Forestry Introductory Forest Mensuration.pptx

Forest Mensuration, Diameter at breast height, Standing tree volume, Fuel wood, timber, Forestry, Hetauda, Nepal

1. Introduction to Forest Mensuration 1

2. I n t r o du c t i o n Forest An area set a side for the production of timber and other forest produce. Forests are the lands of more than 0.5 ha with a tree canopy cover of more than 10% which are not primarily under agricultural or urban landuse (FAO). “Forest” means an area fully or partly covered by trees (Forest Act) Mensuration It means measurement of length, mass and time etc. Art and science of locating, measuring and calculating the length of lines, areas of planes, and volumes of solids. 2

3. Forest Mensuration Forest mensuration concentrates on trees and forests or potentially forested locations. Forest mensuration also includes measuring or calculating growth and change in trees and forests. Forest mensuration then may be defined as the art and science of providing the quantitative information about trees and forest stands necessary for forest management, planning and research. 3

4. Forest Mensuration Estimation of the total and merchantable stand volume and its size class distribution. Estimation of the diameter, basal area, height, and volume growth of single trees and forest stands Estimation of the damages to the quality of individual trees and forest stands In addition, it has to deal with the development of models for the construction of tree volume , taper and biomass functions , the construction of stand tables , as well as the development of growth and yield models . 4

5. Overview of Forest mensuration 5

6. Importance of Forest Mensuration It is the keystone foundation of forestry. What Silvicultural treatment will result in best regeneration and growth? What species is most suitable for reforestation? Is there sufficient timber to supply a forest industry and for an economical harvesting operation? What is the value of the timber and land? What is the recreational potential? What is the wildlife potential? What is the status of biodiversity on the area? What is the status of the forest as a carbon sink? 6

7. What is in the forest now? How is the forest changing? What can we do to manage the forest properly? How can it be assessed? And for what purpose? It helps to answer all these questions and concepts involved in forest management. Forest mensuration is the application of measurement principles to obtain quantifiable information for forest management decision making. 7

8. Unit 1.2 Bias, Precision & Accuracy 8

9. Bias is a systematic distortion arising from such sources as a flaw in measurement or an incorrect method of sampling. For example, measurements of 100 ft units with a tape only 99 ft long will be biased. 1.2 Bias, Accuracy and Precision 9

10. Common sources of bias Flaw in measurement instrument or tool, e. g. survey tape 5 cm short; Flaw in the method of selecting a sample, e. g. some observers always count the boundary trees while others always exclude it; Flaw in the technique of estimating a parameter, e. g. stand volume: using a volume function or model in a forest without prior check of its suitability for application in that forest; inappropriate assumptions about the formulae, and Subjectivity of operators. 1.2 Bias, Accuracy and Precision 10

11. Accuracy and precision Mostly creates confusion with meaning of accuracy & precision True length of the line is 736.72 m Suppose that you are asked to measure the same line five times. The first party reports the following measurements: 736.80, 736.70, 736.75, 736.85, and 736.65 m. October 13 , 202 Unit 2: Errors and accuracy The second party reports the following measurements: 736.42, 736.40, 736.40, 736.42, and 736.41 m. More accurate More precise 11

12. Accuracy and precision Accurate but not precise October 13 , 202 Unit 2: Errors and accuracy Precise but not accurate Accurate and precise 12

13. Accuracy and precision The accuracy is the degree of closeness of measurements of a quantity to that quantity's true value Accuracy depends on Characteristics of trees Varying methods and conditions of felling and conversion Personal bias of the estimator Instruments Used Biological character of the forest Data and methods Cost Good planning October 13 , 202 Unit 2: Errors and accuracy 13

14. Accuracy and precision Precision also known as apparent accuracy Precision is the degree of perfection used in instruments, methods and observation Closeness of one measurement to another Good precision doesn’t mean that good accuracy Meaning of precision in distance measurement In distance measurement, Error of measurements P r e ci s i o n D i st a n c e me a s u r e d N u m b e r 1 = = Suppose in measuring the distance of 500m the error was found to be .20 m then, precision is 0.20/500 = 1/2500. October 13 , 202 Unit 2: Errors and accuracy 14

15. Relationships between bias, accuracy and precision 15

16. How to minimize bias The only practical way to minimise measurement bias is by: Continual check of instruments and assumptions Meticulous training Care in the use of instruments and application of methods Complete elimination of bias may be costly. To avoid bias being introduced via faulty instruments, it is essential to check all instruments before one commences any important measuring project and re-check periodically during the course of the project. 16

17. Accuracy and precision October 13 , 202 Unit 2: Errors and accuracy How to get both accuracy and precision? Answer is simple in saying but hard in practicing So what to do? Use logical thinking Be patience in your work Use good instruments Apply good procedure 17

18. Unit 1.3 System of Measurement and Unit Conversion 18

19. 1.3 Scale of Measurement & Conversion Nominal Scale : determination of equality/identification (numbering and counting), used for attributes, represents the weakest scale of measurement. The observation is assigned to one out of k discrete categories. discrete variables which cannot be arranged in a certain order Eg. Species, provenance, forest type and soil type . Ordinal scale : determination of greater or less (ranking) ranking scale characterized by ordered categories used for ranked variables (discrete categorical variables) The scale is characterized by classes of different but unknown width. Eg. Forest soils, for example, could be categorized as poor, medium or good, the vitality of trees as healthy, sick, dying or dead, social tree classes as dominant, co-dominant, dominated and suppressed. 19

20. Almost all forest mensurational characteristics, such as diameter, height, basal area, volume and increments, are continuous variables , measured on a metric scale . Metric scale divided into two categories Interval scale : determination of the equality of intervals or of differences (numerical magnitude of qty , arbitrary origin) eg . Fahrenheit temp., soil moisture etc. Ratio scale : determination of equality of ratios (numerical magnitude of qty., absolute origin) eg . length of objects, volumes, etc. 1.3 Scale of Measurement & Conversion 20

21. 1.3 Scale of Measurement & Conversion 21

22. 18 Into Metric Out of Metric If you know Multiply by T o g e t If you know Multiply by T o g e t Length Inches 2.54 Centimeters Centimeters 0.039 Inches Foot 30.48 Centimeters Centimeters 0.39 Inches Yards 0.9144 Meters Meters 3.28 Feet Miles 1.609 Kilometers Kilometers 0.62 Mile Area Sq. Inches 6.45 Sq. Centimeters Sq. Centimeters 0.16 Sq. Inches Sq. Foot 0.09 Sq. Meters Sq. Meters 1.196 Sq. Yards Sq. Yards 0.83 Sq. Meters Sq. Kilometers 0.386 Sq. Miles Sq. Miles 2.59 Sq. Kilometers Hectares 2.47 Acres Volume Cubic Feet 0.028 Cubic Meter Cubic Meter 35.31 Cubic Feet Cubic Yard 0.765 Cubic Meter Cubic Meter 1.3 Cubic Yard 1.3 Scale of Measurement & Conversion 22

23. MEASUREMENT OF TREE Diameter and Height 23

24. Measurement of trees: Diameter Measurement DBH measurement and Its significance Rules of DBH Measurement and instruments used Height Measurement Measurement of height of trees in plane and slope Instruments used in height measurement Measurement of logs and fuelwood Measurement of length, diameter and sectional area of logs Formula for log volume calculation Volume of stacked timber and chatta (stacked fuelwood) 24

