1. What Do You See? Message of the Day: Use variable area plots to measure tree volume

2. FOR 274: Forest Measurements and Inventory Variable Radius Plots Measuring BAF Measuring Basal Area Sites Density and Stocking Measures

3. To obtain information about a stand it is very common to sample the area with plots In fixed area plots the probability of selecting a tree about the plot center is constant for all trees Sampling methods exist where the decision to include a tree in a plot depends on the size of that tree These are called probability proportional to size (PPS) methods. PPS methods are used to measure stand volume as the selection probability of the tree will be proportional to its basal area. Fixed and Variable Area Plots: A Note on Probability

4. Fixed and Variable Area Plots: The Factor Concept In forestry we often summarize data in terms of measures per plot but often we really want a per acre measure To convert from per plot to per unit acre we scale the measures by a factor TF = Unit Area (Acre) / Sample Area (Plot) TF = Tree Factor Unit Area = 43,560 ft 2 or for metric: 10,000 m 2 Sample Area = size of plot (ft 2 or m 2 )

5. Fixed and Variable Area Plots: The Factor Concept Therefore, each tree selected for measurement represents *TF* trees per units area: hence “Tree Factor” For this 1/10 th acre square plot each measured tree “represents” 10 trees per acre.

6. Expansion Factors: The Basal Area Factor (BAF) BAF = Basal Area * Tree Factor (TF) BAF = 0.005454*(DBH) 2 *(unit area/plot area) BA per unit area = SUM (BAF) = TF * SUM (BA of all trees) In fixed area plots, the Tree Factor is constant making the calculation of basal area easy. The Basal Area Factor (BAF) is the number of units of basal area per unit area represented by each tailed tree

7. Variable Area Plots: Calculating the BAF In variable probability (or variable area) plots: probability of selecting a tree depends on the size of the tree Source: Husch Beers and Kershaw In variable radius plots calculating the BAF is more tricky as the sample area is not constant.

8. Variable Area Plots: Calculating the BAF At the edge of the plot the constant, k = 2 sin (θ/2) By working through the calculations (p275) we find: BAF = 10890*k 2 Plot radius is proportional to tree diameter: For trees right at edge the Ratio of Diameter (D) to Radius (r) = a Constant, k

9. BAF: Calculating BAF from an angle For an object of fixed width, held a fixed distance away from your eye you can work out the angle θ: Thumb: 2/3 “ held at 24” away θ = tan -1 (half width / distance) = 0.3333/24 θ = 0.79° k = 2 sin (θ/2) = 0.014 BAF = 10,890 k 2 = 2.13 Therefore your thumb “represents 2.13 units of basal area for each tree measured”

10. BAF: Calculating Whether Trees are In For a known BAF, say 10, we can work out k 10 = 10,890 k 2 k = 0.0303 For known tree diameters: We can work out the maximum (or limiting) distance a tree can be at to be “Included” within the plot Remember: k = D/r therefore, r = D/k For example a 10” tree will be “in” if within: r = 10/0.0303 = 330” = 27.5 feet

11. BAF: Calculating Whether Trees are In To make things easier, we often use limiting distance tables to calculate whether the trees are IN or OUT of the plot.

12. Variable Probability Plots: Horizontal Point Sampling The Method: Observed stands at plot center Uses a device to projects an angle horizontally to each tree – aiming at DBH height All trees with diameters > apparent object width are counted Then scale all measures to per unit area using the BAF

13. Measuring Basal Area: Using Your Angle Gauge

14. Thinking About Measurements: Basal Area

15. Prisms –Most commonly used sighting angle gauge –Relatively inexpensive –“Built-in” method for correcting for slope –Infinite number of BAFs available. –Offsets the viewed image slightly Thinking About Measurements: Basal Area

16. Trees is counted if its image overlaps the image seen above and below the prism Borderline trees Trees not counted if image does not overlap Thinking About Measurements: Basal Area

