DEPAR TMENT OF AGRICULT URE

United States 

Department of 

Agriculture

Forest Service

Pacific Northwest 

Research Station

General Technical 

Report

PNW-GTR-872

January 2013

Biomass Production on the Olympic 

and Kitsap Peninsulas, Washington: 

Updated Logging Residue Ratios, 

Slash Pile Volume-to-Weight Ratios, 

and Supply Curves for Selected 

Locations

Jason C. Cross, Eric C. Turnblom, and Gregory J. Ettl
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Authors

Jason C. Cross is with the Olympic Natural Resources Center, University of

Washington, College of the Environment, School of Forest and Environmental 

Sciences, P.O. Box 1628, Forks, WA 98331-1628; Eric C. Turnblom and Gregory 

J. Ettl are with the School of Environmental and Forest Sciences, College of the 

Environment, University of Washington, Box 352100, Seattle, WA 98195-2100. This 

work was performed under Cooperative Agreements 09-CA-11261991-010 (PNW), 

09-CA-11261991-007 (PNW), and DE-FG02-97ER41020 (WSU).
Biomass Production on the Olympic and Kitsap Peninsulas, 

Washington: Updated Logging Residue Ratios, Slash Pile 

Volume-to-Weight Ratios, and Supply Curves for Selected 

Locations

Jason C. Cross, Eric C. Turnblom, and Gregory J. Ettl

U.S. Department of Agriculture, Forest Service

Pacific Northwest Research Station

Portland, Oregon

General Technical Report PNW-GTR-872

January 2013

Published in cooperation with:

University of Washington

College of the Environment

School of Environmental and Forest Sciences

Olympic Natural Resources Center

Forks, Washington

Washington State University Energy Program

Northwest Clean Energy Application Center

Olympia, Washington
Abstract

Cross, Jason C.; Turnblom, Eric C.; Ettl, Gregory J. 2013. Biomass production 

on the Olympic and Kitsap Peninsulas, Washington: updated logging residue 

ratios, slash pile volume-to-weight ratios, and supply curves for selected 

locations. Gen. Tech. Rep. PNW-GTR-872. Portland, OR: U.S. Department of 

Agriculture, Forest Service, Pacific Northwest Research Station. 30 p.

Biomass residue produced by timber harvest operations is estimated for the Olympic and Kitsap Peninsulas, Washington. Scattered residues were sampled in 53 

harvest units and piled residues were completely enumerated in 55 harvest units. 

Production is based on 2008 and 2009 data and is stratified by forest location, 

ownership type, harvest intensity, and harvest method. An additional sampling was 

taken to ascertain the mass of wood present in a pile of biomass: 20 piles of biomass 

were measured for gross volume, processed into hog fuel, and remeasured for 

volume; five samples were drawn from each pile and examined for volume, green 

mass, and bone-dry mass. An equation relating mass of wood in a pile to the gross 

biomass volume is derived. Finally, the availability and average delivered cost per 

ton of biomass is calculated for five delivery centers on the Olympic Peninsula.

Keywords: Biomass, residue, slash, hog fuel, production, volume, density,

supply curve.
Summary

Logging residue (slash) consists primarily of the branches and tree tops of harvested 

merchantable timber; excluding snags, downed logs, and stumps. Residues may 

be scattered about the harvest unit, concentrated in piles, or both—depending on 

the harvest method and equipment used. Accurate estimates of residue production are immediately useful to managers who must marshal resources for smoke 

abatement, fire-risk reduction, and regeneration efforts, and to landowners who 

bear the financial burden of such activities. Additionally, changes in national and 

state energy policies have created opportunities for offsite utilization of residues if 

sufficient quantities can be delivered at competitive prices. This analysis of direct 

field measurements seeks to update the estimators of wood in piled logging residue 

(Little 1982) and biomass supply studies based on those estimators (Hardy 1996; 

Howard 1978, 1981; Kerstetter and Lyons 2001). Specifically, the purpose of this 

project was to quantify (1) the production of logging residue in Clallam, Jefferson, 

Kitsap, Mason, and Grays Harbor Counties for 2008 and 2009; (2) the volume of 

solid wood contained in a slash pile; and (3) the total supply and average price of 

biomass deliverable to the cities of Forks, Port Angeles, Port Townsend, Shelton, 

and Aberdeen, Washington. 

Production

The study reviewed the state of Washington’s 1,400+ Forest Practice Applications 

(FPAs) on the Olympic and Kitsap Peninsulas for calendar years 2008 and 2009. 