25. Diameter measurement and its significance What is Diameter?? A straight line passing through the center of a circle or sphere and meeting at each end of circumference or surface. The most common diameter measurements taken in forestry are of the main stem of standing trees, cut portions of trees and branches. Important because directly measurable dimensions tree cross sectional area, surface area and volume can be computed. 25

26. The point at which diameters are measured will vary with circumstances. The most frequent tree measurement made by forester is diameter at breast height (dbh). DBH is defined as the average stem diameter outside bark, at a point 1.3 m above ground as measured Europe, the UK, and Canada : 1.3 metres US, Australia, New Zealand, Burma, India, Malaysia, and South Africa, :1.4 metres (previously 1.37m) The rationale of DBH measurement of individual trees is to estimate the quantity of timber, fuel wood or any other forest products which can be obtained from them. DBH is important variable to calculate the product quantity. These measurement are also necessary for making inventory of growing stock as well as to correlate height, volume, age, increment with most easily determinable dimension i.e. dbh 26

27. DBH has been accepted as the standard height for diameter m e as u r e m e n t b e c a u se … convenient height for taking measurements Economically fit Time Value escape from abnormalities standardize the measurement Assumption Tree stem sections are circular 27

28. Rules of DBH measurement and instrument used Moss, creepers, lichens and loose bark found on the tree must be removed before measuring the dia. over bark. Breast height (BH) should be marked by means of a measuring stick on standing trees at 1.3m above the ground level. BH point should be marked by intersecting vertical and horizontal lines 12 cm long, painted with white paint. 28

29. Rules of DBH Measurement On sloping land, the diameter at BH should be measured on the uphill side. In case of the tree is leaning, dbh is measured along the tree stem and not vertically, on the side of the lean for trees growing on flat ground and on the uphill side, for trees growing on sloping ground. 29

30. Rules of DBH Measurement Abnormal trees: The dbh should not be measured at 1.3m if the stem is abnormal at the level. BH mark should be shifted up or down as little as possible to a more normal position of the stem and then dia. Measured. Buttressed trees: BH should be taken at the lowest point above which the buttress formation is not likely to extend 30

31. Rules of DBH Measurement Forked trees: When the tree is forked above the BH, it is counted as one tree, but when it is forked below BH, each fork should be treated as though it were a separate tree. 31

32. Inst r um e nt u s e d i n diam e ter me a s u r em e nt The most commonly used instruments for measuring diameters at BH are: Diameter tape, calipers, Biltmore stick, and other optical instruments. 32

33. Diameter tape The diameter of a tree cross section may be obtained with a flexible tape by measuring the circumference of the tree and dividing by π(D=C/ π). The diameter tapes used by foresters, however are graduated at intervals of π units (in or cms), thus permitting a direct reading of diameter. A diameter tape is a measuring tape that has scales on both sides: one side is specially marked to show the diameter of a tree, and the other is a normal scale. 33

34. How to measure diameter using a diameter tape: Wrap the diameter tape around the tree at the required height, ensuring that the tape is not twisted and the correct scale is visible. Make sure the tape is held tightly around the tree and at right angles to the main stem, and Read the tree diameter from the tape and record to the nearest 0.1cm 34

35. How to measure diameter using a diameter tape: Care must be taken that the tape is correctly positioned at the point of measurement that it is kept in a plane perpendicular to the axis of the stem, and that it is set firmly around the tree trunk. These tapes are accurate only for trees that are circular in cross section. The diameter tape is convenient to carry and in the case of irregular trees, requires only one measurement. 35

36. Calipers Calipers are used to measure tree dbh or when diameters are less than about 60 cm. calipers of sufficient size to measure large trees, or those with high buttresses are awkward to carry and handle, and particularly in dense undergrowth. metal, plastic or wood, consists of a graduated beam/rule with two perpendicular arms. One arm is fixed at the origin of the scale and the other arm slides. When the beam is pressed against the tree and the arms closed, the beam of the caliper can be read on the scale. For an accurate reading, the beam of the caliper must be pressed firmly against the tree with the beam perpendicular to the axis of the tree stem and the arms parallel and perpendicular to the beam. These are generally less precise than a diameter tape but may be quicker to use, particularly for small trees, and can take into account some degree of stem eccentricity. 36

37. How to use calipers to measure diameter: Place the calipers over the stem at the required height. Ensure they are held level with the stem and close them gently. Do not apply excess pressure to the calipers as this will compress the bark, resulting in an incorrect measurement. Record the diameter then take another measurement at a right angle to the first and record this measurement and Calculate the average of the two measurements and record to the nearest to 0.1cm. 37

38. Biltmore Stick a tool used to measure various tree dimensions, such as diameter at breast height and height Based on similar triangle principle 38

39. M e a s u r e m e n t o f up p e r s t e m d i a m e t e r s To estimate form or taper and to compute the volume of sample trees from the measurement of diameters at several points along the stem. Diameter measurement can be made at the desired points on the stem after tree felling or by climbing a tree. Instruments for measuring stem diameters of standing trees allow diameters to be determined from the ground at some distance from a tree. Some instruments are: Barr and stroud dendrometer, the wheeler pentaprism, the speigel relaskop etc. 39

40. Height Me a s u rement 1 40

41. Heig h t M e a s ur e ment ▶ Important variable as it reflects the fertility of the si t e a t a gi v en are a s. ▶ o ne o f t he t hree v ari a b l es u s e d i n t he e s t i m a ti o n of tree volume. ▶ Measured from ground level to different points of the tree. 2 41

42. Hei g ht M eas u rem e nt ▶ Height is the linear distance of an object normal to the s ur f ac e o f t he e a r t h. ▶ T ree h e ig h t i s t h e v e r t i c a l dis t a n c e m e a s ur e d fr om t h e ground surface. ▶ t o f i n d o u t v o lu m e . ▶ to find out productive capacity of site ▶ Height of selected trees in a forest are also required to read volume tables, form factor tables, yield tables etc. ▶ C o ns i d e red a s a n i n d e x o f f e r t ili t y an d w i t h t he knowl e d g e o f age it gives a reliable measure of the site quality of a locality. 3 42

43. Height ▶ Total height of a standing tree is the distance along the axis of the tree stem between the ground and the tip of the tree. ▶ Bole height is the distance along the axis of tree b e t w een g r oun d le v e l a n d cro w n poin t . ( cro w n p o i n t i s t h e p o si t i o n o f t h e f i rst c r o w n f o rm i n g b r a n c h ) . ▶ Commercial bole height is the height of bole that is u s u a ll y fit f o r util i zation a s t i mb er. ▶ H eigh t o f s ta n d a r d timber bol e i s t h e h e i g h t o f t h e bole from the ground level up to the point where a v e r a g e d i amete r o v e r b a r k is 2 cm. ▶ Stump height is the distance between the ground and basal position on the main stem where a tree is cut. 4 43

