Historic, archived document Do not assume content reflects current scientific knowledge, policies, or practices. 1959 Occasional Paper 172 A? FjtWo 3 Composite Aerial Volume Table for Southern Arkansas Gene Avery and David Myhre K^NTOFAGW^jl/ SOUTHERN FOREST EXPERIMENT STATION Philip A. Briegleb, Director Forest Service, U.S. Department of Agriculture C O N T Introduction Construction procedure . Photo interpretation techniques Composite aerial volume table Parallax conversion table Direct estimates of gross volume Literature cited NTS Page 1 1 2 3 4-5 7 9 l BOTTOM-LAND HARDWOOD NONTYPED, LESS THAN 10% FOREST Figure 1. — Generalized forest type map of Arkansas, showing the 20 counties covered by this study. ll Composite Aerial Volume Table for Southern Arkansas Gene Avery and David Myhre 1 Aerial photo volume tables are useful for making direct estimates of gross timber vol- umes, for preparing forest maps based on stand-size classes, for planning extensive forest inventories, and for reducing the intensity or cost of field work in photo-controlled ground cruises (3).' The initiation of the third Forest Survey of Arkansas in 1958 presented an op- portunity to collect special data to construct and evaluate an aerial stand-volume table for making direct estimates of gross timber volume in the southern part of the State (fig. 1). In the interests of statistical accuracy, aerial stand-volume tables are ordinarily constructed for a single tree species or a group of similar species. For example, tables have been pre- pared for upland oaks in Pennsylvania (4), Douglas-fir in Oregon (10), and Rocky Moun- tain conifers (7). This refinement has obvious advantages when forest types can be reliably differentiated on aerial photographs, but its importance is lessened when stand mixtures cannot be consistently classified. In southern Arkansas, it was found that southern pines and hardwoods could not be adequately separated on the aerial photo- graphs obtainable from the U. S. Department of Agriculture — 9- by 9-inch prints, at a scale of 1:20,000 made from panchromatic film ex- posed with a minus blue filter. Although pine timber predominates, many stands are com- posed of pine-hardwood mixtures that exhibit minimal tonal contrast on panchromatic prints. Because of the difficulty of separating these species-groups for making photo meas- urements, it was decided that a composite table should be compiled for this area. The feasibility of constructing and using an aerial volume table for both pines and hardwoods had been previously demonstrated in north- east Mississippi (2). CONSTRUCTION PROCEDURE Every fourth Forest Survey location in each of 20 counties was mechanically selected for analysis. This result was a total of 304 paired point-sample locations' arranged on a 6- by 6-mile grid pattern. After elimination of stands that had been cut between the dates of photography and field measurement, 216 locations remained for interpretation. One-acre circular plots were scribed on the 216 stereo pairs of photographs to exactly en- compass the two point-samples at each Forest Survey location. Two photo interpreters meas- ured, on each location, the average total height of the three tallest trees, average diameter of the three largest crowns, and the crown closure percent. The two sets of photo measurements for each location were then averaged for use in the statistical analysis. ' The authors, members of the U. S. Forest Service, are currently located at the Southeastern Forest Experi- ment Station, Asheville, North Carolina, and the Southern Forest Experiment Station, New Orleans, Louisiana, respectively. • Bold face numbers in parentheses refer to Literature Cited, p. 9. In the Forest Survey of Arkansas sample trees were selected from two points located 117.75 feet apart; they were chosen with a prism having a basal area factor of 10. 