The set was narrowed to 975 FPAs—encompassing 66,729 ac by excluding units 

of less than 15 ac as well as single-tree, right-of-way, and salvage operations. As 

federal and tribal timber harvests do not require FPAs, they too were excluded. 

Applications were stratified by four factors thought to be associated with distinct 

production rates: forest location (east/west side of the Olympic Peninsula), harvest 

intensity (clearcut/thinning), ownership type (public/nonpublic), and harvest 

method (ground/cable/mixed). Eighty-nine percent of timber harvest was located

on the west side of the Olympic Peninsula, and clearcuts accounted for 88 percent 

of harvest intensity. To capture mean residue production (ft3

/ac) within 15 percent 

four times out of five, the desired sample size of 86 harvest units was allocated 

among strata according to proportion of harvest activity. In total, 511 transects 

were installed to sample scattered residues on 53 harvest units; all 3,075 slash piles 

were measured on 55 harvest units. An Type II analysis of variance (ANOVA) on 

transect data found ownership to be a factor associated with different production 

rates—1,588 ft3

/ac on public lands versus 1,155 ft3/ac on nonpublic land. A similar 

test on piled residue data resulted in two distinct production groupings: “high” 
production yielded an average 325 ft3

/ac; “low” production yielded 65 ft3/ac. Both 

groups consisted of strata with each level of forest location, harvest intensity, and 

ownership type. Harvest method was not identified as a factor associated with different production levels. Annualized harvest rates and volumes (FPAs) with residue 

production attributes and ratios are summarized below:

• FPA acreage: 33,364 ac

• Harvested timber volume: 885 million board feet

• Transected residues: 1,292 ft3

/ac

• Pile residues: 307 ft3/ac

• Total residues: 1,599 ft3/ac

• Bone dry tons (BDT) of residue per acre: 19

• Ratio of BDT to harvested thousand board feet: 3:4

Volume-to-Weight Ratios

The gross volume of a slash pile is a combination of wood and air. Residue production estimates should reflect only the wood component. The existing ratio estimator for volume-to-weight dates from 30 years ago and does not represent current 

harvest methods or forest conditions. An experiment was conducted to update the 

volume-to-weight ratio estimator: each of 20 selected slash piles was measured for 

gross volume before and after processing; five samples were drawn from each processed hog-fuel pile for further laboratory analyses to determine moisture content, 

compaction, and specific gravity. Results indicated that the volume of processed 

hog fuel is a function of the square root of the original slash pile volume; and the 

solid wood volume of a hog-fuel pile is approximately 38 percent of its volume. 

The green density of the wood component was quantified at 18.72 lb/ft3; bone dry 

density was 9.05 lb/ft3. Given the cubic-foot volume (Vs) of a slash pile, the bonedry mass of the wood component in pounds is given by:

Bone dry mass = (92.18Vs

1⁄2 – 4,468) x 9.05 lb/ft3

Supply Curves

Supply curves describe the behavior of average unit cost as the cumulative supply 

delivered to a specific location increases. The cities of Forks, Port Angeles, Port 

Townsend, Shelton, and Aberdeen were selected as delivery locations on the basis 

that all have existing industrial milling capacity and are therefore more likely to 

utilize logging residues. The components of a logging residue supply curve are site 

production, recovery costs, and transportation costs.

Data from the Washington State Forestland Database were used to identify 

timber-producing parcels and stratify them directly for location and ownership 
type. Parcels were aggregated in 10-minute intervals based on delivery time to a 

given delivery center. Harvest type and method were imposed on the aggregated 

interval acreage in the proportions indicated by the production study. Base rates of 

$35 per BDT for in-woods recovery and $65 per hour for transportation costs were 

assumed; both rates are subject to a fuel surcharge assessed at a rate of 1 percent for 

every 10 cent increase in diesel prices.

The supply curves assembled with the production and cost values indicate Forks 

to be the most competitive delivery site for quantities up to 50,000 BDTs (MBDTs). 

