# Improving Woody Biomass Estimation Efficiency Using Double Sampling

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Description of Data

**Table 1.**Descriptive statistics for original systematic point sample inventories of the 40 properties used in double sample analysis.

Variable | Mean | Min | Max | SD |
---|---|---|---|---|

Area (ha) | 242.1 | 31.2 | 1155.4 | 227.3 |

Points sampled | 104.0 | 47.0 | 226.0 | 49.0 |

Basal area (m^{2} ha^{−1}) | 21.3 | 17.4 | 30.6 | 2.5 |

Average dbh (cm) | 31.0 | 25.7 | 36.1 | 2.3 |

Biomass (mt ha^{−1}) | 144.9 | 114.8 | 202.9 | 17.1 |

Biomass margin of error (%) | 7.4 | 3.2 | 12.0 | 2.2 |

#### 2.2. Analysis

^{−1}were calculated using the following equations, respectively:

_{α,v}= t-statistic for the chosen confidence interval (95%) and appropriate degrees of freedom, and = mean biomass (mt ha

^{−1}).

_{m}) was calculated from the small sample data as follows [2]:

_{s}= number of small sample, n

_{L}= number of points in the large sample, = small sample biomass variance, = small sample basal area variance, and C

_{s}= small sample biomass and basal area covariance. Percent margin of error was then calculated using Equation 3. Departure from the original percent margin of error was simply determined by taking the absolute difference between the percent margin of errors obtained from the original inventory and the double sample inventories. The standard error, percent margin of error, and departure from the original percent margin of error were calculated for each property. Among all properties, the mean standard error, percent margin of error, and difference in percent margin of error was calculated for each double sample intensity.

_{L}= time required to perform a large sample point, T

_{S}= time required to perform a small sample point. Based on operational observation of inventories across the 40 sampled properties, small sample points were estimated to take three times longer to complete than large sample points. This estimate was corroborated by Merten et al. [1] who found that, within the Appalachian hardwood stands, a BAF 10 prism basal area count averaged 1.86 minutes and points where basal area and volume were measured averaged 6.32 minutes. However, time requirements for small and large sample points likely vary within different forest structures, so we completed a sensitivity analysis using 2:1, 3:1, 4:1, and 6:1 small to large sample point time ratios. Travel time would be unaffected by the double sampling method used in this study since all points would be visited regardless of subsampling intensity.

_{SS}= biomass standard error of the original inventory, T

_{SS}= time necessary for the original inventory, SE

_{DS}= biomass standard error of the double sample inventory, and T

_{DS}= time necessary for the double sample inventory. A relative efficiency >100% would be considered more efficient than the original inventory while a relative efficiency <100% would be considered less efficient. For these calculations, 2:1, 3:1, 4:1, and 6:1 small to large sample point time requirement ratios were again considered.

## 3. Results and Discussion

^{−1}of aboveground dry biomass in trees >19.1 cm dbh; Standard error and percent margin of error for aboveground woody biomass was 4.57 mt ha

^{−1}and 7.43%, respectively. Substitution of the systematic point sampling inventory with a double sampling methodology generally caused minimal departure from the original outcomes and improved efficiency when the small sample subsampling intensity was between 70% and 20% (Table 2). Although percent margin of error increased in the double sample inventories as the intensity of the small sample subsampling decreased, mean departure from the original percent margin of error was ≤3% for small sample point subsampling intensities as low as 20% (Table 2). Variability in the percent margin of error among properties also increased as the small sample subsampling intensity decreased (Figure 1).

**Figure 1.**Distribution of percent margin of error (aboveground tree biomass) among 40 properties using a double sample design with different intensities of small sample subsampling from the large sample.

**Table 2.**Margin of error, deviation from original inventory margin of error, time saved, and relative efficiency for different levels of subsampling and four different small to large sample time requirement ratios in double sample biomass inventories.

