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A comparison of methods of determining the allowable cut on the University of British Columbia research… Kovats, Miklos 1962

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A COMPARISON OF METHODS OF DETERMINING THE ALLOWABLE CUT ON THE UNIVERSITY OF BRITISH COLUMBIA RESEARCH FOREST, HANEY, B. C. by Miklos Kovats B.S.F., University of British Columbia (Sopron Division), 1958 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY in the Department of FORESTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January, 1962 In present ing t h i s thes i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the Un i ve r s i t y of B r i t i s h Columbia, I agree tha t the L i b r a r y s h a l l make i t f r e e l y ava i l ab l e f o r reference and study. I f u r the r agree that permission f o r extensive copying of t h i s t h e s i s f o r s cho l a r l y purposes may be granted by the Head of my Department or by h i s representa t i ves . It i s understood tha t copying or pub l i c a t i on of t h i s thes i s f o r f i n a n c i a l ga in s h a l l not be alloiired without my wr i t ten permiss ion. Department of Forestry The Un i ve r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date January 30 > 1962 i i ABSTRACT A COMPARISON OF METHODS OF DETERMINING THE ALLOWABLE CUT ON THE UNIVERSITY OF BRITISH COLUMBIA RESEARCH FOREST, HANEY, B. C. Generally i t i s not adequate to calculate an allowable cut for a property by only one formula or method. Usually i t is preferable to u t i l i z e a l l the information available with as many suitable formulae or methods as possible to obtain reason-able estimates of the yearly u t i l i z a t i o n rates by several approaches. For the University Research Forest fifteen different formulae and methods were selected for comparison, because their basic assumptions appeared applicable to this forest. The methods and formulae tested were: Methods: Area regulation, Area-volume check, Area-volume allotment, Barnes1 and H. A. Meyer's. Formulae: Austrian, Black H i l l s , Grosenbaugh, Hanzlik, Hundeshagen, Kemp, W. H. Meyer, S. Petrini (compound and simple interest) and Von Mantel. Appropriate inventory techniques were developed in order to collect the necessary information regarding rates of growth, mortality and numbers of trees per acre by diameter classes. Present and future decadal growing stocks were estimated. Simple and compound growth rates, including and excluding i i i ingrowth, for a l l types were calculated separately for stands over eighty years of age and for stands under eighty years. The inventory was based on the areas and estimates taken from 1961 aerial photographs supplemented by both temporary and permanent sample plots, employing primarily the principles of the point sampling techniques as described by L. R. Grosenbaugh. After substituting the actual data into the formulae and various methods, allowable cut estimates for 3.1, 9.1, 11.1, and 13.1 inches minimum diameter limits were calculated. Allowances were made for an intermediate standard of u t i l i z a -tion and for waste, breakage and decay. Considering the inventory and the allowable cut calcula-tions i t was found that: 1. Simple area regulation w i l l lead to undesirably large fluctuations in allowable cut. 2. Volume formulae are useful means of determining the yearly harvest volume, though the distribution of the cut on the ground requires definition in terms of area as well. 3. Neither area nor volume control can be used exclusively. Some combination and integration is usually necessary in actual practice. In the case of the Research Forest this can be applied most conveniently by following the area-volume computa-tion basis. i v TABLE OF CONTENTS Page INTRODUCTION 1 METHODS OF CALCULATING THE ALLOWABLE CUT 5 AREA CONTROL 5 VOLUME CONTROL 6 AREA AND VOLUME CONTROL 7 DESCRIPTION OF METHODS USED 8 AREA CONTROL METHODS 8 AREA REGULATION 8 VOLUME CONTROL METHODS 9 HANZLIK'S FORMULA 9 AUSTRIAN FORMULA 9 KEMP'S FORMULA 10 BARNES1 METHOD 12 BLACK HILLS FORMULA 12 HUNDESHAGEN'S FORMULA 13 VON MANTEL'S FORMULA 14 S. PETRINI'S COMPOUND INTEREST FORMULA 15 S. PETRINI'S SIMPLE INTEREST FORMULA 16 W. H. MEYER'S AMORTIZATION FORMULA 16 GROSENBAUGH'S SIMPLE INTEREST FORMULA 17 H. A. MEYER'S METHOD 18 Page AREA AND VOLUME CONTROL METHODS 19 AREA-VOLUME COMPUTATION 19 AREA-VOLUME ALLOTMENT 22 NECESSARY INFORMATION 24 DATA COLLECTION AND CALCULATION METHODS 25 CLASSIFICATION 25 AGE CLASS LIMITS 25. FOREST TYPES 25 SITE CLASSES 26 DIAMETER CLASSES 26 THE USE OF AERIAL PHOTOGRAPHS 27 PHOTO TYPING 27 PHOTOGRAPHIC HEIGHT MEASUREMENTS 27 AREA DETERMINATION 31 THE USE OF McBEE PUNCH CARDS 37 GROUND SAMPLING 41 METHOD OF CALCULATING THE NUMBER OF TREES PER ACRE AND MORTALITY RATES 4 4 METHOD OF CALCULATING FUTURE DIAMETER GROWTH 52 STAND TABLE PROJECTIONS 56 ROTATION AGE 59 MISCELLANEOUS CALCULATIONS 5 9 v i Page ALLOWABLE CUT CALCULATIONS 65 AREA REGULATION 65 VOLUME CONTROL FORMULAE 70 AUSTRIAN FORMULA 70 HANZLIK'S FORMULA 71 KEMP'S FORMULA 72 BARNES' METHOD 74 BLACK HILLS FORMULA 76 HUNDESHAGEN'S FORMULA 77 H. A. MEYER'S METHOD 78 VON MANTEL'S FORMULA 81 GROSENBAUGH'S SIMPLE INTEREST FORMULA 81 W. H. MEYER'S AMORTIZATION FORMULA 83 S. PETRINI'S COMPOUND INTEREST FORMULA 83 S. PETRINI'S SIMPLE INTEREST FORMULA 84 AREA AND VOLUME CONTROL METHODS 85 AREA-VOLUME COMPUTATION 85 AREA-VOLUME ALLOTMENT 88 CONCLUSION 92 BIBLIOGRAPHY 101 v i i LIST OF TABLES Number Page 1. WEIGHTS OF POINTS BY ELEVATION LIMITS 33 2. COMPARISON OF AREAS AS ESTIMATED IN 1958 AND 1961 34 3. AREA SUMMARY FOR THE UNIVERSITY RESEARCH FOREST 35 4. COMPARISON OF PRODUCTIVE AREAS AS ESTIMATED IN 1958 AND 1961 36 5. SITE INDICES AND CORRESPONDING CODES 39 6. AREAS, SITE INDICES, AVERAGE AGES, GROSS CUBIC FEET VOLUMES BY MINIMUM DIAMETER CLASSES, AND SPECIES COMPOSITION BY AGE AND SITE CLASSES 40 7. MINIMUM AND MAXIMUM NUMBER OF DEAD TREES PER ACRE BY SPECIES AND TYPE CLASSES 48 8. NUMBER OF TREES PER ACRE AND 10-YEAR MORTALITY RATES BY AGE AND SITE CLASSES FOR DOUGLAS FIR 49 9. NUMBER OF TREES PER ACRE AND 10-YEAR MORTALITY RATES BY AGE AND SITE CLASSES FOR WESTERN HEMLOCK 50 10. NUMBER OF TREES PER ACRE AND 10-YEAR MORTALITY RATES BY AGE AND SITE CLASSES FOR WESTERN RED CEDAR 51 11. ESTIMATES OF AVERAGE AND MAXIMUM DEVIATIONS AND STANDARD ERRORS OF ESTIMATE OF DIAMETER GROWTH BY SPECIES, AGE AND SITE CLASSES 54 Number Page 12. PREDICTED FUTURE 10 YEARS GROWTH IN INCHES BY DIAMETER, AGE AND SITE CLASSES, AS TAKEN FROM GROWTH CURVES, 55 13. DATA SUMMARY FOR THE RESEARCH FOREST 58 14. MISCELLANEOUS DATA REQUIRED FOR THE ALLOWABLE CUT CALCULATIONS 62 15. A COMPARISON OF ACTUAL AND ESTIMATED OLD GROWTH YIELDS 63 16. A COMPARISON OF SECOND GROWTH VOLUMES AS ESTIMATED IN 1959 (SMITH AND KER) AND IN 1961 64 17. EXAMPLE OF AREA REGULATION 69 18. EXAMPLE OF AREA-VOLUME COMPUTATION 87 19. EXAMPLE OF AREA-VOLUME ALLOTMENT 90 20. YEARLY ALLOWABLE CUT VOLUMES IN CUBIC FEET AS CALCULATED BY DIFFERENT FORMULAE AND METHODS 95 ix LIST OF FIGURES Number 1. ACTUAL AND DESIRED AGE CLASS DISTRIBUTION IN THE RESEARCH FOREST 2 . ACTUAL AND DESIRED CUBIC FOOT VOLUMES IN THE RESEARCH FOREST 3 . GRAPHICAL SOLUTION OF THE PARALLAX FORMULA X ACKNOWLEDGEMENTS Acknowledgement is made to the members of the University of Br i t i s h Columbia Faculty of Forestry, and Research Forest staff, for the advice and assistance they have given during the different stages of my work. In particular, I should like to express my sincere appreci-ation to Dr. J. H. G. Smith for his helpful suggestions through-out the preparation of this work, and to Dr. B. G. G r i f f i t h and Mr. D. Munro for their careful review of the thesis. Generous assistance was obtained from Mr. J. Csizmazia, who helped in the compilation and sorting of the f i e l d measure-ments, using the Alwac III-E electronic computer. A National Research Council Bursary provided the financial support that made my studies possible. Finally, but not last, I should pay a high tribute to the sp i r i t and help of my wife, who cheerfully typed the f i r s t draft. 1 INTRODUCTION The purpose of forest management, i n general, i s to supply the economy of a country with a continuous flow of forest pro-ducts and to furnish the needs of the public for recreation, c o n t r o l l e d water supply, f i s h and game, and protection. The task of forest regulation within the scope of forest management i s , i n general, to supply well-designed plans, i n order that the demands on the forests for timber production and other public benefits - such as s o i l preservation, flood protec-t i o n , and recreation - can be met. To s a t i s f y these demands, the forests must be regulated i n order to maintain the balance between forest u t i l i z a t i o n and forest growth, thus perpetuating cuttings and revenues connected with them. Its purpose, therefore, i s not only to regulate the cuttings themselves but also to describe the r e f o r e s t a t i o n and protection measures necessary to sustain continuous production. Forest regulation must be joined by d i f f e r e n t economic operations i n such a way that they merge the entire management unit into a harmonized working organization. Usually natural forests are not i n a stage where they can assure the most favourable sustained cut r i g h t from the beginning. The object of regulation i s to d i r e c t the management unit i n such a way that i t w i l l reach the desired balanced p o s i t i o n with 2 the least economic loss, in the shortest time. This idea of preserving the forest and maintaining a sus-tained annual cut i s not new. The earliest records of forest regulation date back as far as 1122 B.C. in China, where a Government Commission of Forests regulated the cutting of timber and punished thieves and trespassers (Meyer, Recknagel and Stevenson, 1952). In Europe during the feudal days, some forests were devastated due to overgrazing, and regulations became necessary to protect them. By the last half of the eighteenth century s c i e n t i f i c methods were replacing the earlier methods, giving the basis for modern allowable cut calculations. Naturally, many of the earlier methods are s t i l l in practice, together with the new approaches, and are often used because of their simplicity or assumed applicability to a particular area. However, applying only one favored formula usually i s not enough to j u s t i f y an Important decision on which the future of a large management unit depends. Usually i t i s better to apply several formulae and methods for the determination of the allowable cut, and compare the results. The comparison of various formulae and methods, to aid decision as to which regulation method is most suited to a particular area, was emphasized by Greeley (1935), who evaluated changes in plan techniques and concepts for the Snoqualmie National Forest of the United States. Similarly, Castles (1959) suggested "that to rely on any one method or formula for setting 3 the allowable harvest cut for a management type or working cycle is not as sound as i t i s to make the calculation by as many for-mulae as there are sound data with which to calculate." Naturally, allowable cut volumes, whenever possible, should be allocated to specific stands. There must also be provision for, and recognition of, the need for periodic revision. F l e x i b i l i t y within reasonable limits should be the aim. In general: "Regulatory methods should be regarded as the key working tools of the practising forester, to be used with dis-cretion and understanding" (Davis, 1954). Since the University Research Forest near Haney was used as the basis for a l l comparisons in the thesis, a general visual impression of the present distribution of age classes and volume on the Forest should be gained from study of Figures 1 and 2. The University Research Forest is almost unique among Coastal British Columbia forests in i t s relatively balanced distribution of age classes and i t s lack of an overwhelming surplus of over-mature timber. Actual and desired age-class distribution in the U B C- Research Forest Figure I- /VV~A Actual age-class distribution 10 20 30 40 years and proportionate acres Actual and desired gross cu ft volumes in the U B C Research Forest (III in +) Figure 2 Actual volume Desired empirical volume (FH medium sits) 10 20 30 40 50 60 Years and proportionate acres 70 80 5 METHODS OF CALCULATING THE ALLOWABLE CUT Throughout the history of forestry, many methods have been developed for calculating the allowable cut in various countries for many different forest stands. The principal steps toward forest regulation were taken in Europe, where the necessity of planned forest management arose soon after the effect of excessive u t i l i z a t i o n was realized. Although many allowable cut methods have been developed, they can be grouped into three basic pro-cedures. These principal methods are usually named as: 1. Area control 2 . Volume control 3. Area-volume control, or combined methods. 1. Area control The principle of area control i s very simple: i t means that the volume to be harvested i s controlled by the area al l o -cated for cutting. The forest under management is divided into a number of areas, each of which is cut according to a definite cutting schedule. The simplest expression of area control is in a f u l l y regu-lated even-aged forest, managed according to a clear cutting plan. Then each year of period 1/R or 1/P of the area is clear cut (R = rotation in years; P = period in years), assuming that the area is of the same site quality. Where different qualities 6 of land are present, i t i s necessary f i r e s t to reduce the areas to equal productivity, then to determine the yearly or periodic cutting area, in order to obtain a f a i r l y even flow of products during the rotation. In practice, of course, no forest could be so perfectly regulated that a uniform area could be cut over each year and precisely the same volume obtained. Considerable varia-tions in the yearly cutting areas usually must be introduced. However, this f l e x i b i l i t y does not, and should not, lessen the importance of the basic framework. 2. Volume control In volume control, the determination of the cut is approached through the volume of the growing stock and i t s increment, and can be approximated with various mathematical formulae. In contrast to the area method, where areas of the same productivity are cut during each year of the rotation, the volume method intends to secure an equal volume for each year or period. Usually with some general information about the forest the volume control method gives a sufficiently good guide to the forester to prevent serious mistakes, when urgent estimation of allowable cut is necessary (Davis, 1954). These methods are based either on growing stock or on incre-ment, or, on both growing stock and increment, and they can be applied to even-aged forests as well as to uneven-aged forests. However, the volume control is "most readily and r e a l i s t i c a l l y applied to uneven-aged stands where volume and increment 7 estimates are necessary for management planning at a l l " (Davis, 1954). 3. Area and volume control Since neither area nor volume control provides a complete solution to the problem of determining the allowable cut in a forest other than one completely regulated, i t i s logical to u t i l i z e the advantages of both methods and combine them in one way or another. Thus many methods have been devised and there are endless p o s s i b i l i t i e s to create new ones to meet particular circumstances. In general, these methods are characterized by f l e x i b i l i t y and lack the precision and neatness of volume methods. They are d i f f i c u l t to describe in a few words, since they are more of a procedure or a framework, rather than a specific method. Methods of calculation w i l l be presented later, when the actual calculation for the University Research Forest w i l l be shown. 