Forest Service Rocky Mountain Research Station General Technical Report RMRS-GTR-329 September 2014

United States Department of Agriculture

National FIA Plot Intensification Procedure Report

Jock A. Blackard and Paul L. Patterson
Rocky Mountain Research Station

Publishing Services

Available only online at http://www.fs.fed.us/rm/pubs/rmrs_gtr329.html

About the cover: The cover graphic illustrates FIA’s sampling frame (blue hexagon) subdivided into smaller hexagons or sub-regions using the GRID method. Sub-regions are 

color-shaded to represent a 4x intensification level within each sampling frame. Existing 

FIA plots are shown as black triangles, randomly placed intensified plots are gold stars, 

and the labels identify the corresponding intensity number for each intensified plot. Those 

sub-regions that will not receive a new intensified plot are assigned the number 0. Cover 

artwork by Jock A. Blackard.

Blackard, Jock A.; Patterson, Paul L. 2014. National FIA plot intensification procedure 

report. Gen. Tech. Rep. RMRS-GTR-329. Fort Collins, CO: U.S. Department of Agriculture, 

Forest Service, Rocky Mountain Research Station. 63 p.

Abstract

The Forest Inventory and Analysis (FIA) program of the U.S. Forest Service (USFS) measures a spatially distributed base grid of forest inventory plots across the United States. 

The sampling intensity of plots may be increased in some regions when warranted by 

specific inventory objectives. Several intensification methods have been developed within 

FIA and USFS National Forest Systems regions; however, a national standard routine for 

plot intensification does not exist. This report examines eight candidate intensification 

methods by a developed set of evaluation criteria, and based on those results proposes 

that FIA adopt the GRID method as its national plot intensification procedure. It is also 

suggested that the current version of the GRID method be updated by converting it to an 

ESRI ArcGIS add-in tool.

Keywords: sample intensification, forest inventory, plot intensification, Forest Inventory 

and Analysis 
Authors

Jock A. Blackard is a Forester/GIS Analyst, USDA Forest Service, Rocky Mountain 

Research Station, Inventory and Monitoring Program, Ogden, Utah.

Paul L. Patterson is a Statistician, USDA Forest Service, Rocky Mountain Research 

Station, Inventory and Monitoring Program, Fort Collins, Colorado.

Acknowledgments

The National FIA Plot Intensification Task Team involved many employees from the 

U.S. Forest Service (USFS). The USFS representatives who helped by serving as 

core members of this task team are: Jim Alegria (WO, Forest Management), Larry 

DeBlander (Region 4, RO), Mark Hatfield (NRS-FIA), Kama Kennedy (Region 5, 

RO, Remote Sensing Lab), Andy Lister (NRS-FIA), Joe McCollum (SRS-FIA), Kevin 

Megown (WO, Remote Sensing Application Center), Michael Schanta (Region 9, 

Mark Twain NF), Tom Thompson (PNW-FIA) and Ken Winterberger (PNW-FIA). 

The USFS representatives who supported this effort by serving as consulting 

members of the task team are: Carol Alerich (NRS-FIA), Renate Bush (Region 1, 

RO), John Coulston (SRS-FIA), Don Fallon (Region 4, RO), Kevin Halverson (WO, 

Remote Sensing Application Center), Dennis Jacobs (SRS-FIA), Andrew Kies (Region 

1, RO), James Menlove (IW-FIA), David Meriwether (Region 8, RO), Gretchen 

Moisen (IW-FIA), Carlos Ramirez (Region 5, RO, Remote Sensing Lab), Charles 

Scott (NRS-FIA), Barry Wilson (NRS-FIA) and Joseph D. Zeiler (Region 1, RO). 

Contact information for each member is given in Appendix A. We appreciate 

the assistance from each task team member in testing the various intensification 

methods and developing this report. 

We also thank John Coulston and Joe McCollum for providing valuable support, 

documentation, and various examples for the GRID method. John Coulston also 

provided many R script examples and background information on the Clark & 

Evans and Ripley’s K statistics. Joe McCollum provided additional insights on 

the results obtained from these statistics, as well as produced several figures for 

various intensification methods. 

For assistance with the remaining intensification methods examined by the task 

team, much gratitude to Kirk Evans; a GIS Analyst at Tetra Tech and contractor 

for the USFS Region 5 Remote Sensing Laboratory. Kirk ran the R5 method for 

USFS Region 5 intensification tasks, and detailed this methodology and shared 

its documentation with the task team. Also, thanks to Andy Lister who provided 

many examples, documentation, and an AML script for the NIMAC or SFC method. 

The RIPL program, written by J.D. Zeiler, was developed primarily to support a 

mid-level inventory system for USFS Region 1. Much thanks to J.D. for his patience 

and assistance in the initial setup of the RIPL program and his insight and analysis of the RIPL method. The Python4x method, developed by Tom Thompson, 

has been used for various intensification tasks for the PNW-FIA region. At the 

request of the task team, Tom updated his original program to allow an option of 

conducting either a 2x or a 4x intensification. We appreciate his efforts, analysis, 

and valuable insight of the Python4x method. The R4 intensification method, 

proposed by Larry DeBlander, is used for USFS Region 4 intensification projects. 

Much thanks to Larry for sharing his knowledge of FIA sampling designs (past 

and present), along with his assistance in testing this method. 

While we have tried to thank all that helped, please forgive us if we have omitted 

anyone who assisted in this effort.

i
Executive Summary

This report addresses the need for the U.S. Forest Service (USFS) Forest 

Inventory and Analysis (FIA) program to adopt plot intensification methodologies that meet a set of desired criteria. A variety of methodologies 

exist within FIA and National Forest Systems regions for constructing plot 

intensifications, but there seems to be no consensus on a national procedure for intensifying plot locations.

The primary objectives of this proposal were to 1) identify various intensification methods currently being implemented by FIA or utilized by other 

USFS National Forest Systems regions; 2) develop a set of characteristics 

and assumptions used to evaluate these methods, which are separated into 

two groups: a critical group in which an intensification method was not 

considered further unless it met each criterion, and a non-critical group 

which contains desirable traits but a missing criteria would not eliminate 

that method; 3) examine each intensification method using these characteristics and assumptions; and 4) recommend a potential national FIA plot 

intensification procedure that would adequately address the needs for all 

FIA regions. 

After examining eight plot intensification methods, the core members of 

the task team (Appendix A) recommend a national FIA plot intensification 

procedure that includes adopting the GRID method to create sub-regions 

for each FIA Phase 2 (P2) hexagon, and then randomly assign new plots 

within those sub-regions that do not contain an existing FIA base plot. 

We also suggest that the current version of the GRID method be updated 

and incorporated in an ESRI ArcGIS add-in tool. An FIA analyst would be 

able to execute the GRID method for intensification projects within the 

confines of ArcMap, which would remove the need to import/export files 

from other programs.

We show that for a 4x intensification of the Bighorn National Forest in Wyoming, assigning panels and subpanels to intensified plots using a procedure 

derived from the traditional method of creating a 10-year panel system from 

a 5-year panel leads to an east-west banding of plots. We recommend an 

alternative approach to assigning panel and subpanel values for intensified 

plots as detailed in the Methods section. 

ii
Table of Contents

Executive Summary..........................................................................ii

Introduction.......................................................................................1

Methods............................................................................................3

Critical Group .................................................................................. 4

Non-Critical Group .......................................................................... 5

Statistical Characteristics................................................................ 6

GRID Method .................................................................................11

R5 Method .................................................................................... 15

NIMAC or Space-Filling Curves (SFC) Method ............................ 17

RIPL Method ................................................................................. 19

Python4x Method .......................................................................... 22

Repeating Shapes Method ........................................................... 24

R4 Method .................................................................................... 26

Simple Random Sample Method .................................................. 27

Results............................................................................................28

Clark and Evans Statistic .............................................................. 28

Ripley’s K Statistic......................................................................... 33

Intensification Team Survey .......................................................... 42

Panelizing Plots ............................................................................ 42

Discussion and Conclusions...........................................................48

Intensifying Plots........................................................................... 48

Panelizing Plots ............................................................................ 52

References .....................................................................................54

Appendix A......................................................................................56

Appendix B.....................................................................................57

Appendix C.....................................................................................58

Appendix D.....................................................................................59

Appendix E.....................................................................................60

Appendix F .....................................................................................63

iii

USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 1

Introduction

In the late 1990s, the United States Forest Service (USFS) Forest Inventory 

and Analysis (FIA) program began using a national set of hexagons (approximately 6000 acres each) to spatially distribute the placement of their Phase 2 

(P2) plots. These hexagons (P2 hexagons or P2 hexes in this report) were based 

on the existing Forest Health Monitoring (FHM) hexagon network. This FHM 

national sampling frame was previously derived by performing a spatial offset 

of the EMAP (U.S. Environmental Protection Agency’s Environmental and Assessment Program) hexagon network (Reams and others 2005b).

The same methodology that was used to create the national FIA P2 grid of plots 

can also be used to develop more intensive hexagons in specific geographic areas if needed (Coulston and others 2009). This methodology, however, involves 

the use of C programs and ArcInfo (ESRI 2001) AML (ARC Macro Language) 

programs that were written in the 1990s. The user is typically required to download additional software (CYGWIN for example, www.cygwin.com) to run a 

compiled C program executable file. Additional time may also be required to 

become familiar with the various parameter settings for this program to work 

correctly. Nonetheless, the programs are already written and have been implemented numerous times for such tasks.

As computing and GIS software has made advances over the past few decades, 

so has the number of scripts made available to members of the GIS community. 

These scripts can generate hexagons or other polygon features across a defined 

geographic area and are accessible on various websites, such as ESRI’s GIS 

support forums (http://support.esri.com/en/). A GIS user can simply download 

a script (such as Jenness 2009), install it in ArcMap (ESRI 2009) and generate 

hexagons based on user-specified parameters in a more user-friendly wizardstyle environment. This enables hexagons of various sizes to be created relatively 

quickly for any geographic area.

Other intensification routines are also used within FIA; each method has merit 

and benefits in creating intensified plots locations. However, the potential for a 

standard national routine for plot intensification that incorporates various FIA 

needs should be investigated.

An invitation was issued to all FIA regions and National Forest System (NFS) 

regions soliciting intensification methods, and a core group was formed to evaluate these various methods. In addition to the core group, there was a group of 

consulting members who were asked for advice. The members of the core group 

and consulting members are listed in Appendix A.

Once the core group was established, a list of factors for evaluating plot intensification procedures was rated by each member of the team. These factors and 

results of the survey are shown in Appendix B.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 2

The Bighorn National Forest (BNF) located in north-central Wyoming was selected as a case study to conduct an evaluation of the intensification methods. 

The study area contains 303 P2 hexagons that extend across the BNF boundary 

(figure 1). Actual FIA plot locations were used in these evaluations, which allowed an appraisal of the implementation of these intensification schemes. A 

set of characteristics and assumptions, which are properties each intensification 

method should exhibit, were developed by the core team.

Figure 1—The Bighorn National Forest, primarily located in north-central Wyoming, is the study 

area. Note that with a buffer zone, 303 P2 hexagons extend across the forest boundary. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 3

While some plot intensification tasks may require a relatively large number 

of intensified plots to be established for a given project (experimental forests, 

special projects, etc.), the core group focused their efforts primarily on those 

requirements needed for more commonly used FIA intensification tasks (state or 

forest intensifications, etc.); where 7x was considered a reasonable upper limit. 

The core group selected a 4x level of intensification for the case study, which 

is defined as an existing FIA base plot plus three new intensified FIA plots 

within a given P2 hexagon. This level of intensification generally encompasses 

what is requested from FIA for their statewide intensification tasks (2x to 4x 

levels), and is typically the intensification level that is selected once budgetary 

constraints are examined.

While the focus of the core team was specific to FIA needs, the intensification 

methodology and results presented in this report would likely assist in various 

plot intensification efforts outside the FIA program. Many land management 

agencies typically have some type of sampling routine in place that provides 

“ground-truth” data in support of their efforts to summarize or model natural 

resource assets across their land holdings. The topics presented in this report 

should also benefit those agencies that utilize some type of hexagonal sampling 

program.

The purpose of this report is to:

•	 describe the intensification schemes that were compared,

•	 discuss basic attributes that are common to each intensification scheme,

•	 develop statistical measures used to objectively evaluate the intensification schemes and report results,

•	 state decision rules and technical characteristics used to evaluate the 

intensification schemes and report results, and

•	 recommend an intensification method for FIA to implement.

Methods

The core team members evaluated eight candidate intensification schemes during this effort:

1. GRID method (USFS SRS-FIA; C program and ArcInfo AML)

2. R5 method (USFS Region 5; python script)

3. NIMAC or Space Filling Curves (SFC) method (USFS NIMAC; 

ArcInfo AML)

4. RIPL method (USFS Region 1; ESRI ArcGIS add-in tool)

5. Python4x method (USFS PNW-FIA; python script)
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 4

6. Repeating Shapes method (ESRI download, ArcGIS tool)

7. R4 method (USFS Region 4; utilizing existing B-grid plots)

8. Simple Random Sample method (used for comparison purposes)

Rather than provide descriptions of these schemes, a discussion of basic attributes that—for this study at least—any intensification scheme should satisfy will 

be presented, followed by the statistical measures and technical considerations 

used to evaluate these methods. Afterwards, a description for each of the eight 

candidate intensification schemes is given.

The characteristics and assumptions used to evaluate these schemes may 

be separated into two groups: a critical group in which a candidate scheme 

will not be considered further unless it meets each criterion; and a noncritical group which contains desirable traits but a missing criteria would 

not eliminate a scheme.

Critical Group

One critical assumption is that an intensification scheme must accommodate the 

existing FIA grid; that is, the intensification method must not drop any base grid 

plots. In addition, the existing FIA paneling system and re-measurement cycle 

must be preserved. Additional plots may make use of the existing FIA paneling 

system but cannot change it.

