Determinants of productivity Site index Guide curve method Stem analysis method Repeated measurement method One vs. two equation systems Determining site index Growth intercept Plant indicators Soil-site relationships
Productivity is the inherent capability of the land to produce wood volume or tree biomass of the specified species. GPP = gross primary productivity NPP = net primary productivity = total dry matter production by primary producers (plants) = GPP respiration
RESPIRATION NPP FOREST BIOMASS TREE BIOMASS STEM WOOD GPP
Determinants of productivity Soil Nutrients Water holding capacity Water table level Depth Temperature Texture Climate Daytime temperature Nighttime temperature Rainfall (amount and timing) Humidity (vapor pressure deficit) Solar radiation Length of growing season Extreme events (temperature, vapor pressure deficit,... Soil micro-organisms, including bacteria and mycorrhizae
Estimates of regional site index from an ecophysiological growth model, 3PG Swenson and Waring (2005)
One driving variable for the ecophysiological growth model, 3PG, is soil N. Soil N is integrated with climatic data and other soil variables like water holding capacity Swenson and Waring (2005)
Properties of an "Ideal" Measure of Productivity 1. The measure should be very highly correlated with potential, maximum wood volume (or biomass) for the stand (e.g., maximum MAI). 2. The measure should be independent of stand density. 3. The measure should be independent of thinning regime (i.e., manipulations of stand density). 4. The measure should be specific to the species or genotypes that convert site resources into biomass
The most common measures of productivity applied in forest management are: 1. Site Index 2. Growth Intercept 3. Plant Indicators 4. Soil-Site 5. Net photosynthesis or NPP from an ecophysiological model
Site Index: The total height of the dominant /codominant component of a stand at a specified base age King s (1966) 50-yr site index for coastal Douglas-fir Base age 50 yrs Site index curves for 50 to 160 ft at 50 yrs
Base Age: The reference age for determining site index. Base age can be expressed as either a total, breast height, or plantation age, in years. The base age is often set near the average rotation length for the species. Common base ages in the western United States are 50 and 100 years. In the South, a base age of 25 years is not unusual.
Flewelling et al. (2001) developed site index curves of base age 30 for intensively managed Douglas-fir stands
Site Index Equation: Predicts site index from age (either total, breast height or plantation age) and dominant height. Depending upon the equation, age and dominant height can be either individual tree values or an average for the stand.
Dominant-Height-Growth Equation: Predicts dominant-height from age (either total, breast height, or plantation age) and site index. Depending upon the equation, age and dominant height can be either individual tree values or an average for the stand.
Anamorphic Equations: Exhibit the property that the shape of the height-age curve for a particular site index is the same regardless of the value of the site index. Therefore, all site index curves are proportional to each other, the difference between two curves being proportional to the ratio of their site indices.
Polymorphic Equations: Exhibit the property that the shape of the height-age curve for a particular site index is different from that of other site indices. Therefore, the difference between two curves is not proportional to the ratio of their site indices.
Three common methods of constructing site index equations have been applied: 1. Guide Curve Method 2. Stem Analysis Method 3. Remeasurement Method
Guide curve method for constructing site index equations McArdle - Bulletin 201 site curves Base age 100 years 100 yrs
Guide curve method for constructing site index equations So how is it done? Pairs of height and age measurements are collected from a large number of sampled trees or stands The data points corresponding to the height-age pairs on plotted, age on X-axis and height on Y-axis A guide curve is drawn through the data, or a regression equation is fitted to the data The height at the desired base age for the guide curve is determined
Example from class notes: inland Douglas-fir from Brickell (1968) Guide curve crosses 70 ft at 100yrs. To get site index 50, multiply the guide curve by 50/70.
Guide curve method for constructing site index equations So how is it done? (cont d) Curves for specific site indices (e.g., increments of 10 or 20 feet) are determined by multiplying the guide curve points by the ratio of the desired site index to the guide curve site index: H A,S = H A,G (S/S G ) H A,G = Dominant height at age A from the guide curve H A,S = Dominant height at age A for site index S S G = Site index of the guide curve S = Desired site index
Example from class notes: inland Douglas-fir from Brickell (1968) Guide curve crosses 70 ft at 100yrs. To get site index 50, multiply the guide curve by 50/70.