44. ▶ C r o w n length - T h e ver t i c a l mea s u reme n t o f t h e crown of the tree from the tip to the point half way between the lowest green branches forming green crown all round and the lowest green branch on the bole . ▶ C r o w n heig h t - T h e h e i g h t o f t h e cro w n a s a measured vertically from the ground level to the point half way between the lowest green the lowest green branches forming green crown all round . ▶ C r o p h e ig h t – t he a v e r a ge h e igh t o f a re g ular cr o p . ▶ Mean height – the height corresponding to the mean dia m e t e r o f a gro up o f t re e s o r t he cr o p di a m e t e r o f a stand. ▶ Top height – the height corresponding to the mean dia m e t e r o f 2 5 b i g g e s t dia m e t e rs o f a r e gular cr o p. CROWN AND HEIGHT 44

45. Principle of Height Measurement 45

46. Principles of Height Measurement Two principles of height measurement Trigonometric principles and Principle of similar triangle. 46

47. T r i g o n o m e t r i c p r i n c i p l e s The principles follow the basic rules of trigonometry for deriving heights of trees from distance and angle measurements. Two laws are applicable for this purpose and they are: tangent law and sine law. Brandis Hypsometer, Abney's Level, HAGA Altimeter, Blume- leiss hypsometer, Relaskop 47

48. T a ng e n t L a w Applicable to right angle triangle Instruments based on this principle are Abney's level, clinometers, altimeter etc. For accurate results, trees must not lean more than 5 ° from the vertical, and the fixed horizontal distance must be determined by taped measurement Let ABC be a right-angled triangle. The trigonometrical ratios of angle ACB are defined as follows: AB/AC is called sine. BC/AC is called cosine. 3. AB/BC is called tangent. If AB is assumed to be a tree and C the position of the observer, then AB can be calculated from tangent ratio as follows: AB = BC × tan angle ACB, where BC is the horizontal distance of the observer from the tree and angle ACB can be measured by any angle measuring instrument. This is known as the tangent method. A B C 48

49. Sine Law Applicable to non right angle triangle and is useful in deriving tree height in difficult conditions. A B Trigonometry also tells us that in any triangle, sines of angles are proportional to the opposite sides. Thus in the triangle ABC in fig, Sin <ACB/AB = sin<CAB/BC = sin<ABC/AC C The knowledge on this relationship can also be used in calculation of heights of trees and is known as the sine method. 49

50. Principle of Similar Triangle Two triangles are said to be similar only by one of the following conditions: Each angle of a triangle is equal to its corresponding angle of the other triangle. Each side of a triangle is proportional to the corresponding side of the other triangle and One angle of a triangle is equal to one angle of the other and the corresponding sides which subtend the equal angles are proportional. Eg. Christen's Hypsometer, Smythies Hypsometer, Improvised Calipers 50

51. Principle of Similar Triangle Let ABC and A’B’C be two similar triangles. A'B' and B'C are known in triangle A'B'C and only BC is known in triangle ABC. Then AB can be found as follows: AB/A'B' = BC/B'C Or, AB × B'C = A'B' × BC Therefore, AB = (A'B' × BC)/B'C. This is known as principle of similar triangle. A B C A' B ' 51

52. The basic assumptions in applying these principles for measuring the heights of trees are that: the tree is vertical and the tip and the base of the tree are simultaneously visible. When the base of the tree is not visible from a distance, the sight may be taken on a point on the stem, which is of known height above the base. In such cases, it is better to place a staff of height equal to observer’s eye height against the tree and sight the top of the staff in place of the base. Then the height of the tree can be calculated using principle of similar triangle. 52

53. Methods of Height Measurement O cu l a r E s t i m a t e : by us i ng s p e c i fic l e n g th of p o l e . Non Instrumental methods ▶ Sh a d o w m e t ho d : a po l e of c on v e n i e nt l e ngth i s f i xed u p r i ght i n the g r ound an d i ts he i ght a b o v e the g r ound i s me a s u r e d . The s ha d o w s of the p o l e an d the tr e e a r e a l s o me a s u r e d. B A a b D d A B/ a b = BD / b d , A B = B D x ab/bd W he r e , A B i s the t r ee , a b i s the p ort i on of the p o l e a b o v e the g r ound l e v e l , B D i s the l e ngth of s hadow of the tr e e an d bd i s the sh a do w of a b . 6 53

54. S i ng l e po l e m e t h o d ▶ P o l e o f ab o ut 1 . 5 m l en g t h vertically at arm’s length in o ne ha n d i n s u ch a w a y t h a t p o r t i on o f t he p o l e a b o v e t he h a nd i s eq ual i n l en g t h t o t he d is t a n c e o f t he p o l e f r o m e y e. A B/a b = E B / E b i . e. A B = E B x a b / Eb Where, A B = t r e e , a c = p o l e a b o u t 1 . 5 m l o n g, Eb=ab 7 54

55. I n s t rum e n t a l m e t h o d ▶ B y u s in g a in s t ru m en t s l ik e h y ps o m e t er, clinometer, altimeters, abneys level, i m pr o v erised c a l iper s e t c . ▶ A l l t he s e ins t ru m en t s ar e b a se d ei t her o n geometric principles of similar triangles or on trigonometric principles. 8 55

56. M easure m ent of t ree h ei g h t ( v ert i cal t ree) i n p l a n e a n d slope On level ground ▶ T he height o f t he t ree is ca l c u l a t ed w i t h t he he l p of the tangents of the a n g l e t o t he t o p a nd t he distance of the observer f r o m t he t ree. A B = A D + B D = E D ta n α + B D = B F tan α + EF W he r e, A B = tr e e, E F = eye he i ght of the ob s e r v e r , B F = h o r i zo n tal d i s tan c e 10/13/2020 F o r e s t M e n s u r a t i o n : U n i t 2: H e i g h t M e a s u r e m e n t 9 56

57. O n s l op i ng g round ▶ Where the observer is s t an d in g a t s u c h a p l ace that the top of the tree is ab o v e t he e y e l evel and t he b a s e be l o w i t . A B = A D + D B = E D tan α + E D tan β = E D ( tan α + ta n β ) = E B Cos β ( tan α + tan β ) 10 57

58. O n s l op i ng g round ▶ Where top and base of the tree are above the eye level . A B = A D - BD = E D tan α – E D tan β = E D ( ta n α - tan β ) = E B c os β ( ta n α - tan β ) 11 58

59. O n s l op i ng g round ▶ Where base and top of the tree are be l o w t he e y e l e v el A B = B D – AD = E D tan β – E D tan α = E D ( tan β - tan α ) = E B c o s β ( tan β - tan α ) 12 59

60. M e a s ur e ment of l e anin g t r e e s ▶ He i g h t mea s u r i n g i n s t r u me n t s ass u me t h a t t h e t ree i s ver t i c a l ▶ b u t i n p ra c t i ce, f o re s t t rees ar e rare l y vertical ▶ chance of either over estimating or u n de r es t i m a t i n g t h e t ree h e i g h t . ▶ h e i g h t o f t h e t ree l e a n i n g t o w a rds t h e o b serve r i s o ve r es t i m a t ed a n d t ree l e a n i n g a w a y fr o m t h e o b serve r i s u n der estimated. 13 60