Another assumption is that intensification is performed within each P2 hex primarily to maintain the one-to-one relationship between the unique plot identifier 

and the P2 hex identifier in the FIA database. One implication to using the P2 

hex boundary as the basis for intensification is that the number of intensified 

plots may be reduced after “clipping” the P2 hex area by the boundary of an 

intensification region (or study area). This is done to assure each plot location 

has an equal probability of selection. The result is that the number of intensified 

plots is random and a function of the number of partial hexes found within the 

boundary of the study area. If the intensification boundary is geographically 

coincident with the P2 hex boundary, then the number of plots (base and intensified) will equal the intensification number times the number of P2 hexes in 

the intensification region.

The intensified plots should also be established in a random manner, within a 

design that encourages spatial balance among plots compared to using simple 

random sampling within a P2 hex. Spatial balance is commonly enhanced by 

utilizing “sub-hex” polygons that are fully circumscribed within each P2 hex.

Also, all areas of a P2 hex outside of the sub-hex polygon that contains the base 

plot have an equal probability of being selected for the location of an intensified 

plot; no constraints are imposed for some minimum distance between plots or 

their corresponding hex boundaries.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 5

A related assumption is FIA plot identification numbers are P2 hex centric, 

such that the plot identification number is based on the P2 hex from which that 

plot is located; it is critical that each intensified plot is identified by the P2 hex 

where its plot center is positioned.

Non-Critical Group

For our considerations, plots were deemed “inside” of an intensification region 

boundary (or study area) if their plot centers fell within that boundary. Thus, the 

entire FIA plot was used as a unit of measure, rather than an individual subplot 

location. So-called “partial plots,” or the data utilized from individual subplots 

within an area of interest, were not considered in this study. As a result, an FIA 

plot may be determined to be within the study area boundary, but still have one 

or more of its subplots outside the study area. Alternatively, it is also possible 

that an FIA plot is found to be outside the study area boundary, but still have a 

subplot location within the study area that would not be included. Overall, the 

potential bias generated from these types of situations is acceptable.

We acknowledge that some study areas may contain a patchy network of areas 

(such as National Forest lands) that may be under-sampled by using an entire 

FIA plot as a unit of measure. Alternative units of measure may include other 

parts of an FIA plot, such as a subplot that is totally contained within the intensification area may be measured. If needed, these alternative units of measure 

may be used by an analyst on a case-by-case basis with any of the potential 

intensification methods described in this document. The study area boundary 

was initially buffered by some sufficient distance (typically by two P2 hexes; 

figure 1), so that any possible “border” effect would not influence the placement 

of these newly intensified plots. This “unit of measure” modification will not 

change the geospatial properties of the resulting intensified plots, and it was 

these properties on which we based our decision of intensification method to 

recommend.

The current FIA sample of plots was constructed in the 1990s using the procedure documented by Reams and others (2005b). For additional technical details, 

see Brand and others (2000), McCollum (2001), McCollum and Cochran (2005), 

and McCollum and others (2008). In this procedure, if there were one or more 

“historical” FIA plots within a P2 hex, then one was randomly selected as the 

base plot for that specific hex. Otherwise, a random point was chosen within the 

P2 hex as the new FIA base plot. The construction of the historical plot locations 

differed among FIA regions; some were established along equal intervals while 

others used a random component. An idealized version of the FIA sample locations may be described as a tessellation of the area, with a random plot location 

within each section of the tessellation (Reams and others 2005b).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 6

Statistical Characteristics

An intensification scheme should preserve the spatial distribution characteristics 

of the FIA base grid. Since the current FIA base grid was created in the late 

1990s from previously existing FIA grids (Reams and others 2005b), the spatial 

distribution of FIA base plots varies from region to region; hence, a statistical 

measure is needed to evaluate its spatial properties. Based on the discussion presented in Perry and others (2006), the first-order Clark and Evans (CE) statistic 

and the second-order Ripley’s K (K) statistic were selected as statistical tools to 

provide an evaluation of each intensification method. The CE and K values were 

calculated for three sets of plots: the base FIA plots, the intensified plots, and the 

combined set of base FIA plots and intensified plots. The CE and K values for 

the intensified plots and the combined set of base and intensified plots should 

be similar to the CE and K values for the FIA base grid. The CE statistic is a 

nearest neighbor based estimate that provides a basic measure of clustering or 

ordering of point patterns, and is derived by calculating the mean distance of 

each location to its nearest neighbor. The K statistic is a distance based estimator 

and is typically compared to the theoretical K value for a completely random 

point pattern. These calculations were produced using the CE and K packages 

in R statistical software (The R Foundation for Statistical Computing 2012).

First-order properties typically focus on the mean number of events per unit area, 

while second-order properties are related to its variance (Perry and others 2006). 

These statistics were selected to analyze the resulting spatial point patterns of 

intensified plots locations for our study, since they are widely used and accepted 

in spatial ecology literature (Perry and others 2006). The selection of FIA base 

plot locations within a P2 hex can differ between various FIA regions so both 

statistics were used as complementary measures to compare how closely the 

intensified plot indices mirrored those from the original FIA base plot indices.

While both statistics are commonly used, there are also limitations to using 

Clark and Evans and Ripley’s K statistics. Perry and others (2006) describe how 

first-order tests (for example, CE) are capable of accurately describing patterns at 

shorter distances, but are generally not able to characterize patterns at distances 

further than local interactions. They also indicate that for second-order tests 

(for example, Ripley’s K); values of the statistic for some given distance may be 

strongly influenced by its values at shorter distances. In summary, Clark and 

Evans is highly scale dependent, while Ripley’s K is influenced by a cumulative 

effect from shorter distances.

For the Clark and Evans statistic, ArcMap version 9.3.1 (ESRI, Inc. 2009) was 

used to create point shapefiles from the various intensification methods, and R 

version 2.15.0 (The R Foundation for Statistical Computing 2012) to calculate 

their corresponding CE values. As a point of reference, a completely random point 

distribution has a CE value of 1.0, while a maximum aggregation distribution 

(clumping) has a CE value of 0.0, and a maximum spacing (uniform) distribution has a CE value of 2.1491 (Clark and Evans 1954). Appendix C contains the 

R script template used to calculate the CE value.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 7

For comparison against the CE values calculated for the various intensification 

methods, the distribution of CE values were also found by performing simulations using 4000 iterations, to determine the mean and 95% confidence interval 

values for the following scenarios: (1) 4000 point shapefiles, extending across 

303 P2 hexes (spanning the Bighorn NF boundary), containing one random point 

per P2 hex (303 plots); (2) 4000 point shapefiles, extending across 303 P2 hexes 

(spanning the Bighorn NF boundary), containing 303 random points with no P2 

hex constraints (303 plots); (3) 4000 point shapefiles from (1) above, but with 

points clipped to the Bighorn NF boundary (approximately 186 plots each); and 

(4) 4000 point shapefiles from (2) above, but with points clipped to the Bighorn 

NF boundary (approximately 187 plots each). CE values were calculated for these 

various simulation scenarios to first obtain the CE values from their theoretical 

plot placement procedure, and second to test the effect of clipping to the BNF 

boundary on CE values from these scenarios.

For the Ripley’s K statistic, ArcMap version 9.3.1 (ESRI, Inc. 2009) was used 

to create point shapefiles from the various intensification methods, and R version 2.15.0 (The R Foundation for Statistical Computing 2012) to calculate 

their corresponding K values. The resulting K values are then displayed in a 

zero-line horizontal graph within a simulation envelope, which approximates 

a 95% confidence limit (the R script template used to calculate the K value is 

provided in Appendix D).

To complement the spatial balance obtained by inventorying one FIA base plot 

within each P2 hex, FIA also employs a paneling system to achieve a temporal 

balance of sample plots. A panel represents a given measurement year within 

one full cycle of plot measurements (for example, a 10-year cycle in this study). 

As described in Reams and others (2005b), FIA regions typically schedule their 

annual plot inventories based either on a 5-year (funding for 7-year) or 10-year 

cycle.

FIA assigns panel values to P2 hexes as described in Brand and others (2000), 

McCollum (2001), McCollum and Cochran (2005), and McCollum and others 

(2008). A brief outline of this process is provided since our assignment of panel 

and subpanel (hereinafter panel.subpanel) values for intensified plots is based 

on this procedure. Additional details and related discussions on FIA’s panel and 

subpanel approaches can be found in Reams and others (2005a). For a 5-year 

rotation, the five panels are denoted by 1, 2, 3, 4 and 5; these numbers correspond to each year of the cycle that plots are measured. Figure 2a shows how 

the P2 hexes were assigned to a five-panel arrangement based on the sequence 

1-3-5-2-4, with an offset of three hexagons for each southern-neighboring row 

of P2 hexes. In figures 2a and 2b, the P2 hexes are shown as the smaller-sized 

hexes, while the larger single hex represents an FHM hex. Note that for a 5-year 

cycle, each panel has a corresponding subpanel value of one.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 8

Figure 2b—Assignment of hexagons to a ten-panel 

arrangement (shown by number), as shown in Figure 3 

of Brand and others (2000).

Figure 2a—Assignment of hexagons to one of five panels 

(shown by number), as shown in Figure 2 of Brand and 

others (2000).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 9

For a 10-year rotation, the five panel example above was doubled by utilizing 

two subpanel values (1 or 2). The order of panel.subpanel measurement years 

within a 10-year cycle is given as: 1.1, 2.1, 3.1, 4.1, 5.1, 1.2, 2.2, 3.2, 4.2 and 5.2 

(all the subpanel 1 values are measured first). Note that 1.1, 2.1, 3.1, 4.1 and 

5.1 are denoted by their panel number (which corresponds to their measurement year), and 1.2, 2.2, 3.2, 4.2 and 5.2 are represented by 6 through 10 (their 

measurement year). Thus, a measurement year of 10 would be represented as 

5.2, while a measurement year of 3 would be listed as 3.1. The assignment of 

P2 hexes to a panel.subpanel value was derived from the five-panel assignment 

(figure 2a) and the two panel.subpanel sequences of: 1.2-3.2-5.2-2.1-4.1 and 1.1-

3.1-5.1-2.2-4.2. The first sequence is applied to the first two rows of figure 2a, so 

that the subpanel number was adjoined to the panel number in figure 2a; which 

transforms the sequence 1-3-5-2-4 in the 5-year cycle to the sequence 6-8-10-

2-4 in the 10-year cycle, which is the sequence of the first two rows of figure 

2b. The second sequence is applied to the third and fourth rows of figure 2a, 

transforming 1-3-5-2-4 in the 5-year cycle to 1-3-5-7-9 in the 10-year cycle and 

producing the rows three and four of figure 2b. This process is then repeated; 

that is, the sequence 1.2-3.2-5.2-2.1-4.1 is used to transform rows five and six 

of figure 2a to rows five and six of figure 2b. Notice that the repetition of these 

sequences across two adjoining rows of P2 hexes leads to bands of P2 hexes 

that run basically in an east-west direction, as shown in figure 3a for measurement year 1 (or panel.subpanel 1.1) in the 10-year cycle. Note that the odd years 

are all in one set of bands and even years are in the other set of bands; for this 

reason we will refer to the bands as odd and even bands. Given the sparseness 

of the 10-year panels, this “banding” does not have a clumping effect on the 

distribution of plots (see figure 3a).

As part of the process of assigning panel numbers to intensified plots, an intensity number is assigned to each plot. The intensity numbers run from 1 to the 

intensification level; for example, in a 4x intensification the intensity numbers 

are 1, 2, 3, and 4. The intensity numbers are assigned to plots within a given P2 

hex so that the base plot has an intensity number 1 and the intensified plots are 

assigned the remaining numbers.

To assign a panel.subpanel value to each intensified plot within a given P2 hex, two 

inputs of information were used: (a) the existing base plot’s panel.subpanel value, and 

(b) the intensified plot’s intensity number, and application of the sequences described 

in the previous paragraphs (or a variant of those sequences). A natural approach 

would be to use the base plot’s panel.subpanel value to find a starting place in the 

Brand sequences (Brand and others 2000), and assign the panel.subpanel for the 

intensified plots in the P2 hex based on their intensification numbers. For example, 

assume the base plot of a hex was in panel.subpanel 5.2, and the 1.2-3.2-5.2-2.1-4.1 

sequence was used, starting in the 5.2 position. The intensified plot with intensity 

number 2 would then be assigned to panel.subpanel 2.1, while the intensified plot 

with intensity number 3 would be assigned to panel.subpanel 4.1, and finally the 

intensified plot with intensity number 4 would be assigned to panel.subpanel 1.2. 
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We refer to this method as the Extension of Base Method, or EBM. The problem 

with this approach is the panel.subpanel assignments for the intensified plots in a 

P2 hex are in the same band as the base plot, and the slight appearance of odd or 

even year bands for the base P2 plots (see figure 3a) is accentuated by the higher 

plot density, as shown in figure 3b.

The drawback to the EBM is that intensified plots are in the same band (spatial 

arrangement of plots running basically east-west) as their corresponding base 

plots. To displace some of these intensified plots outside the band of their corresponding base plots, the 1, 3, 5, 2, 4 sequence was used, but then we kept the 

subpanel number the same as that of the base plot’s subpanel number (rather 

than potentially changing the intensified plot’s subpanel number based on the 

EBM). For example, if the base plot was in panel.subpanel 5.2, then an intensified plot with intensity number 2 would be assigned to panel.subpanel 2.2, while 

the intensified plot with intensity number 3 would be assigned to panel.subpanel 

4.2, and the intensified plot with intensity number 4 would be assigned to panel.

subpanel 1.2, which correspond to measurement years 10, 7, 9 and 6 respectively. 

Figure 3—Plot distributions for panel 1 subpanel 1, using the GRID method, clipped to the BNF 

boundary. Figure 3a shows the existing FIA base plots for panel 1 subpanel 1 within the BNF boundary. 

Figure 3b displays the EBM panel.subpanel assignment procedure (switching subpanel values) 

for the intensified plots, while figure 3c shows the distribution of plots when the subpanel value of 

the intensified plots remains the same as that of the FIA base plot, for a given P2 hex (using the 

AM procedure). Contrast the amount of east-west banding of intensified plots between the last two 

figures. Figure 3b has 52 intensified plots, while figure 3c has 57 intensified plots. The black circles 

represent FIA base plots, red circles are intensified plots and the black line depicts the BNF boundary.