Relative efficiency (%) | Time saved (%) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Small sample intensity (%) | Margin of error (%) | Margin of error deviation (%) | 2 to 1 time ratio | 3 to 1 time ratio | 4 to 1 time ratio | 6 to 1 time ratio | 2 to 1 time ratio | 3 to 1 time ratio | 4 to 1 time ratio | 6 to 1 time ratio |

100 * | 7.43 | 0 | 100 | 100 | 100 | 100 | 0 | 0 | 0 | 0 |

90 | 7.52 | 0.1 | 92 | 93 | 94 | 95 | 5 | 7 | 8 | 8 |

80 | 7.64 | 0.22 | 94 | 98 | 100 | 102 | 10 | 13 | 15 | 17 |

70 | 7.76 | 0.34 | 97 | 103 | 107 | 110 | 15 | 20 | 23 | 25 |

60 | 7.94 | 0.52 | 99 | 108 | 113 | 119 | 20 | 27 | 30 | 33 |

50 | 8.15 | 0.72 | 102 | 115 | 122 | 131 | 25 | 33 | 38 | 42 |

40 | 8.5 | 1.08 | 102 | 119 | 130 | 143 | 30 | 40 | 45 | 50 |

30 | 9.01 | 1.58 | 102 | 124 | 139 | 158 | 35 | 47 | 53 | 58 |

20 | 10.37 | 2.95 | 90 | 116 | 135 | 162 | 40 | 53 | 60 | 67 |

10 | 14.54 | 7.12 | 68 | 94 | 115 | 150 | 45 | 60 | 68 | 75 |

^{2 }ha

^{−1}and 31.0 cm, respectively. We cannot speculate whether results of the double sampling and analysis would have been comparable for stands with dissimilar species compositions or diameter distributions. Results presented in this paper were also based on inventories that omitted trees <19.1 cm dbh. In the available biomass inventories, small trees were inventoried using fixed radius plots; therefore, an analysis of point double sampling that included these small stems was not possible. Future research should investigate the use of double sampling in biomass inventories that include smaller diameter trees, use different BAFs, and incorporate nested plot designs with prism sampling and fixed radius plots as these factors may alter the precision and time required to complete forest biomass inventories.

## 4. Conclusions

## Acknowledgments

## Conflict of Interest

## References and Notes

- Merten, P.R.; Wiant, H.V.; Rennie, J.C. Double sampling saves time when cruising Appalachian hardwoods. North. J. Appl. For.
**1996**, 13, 116–118. [Google Scholar] - Avery, T.E.; Burkhart, H.E. Forest Measurements, 5th ed; McGraw-Hill: New York, NY, USA, 2002; pp. 250–252. [Google Scholar]
- Oderwald, R.G.; Jones, E. Sample sizes for point, double sampling. Can. J. For. Res.
**1992**, 22, 980–983. [Google Scholar] - Oderwald, R.G. Stock and stand tables for point, double sampling with a ratio of means estimator. Can. J. For. Res.
**1994**, 24, 2350–2352. [Google Scholar] - Oderwald, R.G. Augmenting inventories with basal area points to acheive desired precision. Can. J. For. Res.
**2003**, 33, 1208–1210. [Google Scholar] - Jenkins, J.C.; Chojnacky, D.C.; Heath, L.S.; Birdsey, R.A. National-scale biomass estimators for United States tree species. For. Sci.
**2003**, 49, 12–35. [Google Scholar] - Woudenberg, S.W.; Conkling, B.L.; O’Connell, B.M.; LaPoint, E.B.; Turner, J.A.; Waddell, K.L. The Forest Inventory and Analysis Database: Database Description and Users Manual Version 4.0 for Phase 2; U.S. Department of Agriculture, Forest Service, Mountain Research Station: Fort Collins, CO, USA, 2009. [Google Scholar]
- Bell, J.F.; Dilworth, J.R. Log Scaling and Timber Cruising; Oregon State University Book Stores, Inc.: Corvallis, OR, USA, 2007; pp. 182–252. [Google Scholar]
- Coble, D.W.; Grogan, J. Comparison of systematic line-point and double sampling designs for pine and hardwood forests in the western gulf. South. J. Appl. For.
**2007**, 31, 199–206. [Google Scholar]

## Appendix 1

**Table A1.**Property characteristics for large tree (dbh > 19.1 cm) inventories used in double sample analysis. Includes stand area, mean site index, mean dbh, basal area, and aboveground biomass.