1 Total heights of the three tallest trees were also determined on the ground for each of the 216 locations. These data, along with tree tallies for computing volumes, were obtained by Forest Survey field personnel. The next step was the selection of those stand variables most valuable for predicting gross cubic volume. A graphical analysis in- dicated that field-measured tree heights were more closely related to location volumes than any other single variable, including heights measured on aerial photographs. It was there- fore decided that the former measurements should be used in the statistical tests, thus eliminating a degree of interpreter bias. Crown closure percent appeared to be the second-best variable and average crown diameter ranked third. A wide span of values was exhibited by each group of stand measurements. Field heights ranged from 23 to 123 feet, crown closures from 5 to 90 percent, crown diameters from 5 to 28 feet, and gross volumes from 15 to 3,880 cubic feet per acre. Several additional variables were formu- lated from combinations of the 3 basic meas- urements. The 9 chosen for regression analysis4 are as follows: 1. Height 2. Crown closure percent 3. Height x crown closure 4. (Height)2 5. (Height)2 x crown closure 6. Height X (crown closure)2 7. Crown diameter x crown closure 8. Crown diameter x height 9. (Crown diameter)2 x height The objective was to obtain the degree of correlation between these 9 variables and the gross cubic volume per acre as determined from Forest Survey field measurements. Data were analyzed by the Southern Forest Experiment Station’s IBM 704 Regression Program (6). From the 511 regressions com- puted, this 5-variable equation5 was selected as best for compiling the aerial volume table: V = 939.065 + 1.258 HC + 0.426 H' - 39.358 C 34.155 H - 0.007 H2C, where: V = Gross volume per acre in cubic feet. H = Average total height of the 3 tallest trees in feet. C = Crown closure percent of all trees over 30 feet tall. This equation includes only the first 5 of the 9 variables analyzed. Average total height proved to be the most valuable single variable for predicting gross stand volume, as illustrated by its presence in 4 terms of the regression. Crown closure percent, included in 3 terms, was of secondary value. As none of the var- iables involving crown diameter contributed significantly to the prediction of volume, they were eliminated from the formula. Because of the importance of tree height, the composite aerial volume table (table 1) was compiled by 5-foot height classes. Ten- percent intervals were maintained for crown closure, though linear interpolations may be made between classes, if desired. PHOTO INTERPRETATION TECHNIQUES Crown closure estimates. — Of the two vari- ables required to enter table 1, crown closure percent6 is the more difficult to evaluate accurately and consistently. As there are no practical means for objectively measuring this characteristic on 1:20,000 photographs, ocular estimates are relied upon. Stands are usually stratified into 10-percent closure classes by comparing the stereo-image with printed den- sity scales (1, 9). The heavy dependence on personal judg- ment can result in widely divergent estimates when a location is assessed by 2 or more inter- preters. In such instances, an arithmetic average can be used. Inexperienced persons tend to overestimate crown closure, often fail- ing to make proper allowance for small stand openings, crown shadows, or trees too sma'll to contain merchantable volume. For apply- ing the composite table, crown closure esti- ' The term “height” used here refers to the average total height of the 3 tallest trees as measured on the ground. Crown closures and crown diameters are photographic determinations. ' Multiple correlation coefficient is 4- 0.834. Standard error of estimate is 436.6 cubic feet. ' The proportion of the forest canopy occupied by tree crowns; also referred to as crown cover percent or crown density. 2 Table 1. — Composite aerial volume table for southern Arkansas Average total height 1 (feet) Crown closure 5 percent 15 percent 25 percent 35 percent 45 percent 55 percent 65 percent 75 percent 85 percent 95 percent per acre 40 175 215 250 290 325 365 400 440 475 515 45 240 295 345 400 450 505 555 610 660 715 50 330 395 460 525 590 655 720 790 855 920 55 395 490 580 675 765 860 950 1,045 1,140 1,230 60 480 600 715 830 950 1,065 1,180 1,300 1,415 1,530 65 585 725 860 1,000 1,135 1,275 1,410 1,545 1,685 1,820 70 715 865 1,020 1,175 1,330 1,480 1,635 1,790 1,945 2,100 75 860 1,025 1,195 1,360 1,530 1,695 1,865 2,030 2,200 2,365 80 1,020 1,200 1,380 1,555 1,735 1,910 2,090 2,270 2,445 2,625 85 1,205 1,390 1,575 1,760 1,945 2,130 2,315 2,500 2,685 2,870 90 1,410 1,600 1,785 1,975 2,165 2,350 2,540 2,730 2,915 3,105 95 1,635 1,820 2,010 2,200 2,385 2,575 2,765 2,950 3,140 3,330 100 1,875 2,060 2,245 2,430 2,615 2,800 2,985 3,170 3,355 3,540 105 2,140 2,315 2,495 2,675 2,850 3,030 3,210 3,385 3,565 3,745 110 2,420 2,590 2,755 2,925 3,095 3,260 3,430 3,600 3,765 3,935 115 2,725 2,880 3,030 3,185 3,340 3,495 3,650 3,805 3,960 4,115 120 3,045 3,180 3,320 3,455 3,595 3,730 3,870 4,005 4,145 4,280 1 As the table is based on field measurements of tree heights, photo heights must be adjusted section. 