Guide curve method is very handy for forest types and geographic regions with little or no history of permanent plots, as was true almost everywhere during early days of forestry in the United States. Bulletin 201 The yield of Douglas-fir in the Pacific Northwest (McArdle et al. 1949) Bulletin 354 Preliminary yield tables for second-growth stands in the California pine region (Dunning and Reineke 1933)
A useful reference of the literature on site index and dominant height growth curves was produced in 1995 by David Hann: Hann, D.W. 1995. A key to the literature presenting site index and dominant height growth curves and equations for species in the Pacific Northwest and California. Forest Research Laboratory, Oregon State University, Corvallis. Research Contribution 7. pdf is posted on T:\Teach\Classes\FOR\publications
Three common methods of constructing site index equations have been applied: 1. Guide Curve Method 2. Stem Analysis Method 3. Remeasurement Method
Stem analysis method for constructing site index equations Small sample of dominant/codominant trees is felled and sectioned at short intervals (e.g., 4-8 ft) At top of each section measure Height from ground Ring-count age in years Reconstruct past height growth of each tree and its interpolated height (site index) at desired base age. (Note that the sample trees have to be at least as old as the desired base age.) Apply regression analysis to develop site index equations dominant height growth equations
Cross-sections showing ring counts on Austrian black pine collected by Dr. Philippe Dreyfuss of INRA, Avignon, France 14 rings 68 rings 116 rings
Stem analysis method for constructing site index equations Stem profile reconstructed by stem analysis. Ring counts and diameters taken at heights marked by arrows. Allow reconstruction of past height growth of tree.
Annual height growth of dominant Austrian black pine reconstructed by stem analysis.
Cumulative height growth of dominant Austrian black pine reconstructed by stem analysis. base age 50 yrs total age base age 100 yrs total age
Stem analysis method for constructing site index equations Example: Douglas-fir tree in Table 2 took 62 years to grow from breast height to current total height of 160.4 ft. So, breast height age is 62 years. BHA i = RC bh RC i where BHA i RC bh RC i = Breast height age for the i th section height = Ring count at breast height = Ring count at i th section height
Stem analysis method for constructing site index equations To get height at base age of 50 years at breast height: SiteIndex 130.5 (138.9 130.5) =130.5 +(8.4)(1/4) =130.5 + 2.1 =132.6 ft 50 53 49 49 50
Total height (ft) FOR Cumulative height growth for sectioned tree. 180 160 140 Tree 370-1-6 120 100 80 60 40 20 0 0 10 20 30 40 50 60 70 Breast height age (yrs)
Stem analysis data can be used to develop dominant height growth equations that are either anamorphic or polymorphic, depending on the selected statistical model. Most are polymorphic, because the detailed analysis of individual tree growth reveals that dominant height growth patterns among different site indices are in fact polymorphic, i.e., not proportional across full age range.
Examples of equations developed from stem analysis methods: Douglas-fir Second growth in western WA (King 1966) High elevations in OR & WA (Curtis et al. 1974) Eastside of Cascades in OR & WA (Cochran 1979) Western Montana and northern Idaho (Monserud 1984) Dry sites on Willamette N.F. (Means and Helm 1985) Southwestern Oregon (Hann and Scrivani 1987) Noble fir High elevations in Cascades of OR & WA (Herman et al. 1978) Ponderosa pine Eastside of Cascades in OR & WA (Barrett 1978) Northern California (Powers and Oliver 1978) Southwestern Oregon (Hann and Scrivani 1987) Other examples in Hann (1995) Key to the literature presenting site index and dominant height growth curves and equations for species in the Pacific Northwest and California
Summary of Douglas-fir site index equations developed from stem analysis Source Sample size Upper age Curtis et al. (1974) 52 trees 400 yrs Means and Helm (1985) 27 trees 280 yrs Hann and Scrivani (1987) 89 trees 136 yrs Means and Sabin (1989) 55 trees 120 yrs King (1966) 85 plots 130 yrs (850 trees) Total 223 trees
Geographic range of Douglasfir site index equations developed from stem analysis General conclusion: Numerous studies of site index in region, but studies have : Small sample sizes Restricted age range Restricted geographic range
Three common methods of constructing site index equations have been applied: 1. Guide Curve Method 2. Stem Analysis Method 3. Remeasurement Method
Remeasurement method for constructing site index equations Sample of stands is selected for installation of permanent plots Dominant trees are identified, typically the largest 40 trees per ac by dbh Initial heights and breast height age measured; or, plantation and/or seedling age is recorded. Total height is measured periodically, and ages computed from initial age to yield height-age pairs The more the frequent measurements and the longer the duration of the permanent plots, the better the resulting dominant height growth and site index equations
Remeasurement method for constructing site index equations Resulting equations can be either anamorphic or polymorphic, depending on choice of the statistical/mathematical model As with equations developed from stem section data, most are polymorphic because dominant stand height development among different site indices is generally polymorphic. Note: King s (1966) widely applied site index curves/equations are most accurately described as being constructed by stem analysis: height-age pairs were determined by measuring heights to successive whorls on Douglas-fir. HOWEVER, dominant height-age pairs were averaged for trees on a plot, so equations apply to top height development of plots vs. individual dominant trees
Height growth implied by Flewelling et al. (2001) site index curves (H40) based on remeasurement of Stand Management Cooperative plots.
