cfc.2014.clean, plot2014,file="../fia_rapidforestinventory/trees2014.pdf") 7