PLANTATION VOLUME ESTIMATES FROM TWO STAND PARAMETERS

Transcription

1 ODC 5243: 1747 CANADA DEPARTfift OF FORESTRY UD RURlL DEVElOPM NT PLANTATON VOLUME ESTMATES FROM TWO STAND PARAMETERS by W M Stiell World Symposium on Manmade Forests Canberra, 1967 Extra;t en francais THS FLE COpy MUST BE RETURNED TO: NFORMATLON SECTON, ORTHERN FOREST RESEARCH CENTRE, STREET, EDMONTON ALBERTA T6H 385 FORESTRY BRANCH DEPARTMENTAL PUBLCATON No

2 Published under the authority of The Honourable Maurice Sauve, Pc, MP, Minister of Forestry and Rural Development, Ottawa, 1967 ROGER DUHAMEL, FRSC QUEEN'S PRNTER AND CONTROLLER OF STATONERY Catalogue No Fo

3 ABSTRACT Volume per acre in plantations of red pine and white spruce was found to be highly correlated with simple expressions combining numbers of trees per acre with either dominant height or average diameter The expressions can probably be applied to a variety of species growing as evenaged planted or natural stands EXTRAT Dans certaines plantations de Pins rouges et d'epinettes blanches a Chalk River, Ontario, e volume a l'acre correspond nettement a des expressions mathematiques simples qui incluent e nombre d'arbres a l'acre associe a la hauteur des dominants ou au diametre moyen; ces expressions s'appliquent probablement aussi a plusieurs autres especes arborescentes croissant en peuplements equiennes naturels ou plantes

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5 PLANTATON VOLUME ESTMATES FROM TWO STAND PARAMETERS by W M Stiell1 NTRODUCTON Rapid estimates of pe r acre volume can be made from average stand characteristics obtained either by ground sampling or from air photos (Husch, 1963) n a review of methods of making measurements from air photos and relating them directly or indirectly to stand volume, Duffy (1963) comments that the most accurate predictions of volume are likely to be made in pure, evenaged conifer stands This is logical since the more uniform the stand the better the opportunity of obtaining reliable estimates from average stand parameters Uniformity as to age and species, and to spacing as well, is displayed par excellence by softwood plantations, which should therefore be ideally suited to stand volume prediction from average values This paper describes methods of estimating volumes per acre from numbers of trees together with either dominant height or average diameter, for plantations of red pine (Pinus resinosa Ait) and of white spruce (Picea glauca (Moench) Voss) METHODS AND MATERALS Data were obtained from 45 permanent sample plots in red pine plantations ranging in age from 1 to 38 years from planting; and from 45 plots in white spruce plantations 12 to 4 years of age The plots were located in areas of uniform stocking and had not been thinned They had been measured from l Research Scientist, Department of Forestry and Rural Development, Petawawa Forest Experiment Station, Chalk River, Onto 1

6 one to four times, and their combined data represented a wide range of stocking, height, and average diameter for each species (Table 1) TABLE 1 RANGE N STAND CHARACTERSTCS Red Pine White Spruce Age (years planted) Trees per acre Dominant height (feet) Average dbh (inches) Total volume (cuft/ac) Merchantable volume (cuft/ac) , , , , ,246 83,667 t is evident that volume per acre increases with stand height and with numbers of trees per acre The problem is to combine these two variables into one mathematical expression that is consistently related to volume This was accomplished by plotting total plot volume against a variety of expressions combining the associated height and the number of trees per acre until a good relationship was so identified Stepwise solution of the regression equation was then performed by BM 162 computer A similar procedure was followed with a combined diameternumbers expression, and finally equations were solved also for merchantable volumes on both expressions The dominant height value used was the average height of the tallest 1 per cent of all trees on the plot Average diameter was derived by the basalarea method, using only those trees greater than 5 inches dbh Numbers of trees were expressed in terms of equivalent square spacing, which is common usage for plantations A value of 5, for example, denotes an average spacing of 5 x 5 feet Total and merchantable volumes per acre had been worked up after each plot remeasurement from the Formclass Volume Tables (Anon, 1948) 2