Overall, Aberdeen had access to the greatest annual quantity of hog fuel (600 

MBDT/year), while hog fuel available for delivery to Shelton had the lowest average 

unit price ($53.26/BDT). Port Angeles and Port Townsend have access to decidedly 

smaller quantities at the highest average prices. Delivery centers are ranked from 

the highest to lowest annual quantity of hog fuel deliverable at an average unit 

price of $50/BDT: Aberdeen (410 MBDT/Y), Shelton (320 MBDT/Y), Forks (280 

MBDT/Y), Port Angeles (110 MBDT/Y), and Port Townsend (100 MBDT/Y).
Contents

1 Introduction

1 Logging Residue Production

3 Materials and Methods

8 Results

12 Discussion and Applications to Management

13 Volume-to-Weight Ratios

13 Methods

16 Results

18 Discussion and Applications to Management

19 Supply Curves

19 Methods

21 Supply Curves

21 Applications to Management

25 Conclusion

26 Acknowledgments

27 Metric Equivalents

27 Literature Cited
1

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

Introduction

Timber harvest activities produce residues (slash) that consist primarily of the 

branches and tree tops of harvested merchantable timber. This material excludes 

snags and downed logs that are required to remain onsite to perform various 

ecologic functions. In the past, this material would likely have been burned in some 

manner to prepare the site for replanting; however, increasing interest in biomass as 

a source of renewable energy has created a market for slash to be removed offsite 

and used as hog fuel. The marketability of slash produced from timber harvest is 

contingent upon (1) the quantity produced and (2) the average unit cost on delivery. 

With respect to quantity, slash may be left scattered about the area after harvest or 

concentrated in piles—methods exist to survey and quantify both types. Similarly, 

previous studies have constructed supply curves that explain the relationship 

between cumulative delivered quantity and average cost per unit. If markets are to 

be created and sustained for the offsite utilization of slash, and those markets are to 

be met with wise policies governing such removals, then the quantities and delivered cost must be known with sufficient confidence. The purpose of this investigation is to capture the quantities and costs for the Olympic and Kitsap Peninsulas of 

Washington.

Logging Residue Production

When timber is harvested, woody biomass of the stand may be divided among three 

broad categories: (1) merchantable products removed from the stand; (2) retained 

trees, snags, stumps, and down logs; and (3) logging residues (slash) that may 

remain, be removed, or some combination thereof. The amount of trees, snags, and 

logs remaining after harvest differs with ownership, harvest intensity, and harvest 

method. Policies differ as to the quantity of trees, snags, and downed logs to be 

retained on federal, state, and private timberlands. Thinning, shelterwood, and 

clearcut harvest types retain decreasing levels of standing timber while increasing 

the expected production of slash. Ground-based harvest methods may result in a 

notably different distribution of biomass than cable-based methods. Whatever the 

quantity and distribution of remaining biomass, it contributes to ecologic functions, 

including shade and large woody debris recruitment potential to nearby streams 

(NCASI 2000), nutrient cycling and site productivity (Titus et al. 2006), and habitat 

for animals (Jacobs et al. 2007). Tree stumps also stabilize soil for years after 

harvest. Of particular interest to this investigation is the production of logging 

slash—consisting primarily of the branches and tree tops from merchantable timber 

products—that often remains but may be removed. 

The marketability of 

slash produced from 

timber harvest is 

contingent upon (1) the 

quantity produced and 

(2) the average unit cost 

on delivery.
2

GENERAL TECHNICAL REPORT PNW-GTR-872

The fate of slash that remains after timber harvest—either scattered about the 

forest floor or concentrated in piles—is to decompose and serve as nutrient capital 

for soil, enter recalcitrant soil pools, or act as fuel for (wild or prescribed) fires. As 

long as slash remains, it is an impediment to reforestation efforts, although piling 

slash has the advantage of exposing the forest floor, thereby promoting the establishment of the subsequent cohort of trees. In addition to providing nitrogen (N) and 

other nutrients through decomposition, slash is a source of carbon (C) emissions to 

the atmosphere, and removal may decrease soil C (Palosuo et al. 2000); however, 

emissions from decay are lower, and more slowly released than if burned (Lee et 

al. 2010). Some N is volatized by prescribed burning or wildfire and the loss can be 

calculated (Little and Ohmann 1988); however, Mroz et al. (1980) noted that not all 

studies confirm a reduction in N, concluding that generalizations about the effect 

of fire on soil N over wide areas and different forest floor materials are difficult. 

Little and Ohmann (1988) concluded that N loss is proportional to consumption of 

the forest floor; however, some sites showed a gain (the largest +171.3 lb/ac), while 

others showed losses (the largest -594.2 lb/ac) in soil N following burning.