61. M ea s u r eme n t of t h e h e i ght of Leaning Tree l ean i n g t rees Case (I) (a) In case of the observer standing at between the top and bottom of the tree (lean away from observer). H e i g h t = d i s t a n c e X s i n ( t op a n g l e + bo t t om a n g le ) Cos ( t op a n g l e + l e a n a n g l e ) ( b ) S a m e a s c a s e ( I ) a , bu t l ean i s t ow a r d t he o b se r v e r . H e i g h t = d i s t a n c e X s i n ( t op a n g l e + bo t t om a n g le ) C o s ( t op a n g l e - l ean a n g l e ) 10/13/2020 F o r e s t M e n s u r a t i o n : U n i t 2: H e i g h t M e a s u r e m e n t 14 β θ A B C D E 90 - ? ? β A C E 90 - θ D B 61

62. C a se ( II) When the observer is below the top and bottom of the tree (lean away from observer) H e i g h t = d i s t a n c e X s i n ( t op a n g l e - b o tt om a n g l e ) C o s ( t op a n g l e + l ean a n g l e ) S a m e a s c a s e ( II ) a , b u t l e a n t ow a r d t h e observer H e i g h t = d i s t a n c e X s i n ( t op a n g l e - b o tt om a n g l e ) C o s ( t op a n g l e - l ean a n g l e) 15 M ea s u r eme n t of t h e h e i ght of Leaning Tree 62

63. C a se ( III) When the observer is above the top and bottom of t h e t r ee ( l e a n a w a y f r om t h e o b se r v e r ) Height= distance X sin (bottom angle – top angle) Cos ( t op a n g l e - l e a n a n g l e ) S a m e a s c a s e ( III ) a , b u t l e a n t ow a r d f r om t h e observer Height= distance X sin (bottom angle – top angle) Cos ( t op an g l e + l e a n an g l e ) 16 M ea s u r eme n t of t h e h e i ght of Leaning Tree 63

64. Measurement of the lean t ree ▶ A plumb bob ▶ D e v i c e r e ad i n g a n g le 17 64

65. M e a s uring h e igh t of l e a n t r e e 18 65

66. Sou r ces of e r ror i n He i ght measurement ▶ I ns t ru m en t a l an d p e rs o n a l err o rs ▶ E rr o rs d ue t o m easure m ent and observation ▶ E rr o rs d ue t o l ean o f t rees T h e h e i g h t o f t h e t ree l ea n i n g t o w ar d s t h e o b serve r i s o v e r es t i m a t ed w h i l e t h a t o f leaning away from the observer is under- estimated T h e p erce n t a g e erro r d u e t o le a n 𝐶𝑜𝑠 (𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛±𝐿𝑒𝑎𝑛 𝑎𝑛𝑔𝑙𝑒) − 1 × 100 𝐶𝑜𝑠 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛 + t ow a r d s , - a w a y 19 66

67. I ns t rument U se d i n H e ight Measurement ▶ V ar i o us I ns t ru m ent ▶ I n s t r u m ent ar e bas e d o n t rig o n o m e t ri c al and geometric principle ▶ I ns t ru m ent b a se d o n t ri g o n o m e t rical ar e m o re accurate than the ones employing geometrical principles 20 67

68. I ns t rument U se d i n H e ight Measurement ▶ Ch r i s t en H y p s o m e t er ▶ B L UM E - L E I S S D e n d r o m e t e r ▶ T h e H A G A D e n d r o m e t e r ▶ S U N T O Cl i no m e t er ▶ Abney's level ▶ Relaskop ▶ Vertex ▶ R a n g e F i n d e r 21 68

69. Some other terminologies Crop diameter – diameter corresponding to the mean basal area of a uniform, generally pure crop . Mean diameter – diameter corresponding to the mean basal area of a group of trees or a stand ; sometimes used for the arithmetic mean of the summated diameters. Top diameter – diameter corresponding to the mean basal area of the biggest trees in a uniform, generally pure crop 69

70. Crown – the upper branchy part of a tree above the bole Canopy – the cover of branches and foliage formed by the crowns of trees in a wood. Crown width – maximum spread of the crown along its widest diameter. Crown cover – the horizontal projection on the ground of the tree crown. Canopy density- measure of relative completeness of canopy (1=closed, 0.75-1 =dense, 0.5 -0.75 = thin and <0.5 =open) 70

71. Me a s u rement of lo g an d f u elwood 1 71

72. L og v o l ume b y d i r e ct mea s urement ▶ volume estimation based on measurements of d i a me t er a n d l e n g t h o f l o g. ▶ measurements made most accurately when the l o gs a re se p a r a t e a n d a cc essi b l e t o me a s u rer. ▶ P i l es of l o gs c a nn o t e a s i l y b e m e a s u red accurately ▶ logs are neither cylinder nor of any regular geometric shape ▶ s h a p e o f a q u a dr a t i c p a r a b o l o i d i s a d o p t ed 72

73. Formu l ae for l og v o l u m e calculation ▶ Volume: traditional and important measure of wood quantity i n s p it e of i n c r ea s i ng u s e of w e i g ht or b i o m a s s a s a m ea s u r e of f o r e s t p r o d u c ti v it y. ▶ Ba s a l p o r ti on: f r u s t u m of N e i lo i d , ▶ the middle portion: frustum of Paraboloid and ▶ t he t op p o r ti on: c on e . ▶ Formula ▶ H u b e r ' s F orm u l a ▶ S m a l i a n ' s F o rm u l a ▶ N e u t o n ' s F orm u l a 73

74. 𝜋𝐿𝑑 2 4 ▶ H u b er ' s f o rm u l a : V = 𝑚 = LSm (paraboloid) 𝜋𝐿(𝑑 2 +𝑑 2 ) 8 ▶ Smalian's formula: V= 1 2 = 𝐿(𝑆 1 +𝑆 2 ) 2 (paraboloid) 𝜋𝐿(𝑑 2 +4𝑑 2 +𝑑 2 ) 24 ▶ Newton's formula: V= 1 𝑚 2 = 𝐿(𝑆 1 +4𝑆 𝑚 +𝑆 2 ) 6 (Neiloid) 74

75. Pr i s m oid a l or N e w to n 's F ormu l a ▶ B e s t a n d A cc u r a t e f or v ol u m e c al c ula t i on ▶ g i v e s v ol u m e of f r u s t u m of N e i lo i d ▶ used to calculate the error in volume calculated by o t h e r f o r m u lae ▶ d i ff i c u l t t o appl y f or s t a c k ed . 75

76. Sma l i a n ' s F ormu l a ▶ g i v e s v ol u m e of t h e f r u s t u m of P a r a b o lo i d & c y l i n d er ▶ o v e r e s t i m a t e s t h e v ol u m e ▶ ea s y t o u se d on s t a c k ed log ▶ P o s iti v e e rr or D i ff e r e n c e b e t we e n S & N = − 2 6 𝑆 1 +𝑆 2 × 𝐿 𝑆 1 + 4𝑆 𝑚 +𝑆 2 × 𝐿 = 𝐿 6 3𝑆 1 + 3𝑆 2 − 𝑆 1 − 4𝑆 𝑚 − 𝑆 2 = 𝐿 6 = 𝐿 3 2𝑆 1 + 2𝑆 2 − 4𝑆 𝑚 𝑆 1 + 𝑆 2 − 2𝑆 𝑚 76