(a) existing FIA base plots (b) EBM procedure (c) AM procedure
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 11

For our case study, the overall effect by using this alternative approach is to 

move two-thirds of the intensified plots into the “opposite” band (odd or even 

years) from that of the base plot. We will refer to this method as the Alternative Method (AM). Figure 3c shows the plot distribution for one representative 

subpanel using AM, while the maps of plot distributions for all panel.subpanel 

combinations using either EBM or AM are presented in figure 4.

Finally, Clark and Evans values were calculated for the various panel.subpanel 

combinations of plots created using both paneling methods (EBM and AM) 

from the GRID method of intensification. In addition, Ripley’s K graphics were 

produced for the various panel.subpanel combinations of plots from both paneling methods using the GRID method. These were produced as a comparison 

to the CE and K values obtained using a full set of intensified plots generated 

from each method.

GRID Method

The GRID method has been used by the Southern Research Station FIA (SRSFIA) region for their intensification projects. This method was initially developed 

by Denis White for the Environmental Protection Agency (EPA) (White 1989). 

It allows for the decomposition of hexagons into smaller hexagons by various 

factors. However, intensification factors of 3x, 4x, and 7x (or multiples thereof) 

will create smaller “children” hexagons that are spatially “nested” within each 

larger “parent” hexagon (figure 5).

The EPA has not publicly distributed the program to generate these hexagons nor its documentation for several years since Denis White retired. The 

GRID program is open-source and comes with supporting documentation; 

however, it requires a C compiler and ArcGIS software. Further details and 

a downloadable file may be obtained from Denis White’s personal website 

(http://people.oregonstate.edu/~whitede/getgrid.htm) or by contacting the authors.

The GRID program was run against our study area of 303 P2 hexagons (or “parent hexes”) to produce a 4-fold decomposition (“child hexes” or “sub-hexes”), 

which produced an intensification pattern similar to that displayed in figure 5b. 

This process involved exporting the P2 hex polygon layer from ArcGIS, running 

the GRID executable file with user-selected parameters for a given intensification level, then importing the results back into ArcGIS as a new polygon layer. 

Although this process can be cumbersome, these programs are open-source and 

have been applied for intensification tasks many times before.

After the resulting intensified hexagons are imported back into ArcGIS, several 

GIS operations are used to split appropriate sub-hexes into halves, which allow 

them to be spatially “nested” within their overlying parent P2 hex, as shown in 

figure 6. One characteristic of the GRID method for a 3x, 4x or 7x intensification 

(or multiples thereof) is that one sub-hex is always centered within each P2 hex, 

which tends to deliver one plot that is relatively near the centroid of each P2 hex. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 12

(a) EBM procedure, Panels 1-5 / Subpanel 1

(a) EBM procedure, Panels 1-5 / Subpanel 2

(b) AM procedure, Panels 1-5 / Subpanel 1

(b) AM procedure, Panels 1-5 / Subpanel 2

Figure 4—Plot distributions for different panel.subpanel combinations are shown, using the GRID method 

and clipped to the BNF boundary. Figure 4a displays the EBM panel.subpanel procedure (switching subpanel 

values), while figure 4b shows the distribution of plots when the subpanel value of the intensified plots remains 

the same as that of the FIA base plot, for a given P2 hex (AM procedure). Compare the amount of east-west 

banding of intensified plots between (a) and (b) for a given panel.subpanel combination. The black circles 

represent FIA base plots, red circles are intensified plots and the black line depicts the BNF boundary.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 13

Figure 5—Depiction of (a) a 3x intensification, (b) a 4x intensification, and (c) a 7x intensification 

using the GRID method (courtesy of Joe McCollum, SRS-FIA).

Figure 6—The GRID method produced a 4x intensification pattern of smaller hexes (sub-hexes) 

within a larger P2 hex. Note the “year” label, produced by the GRID program, was used to identify 

the 4 sub-hexes within a given P2 hex (shown as blue lines). Using this field, each P2 hex contained 

4 nested sub-hexes of equal area (labeled as 0, 1, 2 or 3).

This characteristic is desirable since it guarantees one plot near the centroid of 

each P2 hex, rather than the potential of having several plots clustered near the 

centroid when using some other sub-hex arrangements. The GRID program also 

produces a “year” field, which was used to identify the four sub-hexes within 

a given P2 hex. Using this field, each P2 hex contains four nested sub-hexes of 

equal area (note year label of 0, 1, 2 or 3 in figure 6).

(a) (b) (c)
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Next, the appropriate pairs of sub-hex halves were selected at random to receive 

one randomly placed intensified plot within its boundary. An intensity number 

of 2, 3 or 4 was assigned to each intensified plot, with 1 assigned to the existing 

base plot location, as shown in figure 7. Note that polygons that will not receive 

a new intensified plot, based on random selection, were assigned the number 0. 

This intensity number is used for those situations where only a 2x or 3x intensification is needed; where this number is used to select the appropriate order 

when intensifying plots. As described above, the intensity number is also used 

in the paneling process, which is calculated for each intensified plot.

Figure 7—From the GRID method, intensity numbers are calculated, which are used to indicate 2x, 3x, 4x 

intensification locations for each P2 hex. Note that a label of 1 denotes a polygon that contains an existing plot 

location, which are shown as black triangles. Consequently, a new intensified plot will be randomly placed within the 

polygons designated as 2, 3 and 4 within each P2 hexagon. Those polygons that will not receive a new intensified 

plot are assigned the number 0. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 15

The intensified plots were then clipped to the BNF boundary, based on their 

plot center location. The resulting intensified plots for a given P2 hex using the 

GRID method is shown in figure 8.

R5 Method

The R5 method has been used on USFS Region 5 National Forests for intensification tasks. It is similar to the GRID method in that it splits the parent P2 hex 

into child sub-hexes; however, its primary difference is the placement of those 

sub-hexes within the P2 hexagon. This intensification method is a 4x intensification, with sub-hexes oriented as shown in figure 9. Note that this method creates 

three full sub-hexes (grey) and three partial sub-hex (white) areas, which form 

the 4x portion of the intensification.

Figure 8—Intensified plots for a given P2 hex are shown using the GRID method. Existing FIA plots are shown as 

black triangles, randomly placed intensified plots are gold stars, and the labels identify the corresponding intensity 

number for each intensified plot. Those polygons that will not receive a new intensified plot are assigned the number 0.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 16

The python script for this method is relatively self-contained, but must be edited to specify the input and output file geodatabase feature classes, as well 

as listing the attribute names to be copied over to the child sub-hexes. Other 

considerations are needed to properly execute this script, such as the geographic 

location of the study area and projection of the spatial data, which may influence 

the orientation standard used in the script. After running this script, the userspecified output geodatabase will contain the resulting feature class containing 

the corresponding sub-hexes. A few GIS operations are needed to “nest” the 

three partial sub-hexes, along with the three full sub-hexes, within each parent 

P2 hex. Afterwards, using the same procedures outlined for the GRID method, 

an intensified plot is randomly placed within each sub-hex area, along with its 

intensity number and panel.subpanel assignments.

The intensified plots are then clipped to the BNF boundary, based on their plot 

center location. The resulting intensified plots within a given P2 hex using the 

R5 method is given in figure 10.

Figure 9—Depiction of a 4x intensification of hexagons using the R5 method (courtesy of 

Joe McCollum, SRS-FIA).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 17

The program for this method was written as a python script by Kirk Evans, GIS 

Analyst at Tetra Tech, and a contractor for the USFS Region 5 Remote Sensing 

Laboratory of McClellan, California.

NIMAC or Space-Filling Curves (SFC) Method

The NIMAC or Space-Filling Curves (SFC) method has been advocated by the 

USFS NIMAC (National Inventory and Monitoring Applications Center) group 

for various intensification tasks. This method was initiated by Andy Lister of 

the Northern Research Station FIA (NRS-FIA) (Lister and Scott 2008; contact 

information in Appendix A). It is similar to the GRID method in that it splits a 

P2 hex into smaller, nested polygons, and it supports any integer level of intensification. However, one difference between this method and the GRID method 

is that the smaller polygons can exhibit varied and irregular shapes compared 

to the hexagon patterns of the GRID or R5 methods. Figure 11 shows how 

hexagons may be decomposed using the SFC method, with examples of a 2x to 

7x intensification.

Figure 10—Intensified plots for a given P2 hex using the R5 method. Existing FIA plots are shown 

as black triangles, randomly placed intensified plots are gold stars, and the labels identify the 

corresponding intensity number for each intensified plot. 
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Two versions of this program are available to the user; one is written in AML 

(Arc Macro Language) by Andy Lister for use with ArcInfo workstation (see 

Appendix E), while the other is written in python by Deelesh Mandloi for use 

with ArcMap (Mandloi 2009).

Using the AML version, the user will need to specify the number of clusters, or 

pieces, needed for every P2 hex (in our case, a 4x intensification was used). Input 

layers for the AML include the P2 hex layer (303 P2 hexes for our study), which 

is converted to a 30-meter raster layer. Afterwards, this grid layer is converted 

to a point layer, using the centroid position for every pixel of the grid layer; this 

produces a series of points across the study area at 30-meter spacing. The user 

can then run the AML script, which will create a polygon coverage depicting the 

equivalent of sub-hexes (clusters, zones or pieces). Then, a series of GIS operations will result in a polygon shapefile with one feature for each cluster. After 

the clusters are created, the same procedures outlined for the GRID method is 

used to randomly place intensified plots within each cluster area, along with 

assignment of its intensity and panel.subpanel numbers.

The intensified plots are then clipped to the BNF boundary, based on their plot 

center location. The resulting plots within a given P2 hex using the SFC method 

is presented in figure 12.

Figure 11—Sample output (2x-7x intensification) using the NIMAC or 

Space-Filling Curves (SFC) method (courtesy of Joe McCollum, SRS-FIA).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 19

RIPL Method

The RIPL (Region 1 Intensification Plot Locator) program was written in C# by 

J.D. Zeiler from USFS Region 1 (contact information in Appendix A), and was 

developed to support a mid-level inventory system. For USFS Region 1 National 

Forests, RIPL is used to create intensified plots so additional survey data may 

be acquired over-and-above that provided by the FIA base grid. RIPL also uses 

a heuristic that “...maximizes the separation of point distributions while maintaining spatial balance and randomness.” (Zeiler and others 2010). Figure 13 

shows a sample output using a 3x intensification, and online documentation from 

Region 1 is available at: http://fsweb.r1.fs.fed.us/forest/inv/r1_tools/R1_AT.shtml.

As inputs, RIPL requests the level of intensification, the minimum separation 

between intensifications, the minimum separation between the intensification 

and its parent plot, and the minimum separation between the intensification and 

the edge of the study area. Overall, RIPL offers the user a variety of options 

that it uses as constraints within an optimization (heuristic) problem (Zeiler 

and others 2010).

Figure 12—Intensified plots for a given P2 hex using the NIMAC or SFC method. A 4x intensification 

was generated, with existing FIA plots shown as black triangles, randomly placed intensified plots 

as gold stars, and the labels identify the corresponding intensity number for each intensified plot.
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As shown in figure 13, RIPL does not specifically produce relatively smaller nested 

polygons within a P2 hex, as previously discussed intensification methods have 

done. It will, however, improve spatial balance of intensified plots by utilizing 

one of the user-defined constraints related to minimum distances between plots.

During our testing of this method, we were unable to access a few required layers 

since they were only available on R1 SDE servers (RIPL was written specifically 

as an R1 program). However, it is now available as an ESRI add-in tool that can 

be used within the USFS CITRIX environment. An additional issue that came 

up during testing was that a specific number of points could not be constrained 

within each P2 hex. We were forced to edit the RIPL results so that there were 

exactly three new intensified plots per P2 hex. After speaking with J.D. Zeiler, 

it seemed like a relatively easy change for his team to implement, if requested. 

Figure 13—Sample output (3x intensification) using the RIPL method (courtesy 

of Joe McCollum, SRS-FIA).
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In general, the RIPL tool has many desirable qualities, but also a few issues as 

noted. We remain confident, however, that the RIPL developers are more than 

capable of making any changes or other customizations needed for this tool.

Following the RIPL procedure, the intensified plots received intensity and panel.

subpanel numbers using the same procedures outlined for the GRID method. 

Then, the intensified plots are clipped to the BNF boundary, based on their plot 

center location. The resulting intensified plots within a given P2 hex using the 

RIPL method are shown in figure 14.

Figure 14—Intensified plots for a given P2 hex using the RIPL method. A 4x intensification was 

generated, with existing FIA plots shown as black triangles, randomly placed intensified plots as gold 

stars, and the labels identify the corresponding intensity number for each intensified plot.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 22

Python4x Method

The Python4x method, developed by Tom Thompson (contact information in 

Appendix A) of the USFS Pacific Northwest Research Station FIA (PNW-FIA), 

is a python script that generates intensifications at 2x and 4x. Tom has used this 

script for simple intensifications (primarily 2x) of the FIA base grid in his region.

The Python4x method requires at least python v2.6 software, PYPROJ module 

and PROJ4 (http://trac.osgeo.org/proj/), along with its corresponding environmental variable settings. A CSV file that contains coordinate pairs for the P2 

hex center and for existing FIA plots are also needed as input files. The python 

script is then edited to specify the input and output CSV files, along with the 

field names that designate the coordinate pairs.

This method does not produce relatively smaller nested polygons within a P2 

hex, as with the GRID method. Instead, this method compares the FIA base 

plot’s location to its hex center, and places an intensified point on the opposite 

side of the hex (for a 2x), at a random distance and somewhat random azimuth. 

For the 4x, it again compares an FIA base plot’s location with its hex center 

and places points in the other quadrants of the hex (that is, right angles to the 

2x bearing). All intensified points are within the same P2 hex as the existing 

FIA plot, as shown in figure 15. Python4x is an easy script to run and produces 

intensification results relatively quickly.

