AVERAGE HEIGHT WEIGHTED BY VOLUME IN AIR PHOTO INTERPRETATION

Transcription

1 CANADA Department of Northern Affairs and National Resources FORESTRY BRANCH AVERAGE HEIGHT WEIGHTED BY VOLUME IN AIR PHOTO INTERPRETATION BY F. D. MacAndrews Forest Research Division Technical Note No

2 Published under the authority of The Minister of Northern Affairs and National Resources Ottawa, 1955

3 Average Height Weighted By Volume In Air Photo Interpretation by F. D. MacAndrews A Forestry Branch photo interpreter obtains the heights of trees in vertical photos either by measuring the shadows and applying a ratio factor, or by measuring images around the perimeter of the photo by the displacement method. In oblique photos, any completely visible images may be measured directly. The interpreter seldom obtains heights by parallax methods, except as a last resort, because of the time involved. His object is to determine the average height weighted by volume for the stand being examined. Average height weighted by volume was adopted some years ago, partly because it is a definite value which may be calculated from field plots at any time, whereas the appraisal of the height of the dominants (those trees that, from the interpreter's standpoint, over-top all others) is affected by variations in personal judgment as to what is a dominant, co-dominant or intermediate, especially in open stands. Also, because height in relation to volume is dealt with, the sound procedure is to weight by volume because in this way a proper comparison is obtained between stands of various compositions. The centre page illustration, Figure 1, is one of a series that was made to aid the interpreter of air photographs in estimating average height weighted by volume. Tabulation for Avera e Hei ht Wei hted by Volume (See Figure 1) Class Height D.B.H. Class Trees Volume Volume Volume Per Per Per X Plot Tree Plot Class Height Cubic Cubic Cubic Feet No. Feet Feet Feet "- 4 8" 8 x "- 6 4" 7 x , B' k _oo l "- 8 3" 10 x , "-10 6" 8 x , "-13 5" 4 x , "-17 4" 1 x , Sub-TotaL , "- 4 7" 11 x "- 6 5" 8 x , """m Fk "- 8 5" 6 x , "-10 9" 6 x , "-13 9" 1 x , Sub-TotaL ,289 0 White Birch... { "- 8 2" 1 x "- 2 x , Sub-Total , Total-All Species ,

4 Average Height Weighted by Volume 30, f ee t The simple unweighted average where equal weight is given to all trees is considerably lower than the average height weighted by volume. Unweighted Average Height Sum of all merchantable tree heights Number of trees 3,410 -n feet NOTE.-This tabulation is based on a curve of heights plotted in diameter classes. The height classes shown are based on the average heights of the corresponding diameter classes. Volumes have been employed in accordance with diameter classes, diameter being the independent variable. Consequently the average height weighted by volume as shown by Figure 1 is based on a diameter grouping. The photo interpreter finds it necessary to group in height classes. Nevertheless he will be guided by a diagram based on average height weighted by volume as determined from diameter classes as usually employed in forest inventory. It will of course be understood that the distinction between height grouping and diameter grouping is seldom significant in ordinary photo interpretation.. Stands of the same volume may be of fairly uniform height or may be composed of trees of several height classes. Average height weighted by volume is excellent in providing compensations which tend towards the same estimate of height for stands of equal volume regardless of variations in composition. Another advantage is that average height weighted by volume is generally close to the average height of the co-dominants and is a particularly high value especially suitable for determination by the air photo interpreter. Figure 1 shows that the average height weighted by volume is considerably closer to the height of the dominants than is the simple arithmetic average. The difference between the two heights is greatest in an all-aged forest and decreases as the trees become more uniform in height until with total uniformity the difference becomes o. During the interpretation process most of the measurements for height are made on the dominants because they are naturally the most easily and most accurately measured. In the illustration it can be seen that the average height weighted by volume is within 10 feet of the average height of the dominants and it will be found that this same condition usually holds in other cases. The simple un weighted average height, which is sometimes used in forestry, is difficult to estimate from air photos. It is found somewhere below the average height weighted by volume, and among the smaller trees which usually cannot be measured and often cannot be seen but which, nevertheless, carry as much weight in determining the unweighted average as do the big trees. In Figure 1 this un weighted average is shown by the short dashes at 46 7 feet. Weighting height by volume gives the big trees the proper emphasis, which emphasis is lost without this weighting process. For example a 60-foot tree contains roughly 6 times the volume of one 30 feet high, and therefore it seems logical to give a 60-foot tree 6 times the weight of one 30 feet high. 4