77. Hu b e r ' s F ormu l a ▶ g i v es t he v olu m e of t he f r u s t u m of p a r a b o lo i d ( & c yl i n d e r ) ▶ u n d e r es t i m a t es t he v olu m e ▶ d i ff i c u l t t o a p p l y p a r ti c u l a r l y w h e n the lo g s a r e s t a c k e d ▶ m o r e e a s y a n d a c c u r a t e t h a n s m a l i a n ’ s f o r m u la ▶ N e g a ti v e e r r or D i ff e r e n c e be tw e e n H & N = 𝑆 𝑚 × 𝐿 − 6 𝑆 1 + 4𝑆 𝑚 +𝑆 2 × 𝐿 = 𝐿 6 6𝑆 𝑚 − 𝑆 1 − 4𝑆 𝑚 − 𝑆 2 6 = 𝐿 [2𝑆 𝑚 − (𝑆 1 + 𝑆 2 )] 77

78. Cubic Volume of squared t i m b ers ▶ 𝑉 = ▶ Qu a r t e r gi r t h f o r m u l a i s a l s o k now a s H o p p us formula, gives the under estimate ( only 78.5 % ) ▶ m e a s u r e d b y l og r u l e k no w n a s t he " qua r t e r gi r t h " . o r "H o p p us r u l e " i n w hich gi r t h i s m e a s u r e d i n i nch e s a t t he m i dd l e o f t he l og a nd l e ng t h i n f ee t , t he v o l u m e o f l og i n cub i c f ee t . 2 𝑔 𝐿 × 4 144 ▶ system of measurement used in Great Britain and also in Nepal for sale purpose when round timber i s s o l d b y v o l u m e Vo l u me = 𝜋 𝑟 2 𝑙 g = 2 π r & r = 𝑔 Vo l u me = π 2𝜋 𝑔 2 𝜋 2 𝐿 4 𝜋 F u l l c i r Vo l . ( V1 ) = 𝑔 2 𝐿 16 Q u art e r G Vo l . ( V ) = 𝑔 2 𝐿 T h u s 𝑉 1 16 𝑉 4𝜋 = = 0.785 = 78.5% 78

79. Stacked volume ▶ bulk volume occupied by the pieces of wood one meter long piled on one meter width, and o n e me t er h e i g h t . ▶ V o l u me c o n t a i n s a i r s p a c e ▶ p ili n g c o - eff i c i e n t u se d t o get t h e a c t u a l volume. ▶ If the wood were cylindrical and of the same diameter the piling co-efficient should be 4 ▶ 𝜋 = 0.7854 79

80. So l i d v o l ume of f i r e w ood ( I ) X y lo m e t ric m e t hod ▶ W : w = V : v ▶ Where, W is the weight of the whole stack of wood, w is the weight after submersed into a water, V is the volume of former and v is the volume of later ▶ This method is, however cumbersome and seldom used in practice ( II ) s p ecifi c g r a vi t y m e t hod ▶ if the specific gravity of wood is known then volume can be calculated from the weight of the billet, specific gravity of pieces of wood ▶ w e i g h t o f w o o d w e i g h t of s a me vo lu me of w a t e r ▶ O r r a ti o of t h e de n s it y of w o od a n d d e n s it y of w a t e r 80

81. D i m e ns i o n s of C ha tt a ▶ Standard size of Chatta = 5 ft x 5 ft x 20 ft = 500 cft including air space. ▶ On e C h a t t a i n me t r i c u n i t = 14 . 1 6 m 3 ▶ The following formula should be used in order to calculate the amount of fuelwood that is obtained from the total volume up to 10 cm top-diameter of class III and the remaining portions up to 20 cm top-diameter of class I and II trees which could not be used a s t i mb er. ▶ A mo u n t o f f u e l w oo d i n t erms o f n u mb er o f C h a tt a = (0.8778xvol.I+1.4316xvol.II+3xvol.III)/1000 Where, Vol.I = gross volume of up to 20 cm top-diameter of class I trees, Vol.II = gross volume of up to 20 cm diameter of class II trees and Vol.III = gross volume of up to 10 cm top-diameter of class III trees. 81

82. C l as s I = G reen , de a d o r d y i n g, s t a n d i n g o r u p r o o t ed tree having good and solid trunk in which sign of any disease or wound is not visible from outside. Class II = Green, dead or dying, standing or uprooted tree in which complete volume could not be realised due to hollowness or other sign of defect b u t a t l e a s t t w o s t r a i g h t l o gs o f e a c h 1 . 8 3 m ( 6f t ) l o n g o r o n e s t ra i g h t l o g o f 3 . 05 m ( 1 f t ) l o n g w h i c h sho u l d h a v e a t l e a s t 2 c m d i a me t er c o u l d b e recovered. Class III = Remaining trees which do not belong to class I a n d c l a s s I I 82

83. Me a s u rement of Form 83

84. Su b Headings Form F a c t or s a n d i t s t y p es For m q uo t ien t a n d i t s t y p es T a p e r T a b le 84

85. ▶ 3. 1 Form F a c t o r a n d I t s T y p es ▶ T ree h a s verit ies o f sh a p e a n d si z e ▶ F o r m i s d e f i n e d a s t h e r a t e of t a pe r of a lo g or stem. ▶ T a pe r i s t h e de c r e a s e i n d i a m e t e r of a s t e m of a t r ee or of a lo g f r om b a s e u p w a r d s. ▶ T h e t a pe r v a r i e s n ot only w it h spe c i e s , a g e , s it e and crop density but also in the different parts of the same tree. ▶ Basal portion of the tree corresponds to the f r u s t u m of N e i lo i d , the m i dd l e p o r ti on t o t h e f r u s t u m of P a r a b o lo i d a nd t he t op p o r ti on t o a cone D1 D2 D3 85

86. straight bole fine branches no apparent defects etc. Perfect tree form 86

87. not ideal some kinks in stem evidence of insect attack etc. Acceptable tree form 87

88. crooked bole severe butt sweep forked evidence of diseases e.g. rot Unacceptable tree form 88

89. 89

90. 90

91. 91

92. 92

93. T r e e form - theories Nu t ri t i o n a l t he o ry Water conducting theory H o r m o n a l t he o ry M e c h a nis t i c t he o ry o r M e t z ge r 's be a m t he o ry 93

94. ▶ Nutritional theory and Water conducting theory are b a se d o n i deas t h a t dea l w i th t h e m o v e m en t of liquids t h r oug h p ip e s . They r e l at e tr ee b o l e s ha p e to the need of the tree to transport water or nutrients w i t h i n t h e t r ee ▶ The hormonal theory envisages that growth substances, originating in the crown, are distributed a r ou n d a n d d o w n t h e b ol e t o con t r o l t h e a c t i v i t y of t h e cambiu m . T h e s e s u b stan c es w ou l d r ed u c e or enhance radial growth at specific locations on the bo l e an d t h us affe c t bo l e sha p e. 94