Following the Python4x procedure, the intensified plots received intensity and 

panel.subpanel numbers using the same procedures outlined for the GRID 

method. Next, the intensified plots are clipped to the BNF boundary, based on 

their plot center location. The resulting intensified plots within a given P2 hex 

using the Python4x method are displayed in figure 16.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 23

Figure 15—Sample output using the Python4x method, with (a) a 2x intensification and 

(b) a 4x intensification (courtesy of Joe McCollum, SRS-FIA). 

(a)

(b)
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 24

Repeating Shapes Method

The Repeating Shapes (RS) method is a Visual Basic program written by Jeff 

Jenness of Jenness Enterprises (Jenness 2009), and can be downloaded from 

the ESRI support page at: http://arcscripts.esri.com./details.asp?dbid=14695. It 

is loaded as a custom tool in ArcMap (ESRI 2009); and with its wizard-type 

interface, quickly produces hexagons or other types of polygons based on a 

user-specified area and geographic extent.

However, based on our testing, it does not place intensified hexagons with exact 

spatial coincidence to the P2 grid, as does the GRID method. There are also 

situations where two existing FIA plots may be within the same sub-hex, or 

the centroid of a sub-hex will be in a different P2 hex than that of an existing 

FIA plot that resides in that sub-hex. Other problematic issues frequently arise 

due to the overlapping alignment of the sub-hex boundaries in relation to the 

P2 hex boundaries.

Figure 16—Intensified plots for a given P2 hex using the Python4x method. A 4x intensification 

was generated, with existing FIA plots shown as black triangles, hex centers are gray x symbols, 

intensified plots as gold stars, and the labels identify the corresponding intensity number for each 

intensified plot.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 25

Figure 17—Intensified plots for a given P2 hex using the Repeating Shapes method. A 4x 

intensification was generated, with existing FIA plots shown as black triangles, randomly placed 

intensified plots as gold stars, and the labels identify the corresponding intensity number for 

each intensified plot. Note that the smaller sub-hexes (brown lines) are not spatially aligned with 

the larger P2 hex (blue lines). There are also situations where two existing FIA plots may be in 

the same sub-hex. Other problematic issues frequently arise due to the overlapping alignment 

of the sub-hex boundaries and the P2 hex boundaries.

Following the RS procedure, the intensified plots received intensity and panel.

subpanel numbers using similar procedures as those outlined for the GRID 

method. The intensified plots are then clipped to the BNF boundary, based on 

their plot center location. The resulting intensified plots within a given P2 hex 

using the RS method are shown in figure 17.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 26

R4 Method

The R4 method has been used on USFS Region 4 National Forests for intensification tasks by Larry DeBlander, Vegetation Analyst for Region 4 (contact 

information in Appendix A). This method does not produce relatively smaller 

nested polygons within a P2 hex, as does the GRID method. Instead, it utilizes 

historic plots so that previous survey information from those plots may be retained. For Region 4, they attempt to use existing available FIA B-grid plots for 

their intensification tasks, which are additional FIA plots (not A-grid or base 

plots) that were established in previous surveys. That way, much of the previous 

inventory data from B-grid plots are available for further analysis.

Region 4 has many national forests that contain B-grid plots, and plan to utilize 

those as intensification plots where appropriate. If additional intensification plots 

are still needed for a specific level of intensification, then randomly placed plots 

will be added within a given P2 hex after B-grid plots are selected.

FIA B-grid plots were typically established on a grid pattern at roughly 5000 

meters spacing between plots. If you can imagine the number 5 as represented 

on a die; the FIA base plot would be the center dot, while the B-grid plots would 

be represented by the four surrounding dots. This assumes that the FIA base plot 

is on a grid pattern as well, which may have been accurate in previous inventory 

cycles (periodic inventories that preceded the current annual inventory).

For a 4x intensification such as our study, the following decision rules were used 

when considering B-grid plots. Note that an analyst may need to be involved 

to determine:

1. If more than three B-grid plots exist per P2 hex, then retain the “best” 

plots based on:

a. the most up-to-date, relevant information to retain for further 

analysis,

b. most recently measured plots,

c. closest to the P2 hex centroid,

d. other determining factors that may be relevant to future studies.

2. If three or fewer B-grid plots exist per P2 hex, then retain all as intensification plots.

3. If less than three intensified plots still exist per P2 hex, then randomly 

place additional plot(s) to gain a 4x intensification for each P2 hex.

Following the R4 procedure, the intensified plots received intensity and panel.

subpanel numbers using similar procedures as those outlined for the GRID 

method. Then, the intensified plots are clipped to the BNF boundary, based on 

their plot center location. The resulting intensified plots within a given P2 hex 

using the R4 method are shown in figure 18.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 27

Simple Random Sample Method

The Simple Random Sample (SRS) method was used primarily as a comparison 

to the other intensification techniques under consideration. The SRS method 

does not produce smaller polygons that nest within a given P2 hex, as does the 

GRID method. Instead, for a 4x intensification, it simply places three randomly 

located plots within each P2 hex using a simple GIS operation (ESRI ArcGIS 

Create Random Points tool; ESRI, Inc. 2012). No constraints were placed on 

minimum distances between plots, etc. when using this method.

Following the SRS process, the intensified plots received intensity and panel.

subpanel numbers using similar procedures as those outlined for the GRID 

method. Next, the intensified plots are clipped to the BNF boundary, based on 

their plot center location. The resulting intensified plots within a given P2 hex 

using the SRS method are shown in figure 19.

Figure 18—Intensified plots for a given P2 hex using the R4 method. A 4x intensification was 

generated, with existing FIA plots shown as black triangles, intensified plots as gold stars, and the 

labels identify the corresponding intensity number for each intensified plot. Note that for this example, 

there are two B-grid plots for each P2 hex, which are displayed in a somewhat equidistant pattern. 

The remaining intensified plot for each P2 hex was randomly placed to obtain a 4x intensification. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 28

Results

Clark and Evans Statistic

As a comparison for the Clark and Evans (CE) values calculated for the different intensification methods, simulations with 4000 iterations were conducted 

for various scenarios. The distribution of CE values from the 4000 simulations 

of a random drawing of one plot location within each of the 303 P2 hexes, after 

clipping them to the Bighorn NF (BNF) boundary, is shown in figure 20.

Similar simulations with no P2 hex constraint imposed (303 plots randomly 

placed within the P2 hex boundary) were also conducted. The distribution of 

CE values from the 4000 simulations of a random drawing of 303 plot locations 

within the P2 hex boundary, following clipping to the BNF boundary, is provided in figure 21. Note the bell-shaped pattern and mean value obtained from 

these simulations. The difference in mean values between these two examples 

is due to the constraint of placing one random plot location within each of the 

P2 hexes, as opposed to not having this constraint and randomly placing all 303 

plot locations within the overall boundary of the 303 P2 hexes.

Figure 19—Intensified plots for a given P2 hex using the Simple Random Sample (SRS) method. 

A 4x intensification was produced by placing three randomly located plots within each P2 hex. 

Existing FIA plots are shown as black triangles, intensified plots as gold stars, and the labels 

identify the corresponding intensity number for each intensified plot. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 29

Figure 20—Distribution of Clark & Evans statistic values from 4000 simulation runs of a randomly- placed plot 

located within each of the 303 P2 hexes, clipped to BNF boundary (~186 plots). The mean of the distribution 

is: 1.265407, a standard deviation of: 0.03853602, and a standard error of: 0.000609308. The cdf estimate of 

the CE statistic (which has edge correction) was used, as opposed to the naïve estimate (no edge correction).

The means and other summary statistics obtained from these two simulation 

runs of CE values are also presented in table 1. Note that the “naïve” estimate 

provides a CE estimate without an edge correction applied, while the “cdf” 

estimate is a cumulative distribution function method that has an edge correction. For those simulations with a P2 hex constraint, the mean CE values (cdf 

estimate) are near 1.26, which tends to imply a more uniform distribution than 

those simulations with no hex constraint. The mean CE values (cdf estimate) 

for those simulations without a P2 hex constraint are near 1.0, which indicates 

a random point distribution, and is what would be expected based on theoretical 

properties of the CE estimator.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 30

Figure 21—Distribution of Clark & Evans statistic values from 4000 simulation runs of a randomly placed plot not 

constrained within the P2 hexes, clipped to BNF boundary (~187 plots). The mean of the distribution is: 0.996654, a 

standard deviation of: 0.04430584, and a standard error of: 0.000700537. The cdf estimate of the CE statistic (which 

has edge correction) was used, as opposed to the naïve estimate (no edge correction).

For additional comparisons, table 2 lists the CE values obtained from various 

representative sets of plots, which may provide a reference against those CE 

values obtained from our candidate intensification methods. Note that when 

one random plot per P2 hex was produced, the resulting CE value (cdf estimate) 

is near 1.264, which is similar to the 1.269173 mean value obtained from the 

4000x simulation runs listed in table 1. For the 303 random plots with no P2 

hex constraint, the CE value (cdf estimate) is near 0.933, which is closer to a 

more random point distribution value of 1.0 than compared to those distributions 

created with a P2 hex constraint. For the existing FIA plots on the BNF (from 

the Annual Field Control table entry), the CE value was 1.696, which implies 

a more uniform distribution than the randomly placed plots (with or without a 

hex constraint). For the 303 P2 hex centroids, the CE value was 2.023, which is 

near the upper limit of 2.14 and suggests a more uniform distribution.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 31 Table 1—Four examples of Clark and Evans (CE) statistic values obtained from 4000 simulation runs. Variations include a randomly placed plot either constrained or not constrained within each P2 hex, and clipped or not clipped to the BNF boundary. Various statistics are presented for each of the variations. Clark and Evans values range from 0 (maximum aggregation) to 2.1491 (maximum spacing). A CE value of 1 indicates a random distribution. 95% Conf. Interval for MEAN (sigma unknown) Mean CE value naïve cdf Standard Deviation Standard Error FIA plot examples Description naïve cdf lower upper lower upper naïve cdf naïve cdf 303 P2 hexes | 1 random plot/hex SIM: 4000x 1.322872 1.269173 1.322000 1.323744 1.268306 1.270040 0.028132 0.027977 0.000445 0.000442 303 P2 hexes | no hex constraints SIM: 4000x 1.029719 0.996841 1.028741 1.030697 0.995841 0.997841 0.031550 0.032266 0.000499 0.000510 303 P2 hexes | 1 random plot/hex | CLIP BNF bdry (~186 plots) SIM: 4000x 1.315822 1.265407 1.314693 1.316952 1.264212 1.266601 0.036437 0.038536 0.000576 0.000609 303 P2 hexes | no hex constraints | CLIP BNF bdry (~187 plots) SIM: 4000x 1.048368 0.996654 1.047048 1.049689 0.995280 0.998027 0.042595 0.044306 0.000673 0.000701
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 32

Table 2—Clark and Evans (CE) statistic values obtained from various sets of plots for comparison purposes. Note that the 

Annual Field Control table entry represents FIA plots across portions of Wyoming and Montana that overlap the study 

area (303 P2 hexes around the Bighorn National Forest boundary). Clark and Evans values range from 0 (maximum 

aggregation) to 2.1491 (maximum spacing). A CE value of 1 indicates a random distribution.

Number CE value (R)

Plot Category Description of plots naïve cdf

Annual Field Control (AFC) table 1 plot per hex, nearest 5000m plot 303 1.710588 1.696813

1 random plot per hex Bighorn NF case study 303 1.331633 1.264272

303 random plots (no P2 hex constraint) Bighorn NF case study 303 1.002502 0.933883

1 random plot/hex clipped to BNF boundary Bighorn NF case study 186 1.298888 1.266688

303 random plots clipped to BNF boundary

(no P2 hex constraint) Bighorn NF case study 187 0.972237 0.912466

P2 hex centroids centroid of P2 hex 303 2.02662 2.02347

The CE values for the eight intensification methods, intensified plots only and 

clipped by the BNF boundary, are shown in table 3. Also, the CE values for 

the eight intensification methods, FIA base and intensified plots combined and 

clipped by the BNF boundary, are shown in table 4. Note that the cdf estimate 

for a majority of these methods has a CE value that ranges near 1.2; while RIPL, 

SRS and R4 methods are closer to 1.0.

Table 3—Clark and Evans (CE) statistic values for the eight intensification methods: intensified plots only, all plots clipped within the 

BNF boundary, and estimates adjusted by the BNF boundary. Clark and Evans statistic values range from 0 (maximum 

aggregation) to 2.1491 (maximum spacing). A CE value of 1 indicates a random distribution.

Number CE value (R)

Method (4x intensification) Description of plots naïve cdf

RIPL_4x_ex1 (default distance constraints) no constraint of 3 INT. plots per hex 553 1.278268 1.235146

RIPL_4x_ex2 (zero distance constraints) no constraint of 3 INT. plots per hex 551 0.9879712 0.954247

RIPL_4x_ex3 (zero distance constraints) edited RIPL output to have 3 INT. plots per hex 553 0.9985097 0.954535

Simple Random Sampling (SRS) ArcGIS Create Random Points 559 1.067604 1.030549

GRID Southern Research Station 560 1.205294 1.18114

R5 R5: python script 549 1.241144 1.206019

Repeating Shapes ESRI support script 518 1.246039 1.213996

NIMAC (Space-Filling Curves) Andy Lister’s AML 565 1.304317 1.256817

R4 R4: B-grids 560 1.130563 1.107566

Python4x Tom Thompson’s python script 552 1.268993 1.214638
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 33

Ripley’s K Statistic

As a comparison for the Ripley’s K (K) values calculated for the different intensification methods, K values were derived for various sets of plots. Ripley’s 

K values for a randomly placed plot located within each of the 303 P2 hexes, 

after being clipped to the BNF boundary, is given in figure 22. Note that a statistically significant dispersed (uniform) pattern versus a random distribution 

exists at relatively shorter distances. Using the ESRI ArcGIS Average Nearest 

Neighbor script (ESRI, Inc. 2012), the mean distance between these plot locations was found to be 3193 meters, which seems to be where the actual K values 

line begins to trend upward towards the 95% confidence bands of a random 

distribution. That inflection point in the actual K values line is consistent with 

gaining several new neighbors at that distance, which would typically move the 

trend line from a relatively dispersed pattern toward a more clustered pattern. 