17. Prisms and Slope:

18. Basal Area: The Angle Gauge Select BA Factor (5, 10, 20, 40) to ensure tally of 5-12 trees Center eye over Plot Center Hold chain ‘like an archer’ and aim the gauge at the target trees’ breast height Circle around plot center and aim gauge at tree’s DBH If tree DBH > Angle Gauge Width ADD to tally BA/unit area = BAF * Tally

19. Angle Gauge Example: BAF = 10

21. BAF: Using Reloskops

22. In the next lab we will use these instruments

23. Forest Descriptions: Overview O’Hara et al (1996), http://forestry.sfasu.edu/faculty/jstovall/silviculture The forests we measure are usually described by common terminology.  Stand: A contiguous group of trees sufficiently uniform in some way (age distribution, composition, structure) and growing on a site of sufficiently uniform quality, to be a distinguishable unit  Cohort: A distinct aggregation of trees originating from a single natural event or regeneration activity, or a grouping of trees  Rotation: The period of time required for an entire stand to be successfully established, grown, harvested, and re-established.  Succession: A series of dynamic changes by which organisms succeed one another through a series of plant community (seral) stages leading to potential natural community or climax  Stand Structure: Often described by the 4 stage Oliver and Larson (OL) model of stand initiation, stem exclusion, understory re-initiation, and old growth. Definitions from: http://oak.snr.missouri.edu/silviculture/silviculture_terminology.htmhttp://oak.snr.missouri.edu/silviculture/silviculture_terminology.htm Free online silvaculture book: http://forestry.sfasu.edu/faculty/jstovall/silviculture/index.php/silviculture-textbook http://forestry.sfasu.edu/faculty/jstovall/silviculture/index.php/silviculture-textbook

24. Forest Descriptions: Stand Initiation aaa Fast Facts: Generally produced following a stand-replacement disturbance. At the end of the stand initiation phase the growing space is completely occupied. Generally one cohort with a single canopy stratum, although may have gaps Cohort is young and trees per acre generally very high. Live crown ratios ~ 100%. At start no nutrient or growth limitations present. O’Hara et al (1996), http://forestry.sfasu.edu/faculty/jstovall/silviculture

25. Forest Descriptions: Stem Exclusion Fast Facts: The young / large trees per acre cohort will reach a point where no new individuals establish and some of the older trees die. In Open Stem Exclusion competition by sub-canopy species causes breaks in the dominant species canopy cover by limiting the establishment of new dominant trees. In Closed Stem Exclusion new trees are generally limited by lack of light due to near complete canopy closure. Live crown ratios drop below 100% and understory becomes very shaded. Mortality is driven by density and nutrient limitations. O’Hara et al (1996), http://forestry.sfasu.edu/faculty/jstovall/silviculture

26. Forest Descriptions: Understory Re-initiation Fast Facts: As the stand growth continues, a new cohort initiates in the understory as gaps appear in the canopy of the older cohort. These gaps occur from density independent mortality (e.g., fire, insects, wind throw, etc.,). Multi-story stand, with overstory of snags, poles, or large trees and understory of seedlings and saplings. Snags and large woody debris often present. Shade tolerant species become established. O’Hara et al (1996), http://forestry.sfasu.edu/faculty/jstovall/silviculture

27. Forest Descriptions: Old Growth O’Hara et al (1996), http://forestry.sfasu.edu/faculty/jstovall/silviculture Fast Facts: Late in the lifecycle of a stand, old trees will die off allowing some trees in a younger cohort to also occupy the overstory Live trees with large branches and large diameters present Large amounts of snags and large woody debris present Disease and rots present in many trees

28. Sites: What is a Site Anyway? Site: the environment or area where a tree or stand grows The characteristics of a site drive the type, quality, and quantity of vegetation that can exist there Avery and Burkhart Chapter 15

29. Sites: Why do we Make Site Measurements? Historical records of productivity data do not exist for many forests Several factors affect productivity: Soil nutrients, light availability, topography, etc This leads to indirect methods Avery and Burkhart Chapter 15 An inherent property used to predict the “potential” of a given site to produce products under a given management prescription