8 DESCRIPTION OF METHODS USED Several methods were selected from each basic procedure previously mentioned. The selection was made according to their s u i t a b i l i t y to the natural even-aged stands of the Research Forest, which may have a range of up to 20 years in ages of dominant and codominant trees. Many methods are applicable to both even- and uneven-aged stands and give reasonable estimates for both cases. Area Control Methods Area regulation For this method, described by H. H. Chapman (1950), i t i s important to obtain areas and site conditions for each forest type. If the ages of these stands are also available, then the yearly cutting volumes can be shown. The actual areas must be reduced to standard productivity, using the average or the most commonly occurring condition class as a base. After the area reduction, the yearly cutting area may be calculated as the total reduced area divided by the rotation age. The order of cutting should follow the logical sequence of stands most needing removal; deteriorating mature stands, or stands least in value, must be cut f i r s t . Younger stands may be selected for cutting i f other important reasons suggest the necessity of cutting, e.g. epidemics, or exceptionally good 9 markets for smaller logs. Volume Control Methods Hanzlik's formula The method recommended by E. J. Hanzlik (1922), and in a revised formbby the West Coast Forest Procedures Committee (1950), i s widely used in the western coast forests of North America. Hanzlik's method gives a reasonable volume estimate of the allowable cut for areas with large virgin timber reserves. For use at the Research Forest, the formula has been defined as: ' 80 R * where A. C. i s allowable yearly cut, I i s mean annual increment at 80 years for stands younger than rotation age, R is rotation age (years), and Vmat i s volume of mature stands (above rotation age). The IgQ value i s obtained from empirical yield tables (Fligg, 1960) for immature stands. Empirical mean annual increments of those second growth stands which are close to the cutting age are corrected by their present volume ratio , , present actual volume Volume Ratio (VR) = — ~ : — = present empirical volume Austrian formula This formula differs from Hanzlik's in that the actual volume of the growing stock i s adjusted to the level of the 10 desired growing stock over the period of the rotation, whereas in Hanzlik's formula the entire volume of old growth timber is removed during the rotation. The increment used in the Austrian formula is the mean annual increment of the entire stand at present. The formula i s : Ga - Gr A. C. = I + " K as presented by K. P. Davis (1954), where A. C. i s allowable cut, I i s mean annual increment during the conversion period, Ga i s actual growing stock, Gr i s desired growing stock, and R i s rotation age in years. In Heyer's formula, which is a modification of the Austrian, the volume of the growing stock i s adjusted over a period which is generally much shorter than the rotation. Kemp1s formula If volumes and areas by stand size classes are available, this formula is easy to apply. It is used in properties on which there is a surplus of timber beyond rotation age. The objective in application i s to determine the cut that w i l l achieve an approximately equal distribution of area by age or tree size classes within a rotation with a minimum variation 11 from ultimate sustained yield volumes. For a forest type the expression i s : 7A + 5A-, + 3A„ + Ao A. C. ~ (MA) 4R (U.S. Dept. of A g r i c , 1958), where A. C. is annual cut, A is area of sawtimber stands, A^ is area of poletimber stands, A£ is area of seedling and sampling stands, A-j i s non-stocked area, R is rotation in years, and MA is expected average volume per acre of stands as they are cut. The formula simply represents the distribution of volumes as they should be in a normal forest, i.e., in a triangular diagram of the growing stock in a normal forest, the forest should have: 1/16 of i t s volume in stands between 0 and 1/4 rotation age, 3/16 of i t s volume in stands between 1/4 and 1/2 " " , 5/16 of i t s volume in stands between 1/2 and 3/4 " " , 7/16 of i t s volume in stands between 3/4 and rotation age. This model i t s e l f i s erroneous in that volume plots"over age as a second or third degree curve instead of a straight line. This error is comparatively minor, however, and applies to some other allowable cut formulae as well" (U.S. Dept. of A g r i c , 1958). 12 Barnes' method (Barnes, 1951) Since the annual cut i s closely related to the age at which the stands are harvested, an estimate of the average cutting age during the forest rotation should furnish a good estimate of the annual cut. Therefore, in Barnes' method the average present age must be calculated, to see whether i t i s over or under the average age of a normal forest, with an average cutting age equal to the rotation. For example, in a normal forest with an average cutting age of 80 years, the present average age should be 40 years, but i f the average age of the forest i s more, or less, than 40 years, a discre-pancy w i l l occur, with which the average cutting age must be corrected. The yield at this corrected average cutting age w i l l give a reasonable estimate of the yearly cut accord-ing to the hypothesis. Since empirical yield tables are available for Br i t i s h Columbia, the average yield can be read directly from the yield tables for different types. The weighted average of these yields at the calculated rotation age then w i l l give the allowable cut, based on Barnes' assumption. Black H i l l s formula This formula has been applied on the National Forests in the Black H i l l s of South Dakota, as described by K. P. Davis 13 (1954). Two broad condition classes of merchantable timber are recognized: 1. Mature stands, in which i t i s presumed current losses equal increment. 2. Thrifty merchantable stands, making net increment. The formula is as follows: VM' (CM) + [vt + (It/2)] Ct A. C. = • -—; ; where A. C. i s allowable cut, VM is volume of mature stands, CM is per cent cut in mature stands, an arbitrary figure, developed on the basis of s i l v i c u l t u r a l and related considerations, Vt i s volume of th r i f t y merchantable stands, It is increment of t h r i f t y merchantable stands during the cutting cycle, Ct i s per cent cut in t h r i f t y merchantable stands (an arbitrary figure determined in the same way as for CM), and Y i s cutting cycle in years. Hundeshagen's formula Hundeshagen1s assumption was that growth or yield in an actual forest, approximately regular in distribution, bears the same relation to i t s total growing stock as growth in a f u l l y stocked regulated forest, as represented by normal yield tables, bears to i t s growing stock (K. P. Davis, 1954). Expressed as a proportion: 14 Ya = Yr . Ga = Gr ' where Ya is growth or yield in an actual forest, Ga i s growing stock in an actual forest, Yr is growth or yield in a f u l l y stocked forest, and Gr is growing stock in a fu l l y stocked forest. The f i n a l equation i s : Yr Ya = — Ga . Gr Yr If the — ratio is expressed as a percentage a quick approxima-tion of the yield in the actual forest can be made by merely multiplying this percentage by the actual growing stock. This method, however, has many limitations regarding comparability of data, such as standards of u t i l i z a t i o n , effect of understocking and the l i k e , inherent to the direct application of normal yield table data to actual stands. Although some of these factors can be eliminated using empirical yie l d tables, the method s t i l l should be used with caution and at best i s useful only for a rough approx imat ion. Von Mantel's formula It has been observed that in an approximately f u l l y regulated forest there i s a f a i r l y regular and often linear increase in volume by age classes. This suggests the possibi-l i t y that the growing stock can be represented by a right angled triangle. The area of this triangle therefore represents the total growing stock of the forest, "Ga", having the base of 15 "R" acres, and the altitude, the yield at rotation age, "Ya", indicating the annual cut. Thus the area of the triangle i s given by the formula: R(Ya) . iia = hence the actual yield i s : 2Ga Ya - — . The accuracy of the formula i s greatly affected by the regularity of the forest. It is obviously inapplicable unless there is some semblance of regularity. Sven Petrini's (1956) compound and simple interest formulae If the annual cut m i s to be calculated for a period of t years, where the present wood capital i s k cu. f t . , the actual percentage of increment i s £ per cent and the f i n a l capital of wood is set as K cu. f t . at the end of t period; then m can be calculated using the compound interest formula: k(1.0p) t - K m " 0 * 0 p l.Opt - 1 • If we assume that the capital k increases an equal annual amount, then the actual annual percentage increment in rea l i t y is continually diminishing during the period, which i s usual for older stands. Thus the formula given below i s better suited to stands with slow growth, while the equation above w i l l more l i k e l y give a better answer for faster growing t h r i f t y stands, 16 The simple interest formula i s : k ( l + TUTD - K m = tp t ( l + 200 + tp) In this formula i t i s assumed that the volume of the fel l i n g s , when made continually each year, can be reckoned as having been growing during half the period in question, i.e., t/2 years. W. H. Meyer's amortization formula This method, originally developed by W. H. Meyer in 1943, has been modified and described by him in 1952. It i s almost identical to Sven Petrini's compound interest formula, except that Meyer includes ingrowth in his calculations, and therefore obtains a higher allowable cut volume than Petrini. Meyer's formula i s as follows: v G ( i + g t ) m - v m A. C. = gM 5 ; where A. C. i s yearly allowable cut, e i s compound growth rate for the merchantable stands alone excluding ingrowth, V Q i s present volume, V m is volume at the end of the period, m is period for which the allowable cut is desired, and gt is compound growth rate of the entire stand. In comparing overall accuracy, the W. H. Meyer method can be judged more accurate, because of his corrections regarding 17 ingrowth, than Petrini's formula. Grosenbaugh1s simple interest formula Grosenbaugh (1956) developed his formula to suit the techniques of diagnostic t a l l i e s of basal area and assumes periodic remeasurements of the area for which the allowable cut estimation i s desired. His formula has the advantages of separating speculative growth from measured growth rates, and of confining the allowable cut to a short period, for which periodic remeasurements of management plots are necessary. The formula i s : A. C. -Vn-1 + nG9 - w— *• o nG 0 mG, m 1 + 2 G, 1 + m G o J where n i s number of years allowed between start of current period and time when ultimately desired stand w i l l be attained, m i s number of years in shorter period for which periodic allowable cut w i l l be calculated, V Q i s original stand volume at start of m year period, V n i s stand residual volume ultimately desired n years hence, G i s simple periodic net annual growth rate of merchantable trees comprising allowable cut (static or slow survivor growth less corresponding mortality; no ingrowth), G.. i s simple periodic net annual growth rate of entire stand over m year period ( a l l survivor growth less mortality, plus expected m year ingrowth), and G2 is simple periodic net annual growth rate expected for entire stand over n year period, including future n year ingrowth anticipated from various sources, such as planting, and net growth stimulation; anticipated as a result of future timber stand improvement, (thinning, 18 salvage, and removal of slower-growing items). H. A. Meyer method (Meyer. Recknagel. Stevenson. 1952) This i s a time-consuming method to apply when detailed data are available. Originally i t was designed for all-aged stands but i t is applicable to even-aged stands as well. The method involves the calculation of the average number of trees by diameter classes, average volume per tree, average volume per acre, and decadal growth rates for the total area, including a l l species. The number of trees per acre and volume per acre values must be weighted by the appropriate areas to obtain the correct average values. The decadal growth rates are not weighted. When a l l these data are available, then a regression equation i s calculated, using the logarithm of the number of trees per acre in each diameter class, and de Liocourt's quotient i s evaluated, using the equation: -D N = k q T where N i s number of trees per acre, k is constant, D is diameter at breast height (inch), and i i s diameter class interval (inch) (Sammi, 1961). The k i s calculated from the equation by inserting D = 0 in the exponent. Thus the equation becomes: N = k. Substituting this k value together with an N and a D value calculated from the 19 regression equation, £ can be easily obtained as: Knowing £ and the average growth rates of the diameter classes, the per cent volume increase can be read from a table presented by Meyer, Recknagel and Stevenson (1952, p.159). Multiplying the per cent volume increase by the average volume per acre values, the volume increase by diameter classes can be obtained. By subtracting the average mortality rates from the corresponding volume increase figures and summing up these reduced values, a net volume increase for the total forest can be shown in a table form, similar to Table 33 in Meyer, Recknagel and Stevenson (1952). Usually when determining the allowable cut, a reduced £ is used and a maximum diameter limit is set, beyond which a l l trees are cut in a certain period of time. Generally the £ i s compared to the £ of well-managed Swiss forests and reduced accordingly. However, i f the present £ i s lower than that of the Swiss forests, reduction may not become necessary. Area and Volume Control Methods  Area-volume computation The formulae described above usually give only a guide con-cerning the quantity of the yearly allowable cut. The West Coast Forest Procedure Committee (1950) recommended that a l l 20 formula methods should be followed by an area-volume check, described in detail in the report. This check requires knowledge of the areas, stocking, site, and species composition by age classes. If empirical yie l d tables are used " as in this case -stocking data are not essential. The procedure begins with the statement of the areas, and the statement of a t r i a l allowable cut figure obtained by one of the methods described previously. When different type groups are present i t i s necessary to reduce the areas to a basic type as when area regulation is used. The next step i s to obtain a preliminary estimate of the duration of cut, by dividing the area of the f i r s t type or age group by the yearly cutting area. Half of this duration age then i s added to the age of the stand when cutting begins, thus obtaining a preliminary estimate of the average cutting age. For this average cutting age the corresponding yield i s read from the empirical yield table, and multiplied by the actual number of acres, thus obtaining the total cut in that type. This volume then i s divided by the preliminary allowable cut estimate, to see how many years the volume would last in that particular type. This period usually does not coincide with that estimated previously, using the yearly cutting area, and therefore half of the revised duration period must be added to the age of the stand when cutting begins, to obtain a new revised average cutting age. 21 A new yield per acre based on the revised average cutting age, and multiplied by the actual acres in the type, w i l l give the actual revised yield for the whole type when cut. The f i n a l two columns show the duration of the cut per type and cumulative times, assuming that the indicated allowable cut volume w i l l be cut each year. The next age group or type naturally w i l l have an age, when cutting begins in i t , equal to the sum of i t s present age and the figure shown in the cumulative column. Otherwise a l l calculations are the same for this type as have been described for the previous type. At the end of the calculation the f i n a l cumulative column must coincide with the rotation age, or must be at least within 5 per cent of the rota-tion to j u s t i f y the indicated cutting rate (The Westn. For. and + Cons. Assn., 1950). If the difference is more than - 5 per cent of the rotation age, the process must be repeated with a higher or lower allowable cut volume, u n t i l the calculated rotation age is within the required l i m i t . . This figure of allowable cut i s used only for the f i r s t decade and then the allowable cut is again determined on a basis of data then available. Naturally this method is highly dependent on the yields per acre read from the empirical yield tables. This can give an erroneous estimate 70 or 80 years hence, particularly for pre-sently immature or recently-planted areas. 