As the distance increases and additional neighbors are obtained, the actual K 

values line eventually moves into the 95% confidence band. The abrupt changes 

in slope of the actual K values line may be affected by a relatively sudden increase in neighbors at a certain distance, or possibly an edge effect influence 

where points would not have a full complement of neighbors.

Table 4—Clark and Evans (CE) statistic values for the eight intensification methods when 

intensified plots are combined with the 303 FIA base grid plots, all plots clipped 

within the BNF boundary, and estimates adjusted by the BNF boundary. Clark 

and Evans statistic values range from 0 (maximum aggregation) to 2.1491 

(maximum spacing). A CE value of 1 indicates a random distribution.

Combined with MT-WY AFC table plots (n = 192)

Number CE value (R)

Method (4x intensification) of plots naïve cdf

RIPL_4x_ex1 745 1.039565 1.023244

RIPL_4x_ex2 743 0.9821773 0.9539735

RIPL_4x_ex3 745 0.9701635 0.9345374

Simple Random Sampling (SRS) 751 1.048709 1.004608

GRID 752 1.231287 1.199543

R5 741 1.243387 1.209682

Repeating Shapes 710 1.282263 1.251283

NIMAC (Space-Filling Curves) 757 1.289631 1.251443

R4 752 1.073348 1.059302

Python4x 744 1.350058 1.299343
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 34

Figure 22—Ripley’s K statistic values for a randomly placed plot located within each of the 

303 P2 hexes, clipped to BNF boundary (~186 plots), where the mean distance between plots 

is 3193 meters. The horizontal axis indicates distances in meters, while the red-line is the 

theoretical K value and the shaded area represents a 95% confidence band for this K estimate.

K values were also calculated for plots with no P2 hex constraint imposed (303 

plots randomly placed within the P2 hex boundary). The distribution of K values from a random drawing of 303 plot locations within the P2 hex boundary, 

clipped to the BNF boundary, is provided in figure 23. The mean distance between these plot locations is 2383 meters, which is a much shorter distance than 

that obtained with the P2 hex constraint in place (figure 22). Note that without 

the P2 hex constraint in place, a large majority of K values for these plots are 

within the 95% confidence bands.

For additional contrasts to the intensification methods, graphs of the K values 

were created for existing FIA base plots as well as P2 hex centroids. In figure 24, 

K values are shown for the existing FIA base plots within the study area’s 303 

P2 hexes, after this plot set has been clipped to the BNF boundary (192 FIA 

plots). The mean distance between these plot locations is 4196 meters, which is 

somewhat near the point where the actual K values line begins moving upward 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 35

Figure 23—Ripley’s K statistic values for randomly placed plots not constrained within the P2 

hexes, clipped to BNF boundary (~187 plots), where the mean distance between plots is 2383 

meters. The horizontal axis indicates distances in meters, while the red-line is the theoretical K 

value and the shaded area represents a 95% confidence band for this K estimate.

towards the 95% confidence bands. This figure displays a similar trend as shown 

in figure 22 regarding statistically significant dispersion patterns at relatively 

shorter distances. The somewhat irregular, spiky pattern shown in figure 24 may 

be due in part to the manner in which the existing FIA base plots were selected. 

FIA plots had previously been established along a 5000 meter grid in Wyoming. 

After the annual inventory system was initiated and P2 hexagons were created, 

the closest existing plot to the P2 hex centroid was selected to represent that 

particular P2 hex. Consequently, the FIA base plots in Wyoming are typically 

more uniformly spaced at approximately 5000 meters when compared to creating a randomly selected point within a given P2 hex. This spatial pattern is also 

evident when comparing the mean distance of the existing FIA base plots for 

figure 24 (4196 meters) to that of the randomly placed plot locations for figure 

22 (3193 meters).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 36

Figure 24—Ripley’s K statistic values for the existing FIA base plots within the 

303 P2 hexes, clipped to BNF boundary (192 FIA plots), where the mean distance 

between plots is 4196 meters. The horizontal axis indicates distances in meters, 

while the red-line is the theoretical K value and the shaded area represents a 

95% confidence band for this K estimate.

Figure 25 provides K values for the centroids of the 303 P2 hexagons after being clipped by the BNF boundary (183 plots). The mean distance between these 

plot locations was found to be 4972 meters, which is about where the actual 

K values line begins to move upward towards the 95% confidence bands of a 

random distribution. This figure was expected to indicate a somewhat uniform 

distribution (below the red-line), which is generally the case. However, the 

actual K value line is very erratic, jumping from a dispersed (or uniform) to a 

clustered pattern over relatively short distances. This pattern is likely a result 

of the number of new neighbors (typically six in this scenario) being acquired 

over specific intervals, which likely causes the actual K line to move from dispersed (below the lower 95% confidence band) to clustered (above the upper 

95% confidence band).

For example, as shown in figure 25, the actual K line slope changes abruptly 

near 5000 meters, moving sharply from a dispersed to a clustered pattern. This 

tends to correlate with the mean distance of 4972 meters, where six new neighbors are gained. From this point, there will be no new neighbors until about 

9000 meters, where six new neighbors are again added, and the actual K line 

moves upward from about 9000 meters to near 1100 meters. Consequently, this 

pattern repeats itself over increasing distances for the P2 hex centroid plots, as 

new neighbors are gained at specific intervals (Joe McCollum, USFS, personal 

communication, 2014).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 37

Figure 25—Ripley’s K statistic values for the P2 hex centroid points within the 303 

P2 hexes, clipped to BNF boundary (183 plots), where the mean distance between 

plots is 4972 meters. The horizontal axis indicates distances in meters, while the 

red-line is the theoretical K value and the shaded area represents a 95% confidence 

band for this K estimate.

Next, K values for the eight intensification methods under consideration were 

determined. For each method, K values were calculated for FIA base and intensified plots combined within the 303 P2 hexes, then clipped to the BNF boundary.

For the GRID method, K values are given in figure 26. Next, the K values for 

the R5 method are shown in figure 27, while those for the NIMAC or SFC 

method are provided in figure 28. The RIPL method is given in figure 29, and 

the Python4x method is displayed in figure 30. The Repeating Shapes method 

is provided in figure 31, with the R4 method given in figure 32. Finally, the 

Simple Random Sample (SRS) method is shown in figure 33.

All of these distributions tend to initially fall below the lower 95% band and then 

“bottom-out” near their mean distance value, and then climb within the 95% 

band range at longer distances. These are similar results as those for the previous 

plot sets examined, where a statistically significant dispersed (uniform) pattern 

(compared to a random distribution) exists at relatively shorter distances. As 

previously noted, the overall trend seems to become more randomly distributed 

as distance increases and more neighbors are obtained.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 38

Figure 26—Ripley’s K statistic values for the GRID method (includes 192 

FIA base plots and 560 intensified plots), clipped to BNF boundary (752 total 

plots), where the mean distance between plots is 1505 meters. The horizontal 

axis indicates distances in meters, while the red-line is the theoretical K value 

and the shaded area represents a 95% confidence band for this K estimate.

Figure 27—Ripley’s K statistic values for the R5 method (includes 192 FIA 

base plots and 549 intensified plots), clipped to BNF boundary (741 total plots), 

where the mean distance between plots is 1531 meters. The horizontal axis 

indicates distances in meters, while the red-line is the theoretical K value and 

the shaded area represents a 95% confidence band for this K estimate.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 39

Figure 28—Ripley’s K statistic values for the NIMAC or SFC method (includes 

192 FIA base plots and 565 intensified plots), clipped to BNF boundary (757 total 

plots), where the mean distance between plots is 1571 meters. The horizontal 

axis indicates distances in meters, while the red-line is the theoretical K value 

and the shaded area represents a 95% confidence band for this K estimate.

Figure 29—Ripley’s K statistic values for the RIPL method (includes 192 FIA 

base plots and 553 intensified plots), clipped to BNF boundary (745 total plots), 

where the mean distance between plots is 1191 meters. The horizontal axis 

indicates distances in meters, while the red-line is the theoretical K value and 

the shaded area represents a 95% confidence band for this K estimate.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 40

Figure 30—Ripley’s K statistic values for the Python4x method (includes 192 

FIA base plots and 552 intensified plots), clipped to BNF boundary (744 total 

plots), where the mean distance between plots is 1659 meters. The horizontal 

axis indicates distances in meters, while the red-line is the theoretical K value 

and the shaded area represents a 95% confidence band for this K estimate.

Figure 31—Ripley’s K statistic values for the Repeating Shapes method (includes 

192 FIA base plots and 518 intensified plots), clipped to BNF boundary (710 total 

plots), where the mean distance between plots is 1613 meters. The horizontal 

axis indicates distances in meters, while the red-line is the theoretical K value 

and the shaded area represents a 95% confidence band for this K estimate.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 41

Figure 32—Ripley’s K statistic values for the R4 method (includes 192 FIA base 

plots and 560 intensified plots), clipped to BNF boundary (752 total plots), where 

the mean distance between plots is 1312 meters. The horizontal axis indicates 

distances in meters, while the red-line is the theoretical K value and the shaded 

area represents a 95% confidence band for this K estimate.

Figure 33—Ripley’s K statistic values for the Simple Random Sample method 

(includes 192 FIA base plots and 559 intensified plots), clipped to BNF boundary 

(751 total plots), where the mean distance between plots is 1283 meters. The 

horizontal axis indicates distances in meters, while the red-line is the theoretical K 

value and the shaded area represents a 95% confidence band for this K estimate.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 42

Intensification Team Survey

In an attempt to capture various subjective measures under consideration during 

plot intensification procedures, a brief survey with eleven questions was posed 

to the team members. These questions and their corresponding results are listed 

in Appendix B.

From the survey results, some of the highest “above neutral” rankings indicate the 

following: (a) intensification should be based on the existing FIA P2 hex framework, (b) it is critical to maintain the statistical properties of existing FIA design 

and layout when doing plot intensification (as described in the Methods section), 

(c) it is important for an intensification program to have adaptability to various 

intensification levels (2x, 3x, etc.), and (d) a consistent intensification procedure 

between neighboring Regions (both FIA and NFS Regions) is important.

The second highest rankings included the following: (a) it is important to have 

a simple routine, ease of use, adaptable GIS-based tool for plot intensification 

purposes, and (b) it is important for the user to understand the processes involved in plot intensification, compared to those methods with a “black-box” 

transparency.

The only question that failed to receive a response in its highest category was: 

“How open is your Region to consider new intensification methods?” although 

this question did receive 45% above neutral category ranking.

Panelizing Plots

The CE values were calculated for all panel.subpanel combinations for both the 

EBM and AM panel assignments for the intensified plots that were generated 

using the GRID method. Table 5 contains the CE values using plots from the 

303 P2 hexes after being clipped by the BNF boundary, when EBM was used. 

Also, table 6 contains the CE values when AM was used for plots within the 

303 P2 hexes and clipped by the BNF boundary. The CE values calculated for 

both EBM and AM are comparable. For both procedures, the FIA base plots 

(labeled GRID Base Plots in the tables) tend to have a higher CE value than 

their intensified plot counterparts (labeled GRID INT Plots in the tables). Also, 

except for panel.subpanel 2.2, the CE values for the AM approach are higher 

than the CE values for their corresponding entry with the EBM approach. And 

for all but two panel.subpanels, the CE values for intensified plots assigned using the EBM approach are less than one, indicating these sets of plots are more 

clumped than would be expected for randomly assigned plots. Both of these 

observations are not surprising since the EBM approach assigns the intensified 

plots to a panel.subpanel in the same band as the base plot (see the Methods 

section). In addition, figures 3 and 4 visually indicate that those plots assigned 

to panel.subpanels using the EBM procedure appear to be more clumped than 

those assigned using the AM procedure.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 43

Table 5—Clark and Evans (CE) statistic values for the GRID method by 

panel.subpanel assignments using the EBM procedure, all plots 

clipped within the BNF boundary, and estimates adjusted by the 

BNF boundary. 

Method (4x intensification)

Number

of plots

CE value (R)

naïve cdf

Panel = 1 AND Subpanel = 1

GRID Base Plots 19 1.607828 1.400854

GRID INT Plots 52 1.05519 0.9915176

GRID Merged Plots 71 1.0222332 0.9849817

Panel = 2 AND Subpanel = 1

GRID Base Plots 22 1.636066 1.144658

GRID INT Plots 57 0.9450777 0.8841021

GRID Merged Plots 79 1.0009643 0.9860507

Panel = 3 AND Subpanel = 1

GRID Base Plots 17 1.545258 1.215154

GRID INT Plots 56 1.0536045 0.9817857

GRID Merged Plots 73 1.064819 1.011784

Panel = 4 AND Subpanel = 1

GRID Base Plots 20 1.553358 1.283203

GRID INT Plots 59 1.0352277 0.9892683

GRID Merged Plots 79 1.070693 1.020971

Panel = 5 AND Subpanel = 1

GRID Base Plots 19 1.761144 1.411915

GRID INT Plots 55 1.0053288 0.9044992

GRID Merged Plots 74 1.1039951 0.9641386

Panel = 1 AND Subpanel = 2

GRID Base Plots 18 1.445129 1.289399

GRID INT Plots 60 1.101987 1.08957

GRID Merged Plots 78 1.148238 1.073027

Panel = 2 AND Subpanel = 2

GRID Base Plots 18 1.695251 1.390884

GRID INT Plots 53 1.0061688 0.9395895

GRID Merged Plots 71 1.0598921 0.9911559

Panel = 3 AND Subpanel = 2

GRID Base Plots 18 1.547681 1.40584

GRID INT Plots 56 0.9426903 0.9191406

GRID Merged Plots 74 0.9664182 0.9028755

Panel = 4 AND Subpanel = 2

GRID Base Plots 20 1.661935 1.461924

GRID INT Plots 53 0.9874192 0.9107843

GRID Merged Plots 73 1.004806 1.003047

Panel = 5 AND Subpanel = 2

GRID Base Plots 21 1.717448 1.470648

GRID INT Plots 59 1.072981 1.003578

GRID Merged Plots 80 1.065801 1.019942
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 44

Table 6—Clark and Evans (CE) statistic values for the GRID method by panel.subpanel assignments using the AM procedure (same subpanel as base plot), 

all plots clipped within the BNF boundary, and estimates adjusted by the 

BNF boundary.