95. Metzger’s Theory Has received greatest acceptance so far Tree stem - a bea m o f u nif o rm res i s t an ce t o bending, anchored at the base and f un c t i o ning a s a l e v er  a s a C a n t i l e v er b e a m o f u ni f o rm s i z e a g a ins t t he b e n d ing force of the wind Maximum pressure is on the base so the tree rein f o rces t o w a r d s t he b a s e a nd m o re m a t eri a l d ep o si t ed a t l o w er en d s 95

96. Metzge r ’s Theo r y o r Gi r der Theo r y ▶ M e t z ger ▶ a Ge r m a n f o r e s t e r ▶ t h e o r y to e x p l a i n v a r i a t i o n s i n t a p er f r o m t r ee to t r e e a n d i n t h e s a m e t r ee . ▶ t h e t r ee s t e m s h o u l d b e c o n s i d e r ed a s a c a n t i l e v e r b e a m o f u n i f o r m s i z e a g a i n s t t h e b e n d i n g f o r ce o f t h e w i n d . ▶ T h e w i n d p r e s s u r e a cts o n t h e c r o w n a n d i s c o n v e y e d to t h e l o w e r p a r ts o f t h e s t e m i n a n i n c r e a s i n g m e a s u r e w i th t h e i n c r e a s i n g l e n g th o f the bole. ▶ Thus the greatest pressure is exerted at the base a n d t h e r e i s a d a n g er o f t h e t r ee s n a pp i n g a t t h a t place. ▶ To counteract this tendency, the tree reinforces i t s e l f t o w a r d s t h e b a s e. d L P 96

97. Metzge r ’s Theo r y o r Gi r der Theo r y ▶ The limited growth material is so distribute among the trees stem that it affords a uniform resistance all along its length to that pressure. ▶ As the pressure in the upper part of the tree is less, due to smaller l e n g t h o f t h e l ever i n t h a t p o r t i o n i t i s a ll o c a t ed l ess er gro w t h material than the lower part where the pressure gets increased with t h e i n c re a se d l e n g t h o f t h e b o l e. ▶ The pressure of wind on crowns keeps on changing as the tree is gro w i n g i n o p en o r c r o w ed p o r t i o n . 97

98. ▶ T r ee s g r o w i n g i n c o m ple t e i sol a ti on h a v e lar g e r c r o w n s and so the pressure exerted on them is the greatest. ▶ If such a tree is to exist, it should allocate most of the growth material towards the base even though it may have to be d one a t t h e e xpe n s e of h e i g h t g r o w t h . ▶ That is why trees growing in complete isolation or exposed situations have short but rapidly tapering boles while the trees growing in dense crops have long and nearly c yl i n d r i c a l bol e s. 98

99. Metzge r ’s Theo r y or G i r de r Theo r y ▶ T h i s c a n b e p r o v ed m a t h e m a t i c a l l y a s f o ll o w s : t h e n b y t h e r u l e o f m e c h a n i c s , ▶ S = [ ( P × l ) / d 3 ] × ( 32 / π) ▶ As the force P in case of trees consists of components W = wind pressure per unit area and F = crown area, it will be P = W ×F. Then, ▶ S = [ ( W × F × l ) / d 3 ] × ( 32 / π ) ▶ O r , d 3 = ( 3 2 × W × F × l ) / π × S ▶ For a given tree W, F and S can be considered as constant. Therefore, ▶ d 3 = k l , w h e r e k i s a c o n s t a n t. ▶ Thus, the diameter rose to the third power increases proportionately with lengthening of the lever or with the increasing distance from the central point of application of wind force, which can be assumed to be at the c e n t r e o f g r a v i ty o f t h e c r o w n . 17 P = f o r c e a p p l i ed t o a c a n ti l e v e r bea m a t i t s f r ee end l = the d i s t a n c e of a g i v e n c r o s s se c ti on f r om the po i n t of a p p l i c a ti on of th i s f o r c e , D = the d i a m e t e r of t h e be a m a t t h i s p o i nt a nd S = the be n d i n g s t r e ss kg/cm 2 , 99

100. 19 100

101. H ig h T a per ▶ Solitary ▶ Widely spaced ▶ H ea v i l y t h i n n ed L o w T ap er ▶ Groups ▶ Closed t o g e t h e r ▶ L i g h t l y t h i nn e d Co m pe t iti on f or Light Water Nutrients L e s s c o m pe t iti on H i g h c o m pe t iti on 101

102. De f inition o f F or m Factor ▶ Form factor is defined as the ratio of the volume of a t ree o r i t s p a rt t o t he v o l u m e o f a c y l ind er h a v ing the same length and cross-section as the tree. ▶ the ratio between the volume of a tree to the product of basal area and height. ▶ F = V / ( S × h) ▶ W here F i s t he f o rm f a c t o r, ▶ V i s t h e t ree v o l u me i n c u b i c u n i t s, ▶ S is the basal area at breast-height in area units, and ▶ h i s t h e h e i g h t o f t h e t ree i n li n e a r u n i t s. 102

103. Types o f F or m Facto r s ▶ D epen d in g o n t he height o f measurement of basal area and on t he p a r t s o f t he t ree c o nsi d ere d , f o rm f ac t o rs ar e o f t hree t y pe s . T hey are: Artificial (or breast height) form factor A b s o l u t e f o rm f a c t o r N o rm a l ( o r t r u e) f o rm f a c t o r 103

104. A r ti f ic i al ( or breas t h e igh t ) form factor ▶ For this form factor, basal area is measured at the breast height and the volume refers to the whole tree both above and below t h e po i n t of m e as u r e m e n t . Why is the artificial form factor not reliable? ▶ The point of diameter measurement is fixed and it bears no fixed relation to the height of the tree which is that of the whole tree a n d n ot of the po r ti on abo v e t h e b r e as t h e i g h t . ▶ So the trees of same form but different heights will have different f o r m f a c t o r s. ▶ Not withstanding its unreliability as a measure of tree form, the artificial form factor is universally used because its computation involves handy measurement. 104

105. Specific breast height form facto r s Cylinder 1 . ( > . 9) Neiloid . 2 5 ( . 2 - . 3) Conoid . 3 3 ( . 3 - . 4 5 ) Q u a dra t i c p ara b o l o i d . 5 ( . 45 - . 5 5 ) C ub i c p ara b o l o i d . 6 ( . 55 - . 6 5 ) I f t h e a p p r o p r i a t e b h f o rm fa c t o r f o r a t ree o f a g i ven age, species and site can be determined, then the s t em v o l u me i s ea si l y c a l c u l a t ed b y m u l t i p l y i n g t h e f o rm fa c t o r b y t h e t ree h e i g h t a n d b a sa l a re a . 105

106. Abso l u t e form f a c t or ▶ For this form factor, basal area is measured at any convenient height and the volume refers only to that part of the tree above the point of measurement. 106

107. N o rmal ( or t ru e ) form fac t or ▶ In this form factor, basal area is measured at a constant proportion of the total height of tree, e. g., 1/10th, 1/20th etc., of the total height and the volume refers to the w h o l e t ree a b o v e gr o u n d l eve l . ▶ This form factor has several disadvantages, viz., the height of the tree has to be determined before the point of m e a s u r e m e n t c a n be f i xe d , a n d T he po i nt of m ea s u r e m e n t m a y be v e r y i n c on v e n i e n t i n c a se of very tall as well as very short trees. ▶ Absolute and normal form factors are no longer used. 107