30. Sites: Tree Height as a Site Measurement Relations between Tree Height and Age: Practical & Consistent Sensitive to site characteristics Relatively insensitive to thinning intensity Strongly related to volume We define this measurement of a site as a Site Index Avery and Burkhart Chapter 15

31. Sites: Tree Height as a Site Measurement A site index tells us how fast trees grow in height, diameter, and crown widths and how fast a yield will be obtained from the site Yield: The total amount available for harvest at a given time Growth: Incremental increase in a unit time interval

32. Sites: Tree Height as a Site Measurement Site Index: Average total height of dominant and codominant trees in well- stocked even-aged stands Avery and Burkhart Chapter 15 When relations between tree height and age have been established for certain species we can produce predictive curves

33. Sites: Species-Specific Height Index Curves Q: Tree is 20 years old and 45 feet, what will be its height at 70 years? Avery and Burkhart Chapter 15

34. Sites: Species-Specific Height Index Curves Q: Tree is 30 years old and 50 feet, what age will it be when its height is 75 feet? Avery and Burkhart Chapter 15

35. Sites: Species-Specific Height Index Curves Avery and Burkhart Chapter 15 Age can be: Age at DBH Plantation Age Total Age If total age used, remember to add the years of growth to DBH A Note on Age …

36. Sites: Species-Specific Height Index Curves Avery and Burkhart Chapter 15 Standard Site Index age values: The height of the stand at which the mean annual growth (as compared to the lifetime of the tree) occurs Western Forests: 100 yrs Eastern Forests: 50 yrs

37. Sites: Other Index Curves A Soil Depth and Elevation Site Index: Avery and Burkhart Chapter 15

38. Sites: Measuring Site Trees Avery and Burkhart Chapter 15 Site Trees: Dominant or Codominant in even-aged stands with no evidence of damage, suppression, or deformity Measurements: Max Tree Height – clino/hypsometer Tree Age - corer

39. Sites: Problems with Site Indices Avery and Burkhart Chapter 15 Stand age is difficult to measure precisely and small errors can lead to very LARGE differences Not optimal in non even-aged stands Age and Height may not provide enough information in some sites The values for a site can change due to climate or management activities Most indices are species specific

40. Site Density: How Thickly do Trees Grow? Stand Density - stem spacing and separation (e.g., stems per acre) An important variable that foresters manipulate to develop a stand Site and Density together define how much timber is expected to be produced Stocking: The degree to which a stand meets a given management objective

41. Site Density Measures: Basal Area per Acre Basal Area per Acre: Easy to understand Easily measured from point sampling Highly correlated with volume and growth

42. Site Density Measures: Trees per Acre Trees per Acre: Plantation measure Limited value in natural stands

43. Site Density Measures: Relative Spacing Average Distance between trees is divided by height of the dominant canopy RS = [√(43,560/trees per Acre)] / Height Dominant Height

44. Site Density Measures: Crown Competition Factor Area available to the average tree in a stand as compared to the maximum area it would use if it were open grown

45. Site Density Measures: The Stand Density Index Stand Density Index (SDI): Developed by Reineke in 1933 Uses diameter, D q, of tree with the average BA (quadratic mean diameter) and number of trees per unit area (N) Reineke Observed that for each species: Different fully stocked even-aged stands with the same D q have ~ maximum N

46. Site Density Measures: The Stand Density Index Davis Chapter 4 Stand Density Index (SDI): Constant slope Intercept varies with species log N = -1.605log D q + k N = number of trees per acre D q = Quad Mean Diameter k = species constant Via Mathematical Gymnastics!!! SDI = N(D q /10) 1.065

47. Site Density Measures: The Stand Density Index Davis Chapter 4 Use: Parallel Lines - Equal Stand Density Convert number of trees at any quadratic mean diameter, D q, to the equivalent density at a D q = 10”

48. Site Density Measures: The Stand Density Index Davis Chapter 4 Maximum SDI by Species in natural stands: Redwood = 1000 Douglas Fir = 595 Longleaf Pine = 400 Stocking = SDI Actual / SDI Maximum