2 Gross volumes are inside bark and include the merchantable stems of all live trees 5 inches to a variable top diameter not smaller than 4 inches i. b. as explained in the following d.b.h. and larger from stump mates should include only those trees that are taller than 30 feet. Crowns of shorter trees should be ignored, as they presumably repre- sent stems smaller than 5 inches d.b.h. Height measurements and parallax con- version. — Tree heights can be determined within + 5 to 10 feet on aerial photographs from stereoscopic measurements of differen- tial parallax (dP). Two basic types of floating dot instruments are used for this purpose: parallax wedges reading to 0.002-inch dP, and parallax bars reading to 0.01-millimeter dP. Measurements with either device are convert- ed to tree heights by substitution in the paral- lax formula: ho = height of object H = height of aircraft , above ground da- ho = — — , where: turn P + dP P = average photo base length dP = differential par- allax If object heights are to be determined in feet, the height of the photographing aircraft must also be expressed in feet. Average photo base length (P) and differential parallax (dP) may be expressed either in inches or millimeters, but both must be in the same units. Solution of the formula is not difficult, but conversion of parallax readings can be simplified by use of special tables. For ex- ample, table 2 was prepared for quickly con- verting parallax-bar readings to tree heights in feet. A similar table is available for con- verting parallax wedge measurements (8). To apply table 2, the interpreter must make three determinations: a. Differential parallax of the tree or ob- ject, measured with a parallax bar (fig. 2) and recorded to the nearest hundredth of a milli- meter. For use with the composite aerial volume table, height measurements should re- present an average for 3 to 5 of the tallest trees on the acre. b. Average photo base for the stereo-pair. This corresponds to the average distance be- tween principal and conjugate principal points. It should be measured with an engineer’s scale and recorded to the nearest 0.1 inch (conversion to millimeters was accounted for in construct- ing the table). c. Average flying height of aircraft, deter- mined by multiplying the photo scale denom- inator by the camera’s focal length in feet. For example, if photo scale in the area of measurement is 1:19,000 and camera focal 3 Table 2.— Parallax-bar height conversion factors ’ Average Average flying height (H) above ground datum in feet base (P) 2,500 3,000 3,500 4,000 4,500 5,000 5.500 6,000 6,500 Inches — — Object heights (ho) in feet per millimeter — — 2.1 46 55 64 74 83 92 101 110 120 2.2 44 53 62 70 79 88 97 105 114 2.3 42 50 59 67 76 84 93 101 109 2.4 40 48 56 65 73 81 89 97 105 2.5 39 47 54 62 70 78 85 93 101 2.6 37 45 52 60 67 75 82 90 97 2.7 36 43 50 57 65 72 79 86 93 2.8 35 42 49 55 62 69 76 83 90 2.9 33 40 47 54 60 67 74 80 87 3.0 32 39 45 52 58 65 71 78 84 3.1 31 38 44 50 56 63 69 75 82 3.2 30 36 43 49 55 61 67 73 79 3.3 29 35 41 47 53 59 65 71 77 3.4 29 34 40 46 51 57 63 69 74 3.5 28 33 39 44 50 56 61 67 72 3.6 27 32 38 43 49 54 60 65 70 3.7 26 32 37 42 47 53 58 63 68 3.8 26 31 36 41 46 51 56 62 67 3.9 25 30 35 40 45 50 55 60 65 4.0 24 29 34 39 44 49 54 58 63 4.1 24 29 33 38 43 48 52 57 62 4.2 23 28 32 37 42 46 51 56 60 4.3 23 27 32 36 41 45 50 54 59 4.4 22 27 31 35 40 44 49 53 58 4.5 22 26 30 35 39 43 48 52 56 Average Average flying height (H) above ground datum in feet base (P) 11,500 12,000 12,500 13,000 13,500 14,000 14,500 15,000 15,500 Inches — — Object heights (ho) in feet per millimeter — — 2.1 212 221 230 239 249 258 267 276 285 2.2 202 211 220 228 237 246 255 264 272 2.3 194 202 210 219 227 236 244 253 261 2.4 185 194 202 210 218 226 234 242 250 2.5 178 186 194 202 209 217 225 256 264 2.6 172 179 187 194 201 209 216 224 231 2.7 165 172 180 187 194 201 208 216 223 2.8 159 166 