Stand | Area (ha) | Site index (m) | Dbh (cm) | Basal area (m^{2} ha^{−1}) | Aboveground biomass (mt ha^{−1}) |
---|---|---|---|---|---|

1 | 31.2 | 26 | 29.5 | 17.6 | 117.6 |

2 | 32.4 | 24 | 32.3 | 18.8 | 136.1 |

3 | 32.8 | 21 | 28.9 | 21.6 | 116.3 |

4 | 36.0 | 27 | 31.9 | 22.6 | 160.7 |

5 | 49.8 | 25 | 35.8 | 24.9 | 169.1 |

6 | 54.2 | 18 | 30.3 | 17.4 | 114.8 |

7 | 59.1 | 25 | 29.8 | 21.4 | 144.1 |

8 | 78.1 | 24 | 32.0 | 21.9 | 150.6 |

9 | 88.2 | 20 | 29.2 | 25.5 | 151.1 |

10 | 88.2 | 29 | 28.9 | 21.3 | 139.0 |

11 | 99.1 | 22 | 32.1 | 22.7 | 161.1 |

12 | 100.0 | 25 | 28.4 | 20.0 | 127.3 |

13 | 117.4 | 21 | 32.3 | 19.1 | 136.3 |

14 | 119.0 | 20 | 30.1 | 19.3 | 118.8 |

15 | 120.2 | 20 | 32.9 | 19.3 | 143.1 |

16 | 122.2 | 22 | 30.0 | 19.0 | 131.1 |

17 | 146.1 | 21 | 31.8 | 22.5 | 158.8 |

18 | 161.5 | 26 | 29.7 | 22.6 | 160.1 |

19 | 170.0 | 24 | 28.5 | 24.1 | 151.0 |

20 | 173.6 | 22 | 29.4 | 20.2 | 135.8 |

21 | 174.8 | 30 | 30.6 | 25.1 | 167.2 |

22 | 174.8 | 23 | 34.6 | 22.2 | 159.0 |

23 | 177.3 | 25 | 33.2 | 18.4 | 125.6 |

24 | 177.3 | 23 | 33.0 | 19.5 | 141.8 |

25 | 211.2 | 26 | 30.5 | 21.6 | 148.9 |

26 | 219.3 | 22 | 30.6 | 21.1 | 148.4 |

27 | 235.1 | 26 | 31.3 | 19.4 | 138.6 |

28 | 271.5 | 19 | 29.2 | 22.3 | 140.6 |

29 | 300.3 | 20 | 36.0 | 20.7 | 149.4 |

30 | 300.7 | 25 | 30.1 | 30.6 | 203.0 |

31 | 337.5 | 25 | 35.0 | 22.3 | 150.5 |

32 | 348.0 | 23 | 31.9 | 21.3 | 149.0 |

33 | 399.4 | 24 | 33.2 | 18.4 | 125.6 |

34 | 412.8 | 21 | 28.8 | 21.0 | 143.8 |

35 | 478.7 | 24 | 34.1 | 23.2 | 165.7 |

36 | 538.2 | 22 | 30.5 | 19.4 | 137.8 |

37 | 601.8 | 23 | 30.0 | 20.5 | 142.0 |

38 | 625.2 | 23 | 25.7 | 22.1 | 149.2 |

39 | 664.5 | 21 | 26.3 | 19.5 | 130.5 |

40 | 1155.4 | 23 | 32.3 | 23.3 | 156.3 |

© 2012 by the authors; licensee MDPI, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Parrott, D.L.; Lhotka, J.M.; Fei, S.; Shouse, B.S. Improving Woody Biomass Estimation Efficiency Using Double Sampling. *Forests* **2012**, *3*, 179-189.
https://doi.org/10.3390/f3020179

**AMA Style**

Parrott DL, Lhotka JM, Fei S, Shouse BS. Improving Woody Biomass Estimation Efficiency Using Double Sampling. *Forests*. 2012; 3(2):179-189.
https://doi.org/10.3390/f3020179

**Chicago/Turabian Style**

Parrott, David L., John M. Lhotka, Songlin Fei, and B. Scott Shouse. 2012. "Improving Woody Biomass Estimation Efficiency Using Double Sampling" *Forests* 3, no. 2: 179-189.
https://doi.org/10.3390/f3020179