Examples of equations developed by the remeasurement method: Douglas-fir Second growth in northwestern OR & western WA (Bruce 1981) Young plantations in northwestern OR & western WA (Flewelling et al. 2001) Western hemlock Southwestern BC, western WA & northwestern OR (Bonner 1995)
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Comparison of the three methods for constructing dominant height growth and site index equations Assumptions built into the guide curve method: 1. All site indices are equally represented across the full range of stand ages. 2. The shape of the height-age curve is independent of site index. 3. The frequency and severity of height damage that the sampled plot experienced in the past are typical of the population to which the equations will be applied.
Violation of any of the three assumptions built into the guide curve method can result in biased site index and dominant height growth curves. 1. Example of UNEQUAL representation of all site indices across the full range of stand ages.
Equal distribution of all site indices across all ages High Medium Low
Lack of plots at high site indices at later ages FOR
Lack of plots at high site indices at later ages FOR
Assumption 1: Violated if historical trend of harvesting the highest sites first (higher volumes), resulting in overrepresentation of high sites at young ages and under-representation of high sites at old ages. Declining site index over age (e.g., Monserud 1984) would make dominant height growth curves too high below the base age and too low above the base age, resulting in flatter growth curves.
Monserud guide curves vs. stem analysis curves fitted to same dataset.
Assumption 2: REALITY: Objective statistical analysis of data from stem analysis and plot remeasurement typically result in polymorphic curves forms. This result suggest that assumption 2 is probably not biologically realistic.
Assumption 3: Trees which appear perfectly sound and healthy while standing often exhibit hidden height damage when sectioned (e.g., 51 out of 140 Douglas-fir in southwestern Oregon). Single measurement data used to develop guide curves usually do not include information on frequency and severity of past height damage, so it is impossible to assess whether or not the modeling data are typical.
Problems associated with stem analysis method Elimination of sectioned trees with any past height damage Under-estimate site index if applied to dominant trees with hidden height damage Over-predict dominant height growth of real stands with typical frequency of height damage All sample trees must be older than base age Resulting height growth curves describe population of trees that survive to older ages, so may not be representative of stands at young ages Shooters with rapid early growth, stayers with slow early growth and faster later growth
Height FOR stayers shooters Fitted curve misses shooters so underestimates height growth at young ages Base age Age
Relative merits of remeasurement method Advantages: Avoids problem of shooters and stayers if remeasurements cover both the shooter phase and stayer phase of stand development. Represents the top height development of stands that experience the same frequency and severity of top damage as occurred in sampled plots. Disadvantages: More subject to error in height measurements than stem analysis Requires large investment in time and money to collect adequate data. Historically restricted to even-aged stands of commercially important species.
Y (SITE INDEX) FOR Two-equation site index/h40 system (AGE fixed) X on Y Y on X X (H40)
One- vs. two-equation systems for site index and dominant height growth Site index curves constructed with top height on Y-axis and age on X-axis; site index determined by matching an observed height-age pair to nearest or interpolated site index Early site index equations similarly expressed top height as function of age; solve equation for site index for a given height-age pair In regression analysis get different equation for: Site index = f( age, top height) Top height = g( age, site index) Solution has been to develop two separate equations
Dominant height growth curve for Douglas-fir in southwestern Oregon (Hann and Scrivani 1987)
Site index curve for Douglas-fir in southwestern Oregon (Hann and Scrivani 1987)
Interesting results of two-equation systems Hann and Scrivani (1987) found that estimating site index from the dominant height growth equation gave better predictions of future height growth rates than using the twoequation system
Determining site index for a stand 1. For what kind of stands is the application of the site index curves appropriate? 2. What kind of trees should be selected for measurement of site index? 3. How many trees should be measured in the stand? 4. What age (i.e., total, breast height or plantation) does the site curve use? 5. How should multiple species stands be measured? 6. Should the heights and ages be averaged for the stand before using the site index equation or should site index be determined for each tree and the site index values averaged to determine average stand site index?