173 180 187 194 201 208 215 2.9 154 161 167 174 181 187 194 201 207 3.0 149 155 162 168 175 181 188 194 201 3.1 144 151 157 163 169 176 182 188 194 3.2 140 146 152 158 164 170 176 182 188 3.3 136 142 147 153 159 165 171 177 183 3.4 132 137 143 149 154 160 166 172 177 3.5 128 133 139 145 150 156 161 167 172 3.6 124 130 135 141 146 152 157 162 168 3.7 121 126 132 137 142 147 153 158 163 3.8 118 123 128 133 138 144 149 154 159 3.9 115 120 125 130 135 140 145 150 155 4.0 112 117 122 127 132 136 141 146 151 4.1 109 114 119 124 128 133 138 143 147 4.2 107 111 116 121 125 130 135 139 144 4.3 104 109 113 118 123 127 132 136 141 4.4 102 106 111 115 120 124 129 133 137 4.5 100 104 108 113 117 121 126 130 134 » To use table, measure parallax difference (dP) of object to nearest hundredth of a millimeter (as 0.41 mm, for example). If average photo base (P) is 3.1 inches and flying height (H) is Average flying height (H) above ground datum in feet Average photo base (P) 7,000 7,500 8,000 8,500 9,000 9,500 10,000 10,500 11,000 — — Object heights (ho) in feet per millimeter — — Inches 129 138 147 157 166 175 184 193 203 2.1 123 132 141 149 158 167 176 185 193 2.2 118 126 135 143 152 160 168 177 185 2.3 113 121 129 137 145 153 161 169 177 2.4 109 116 124 132 140 147 155 163 171 2.5 104 112 119 127 134 142 149 157 164 2.6 101 108 115 122 129 136 144 151 158 2.7 97 104 111 118 125 132 139 146 153 2.8 94 100 107 114 120 127 134 141 147 2.9 91 97 104 110 117 123 130 136 142 3.0 88 94 100 107 113 119 125 132 138 3.1 85 91 97 103 109 115 122 128 134 3.2 83 88 94 100 106 112 118 124 130 3.3 80 86 92 97 103 109 114 120 126 3.4 78 83 89 95 100 106 111 117 122 3.5 76 81 87 92 97 103 108 114 119 3.6 74 79 84 89 95 100 105 111 116 3.7 72 77 82 87 92 97 103 108 113 3.8 70 75 80 85 90 95 100 105 110 3.9 68 73 78 83 88 93 97 102 107 4.0 67 71 76 81 86 90 95 100 105 4.1 65 70 74 79 84 88 93 97 102 4.2 64 68 73 77 82 86 91 95 100 4.3 62 66 71 75 80 84 89 93 98 4.4 61 65 69 74 78 82 87 91 95 4.5 Average flying height (H) above ground datum in feet Average photo base (P) 16,000 16,500 17,000 17,500 18,000 18,500 19,000 19,500 20,000 — — Object heights (ho) in feet per millimeter — Inches 295 304 313 322 331 341 350 359 368 2.1 281 290 299 308 316 325 334 343 352 2.2 269 278 286 295 303 311 320 328 337 2.3 258 266 274 282 290 298 306 315 323 2.4 248 256 264 271 279 287 295 302 310 2.5 239 246 254 261 269 276 284 291 298 2.6 230 237 244 251 259 266 273 280 287 2.7 222 229 236 243 250 257 264 270 277 2.8 214 221 228 234 241 248 254 261 268 2.9 207 214 220 227 233 240 246 253 259 3.0 201 207 213 220 226 232 238 245 251 3.1 194 200 207 213 219 225 231 237 243 3.2 189 195 200 206 212 218 224 230 236 3.3 183 189 194 200 206 212 217 223 229 3.4 178 184 189 195 200 206 211 217 222 3.5 173 179 184 189 195 200 206 211 216 3.6 168 174 179 184 189 195 200 205 211 3.7 164 169 174 179 185 190 195 200 205 3.8 160 165 170 175 180 185 190 195 200 3.9 156 161 166 171 175 180 185 190 195 4.0 152 157 162 167 171 176 181 186 190 4.1 149 153 158 162 167 172 176 181 186 4.2 145 150 154 159 163 168 172 177 181 4.3 142 146 151 155 160 164 168 173 177 4.4 139 143 147 152 156 160 165 169 173 4.5 15,000 feet, the conversion factor of 188 is multiplied by 0.41 for an object height of 77 feet Linear interpolations may be made in the table for determining conversion factors not shown. length is six inches, H = 19,000 X 0.5 or 9,500 feet. Thus, if P = 3.2 inches and H = 9,500 feet, the conversion factor of 115 is read from table 2 and multiplied by dP (as 0.44 mm, for ex- ample) for a height of 51 feet. Table 2 may be safely applied only when dP is small with relation to P. With ordinary 9- by 9-inch aerial photos and an average over- lap of 60 percent, the ratio of dP to P is 1:100 or smaller. If the ratio becomes as large as 1:50, however, values should be substituted directly in the parallax formula. The range of photo base lengths used in compiling this table (2.1 to 4.5 inches) was chosen on the assumption that the table would be used with 7- by 7-, 7- by 9-, or 9- by 9-inch aerial prints having an average forward over- lap of 50 to 70 percent. The range of flying heights above ground (2,500 to 20,000 feet) covers photo scales from 1:2,500 to 1:40,000, assuming use of cameras with 12- and 6-inch focal lengths, respectively. Individual adjustments of photo