22 Combined method of allotment This method, as described by Professor Z. Fekete (1950), intends to combine the advantages of the area regulation and the volume regulation in such a way that the yields on nearly similar cutting areas w i l l become close to equal. In a forest where the distribution of the age classes is f a i r l y even, area regulation and volume regulation give almost the same answer. But, where the age class distribution is irregular, the area regulation might indicate irregular yields, while the volume regulatory methods might indicate irregular cutting areas. In this case the combined method of allotment may be used. This lessens the irregularity of the yields obtained by the area method and at the same time reduces the differences between the periodic cutting areas. The combined method starts out from the area regulation with the simplification that the yields are shown only in the f i r s t and second cycle. These yields are equalized (averaged) and corresponding areas calculated. The cuttings of the f i r s t cycle proceed according to this plan. Before the beginning of the cuttings in the second cycle another cutting plan must be prepared, equalizing the yields of the second and third cutting cycles. A l l the other cutting plans are prepared the same way. 23 The combined method gives a more even periodic yield than the yields obtained by area regulation, and the differences between the periodic cutting areas w i l l also be less than those obtained by volume regulation. This method reduces the disadvantages of the two methods just mentioned and is a simpler process. Therefore i t became a popular regulatory method in central European practice. The area-volume method calculates with periodic cutting volumes, giving room for some variation in the yearly cuts. It uses volumes available for cut in the immediate future (within two cutting cycles), and reduces the possibility of making undetectable errors for future stand-volume conditions. 24 NECESSARY INFORMATION For t r i a l of the widely different allowable cut calcula-tion methods, a wide variety of data was needed. In the case of the University Research Forest, much informa-tion was available, but this was inadequate because i t was in various units of measurement, and taken at different times. Therefore i t was decided to undertake a small scale survey to obtain the data in one uniform measurement of wood (cu. ft.) and in such a way that a l l the necessary information for the formulae and methods mentioned previously could be evaluated. The headings of the cruise sheets had to be planned to include necessary stand information, and classification standards. After considering many p o s s i b i l i t i e s , i t was decided that a combined method of photo- and ground-cruising would be employed, using the up-to-date photographs of the Research Forest and the point-sampling method, devised by B i t t e r l i c h in 1948 and further developed by Grosenbaugh (1952, 1955, 1958). 25 DATA COLLECTION AND CALCULATION METHODS  Classification Before ground sampling could begin the stratification of forest types had to be completed to provide a good base for the distribution of sample plots. Therefore classification limits were set up and a l l forest types were sorted into these classes. The following age classes were established: Age Classes Limits (years) Old Growth (O.G.) 160 + Second Growth (S.G.) 30 - 159 Young Growth (Y.G.) 1 0 - 2 9 Planted (PL.) 0 - 9 Forest types Types were determined according to the order of predominance in the crown closure or volume of a species depending on whether the type was just estimated from photographs or was also visited and sampled on the ground. A l i s t of a l l tree species found on the University Forest was given by the U.B.C. Forest Committee (1959). However, in this work only Douglas f i r (Pseudotsuga menziesii var. menziesii (Mirb.) Franco), western hemlock (Tsuga heterophylla (Raf.) Sarg.), and western red cedar (Thuja plicata Donn) volumes were considered. 26 The present study showed that these three species comprise approximately 98 per cent of the total volume in the Research Forest. To f a c i l i t a t e the later use of empirical yield tables the same type groups were selected as they are shown in the empirical yield tables in Zone 2 (Fligg, 1960), from which the following types were recognized: Douglas f i r types (Growthttype 2), Cedar types (Growth type 5), Hemlock types (Growth type 7). Site classes Similarly to the forest type classification, the chosen site class limits were identical to those established in Fligg 1s (1960) Empirical Yield Tables (p.11), separating good G, medium M, poor P and low L sites for different types, and showing the site index limits based on heights at 100 years of age. Diameter classes Two-inch diameter classes were chosen, because in most cases this proves satisfactory for management purposes, and eliminates a great deal of extra work. It is necessary to mention that the estimates made from the photographs or taken on the ground were measured and recorded as accurately as possible, though later they were sorted into the classes described above. 27 The Use of Aerial Photographs Photo typing The photographs used were black-and-white, semi-matte in finish, 9 x 9 inches in size, had a representative fraction (R.F.) of 1:15,900, and were taken in June, 1961. The minimum area in any type was five acres. Types were separated with a black b a l l point pen using a pocket stereoscope on the basis of the previously stated classification standards. Ages were not directly estimated from the photographs, but were taken from an age map prepared from previous forest cruises of the area. The forest types (species composition) were directly e s t i -mated from the photographs, using existing forest cover maps as a reference in doubtful cases. Stand site indices were obtained from two separate estima-tions, namely: from the age estimation and photographic height measurements. The latter were carried out for each individual type, measuring the height of one or two trees, representing the ave-rage maximum height of the stand (roughly average height of domi-nant and codominant trees). The site index then was taken from the appropriate B.C. Forest Service site index curves (Fligg, 1960). Photographic height measurements Photographic height measurements of trees were carried out using an Abrams height finder and the most commonly used parallax 28 formula: H dp h = P + dp where h i s height of the tree in feet, H i s flying height above ground in feet, dp i s parallax difference read from the height finder (mm), P i s base length as measured from photographs (mm,). To speed up measurement a combined graphical solution of ' the parallax formula was used which corrected the errors re-sulting from the tree's being on an elevation different than the average height of the two principal points: F i r s t , basic lines were calculated for each different P value measured from the photographs from which the equivalent height in feet for one mm. parallax difference could be read. The equation of these lines was: 0.01  h p = H P + 0.01 where hp i s height in feet at elevation of average value of the principal points ( f t . ) , H i s flying height ( f t . ) , and P is average length of the principal points (mm.). The calculation was carried out only for two different flying heights, because the equation above indicates a straight line, for which two points are adequate. The next step was to construct the correction lines by cal-culating the parallax differences, which occur when trees are 29 higher or lower than average elevation of the principal points. For this purpose the equation used was: H - h where dp is parallax difference between the base of the tree and the average height of the two principal points (mm.), P i s average base length between principal points (mm.), H i s average height of the two principal points ( f t . ) , and h i s elevation difference between the average height of the principal points and the base of the tree (mm.). When different values of h were substituted in the equation a slightly curved line resulted. These correction lines were plotted on the same graph, showing the height corrections in feet for differences in elevation. To obtain a tree height the steps outlined below were followed: 1. Calculate average base length of the stereo pair. 2. Calculate average flying height above principal points. 3. Obtain elevation of the tree base. 4. Measure parallax difference of tree. 5. Find average flying height H on the x axis of the graph. From that point go perpendicular u n t i l the line of the average base length is met. (From this point the correction lines must be followed paral l e l , u n t i l the corresponding vertical line marking the elevation of 30 Graphical solution of the parallax formula Figure 3 / Elevation above sea level (ft) 2000 1500 1000 500 140 145 150 155 159 Flying height above ground (100 ft) 31 the tree base is hit.) At this point the correct value of the 0.01 mm. parallax can be read from the y_ axis. For example, P = 89.65 mm., H = 14,640 f t . , elevation of the tree base 1,000 f t . , then the 0.01 mm. parallax difference corresponds to 1.690 f t . on the ground. Multiplying the value read from the y axis by the total parallax difference read from the height finder gives the total height of the tree (Figure 3). Area determination Although the total area of the Forest was known (9,774 a c ) , a detailed area determination was necessary for each individual type, to furnish the base for stand-table projection, and for the allocation of future cutting areas. It was decided to usethe grid area-determination system described in Spurr (1960), combined with a correction method suitable for mountainous areas. The calculation of the number of points necessary to give a desired accuracy was given by Spurr (1960). M i - P) (t2) N - E P 2 - - • ; where N is number of points necessary, P i s per cent of class limit of the total area, Ep is error per cent of class limit, and t is s t a t i s t i c a l constant. 32 Using the values of the 5 acre class limit: P = 5 x 100 = 0.0512, 9774 Ep = 0.009, and t = 1.96, N = = 2,351 points at sea level. The distance in inches of these points on the photograph when distributed evenly i s : Rounding this distance to 0.300 inches and recalculating Ep and N, we obtain 0.0083 per cent and 2,694 points respectively. Since the photographs were taken over mountainous terrain, i t was necessary to weight the areas represented by these points by elevation. For example, because of scale differences, a point appearing at 2,000 feet elevation w i l l represent a much smaller area than one appearing on sea level, assuming the spacing of these points is even. Reduction factors were calculated using the equation: Dp = 12 = 0.321 inches. 15,900 EL W = (1 - 15,900 where W i s weight of the plot, and EL is elevation in feet. 33 TABLE 1 WEIGHTS OF POINTS BY ELEVATION LIMITS Elevation Limits (ft.) Weights 0 - 200 0.9875 201 - 600 0.951 601 - 1,000 0.902 1,001 - 1,400 0.855 1,401 - 1,800 0.809 1,801 - 2,200 0.764 2,201 - 2,600 0.721 The evenly-spaced points were pricked on the photographs and a transparent overlay was prepared showing the elevation limits. Counting the number of points f a l l i n g into a type multi-plied by the corresponding weight gave the number of points which would have fallen into that type i f i t were at sea level. The influence of sloping terrain became evident when the fi n a l total reduced number of points was counted and compared to the calculated number of points at sea level. A discrepancy of -3.12 per cent of the total area resulted and had to be d i s t r i -buted proportionally to the individual types. This underestimate is due to the steep sloping terrain on many parts of the Research Forest, especially the so-called " P i t t Lake slope". (Corrected areas are shown in Tables 3 and 6.) A brief comparison of the areas shown in 1958 to the present condition was based on the data published by the University Forest Committee (1959). 34 TABLE 2 COMPARISON OF AREAS AS ESTIMATED IN 1958 AND IN 1961. Difference Class 1958 (ac.) 1961 (ac.) based on 1958 (ac.) Productive land Road Rock 9,100 80 180 313 90 11 9,282 48 30 340 57 17 - 32 - 150 182 Swamp Urban Water 27 - 33 6 TOTAL 9,774 9,774 Considerable differences between the two area estimates are present. The reason of these discrepancies can be explained mainly by the actual changes in the areas (e.g. urban) and partly by the sampling approach of the point-grid area-estimation method. However, other facts which may cause large differences between the two estimates must also be mentioned. In the present method, some of the areas which were classifi e d as rock and poor and rocky on the Abernethy and Lougheed (AV&L.) part of the forest were classified as poor stocking and l i s t e d in the productive land area. Also, i t should not be forgotten that since 1958 the vegetation might have covered a large part of these small rocky areas, therefore many of these small rock outcrops may have appeared on the 1961 photos as productive sites. 35 TABLE 3 AREA SUMMARY FOR THE UNIVERSITY RESEARCH FOREST East Side West Side Total Forest (Y.G.) * (O.G.. S.G.) * TYPE AREA (ACRES) Stocked 3,793 5,489 9,282 Road 29 19 48 Rock 7 23 30 Water 46 294 340 Swamp 42 15 57 Urban 17 17 TOTAL 3,917 5,857 9,774 * Y.G. stands average 25j years in age; S.G. stands average 80 years, and O.G. stands are more than 300 years old. The differences in the water and swamp classes may be due to the season when the measurements were made. Hence, in one case, swamps could have been classifi e d as water, while in a drier part of the year they obviously appear as swamps, and could have been sorted into the swamp class. Note that only 6 acres difference appears between the sum of water and swamp classes between the two measurements (1958 and 1961). Another comparison of the areas in the productive class is shown below: 36 TABLE 4 COMPARISON OF PRODUCTIVE AREAS AS ESTIMATED IN 1958 AND IN 1961 Type 1958 (ac.) 1961 (ac.) Difference from 1958 (ac.) O.G. 916 994 + 78 S.G. and scattered O.G. 3,162 3,701 + 539 Y.G. P. 3,340 3,676 + 336 Planted and cultivated 440 558 + 118 Hardwood and scrub 1,242 353 - 889 TOTAL 9,100 9,282 About 250 acres of old growth (O.G)) were logged 1958-1961. The largest discrepancy is in the scrub type, and is caused by the extreme overestimation of scrubby areas in 1958, on the P i t t Lake slope and on the A.&L. part of the Forest. The recent estimates, however, show that no such large acreage of scrub exists on these areas. On the P i t t Lake slope there are mostly well growing, satisfactorily stocked stands of low site quality, leaving just a small area for scrub and several stands of alder and maple. No definite evaluation has been made regarding productive stands of the A.&L. part of the Forest, since only the areas of the following classes were estimated by the writer: Total area, Stocked, Road, Rock, Water, and Swamps. Detailed area estimates of the stocked classes in the A.&L. part of the Forest as shown by Bajzak (1960), were proportionally distributed to the recent estimate of the stocked area. 37 The Use of McBee Punch Cards The individual measurements of the types were recorded on McBee punch cards for easier selection. The card was divided into columns where the number of the type, estimated crown closure, species composition, etc. were recorded. The actual order of numbers and headings on a McBee card appeared as follows: Photo Type Crown Species Date Height His- Area S.I. S.I. number number clo- compo- of tory code sure sition esta-blish-ment The descriptions of the items are as follows: Photo number: Gives the number of photograph on which the type represented by a type number (second column) appears. Crown closure: Is a number which shows the area covered by the crowns in relation to the total area, in 10 per cent units. Species composition symbols are similar to those appearing in the empirical yield tables. Date of establishment marks the century and decade in which the stand was regenerated. For example, a stand re-generated in 1860 w i l l have a date of establish-ment "86". Height of the stand in feet appears as i t was measured on the photographs. History: A sign indicates the cause responsible for re-establishment. Thus © designates clear cutting, 0 designates f i r e , and ^ designates selective cutting. The combination of these signs can also appear. 38 Area of the type is shown in acres. Site index is shown as taken from the corresponding B.C. Forest Service site index curves. For example, in a type having a species composition of FH (Douglas fir-hemlock), the site index appearing was taken from the Douglas f i r site index curve, but where HC (hemlock-cedar) or CH type was present, the site index was taken from the HC site index curve. Site indices taken from the various site index curves were not considered adequate for some calculations. Therefore a site index code was established for reducing site indices to the same level. This was done using the B.C. Forest Service Site Index curves, which show that the limits of the site index classes are higher by 10 feet for Douglas f i r , than for hemlock and cedar. Thus: The site index code for Douglas f i r types = (S.I. - 20) 0.025 The site index code for hemlock and cedar types = (S.I. - 10) 0.025. After the substitution of the various site indices into the appropriate equation above, the calculated code gave the equiva-lent ranges of the site classes in the same units. Thus the site indices regardless of species became equivalent to the codes shown as follows: 39 TABLE 5 SITE INDICES AND CORRESPONDING CODES Site classes S.I. Limits (ft.)  