5 Since this weighting gives a truer picture of volume and since it brings the height so close to the height of the dominants, it is considered that the average height weighted by volume is more easily and accurately estimated on air photos than is any other height figure. Canopy Density Figure 1 includes plan views corresponding to certain sections of the drawing, to illustrate the proportions of total surface which are covered by tree crowns. It should be noted that both stand elevations and plans are based on a strip width of 22 feet. Actual field measurements are usually taken on plots 11 feet wide. Source oj Data Fifth-acre plots, and in some cases quarter-acre plots, were measured for volume by members of the Inventories Section staff at Sault au Cochon on the north shore of the St. Lawrence River in Quebec (all-aged spruce and fir); at Lievre River in Quebec (even-aged jack pine and even-aged swamp black spruce); and at Dorset in Ontario, (all-aged hardwood). Canopy density readings and crown characteristic measurements were also made in these areas. In some instances the data were the result of the joint efforts of the Inventories Section staff working on a common experimental project with the staff of some paper company. In order to develop suitable illustrations, efforts were made to find data covering stands of various heights, densities and compositions. Variations in distribution of age-classes and of different crown shapes were also investigated. Procedure The drawings are based on the field data from which came the count for trees per plot and the dimensions of tree crowns. Trees dealt with are of merchantable size, that is, 26 feet and higher. Those below this height are not used in the calculations and are omitted from the drawings for the sake of simplicity. It should be noted that 26 feet is too low for merchantability in some districts though it is suitable in others, for example, in some eastern pulpwood forests. As a rule 30 feet is considered to be the lower limit of merchantability but the influence of the volume of trees between 26 feet and 30 feet on the average height weighted by volume is negligible. Therefore, to maintain uniformity in the spread of the height classes this figure, 26 feet, was used, giving for the 30-foot class a spread of 26 to 35 feet, for the 40-foot class a spread of 3G to 45 feet, and so on. Each chart in the series shows the average height weighted by volume for some particular cover type. Normally the interpreter divides the forest int.o strata which may include, to cite one example, a lo-foot height class, a cover type, and a 10 per cent canopy density class. For purposes of this project the only criteria were height and cover type. Plots were grouped into lo foot height classes, by types. For this project the height classes were 30 feet (i.e ), 40 feet (36-45), and so on, and the types consisted of softwood (spruce and fir), black spruce, jack pine, and hardwood. Canopy density was accepted as it occurred in each plot. For the sake of emphasizing the height classes in the drawings the number of trees per plot in each lo-foot height class was converted to the central value of the class so that, as the drawings indicate, the trees shown are all multiples of ten feet in height. 5

6 I itparlmtnt of.norl trn : anh.national.ltr50 tc'5 FORE?ANCH AVERAGE HEIGHT \GHTED BY TREES 4NI1ND GREATER VOLUME!;&!!Qpy Density - The above chart is a plan view of the section below and shows a Canopy Density of 48% PERCENTAGE OF TREES IN EACH HEIGHT CLASS HEIGHT PER CLASS CENT I NO. OF STEMS PER ACRE: 365!;&!!Qpy Density - The above 'Chart is Q plan view of the section below and shows a Canopy Density of 33% m z W J: F