Method (4x intensification)

Number

of plots

CE value (R)

naïve cdf

Panel = 1 AND Subpanel = 1

GRID Base Plots 19 1.607828 1.400854

GRID INT Plots 57 1.252529 1.1529

GRID Merged Plots 76 1.212677 1.078708

Panel = 2 AND Subpanel = 1

GRID Base Plots 22 1.636066 1.144658

GRID INT Plots 53 1.0061688 0.9395895

GRID Merged Plots 75 1.143829 1.071205

Panel = 3 AND Subpanel = 1

GRID Base Plots 17 1.545258 1.215154

GRID INT Plots 56 1.238285 1.131449

GRID Merged Plots 73 1.224895 1.139537

Panel = 4 AND Subpanel = 1

GRID Base Plots 20 1.553358 1.283203

GRID INT Plots 54 1.316243 1.220132

GRID Merged Plots 74 1.257403 1.186814

Panel = 5 AND Subpanel = 1

GRID Base Plots 19 1.761144 1.411915

GRID INT Plots 56 1.0705954 0.9105516

GRID Merged Plots 75 1.00134 0.887915

Panel = 1 AND Subpanel = 2

GRID Base Plots 18 1.445129 1.289399

GRID INT Plots 55 1.1867 1.1529

GRID Merged Plots 73 1.220516 1.169793

Panel = 2 AND Subpanel = 2

GRID Base Plots 18 1.695251 1.390884

GRID INT Plots 57 0.9450777 0.8841021

GRID Merged Plots 75 1.0472238 0.9777041

Panel = 3 AND Subpanel = 2

GRID Base Plots 18 1.547681 1.40584

GRID INT Plots 56 1.336255 1.203079

GRID Merged Plots 74 1.207627 1.133973

Panel = 4 AND Subpanel = 2

GRID Base Plots 20 1.661935 1.461924

GRID INT Plots 58 1.324649 1.27467

GRID Merged Plots 78 1.219833 1.199673

Panel = 5 AND Subpanel = 2

GRID Base Plots 21 1.717448 1.470648

GRID INT Plots 58 1.250365 1.19005

GRID Merged Plots 79 1.155314 1.153889
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 45

As done for the Clark and Evans statistic, Ripley’s K values were calculated 

for each panel and subpanel combination using the GRID method. As a 

comparison, the K values for panel 1 and subpanel 1 generated from both 

EBM and AM, for plots within the 303 P2 hex area and clipped by the BNF 

boundary, are shown in figure 34. Note that the mean distance between EBM 

plot locations is 4067 meters, while that for the AM plot locations is 4663 

meters. From figure 34a, the K values calculated from the EBM tend to drop 

below the lower 95% line at distances between 10,000 and 12,000 meters, 

then returns above that line near 20,000 meters. This distribution seems to 

be different from the observed trends we have reviewed for other plot sets, 

as well as for the overall GRID method results shown in figure 26. In those 

cases, the K values fell below the lower 95% line for distances typically less 

than 5000 meters but then climbed within the 95% range at longer distances. 

Similarly, the K values calculated from the AM in figure 34b also dropped below the lower 95% line at a point near 5000 meters and then climbed into the 

95% range near the 13,000 meter mark. For this case, the K values calculated 

from the AM seem more similar to the observed trends from the overall GRID 

method results than those calculated from the EBM.

Rather than display the remaining panel.subpanel combinations as individual 

figures, each of the ten panel.subpanel combinations for the GRID method were 

combined into one figure. In figure 35, the K values for the GRID method with 

different panel.subpanel combinations, using all 303 P2 hexes (then clipped to 

the BNF boundary), are shown for both the EBM and the AM. Note that in most 

panel.subpanel combinations for the EBM, there tends to be a similar trend as 

shown for the panel 1 subpanel 1 figure. It seems that at 15,000 meters, the K 

values for these individual panel.subpanel combinations are at their maximum 

dispersed pattern. For the AM, many of the panel.subpanel combinations tend to 

follow the trend from their corresponding panel 1 subpanel 1 figure as well. But, 

it also looks as though the K values for these individual panel.subpanel combinations are more varied at their maximum dispersed pattern; some combinations 

peak at less than 5000 meters, while others are somewhere near 12,000 meters.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 46

Figure 34—Ripley’s K statistic values for the GRID method with both FIA base 

plots in panel=1 and subpanel=1 and intensified plots that were assigned to 

panel=1 and subpanel=1, clipped to the BNF boundary. Figure 34a displays the 

K values using the EBM panel.subpanel assignment procedure (mean distance 

between plots is 4067 meters) for the intensified plots, while figure 34b shows the 

alternative (AM) panel.subpanel assignment procedure (mean distance between 

plots is 4663 meters). The horizontal axis indicates distances in meters, while 

the red-line is the theoretical K value and the shaded area represents a 95% 

confidence band for this K estimate.

(a)

(b)
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 47

Figure 35—Ripley’s K statistic values for the GRID method with both FIA base and intensified plots for different panel.subpanel 

combinations, clipped to the BNF boundary. Figure 35a displays the K values using the EBM panel.subpanel assignment procedure 

for the intensified plots, while figure 35b shows the alternative panel.subpanel assignment procedure. The horizontal axis indicates 

distances in meters, while the red-line is the theoretical K value and the shaded area represents a 95% confidence band for this K 

estimate.

(a) EBM procedure, Panels 1-5 / Subpanel 1

(b) AM procedure, Panels 1-5 / Subpanel 1

(b) AM procedure, Panels 1-5 / Subpanel 2

(a) EBM procedure, Panels 1-5 / Subpanel 2
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 48

Discussion and Conclusions

Intensifying Plots

As shown in table 1, the CE value for an idealized FIA sample (1 random plot 

per P2 hex) is approximately 1.26. This CE value is also supported by the values 

obtained for the same category in table 2, as well as the simulation runs presented 

in figure 20. For comparison, figure 21 represents CE values without any P2 hex 

constraint, which are centered on a mean near 1.0, as expected.

The CE values obtained from both the intensified plots only (table 3) as well as 

the combined set of plots (table 4) suggest that all the methods except for SRS, 

R4, and RIPL (zero distance constraints) have estimates close to this idealized 

FIA sample (near 1.26).

For the SRS method (table 3, CE value of 1.03), this was somewhat expected 

since it is the method that more closely resembles a total random placement of 

intensified plots (which would result in a CE = 1.0). The R4 method (table 3, 

CE value of 1.10) is also near the value of 1.0, likely influenced by placing one 

random plot and two systematic B-grid plots for every P2 hex. For the RIPL 

method, as mentioned earlier, the output was edited to ensure that three intensified plots were placed within each P2 hex (since this was not an option in the 

version we tested). This editing procedure allowed for a large proportion of plots 

being randomly placed within applicable P2 hexes.

As shown in figure 22, the Ripley’s K values for an idealized FIA sample (1 

random plot per P2 hex) are shown with statistically significant dispersion at 

relatively shorter distances (near 4000 meters). In contrast, figure 23 shows the 

distribution of K values with no P2 hex constraint, with no corresponding break 

from the 95% confidence band. This comparison demonstrates the influence of 

having a P2 hex constraint on Ripley’s K calculations.

While viewing the various Ripley’s K graphs for the eight intensification methods, it seems apparent that the same three methods identified above (SRS, R4, 

RIPL) exhibit a different K line than that of the remaining five methods. While 

the GRID (figure 26), R5 (figure 27), SFC (figure 28), Python4x (figure 30) 

and RS (figure 31) methods all tend to have similar K lines as an idealized FIA 

sample (figure 22); the SRS (figure 33), R4 (figure 32) and RIPL (figure 29) 

all seem to display a more erratic K line with greater amplitude, which may 

frequently travel above and below the 95% confidence bands. After reviewing 

these trends, we would be prone to support those five intensification methods 

that exhibit similar K lines as that of an idealized FIA sample.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 49

We had difficulty implementing our version of RIPL without access to USFS 

Region 1 data layers. We did eventually run RIPL over CITRIX as an ESRI 

add-in tool, which worked more easily than our previous test version. However, 

we still needed to edit the resulting set of plots so that each P2 hex contained 

only three intensified plots. This method appears to be more appropriate when 

intensification is needed for an area without P2 hex centric restrictions. We 

remain confident, however, that a RIPL package can be developed to suit FIA 

intensification needs, if desired. RIPL offers a wide assortment of constraints 

to the user, who can then conduct an intensification task that approaches an 

optimal solution. But as with most optimization procedures, additional time is 

required for the tool to find a “best” solution. RIPL displays much promise with 

its heuristic approach and adaptability to various constraints, and we remain 

open to investigating future versions.

We also had concerns for the applicability of the R4 method for those regions 

that do not have B-grid or other historic plots available for their intensification needs. While these historic plots do provide useful information, there is 

no guarantee that their plot design, quality control, placement criteria or other 

related issues meet the current FIA annual plot standards. The R4 method also 

does not incorporate any type of nested polygon within a P2 hex, which was 

one of our desired traits when comparing candidate intensification methods.

While the SRS method was generally used as a comparison method of intensification in our study, it has an advantage in that an analyst can easily add additional plots to a given P2 hex after that area has previously been intensified. 

However, the SRS also has many disadvantages that are well summarized in 

Lister and Scott (2008).

Due to their resulting CE and K values as well as other concerns, we are reluctant at this time to recommend the SRS, R4 or RIPL method as a national FIA 

plot intensification procedure.

One of the advantages of the Repeating Shapes (RS) method is that it is very 

easy to download, install, and run in ESRI’s ArcMap. It enables the user to 

create hexagons, or other types of polygons, based on a user-defined area as 

well as other parameters. So, while it is a good product to create intensified 

polygons for a given area, it is very hard to align new polygons within an existing framework of P2 hexes. During our testing, we were unable to “snap” 

(geographically coincident) the new hexagons to the P2 hexes, which created 

overlaps such as those depicted in figure 17. With this spatial alignment problem, there are several challenging issues that can frequently arise. Since one of 

our basic assumptions is that the intensification should be P2 hex centric, we 

cannot recommend the Repeating Shapes method to be used as a national FIA 

plot intensification procedure.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 50

We were intrigued by the Python4x method of intensification, which is based 

on the coordinates of the P2 hex centroid and the location of an existing FIA 

base plot. In a process that simulates having sub-hexes nested within a given 

P2 hex, Python4x places an intensified plot on the opposite side of the hex from 

the existing FIA base plot, at a random distance and slightly random azimuth. 

It then compares this plot’s location with its corresponding P2 hex center and 

places random points in the other quadrants of the hex (at right angles to the 

initial bearing). It is also written in python, which has frequently been used for 

various GIS applications.

While Python4x simulates having sub-hexes in place, it does not permit a plot 

to be located within all parts of the overlying P2 hex. The script allows a user 

to specify a maximum distance to extend beyond the P2 hex centroid, and a 

random number is then generated to select some percentage of distance from 

the hex centroid based on that user-provided maximum distance. Since we want 

all intensified plots to lie within the same P2 hex as the existing FIA plot, the 

user must base this maximum amount on the distance from the hex centroid to 

the edge of the hexagon. If the P2 hexagon was shaped as a circle, this approach 

would be adequate. However, a hexagon will have portions that are not included 

in this circular area. That is, those areas near the hexagon vertices will likely 

not be available for intensified plot placement, which goes against our basic 

assumption that all areas within a P2 hex should be eligible for plot placement.

Since this method produces areas within a P2 hex without an equal probability 

of selection, we cannot recommend that the current version of Python4x be used 

as a national FIA plot intensification procedure.

Each of the three remaining intensification methods (GRID, R5, and SFC) has 

similar properties related to their respective CE and K statistics. They also produce smaller polygon areas that are nested within an overlying P2 hexagon. This 

trait demonstrates one of our basic assumptions that plots should be established 

within a framework that encourages more spatial balance between plots. Another commonality between these three methods is that after this framework has 

been created, the resulting intensified plots are established in the same manner 

(randomly placed within each smaller polygon, random assignment of intensity 

number, calculation of panel.subpanel numbers, and clipped to the BNF boundary). Consequently, we will compare these remaining three methods, based in 

part, on some of the decision rules and technical characteristics presented in 

the Methods section.

First, each of these three remaining methods produces smaller polygon areas that 

are nested within an overlying P2 hexagon. However, the shape and/or pattern of 

these smaller polygon areas are different. Both the GRID and R5 methods produce sub-hexes that align somewhat differently within their respective P2 hexes. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 51

The GRID method (figure 6) contains one sub-hex centered within the P2 hex, 

while the R5 method (figure 10) creates three whole sub-hexes aligned in a 

triangular-shape that is centered near its P2 hex centroid. This difference may be 

a minor consideration for some analysts, but for others it presents an undesirable 

trait—having three sub-hexes intersecting near the P2 hex centroid—due to the 

potential of having from zero to three plots clustered near the P2 hex centroid.

While the GRID and R5 methods produce sub-hexes, the SFC method generates “clusters,” (figures 11 and 12) for their nested polygon shapes. For a 4x 

intensification, these clusters typically bisect the P2 hex centroid, similar to 

the R5 method. Overall, the 4x intensification pattern seems to split the P2 hex 

into quadrants. All three methods enable their smaller polygons (clusters or 

sub-hexes) to “nest” within the overlying P2 hexagon.

Based on the position of the sub-hex shapes within each P2 hex, we would tend 

to prefer those produced by the GRID method over the R5 and SFC methods for 

typical FIA intensification tasks. The rationale for our preference of the sub-hex 

position produced by the GRID method is that one sub-hex is spatially centered 

within each P2 hex, which results in one plot relatively near its respective P2 

hex centroid.

Another aspect to consider is the degree of flexibility in selecting an intensification factor for each method. While the GRID method has some limitations 

upon which intensification factors are available, the SFC method allows the 

user to select a factor without restriction. The R5 method script is hardcoded to 

produce a 4x intensification, while both the GRID and SFC methods require the 

user to specify this factor. Although the R5 method is easily implemented as a 

python script, this limitation to the intensification factor may be a disadvantage 

to some analysts.