Nitrogen is the major growth-limiting nutrient among forests of the Pacific 

Northwest (Peterson and Gessel 1983). Changes in nutrient budgets owing to

timber harvest operations and various slash treatment strategies have been well 

studied (Feller 1988, Feller and Kimmins 1984, Jurgensen et al. 1997, Kraemer

and Hermann 1979, Little and Ohmann 1988, Mroz et al. 1980). Nitrogen enters

the forest floor and soil through decomposition and mineralization of parent material (Edmonds 1980) and is rapidly taken up by plants. Little and Ohmann (1988) 

noted that decaying organic matter on the forest floor excludes sound woody material 0.1 in and larger (properly considered woody fuel). Thus, during early stages 

of postharvest stand development, where the forest floor is the primary source of N 

(Grier et al. 1974), slash seems not to be a significant source. 

Increasing demand for renewable energy has created markets for slash to be 

used offsite as a boiler fuel. When slash displaces a fossil fuel in a boiler, greenhouse gas (GHG) emissions of slash are less than half that of onsite combustion or 

decomposition (Lee et al. 2010), even after accounting for the emissions produced 

by processing and transportation. The effects of slash removal on soil nutrient 

budgets are likely to differ among sites: If slash removal is similar to the effects of 

prescribed fire, we would expect a substantial reduction in available C, a general 

reduction in total N, although responses range widely (Little and Ohman 1988), 

and an increase in the available N (Antos et al. 2003), perhaps owing to a lowering 

of the C/N ratio. Although initial studies in western hemlock (Tsuga heterophylla

(Raf.) Sarg.) forests found no relationship between site productivity and soil C 
3

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

and N or C/N ratios (Edmonds and Chappell 1994), the impacts of mechanical 

slash removal will require further research. Slash removal also reduces the risk of 

unintended fires by reducing fuel loads; lowers the risk of producing smoke from 

any type of fire; and aids in reforestation efforts by exposing a larger proportion 

of the forest floor to sunlight, allowing reforestation on areas that might otherwise 

be occupied by slash piles. The increased interest in offsite slash utilization alone 

warrants investigation into its production, but also the need to develop management 

guidelines for utilization to protect against deleterious effects of removal. This 

paper reports on a study that updates the estimates of logging residue production on 

the Olympic and Kitsap Peninsulas in Washington state for calendar years 2008 and 

2009. This study examines slash postharvest and does not consider differences in 

C storage in relation to stand age (Harmon et al. 1990) or differences of intrastand 

storage pools (Janisch and Harmon 2002, Pregitzer et al. 2004) or silvicultural 

practices in the more general sense (Foley et al. 2009, Harmon and Marks 2002).

Materials and Methods

The study reviewed all Forest Practice Applications (FPAs)1 received by the 

Washington State Department of Natural Resources (DNR) from January 1, 2008, 

through December 31, 2009. The study area included the five counties of the Olympic and Kitsap Peninsulas of Washington shown in figure 1: Clallam, Jefferson, 

Kitsap, Mason, and Grays Harbor. The FPAs were stratified by factors suggested 

by Kerstetter and Lyons (2001) thought to influence production of logging residues: 

forest location, harvest intensity, ownership type, and harvest method. Forest location was composed of east (denoted Le

) and west (Lw) levels, divided by the boundary between ranges 6 and 7 west (roughly at the Elwha River in Clallam County 

and the longitudinal boundary between Mason and Grays Harbor Counties). Levels 

of harvest intensity were clearcut (Ic) or thinning (It). Ownership consisted of public 

(Op) or nonpublic (On) levels, where nonpublic lands may include private industrial, 

nonindustrial, timber investment management organizations, real-estate investment 

trusts, and land conservation organizations. Harvest method had levels of ground

(Mg), cable (Mk), or mixed (Mx). Levels of each stratum correspond to explicit

declarations in each FPA, making stratification a straightforward process. Excluded 

from the study were operations producing insignificant or noncommercial quantities of biomass such as cedar salvage, individual tree salvage, right-of-way-only 

harvests, and units smaller than 15 ac; also excluded were FPAs that were denied, 

1

 Forest practices are related to growing, harvesting, or processing timber, including, but 

not limited to, road and trail construction and maintenance, thinning, salvage, harvesting, 

reforestation, brush control, suppression of diseases and insects, and using fertilizers. 