Douglas f i r Hemlock and Cedar Codes Low 0 - 6 0 0 - 5 0 0 - 1.0 Medium Poor Good 61 - 100 101 - 140 141 + 51 - 90 91 - 130 131 + 1.1 -2.1 -3.1 + 2.0 3.0 Example: If a medium site land bearing a Douglas f i r stand shows a site index of 130, the same land, bearing a hemlock stand, would show only a 120 site index. Using a code, both stands less of species. Naturally the codes can be easily reversed to either Douglas f i r or hemlock site index values, by rearranging the equations above. These values were then available for use with the empirical yield tables and for converting cover types to the FH medium site standard. Also, using these reduced values, the calculations of the weighted average site index for the types and for the whole of the Forest were easily carried out, by converting the average codes to Douglas f i r site index values. The summary of the average ages and site indices is shown in Table 6. would have a 2.75 code, indicating a medium site quality regard TABLE 6 AREAS, SITE INDICES, AVERAGE AGES, GROSS CU. FT. VOLUMES BY MINIMUM DIAMETER CLASSES, AND SPECIES COMPOSITIONS BY AGE AND SITE CLASSES * Class O.G.G. O.G.M. O.G.P. AREA (ac.) 159 671 164 S.I. (F) (ft.) 161 117 76 AVG. AGE (yrs.) 230 260 240 • • 3.1 2,197,062 9,200,752 1,587,028 GROSS * -5 VOLUME W . w 9.1 11.1 2,161,923 2,145,387 8,928,997 8,852,503 1,483,544 1,406,792 Q (CU.FT.) . H 55 S 13.1 2,136,006 8,694,818 1,296,092 a Species Composition HF CH CH Class S.G.L. Y.G.G. Y.G.M. AREA (ac.) 43 2170 1171 S.I. (F) (ft.) 50 135 125 AVG. AGE (yrs.) 90 30 25 • / • — » 3.1 208,034 2,444,288 238,685 GROSS w* ^  9.1 968,666 49,861 VOLUME Q ^ 11.1 561,856 19,333 (CU. FT.) g ' g M M 13.1 304,429 11,452 Species Composition FH HC HC S.G.G. 805 161 70 7,430,150 6,802,250 6,206,550 5,535,180 FH Y.G.P. 335 85 20 5,236 12,737 3,645 S.G.M._ . S.G.P. 1885 121 80 20,587,970 17,984,785 10,599,310 14,446,640 FH PL. 558 134 5 968 83 90 6,578,528 3,554,496 2,269,960 1,466,520 HF HW. 353 113 40 CH Abbreviations of classes are explained on pages 44 and 45. 41 Ground Sampling It was decided that probability (point) sampling techniques would be used for determination of the number of trees per acre, diameter growth, and bark thickness values in different types. Only 98 point samples were distributed to the different strata. In addition to these, the existing permanent sample points and temporary plots from the A.&L. part of the Research Forest (Bajzak, 1960) were used to furnish the required data for the stand table projection purposes. The numbers of those types sampled were selected using a random number table. The sample centre points were located measuring f u l l chain lengths from a clearly distinguishable point v i s i b l e on the photograph, f a l l i n g in or close to the type. The bias from personal judgement was thus eliminated, and reasonable randomness in the location of the sample points was achieved. For the determination of trees f a l l i n g into the sample, and tree height measurements, the Austrian-made Spiegel relascope was used. It was found to be a very convenient, accurate and handy instrument, although the optical distance measurement in old growth stands was not very practical. For checking "border trees", Stage's (1959) cruising computer was used, which was also found convenient for the rapid calculation of tree heights. The role of the Spiegel relascope in the sampling was 42 simply to determine the trees which had to be measured. Then the diameter of the selected trees was measured with a diameter tape, and recorded to the nearest tenth of an inch. A l l trees larger than 3.0 inches at breast height were measured. For age, diameter growth, and bark thickness determina-tions, increment borers were used. Every fourth tree in the plot was bored. Measurements were recorded to the nearest hundredth of an inch, for both the increment core lengths and bark thicknesses. Decayed, or partly-living boles (as was common on cedars) were not bored. The following headings were used on the t a l l y sheet: Type No.: B.A. Factor: Date: Spec. D.B.H. Cond. Crown Double 10 yrs. 20 yrs. Age at Height class class bark growth growth B.H. thick-ness Species symbols used in the inventory are l i s t e d below: Symbol Species F Douglas f i r H Western hemlock, or hemlock C Western red cedar, or cedar Cy Yellow cedar B Abies species D Red alder PI Lodgepole pine Pw White pine 43 Under the heading of condition class (cond.class) the following were recorded: 1 l i v i n g tree, 2 a dead tree (died within the last five years). Trees that died before 1956 were not included in the cruising. Four different crown classes were also distinguished as: 1 dominant, 2 codominant, 3 intermediate, 4 suppressed. Heights (Ht.) were measured to the nearest foot. It may be of interest to note the r e l i a b i l i t y of photo e s t i -mates and compare them with the results obtained by the ground measurements. Species composition estimates were correctly recorded (f a l l i n g within the same type group) 88 per cent of the time, while age class determinations were 91 per cent correct in compari-son with the ground checked types. Height measurements, however, in most cases showed a great variation on the photographs as well as on the ground. Naturally, ground estimates, in a stand with widely variable heights, taken from an inadequate number of samples, cannot be considered as a sufficient base for comparison. Photo estimates of average stand heights in this situation should provide a more reliable, but slightly conservative, source of information for stand site index calculation purposes. 44 In this particular case, after ground checking, the measure-ments taken from the aerial photographs were corrected and used for site index determination. Calculations Having finished the photo and ground sampling, the necessary calculations for the stand table projection process had to be carried out. The method of the stand table projection was that described in detail by W. H. Meyer (1952). The required data are: Number of trees per acre, Mortality ratios, and Periodic diameter growth by diameter classes. The stand table projections were carried out only for the main species, namely, Douglas f i r , hemlock, and cedar. Method of Calculating the Number of Trees per Acre. and Mortality Rates Because some of the allowable cut methods required separate data by age, site, and condition classes, i t became necessary to select trees by species for the following age and site classes: Old growth, good site (O.G.G.) Old growth, medium site (O.G.M.^  Old growth, poor site (O.G.P.) Second growth, good site (S.G.G.) Second growth, medium site (S.G.M.) Second growth, poor site (S.G.P.) 45 Second growth, low site (S.G.L.) Planted (PL.) Hardwood (HW.) Although in the young growth (Y.G.) stands the data given by Bajzak (1960) were not similar to the site classes required for this work, his good, medium and poor stocking classes could be f i t t e d into the present site classification. His nomenclature has been kept, but i t should be noted that i t means stocking classes here, and not site classes. Young growth, good (Y.G.G.) Young growth, medium (Y.G.M.) Young growth, poor (Y.G.P.) Prior to computer calculations on the Alwac III-E a l l data for the computation of the number of trees and for further sorting had to be transferred to numerical symbols. Species codes F i r (1), H (2), C (3) , diameter at breast height in inches, codes defining whether the tree was alive (1), or had died within the last five years (2), and the horizontal point factor (H.P.F.) which is equal to 183.346 times basal area factor (Grosenbaugh, 1958, p.16), were typed, starting with the species code in each line. Simultaneously, these data were automatically punched on a tape to make the data readable for the machine. When calculating, the computer took in a row of data and executed the following 46 equation: D Z where N i s number of trees per acre, H.P.F. is horizontal point factor, and D is diameter at breast height. The theoretical base of these calculations i s inherent to the point sampling theory: "It must be remembered that point-sampled trees are not sampled proportionally to their frequency as plot-sampling would do. Hence, their basal areas, volumes, frequency, etc. should not be given the same equal weight as in plot-sampling. Instead, before any further calculations are made, each point-sampled tree should have i t s basal area, volume, frequency, etc. weighted inversely as i t s probability of being sampled. Dividing each sample-tree basal area, volume or frequency by i t s own basal area does this." (Grosenbaugh, 1955, p.19.) Finally, "blow up" factors or multipliers are needed to convert point sample ratios to a per acre basis. The horizontal point factor (H.P.F.) assumes that the denominators of the ratios w i l l be tree diameters in square inches. (This constant i s called basal area factor, when denominators of the ratios are tree basal areas in square feet.) After computer calculation of the number-of-trees-per-acre value, the sorting of the different tree species into 2-inch 47 diameter classes was carried out. The summation of the number-of-trees-per-acre values f a l l i n g into the same diameter class within a type group was done by hand, as well as other calcula-tions after this point. To obtain the f i n a l value of the number of trees in a diameter class for an age and site class, the sum obtained this way had to be divided by the number of point samples f a l l i n g into that type group. In a similar way the number of trees per acre that died within the last five years was calculated. These latter values had to be multiplied by two, to obtain ten-year mortality. From these two number-of-trees-per-acre values, mortality ratios were easy to get, by dividing the number of dead trees per acre by the number of li v i n g trees per acre. These values appear in Tables 8, 9 and 10. Some indication of the v a r i a b i l i t y of the mortality e s t i -mates can be given by showing the minimum and maximum estimates of number-of-trees-per-acre mortality during the past decade, in the various forest type classes. For Douglas f i r , hemlock and cedar species, mortality ranges per acre by forest type classes are presented as follows: 48 TABLE 7 MINIMUM AND MAXIMUM NUMBER OF DEAD TREES PER ACRE BY SPECIES AND TYPE CLASSES Type No. of dead trees per acre Number • of Minimum Maximum plots or sample F H C F H C points O.G.G. 0 0 0 3.87 216.51 65.19 14 O.G.M. 0 0 0 4.61 482.17 358.10 33 O.G.P. 0 0 0 0 255.52 40.63 13 *S.G.G. 2.3 3.1 6.8 28.2 87.50 62.50 5 *S.G.M. 0 2.3 0 61.50 84.10 50.00 15 *S.G.P. 2.1 50.0 2.5 30.00 87.50 17.50 3 Y.G.G. 0 0 0 0 126.88 0 100 Y.G.M. 0 0 0 0 83.86 0 96 Y.G.P. 0 0 0 0 0 0 72 * Data taken from permanent sample plots. The values clearly indicate that hemlock has the largest mortality range among the species considered. In the old growth stands this mortality was concentrated on the smaller diameter trees (approximately 0 - 1 6 inches). The mortality of the Douglas f i r was low in a l l stands. It must be noted that in the second growth stands, as well as in the young growth stands, about 80 per cent of the existing white pines died within the last five years, and the few remaining l i v i n g trees appear to be unhealthy or dying. 49 TABLE 8 NUMBER OF TREES PER ACRE (NT) AND 10-YEAR MORTALITY RATES (MR) BY AGE AND SITE CLASSES FOR DOUGLAS FIR D.BoH. in . OoG.G, NT MR OoG.M. NT MR O.G.P. NT MR S.G .G. S oG0 Mo S.G.P. S *G .L. Y<> G «G. Y.G.M. NT MR NT MR NT MR NT MR NT MR NT MR 0.47 895.28 7.11 7.05 6027 0.45 8o05 0.23 231045 5o24 5.00 13.16 0.56 3.18 0.17 10o35 0.11 162o14 3.09 0.79 0.01 10o22 0.06 16.03 0.04 - 2.55 1.05 11.20 0.21 3.99 0.03 4o59 - 2.01 0.26 2052 0.01 10.09 0.02 11.07 - 0.81 0.26 2o81 - 14.56 0.04 = - 0.13 5o39 0.20 5o82 - 2.08 - 0.13 1.06 - 2.51 - 1.77 - 0.13 8.35 - 1.27 0.84 - 3.96 1.29 - 0o60 lo20 2.05 - 0.22 1.37 - 0.20 1.53 0.35 0.33 0o84 - 0.13 - - 0.12 Y.G.P. NT MR 4 6 8 10 12 14 1.26 -16 18 20 1.92 0?53 22 24 0.47 26 0.41 0.48 28 0c62 0.29 30 1.16 0.28 0,51 32 IcOl 0.22 34 1.36 0.39 36 0„62 0.17 38 0.19 -40 1.94 0.41 42 0.95 44 0.40 0.28 46 0.31 0.11 48 0.18 0.05 50 0.31 0.05 52 0.15 0.04 54 0.09 -56 0.10 0.04 58 0.27 0.10 60 0.33 62 0.07 64 0.20 66 0.18 68 70 0.10 0.05 72 74 0.05 76 78 90 0.14 0.91 0.75 0.52 0.81 0.38 0.92 0.23 0.15 4.17 2.92 2.08 0.42 0.42 0.09 0.07 0.07 0.06 50 TABLE 9 NUMBER OF TREES PER ACRE (NT) AND 10-YEAR MORTALITY RATES (MR) BY AGE AND SITE CLASSES FOR WESTERN HEMLOCK DoB .Ho OoG o G. O.G. Mo O.G S. G o G. S .G o M. S.G «P p S.GoL. Y.G.G. in. NT MR NT MR NT MR NT MR NT MR NT MR NT MR NT MR 4 6.69 1.00 64.80 0.31 172.02 0.10 0.62 61.23 0.34 196.50 0.39 63.80 0.07 6 18.29 - 26.60 0.14 17.38 - 12.32 0.20 57.45 0.13 117.25 0.22 30.10 0.14 8 3.99 - 14.54 - 13.05 - 30.06 0.30 22.24 0.04 79.04 0.07 14.27 10 5.14 - . 5.70 - 21.32 0.12 17.72 0.08 16.00 - 37.60 0.01 6.58 0.12 12 2«13 1.00 6.36 0.10 5.92 0.34 10.74 - 27.16 - 18.71 0.17 1.88 14 6.82 0.37 5.43 - 5.52 0.55 5.84 - 12.79 - 9.08 - 0.81 16 6o50 - 3.31 - 9.17 - 3o58 - 6.51 - 2.35 - 0.26 18 4o81 - 4.05 - 6o07 0.14 - - 3.21 - - - 0ol3 20 2,66 - 1.91 - 3o91 - - - 2.93 22 1.66 - 3.48 0.07 2o36 0.23 - - 0.40 24 0.24 - 3.22 - 0o92 - 0.76 - 0.71 26 0.22 - 2.27 0.07 0.82 - 1.68 - - - 0o49 28 1055 0.10 1.81 - 1.42 - 0.29 - - - 0.43 30 0.58 - 0.84 - 0o61 - 0.26 32 0.27 - 1.40 0.07 0.28 34 1.16 - 0.58 0.47 0.73 36 0.51 - 0.43 0.42 38 0.47 - 0.38 0.21 40 0.67 - 0.21 - 0.17 - - - 0.12 42 0.61 - 0.19 44 0.54 - 0.35 46 0.13 - 0.11 48 0.34 - - - 0.12 Y.G.Mo NT MR Y»G. P. NT MR 21.85 3.03 2.46 0.02 0.06 11.67 4ol7 0.42 0.05 0.09 51 TABLE 10 NUMBER OF TREES PER ACRE (NT) AND 10-YEAR MORTALITY RATES (MR) BY AGE AND SITE CLASSES FOR WESTERN RED CEDAR DTB?H 0 O.G. G. O.G. Mo O.G. p. S o G o G. S 0Go M. S • G. P o SoG.Lo Y 0' NT MR NT MR NT MR NT MR NT MR NT MR NT MR NT 4 14.51 - = - 110.40 0.17 146.77 0.19 241.70 - 56.40 6 5.35 - - - 5.92 - 25.33 0o28 56.59 0.09 57.29 0.31 21o90 8 - 1.00 10.11 - 20.95 - 14.71 0.21 19.26 0.02 49.50 7.11 10 1.35 - 1.31 0.27 8014 0.38 27.01 - 13.33 0.02 23.68 2.95 12 - - 2.78 - 23.87 0.17 7.90 - 7.30 - 9.33 0.94 14 1.50 - 5.50 - 10.31 - 2.33 - 3.93 - 2.51 0.40 16 1.81 - 2.65 0.31 15.15 - 3.74 - 5.72 - 1.17 0.27 18 - - 5.08 0.14 7.56 - 3.05 - 5.45 20 - - 2.79 - 11.26 - 0.57 - 1.65 - 0.89 22 1.43 0.36 2.26 - 5.26 - 0.92 - 2.07 - 0.66 24 0.23 - 2.16 - 2.46 - - - 1.05 - 0.59 26 1.53 0.13 3.55 - 2.47 - - - 0.63 28 0.18 - 4.65 - - 1.00 - - 0.52 30 0o28 0.54 2.47 - 1.25 - - - 0.78 32 0.13 - 3.31 0.03 0.28 34 0.78 - 2013 - 0.73 - - - 0.18 36 0.60 - 1.89 - 0.22 - - - 0.15 38 0.81 - 1.00 • - 0.19 - - - 0.15 40 0.67 - 1.26 - - - - - 0.12 42 0.51 - 0.85 - - - - - 0.12 44 0.28 - 0.36 - - - - - - 0.11 46 0.55 - 0.42 48 0.23 0.96 0.53 - - - - - 0.09 50 0.16 - 0.09 - - - 0.57 - 0.08 52 0.35 - 0.12 - 0.10 54 0.18 - 0.15 - - - 0.16 - 0.07 56 0o09 - 0.14 - - - - - 0.07 58 0.20 - 0.07 0o43 - - - - 0.06 60 0.18 - 0.12 62 0.07 64 0.25 66 0.12 68 0.06 - 0o02 70 -72 - - 0.02 74 -76 -78 0.04 - - - - - - - 0.03 94 - - 0.01 GoGo YoG.M. Y.GpP o MR NT MR NT MR 14.74 - 9.58 2,63 - 4.58 0.80 - 1.25 0.53 - 1.25 52 For the A.&L. part of the forest the number of trees per acre of the good, medium and poor stocked types were taken from Bajzak's thesis (1960). The mortality rates were based on a mortality cruise carried out by the author during the summer of 1961. Mortality rates for the second-growth stands obtained from point samples were not used; instead, data available from permanent sample measurements were employed. Since permanent sample plots covered a wide range of site classes within the second growth type, a selection of the plots had to be carried out, to sort these plots into the presently used site classes. After sorting, the required mortality rates (M.R.) were obtained from the corresponding age and site groups of the present c l a s s i -fication and substituted for the incomplete mortality estimates of the recent cruising. Method of Calculating Future Decadal Diameter Growth Giving consideration to a number of assumptions, f i n a l l y the method which assumes linear growth rate in basal area was accepted. This growth calculation method was not previously used because of the large number of calculations required, but with the ALWAC III-E electronic computer, the method can be used successfully. The derivation of the formula used, which combines the approaches of Stage (1960) and Spurr (1952), is presented as follows: 53 If the following symbols are used: present diameter at breast height outside bark, d ^ diameter at breast height outside bark 10 years ago, S diameter at breast height outside bark 10 years hence, present diameter at breast height inside bark, and d ^ diameter at breast height inside bark 10 years ago, and assume that the basal area growth in the past 10 years w i l l be equal to the future basal area growth, then: 2 2 2 2 D , - d , = - D : ob ob ob 2 2 2 hence 8 = 2D , - d , ; ob ob ' 2 2 D 2 but d , = d., 6b ob ib —7T~ 9 U i b ob (assuming that the —s— ratio i s constant), then ib 2D2, - d 2 V - D . \ ll - ^ ob ib D2 ob ib D., ib v y i b Finally the 10-year-diameter growth outside bark i s : S - D , - D . \ 2-1 l i b ] - 1 Using this equation, the future 10 years' growth for each sample tree was calculated. An attempt was made to f i t a regres-sion equation to the measured data to find future diameter growth for any given diameter, but the equations did not show s i g n i f i -cant relationship to the present diameters, nor to the crown 54 classes. Consequently future diameter growth values were plotted against diameters for each species within each type group and freehand curves were f i t t e d to them. Ten-year-growth data taken from these curves are shown by diameter classes in Table 12. Approximate estimates of deviations and standard error of estimates of diameter growth are shown in Table 11. In this table the average and the maximum deviations of the actual growth from the curved values appear in per cent, and the estimated standard error in inches ( i . e . , the limits within which two-thirds of the points f e l l ) . ESTIMATES OF AVERAGE AND MAXIMUM DEVIATIONS AND STANDARD ERRORS OF ESTIMATE OF DIAMETER GROWTH BY SPECIES, AGE AND SITE CLASSES TABLE 11 DEVIATION  Avg;. Max. S.E.E. In. No. of trees Species Type F O.G.G. F O.G.M. F O.G.P. H O.G.G. H O.G.M. H O.G.P. C O.G.G. C O.G.M. C O.G.P. F S.G.G. F S.G.M. F S.G.P. H S.G.G. H S.G.M. H S.G.P. C S.G.G. C S.G.M. C S.G.P. 40 83 45 141 50 150 55 148 60 90 35 73 45 132 50 100 55 110 36 125 36 65 31 63 20 60 25 43 40 110 23 50 40 50 20 43 .60 .50 .50 .45 .40 .10 .45 .37 .65 .50 .67 .32 .45 .40 .25 .20 .80 .25 40 53 22 26 19 5 29 75 22 44 23 18 20 24 16 8 22 12 55 TABLE 12 PREDICTED FUTURE 10-YEAR DIAMETER GROWTH IN INCHES BY DIAMETER, AGE AND SITE CLASSES, AS TAKEN FROM GROWTH CURVES TYPE O.G.G. O.G.M. O.G.P. S.G.G. S.G.M. S.G.P. Y.G.G. Y.G.M. Y.G.P. SPEC. F H C F H C F H C F H C F H C F H C F H C F H D.B.H. 10-YEAR DIAMETER GROWTH IN INCHES  ____________________________ ,— , m . 