King s (1966) method: 1.Establish a fixed area plot that encompasses 50 Douglas-fir trees that are 1.6 inches in dbh or larger. 2.Measure total height and breast height ages on the 10 trees with largest diameter. 3.Compute the average height and age of the 10 trees. 4.Use these average values to estimate site index.
Example of King s (1966) method: 1. Sort sample trees by decreasing DBH 2. Accumulate expansion factors 3. Find tree at which cumulative expansion factor equals or exceeds 40 trees per acre 4. Determine each tree s weight (tpa) for computing H40 (height of 40 largest trees per ac) - For all but the smallest tree, this contribution will be the expansion factor - For the smallest tree, this contribution will be the amount of its expansion factor need to total 40 trees per ac 5. Compute H40 as weighted mean using expansion factors as weights
Expansion Cumulative Contribution DBH HT Factor to H 40 13.5 75.2 15.00 15.00 15.00 12.5 76.8 10.00 25.00 10.00 11.4 73.8 30.00 55.00* 15.00# 10.6 71.8 55.00 110.00 0.00 9.5 69.9 80.00 190.00 0.00 8.6 67.5 100.00 290.00 0.00 7.5 64.5 100.00 390.00 0.00 6.5 61.6 150.00 540.00 0.00 5.5 57.2 155.00 695.00 0.00 4.6 52.0 180.00 875.00 0.00 3.5 45.2 75.00 950.00 0.00 3.0 39.4 15.00 965.00 0.00
H 40 = [(15.0x75.2) + (10.0x76.8) + (15.0x73.8)]/40.0 = 3,003.0/40.0 = 75.075-feet The breast height age (A b ) of example stand was: 23-years.
Calculation of King's (1966) site index: S = 4.5 + (2500.0 X 6 )/(X 7 - X 8 ) Where, S = Site index of the stand, feet X 6 = 0.109757 + 0.00792236 A b + 0.000197693 A 2 b X 7 = A b2 /(H 40-4.5) X 8 = -0.954028 + 0.0558178 A b - 0.000733819 A 2 b Site index = 4.5+[2500(0.396550877)]/[7.495572086-(-0.058408851)] = 135.7 feet at 50 years
Calculation of King's (1966) dominant height growth: H 40 = 4.5 + A b2 /(X 1 + X 2 A b + X 3 A b2 ) Where, X 1 = -0.954028 + 0.109757 [2500./(S-4.5)] X 2 = 0.0558178 + 0.00792236 [2500/(S-4.5)] X 3 = -0.000733819 + 0.000197693 [2500/(S-4.5)] Predicted H 40 at age 70 would be: H 40 =4.5+70 2 /(1.13737825+0.206777404(70)+0.003033197(70 2 ) H 40 =165.3 feet
Advantages of site index: 1. Because height growth is highly correlated with volume growth, height at an index age should be highly correlated with maximum potential volume in stands without stockability problems. 2. For a number of species, height growth of dominant trees is relatively unaffected by stand density. However, for some species dominant height growth is affected by density. 3. Height growth rate of a specified species is usually unaffected by the species composition of the stand.
Diadvantages of site index: 1. Site index values do not allow easy comparison of productivity potential between species. Different base ages may have been used for each species, or each species may approach different maximum size-density relationship which would result in different potential volume for a given site index. 2. It is difficult to apply site index in mixed species stands. 3. It is difficult to apply site index in uneven-aged stands because many dominant trees have not been free growing throughout their life spans. 4. In stands with stockability problems, site index may not be highly correlated with maximum potential volume.
Disadvantages of site index (cont d): 5. Site index may change over time due to changes in climate, or to treatments such as fertilization, drainage of soils, or introduction of genetically improved trees. 6. The measurement of height and age and the subsequent calculation of site index can be complicated, resulting in substantial estimation error. 7. Site index equations are usually very imprecise at young ages (under 20 years). 8. Site index equations cannot be applied to areas that currently have no trees. 9. Site index should not be applied in high-graded stands or stands that have been thinned from above (removing all dominants).
