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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