4 - 0.15 - - 0.20 - - 0.37 0.38 - 0.75 0.33 0.40 0.60 0.74 4.11 3.61 5.94 2.95 3.49 5.68 3.32 2.99 4.60 6 - 0.17 0.48 - 0.32 0.34 - 0.48 0.46 - 0.69 0.33 0.54 1.00 0.35 0.42 0.70 0.76 4.36 3.71 6.11 4.20 3.59 5.85 3.57 3.00 4.77 8 - 0.22 0.62 - 0.49 0.42 - 0.59 0.55 0.70 0.80 0.47 0.56 1.18 0.44 0.46 0.83 0.80 4.60 3.81 6.28 4.44 3.69 6.02 3.81 3.19 4.94 10 - 0.30 0.80 0.66 0.51 - 0.72 0.65 0.88 0.95 0.75 0.61 1.38 0.75 0.52 0.93 0.86 4.85 3.91 6.46 4.69 - 6.20 4.06 = 5.12 12 - 0.44 0.94 - 0.82 0.62 - 0.85 0.76 1.10 1.09 1.12 0.70 1.58 1.12 0.60 1.14 0.94 5.09 4.01 6.63 4.93 - - 4.30 14 0.87 0.61 1.03 - 0.97 0.75 - 0.97 0.85 1.40 1.24 1.48 0.85 1.76 1.48 0.70 1.31 1.04 5.34 4.10 6.80 5.18 16 0.95 0.86 1.06 - 1.10 0.86 - 1.04 0.91 1.75 1.34 1.85 1.15 1.90 1.75 0.81 1.42 1.18 5.58 4.20 6.98 18 1.04 1.00 1.07 - 1.17 0.96 0.28 1.05 0.96 2.05 1.37 2.15 1.58 1.99 1.91 0.95 1.46 1.34 5.83 4.30 20 1.10 1.02 1.06 0.20 1.21 1.02 0.32 0.98 0.98 2.25 1.35 2.38 1.85 2.02 1.98 1.12 1.41 1.42 6.08 22 1.15 0.99 1.05 0.21 1.23 1.05 0.37 0.90 0.96 2.38 1.29 2.50 1.95 2.00 1.95 1.23 1.30 1.37 24 1.17 0.91 1.02 0.23 1.23 1.07 0.42 0.82 0.93 2.47 1.20 2.49 li98 1.96 1.83 - 1.16 1.26 26 1.18 0.83 0.99 0.26 1.22 1.07 0.49 0.75 0.87 2.50 1.12 2.42 1.95 - 1.67 - 1.00 1.11 28 1.17 0.76 0.96 0.28 1.19 1.05 0.55 0.70 0.81 2.40 1.06 - 1.89 - 1.52 - 0.85 30 1.16 0.70 0.94 0.31 1.15 1.02 0.62 0.66 0.75 2.44 1.00 - 1.80 - 1.35 - 0.71 32 1.13 0.65 0.91 0.35 1.10 0.97 0.65 0.62 0.69 2.35 0.95 - 1.74 - 1.18 34 1.07 0.60 0.89 0.39 1.02 0.92 0.65 0.59 0.62 2.22 - - 1.68 36 1.02 0.56 0.87 0.44 0.95 0.88 0.62 0.57 0.58 2.11 - - 1.62 38 0.97 0.54 0.85 0.48 0.90 0.85 - 0.55 0.54 2.01 - - 1.58 40 0.92 0.52 0.83 0.52 0.84 0.82 - 0.54 0.50 1.92 - - 1.53 42 0.88 0.50 0.82 0.56 0.80 0.80 - 0.52 0.47 1.84 - - 1.50 44 0.84 0.50 0.80 0.59 0.75 0.77 - 0.51 0.45 1.77 - - 1.47 46 0.81 0.50 0.78 0.61 0.72 0.75 - 0.50 0.42 - - - 1.44 48 0.77 0.50 0.77 0.63 0.70 0.73 - 0.40 0.40 - 1.42 50 0.75 0.50 0.75 0.64 - 0.71 - - 0.39 - 1.39 52 0.72 - 0.74 0.65 - 0.70 - - 0.38 - 1.37 54 0.69 - 0.72 0.65 - 0.68 - - 0.38 - 1.34 56 0.67 - 0.71 0.65 - 0.67 1.32 58 0.65 - 0.70 0.65 - 0.66 60 0.63 - 0.68 0.64 - 0.65 62 0.61 - 0.67 0.63 - 0.65 64 0.60 - 0.65 0.62 - 0.64 66 0.58 - 0.64 0.60 - 0.64 68 0.57 - 0.62 0v58, - 0.63 70 0.56 - 0.61 0.56 - 0.62 72 0.55 - 0.59 0.53 - 0.62 74 0.54 - 0.58 - - 0.61 76 0.53 - 0.56 - - 0.60 78 0.55 - - 0.60 80 0.54 - - 0.59 94 0.55 96 0.54 56 The growth values of the young stands were not based on the calculations presented above, but were evaluated from the equations for them, taken from U.B.C. Forestry Bulletin No. 3, Table 37. The regression equations are: R.G. - 10.0 + 0.10 S.I. + 0.78 D.B.H., F R.G.„ = 11.3 + 0.08 S.I. + 0.31 D.B.H., n R.G.C = 13.4 + 0.17 S.I. + 0.55 D.B.H.; where R.G. is radial growth of Douglas f i r in millimeters for the past five years, S.I. i s site index in feet at hundred years of age, D.B.H. i s present diameter at breast height in inches, R.G. i s radial growth of western hemlock in millimeters H for the past five years, and R.G. i s radial growth of western red cedar in millimeters ^ for the past five years. The equations transformed to give diameter growth in inches for the past ten years appear as follows: D.G. = 1.57 + 0.0158 S.I. + 0.1228 D.B.H., F D.G. - 1.78 + 0.0126 S.I. + 0.0488 D.B.H., H D.G. = 2.11 + 0.0268 S.I. + 0.0866 D.B.H.; C where D.G. i s diameter growth at breast height in inches for the past ten years. Stand Table Projections Future volumes by species, age, site and condition classes were essential for later calculations and were calculated using the stand table projection method described in detail by W. H. Meyer (1952). 57 Local volume tables, constructed for the Research Forest, were used for the estimation of present and future gross cubic foot volumes. In these tables, volumes for different species of various maximum heights (H m^) a r e given by one inch diameters. The following values of H were used: & max Type, H J t r max S.G.G. 180 S.G.M. 160 S.G.P. 80 S.G.L. 60 Y.G.G., Y.G.M., Y.G.P. 240 Determinations of the H classes were based on actual max height and diameter measurements. The H/D line i s nearly straight for the young age class. No H__„ was truly suited, but H m a x 240 was f i n a l l y chosen. For old growth stands, having only one local volume table, for each species, determina-tions were not necessary. Finally cumulative present and future volumes were calculated for the 3.1, 9.1, 11.1 and 13.1-inch minimum diameter class limits (Tables 6, 13, 14), which are those used as the bases of Fligg's (1960) tables. TABLE 13 DATA SUMMARY FOR THE RESEARCH FOREST D.B.H. Limit i n . 3.1 9.1 11.1 13.1 Actual Gross Volume Actual Net  Volume CUBIC FEET Predicted  Gross Volume 50,528,733 38,748,893 41,947,259 35,660,343 55,838,019 38,065,336 32,634,095 49,069,255 33,891,138 29,018,271 43,297,373 Growth Factor 1.331148 1.289079 1.277542 1 vr. Compound  Growth % 2.90 2.57 2.48 Stocked Avg. Area acres yrs, 9,282 70 Average  S.I.(F) f t . 124 Average  Species  Comp. HF 00 59 Rotation Age The determination of the rotation for the University Research Forest has been dealt with by D. Littleton, A. Strother, H. Eidsvik and T. Jeanes (1957), University Research Forest Committee (1959), B. Iverson and R. G. Richards (1959), and R. C. Robertson and J. N. McFarlane (1960). For this reason, in this work, calculations to determine the rotation age were not made, but the recommended rotation age of 80 years for the average site of the Research Forest was accepted. Miscellaneous Calculations In addition to the calculations mentioned above, other information necessary for use in the various formulae and methods were determined. The calculations of the number of l i v i n g and dead trees per acre were based on the "blown up" number of trees-per-acre values of the individual trees, previously calculated and sorted by the electronic computer. The sum of the numbers of trees-per-acre values in each diameter class was divided by the number of point samples taken in that age and site class, to supply the f i n a l number of trees-per-acre values for the stand table projection. The ratio of the number of trees per acre that died within the last ten years and the number of l i v i n g trees per acre in a diameter class gave the desired mortality ratios. Further valuable information, such as actual and 60 future growing stocks, and simple and compound growth rates, including and excluding ingrowth, were obtained by following the stand table projection method described by W. H. Meyer (1952). Some of the formulae (W. H. Meyer, Grosenbaugh) necessitated the calculation of the total volumes, volume increments, simple and compound increment rates excluding ingrowth, of stands presently over rotation age. To obtain these data, a l l samples representing stands over 80 years were selected by age and site classes. After selection, using the newly-obtained number of trees and mortality rates, stand table projections were carried out, which supplied the raw data for the calculations of above-mentioned information. The transformation of gross cubic foot values to merchantable cubic feet required the use of Brit i s h Columbia Forest Service reduction factors which were combined to include corrections caused by decay, waste, and breakage, and by intermediate u t i l i z a t i o n practices. These reduction factors are shown separately for the various species by tree and diameter classes in the Forestry Handbook (1959). Applying these tables to the condition of the U.B.C. Research Forest, i t was reasonable to assume that the reduction factors given under tree class one (trees with no vi s i b l e signs of decay) are suited to second growth and young stands, while the reduction factors under tree class two (trees bearing v i s i b l e signs of decay) w i l l apply better to the condition of the older growth stands. Regarding 61 merchantable volume factors, i t was assumed that intermediate u t i l i z a t i o n practices w i l l apply to the Research Forest. When obtaining net volumes, these factors were multiplied by the volumes appearing in the corresponding diameter classes of the stand tables, and summed to the same minimum diameters as the gross volumes. The ratio of the sum of the net cubic foot volumes to the gross volumes at each minimum diameter limit was used as the reduction factor. These factors are shown for old growth and second growth stands in Table 14. It was necessary to know the average species composition of the age and site classes. The most convenient way to approach this problem was to select the McBee punch cards according to their species composition, and sum their areas. The species composition occupying the largest area of the type was chosen as the representative type of the age and site class and was applied when using the empirical yield tables. Other calculations, such as average growth and mortality rates, average number of trees, volume ratios, desired growing stock volumes, reduced areas, etc., are described in detail with descriptions of the method or formula in which they were used. The r e l i a b i l i t y of the estimated volumes was tested by a comparison which was made between the actual mean yields har-vested and recorded during the past, and the estimated yields obtained from the recent survey. The result of this comparison showed a 9.72 per cent underestimate of the recently-estimated 62 TABLE 14 MISCELLANEOUS DATA REQUIRED FOR THE ALLOWABLE CUT CALCULATIONS D.B.H. V M . V m Ga;k;V LtrniT M e r c h T o t a l in. cu.ft. cu.ft. cu.ft. 3 d 12,984,842 37,543,891 50,528,733 9.1 12,554,464 29,392,795 41,947,259 11.1 12,404,682 25,660,654 38,065,336 13.1 12,126,916 21,764,222 33,891,138 Gd;Vn;Gr V _ mat ^ 0 I MA I MA II \ cu.ft. cu.ft. cu.ft. cu.ft. cu.ft. cu.ft. cu.ft. 24,434,865 19,475,956 16,323,557 13,924,160 23,045,882 20,331,242 18,935,319 17,613,700 679,305 592,148 537,897 472,826 599,246 543,790 484,159 12,630 12,479 12,200 6,959 6,452 5,823 13,234,343 10,365,840 8,714,018 G o Y110 cu.ft. Y 123 cu.ft. (1.0 p ) * 3.1 9.1 11.1 13.1 0.01010 0.00934 0.00875 0.033115 0.028908 0.027754 7,935 7,398 6,890 6,301 9,022 8,685 8,103 7,487 1.33115 1.28908 1.27754 (1+%) 1.100997 1.093447 1.0875149 % s t;o.o P 0.0097 0.0090 0.0084 0.0290 0.0257 0.0248 V ;K m cu.ft. 47,267,000 39,138,346 35,347,614 31,395,266 Yr Merch. Red. Fact.OoG. 6119 0.57852 5250 0.58122 4774 0.58064 4290 0.57947 Merch.Red.  Fact.S.G. 0.61106 0.76891 0.77965 0.78125 NOTE: COLUMN HEADINGS ARE IDENTICAL TO THOSE USED IN FORMULAE AND ALL TERMS ARE DEFINED IN EXAMPLES GIVEN LATER. 63 volumes, when the volume per acre at a minimum diameter of 9.1 inches was compared to the average actual cutting volume per acre. Naturally a discrepancy of this scale can be due to the difference in the actual and the estimated losses caused by waste, breakage and decay, or in minor differences in site index or stocking. It can be r e a l i s t i c a l l y assumed that in the case of the Research Forest the losses through breakage and waste were smaller than those indicated by the B.C. Forest Service for an average logging operation. TABLE 15 A COMPARISON OF ACTUAL AND ESTIMATED OLD GROWTH YIELDS Estimated Actual Difference D.B.H. Vol./ac. Red. Vol./ac. Vol./ac. Net  Type limit Gross fact. Net Net cu.ft. per cent in. cu.ft. cu.ft. cu.ft. O.G.M. 9.1 13,307 0.58122 7,734 8,486 752 9.72 The actual net cubic foot volume per acre is an average, calcu-lated from the recorded board feet harvest volumes of the timber sales 3, 12, 13, 14, 16A, 16B, 17, 19, 22, 23, 26, using a con-version factor of 0.1666. These sales were mostly in old growth and covered about 504 acres. In second growth stands data published by Smith and Ker (1959) gave the bases for volume comparison. In this publication average volumes of 87 plots covering a total of 28 acres were given, together with the average age, site index and other data. The comparison showed that the recently estimated weighted average 64 volumes in the second growth types were 9.6 per cent higher than the average volumes shown by Smith and Ker. However, i t must be noticed that the average age of the plots used by Smith and Ker (66 years) was considerably lower than the one estimated in 1961 (80 years). On the other hand, the average site index given by Smith and Ker was higher by 11 feet than the recent estimate. TABLE 16 A COMPARISON OF SECOND GROWTH VOLUMES AS ESTIMATED IN 1959 (SMITH AND KER, 1959) AND IN 1961 D.B.H. Volume per acre Difference  Type Limit (1959) (1961) Vol./ac. Per cent  i n . cu.ft. cu.ft. cu.ft. S.G. 3.1 8,623 9,407 781 9.06 Total volumes of Douglas f i r , hemlock, and cedar on the Forest might be increased by 16, 15, 14 and 12 per cent corres-ponding to 3.1, 9.1, 11.1 and 13.1 inches minimum diameter limits, i f areas occupied by deciduous species are added. Not more than a further 5 per cent would be in coniferous species other than Douglas f i r , hemlock, and cedar. 65 ALLOWABLE CUT CALCULATIONS Under this t i t l e , for each method or formula a detailed evaluation w i l l be presented and w i l l apply to a minimum diameter limit of 11.1 inches. The results for the other minimum diameter classes together with the 11.1 inch class appear in Table 20. Area Regulation For this method, a series of calculations had to be made. It was assumed that the present ratio of the actual volume to the empirical volume w i l l remain the same in the S.G.G., S.G.M. and S.G.P. stands u n t i l cutting. The method used is described in detail below. Before calculations could begin, the types had to be listed in the order of preference for cutting. The logical order was to cut the overmature stands, cutting the best sites f i r s t , ensuring that these good sites w i l l return f i r s t to production from the present stagnant or decadent stage. In second growth stand, however, the reason for cutting the better sites is different. Here the poorer sites need a longer rotation to produce the same size of wood as a better site.could in a shorter rotation period. Concerning the younger age classes, i t was assumed for the purpose of these calculations that within the next ten years the deciduous stands w i l l be cut, and replaced by establishing a FH 66 type stand, which has a -5 year average present age. Having decided the order of cutting, the corresponding average ages and actual areas in acres had to be shown. The next step was to reduce the actual areas to standard productivity. For this purpose a FH medium type was chosen as standard. The required reduction factor (RF) then becomes: Volume of actual type at approximate rotation age Volume of HF medium type at approximate rotation age . For old growth stands the present volume was substituted into the numerator, while in the denominator the empirical volume of HF medium type at 375 years was inserted. For second growth stands, with the exception of second growth low site class, the empirical yield for cutting age was multiplied by the actual volume ratio (VR), t m present volume VR = r . .