108. Use s o f F or m Facto r s T h e form f a c t o rs m a y b e u se d for fol l o w i n g p u r p o ses: 1 . T o es t i m at e v o l u m e o f s t a n d i n g t rees ▶ Form factors may be compiled into tabular form giving average form factor of trees of different dimensions by diameter and height classes. ▶ These tables can be used to estimate the volume of standing trees b y m e a s u r i n g the i r d i a m e t e r a n d h e i g h t . ▶ T o s t u d y t h e l a w s of g r ow t h ▶ F orm f a c t or a lon g w i t h f orm po i nt a nd f orm q u o t i e n t g i v e a n i ns i g ht into the laws of growth, particularly the stem form, of trees. 108

109. Fo r m q u otient Ratio of the diameter at two d i f f erent p l a c es o n t he t ree Gene r a l l y c a l c u l a t ed f o r s o m e point above bh to the dbh Abs o l ut e f o rm q u o t ien t – m o st common dbh bh 109

110. Fo r m Q u otien t an d Its Types Basically there are two types of form quotients Normal form quotient – postulated by A. Schiffel Absolute form quotient – postulated by T. Jonson i . N o r m a l f o r m q u o t i e n t ▶ I t i s t h e ra t i o b e t w ee n t h e m i d - d i a m e t e r a nd t he d b h . ▶ F Q = m i d - d i a m e t e r / d b h ▶ Drawback ▶ Schiffel’s formula was, obviously, not always true because in case of a tree of 2 × 1.3 m height, the mid-point will be breast height and therefore FQ will be 1. 110

111. ii . A b s o l u t e f o rm q u o t i e n t ▶ I t i s t he r a ti o of d i a m e t er or g i r t h of a s t em a t one h a l f of it s h e i g h t ab o v e the b r e a s t h e i g h t to the d i a m e t er or g i r t h a t b r ea s t - h e i g h t . ▶ Absolute form quotient is used in practice t h r ou g ho u t t he w o r l d . Form point - the point in the crown as which wind pressure is estimated to be centered. Form point ratio is defined as the relationship of t h e f o rm p o i n t a b o v e gro u n d l evel t o t h e t o t a l h e i g h t o f t h e t ree. 111

112. Taper Table and Formulae ▶ The rate of tree taper varies not only by species but also by age, dbh a n d t r ee h e i g h t. ▶ Taper tables are compiled by a series of diameter measurements t a k en a t i n t e r v a l s a l o n g t h e b o l e. Formulae ▶ Kozak et al. (1996) have shown that for certain coniferous species, upper stem diameters (dib) can be reliably predicted from this p a r a b o l i c f u n ct i o n : ▶ d 2 /d b h 2 = b + b 1 ( h / H ) + b 2 ( h 2 / H 2 ) ▶ T h e r e f o r e, d = d b h √[ b + b 1 ( h / H ) + b 2 ( h 2 / H 2 )] ▶ Where d = stem diameter at any given height h above ground ▶ H = t o t a l t r ee h e i g h t ▶ b 0, b 1, b 2 = R é g r e ss i o n c o e ff i c i e n ts 112

113. ▶ Diameter Taper Table : gives taper directly for dbh without referring to the tree form ▶ Form Class Taper Table : Dia at different fixed points on the stem expre s s e d a s % o f d b h ( u b ) f o r d i f f ere n t f o rm c lasses 113

114. G e n e r a l f or m u la e or eq u a ti ons f or t r ee f or m ; Ho j er ` s for m ula ▶ d / d b h = C l og c + l c ▶ Where, C and c are constants, l is the distance from the top of the tree to the point at which d is measured, expressed in percentage B ehre ` s for m ula ▶ d / d b h = l/ ( a + b l ) ▶ W h e r e , a a n d b a re c o n s t a n t s fo r e a c h c l a s s , s u c h t h a t a + b = 1 a n d d a n l h a v e t h e s a m e m e a n i n g a s g i v e n fo r H o j e r ` s fo rm u l a ▶ This formula is more consistent ( Reliable ) 114

115. Crown and foliage 115

116. Crown Measurement 116

117. Tree Crown The tree crown is the upper part of a tree that consists of the branches, leaves, and reproductive structures. It is the part of the tree that is visible above the trunk and is often referred to as the "canopy." The size, shape, and density of the crown can vary depending on the species of the tree, its age, and its growing conditions. The crown plays a vital role in the tree's survival by providing the tree with the ability to photosynthesize and produce energy, as well as protect the tree from environmental stressors such as wind, drought, and extreme temperatures. The crown is also important for ecological functions, such as providing habitat for wildlife and contributing to the overall biodiversity of the forest ecosystem. 117

118. Importance of Crown Measurement Estimating tree volume : Crown measurement provides an accurate estimation of the size and shape of the tree crown, which is used to calculate tree volume. Accurate tree volume estimation is essential for forest management and planning, such as predicting timber yield and planning harvesting operations. Assessing forest health : The size, shape, and condition of the crown can indicate the health status of the tree. A healthy tree will typically have a full, symmetrical crown with uniform branching, while a tree with a small or irregular crown may be suffering from stress, damage, or disease. Monitoring growth and stand dynamics : Crown measurement can be used to track the growth and development of individual trees over time. This information can be used to assess the overall health and productivity of the forest stand, as well as to predict future growth and yield. 118

119. Importance of Crown Measurement Evaluating competition : Crown measurement can help to identify competition for resources, such as light, water, and nutrients, between trees in the stand. This information can be used to develop management strategies that promote the growth and productivity of the most valuable trees. Planning silvicultural treatments : Crown measurement is essential for planning silvicultural treatments, such as thinning or pruning, which can improve the quality and value of the timber stand. Accurate crown measurements can help to determine which trees should be removed or pruned to achieve specific management objectives. 119

120. Methods of Crown Measurement Visual estimation : This involves making an approximation of the size and shape of the crown by eye. This method is quick and easy but may be less accurate than other methods. Tape drop method : This involves dropping a weighted tape measure from the top of the tree and measuring the distance between the ground and the tape measure. This measurement can be used to estimate the height and size of the crown. Point sampling : This involves measuring the distance from a fixed point to the edge of the crown at regular intervals around the tree. These measurements are used to calculate the average radius and area of the crown. 120

121. Tape drop method 121

122. Methods of Crown Measurement Photogrammetry : This involves taking aerial photographs of the tree and using software to create a three-dimensional model of the crown. This method can provide highly accurate measurements of crown size and shape. LiDAR : This involves using laser technology to create a three-dimensional model of the tree and its crown. This method can provide highly accurate measurements of crown size and shape, as well as information about the structure of the tree and the surrounding forest. Allometric equations : This involves using mathematical equations to estimate the size and shape of the crown based on measurements of other tree characteristics, such as diameter at breast height and height. This method is less accurate than other methods but can be useful when direct measurements are not feasible. 122

123. Leaf Area Index (LAI) 123

124. Leaf area index (LAI) Leaf area index (LAI) is a measure of the total area of leaves in relation to the ground surface area. It is an important parameter for characterizing vegetation structure and function, and is commonly used in ecological research, agriculture, and forestry. 124