Another issue to consider is the study area represented by an intensification 

project. Both the GRID and R5 methods primarily utilize polygon layers, while 

the SFC method incorporates raster layers and their corresponding pixel-centroid 

point layers for relatively short distances (30-meter pixels). It is generally accepted that GIS-based storage requirements and processing speed of relatively 

large geographic areas is greater and more time consuming for raster layers 

compared to vector geospatial layers. Thus, using the SFC method to conduct a 

state-wide intensification task, using 30-meter pixels, would likely require more 

time and resources as compared to a similar operation based on vector layers. 

Some analysts working on intensification projects with such limitations may 

select the GRID or R5 methods over the SFC method based on these factors.

Another issue when using raster layers would be the “stair-step” effect that 

is produced when converting a study area boundary from pixels to a polygon 

feature. For some applications, this may be a disadvantage for their project, depending on the relative size and shape of the study area as well as its sensitivity 

to representing an exact study area boundary. Depending on the analyst and 

the intensification project, this aspect of the SFC method may be a deterrent.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 52

As for ease of use, all three of these methods have scripts that are already written and successfully demonstrated in previous intensification tasks. They are 

also transparent in their design and operations, without any “black box” mystic 

surrounding them. The SFC method uses an AML program and common GIS 

functionality to develop its clusters, while the R5 method uses a python script to 

establish its sub-hexes. The GRID method has a more convoluted approach that 

involves the use of C and AML programs, with a variety of program parameters 

to learn. However, once an analyst becomes accustomed to this approach, it turns 

out to be a very resourceful tool for plot intensification tasks.

Overall, based on the topics previously discussed, we would recommend the GRID method as the technique for FIA to adopt as a national plot intensification procedure. However, we would also suggest that 

the current version of the GRID method be updated by converting the C 

scripts and AMLs to an ESRI ArcGIS add-in tool (ESRI, Inc. 2012; also 

http://blogs.esri.com/esri/arcgis/2010/05/05/add-ins-for-arcgis-desktop-10/). The 

update will make it more user-friendly; an FIA analyst would be able to execute 

the GRID method for some intensification project within the confines of ESRI’s 

ArcMap, and not need to rely on importing/ exporting files from other software 

programs that may or may not be available on their workstation. Other alternatives, such as Oracle Spatial, may also be utilized for such an update or conversion process. However, since the USFS has employed ESRI products for many 

years and likely for many more, it seemed appropriate at this time to recommend 

creating an updated version of the GRID method as an ESRI ArcGIS add-in tool.

Panelizing Plots

A temporal partitioning was achieved by assigning panel.subpanel values to 

intensified plots based on the procedures described in the Methods section. 

The plot distributions created using EBM for panel 1 subpanel 1 plots from the 

GRID method are shown in figure 3b, while figure 4a gives the plot distributions for all ten panel.subpanel combinations, where the banding phenomenon 

is quite evident.

In an effort to distribute the intensified plots with more spatial balance over each 

year of a 10-year cycle, we investigated the effect of keeping the subpanel value 

of intensified plots the same as that of the existing base plot for each P2 hex, a 

procedure we designated as AM. The plot distributions using AM for panel 1 

subpanel 1 plots using the GRID method are shown in figure 3c. Note how the 

spatial banding effect was reduced using this alternate method as compared to 

EBM shown in figure 3b. Figure 4b gives the plot distributions using AM for 

all ten panel.subpanel combinations using the GRID method, which generally 

supports this assessment.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 53

We also determined the CE statistic values for these intensified plots using the 

AM procedure. Table 6 presents CE statistics for those plots using the GRID 

intensification method and panel.subpanel assignments by the AM procedure 

for all plots within the 303 P2 hexes clipped by the BNF boundary. Overall, CE 

values for these plots obtained from the AM panel.subpanel assignments seem to 

be closer to our desired distribution pattern obtained by placing one random plot 

per P2 hex (CE values near 1.26), as compared to the EBM procedure listed in 

table 5 (CE values near 1.0). Based on these findings, we recommend using the 

alternative panelizing procedure for the BNF. We qualify “for the BNF” since 

the panel.subpaneling procedure will likely depend somewhat on the overall 

geospatial properties of a given region utilizing a ten-panel arrangement.

Since the panel.subpaneling procedure used is likely dependent on the geospatial 

properties of a specific region, this may lead other analysts to investigate other 

panel.subpaneling routines than what we have suggested. One way to contemplate 

plot panelization tasks is to consider the graphical representations given in Appendix F, which details how we calculated panel.subpanel values for intensified 

plots from using the EBM or AM procedures. If an analyst lets x = 1 and x = 

2 (creating two tables), then each panel.subpanel will appear once in the “Base 

Plot” column and three times in the combined three columns for “Intensity 

Numbers.” Other panel.subpaneling procedures would be rearrangements of 

panel.subpanel numbers in the last three columns with the restriction that each 

panel.subpanel number occurs exactly three times. Since the intensification of 

BNF was only for a test study of the various methods, we did not investigate 

any other panel.subpaneling procedures besides the AM procedure.

Another approach for assigning panel.subpanel values to intensified plots is 

to utilize either the HIERARCHICAL_ID field or PANEL_70 field in FIA’s 

NIMS_BASE_HEX table (John Coulston, USFS, personal communication, 

2012). An analyst may visually compare panel.subpanel values as they span 

across several years of an inventory cycle. Any such banding or clumping of 

intensified plots, as we noticed in our case study, could potentially be adjusted 

using these attributes so that plot distributions exhibit a more spatially balanced 

spread across the landscape. Additional details or suggestions for using this approach varies, and could involve several trial-and-error attempts by an analyst so 

that plot distributions are adequate visually, as well as spatially and temporally 

balanced over an intensification area.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 54

References

Brand, Gary J.; Nelson, Mark D.; Wendt, Daniel G.; Nimerfro, Kevin K. 2000. The hexagon/

panel system for selecting FIA plots under an annual forest inventory. In: McRoberts, 

Ronald E.; Reams, Gregory A.; Van Deusen, Paul C., eds. Proceedings of the first annual 

forest inventory and analysis symposium. Gen. Tech. Report NC-213. St. Paul, MN: U.S. 

Department of Agriculture, Forest Service, North Central Research Station: 8-13.

Clark, P.J.; Evans, F.C. 1954. Distance to nearest neighbor as a measure of spatial 

relationships in populations. Ecology 35: 445-453.

Coulston, John W.; Koch, Frank H.; Smith, William D.; Sapio, Frank J. 2009. Developing 

survey grids to substantiate freedom from exotic pests. In: McRoberts, Ronald E.; Reams, 

Gregory A.; Van Deusen, Paul C.; McWilliams, William H., eds. Proceedings of the 

eighth annual forest inventory and analysis symposium; 2006 October 16-19; Monterey, 

CA. Gen. Tech. Report WO-79. Washington, DC: U.S. Department of Agriculture, Forest 

Service: 91-97.

ESRI, Inc. 2001. ArcInfo Workstation 8.1. Redlands, CA: ESRI, Inc. Online: 

http://www.esri.com.

ESRI, Inc. 2009. ArcMap 9.3.1. Redlands, CA: ESRI, Inc. Online: http://www.esri.com.

ESRI, Inc. 2012. ArcGIS 10.1. Redlands, CA: ESRI, Inc. Online: http://www.esri.com.

Jenness, Jeff. 2009. Repeating Shapes for ArcGIS. Jenness Enterprises. Online: 

http://www.jennessent.com/arcgis/repeat_shapes.htm.

Lister, Andrew J.; Scott, Charles T. 2008. Use of space-filling curves to select sample 

locations in natural resource monitoring studies. Environmental Monitoring Assessment 

149: 71-80.

Mandloi, Deelesh. 2009. Partitioning tools – generic tools. Online: 

http://arcscripts.esri.com/details.asp?dbid=16021.

McCollum, Joseph M. 2001. Honeycombing the Icosahedron and Icosahedroning the 

Sphere. In: Reams, Gregory A.; McRoberts, Ronald E.; Van Deusen, Paul C., eds. 2001. 

Proceedings of the second annual forest inventory and analysis symposium; 2000 October 

17-18; Salt Lake City, UT. Gen. Tech. Rep. SRS-47. Asheville, NC: U.S. Department of 

Agriculture, Forest Service, Southern Research Station: 25-31.

McCollum, Joseph M.; Cochran, Jamie K. 2005. Forest inventory and analysis and forest 

health monitoring: Piecing the quilt. In: Proceedings of the fifth annual forest inventory 

and analysis symposium; 2003 November 18-20; New Orleans, LA. Gen. Tech. Rep. 

WO-69. Washington, DC: U.S. Department of Agriculture Forest Service: 175-182.

McCollum, Joseph M.; Cochran, Jamie K.; Rose, Anita K. 2008. A discrete global grid of 

photointerpretation. Res. Pap. SRS–44. Asheville, NC: U.S. Department of Agriculture 

Forest Service, Southern Research Station. 7 p.

Perry, G.L.W.; Miller, B.P.; Enright, N. 2006. A comparison of methods for the statistical 

analysis of spatial point patterns in plant ecology. Plant Ecology 187: 59‐82.
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Reams, Gregory A.; Smith, William D.; Bechtold, William A.; McRoberts, Ronald E.; 

Spirek, Frank; Liff, Chuck. 2005a. Three proposed data collection models for annual 

inventories. In: Proceedings of the fifth annual forest inventory and analysis symposium; 

2003 November 18-20; New Orleans, LA. Gen. Tech. Rep. WO-69. Washington, DC: U.S. 

Department of Agriculture Forest Service: 1-7.

Reams, Gregory A.; Smith, William D.; Hansen, Mark H.; Bechtold, William A.; Roesch, 

Francis A.; Moisen, Gretchen G. 2005b. The forest inventory and analysis sampling 

frames. In: Bechtold, William A.; Patterson, Paul L., eds. The enhanced forest inventory 

and analysis program - national sampling design and estimation procedures. Gen. Tech. 

Rep. SRS-80. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern 

Research Station: 11-26.

The R Foundation for Statistical Computing. 2012. R version 2.15.0 (2012-03-30). Online: 

http://www.r-project.org/. 

(CE package: http://www.inside-r.org/packages/cran/spatstat/docs/clarkevans; 

K package: http://www.inside-r.org/packages/cran/spatstat/docs/Kest).

White, Denis. 1989. Original EMAP grid generating system. EPA Western Ecology 

Division. Online: http://people.oregonstate.edu/~whitede/getgrid.htm.

Zeiler, J.D.; Bush, Renate; Berglund, Doug. 2010. Region 1 Intensification Plot Locator 

(RIPL) Program. USDA Forest Service, Region 1. Report 10-3 v2.0. Online: 

http://fsweb.r1.fs.fed.us/forest/inv/r1_tools/ripl_overview.pdf.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 56

Appendix A: National FIA Plot Intensification Task Teama

Core Members

Last Name First Name Office E-mail Address Phone Number

Alegria Jim R6PNW jalegria -at- fs.fed.us 503-808-6090

Blackard Jock IW-FIA jblackard -at- fs.fed.us 801-625-5393

DeBlander Larry R4, RO ldeblander -at- fs.fed.us 801-625-5204

Hatfield Mark NRS-FIA mahatfield -at- fs.fed.us 651-649-5169

Kennedy Kama R5, RSL kkennedy -at- fs.fed.us 916-640-1253

Lister Andy NRS-FIA alister -at- fs.fed.us 610-557-4038

McCollum Joe SRS-FIA jmccollum -at- fs.fed.us 865-862-2065

Megown Kevin WO, RSAC kamegown -at- fs.fed.us 801-975-3826

Patterson Paul IW-FIA plpatterson -at- fs.fed.us 970-295-5966

Schanta Michael R9, Mark Twain NF mschanta -at- fs.fed.us 573-341-7447

Thompson Tom PNW-FIA tthompson03 -at- fs.fed.us 907-743-9401

Winterberger Ken PNW-FIA kwinterberger -at- fs.fed.us 907-743-9419

Consulting Members

Last Name First Name Office E-mail Address Phone Number

Alerich Carol NRS-FIA calerich -at- fs.fed.us 610-557-4068

Bush Renate R1, RO renatebush -at- fs.fed.us 406-329-3107

Coulston John SRS-FIA jcoulston -at- fs.fed.us 865-862-2008

Fallon Don R4, RO dfallon -at- fs.fed.us 801-625-5361

Halverson Kevin WO, RSAC kahalverson -at- fs.fed.us 801-975-3755

Jacobs Dennis SRS-FIA djacobs -at- fs.fed.us 865-862-2060

Kies Andrew R1, RO afkies -at- fs.fed.us 406-329-3443

Menlove James IW-FIA jmenlove -at- fs.fed.us 801-625-5426

Meriwether David R8, RO dmeriwether -at- fs.fed.us 404-347-4663

Moisen Gretchen IW-FIA gmoisen -at- fs.fed.us 801-625-5384

Ramirez Carlos R5, RSL carlosramirez -at- fs.fed.us 916-640-1275

Scott Charles “Chip” NRS-FIA ctscott -at- fs.fed.us 610-557-4020

Wilson Barry “Ty” NRS-FIA barrywilson -at- fs.fed.us 651-649-5189

Zeiler Joseph D. R1, RO jzeiler -at- fs.fed.us 406-249-0179

a All members are with the U.S. Forest Service.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 57 FIA	
  Plot	
  Intensification	
  Team	
  Survey Characteristics	
  and	
  Assumptions	
  to	
  consider	
  for	
  Plot	
  Intensification Response	
  Options No Total	
  # %	
  Highest %	
  Above Response Responses Category Neutral 1. Should	
  intensification	
  be	
  based	
  on	
  the	
  existing	
  FIA	
  P2	
  hex	
  framework? Strongly Somewhat Neutral Somewhat Strongly Disagree Disagree Position Agree Agree 2 2 7 11 64 82 2. How	
  important	
  is	
  having	
  a	
  simple	
  routine,	
  ease	
  of	
  use,	
  adaptable	
  GIS-­‐based	
  tool? Not Alittle Neutral Somewhat Strongly Important Important Position Important Important 3 7 1 11 9 73 3. Are	
  there	
  any	
  requirements	
  for	
  intensification	
  related	
  to	
  FIA	
  or	
  NFS	
  national	
  databases? Yes No don't	
  know no	
  opinion 6 2 1 2 11 55 n/a 4. Are	
  there	
  significant	
  statistical	
  issues	
  or	
  other	
  considerations	
  when	
  doing	
  intensifications? Yes No don't	
  know no	
  opinion 7 2 2 11 64 n/a 5. Are	
  there	
  statistical/design	
  implications	
  between	
  ‘nested’	
  sub-­‐hexes/interior	
  polygons	
  vs.	
  	