7 RESULTS Height and Spacing The best expression combining height and spacing was dominant height/ 3 ;spacing, with both values stated in feet The regressions relating volume per acre to the expression are illustrated in Figures 14, and associated statistics are presented in Table 2 Where Vt = Vm = total volume in cubic feet per acre merchantable volume in cubic feet per acre HS = heightspacing expression Red pine = Vt HS (HS) 2 = Red pine Vm HS (HS) 2 White spruce Vt = HS (HS) 2 White spruce Vm = HS (HS) 2 These regressions indicate a direct, strong correlation between volume and the heightspacing expression, the latter accounting for more than 92 per cent of the variation in volume in all cases For both pine and spruce the relationship is slightly stronger for total than for merchantable volume Diameter and Spacing The expression derived from these variables was spacing in feet/average dbh in inches Where DS diameterspacing expression, and the other symbols are as previously = defined, Red pine log Vt log DS (log DS) 2 Red pine log Vm log DS (log DS) 2 = White spruce log Vt log DS (log DS) 2 White spruce log Vm log DS 6166 (log DS) 2 On logarithmic paper, the association between volume and the diameterspacing expression appears as inverse and almost 3

8 / PLANTED RED PNE V "/ 45 : :::; U u C( 411 a E :J ' > c; J "/" "V " ": V J "/: V J j"' o f (Dominant Height and Spacing) Figure 1 Red pinerelationship of total volume per acre to dominant height/ 3 spacing 4

9 : :: (,) G» 3 (,) C[ G» 25 e 2 >!! c s:; (,) CD :E l PLANTED RED PNE l'j V',, / 1 V / V' } v i / o 5 V M i f (Dominant Height and Spacing) Figure 2 Red pinerelationship of merchantable volume per acre to dominant height/3spacing 5

10 5 PLANTED WHTE SPRUCE 45 4 : :j () 35 CD 3 () <{ CD CD 25 E :! " :1 { J V : 1 o 5 / / 1(' f (Dominant Height and Spacing) Figure ;5 White sprucerelationship of total volume per acre to dominant height/;5/spacing 6

11 5 PLANTED WHTE SPRUCE 45 4 : :i (,) 35 3 (,) C[, 25 E 2 > a c c (,), 2 15 J t!: j il 1 5 j / o 5 1/ f (Dominant Height and Spacing) Figure 4 White sprucerelationship of merchantable volume per acre to dominant height/ 3 /spacing 7

12 TABLE 2 STATSTCS FOR REGRESSON OF VOLUME ON HEGHT AND DAMETERSPACNG EXPRESSONS HeightSpacing DbhSpacing Mean Volume andard Error of Estimate 21 Species Volume (cuft/ac) N R R 2 cuft/ac % of mean vol Red pine total 2, (Xl Red pine merchantable 1, White spruce total 1, White spruce merchantable 1, l All significant beyond the lpercent level

13 straightline (Figures 5 8) This expression shows slightly stronger correlations for spruce than are found with the heightspacing relationship Pine merchantable volume exhibits the least satisfactory association with diameter and spacing, yet even here the expression accounts for 86 per cent of volume variation DSCUSSON Similar associations between volume and these expressions can be expected to exist for plantations of other species and for natural pure stands as well n fact, data from published normal yield tables for several Canadian hardwood and softwood species have been used to test the heightspacing expression, in all cases demonstrating excellent relationships This is not to be taken as conclusive, owing to the smoothed and harmonized nature of yield table values, but it does indicate that the association is consistent with the natural development of evenaged stands The expressions are therefore likely to have considerable scope, and their application to a variety of species and volume tables should be explored A trial with data from treated plantations indicates that the relationships existing between volume and the heightspacing expression before and immediately after thinning are dissimilar, probably owing to the manner in which dominant height is defined Other measures of dominant height for example, the tallest 1 trees per acre or even average stand height, would doubtless give satisfactory if somewhat different results the interrelationships of these measures in plantation red pine and white spruce are reasonably simple (Stiell, 1965) Average spacing can be found conveniently from Table 3, which presents interpolated values to onetenth foot, and corresponding cube roots as well Of course numbers of trees per acre can be substituted for spacing, since spacing in feet = /43,56/trees per acre, and therefore: 9