— z , empirical volume to obtain correct future volumes. The volume obtained this way then had to be divided by the volume of the HF medium stand to give a r e a l i s t i c reduction factor. Knowing the reduced acre values of each condition class, the determination of the allowable cutting area was now easily calcu-lated by summing up the reduced areas and dividing the sum by the rotation age (131.325 reduced acres). The duration of the cut within a type can be computed i f the area of the type i s divided by the yearly cutting area. If this duration of cut i s added to the present age of the next 67 type, the age when cutting begins is obtained. The average cutting age for the second type now is given i f half of i t s cutting duration time i s added to the age when cutting begins. At the average cutting ages, the corresponding empirical volumes are read from the empirical yield table and multiplied by the present area of the type. This value w i l l be the f i n a l yield when the type w i l l be cut. (Obviously the empirical volumes for S.G.G., S.G.M., S.G.P. are corrected by the present volume ratio.) If the sum of the f i n a l yields at cutting age is divided by the rotation the average yearly cut is readily obtained. Detailed calculation of the method is shown in Table 17. The calculation clearly indicates the large yearly volume differences, i f the given cutting sequence were followed. By this method the old growth types would be removed very quickly (8 years) during which period large yearly harvest volumes would appear (approximately 1,560,000 gross cu. f t . per year). After this period the yearly cutting volume would drop sharply, to the v i c i n i t y of 70-80,000 cu. f t . per year, with occasional fluctuations, averaging for the whole rotation period a figure of 847,000 cu. f t . per year. The above calculation presupposes that the deciduous types w i l l also be cut and regenerated within the next 10 years. (The volumes presently standing on these types were not taken into consideration.) TABLE 17 EXAMPLE OF AREA REGULATION Act. Avg, Yield Avg.T Act. Age per ac. Age Area Red. When When Tot.Exp. Yrs. to Cut Yearly Spec. Red. Area Cut Cut Yield Yrs. Cut Type Comp. Site yrs. ac. Fact. ac. yrs. cu.ft. cu.ft. Per. Cum. cu.ft. O.G.G. HF G M 159 1.118 178 M 13,493 2,145,387 1.4 1.4 1,532,419 O.G.M. CH M M 671 1.093 734 M 13,193 8,852,503 5.6 7.0 1,580,804 O.G.P. CH P M 164 0.711 117 M 8,578 1,406,792 0.9 7.9 1,563,102 S.G.G. FH G 70 805 1.751 1410 85 10,031 8,074,955 10.7 18.6 754,669 S.G.M. FH M 80 1885 1.784 3363 113 9,850 18,567,250 25.6 44.2 725,283 S.G.P. HF P 90 968 0.391 378 137 3,467 3,356,056 2.9 47.1 1,157,261 S.G.L• FH L 90 43 0.212 9 139 1,787 76,841 0.1 47.2 768,410 Y.G.G. HC M 30 2170 1.000 2170 87 5,783 12,549,110 16.5 63.7 760,552 Y.G.M. HC M 25 1171 1.000 1171 95 6,348 7,433,508 8.9 72.6 835,226 Y.G.P. CH P 20 335 0.481 161 95 3,127 11,047,545 1.2 73.8 872,954 PL. FH M 5 558 0.904 505 82 4,937 2,754,846 3.8 77.6 724,959 HW. FH M -5 353 0.878 310 74 4.300 1,517.900 2.4 80.0 632.458 TOTAL 10,506 67,782,693 TOTAL REDUCED AREA: 10,506 acres. YEARLY CUTTING AREA - 10,506 : 80 = 131.325 reduced acres. AVERAGE YEARLY VOLUME CUT = 67,782,693 : 80 « 847,284 cu. f t . (continued) 69 TABLE 17 EXAMPLE OF AREA REGULATION (Continued) Calculation of the Reduction Factors Yield of Emp. Yield at HF med. at Approx. Yield at Cutting Cutting Spec. Cutting Cut.age. Volume Age Age Red. Type Comp. Age(yrs) cu.ft. Ratio cu.ft. cu.ft. Fact. O.G.G. HF M 13,493 12,067 1.1181 O.G.M. CH M 13,193 12,067 1.0933 O.G.P. CH M 8,578 12,067 0.7108 S.G.G. FH 80 6,076 1.5213 9,243 5,278 1.7512 S.G.M. FH 110 7,084 1.8446 13,067 7,324 1.7841 S.G.P. HF 130 5,124 0.6492 3,226 8,510 0.3908 S .G .L. FH 140 1,914 1,914 9,021 0.2121 Y.G.G. HC 80 5,278 5,278 5,278 1.0000 Y.G.M. HC 90 5,999 5,999 5,999 1.0000 Y.G.P. CH 90 2,888 2,888 5,999 0.4814 PL. FH 80 4,774 4,774 5,278 0.9045 HW. FH 70 3,982 3,982 4,534 0.8782 Although, this way within an 80-year period a complete regularity could be achieved, the classical area method i s not flexible enough to take into consideration the changing market conditions, av a i l a b i l i t y of manpower, demand for specific log sizes, etc., and therefore the s t r i c t application of the method usually is neither practical nor economical. At the present time the area method of regulation is being applied rather flexibly on the University Research Forest. Actual area harvested is to be within 30 per cent of the allowable for any one year, within 10 per cent for a decade, and should balance in a 20-year period. There i s no doubt that i t is both simple and convenient in planning and in application. Costs of 70 operational cruising can be reduced and records can be based on scaled volumes and actual areas logged. The large volumes and values of the old growth stands currently being logged can be used to finance the high costs of road building associated with a staggered setting pattern of logging. In addition, logging of the large volumes in dead cedar trees k i l l e d by the f i r e of 1868, and the snags, chunks and logs l e f t after the original logging by the Abernethy and Lougheed company are actually considered as salvage operations. These have been scheduled to be completed by approximately 1970 and have not been entered directly into either area or volume calculations presented here. It i s to be hoped that volumes and values secured from these activities w i l l be compensated by thinnings by 1970. Areas thinned can also be excluded from area calculations provided there is reasonable assurance that values of the f i n a l crop w i l l not be diminished by thinning. Volume Control Formulae Austrian formula The only assumption that had to be made for this formula was concerned with the future or desired growing stock at the end of the rotation. It was assumed that future plantations, w i l l also use Douglas f i r seedlings. These plantations l i k e l y w i l l be f i l l e d In with natural regeneration of hemlock and cedar, to form a FH-type stand. Using the average Douglas f i r site index value (124) for the Research Forest, the 71 empirical growing stock for a FH medium type was calculated and inserted into the equation as the desired growing stock. A„ _ Ga - Gr _ n n , 38.065.336 - 16.323.557 AC » I + £ - 543,790 + — 1 1 £7j— 1 1 -815,562 gross cu. ft./year. The increment in this case is the mean annual increment of the total stand, obtained as total actual volume divided by the average weighted age. Comparing this result to the average volume value indicated by the area regulation i t appears that the two values are very similar. Hanzlik's formula Data taken from Table 14 applicable to this formula are as follows: I - 556,615 cu. f t . 80 V _ - 18,935,319 cu. f t . mat I i s the mean annual increment taken from the empirical yield table at R = 80 years for each type and multiplied by the area of the type. The values read for S.G.G., S.G.M., and S.G.P. were corrected with the present volume ratio. Because these stands are very close to the rotation age, i t can be assumed that they w i l l retain the existing ratio to the empirical values for this short period. V"mat i s the volume of stands over 80 years of age. The rotation used in this formula is 80 years. The allowable cut i s : 72 18.935.319 80 774,588 gross cu. ft./year. Although this formula i s widely used on the West Coast of North America in the Douglas f i r type, i t has the weakness that the mean annual increment of the presently young stands cannot be accurately predicted for a long period of time. Also, through improvement in silviculture and management, the mean annual increment may be far greater than that indicated in empirical yield tables. Therefore, for rough estimation i t gives a satisfactory allowable cut estimate in virgin stands, but in managed stands the answer i s usually conservative. Kemp1s formula The result of this formula can be greatly influenced by the decision of the forest manager concerning the areas which he inserts into the formula. The decision usually cannot be made simply by considering the present age class distribution because the actual stands may be of different sites, and pro-duce greater or lesser volumes than were presupposed by the creation of the formula. An approximate estimation based on size classes can substitute for the definition based on the age classes (Kemp I, II) or a standard age and site class must be chosen and the ages reduced accordingly. That i s , the volume of each actual age and site class w i l l be compared to the basic age and site class for which the corresponding age w i l l be read from the empirical yield table. 73 This way a r e a l i s t i c age class distribution for a l l the existing types and sites w i l l be obtained, and the decision of classes can be easily made (Kemp IX!). In the f i r s t t r i a l (Kemp I) the following types were included in the classes: A (area of saw timber stands) = O.G.G., O.G.M., O.G.P., A^ (area of pole timber stands) = S.G.G., S.G.M., S.G.P., S.G.L., Y.G.G., A£ (area of seedlings, saplings) = Y.G.M., PL., HW., A (non-stocked area) = Y.G.P. 3 A = 994 ac. A1 - 5,871 ac. A 2 =2,082 ac. A 3 = 335 ac, Using the average volume of O.G.G., O.G.M., O.G.P., stands MA. I = 12,479 cu. f t . per acre, the allowable cut: 7(994) + 5(5,871) + 3(2,082) + 335 _ A.L>. - 4(80) (i-,*f/y; -1,672,812 gross cu. ft./year. This indicated cut i s high compared to the other formulae. The reason for this high volume is that the per-acre yield is very large in the old growth stands. However, i f we compute the average volume of a l l stands at rotation age the allowable cut becomes more reasonable (Kemp I I ) . Using the same A values, and the average yield when stands are cut (MA..11), taken from area regulation, we obtain: 7(994) + 5(5.871) + 3(2.082) + 335 _ A.C. - 4(80) (6,452) -864,850 gross cu. ft./year. 74 The most logical approach for these stands may be the third one, suggested previously. The basic type to which a l l ages were reduced was arbi-t r a r i l y decided (HF medium). This way the selection into four age classes with the reduced ages was more r e a l i s t i c than the previous size selections. The new grouping,done by 20-year age classes, i s shown below: A ( 60+ years) O.G.G., O.G.M., O.G.P., S.G.G., S.G.M. = 2,518 reduced acres, A^ (40-60 years) S.G.P. = 968 reduced acres, A^ (20-40 years) = 0 reduced acres, A ( 0-20 years) S.G.L., Y.G.G., Y.G.M., Y.G.P., PL., HW. = 4,630 reduced acres. Here MA I was taken as the average cutting volume of old growth stands. Introducing these values into the formula: A.C. = 7(2,518) + 5(968)^ 3(0) + 4,630 ( 1 2 > „ 9 ) . 1,056,659 gross cu. ft./year. This cut is higher than those obtained by Hanzlik's or the Austrian formula, but may be j u s t i f i e d for the f i r s t 10 or 20 years to eliminate the large quantities of mature volumes. Barnes1 method When the average age of the hardwood stands was taken as -5 years, the average weighted age of the present stand calcu-lated from a l l the individual types gave the figure of 70 years. Using a rotation of 80 years, the average age should have been 75 40 years, i f the stand were normal. The discrepancy is there-fore 70 - 40 = 30 years, with which the average cutting age of the present stand w i l l have to be increased, i.e., the average cutting age w i l l become 80 + 30 = 110 years. An estimation of the yield at this age w i l l give the allowable cut for the present stands. Yields at age 110 years were read from the empirical yield tables for each age and site class, and weighted by the area of the class. The f i n a l value calculated was the average weighted yield of a l l classes at 110 years, which had to be multiplied by the yearly reduced cutting area (A ), taken from the area regulation method, to obtain a correct answer. To c l a r i f y : - If l/80th of the total actual area was taken, the average yearly cutting area would indicate a mixed, indefi-nite type, and site class. The reduced areas show an area-equivalent of the present types and sites, as i f they a l l were HF type, and medium site quality. In other words, the areas were reduced to standard productivity. The allowable cut i s : A.C. = (Aj^ (Y 1 1 ( )) - (131.325) (6890) = 904,775 gross cu.ft./year. An improvement of the method would be to use reduced ages for the determination of the average present age, instead of the actual ages. The reduced ages are obtained in a similar way 76 to that described for the Kemp III formula. These must be weighted by the appropriate areas to obtain the correct average reduced age for the whole area. By evaluating the new average age we obtain 83 years, which is 13 years more than the average age of the actual types. Hence the new estimate of the average cutting age w i l l increase also, giving the value of 132 years. At this age the yield of a HF medium site stand ( Y ^ ) i s 8 » 6 1 2 cu. f t . above the 11.1 inch minimum diameter, and the new allowable cut becomes: A.C. = (131.325) (8,612) « 1,130,971 gross cu. ft./year. This allowable cut corresponds f a i r l y well with the one obtained with the Kemp III formula. Black H i l l s formula For this formula, the following assumptions and definitions had to be made: 1. Since in the University Research Forest there is no marking practice at present, i t had to be assumed that a l l volumes w i l l be taken from the presently overmature stands. 2. V was interpreted as the volume in overmature stands M (O.G.G., O.G.M., O.G.P.) and i t was assumed that half of their volume would be cut within the coming ten years (C^ = 0.50). 3. V became the volume of a l l other stands above minimum t diameter limits. 4. It was assumed that l/8th of the volume of V t and half of i t s increment during the cutting cycle would also be cut. 77 5. The period of the cutting cycle y. was taken as 10 years. Inserting the assumed and actual values into the formula, the allowable cut became: 10.365.840 A r = 12.404.682(0.50) 4- (25.660,654 + 2 ) 0.125 1,005,804 gross cu. ft./year, which, in comparison with the other allowable cut estimates indi-cates a reasonable level of cut for the coming decade. Hundeshagen's formula On the basis of the average site and the assumed future species composition, the desired growing stock was calculated from the empirical yield table (Fligg, 1960), for FH medium site. G r = 16,323,557 cu. f t . , whereas the actual growing stock i s G = 38,065,336 cu. f t . a The ratio of these figures: fa = 38,065.336 = 2.33192. G 16,323,557 r The empirical yield at 80 years of a FH medium type stand i s : Y = 4,774 cu. ft./acre, r The empirical yield for one year, therefore, i s 4,774 = 59.675 cu.ft, 80 Hence the actual yield per acre: Y = (2.33192) (59.675) = 139.1573 cu. ft./year, a The total yield for the Forest, therefore, i s : Y (total) = 9,282(139.1573) = 1,291,658 gross cu. ft./year. a The r e l i a b i l i t y of this figure - because of the inherent 78 faults of i t s assumptions - is not very high. Though, i t might be used as an auxiliary or control for the other allowable cut estimates. H. A. Meyer's method When calculating the allowable cut with this method, the process outlined below was followed: 1. The weighted average number of trees per acre including a l l species was calculated for each diameter class. That i s , the number of trees per acre of each age and site class weighted by the actual areas they occupy. 2. The average weighted volume per acre including a l l species was computed. 3. The average diameter growth per year including a l l species (average of the data in Table 3) was calculated. 4. A regression equation was f i t t e d to the logarithmically-transformed data of the average number of trees per acre calcu-lated for the whole Forest: log N - 1.7985 - 0.05972 D.B.H., where N = number of trees per acre in diameter class, D.B.H.*5 diameter at breast height in inches. The regression equation was highly significant at the 1 per cent level. 5. Through the substitution of the appropriate values into the equation, given by Sammi (1960), the de Liocourt's quotient 79 was obtained (q • 1.3293). This value was under the shown for we 11-managed Swiss forests, and needed no reduction. 6. Knowing £ a n < i the average growth rates by diameter classes, the per cent volume increase could be read from Table 32 (Meyer, Recknagel and Stevenson, 1952). 7. The volume per cent read from the table multiplied by the volume per acre value of a diameter class shows the yearly volume increase of the class. 8. Summing up the volume increases of each diameter class up to the desired minimum diameter limit, the yearly gross volume increase of the stand is obtained. 9. Average yearly mortality in number of trees per acre was calculated by diameter classes. 10. The average volume of a tree in a diameter class was obtained as average volume per acre number of l i v i n g trees per acre* 11. The multiplication of the average volume per tree by the number of dead trees in a diameter class gave the mortality losses within that class. 