Forest Service Stand Size Class Maps Enhance FIA Volume Estimates

Forest Service Stand-size-class Maps Enhance FIA Volume Estimates

Dale D. Gormanson[1], Craig Merriman[2], Mark H. Hansen[3]

Introduction

Forest Inventory and Analysis (FIA) is thenational forest resource inventoryprogram of the U.S. Forest Service. Bechtold and Patterson (2005)provide FIA sampling protocols and estimation procedures. FIA uses post-stratification and does not conditionally allocate samples to specific strata. FIA’s estimate of precision is governed by many factors including the sample intensity and quality of the stratification data used for estimationas described in Hansen (2001) and McRoberts et al. (2006).

In this study, we compare stratified growing stock volume estimates using FIA plot data and two independent map classifications: (1) the National Land Cover Database tree canopy density map,and (2) stand exam size-class maps for the six national forests in Michigan, Minnesota, and Wisconsin. Relative precision is used to estimate precision gain relative to a simple random sample estimate. In addition, observed FIA size-classdata and plot areaexpanders were used to simulate accuratesize-classmapping and examine the expected relative gains in precision of FIA volume estimates for each National Forest.

Data and Methods

The study area (fig. 1) consisted of six national forests in Minnesota(Chippewa, Superior—excluding the Boundary Waters Wilderness Area),Michigan(Hiawatha, Huron–Manistee, and Ottawa),andWisconsin(Chequamegon–Nicolet).Observations on plots measured over the period 2003 to 2007, included diameter-at-breast-height(DBH) (1.37 m) for all trees at least 12.5-cm DBH.Growing stock volume was calculatedasthe sum of individual tree volumes,estimatedwith models using observed DBHand predictor variables and expandedto a plot-level cubic meter per hectare estimate. Figure 1. National Forests in the study area.

The National Land Cover Database (NLCD) 2001 tree canopy layer for the USA was produced through a cooperative project conducted by the Multi-Resolution Land Characteristics (MRLC) Consortium ( The method employed to map tree canopy density for NLCD 2001 is described in detail in Huang et al. (2001). The layer characterizes subtle variations of tree canopy density as a percentage estimateof tree canopy cover (0 – 100) within every 30 meter pixel over the United States.

Stand-size-class was derived from National Forest Service common stand exam maps depicting stand-level data as polygonswith associated databases (CNF,2003). Each map consists of tens of thousands of polygons describing the existing vegetation which exhibits enough homogeneity to make it distinguishable from the surrounding areas. Using observed FIA plot data as ground truth, on a forest-wide basis, accuracy assessments of the stand exam maps stand-size classes ranged between 50 and 60 percent.

Stratified Estimation

Post-stratification, narrowly defined, refers to a method for increasing estimate precisionwithout increasing sample size (Holt and Smith, 1979). Under this system, FIA precision gains from stratified estimation are greatest when the stratification isolates classes that have different means and estimated variances. If samples are poorly distributed (mixed in with other strata), if the variable of interest makes up a small component of the overall population, or if the variable(s) observationsdo not relate well to the stratification variable then the gain in estimate precisionis diminished. The main drawback with post-stratification is that sample allocation cannot be

controlled. Stratified estimates and sampling errors were calculated using standard methodsfound in Cochran (1977) with finite population correction ignored.

Estimates of population totalswere calculated using

[1]

Sampling error estimateswere calculated using

[2]

where, h denotes stratum, L is the number of strata, n is the total number of plot observations,Wh

is the weight for stratum h calculated as the area proportion assigned the stratum, is the

meangrowing stock volume in stratumhin cubic meters per hectare,is the growing stock volume variancein stratum h, and A is the population area defined foreach respective national forest.

Simple random sampling (SRS) uses no stratification and was the basis for comparison of the two stratification alternatives. The stratified estimates of total [1] and sampling error [2] reduce to the SRS estimators when L= 1. That is, and whereand s2are the sample mean and variance of the n sample plots.

Strata Construction

The percent canopy cover strata consisted of five groupings:(1) 0-5%, (2) 6-50%, (3) 51-65%, (4) 66-80%, and (5) 81-100%. Strata are classes whose boundaries are based on intuitive natural breaks where there are relatively big jumps in the pixel values and are the same as the Northern Research Station FIA region usesfor stratified estimation. The size-class strata consisted of four groupings that closely mirror FIA’s tree size-class definition: (1) Nonstocked, (2) Seedling-sapling–seedlings less than 2.5 cm DBH and saplings 2.5 to 12.5 cm DBH, (3) Poletimber - 12.5 to 22.9 cm DBH (softwood) and 12.5 to 27.9 cm DBH (hardwood), and (4) Sawtimber - larger than poletimber. In addition an algorithm approach incorporated observed FIA size-class data and respective plot to area expanders to simulate forest-wide size-class distribution. For each national forest, the algorithm approach serves as a precision gains scenario assumingaccurate size-class mapping.

Stratified estimation required two procedures: (1) plot-stratum assignment, and (2) calculation of the proportion of the land area for each stratum. Stratification utility for increasing volume estimate precision was evaluated using relative precision, RP, calculatedas the ratio of the simple random sample sampling error estimate squared, and the stratified estimate sampling error squared, .