These practices are regulated by the Washington Forest Practices Act and its corresponding 

rules, promulgated by the Department of Natural Resources.
4

GENERAL TECHNICAL REPORT PNW-GTR-872

Mason

Port 

 Townsend

Forks

Aberdeen

Shelton

Kitsap

Clallam

Jefferson

Grays

Harbor

Mason

Kitsap

Clallam

Jefferson

Grays

Harbor

60 km

40 mi o

WASH INGTON

 Port 

 Angeles

Figure 1—Study area with selected 

supply curve delivery locations. The 

Olympic and Kitsap Peninsulas of 

Washington are composed of Clallam, Jefferson, Grays Harbor, Mason, 

and Kitsap Counties. The cities of 

Aberdeen, Forks, Port Angeles, Port 

Townsend, and Shelton were selected 

as supply curve delivery locations.

withdrawn, and subsequently renewed. Federal and tribal lands do not require an 

FPA and were not included. Exclusions and omissions narrowed the set of FPAs in 

the study to 974 covering 66,729 ac. 

A sample size of 86 harvest units was found to be sufficient to capture mean 

cubic-foot volume of residue produced per harvested acre within 15 percent of 

the true mean 4 times out of 5. This is a slight deviation in targeted precision and 

accuracy from Howard (1981), who sought to capture residue production per acre 

within 20 percent of the true mean 9 times out of 10. A coefficient of variation of 

85 percent was employed to compute sample size as residue volume per acre was 

the major contributor to total variance. Proportional allocation was used to assign 

sample sizes to the defined strata with an imposed minimum of two sample units 

regardless, in order to offer minimal assurance against extreme values and to allow 

for variance calculation. The proportion of harvested acres and associated sample 

size by stratum is detailed in table 1.
5

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

Table 1—Harvest acreage proportion and sample size by stratum for calendar years 

2008 and 2009 

 Clearcut Thinning

Forest

location Ownership Ground Cable Mixed Ground Cable Mixed

East Public 0.012 (2) 0.001 (2) 0.017 (2) 0.002 (2) 0.000 (2) 0.002 (2)

Nonpublic 0.027 (2) 0.002 (2) 0.036 (3) 0.004 (2) 0.000 (2) 0.005 (2)

West Public 0.102 (6) 0.008 (2) 0.138 (8) 0.014 (2) 0.001 (2) 0.019 (2)

Nonpublic 0.221 (13) 0.017 (2) 0.296 (17) 0.031 (2) 0.002 (2) 0.042 (3)

Note: Each cell details the proportion of 66,729 ac included in the study by factors thought to be associated with 

different levels of residue production: forest location, harvest type, ownership type, and harvest method. Each 

proportion is accompanied by the harvest unit sample size in parentheses required to capture mean residue production 

within 15 percent at 80 percent confidence, assuming a coefficient of variation of 85 percent. A minimum of two 

sample units is assigned even if the proportion warrants fewer.

For each harvest unit sampled, transects were installed to sample the biomass 

scattered about the forest floor following timber harvest operations. Harvest units

in excess of 30 ac had 10 initiation points; harvest units less than 30 ac were 

sampled at a rate of one initiation point per 3 ac. With transect subsampling 

intensity thus defined, the dimensions of a square grid were derived. The first 

transect initiation point was located by randomly placing an intersection nearest a 

convenient harvest unit access point. Subsequent initiation points were located at 

the systematic grid intersections on a map or aerial photograph. From each initiation point radiated three 100-ft large-fuel transects; the direction of the first was 

assigned randomly, with the second and third at azimuths ± 120° to the first. Large 

fuels were defined as pieces with diameters greater than 3 in and lengths greater 

than 1 ft. The diameter of each large piece at its intersection with the transect was 

recorded. Three shorter transects were nested within each large-fuel transect to 

capture progressively smaller material: a 4-foot transect—from 14 to 18 ft along 

the large fuel transect to capture pieces between 0.10 and 0.25 in diameter; a 6-ft 

transect (14 to 20 ft) for pieces between 0.26 and 1.00 in diameter; and a 10-ft transect (14 to 24 ft) for pieces between 1.10 and 2.90 in diameter. Pieces were tallied 

for each fine-fuel transect and included only intact dead sticks and twigs that were 

detached woody pieces visible on the surface of the forest floor. Material smaller 

than 0.1 inch in diameter, bark chunks, cones, and splinters were not tallied as they 

are considered litter/duff (Little and Ohmann 1988). Logs rotted to the point that 

they could not support their own weight, or those that had lost their original form, 

were also excluded. Transects falling near unit boundaries or riparian management 

zone (RMZ)2

 or road edges within units were handled according to the reflection

2

 RMZs are terrestrial areas adjacent to water courses where forest and aquatic dynamics 

overlap and interact. They are generally measured horizontally from the outer edge of the 

bankfull width or channel migration zone and extend to limits prescribed by the appropriate law or policy.