12. The cumulative mortality losses subtracted froml-fcae cumulative annual volume increase figures equalled the cumulative net volume increase of the Forest in cu. f t . 13. A maximum diameter limit of 30 inches was set, beyond which a l l trees were to be cut within a predetermined period. 14. The elimination of trees larger in diameter than 30 80 inches was set to 80 years, and also for comparative purposes to 20 years. 15. During the elimination period, i t was assumed that a l l the net volume increment below 30 inches in diameter, plus l/8th (or respectively l/20th) of the volume of trees 30 inches and larger and half of the increment of this latter class, would be cut. Since the necessary information for this method was calcu-lated in merchantable cubic feet, the allowable cut obtained for the two different assumptions is also given in the same units: A.C. = 531,585 net cu. ft./year, oO A . C 2 0 = 745,858 net cu. ft./year, where A.C. = the yearly allowable cut, when the 80-year con-version period is used, and A.C. = the yearly allowable cut, when the 20-year con-version period i s used. Assuming that the cut w i l l be taken in mature stands, the gross volumes w i l l read: A.C. = 914,326 gross cu. ft./year, 80 A.C. 2 o = 1,282,876 gross cu. ft./year. The possible reason for the lower estimate in the 80-year conversion period is that the £ value might have been under-estimated as a result of the present understocked condition of the young growth stands, or because of the use of unweighted average growth rates. As a f i n a l conclusion concerning the use of the method, 81 i t might be stated that, considering the long and tiresome calculations, which are open to the risk of human error, the effort spent in obtaining an estimation of the allowable cut with this method is not j u s t i f i e d . Nevertheless, there is some value in the stand table and the growth and mortality data for their own sake as a guide to management. Von Mantel's formula In contrast with H. A. Meyer's somewhat complicated method, Von Mantel's formula, often called one of "glorious simplicity", with the substitution of only two figures, gives the following result: . „ 2(38.065.336) 0_. _ , A.C. - — 1 rQQ r *• = 951,633 gross cu. ft./year, where the figure 38,065,336 means the actual growing stock in cubic feet, and 80 i s the rotation in years. Considering the volume distribution of the Forest (Figure 2) the allowable cut indicated by this formula should be f a i r l y reasonable. However, because of the fast growth rate of the young stands, and the large areas of overmature timber in need of removal, the result might be judged somewhat conservative for the coming decade. Grosenbaugh's simple interest formula The following actual and estimated values were used in this formula: m =10 years, n =80 years, 82 V Q = 38,065,336 cu. f t . , V = 16,323,557 cu. f t . n V^, the future growing stock figure, was assumed for 80 years hence, and was read from the empirical yield table for FH stands at medium site. G„ - 0.0093, o ' G L = 0.0289; G was calculated from the increment values of stands o presently older than 80 years, whereas shows the growth rate of the entire growing stock predicted for the next 10 years. G 2 = 0.05. This figure is an estimated value of the growth rate expected over the 80-year period, and i s estimated to come from the results of improved management, silviculture (thinning, salvage, removal of slow-growing old growth stands), planting, etc. By substituting these figures into Grosenbaugh's formula, the estimated allowable cut for the next decade i s : A.C. - 38,065,336 1+80(0.05)-^;^;^ 10(0.0289) 10 1+ 2(0.00934) 1+10(0.00934) 80(0.05) 12,037,782 cu. ft./lO years, or 1,203,778 cu. ft./year. After the f i r s t ten-year period this high indicated cut would l i k e l y be reduced because most of the slow-growing stands of the Research Forest w i l l be removed. 83 W. H. Meyer's amortization formula Information needed for this formula, as applied to the Research Forest, is li s t e d and explained below: V D = 38,065,336 cu. f t . , V » 35,347,614 cu. f t . m Assuming that 80 years hence the Research Forest w i l l have the growing stock of a FH medium site (16,323,557 cu. f t . ) , and in the next decade l/8th of the volume difference of the present and desired growing stock w i l l be cut, then the future volume 10 years hence can be calculated as: The present growing stock minus l/8th of the volume difference. I.e. ir - is n « 38.065.336 - 16.323.557 _ A 1 / . V Q = 38,065,336 - g = 35,347,614 cu. f t . , where n =10 years, (l+g^* = 1.28908, ( l + g ^ = 1.0934, -8^ - 0.009, A.C. = 0.009 38 1065 1336(1.8908) / i35,347 1614 = ^ cu. ft./year. Sven Petrini's interest formulae  Compound interest (I) This formula is identical to the one which was originally devised by W. H. Meyer in 1943, and gives a slightly lower estimate of the allowable cut than the amortization formula above. Using the corresponding values of the Research Forest, 84 the following values can be substituted into the formula: (1.0p) t = 1.28908, k - 38,065,336 cu. f t . , K = 35,347,614 cu. f t . and O.Op » 0.0257. t t Here (l.Op) , k, and K are similar to W. H. Meyer's (l+g t) , V and V values respectively. The only exception i s , in this o m formula, the compound interest rate of the whole stand (O.Op) is used in the places of Meyer's g^ value, giving an allowable cut of: A.C. - 0.0257 38,065,336a.28908)-35,347,614 _ ^ & J year. Since the largest ingrowth occurs in the young stands, which at present are understocked and need to be increased in stocking, the allowable figure given by this formula may better f i t the actual situation than the improved W. H. Meyer's amortization formula. Simple interest formula (II) Using the values of the Research Forest the following figures were substituted into the formula: t «= 10 years, p = 2.8908 per cent, k - 38,065,336 cu. f t . , K » 35,347,614 cu. f t . , and tt+mn> - L28908, 85 hence, the allowable cut i s : _ 38.065.336 (1.28908) - 35.347.614 A.C. = 10 1 + 10 (2.8908) 200 + 10 (2.8908) 1,218,306 cu. ft./year, This figure, from the management point of view, is identical to the one obtained by the compound interest formula, and the fi n a l comments made previously apply to the simple interest formula as well. Area and Volume Control Methods  Area-volume computation This is a method adapted for the use of empirical yield tables, from the Reports of the West Coast Forest Procedures Committee (1950). The method starts out stating the types, present ages, and actual and reduced areas, as in the area regulation, and must be accompanied by an approximate yearly cut figure obtained from one of the allowable cut formulae. Then a preliminary estimate is obtained of the cutting age and total yield for each age and site class, in a similar way to that described in the area method. This estimate of the total yield is divided by the preliminary allowable cut figure, to see how long this volume w i l l last, i f this preliminary figure were cut each year. When half of the duration period i s added to the age when cutting starts, the sum w i l l give the f i n a l cutting age of the age and site class in question. At this age the yield is read from the empirical yield table 86 (for S.G.G., S.G.M., S.G.P., yields are corrected by the present volume ratio) and multiplied by the actual acres of the type. Finally this volume, divided by the preliminary allowable cut, w i l l give the f i n a l duration of the cut within that class, which then is added to the cumulative column of the table. Turning to the next age and site class, the i n i t i a l cutting age i s obtained, when the last figure of the cumulative age column is added to the present age of this class. A l l further calculations from here on proceed as described above. If the f i n a l figure in the cumulative age column is within the range of the desired limit R(l*0.05), then the pre-liminary allowable cut figure i s acceptable. If not, a new allowable cut estimate must be set, making the new estimate higher, when the f i n a l cumulative age was high, or lower, i f It was low, and the process repeated accordingly. For the Research Forest the f i r s t estimate of 870,000 cu. f t , of the allowable cut proved to be low. With a second t r i a l figure of 970,000 cu. f t . , the f i n a l figure of the cumulative column was within the limit, but lower than the rotation age (77 years). Taking this into consideration, the 970,000 cu. f t . was lowered to 960,000 cu. f t . and accepted as the fi n a l estimate. The method i s presented in detail in Table 18. 87 TABLE 18 EXAMPLE OF AREA-VOLUME COMPUTATION, USING PRELIMINARY ALLOWABLE CUT ESTIMATE OF 970,000 cu. f t 0 Yield Cut Yield Actual Per Actual Avg. Begins Ave. per acre Approx. Avg. Acre Yield Actual Actual at Cut. When Yield Cut. When When Years Spec. Site Age Area Red. Age Age Cut When Cut Age Cut Cut to Cut Type Comp. Class yrs. ac. R. F» Acres yrs. yrs. cu.ft. M.cu.ft. yrs. cu.ft. cu.ft. Per. Cum. O.G.G. HF G M 159 1.118 178 M M 13,493 2,140 M 13,493 2,145,387 2.2 2.2 O.G.M. CH M M 671 1.093 734 M M 13,193 8,850 M 13,193 8,852,503 7.1 11.3 O.G.P. CH P M 164 0.711 117 M M 8,578 1,380 M 8,578 1,388,096 1.4 12.7 S0GoGo FH G 70 805 1.751 1,410 83 88 10,504 8,470 87 10,346 8,328,530 8.6 21.3 S.G.M. FH M 80 1,885 1.784 3,363 101 114 13,550 25,500 114 13,609 25,652,965 26.5 47.8 S. G. P o HF P 90 968 0.391 378 138 139 3,510 3,350 140 3,512 3,339,616 3.4 51.2 S. G oL o FH L 90 43 0.212 9 141 141 1,925 80 141 1,925 82,775 0.1 51.3 Y.GoG a HC M 30 2,170 1.000 2,170 81 90 5,963 12,900 88 5,847 12,687,990 13.1 64.4 YoG.Mo HC M 25 1,171 1.000 1,171 89 94 6,278 7,340 93 6,222 7,285,962 7.5 71.9 Y o G o P o CH P 20 335 0.481 161 82 83 2,541 850 82 2,519 843,865 0.9 72.8 PL. FH M 5 558 0.904 505 78 80 4,750 2,650 79 4,702 2,623,716 2.7 75.5 HW. FH M -5 353 0.878 310 71 72 4,117 1,450 71 4,077 1,439,181 1.5 77.0 10,506 YEARLY CUTTING AREA: 10,506 : 80 = 131.325 reduced acres 88 Area-volume allotment As a necessary step to begin the calculations, the cutting cycle had to be chosen, for which the allowable cut w i l l be calculated. This was set at ten years, which is comparable to the period for some of the other calculations. In this method, the same types, actual ages, actual and reduced areas were used as in the area regulation, or as in the area-volume computation. The reduced cutting area during the cutting cycle became ten times the size of the one year cutting area, giving a figure of 1,313 reduced acres. The reduced areas of the condition classes, l i s t e d in their order of cutting sequence, were added u n t i l the sum was equal to 1,313 acres. The next step was to set the average cutting age of the age and site classes, at which the yields had to be found in the empirical yield table. This age was assumed to be equal to the i n i t i a l age plus half of the cutting cycle (5 years) for the f i r s t period, and the i n i t i a l age and one and one-half cutting cycles (15 years), for the second period. At this age, the yields read from the empirical yield table represented the f i n a l yields of the age and site class. (At this point i t must be noted that similarly to the area regulation and to the area-volume computation, for the old growth stands, the present volumes were assumed as cutting volumes. For the second growth stands the future empirical yields were multiplied by the 89 present volume ratios, assuming that this ratio w i l l remain constant during the next five- or fifteen-year period.) The sum of the volume per acre figures multiplied by the actual areas of the age and site classes gave the total gross cubic foot volumes cut during the cutting cycles. As a result of the large harvest volumes in the old growth stands, in the f i r s t cutting cycle nearly twice as much volume appeared as in the second, which was composed of second growth stands. To moderate the large volume differences occurring between the two cutting cycles, the total yields obtained for the two cycles were averaged and the corresponding reduced acres recalculated. Obviously, the reduced acre values became lower in the f i r s t cycle and larger in the second, as a consequence of the equa-lized volume cut figure. It is essentialfbr the method that before the f i r s t cutting cycle ends, a new allocation is carried out, using the age and site classes presently in the second cutting cycle, and the ones f a l l i n g into the third decade of the regulation. This way a gradual equalization of the volumes and cutting areas is brought about; thus a continuous trend towards normality can be achieved, with less sacrifice than i t would be using a pure area regulation. (See detailed calculations in Table 19.) TABLE 19 EXAMPLE OF AREA-VOLUME ALLOTMENT Average Actual Yield Total Actual Actual Cut. Area per Exp. Spec. Area Age Age Red? Cut Acre Yield Type Comp. Site acres R.F. years years Acres acres cu.ft. cu.ft. FIRST CYCLE O.G.G. HF G 159 1.118 M M 178 159 13,493 2,145,387 O.G.M. CH M 671 1.093 M M 734 671 13,193 8,852,503 O.G.P. CH P 164 0.711 M M 117 164 8,518 1,406,792 S.G.G• FH G 805 1.751 70 75 284 162 8,476 1.373.112 TOTAL: 1,313 13,777,794 f SECOND CYCLE S.G.G• FH G 85 1.751 70 85 1,126 643 10,031 6,449,933 S.G.M. FH M 1,885 1.784 80 95 187 105 11,017 1.156.785 TOTAL: 1,313 7,606,718 REVISED ALLOTMENT FIRST CYCLE O.G.G. HF G 159 1.181 M M 178 159 13,493 2,145,387 O.G.M. CH M 671 1.093 M M 706 646 13,193 8,526,869 TOTAL: 884 10,692,256 SECOND CYCLE O.G.M. CH M 671 1.093 M M 28 25 13,193 329,825 O.G.P. CH P 164 0.711 M M 117 164 8,578 1,406,792 S.G.G. FH G 805 1.751 70 85 1,410 805 10,031 8,074,955 S.G.M. FH M 1,885 1.784 80 95 130 73 11,017 800.584 TOTAL 1,685 10,692,256 (continued) 91 TABLE 19 (Continued) EXAMPLE OF AREA-VOLUME ALLOTMENT 10-year CUTTING AREA » 1 ° ^ 5 0 6 = 1,313.25 acres AVERAGE YIELD = A.C. - 13,777,794+7,606,718 = 10,692,256 gross cu. ft./lO years 92 CONCLUSION Before considering the results obtained from this study, i t must be emphasized that for practical allowable cut e s t i -mates a statistically-planned sampling to a required level of confidence would be essential. When planning a more intensive inventory, data obtained with this small scale survey could be used profitably for the calculation of the necessary number of measurements in each phase s (number of point samples, number of increment cores, height measurements, etc.). Further divisions of the present classes into more detailed age classes and stocking classes would also be advisable. This thesis did not involve the calculation of actual sampling errors, as would be necessary for practical purposes. It simply stressed the importance of calculating and applying several allowable cut methods to a forest, and developing an inventory procedure, where the necessity of such allowable cut estimations arises. This importance can be realized i f we take a look at the f i n a l summary table of the allowable cut calculations (Table 20), where the calculated allowable cut volumes are presented in gross and net merchantable cubic feet. It was assumed that cuts would be taken from the old growth stands in the coming ten years 93 and when calculating net merchantable volumes, corresponding merchantable reduction factors were therefore used. Factors are given in Table 14. It should be noted that no allowances have been made for research reservations or possible additions to the area of the Forest. Except S. Petrini's two formulae - which are based on the same principles - a l l methods show different answers, caused by the difference in their basic assumptions, or by their applica-tion to a certain condition. Naturally in this case a simple s t a t i s t i c a l comparison of these figures would not be r e a l i s t i c . They have to be judged by considering many aspects of the pre-vailing forest management methods, present condition of stands, and possible future improvements. Most of these aspects were touched upon in the general description of the formulae and further elaborated and commented on in the discussions of the actual calculation. Some points, however, need further explanation. It i s seen from Figure 2 that volume distribution in the Research Forest is far from normal. The cruise data used in this study showed that old and second growth stands are overstocked, whereas the younger 20-30-year age classes are understocked by comparison with Fligg's (1960) estimates. (See reduced age distribution in the calculation of the Kemp III formula.) Obviously the objects of management w i l l be to reduce these irregularities in the shortest time with the least sacrifice. Pure area regulation would be the 94 easiest way to attain normality, but this would result in large harvest volume differences during the f i r s t rotation. Errors in the estimation of future yields could also appear from the determination of sites and areas of presently young, understocked stands. These stands, during the long estimation period, might not develop to the level of the empirical yields, as expected. These uncertainties naturally can be corrected and empirical yields exceeded by employing intensive s i l v i c u l t u r a l practices, together with regular checks on the stands, recurrent inventories, and by using short yield prediction periods. In contrast to area regulation, volume methods w i l l result in even yearly or periodic harvest volumes, but this way the trend towards a normal forest w i l l slow down. For example, allowable cut volumes (Table 18), calculated from volume formulae, gave much lower estimates than are indicated for the f i r s t eight years in the area regulation method (see area regulation calculations). It must also be noticed that formulae based on periodic annual increments show higher allowable cut volumes than formulae based on mean annual increment. These might be con-sidered as slight overestimates, since i f the young growth stands are presently understocked, i t follows that their incre-ment should not be allocated for cutting, rather, i t should be considered on the account of stocking improvement. 