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Comparison between intensity based inventory and sampling based inventory
Bogdan StrimbuLouisiana Tech University
Issue
• Inventory of the forest resources
• Practical applications: preset intensity
• Alternative: sampling design
• Legal constraints
2
Objective
• Questions to answer:
1. Is preset-intensity inventory legally defendable?
2. Are there significant differences between preset-
intensity inventories and sampling based
inventories?
3
Approach
• USFS and Florida Assessor guidelines
• Sampling error standards dependent on the
estimated value of the sale
• alpha=5%
4
Sampling error standardsUSFS Alpha=5%
Value SE
<15000 20%
<35000 19%
<55000 16%
<75000 14%
<95000 12%
>95000 10%
Florida merchantable planted pine alpha=5% SE=10%
merchantable natural timber alpha=10% SE=10%
pre-merchantable pine alpha=32% SE=10%
5
Settings• Preset - intensity inventories: 5% and 10%
• Alpha=5%→Approximate t=2
• Plot size: 0.1. ac
• Simple Random Sampling without replacement
• Homogeneous stand → No stratification
• The population has a mean
6
Formulae
222
1
1
1
1
1
1
:
:
tCVAE
NtCVAE
NN
N
ni
tCVAE
N
n
SRSdesignSampling
N
niNi
plotArea
Areain
Intensity
7
Sample size vs. CV• Area=10 ac
8
Sample size vs. CV• Area=20 ac
9
Sample size vs. CV• Area=50 ac
10
Sample size vs. CV• Area=100 ac
11
Sample size vs. Sample error• Area= 10 ac
12
Sample size vs. Sample error• Area= 20 ac
13
Sample size vs. Sample error• Area= 50 ac
14
Sample size vs. Sample error• Area= 100 ac
15
Intensity – CV for a=10%
16
0 5 10 15 20 25 30 35 40 45 500%
1%
2%
3%
4%
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
20 ac @SE=10% 20 ac @SE=20% 50 ac @SE=10% 50 ac @SE=20%
100 ac @SE=10% 100 ac @SE=20% 200 ac @SE=10% 200 ac @SE=20%
10 ac @SE=10% 10 ac @SE=20%CV [%]
Inte
nsit
y fo
r sta
nd a
rea>
20 a
c
Inte
nsit
y fo
r sta
nd a
rea
= 10
ac
Intensity – CV for a=5%
17
0 10 20 30 40 50 600%
1%
2%
3%
4%
5%
0%
10%
20%
30%
40%
50%
60%
20 ac @SE=10% 20 ac @SE=20% 50 ac @SE=10% 50 ac @SE=20%100 ac @SE=10% 100 ac @SE=20% 200 ac @SE=10% 200 ac @SE=20%10 ac @SE=10% 10 ac @SE=20%
CV [%]
Inte
nsit
y fo
r sta
nd a
rea>
20 a
c
Inte
nsit
y fo
r sta
nd a
rea=
10
ac
Summary• USFS guidelines more strict then state guidelines• Intensity based inventory – legally defendable
using USFS or state guidelines (Florida) most of the cases
• Stratification recommended for high variable stands
• Intensity based inventory for stands>20 ac at least double the cruising effort
• For stands larger than 50 ac the cruising effort is almost comparing with the sampling based inventory 18
Cauchy distribution
19
2
0
0
1
1),;(
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