[3]

RP values close to 1.0 indicate that the stratification has little use in increasing precision; RP values greater than 1.0 indicate increasing utility. RP is equivalent to the factor by which the sample size must be increased to obtain the same sampling error under SRS as one obtained using stratified estimation.

Results

For each national forest, Table 1 compares the growing stock volume SRS estimatetothe percent canopy and size-class map(s) post-stratified estimates. Estimatesare not significantly different, i.e., all estimates are within one standard error (SE) of one another.

Table 1—Stratification growing stock volume estimates and sampling errors (SE).

Relative precisions for each national forest stratification are shown in figure 2. SRS serves as base (red). When compared to the percent canopy stratifications (green), size-class stratifications (brown) yield moderate precision gains for volume. Assuming the same sampling intensity, the algorithm (blue) indicates that with improvements in the nonstocked, seed-sap, pole, and sawtimber classifications, for growing-stock volume estimates, precision gains near or over 2x in national forests are possible.

Figure 2. Stratification relative precisions.

RP is equivalent to the factor by which the sample size must be increased to obtain the same estimate sampling error under SRS as one obtained using stratified estimation. For each national forest, Table 2 shows the number of plots required to produce a simple random sample estimate with the same sampling error as that obtained with the stand examsize-class map stratified approach. Cost of travel and observation of an average FIA plot is about $600; added together it is equivalent to installing 860 more plots or investingover $500,000 U.S. dollars.

Table 2. Relative precision gains for each national forest using the stand-size-classstratification.

Analysis of the details of the ChippewaNational Forest stratifications provides insight into theresults (Table 3).

Table 3. Summary statistics for ChippewaNational Forest volume (cubic meters per hectare) stratifications.

Both stratifications group volumeand variability into meaningful classes. The percent canopy stratification has the most volume in strata with the most tree cover. The size-class stratification has greater volume in pole and sawtimber strata. The algorithm indicates that the realized sampling effort in the nonstocked (nonforest) stratum of the size-class map includessize-class diversity that is ideally isolated in another size-classstratum. It also isolates volume variability and minimizes the overall variance.

Discussion and Conclusion

Some of the advantages of stratified estimation in an application like this becomes diminished because of misclassification. Although accurate mapping of stratum weights is critical, as unbiased estimation relies on weights that are without error, in this application misclassification mostly decreases RP. The variability will be there whether isolated or not, however, it does not vitiate the estimate total but mostly affects the sampling error surrounding it. Stratified estimation is effective if the population is delineated such that it recognizes the sources of variability present and uses that information advantageously to increase estimate precision. Overall gains in precision depend largely on the dispersion of the stratum means into meaningful groupings. Both a percent canopy map and a stand exam size-classmap supplement volume estimation by increasing precision.If size-class mapped polygons could be updated more frequently,i.e., with improvements in the nonstocked, seed-sap, pole, and sawtimber classifications, for growing-stock volume estimates, additional precision gains in the national forests presented here are possible.

Literature Cited

Bechtold, William A.; Patterson, Paul L., Editors. 2005. 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. 85 p.

CNF, 1993. Chequamegon-Nicolet National Forests. 2003. Data Dictionary, Combined Data systems (CDS)—Stand Data Table. United StatesForest Service. Retrieved February 27, 2009,from

Cochran, W. G. 1977. Sampling techniques, 3rd ed. New York: John Wiley and Sons. 428 p.

Hansen, M.H. 2001. Remote sensing precision requirements for FIA estimation. In G.A. Reams, R.E. McRoberts, and P.C. Van Deusen, Eds. Proceedings of the second annual forest inventory and analysis symposium. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern Research Station. General Technical Report SRS-47. pp. 43-51.

Holt, D. and T. M. F. Smith. 1979. Post stratification. Journal of the Royal Statistical Society. Series A (General) 142: 33-46.

Huang, C., Yang, B. Wylie, and C. Homer, 2001. A strategy for estimating tree canopy density using Landsat 7 ETM+ and high resolution images over large areas. In: Third International Conference on Geospatial Information in Agriculture and Forestry; November 5-7, 2001; Denver, Colorado. CD-ROM, 1 disk.

McRoberts, R.E., Holden, G R., Nelson, M. D., Liknes, G.C., and D.D. Gormanson. 2006. Using satellite imagery as ancillary data for increasing the precision of estimates for the Forest Inventory and Analysis program of the USDA Forest Service. Can. J. For. Res. 36: 2968-2980.

[1] USDA Forest Service, Forest Inventory and Analysis, Northern Research Station, 1992 Folwell Avenue, St. Paul, Minnesota, USA, 55108; 1-651-649-5126;

[2]USDA Forest Service, Superior National Forest, Kawishiwi Ranger District, 1393 Highway 169, Ely, Minnesota,USA, 55731; 1-218-365-7616;

[3] USDA Forest Service, Forest Inventory and Analysis, Northern Research Station, 1992 Folwell Avenue, St. Paul, Minnesota, USA, 55108; 1-651-649-5148;