95 DoB.H, GROSS NET  Limit i n . Area Regulation 3.1 9.1 910,494 529,197 11.1 847,284 491,967 13.1 813,557 471,832 Barnes I 3.1 1,042,174 602,918 9.1 971,481 654,644 11.1 904,775 525,348 13.1 827,501 479,512 Grosenbaugh 3.1 9.1 1,502,849 873,486 11.1 1,203,778 698,962 13.1 1,035,659 600,133 Area-Volume Allotment 3.1 9.1 1,088,324 632,556 11.1 1,069,226 620,835 13.1 976,641 565,934 TABLE 20 YEARLY ALLOWABLE CUT VOLUMES AS CALCULATED BY DIFFERENT FORMULAE AND METHODS YIELD IN CUBIC FEET GROSS NET Austrian 880,137 511,553 815,562 473,548 733,746 448,362 Barnes II 1,246,799 721,298 1,199,917 697,415 1,130,971 656,687 1,048,761 627,725 Wo H. Meyer 1,603,836 932,181 1,321,528 767,332 1,142,362 661,964 GROSS NET Hanzlik 958,334 554,415 846,289 491,880 774,588 449,757 692,997 401,571 Hundeshagen 1,468,112 849,332 1,319,442 766,886 1,291,658 749,988 1,211,506 702,031 Petrini I 1,462,456 850,009 1,219,892 708,318 1,063,511 616,273 GROSS NET  Kemp I 1,692,972 983,989 1,672,812 971,301 1,635,334 947,627 H0 A. Meyer I 1,085,543 631,130 1,018,176 591,963 914,326 531,585 783,265 455,387 Petrini II 1,462,249 849,888 1,218,306 707,397 1,060,924 614,774 GROSS NET Kemp II 932,810 542,168 864,850 502,166 780,537 452,298 H. A. Meyer II f,449,103 842,502 1,386,559 806,139 1,282,876 745,858 1,151,917 669,719 Black H i l l s 1,077,848 626,467 1,005,804 584,010 932,861 540,565 GROSS NET Kemp III 1,069,445 621,583 1,056,659 613,538 1,033,035 598,613 Von Mantel 1,263,218 730,797 1,048,681 609,514 951,633 552,556 847,278 490,972 1,035,783 602,018 960,000 557,414 884,205 512,370 Area-Volume Computation 96 As a transition between the area regulation and the volume formulae, the area-volume control methods gave a more or less in-between answer concerning cutting volumes, simultaneously ensuring a continuous trend towards a normal forest. In consideration of which method actually is to be used, the general objectives of management of any property must be known. For the University Research Forest, these were stated by the U.B.C. Forest Committee in 1959 as: "The University Forest is managed to provide a sustained and maximum income. This management is to be consistent with effective use of the property for teaching, demonstration, research, and public recreation. Income from the Forest w i l l be used to maintain the capital value of the Forest in such a manner that these prime uses w i l l be maximized." Since a l l forest products from the University Research Forest are sold on the open market there i s no need to consider the special problems that might arise i f demands of a particular manufacturing plant had to be satisfied. From the regulation point of view a decision should be made as to what level of cut can be sustained and at the same time provide a maximum income indefinitely into the future. The high allowable cut values suggested by the Grosenbaugh, W. H. Meyer, H. A. Meyer II, and Petrini formulae are the result of application of approaches that are not suited to the present intensity of management of the Forest. Their application would 97 assume salvage of dead trees and thinning regimes not yet practic-able. The present large surplus of big trees makes d i f f i c u l t the application of systems based on diameter distributions. The period over which surplus volumes are to be harvested would depend very much on the objectives of management. It ranges from several decades to a whole rotation in different methods. From the economic point of view existing old growth volumes should be harvested as rapidly as possible to provide the capital for development of roads and improvement of amount and value of growth on the whole forest. This suggests the use of a short period of adjustment but requires careful planning of the transi-tion from logging of old growth to logging of younger stands. In this regard the surplus of stands above rotation age w i l l f a c i l i t a t e the transition and the road system developed for logging of old growth w i l l provide an excellent basis for more intensive management of young stands. It i s obvious that without intensive management, average volumes harvested per acre must decrease. If intensive manage-ment can be j u s t i f i e d economically and applied immediately, the level of cut eventually might approach that indicated by simple area regulation for the next two decades. The most conservative formula (Hanzlik) allocates surplus growing stock over the rotation, and uses mean annual increment at 80 years. These assumptions should be subject to review as conditions change. 98 It is obvious that none of the foregoing formulae or methods can be selected as absolutely correct. However, area-volume control methods seem to provide the most r e a l i s t i c approach as a compromise between pure area and volume approaches. If the area-volume computation and the area-volume allotment methods are compared, the allowable cut obtained by the area-volume allotment w i l l show a figure approximately 100,000 gross cu. f t . higher for the next decade. This presents the problem of choosing the level of cut which is better suited to the condi-tion of the Forest. Before the f i n a l decision is made, the possible development of the 30-year-old stands on the Forest also should be discussed. Parts of the Research Forest now covered by the presently 30-year-old stands were burned in the years 1925, 1926 and 1931 (Walters and Tessier, 1960). After the burning and u n t i l 1953, this area was l e f t to Nature without any provision for a r t i f i c i a l restocking. In 1953, forestry students planted a few acres of the understocked areas with Douglas f i r , Scots pine and Norway spruce. Restocking to reasonably satisfactory levels, however, was completed in 1959, when the last large poorly stocked area was planted with 6,500 Douglas f i r seedlings and 6,000 Scots pine seedlings on 117 acres. In a l l , more than 90,000 seedlings were planted on 700 acres. Stocking probably w i l l continue to improve as a result of natural regeneration. 99 Because the A.&L. portion of the Forest i s in the i n i t i a l stages of planned management, there are s t i l l large areas which have volumes well below Fligg 1s (1960) empirical volume e s t i -mates, and their complete recovery cannot be expected within the coming 10 or 20 years. Although Fligg 1s data may be misleading because of curving at lower ages, the problem of indicated understocking remains. In spite of the efforts spent on regeneration, caution must therefore be used when calculating the allowable cut for the coming two decades. A supplementary volume regulation formula, which bases i t s estimate on actual volumes, may be used as a guide for the selection of a f a i r l y safe allowable cut estimate from the two favoured area-volume method. For this purpose Von Mantel's formula should provide a reasonable comparison. Fortunately the allowable cut obtained by Von Mantel's formula is almost identical to that obtained by the area-volume computation method and thus verifies the f i n a l selection of the allowable cut indicated by the area-volume method. Naturally, as time passes, more experience w i l l be gained, more w i l l be learned about the Forest and more intensive s i l v i -cultural and u t i l i z a t i o n techniques w i l l be applied. Although rotation length has been assumed to average 80 years, this may not be optimum. It i s hoped i t can be reduced by improving standards of u t i l i z a t i o n and more intensive management. It is thus reasonable to expect that the growth and yield of the 100 Research Forest w i l l increase. However, at the present stage a short prediction period and a method providing a moderately conservative allowable cut should be used. When complete recovery of the presently understocked areas is assured, the use of the simpler area-volume allotment method may be more convenient. However, u n t i l then i t would appear safer to use the area-volume computation method, which gives a lower allowable cut. 101 BIBLIOGRAPHY Allen, R. H. Jr. and E. W. Morgen. Range mean ratio of basal area as an indicator of B i t t e r l i c h sampling intensity in lodgepole pine." College of Forest and Range Management, Colorado State University. Fort Collins, Colorado. Research Note No. 13. 2pp. Allison, G. W. and R. E. Breadon. 1960. Timber volume e s t i -mates from aerial photographs. For. Survey Notes. No. 5. Department of Lands and Forests. Victoria, B. C. 25pp. Bajzak, D. 1960. Forest inventory on aerial photographs of part of the University of Bri t i s h Columbia Research Forest, Haney, B. C. University of Bri t i s h Columbia, Faculty of Forestry. Vancouver 8, B. C. Unpublished report. 11pp. . 1960. An evaluation of site quality from aerial photographs of the University of Bri t i s h Columbia Research Forest, Haney, B. C. University of Bri t i s h Columbia, Faculty of Forestry, M.F. thesis. Vancouver 8, B. C. 113pp. Baker, F. S. 1960. A simple formula for gross current annual increment. Jour. For. 58(6):488-489. Barnes, G. H. 1951. A new method of volume regulation. Jour. For. 49(4):272-277. B e l l , J . F. and L. B. Alexander. 1957. Application of the variable plot method of sampling forest stands. Oregon State Bd. of Forestry. Forest Research. Note 30. 21pp. Briscoe, C. B. 1957. Stand table construction from relascope plots. La. Agr. Exp. St. Forestry. Note 15. 3pp. Castles, J. R. 1959. Calculating allowable harvest cuts in the National Forests of the Northern Rocky Mountain Region. Society of American Foresters. Proceedings. Society of American Foresters meeting. Mills Building, Washington 6, D.C. pp.109-151. Chapman, H. H. 1950. Forest Management. The Hildreth Press Publishers. B r i s t o l , Conn. 582pp. 102 Cunia, T. 1959. Notes on cruising intensity by the B i t t e r l i c h method. Jour. For. 57(11):849-850. Davis, K. P. 1954. American Forest Management. McGraw-Hill Book Co. Inc. Toronto. 482pp. Fekete, Z. 1950. Erdorendezestan. Agrartudomanyi Egyetem Erdo- es Foldmernoki Kar. Sopron. Hungary. 133pp. Mimeo. Fligg, D. M. 1960. Empirical yield tables. Forest survey notes. No. 6. Br i t i s h Columbia Forest Service, Department of Lands and Forests. Victoria, B. C. Greeley, A. W. 1935. Development of management plans on Snoqualmie National Forest. Yale University. School of Forestry, M.F. thesis. 155pp. Grosenbaugh, L. R. 1952. Plotless timber estimates...new, fast, easy. Jour. For. 50(1):32-37. j_ 1955. Better diagnosis and prescription in Southern Forest Management. Southern For. Expt. Sta. Occasional paper. 145. 27pp. j_ 1958. Allowable cut as a new function of growth and diagnostic t a l l i e s . Jour. For. 56.(10): 727-730. 1958. Point-sampling and line-sampling: Probability theory, geometric implications, synthesis. Southern For. Expl. Sta. Occasional paper. 160. 34pp. Gross, L. S. 1950. Timber Management Plans on the National Forests. U. S. Dept. of Agr. Washington 25, D.C. 59pp. Hanzlik, E. J. 1922. Determination of the annual cut on the sustained basis for virgin American forests. Jour. For. 20(6):611-626. Hough, A. F. 1954. The control method of forest management in an age of aerial photography. Jour. For. 52(8):568-574. Hughes, W. G. 1956. Management plan considerations in i n i t i -ating sustained yield forestry. The Empire Forestry Review. 35(1):29-35. Jerram, M. R. K. 1945. A Textbook on Forest Management. Chapman and Hall Ltd. London. 154pp. 103 Johnson, F. A. and V. E. Hicks. 1956. Estimating allowable cut without a type map in forests of Western Washington and Western Oregon. Jour. For. 54(8):522-524. j_ 1961. Standard error of estimated average timber volume per acre under point sampling, when trees are measured for volume on a subsample of a l l points. U. S. Dept. of Agr. Pac. Northern For. and Range Expt. Sta. Res. Note. No. 201. 5pp. Kendall, R. H. and L. Sayn-Wittgenstein. 1959. An evaluation of the relascope. Canada Dept. of Northern Affairs and Natural Resources. For. Research Div. Tech. Note. No. 77. 26pp. Ker, J. W. 1953. Growth of immature Douglas f i r by treeaclasses. For. Chron. 29:367-373. j_ and J. H. G. Smith. 1957. How much and how fast — forest measurements today. British Columbia Lumberman. February and March. 6pp. t J. H. G. Smith, and J. Walters. 1957. Observations on the accuracy and u t i l i t y of plotless cruising. British Columbia Lumberman. November. 2pp. Littleton, D., A. Strother, H. Eidsvik and T. Jeanes. 1957. Re-appraisal of the allowable annual cut on the U.B.C. Research Forest, Haney, B. C. University of British Columbia, Faculty of Forestry. Vancouver 8, B. C. Unpublished report. 6pp. Meyer, H. A., A. B. Recknagel and D. D. Stevenson. 1951. Forest Management. The Ronald Press Co. New York. 290pp. •_ 1952. Structure, growth and drain in balanced uneven aged forests. Jour. For. 50(2):85-92. s_ 1952. Accuracy of forest growth determination based on the measurement of increment cores. Agr. Expt. Sta. State College, Pennsylvania. Bulletin 547. 25pp. Meyer, W. H. 1943. Amortization in stand growth and depletion problems. Jour. For. 41(12):920-922. j_ 1952. Regulation of cut in immature understocked forests. Jour. For. 50(12):934-939. 104 Petrini, S. 1956. Determining the possible yield. Bulletin No. 21. Royal School of Forestry. Stockholm, Sweden. 9pp. Recknagel, A. B. 1917. The theory and practice of working plans. John Wiley and Sons. New York, N. Y. 265pp. Robertson, R. C. and J. N. MacFarlane. 1960. Growth in volume and value on the U.B.C. Research Forest during the next decade. University of British Columbia, Faculty of Forestry. Vancouver 8, B. C. Unpublished report. 13pp. Sammi, J. C. 1961. De Liocourt's method modified. Jour. For. 59(4):294-295. Smith, J. H. G. 1952. A c r i t i c a l appraisal of methods of forest regulation. Yale School of Forestry, Directed Study. 146pp. typed. t and J. W. Ker. 1957. Timber volume depends on D2H. Bri t i s h Columbia Lumberman. September. 2pp. 1958. Management planning and determination of the allowable cut in forests of the United States and Canada. The Empire Forest Review. 37.(91):43-48. ^ and J. W. Ker. 1959. Empirical yield equations for young forest growth. British Columbia Lumberman. September. 2pp. j_ J. W. Ker and J. Csizmazia. 1961. Economics of Douglas f i r , western hemlock and western red cedar in the Vancouver Forest D i s t r i c t . The University of Bri t i s h Columbia. Vancouver 8, B. C. Forestry bulletin No. 3. 144pp. Spurr, S. H. 1952. Forest Inventory. The Ronald Press Co. New York, N.Y. 476pp. j . 1954. Simplified computation of volume and growth. Jour. For. 52(12):914-922. s_ 1960. Photogrammetry and photo interpretation. Second Edition of Aerial Photographs in Forestry. The Ronald Press Co. New York, N.Y. 472pp. Stage, A. R. 1959. A cruising computer for variable plots, tree heights and slope correction. Jour. For. 57(11): 835-836. 105 Stage, A. R. 1960. Computing growth from increment cores with point sampling. Jour. For. 58(7):531-533. The Western Forestry and Conservation Association. 1950. Reports of the West Coast Forestry Procedures Committee on various recommended practices and techniques. Portland, Oregon. University of Br i t i s h Columbia Research Forest Committee. 1959. The f i r s t decade of management and research on the U.B.C. Forest, 1949-1958. University of B r i t i s h Columbia. Vancouver 8, B. C. 82pp. University of British Columbia Forest Club. 1959. Forestry Handbook for British Columbia. Second edition. University of Br i t i s h Columbia Forest Club. Vancouver 8, B. C. 800pp. U. S. Dept. of Agriculture. 1958. Explanatory notes on the allowable cut task force report. Forest Service, Washing-ton, D.C. 63pp. Walters, J. and J. P. Tessier. 1960. U.B.C. researchers put "A.&L." back in production. British Columbia Lumberman. December. 3pp. Yoder, R. A. 1961. Accumulation and processing data for deci-sion making in forest management. Proceedings. Sixteenth Yale Industrial Forestry Seminar, Oregon State College. Corvallis, Oregon. 12pp. 

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