14 6 : 5 4 PLANTED RED PNE : : :::J U f u <l i E :::J (; > (; o o o o " ' f (Averoqe Diameter and Spocing) FiguT'e 5 Red pine T'elationship of total volume pet' act'e to spacing/ avet'age dh h 1

15 :: " u '" l:; <t C E " '" : 2 c s::; ::;: R Y Y ' ' PLANTED RED PNE, 1 ' Figure f (Average Diameter and Spacing) 25 3D 35 4 Red pinerelationship of merchantable volume per acre to spacing/average dbh 11

16 , PLAN+ED WJTE PRJE e 9 " <l 8 Q E 7 " (5 > 6 ;; (; K " 2 f (Avera,e Diameter and SpaCill9) " :: " 1 Figure? White sprucerelationship of total volume per acre to spacing/average db h 12

17 4 3 j PLANTED WTE SPRUCE 2 ' " e u 4 E " ;; > : C J: U j jo Figure 8 1 S f (Avtroge OiClmete, and Spacng) White sprucerelationship of merchantable volume per acre to spacing/average d b h 13

18 TABLE 3 NUMBER OF TREES PER ACRE AT SQUARE SPACNGS spac Treee Spacing Trees Spacing Treee Spacing Trees in FeeLS) i :eer acre in Feet {sl i :eer acre in Feet {S) i :ear acre in Feet!S) i :eer acre 1 1 4) ) )2 ) , )1 ) ) ) )7 11)) 22)7 2 25:3 166 ) ,98 ) 2244 )41 ) 25) ) ,6) :)) ) : ) ) ) 157) ) ), ) )9 12, ) ) ) ) ) ) )2 82) ) 2)8 288 ) )15 28) ) ) ) ) ) )6 1 ) 4 1))9 5 1)75 1) ) ) ) ) 2) ) )6) ) 1)2 ) )2 2) )5 1) )768 2)) ) ) 2) )) ) ) ) ) )) 7 45)) 4254 J ) 2))) 2))9 2)45 2)57 )47 29) ) 4 2)75 24) 4 5 2)87 7 2)9) 2)99 2) ) ) ) )56 21) 54 J ) J J J 5 24) ) ) ) )) 46) J ) ) )2 1,61l ) ) '48J 186 J ) ) ) ,) ) ) ,) ) , )7) J ) , ) J 1 7 ) 24)) ) ) )9 1)) log HS = log dominant height log number of trees The diameterspacing expression can readily be determined by a dbh tally, or, if relascope techniques are preferred, the expression can be stated in the form /basal area in square feet per acre Sampling would in all cases be subject to the usual preliminary stratification procedures 14

19 Besides its application for estimating actual stand volumes, the heightspacing regression could be used for predicting values at various spacings Yields could be projected with data from height/age curves and any chosen numbers of trees per acre CONCLUSONS 1 The expressions of spacing combined with height or diameter described herein provide a means of rapidly estimating total and merchantable volumes per acre in pure red pine and white spruce plantations that have developed without serious interference 2 The expression of heightspacing is well suited to the use of air photos, on which height is the most readily measured tree dimension 3 The diameterspacing expression lends itself best to ground cruising methods, where dbh or basal area is the measurement most easily taken 4 The expressions, used in conjunction with appropriate volume tables, should be applicable to evenaged pure natural stands REFER ENCES Anon, 1948 Formclass volume tables (second edition) Canada Dept Mines and Resources, Mines, Forests, and Scientific Services Branch, Dominion Forest Service Duffy, PJB 1963 Estimation of stand volume from air photos Can Dept of Forestry, Proc Seminar on Airphoto nterpretation in the Development of Canada: 2636 Husch, Bertram, 1963 Forest mensuration and statistics The Ronald Press Co, New York, 474 p Stiell, WM 1965 Height sampling in red pine and white spruce plantations For Chron 41: M 15