125. Methods for measuring LAI Direct measurement : This involves physically collecting and measuring all of the leaves within a defined area. This can be time-consuming and labor-intensive, but provides the most accurate measurement of LAI. Non-destructive measurement : This involves using instruments such as a LAI-2000 plant canopy analyzer or hemispherical photography to indirectly measure LAI without collecting or damaging the leaves. This method is less labor-intensive but may not be as accurate as direct measurement. Remote sensing : This involves using satellite or aerial imagery to estimate LAI. This method is useful for large-scale monitoring but may be less accurate than direct or non-destructive methods. 125

126. Direct measurement of LAI Define the measurement plot : Define a plot within the selected area, typically 1-4 m² in size. The plot size should be large enough to capture the variability of the vegetation within the area. Harvest the leaves : Harvest all the leaves within the plot using a hand-held leaf area meter or scissors. The leaves should be collected in a way that ensures they are not damaged or crushed. Measure the leaf area : Measure the area of each individual leaf using a leaf area meter or by manually tracing the outline of each leaf onto graph paper and counting the squares. For small leaves, a leaf area meter is typically used, whereas for larger leaves, manual tracing is more common. Select a representative area: Choose a representative area of the vegetation that is typical of the whole vegetation type being studied. 126

127. Direct measurement of LAI Calculate LAI : Calculate the LAI by summing the leaf area of all leaves collected within the plot and dividing by the ground surface area of the plot. The ground surface area can be calculated by measuring the length and width of the plot and multiplying them. Repeat measurements : Repeat the above steps in multiple plots to obtain a representative estimate of LAI for the entire area of interest. Direct measurement of LAI can be time-consuming and labor-intensive, especially for larger areas, but it provides the most accurate measurement of LAI. It is important to ensure that the sampling design is representative of the vegetation being studied to obtain accurate and meaningful results. 127

128. Non-destructive measurement The LAI-2000 plant canopy analyzer is a portable device that measures LAI by detecting the amount and distribution of photosynthetically active radiation (PAR) within a plant canopy. The following are the general steps involved in using the LAI-2000 plant canopy analyzer: Set up the instrument : Set up the LAI-2000 plant canopy analyzer according to the manufacturer's instructions. This typically involves attaching the instrument to a tripod, connecting the sensor head to the main unit, and calibrating the instrument. Define the measurement plot : Define a plot within the vegetation being studied. The plot size should be large enough to capture the variability of the vegetation within the area. 128

129. Non-destructive measurement Take measurements : Hold the sensor head of the LAI-2000 plant canopy analyzer at a fixed height above the vegetation and take multiple readings at different angles to capture the amount and distribution of PAR within the plant canopy. The instrument records the PAR values and calculates the LAI. Calculate LAI : Calculate the LAI from the PAR readings using the software provided with the LAI-2000 plant canopy analyzer. The software uses algorithms to calculate the LAI based on the PAR readings and the angle of the sensor head 129

130. Using Remote Sensing to estimate LAI The following are the general steps involved in using remote sensing to estimate LAI: Acquire satellite or aerial imagery : Acquire satellite or aerial imagery of the area of interest. The imagery should have sufficient spatial resolution to capture the vegetation structure and cover the entire area of interest. Extract vegetation indices : Extract vegetation indices, such as the Normalized Difference Vegetation Index (NDVI) or Enhanced Vegetation Index (EVI), from the imagery. Vegetation indices are mathematical combinations of reflectance values in different spectral bands that are sensitive to the amount and health of vegetation. 130

131. Using Remote Sensing to estimate LAI Calibrate the vegetation indices : Calibrate the vegetation indices to LAI using ground-based measurements of LAI. This involves establishing a relationship between the vegetation indices and LAI using statistical models. Estimate LAI : Use the calibrated vegetation indices to estimate LAI for the entire area of interest. This can be done by applying the statistical models to the vegetation indices for each pixel in the image. Validate the LAI estimates : Validate the LAI estimates by comparing them to ground-based measurements of LAI or other independent sources of information. 131

132. Uses of Leaf Area Index (LAI) LAI is used to estimate crop yield and productivity by providing information on the amount of photosynthetic area available for plant growth and carbon assimilation. LAI is used to monitor the health and vitality of forests, as changes in LAI can indicate changes in forest structure, biomass, and productivity. LAI is used in climate models to estimate the exchange of energy, water, and carbon dioxide between the atmosphere and vegetation, which is critical for understanding the global carbon cycle and climate change. LAI is used in hydrological models to estimate the amount of water that is intercepted by vegetation, which is important for understanding water balance and water availability. 132

133. Uses of Leaf Area Index (LAI) LAI is used in ecological studies to understand the structure and function of plant communities, including species diversity, resource use, and competition. LAI is used in precision agriculture to optimize crop management practices, such as fertilization and irrigation, by providing information on the spatial and temporal variability of LAI within a field. LAI is used in remote sensing applications to estimate biophysical variables, such as vegetation cover, biomass, and productivity, which are important for monitoring land use and land cover changes, and for informing natural resource management policies. 133

134. Types of Sampling 134

135. Types of sampling ▶ Probability/random sampling ▶ Simple random sampling ▶ Stratified random sampling ▶ Multistage sampling ▶ Multiphase sampling ▶ Sampling with varying probabilities ▶ Non random sampling ▶ Selective sampling ▶ Systematic sampling 135

136. Simple Random Sampling ▶ I t is a selection process in which every possible combination of sample units has an equal and independent chance of being selected in the sample. ▶ Sampling units are chosen completely at random . ▶ For theoretical considerations, SRS is the simplest form of sampling and is the basis for many sampling methods. ▶ It is most applicable for the initial survey in an investigation and for studies that involve sampling from a small area where the sample size is relatively small. 136

137. Selection of SRS by lottery and random number table method When to use ▶ If the population is more or less homogenous with respect to the characteristics under study and If the population is not widely spread geographically . 16 samples are selected randomly from a population composed of 256 square plots 137

138. Advantages ▶ SRS is a scientific method and there is no possibility of personal bias . ▶ Estimation method are simple and easy . Disadvantages ▶ If the sample chosen is widely spread, takes more time and cost . ▶ A population frame or list is needed . 138

139. Systematic sampling ▶ In this sampling technique, first unit is chosen randomly and the rest being automatically selected according to some predetermined patterns . ▶ Systematic sampling is a commonly employed technique if the complete and up to date list of the sampling units is available . ▶ In this sampling, the sampling units are spaced at fixed intervals throughout the population. ▶ Measure of every i th tree along a certain compass bearing is an example of systematic sampling. ▶ A common sampling unit in forest surveys is a narrow strip at right angles to a base line and running completely across the forest, i.e. systematic sampling by strips. 139

140. ▶ Another possibility is known is systematic line plot sampling where plots of fixed size and shape are taken at equal intervals along equally spaced parallel lines. ▶ When to use - if the complete or up to date lists of the sampling units are available. 16 samples are selected systematically from a population composed of 256 square plots . 140

141. Jeetendra Gautam, Agriculture and Forestry University 141 Volume Calculation as per Forest Regulation 2079: Refer to next PDF