   Yes No don't	
  know no	
  opinion overlapping	
  sub-­‐hexes/polygons	
  in	
  relation	
  to	
  the	
  existing	
  FIA	
  P2	
  base	
  hexes? 6 3 2 11 55 n/a 6. Are	
  there	
  statistical/design	
  implications	
  when	
  using	
  a	
  simple	
  random	
  placement	
  of	
  intensified	
  plots	
   Yes No don't	
  know no	
  opinion within	
  a	
  P2	
  hex	
  (with	
  no	
  sub-­‐hexes	
  created)	
  vs.	
  having	
  a	
  more	
  spatially-­‐balanced	
  distribution	
   provided	
  by	
  creating	
  sub-­‐hexes/polygons? 9 2 11 82 n/a 7. How	
  critical	
  is	
  it	
  to	
  maintain	
  'statistical	
  properties'	
  of	
  existing	
  FIA	
  design	
  &	
  layout	
  when	
  doing	
  plot	
   Not Alittle Neutral Somewhat Strongly intensification	
  (i.e.,	
  Paul’s	
  document)? Critical Critical Position Critical Critical 3 6 2 11 55 82 8. How	
  important	
  is	
  it	
  for	
  an	
  intensification	
  program	
  to	
  have	
  adaptability	
  to	
  various	
  intensification	
   Not Alittle Neutral Somewhat Strongly levels	
  (2x,	
  3x...	
  10x,	
  etc)? Important Important Position Important Important 2 6 3 11 27 82 9. How	
  important	
  is	
  user-­‐understanding	
  of	
  processes	
  vs.	
  transparency	
  (black	
  box)	
  for	
  intensification	
  routines? Not Alittle Neutral Somewhat Strongly Important Important Position Important Important 1 1 4 4 1 11 36 73 10. How	
  open	
  is	
  your	
  Region	
  to	
  consider	
  new	
  intensification	
  methods	
  vs.	
  a	
  preference	
  to	
  keep	
  the	
   Not Alittle Neutral Somewhat Strongly current	
  intensification	
  routine	
  in	
  your	
  Region? Open Open Position Open Open 2 1 3 5 11 0 45 11. How	
  valuable	
  is	
  it	
  in	
  your	
  Region	
  to	
  have	
  a	
  consistent	
  intensification	
  approach	
  or	
  procedure	
  being	
   Not Alittle Neutral Somewhat Strongly utilized	
  between	
  neighboring	
  Regions	
  (both	
  FIA	
  and	
  NFS	
  Regions)? Valuable Valuable Position Valuable Valuable 2 4 5 11 45 82 Appendix B: FIA Plot Intensification Team Survey Results
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 58

Appendix C: R Script Example to Calculate the 

Clark and Evans Statistic

R script example, with assistance from John Coulston:

------------------------------------------------------------------------

library(maptools)

library(spatstat)

#read in shapefiles

bnf<readShapeSpatial(“C:/.../bnf_noholes.shp”) # boundary shapefile

bnf.plt<-readShapeSpatial(“C:/.../MTWY_afc_clip.shp”) # base grid shapefile

bnf.4x<-readShapeSpatial(“C:/.../x4.shp”) # 4x intensification plots

bnf.plt.b<-readShapeSpatial(“C:/_.../Bnf_grid_plots_alb83_reportclip.shp”) # both plots

#show plots

plot(bnf)

points(bnf.plt,col=”black”)

plot(bnf)

points(bnf.4x,col=”red”)

plot(bnf)

points(bnf.plt.b,col=”green”)

#do clark and evans

pts<-coordinates(bnf.plt)

the.pat<-ppp(x=pts[,1],y=pts[,2],window=as.owin(bnf))

ce.pat<-clarkevans(the.pat)

pts.4<-coordinates(bnf.4x) 

the.pat4<-ppp(x=pts.4[,1],y=pts.4[,2],window=as.owin(bnf))

ce.pat4<-clarkevans(the.pat4)

pts.b<-coordinates(bnf.plt.b)

the.pat.b<-ppp(x=pts.b[,1],y=pts.b[,2],window=as.owin(bnf))

ce.pat.b<-clarkevans(the.pat.b)

#examine results look at the cdf corrections

ce.pat

ce.pat4

ce.pat.b

------------------------------------------------------------------------
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 59

Appendix D: R Script Example to Calculate the Ripley’s K Statistic

R script example, with assistance from John Coulston:

------------------------------------------------------------------------

#horizontal line graph procedure

library(maptools)

library(spatstat)

#read in shapefiles

bnf<-readShapeSpatial(“C:/.../bnf_noholes.shp”) # boundary shapefile

bnf.BASE<-readShapeSpatial(“C:/.../MTWY_afc_clip.shp”) # base grid shapefile

bnf.INT<-readShapeSpatial(“C:/.../BNF_GRID_REPORTclip.shp”) # GRID_4x

bnf.BOTH<-readShapeSpatial(“C:/.../BNF_GRID_plots_merge_afc_clip.shp”) # both plots

#show plots

plot(bnf)

points(bnf.BASE,col=”black”)

points(bnf.INT,col=”red”)

#do Ripleys K

ptsBASE<-coordinates(bnf.BASE)

ptsINT<-coordinates(bnf.INT)

ptsBOTH<-coordinates(bnf.BOTH)

the.patBASE<-ppp(x=ptsBASE[,1],y=ptsBASE[,2],window=as.owin(bnf))

the.patINT<-ppp(x=ptsINT[,1],y=ptsINT[,2],window=as.owin(bnf))

the.patBOTH<-ppp(x=ptsBOTH[,1],y=ptsBOTH[,2],window=as.owin(bnf))

#graphs using zero horizontal adjustments, simulation envelopes=50sims

HGenvINT <- envelope(the.patINT, Kest, nlarge=Inf, nsim=50)

plot(HGenvINT, sqrt(./pi)-r~r, lty=c(1,2,3,3), col=c(1,2,3,3), ylab=”L(t)”)

HGenvBOTH <- envelope(the.patBOTH, Kest, nlarge=Inf, nsim=50)

plot(HGenvBOTH, sqrt(./pi)-r~r, lty=c(1,2,3,3), col=c(1,2,3,3), ylab=”L(t)”)

------------------------------------------------------------------------
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 60

Appendix E: NIMAC Method AML Script

/* This AML runs a spatialorder and collocate in order to locate INTENSIFIED

/* PLOTS within specific area. Initial development by Andy Lister.

&s pts = bhhxptc /* INPUT: name of the gridpointed hex file (hexes turned to a grid 

where hexid=value, then gridpointed)

&s grid_code = grid_code /* name of item that identifies the hexid (created from the arcmap 

spatial analyst routine)

&s numclust = 4 /* number of clusters you want (ie, intensification level... 4x would 

be a 4 numclust value)

&s hexes = bhhexa83 /* INPUT: original hex id as a polygon coverage

&s hex_id = USFIAPT_ID /* hex identifier for the hex poly coverage

&s numrec = 304 /* number of records in hex coverage + 1

&s ptgrid = bh_ahxg /* INPUT: name of grid used to make points

&s pixsize = 30 /* size of the pixels used to convert hex poly coverage to a hex 

grid

&s coll_fld = class /* field name for collocate class

&s i = 1

&if [exists tmpgr -grid] &then

 kill tmpgr all

&else

 &type /// checked tmpgr

grid

tmpgr = %ptgrid%.count

quit

&describe tmpgr

/* this is the cluster capacity for collocate

&s clustsize = [calc %grd$zmax% / %numclust%] 

/* Note, hex coverage must have labels created; if you use shapearc, 

/* you need to run the createlabels command in arc

createlabels %hexes% 

/* cycle through each hex_id value in points coverage

&do &until %i% = %numrec%

 /* get hex_id value

 ae

 editcov %hexes% 

 &s v = [show label %i% item %hex_id%]

 quit

 /* spatialorder-collocate routine for each hex_id value

 ap

 reselect %pts% points %grid_code% = %v%
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 61

 spatialorder %pts% point order

 calculate %pts% point %grid_code% = 1

 collocate %pts% point order %grid_code% %clustsize% %coll_fld%

 calculate %pts% point %grid_code% = %v%

 clearselect

 &type ///

 &type /// Finished record number %i% (hex %v%) !!!

 &type ///

 &s i = %i% + 1

 quit

&end

grid

setwindow %ptgrid% %ptgrid%

setcell %ptgrid%

&if [exists tmpptgr -grid] &then

 kill tmpptgr all

&else

 &type /// checked tmpptgr

/* points-to-grid for points coverage

tmpptgr = pointgrid(%pts%, %coll_fld%, #, #, %pixsize%)

&if [exists polygr%numclust% -grid] &then

 kill polygr%numclust% all

&else

 &type /// checked polygr%numclust%

/* grid-to-poly for points coverage

polygr%numclust% = gridpoly(tmpptgr, .000000001)

&if [exists tmpcov -cover] &then

 kill tmpcov all

&else

 &type /// checked tmpcov

/* grid-to-poly for original hex grid

tmpcov = gridpoly(%ptgrid%, .000000001)

quit

&if [exists final%numclust% -polygon] &then

 kill final%numclust% all

&else

 &type /// checked final%numclust%

/* UNION: points coverage (cluster value) with original hex grid 

/* union polygr%numclust% tmpcov final%numclust% .000000001 join

&type ///

&type /// Done. Your final polygon zone (subhex) coverage is final%numclust%. 

&type ///

&type /// You need to the arctoolbox (data management) dissolve tool (with

&type /// tmpcov-id, grid-code as the dissolve fields) to dissolve to create 

&type /// 1 record for each subhex, even though they are spatially 

&type /// nonconitugous (final%numclust%_diss). 

&type ///
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 62

&type /// After dissolving, AddItem (Hex_ID, long) to the dissolve shapefile,

&type /// then join it back to tmpcov (both by tmpcov_id), then calculate

&type /// Hex_ID = joined.GRID-CODE... release join.

&type /// 

&type /// From the dissolve coverage output, choose one random point per 

&type /// polygon (Create Random Points-management). Then, join (CID) back to

&type /// the dissolve shapefile (FID) to get HEX_ID and GRID_CODE fields.

&type /// Remove join after creating final random_pts shapefile.

&type ///

&type /// To remove a random point that lies in same polygon as an existing

&type /// FIA plot, use select by location, then export random plots...

&type ///
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-329. 2014 63

Appendix F: 10-year Panel.Subpanel Assignments for Intensified Plots

Table F.1—The panel.subpanel assignments for intensified plots using the Extension 

of Base Method or EBM procedure, based on the sequences used to generate the 

10-year cycle panel assignments from the 5-year cycle panel assignments.

Panel.Subpanel 

Value of 

Base Plot

Intensity Number of Intensified Plot

2 3 4

1.x 3.x 5.x 2.y

2.x 4.x 1.y 3.y

3.x 5.x 2.y 4.y

4.x 1.y 3.y 5.y

5.x 2.y 4.y 1.x

Panel values for intensified plots are shown in bold, and are based on the panel.subpanel value of 

the base plot and the intensity number of the intensified plot. 

Subpanel values {1, 2} for intensified plots will alternate from the base plot’s subpanel value when 

the intensified plot’s panel value (1-3-5-2-4 sequence) moves from the 1-3-5 value range to the 2-4 

value range, and vice-versa. This subpanel “switch” is denoted by the {x, y} identifier; where a “x” 

listed for the intensified plot’s subpanel value indicates the same value as the base plot’s subpanel 

value, and a “y” designates a different subpanel value from the base plot’s subpanel value.

For example, an existing FIA plot has a panel=3 and subpanel=1. For the 3 intensified plots for 

that P2 hex, the following assignments will be made based on their intensity number:

Intensity Number=2: panel=5, subpanel=1

Intensity Number=3: panel=2, subpanel=2

Intensity Number=4: panel=4, subpanel=2

with 3.1 (year 3), 5.1 (year 5), 2.2 (year 7) and 4.2 (year 9) all in the odd year band.

Table F.2—The panel.subpanel assignments for intensified plots using the Alternative 

Method or AM procedure, based on a variation of the sequences used to generate 

the 10-year cycle panel assignments from the 5-year cycle panel assignments.

Panel.Subpanel 

Value of 

Base Plot

Intensity Number of Intensified Plot

2 3 4

1.x 3.x 5.x 2.x

2.x 4.x 1.x 3.x

3.x 5.x 2.x 4.x

4.x 1.x 3.x 5.x

5.x 2.x 4.x 1.x

The panel.subpanel assignment is based on the sequence (1-3-5-2-4) and the subpanel values 

{1, 2} for intensified plots remain the same value as its base plot’s subpanel value. Intensified plots 

whose odd or even year band is opposite of the odd or even year band of its base plot are shown in 

bold.

For example, an existing FIA plot has a panel=3 and subpanel=1. For the 3 intensified plots for that 

P2 hex, the following assignments will be made based on their intensity number:

Intensity Number=2: panel=5, subpanel=1

Intensity Number=3: panel=2, subpanel=1

Intensity Number=4: panel=4, subpanel=1

with 3.1 (year 3) and 5.1 (year 5) in the odd year band and 2.1 (year 2) and 4.1 (year 4) in the even 

year band.
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an individual’s income is derived from any public assistance program, 

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bases will apply to all programs and/or employment activities.)

United States Department of Agriculture

Forest Service

Rocky Mountain Research Station