Christie Staudhammer, Francisco Christie Staudhammer, Francisco Escobedo, and Luis Fernando OsorioEscobedo, and Luis Fernando Osorio

School of Forest Resources and Conservation School of Forest Resources and Conservation

Background Accurate estimates of tree biomass are

important to support research in carbon storage, bioenergy, harvest studies

Urban tree biomass is of interest to communities who have generated debris during wind and ice storms or are interested in the supply of green waste from tree maintenance and removal activities

As part of a project to develop a predictive model for urban tree damage and debris related to hurricanes, we wanted to accurately quantifying urban forest biomass in hurricane-prone areas

Background - 2 Existing data:

Urban tree data from 5 communities across the southeastern US (SEUS) collected under the Urban Forestry Effects (UFORE) model sampling protocol

Post-hurricane sample data describing the state of urban trees subjected to the most severe winds from Hurricanes Rita, Ivan, and Katrina (2005)

Existing biomass equations: Widely available, but… Not applicable

Non-urban (i.e., natural forest-grown) trees Based on trees sampled outside the SEUS Estimates for some of the most prevalent species varied greaty (e.g.,

two estimates for Liquidambar styraciflua L. are 1343 tons/ha and 3.3 tons/ha)

Study objectives and methods To better estimate the above-ground

biomass of two common urban tree species in the SEUS:

Quercus virginiana (live oak); and Quercus laurifolia (laurel oak)

We measured 10 trees removed in and around the University of Florida campus and the city of Gainesville, FL

Wet total tree weights (sub-samples dried) Randomized branch sampling (RBS) estimates for

tree components

Live oak

Laurel oak

Preliminary results RBS substantially over-estimated

actual tree weights in most trees Biomass equations substantially

under-estimated tree weights in all trees

0

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0 10 20 30 40 50 60 70DBH (cm)

Tota

l Tre

e Gr

een

Wei

ght (

kg)

actual weight

UFORE pred

actual RBS UFOREweight Bias bias

Live OakQv-2 108 26% -34%Qv-1 139 51% -40%Qv-11 1213 79% -25%Qv-5 2970 24% -44%Qv-3 2331 55% -19%Qv-4 3278 32% -14%

Laurel oakQl-7 85 -15% -40%Ql-5 163 14% -39%Ql-2 549 32% -45%Ql-3 2699 22% -65%

Average 36% -37%

Objective of presentation

To investigate the effect of selection probability methodology on RBS bias

To explore the paradigms behind the RBS method which may be problematic for these species

Methods - Data A non-random sample of 6 live oak and 4 laurel oak trees were

obtained in and around the UF campus (north central Florida)

http://cruises.about.com/library/pictures/jekyll/bljekyll024.htmChampion live oak near Gainesville, Fl. Source: www.floridahikes.com

•Oaks exhibit decurrent crowns, and are refractory species, i.e., they have widely spread crowns, and can endure high temperatures and pressures (Douglas fir is another refractory species)

Methods – Data Collection with Randomized Branch Sampling (RBS)

L=1 m

D=20 cm

L=0.5 m

D=50 cm

Selection probabilities (qk) based on the pipe model:

Using probability D2, the probability of each choice in path for segment 2:q2 =P(20cm segment)=0.138q2 =P(50cm segment)=0.862

Using probability D2L:q2=P(20cm segment)=0.242q2 =P(50cm segment)=0.758

Note: q1

=1.00

L=1 m

D=20 cm

L=0.5 m

D=50 cm

For example, to choose segment 2 in path-> use D2 probabilities D q2 Q2 ------------------------------------------------------------------------------------------

20 0.138 0.138 50 0.862 1.000

-> select a random number ~U[0,1] to choose Qk

e.g., 0.54 -> select D=50 path -> Q2 = 1.00 * 0.862 =0.862

Using qk D2:P(10cm segment)=0.11P(28cm segment)=0.89

Cumulative probability along path:Q3= 0.86 * 0.89 = 0.76

Using qk D2:P(10cm segment)=0.24P(18cm segment)=0.76

Cumulative probability along path:Q4 = 0.76 * 0.76 = 0.68

Using qk D2:P(6cm segment)=0.26P(10cm segment)=0.74

Cumulative probability along path:Q5 = 0.68 * 0.74 = 0.56

Q5 = inflation probability = 0.56

If leaves at end of path weigh 5.6 kg, then all leaves in tree weigh 5.6kg/0.56=10kg

If branches<5cm at the end of that path weigh 11.2 kg, then all branches in tree<5cm weigh 11.2kg/0.56=20kg

Note: example assumes no epicormic branches

However… The weight of the stem is usually calculated by taking a disk, or ‘cookie’ at a selected point along the path using Importance sampling (Valentine, et al 1984).

To arrive at the bole weight, each segment in the selected path is inflated, so that the path represents the entire tree.

• Imagine that this segment is cut into thin discs of known volume and thickness• We select a disc at random with probability its volume• The inflated disc volume is then an unbiased estimate of the weight of the whole tree.

•How to inflate?

Consider the discrete case, where each segment in the selected path is inflated, so that the path represents the entire tree.

