Methods

Fig. 1 - Study area with flight line locations.

A multistage sample design was developed and evaluated in a study area located west of Flagstaff, AZ, in and around the Williams Ranger District of the Kaibab National Forest. The footprint of a SPOT 5 satellite image (60 by 60 km) provided the approximate geographical boundary for the study (Figure 1). In this region, a mixture of piñon pine and juniper (Juniperus sp.) dominates lower elevations whereas the upper-elevation forests are predominantly ponderosa pine (Pinus ponderosa) interspersed with aspens (Populus tremuloides) and higher-altitude conifers.

Stage 1—Piñon/Juniper Woodland Cover Type (PSUs)

Fig. 2 - Vegetation-cover map

The first stage of the multistage sample design consisted of locating the piñon/juniper cover type within the study area to eliminate non-piñon/juniper areas from further analysis. Existing cover-type maps, (i.e., from the Gap Analysis Program, the Rocky Mountain Resource Information System, the National Landover Dataset, and other sources) were evaluated for this purpose. These data sets were deemed unsatisfactory for this study because changes in cover type from vegetation management activities were sometimes not reflected in these maps and some obvious fine-scale errors were also present. Therefore, a three-class vegetation map (piñon/juniper, ponderosa pine and other conifers, and meadow/bare ground/other) was developed for the study area using image segmentation and regression tree classification (Figure 2) (Hamilton and others 2004). This map formed the PSUs. For this study, the entire 332,000-acre piñon/juniper cover type was advanced to the second stage of the sample.

Stage 2—Percent Cover Strata (SSUs)

Negron and Wilson (2003) reported that the likelihood of piñon ips infestation increased with stand density in Arizona. To reduce sample variance, this known source of variability was incorporated into the sample design by stratifying the piñon/juniper vegetation class by percent cover. The percent-cover strata became the SSUs. Breaks for the percent-cover strata were based on the broad level vegetation cover categories established by the USDA Forest Service Existing Vegetation Classification and Mapping Technical Guide (Brohman and Bryant 2005) (Table: Percent-cover ranges). The first vegetation-cover category (0–29.9 percent), was further subdivided into 0–9.9-percent and 10–29.9-percent categories to refine the SSUs.

Fig. 3 - Percent cover strata

Because no existing percent-cover maps were available for the study area, a map was created from 1992 digital orthophoto quadrangles (DOQs). The DOQs were not current, and we anticipated that the mapped percent cover would generally be lower than the actual percent cover. However, as the objective of this exercise was to stratify the study area (not to measure percent cover), relative differences in actual percent cover compared to mapped percent cover would still allow the map to serve its purpose of stratifying the study area. The relative differences in percent cover are inconsequential so long as percent cover and, consequently, mortality, is more homogeneous within than between strata. To create the percent-cover map, a two-class classification (tree and nontree) was created from the DOQs in ERDAS Imagine. Then, for each image segmentation polygon (average size≈2.5 acre) used in the vegetation classification, the percentage of the polygon occupied by mapped trees was calculated (Figure 3). No accuracy assessment was conducted for the percent-cover map. However, final sample results verified that percent cover and mortality were more homogeneous within than between strata.

Stage 3—Digital Aerial Imagery Plots (TSUs)

Tertiary sampling units for this study consisted of 60-by 60-m digital aerial imagery plots. Plots were sampled for mortality using a digital dot grid. On March 30 and April 24, 2004, high-resolution digital camera (Kodak Pro Back 645C digital back attached to a Contax 645 medium format camera) imagery was acquired in 18 flight lines at various locations across the study area (Figure 1). The imagery was acquired with an 80 mm lens at an altitude of approximately 1,375 m, producing 16 cm spatial-resolution imagery with a swath width of approximately 640 m. The imagery was orthorectified using OrthoBASE in ERDAS Imagine. Thirty TSU plots were randomly located within each percent-cover stratum (for a total of 120 plots) and the geographic boundaries of the aerial imagery. Although the percent-cover strata were not equal in size (Table: Percent-cover ranges), they were sampled equally to ensure a minimum number of samples in each stratum.

The plot size and dot density were chosen to optimize the accuracy and precision of the sample while minimizing the total number of dots per sample, (i.e., minimizing costs). This was accomplished by sampling several areas from each percent-cover stratum using multiple dot grids, ranging in size from 30 by 30 m to 240 by 240 m with dot densities of 364, 648, or 1,012 dots per acre. A plot size of 60 by 60 m with dot density of 364 dots per acre (18 by 18 dots per plot) was considered optimal as the precision of the estimate increased only slightly with increased plot size or dot density or both. The dot grid was created from graphic elements in ArcGIS 8.3, allowing it to be moved easily from one plot to the next by dragging and dropping. Although this graphic dot grid worked well for this study, a new tool for ArcGIS 8.3 and 9.x, Digital Mylar—Image Sampler, was recently developed by the USDA Forest Service Remote Sensing Applications Center and now provides a more automated and user-friendly approach to dot grid sampling (USDA Forest Service 2005).

Fig. 4 - Natural-color, digital aerial imagery

At each sample location, the dot grid was placed over the high-resolution imagery (Figure 4). The total number of dead-tree, live-tree, and ground hits from the dots was counted. First-year and later mortality were all grouped into the dead-tree category for this study. In this sampling procedure, piñon pines were not distinguished from junipers due to the difficulty of distinguishing the two species on this imagery by photo interpretation. The proportion of each plot covered by dead trees, live trees, total tree cover, (i.e., live plus dead trees), and other (typically bare ground) was calculated from the dot grids by tallying the hits of the individual variables and dividing by the total number of dots in the sample. Subsequently, mean values of these variables were calculated for each percent-cover stratum. The mean proportion of the entire piñon/juniper region, (i.e., across all strata) covered by dead trees, live trees, total tree cover, and other was calculated from the estimates of each percent-cover stratum. These estimates were made using a standard weighted disproportionate-strata estimation equation, with the strata areas from Table: Percent-cover ranges as weights (Equation 1) (Scheaffer and others 1990). Because relative proportions of strata areas for the entire piñon/juniper region were similar to those falling within the boundaries of the aerial imagery (Table: Percent-cover ranges), no adjustments were needed to extrapolate the estimate from the extent of the aerial imagery to the entire study area.

Equation 1 - Proportion of Area Covered by Trees

In Equation 1, p-hat_st is the mean across-strata proportion of land area covered by dead trees, live trees, total tree cover, or other; p-hat_i is the mean proportion of land area within each percent-cover stratum, indexed by i, covered by dead trees, live trees, total tree cover, or other; N is the total possible number of individual dot samples within the entire study area; and N_i is the weight of the i^th percent-cover stratum, (i.e., the proportion of possible dot samples within the piñon/juniper forests of the i^th percent-cover stratum to the total possible number of dot samples within the entire piñon/juniper forested area).

Standard errors of the across strata mean proportion estimates were also calculated (Equation 2). From these results, the mean proportions of total tree cover that had died were calculated for each percent-cover stratum as well as across strata for the entire piñon/juniper population.

Equation 2 - Standard Errors of the Across-Strata Mean Proportion Estimates

In Equation 2, E-hat(p-hat_st) is the error of the mean across-strata proportion of land area covered by dead trees, live trees, total tree cover, or other; n_i is the number of dot samples taken from each percent-cover stratum; and N_i, N, p-hat_i are as described in Equation 1.