### Fixed Plot Sampling

```Cruise Design
Measurement
Computations
Sampling Intensity
Determined by
1. Value of product(s)
2.Variability within the stand
3. Budget limitations
Application
Trees in the population are selected with equal
probability
Normally plot locations are allocated on an
unbiased grid pattern
Works best for large areas with relatively uniform
density and species distribution
Potential Problems
If highly variable stand, large plots
and/or large numbers of plots may be
needed to get accurate estimates.
Sampling Intensity
USFS Way
Sample Selection – from Precruise data
1. Determine the sampling error for the sale as a whole. (set to 10%)
2. Subdivide (or stratify) the sale population into sampling components as
needed to reduce the variability within the sampling strata.
3. Calculate the coefficient of variation (CV) by stratum and a weighted CV
over all strata. (this will be covered more later in the statistics lectures)
4. Calculate number of plots for the sale as a whole and then distribute by
stratum.
Number of Plots
Value of t is assumed to be 2
Error is set at 10%
Distribute Plots by Stratum
For each stratum, the calculation would look like this:
n1 = (17.6 * 185) / 67.9 = 48 plots
n2 = (7.7 * 185) / 67.9 = 21 plots
n3 = (7.2 * 185) / 67.9 = 20 plots
n4 = (35.4 * 185) / 67.9 = 96 plots
Which totals to the 185 plots for the sale.
Tree Expansion Factor
1 divided by the fixed plot size times the number of plots
Sample Error step 1 (Calculate Standard Error)
Sample Error – Step 2
36.2% is a bit larger than the level we set to begin with (10%) – Implications?
Sampling Intensity
• Without Precruise data (cheaper)
• Assumes fairly uniform distribution of species,
• Can work for even-aged or uneven-aged stands if
assumptions are met
Fixed Area Plot Sampling
Plot Cruising
Plot cruise planning:
160 acre tract
Given
10% cruise (sample)
1/5 acre plots
1. Area to be sampled:
Areasampled Tractarea)(cruisepercent
Areasampled (160 ac) (0.1) 16.0 acres
Fixed Area Plot Sampling
Plot Cruising
Plot cruise planning:
160 acre tract
10% cruise (sample)
1/5 acre plots (0.2 ac.plots)
area sampled = 16.0 ac.
2. No. of plots needed:.
 Area sampled 

No.of plots 
 plotarea 
 16.0 
No.of plots 
  80 plots
 0.2 
Fixed Area Plot Sampling
Plot Cruising
Plot cruise planning:
160 acre tract
10% cruise (sample)
1/5 acre plots
area sampled = 16.0 ac.
80 plots needed
3. Samples represent how much area?
 Tract area 
Representative area  

 plots 
 160 acres
  2 ac  20 sq. ch.
Representativearea 
 80 plots 
Fixed Area Plot Sampling
Plot Cruising
Plot cruise planning:
160 acre tract
each represents 2 acres (20 sq. chains)
10% cruise (sample)
1/5 acre plots
area sampled = 16.0 ac.
80 plots needed
Representative Area Dist between plots)(Dist between lines
4. Plot spacing?
Distance between plots
 Representativearea

Dist between plots 
Dist
between
lines


 Representative area 

Dist between lines  
Dist
between
plots


Fixed Area Plot Sampling
Plot Cruising
Plot cruise planning:
160 acre tract
each represents 2 acres (20 sq. chains)
10% cruise (sample) 5 chain spacing between lines
1/5 acre plots
area sampled = 16.0 ac.
80 plots needed
5. Plot spacing?
Distance between lines
20 sq. chains (distance between plots)(5 chains)
 20 sq. chains
Distancebetween plots 

5
chains


Office Procedures
Number of Plots
Tract size times percentage sampling intensity gives you total sample area needed
Example: 23 acre tract X 10 percent sample = 2.3 acres
Area needed times plot area gives plots needed.
Goal: Select plot size that yields around 4 to 8 trees per plot
Example 1: 2.3 acres X 5 (fifth acre plots per acre) = 11.5 plots (make it 12)
each represents 2 acres
Example 2: 2.3 acres X 10 (tenth acre plots per acre) = 23 plots
each represents 1 acre
Operational Features
Plot center is marked
Often 10 percent sampled
• Unless huge forest with limited budget
• Or highly variable forest
• Or high valued forest
Fixed Plot – 1/10th acre
Plot Allocation
Can be unbiased yet systematic by randomizing location of start point and
bearing of sample lines.
Example of Systematic Layout
Fixed Plot Cruising
Procedure
Mark plot center
Start checking trees for tally clockwise
from the North for consistency
Mark each finished tree to prevent
tallying the same tree twice
Slope Correction
/
=
cos
Boundary Plots
If entire plot doesn’t fall
within the survey area, don’t
simply shift the plot center so
it fits into the tract. This
results in fewer edge trees
sampled.
Boundary Plots – Half plot
If entire plot doesn’t fall within the survey area, double count the half that
does.
Boundary Plots – Quarter plots
can be used in corners where all tally trees are counted 4 times.
Boundary Plots - Mirage Plots (preferred)
Imagine folding the plot back on itself
Boundary Plots - Walkthrough plots
If a line the same
distance from the plot
center to the tree,
when projected
through the tree
crosses the boundary,
count it twice.
Tally Sheet
Date = 8/19/2013 Size = 1/10 th acre Forest Cover Type =
Stand Size and Condition =
Stand Age =
Site Index =
Soil Classification =
Slope =
Understory Vegetation =
Stocking or Density Class =
Treatments needed =
Plot = 1
Tree
Species DBH
Form Class
Height
1
RO
14
78
1.5
2
2
SP
16
80
2
2
3
YP
18
82
2.5
1
Plot = 2
Etc.
Crown Class
Notes
Computations
Can be preformed by hand, in Excel or in Two Dog
Trees per acre – by species and/or by size
Basal Area per acre – by species and/or by grade
Expansion Factor equals percent area sampled
Combined Stand and Stock Table
No. of trees
Cubic-foot volumes
-------------------------------------------------------------------DBH
Per acre
Per acre
(in.)
Tract total
average
Tract total
average
------------------------------------------------------------------------------------------5
1195.5
11.2
1730.4
16.1
6
1432.6
13.4
3767.6
35.1
7
1455.1
13.6
5667.8
52.9
8
1150.6
10.7
6294.4
58.7
9
1128.0
10.5
8379.0
78.2
10
1082.9
10.1
10622.4
99.1
11
823.4
7.7
11142.7
103.9
--------------------------Total
8268.1
77.2
47604.3
444.0
Stand table gives estimated number of stems by size (in this case) and per acre
Stock table gives total volume and per acre volume (could be board foot or cubic foot)
107.2 acre tract of small mixed hardwoods
Cruise Summary (by species not sizes)
```