Methods – Importance Sampling Measure the taper along the path Define a quantity to the inflated cross-sectional area

of the stem at a distance Ls from the butt:A(Ls) = D(Ls)2/Qk

where: D(Ls)= Diameter of stem at Ls

Qk = inflation probability of segment k Fit an interpolation function S(L) to the values of

A(Ls) using Smalian’s formula Integrate this function over the length, , of the path V() will approximate a quantity to the inflated

volume of path

Methods – Importance Sampling (cont’d) A disc is cut at a random point Θ along the path,

selected with probability to S(L) This point is found by solving V(Θ)=uV()

where: u ~ U[0,1]

Determine the weight per unit thickness of the disc: B(Θ)

The inflated weight per unit thickness of disc is: B*(Θ)=B(Θ)/Qk

The estimated woody weight of the tree is then:)(/)()(*ˆ SVBw

Data collection goals >= 10 trees 6 paths per tree (two in bottom 1/3rd of tree,

two in middle 1/3rd, two in last 1/3rd) 5 cookies per tree

In theory, our trees are simple…

Reality is a…

In reality, we were confronted with an average of 11 segments per path, with each path having 2-8 choices…

Did this complication lead to

our preliminary results?...

Back to Preliminary Results

The question:What makes urban oak trees so different that path selection probabilities are underestimated?

The problem:We consistently over-estimate the weight of both the leaves and branches, and the stem of the tree

Methods to accomplish presentation objectives To investigate the effect of selection

probability methodology on RBS bias Investigate and describe how results

vary with selection probability methodology

To explore the paradigms behind the RBS method which may be problematic for these species

Model bias as a function of tree and sample characteristics

Methods & Results- selection probabilities We investigated several post-hoc probability

formulae, computing each Qk as if we had used: D2 * L, D2, D2.67, D2.67 * L0.5

RBS weight was computed for tree bole, and for leaves + branches

RBS weights were compared to actual tree weight, with bole weight % computed as a function of dbh (see Jenkins, et al. 2004)

Results Worst bias with D2 * L Best bias with D2, D2.67 , but still overestimated > 35%

Path #1

Question:What path (and therefore which selection probabilities) is used to inflate the segments in the interpolation function and obtain bole weight?

Issue:When a disk is selected, it often is located along a part of several selected paths

Path #2

The answer to this question is obvious when there is a “main stem”, but not so when many paths appear to be “main”.

Methods – path selection for disks

Path #1

Issue:Which path is the most appropriate for those disks located along several paths, given a decurrent tree form?

For example:We could use the V() indicated by Path #1 or the V() indicated by Path #2 for disks 2 and 3.

Path #2

Disk 1 Disk 2

Disk 3

Example of bole weights obtained from 5 disks, using 6 paths on one tree

DiskHt of

disk (m)Fresh Wt

(kg)Thickness

(m)Wt per unit thickness path 1 path 2 path 3 path 4 path 5 path 6

BASE 0.2 24.3 0.075 324.4 1892 3026 3323 3398 3774 3741DBH 1.3 20.3 0.092 221.0 1757 2811 3086 3156 3505 347425% 3.25 17.8 0.100 177.7 2901 2967 3295 326650% 6.5 2.5 0.076 33.2 2506 2783 275875% 9.75 0.2 0.050 3.6 1111 1102

Estimated bole wt (kg)

Tree Qv-3Actual bole wt = 1840 kg

Methods – evaluation of path selection for disks and for other tree parts 10 trees (6-live oak; 4- laurel oak)

4-6 paths per tree, 2-5 disks per tree Modeled RBS bias for bole and for leaves +

branches as a function of:

DBH, height of tree, crown area, species height of disk (absolute and relative), strata (tree

divided into thirds) Explicit correlative structure to account for

correlations within tree NOT a random sample, so inference limited

Results - bole Significant interaction between strata (where

path ended) and relative length associated with location of disk (length along path versus total tree height)

Results – bole (continued) Significant interaction between strata (where

path ended) and tree DBH

Results – leaves, branches, etc. Significant interaction between tree DBH and

relative length associated with the path (length along path versus total tree height)

Discussion - What makes oak trees so different from other species of trees?

Tyloses make live oaks wood much different from red oak; however, laurel and live oak did not show different biases

Whereas total sapwood in pines is correlated with leaf biomass, in oaks, it is current sapwood

In softwoods, specific gravity/wet weight decreases from bottom to top & pith to bark. In oaks, this may not follow - large branches with compression wood cause specific gravity/weight to vary depending of the location of the disk

BUT Other forest grown oak species (e.g., red oak; Valentine and Hilton 1977 and Valentine, et al. 1984) were successfully estimated by RBS

Discussion - What makes urban trees so different from forest-grown trees

Degree of taper in stem due to pruning? Leaf aggregation due to pruning? Faster growth in stem due to light availability? BUT There are other urban species that are

well-estimated by RBS, e.g., cherry and mulberry (Peper and McPherson 1998)

Note: many RBS papers in the literature are “light” on methods

Conclusions/opportunities (1 of 3) Obviously, more investigation is required

to make accurate RBS estimates with urban-grown Quercus Random sample Wider geographic area Pruning histories

Results from this study indicate a decision framework for methods of estimating foliage versus bole weight…

Conclusions/opportunities (2 of 3) Possible decision framework for bole:

Disks should be associated with inflation probabilities of paths ending in the same strata of the tree as where they were cut from.

When trees are smaller (< 25 cm DBH), the best estimates are obtained using paths that end in the first third of the tree, and

When trees are larger (> 40cm DBH), the best estimates are obtained using paths that end in the last third of the tree.

Conclusions/opportunities (3 of 3) Possible decision framework for

leaves/branches: Paths that are about as long as the trees are

tall provide the best estimates of leaf and branch weights, especially when trees are of moderate–large size (>30 cm DBH)

Questions/suggestions?

Acknowledgements USDA Forest Service, Florida Division of Forestry,

Wood to Energy (USDA grant) Grad students:

Brian Roth, Alicia Lawrence, Ben Thompson

Volunteers from UF-SFRCNatural Resources Sampling classes