heights. — The composite aerial volume table (table 1) was based on field-measured tree heights. As individuals may differ widely in deter- mining heights on aerial photos, each inter- preter should make his own corrections for converting photo heights to actual tree heights. This can be done as follows: Select 15 or more trees within the area to be interpreted, and determine their total heights by ground measurement. These sam- ple trees should span a wide range of heights and be readily identifiable on the aerial photo- graphs. Measure each sample tree at least three times to determine its average photo height. On cross-section paper, plot field heights over photo heights, and fit a line to the plotted points by either the graphical or least squares method. Use the graph to correct all subsequent photo height determinations prior to entering the aerial volume table. Figure 2. — Abrams parallax bar used for making stereoscopic determinations of tree heights. Differential parallax readings in millimeters can be converted to feet by reference to table 2. 6 DIRECT ESTIMATES OF GROSS VOLUME The accuracy of aerial timber estimates de- pends on the scale and quality of available photography, the ability of photo interpreters to make required stand measurements, and the statistical reliability of the aerial volume table. Even when these circumstances are favorable, individual location volumes can rarely be determined with precision. How- ever, reliable estimates of average volume per acre may be obtained by interpreting large numbers of locations. Field check 1. — One hundred additional Survey locations in southern Arkansas were selected for evaluation by two interpreters. Each man made independent determinations of cubic volume for the 100 locations by enter- ing the composite aerial volume table. Neither interpreter had participated in the collection of field data, and actual volumes were unknown. Photo and field comparisons of average volume per acre are presented in table 3. Estimates by both interpreters showed good agreement with average field volumes. On the first 50 locations, the maximum interpre- ter error was minus 16 percent; for the second group, the greatest deviation was plus 17 per- cent. For each interpreter, negative differ- ences on the first 50 locations were compen- sated by higher readings on the second set of 50 measurements. When the 100-location averages were used for comparison, interpre- ter errors decreased to less than 3 percent of the average field volume per acre. Comparison for individual locations were much more erratic than the checks of average volumes. Photo estimates occasionally dif- fered by 75 to 90 percent from field values. Such variations were not unexpected, however, as the standard error of estimates for the com- posite table was 437 cubic feet, or about 45 percent of the mean field volume. Some dis- agreements between individual estimates can be attributed to the fact that photo measure- ments were made on 1-acre circular plots, while field volumes were determined from 2 point-samples spaced 117.75 feet apart at each ground location. Field check 2. — To further evaluate the composite aerial volume table, two 160-acre tracts in southern Arkansas were chosen for a comparison of photo and field cruises on small ownerships. Tract 1 had a predominant forest cover of loblolly-shortleaf pines and tract 2 was in a stand of mixed pines and up- land hardwoods. A transparent template was used to locate 32 one-acre plots on 1:15,840 infrared photographs of each tract. These circular sample areas were mechanically spaced at 5- by 10-chain intervals. Two inter- preters determined the volume of each plot by use of table 1. Average per-acre volumes were then multiplied by tract areas to obtain estimates of total gross volume for each tract. As in the previous test, field volumes were determined by point-sampling (5). Tree tal- lies were made at 80 points systematically located within each tract. A wedge prism having a basal area factor of 10 square feet per acre was used to select sample trees for meas- urement. Photo and field estimates of total cubic vol- ume for the 2 tracts are summarized in table 4. The relatively small interpreter errors again demonstrate the feasibility of aerial timber cruising. All photo estimates were within 12 percent of field values. This improvement in