7 Steps Leading up to Calculations jor Average Height Weighted by Volume jor the Average Plot In a Height-type Class Average height weighted by volume was calculated for each plot from the field data so that the plot could be placed in its proper lo-foot height class. Plots in a given cover type were then grouped by height classes and stand tables were prepared showing the numbers of trees of each diameter class occurring on the average plot. These I-inch diameter classes were converted to corresponding height ranges by means of diameter-height curves, and cumulative curves showing numbers of trees over height classes were prepared. It will be noted that each diameter class corresponds to a specific height range. For example, in a specific instance the 4-inch diameter class may include trees having heights of from 26 to 33 feet. When preparing cumulative curves, care must be taken to ensure that the number of trees represented by each plotted point will be placed over the height value corresponding to the upper limit of the range if the accumulation is to proceed from lower values upward, and above the lower limit of the height range if cumulation proceeds from high values downward. For example, see Tables A, B, and C and the Chart in the Appendix. On the curve in the Appendix the 40-foot class is indicated by the vertical lines that cut it off at 35 feet and 45 feet; the 50-foot class is indicated by the lines at 45 feet and 55 feet, and so on. Within these intervals the number of trees in each lo-foot height class will be found by subtracting the number of trees at the bottom of the class from the number of trees at the top. From the average number of trees per height class in all the plots involved, the average height weighted by volume was calculated for the average plot. Crown Dimensions From the field sheet form for Crown Characteristics the data were grouped in I-inch diameter classes for each species and averages,vere calculated for each characteristic, i.e. total height of a tree, length of crown, width of crown, and point of crown reading (height of widest point of crown). From these averages, curves were drawn with each characteristic plotted over D.B.H. The characteristics for the mid-point of each height class were read from these curves. This arrangement served quite well for the narrow-crowned softwood species but for the broader-crowned hardwoods the height range was divided into three evenly-spaced height groups (crown classes) that were intended to be the equivalent of suppressed, intermediate, and dominant groups. From these groups curves were drawn as before and average measurements of the characteristics obtained for each 10-foot height group in these crown classes. Unfortunately the field,york 'vas not designed for this particular project. Consequently when crown characteristic measurements were made in the field, crown class was not indicated. However, from the results achieved the grouping described above seems to be satisfactory in that the shortest crown class has crowns much smaller than the other groups on a ratio basis. Figure 1 is derived from data from 13 one-fifth-acre plots. In order to show the trees in the drawing to best advantage and to achieve a convenient size, one-third of a chain was chosen as the width of the plot and 6 chains as the length. In actual practice the Inventories Section generally measures fifthacre plots that are 12 chains long by 11 feet wide. The illustration presented here is typical of an eastern Canadian coniferous forest. Other illustrations showing different forest conditions and different species are available and may be obtained in limited quantities on application to the Director, Forestry Branch, Department of Northern Affairs and National Resources, Ottawa. 8

8 APPENDIX TABLE A-CUMULATIVE CURVES FOR SPRUCE AND FIR SHOWN IN FIGURE 1, SHOWING HOW TO FIND NUMBER OF TREES PER PLOT IN EACH 100FOOT HEIGHT CLASS From the field data: SPRUCE D.B.H Average Height (of 13 plots) Average Number of Trees per Plot., FIR D.B.H Average Height (of 13 Plots) Average N um ber of Trees per Plot., TA BLE B-CUMULATIVE TOTALS FOR BUILDING UP THE CURVE. In the "Spruce" column below note that 64 (for example) is the low limit of the diameter class that centres around a height of 66 feet. SPRUCE FIR Low Limit of Height Range Number of Trees Per Height Range Cumulation Low Limit of Height Range Number of Trees Per Height Range Cumulation Ft. Ft

9 CUMULATIVE CURVES DESIGNED TO GIVE NO. OF TREES PER PLOT BY HEIGHT CLASSES FOR SPRUC E a FIR IN FIGURE I (/) I.LI I.LI a: "' 3 0 &I.. o g o eo HEIGHT IN FEET 10

10 TABLE C From the curve read the "Number of Trees" at the high and low limits where the vertical lines delineating the height classes cross the curve, then subtract to find the number of trees in each height class SPRUCE I Height High Low Number Height High Low Number Class Limit Limit of Trees Class Limit Limit of Trees I 10' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' FIR 11

11 EDMOND CLOUTIER, C.M.G., O.A., D.S.P. ' QUEEN'S PRINTER AND CONTROLLER OF STATIONERY OTTAWA, 1955