Growth intercept method Uses a measure of the periodic height growth rate near breast height for dominant trees as an indicator of productivity.
Growth intercept method Periodic height growth rate is determined by measuring the distance between a specified number of whorls (or, the length of a specified number of internodes). The method can only be applied to species with distinct whorls. The number of internodes used varies between three and five depending upon the study. Which internodes to use for the length measurement also varies between studies and is usually defined in relation to breast height.
Growth intercept method Measure distance between n th and (n+i) th whorl above breast height, where i= 3, 4, 5
Growth intercept method The growth intercept value can be used to predict site index by the relationship: Site Index = b 0 + b 1 (Growth Intercept Value) As an example, Powers and Oliver (1978) presented the following equation for ponderosa pine in northern California growing on soils other than schist inceptisols: S = 21.94 + 8.68(HI) HI = height increment between first 5 whorls (4 yrs) above breast height
Growth intercept method Measure distance between n th and (n+i) th whorl above breast height, where i= 3, 4, 5
Advantages and disadvantages of growth intercept: Advantages of Growth Intercept Method Some feel that the method is superior to standard site index methods for determining productivity of young stands. Growth intercept is generally considered to be easier to measure than the total height and age values needed to estimate site index directly. Disadvantages of Growth Intercept Method The method is based only on early height growth rate which may not be representative of the rate that can be expected throughout the tree`s lifetime. The method can be more easily influenced by relatively short term climatic fluctuations because of the relatively short growth period length.
Plant Indicators The presence of certain overstory and/or understory plant species to indicate productivity is based on the proposition that these plants integrate the environmental conditions that determine potential productivity of the site. Habitat type or plant association can be correlated with site index; however, a substantial range in site indices can also be observed on a given habitat type or plant association. Therefore, other topographic, physiographic, geologic and/or landform information is often used to further refine the estimator of productivity (e.g., slope, aspect, elevation).
Plant Indicators Carmean (1975) lists the following reasons why plant indicators have not been more widely used as productivity variables in the United States: Topographic, geologic and soil features often explain the same site characteristics as plant indicators. Overstory species composition can affect the vigor and composition of the understory, even on similar soils. Overstory density can affect the abundance, vigor and composition of the understory. Overstory trees are affected by the characteristics of soil horizons deeper than those affecting the understory. Many understory species die back during winter making their use as indicators difficult or impossible during that time.
Plant Indicators Plant indicators have also been used to refine dominant height growth and site index equations. For example, it has been shown that the dominant height growth and site index equations for Douglas-fir (Monserud 1984) in northern Idaho and western Montana differ by habitat type. Differences by habitat type have also been found for mountain hemlock in the Cascade Mountains of Oregon and for Douglas- fir in the Coast Range of Oregon.
Soil-site relationships Recognizing that soil properties are one of the basic factors affecting productivity, there have been a large number of studies that have related soil properties to a measure of stand productivity. Most of these studies have predicted site index as a function of soil attributes. Often these equations also contain variables related to topographic, physiographic, geologic and/or landform attributes.
Soil-site relationships For example, Steinbrenner (1979) reported the following equation for predicting site of Douglas-fir index growing in western Oregon on sites receiving less that 60 inches of annual precipitation: S = b 0 + b 1 (ED) 2 + b 2 (PR) 3 + b 3 (SL) + b 4 (EL)(POS) + b 5 (EL)(SL) + b 6 (TC)(DA) + b 7 [(TC)(DA)] 2 (R 2 =0.74) S = King s site index ED = effective soil depth PR = precipitation SL = slope percent POS = position on slope EL = elevation TC = total clay DA = depth of A horizon
Soil-site relationships Carmean (1975) claims that "most of the successful soil-site studies explain perhaps 65-85% of the variation in tree height, or site index..." However, Monserud et al. (1990) found that: Physiographic variables and plant indicators alone could explain 42% of the variation in Douglas- fir site index in northern Idaho and western Montana Soil variables alone could explain only 16% of the variation in site index The addition of soils variables to physiographic and plant indicator variables explained a total of 49% of the variation (7% over the physiographic and plant indicators alone).
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