interpreter accuracy over the previous check (table 3) is partly due to the fact that the forest on the two 160-acre tracts was relatively homogeneous and even-aged, while the 100 Forest Survey locations encompassed a much wider range of stand-size classes. Table 3. — Comparison of average volumes from 100 Forest Survey locations with photo estimates by two interpreters Number of locations ' Average field volume per acre Interpreter A Interpreter B Volume per acre Error - Volume per acre Error 2 Cubic feet Cubic feet Percent Cubic feet Percent 1-50 1,544 1,297 -16.0 1,430 - 7.4 51-100 1,101 1,288 + 17.0 1,254 + 13.9 All 100 1,323 1,293 - 2.3 1,342 + 1.4 1 Randomly selected from 20 counties in southern Arkansas. : Difference between photo and field volume expressed as a percent of field volume. 7 Another factor was the availability of better aerial photographs for the small tracts. In- frared prints at a scale of 1:15,840 were sup- plied by The Crossett Company for this check, while the previous analysis required the use of 1:20,000 panchromatic photographs. Ordinarily, it is inadvisable to rely strictly on aerial-photo determinations. Prior to com- putation of total tract volumes, 5 to 10 percent of the photo plots should be field-checked to derive local per-acre correction factors (1). Such corrections not only improve the relia- bility of the final estimate, but also increase its acceptability to persons unfamiliar with aerial cruising techniques. Aerial timber cruising cannot be expected to replace ground work for obtaining detailed breakdowns of tree species, diameter classes, growth, cull, and mortality. Thus, airphoto and field techniques are ordinarily not mutual- ly exclusive alternatives. Instead, the advan- tages of both methods are logically combined in a forest inventory design that has greater efficiency than either approach considered singly (3). As aerial volume tables are occasionally ap- plicable outside the areas for which they were originally constructed, the authors would be interested in hearing from users of the com- posite table, particularly those in east Texas, north Louisiana, and central Mississippi. Ap- plications in these areas should be feasible, provided local adjustments are derived by field checks. Table 4. — Comparison of photo and field volumes for two 160-acre forest tracts in southern Arkansas Tract Total field volume 1 Interpreter A Interpreter B Volume 1 Error - Volume ' Error 2 Cubic feet Cubic feet Percent Cubic feet Percent Mixed loblolly-shortleaf pines 336,480 361,600 + 7.5 376,000 + 11.7 Mixed pines and hardwoods 342,720 305,600 -10.8 311,200 - 9.2 ' Tract volumes may be converted to rough cords by dividing by 79. •Difference between photo and field volumes expressed as a percent of field volume. 8 LITERATURE CITED (1) Avery, Gene 1957. forester’s guide to aerial photo inter- pretation. U. S. Forest Serv. South. Forest Expt. Sta. Occas. Paper 156, 41 pp., illus. [Processed.] (2) 1958. COMPOSITE AERIAL VOLUME TABLE FOR SOUTHERN PINES AND HARDWOODS. JOUr. Forestry 56: 741-745, illus. (3) Bickford, C. Allen 1953. INCREASING THE EFFICIENCY OF AIRPHOTO FOREST SURVEYS BY BETTER DEFINITION OF classes. U. S. Forest Serv. Northeast. Forest Expt. Sta. Sta. Paper 58, 9 pp. [Processed.] (4) Gingrich, S. F., and Meyer, H. A. 1955. construction of an aerial stand volume table for upland oak. Forest Sci. 1:140- 147, illus. (5) Grosenbaugh, L. R. 1952. PLOTLESS TIMBER ESTIMATES NEW, FAST, easy. Jour. Forestry 50: 32-37, illus. (6) Grosenbaugh, L. R. 1958. THE ELUSIVE FORMULA OF BEST FIT: A COM- PREHENSIVE NEW MACHINE PROGRAM. U. S. Forest Serv. South. Forest Expt. Sta. Occas. Paper 158, 9 pp., illus. [Processed.] (7) Moessner, K. E. 1957. PRELIMINARY AERIAL VOLUME TABLES FOR CONIFER STANDS IN THE ROCKY MOUNTAINS. U. S. Forest Serv. Intermountain Forest and Range Expt. Sta. Res. Paper 41, 17 pp., illus. [Processed.] (8) and Rogers, E. J. 1957. PARALLAX WEDGE PROCEDURES IN FOREST surveys. U. S. Forest Serv. Intermountain Forest and Range Expt. Sta. Misc. Pub. 15, 22 pp., illus. [Processed.] (9) Brunson, D. F., and Jensen, C. E. 1951. AERIAL VOLUME TABLES FOR HARDWOOD STANDS IN THE CENTRAL STATES. U. S. Forest Serv. Central States Forest Expt. Sta. Tech. Paper 122, 15 pp., illus. [Pro- cessed.] ( 10) Pope, R. B. 1950. aerial photo volume tables. Photogram. Engin. 16: 325-327. 9