Material smaller than 

0.1 inch in diameter, 

bark chunks, cones, 

and splinters were 

not tallied as they are 

considered litter/duff. 
6

GENERAL TECHNICAL REPORT PNW-GTR-872

method as described in Gregoire and Valentine (2008). Rooted materials including 

live trees, stumps, snags, or branches were not tallied, nor were rooted materials 

resting on the ground surface. It was also imperative to separate slash piles found 

along transects to avoid double counting of material. Any portion of a transect that 

intercepted a pile was treated as bare ground. Prior to analysis, diameters and piece 

counts were converted to cubic feet per acre values with methods described by

Gregoire and Valentine (2008). Fine-fuel tallies were converted using the midpoint 

of the transect’s diameter range. The mean cubic feet per acre residue volume for 

each transect type was calculated and the total volume was associated with the 

initiation point for analysis. 

Slash pile volumes were completely enumerated across sampled units. The 

methods used to evaluate pile volumes were first introduced by Howard (1981) and 

Little (1982); we employed the expanded set of pile geometries described by Hardy 

(1996) to increase precision of estimates. Pile origins were recorded as ground or 

cable. The percentage of gross pile volume consisting of pieces > 1 ft3 was estimated and recorded. The volume of soil was also estimated as a percentage of gross 

pile volume. Lengths and widths were measured at ground level with tapes, while 

heights were measured with a Laser Technology “TruPulse 200”3 laser rangefinder/

heightfinder with a precision of 0.10 ft. Residue piles consist of a mixture of wood 

and air but only the wood component was to be analyzed. Gross slash pile volumes 

were scaled by a factor of 0.3324—an updated version of Little’s (1982) ratio that is 

derived in the “Volume-to-Weight Ratios” section—relating hog fuel pile volume to 

gross slash pile volume. Hog fuel pile volumes were scaled by 0.377 to account for 

the air portion of the hog fuel pile—a factor also derived in the “Volume-to-Weight 

Ratios” section—resulting in cubic feet of solid biomass. Solid biomass volumes 

were summed within sample units and divided by unit acres resulting in cubic feet 

per acre values for analysis.

Overall sample size reflected the anticipated degree of dispersion within strata 

that relied, in part, on the results from similar efforts by Howard (1981) and Hardy 

(1996). As described, the methods to acquire our data define a stratified random 

sampling process (Cochoran 1977). However, we analyze our data using a model 

derived from an experimental design context to serve a secondary objective of 

simultaneously testing our strata definitions. Although there are reasons to believe 

that our strata definition factors will be associated with different slash production 

values (Kerstetter and Lyons 2001), we seek to test these assumptions. The reader 

should not infer that significant stratum definition factors are in any way causative in nature; on the contrary, significant strata differences are merely useful

3

 The use of trade or firm name in this publication is for reader information and does not 

imply endorsement by the U.S. Department of Agriculture of any product or service.
7

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

associations with slash production values. Using the analysis to finalize strata 

definitions simultaneously with producing estimates for them may slightly degrade 

estimator optimality, but probably not significantly. Since sample sizes differ by 

stratum, the model describing residue production by harvested acre will be unbalanced. Further, the strata being analyzed for differences in production rates contain 

fixed effects (the factors comprising the defined strata) as well as random, nested 

effects owing to subsampling; therefore, the model is also a mixed-effects model 

(Oelhert 2000). Hasse diagrams (Lohr 1995, Oehlert 2000) are useful for visualizing and quantifying experimental models; a diagram representing the sampling 

model is presented in figure 2. 

Figure 2—Hasse diagram of residue production model. The diagram starts 

with the grand mean, G, at the top. Each node at the second level corresponds to a factor thought to be associated with residue production: forest 

location (L2

1

), harvest intensity (I2

1

), ownership type (O2

1

), and harvest 

method (M3

2

). Superscripts indicate the number of levels for factors or 

interactions; subscripts denote associated degrees of freedom. Nodes at 

the third, fourth, and fifth levels represent 2-, 3-, and 4-way interactions. 

Nodes in parentheses indicate random effects: (U) represents randomly 

sampled transect harvest units with nested initiation points (E). Piles were 

completely enumerated (E) across harvest units on the right-hand side (no 

nesting).
8

GENERAL TECHNICAL REPORT PNW-GTR-872

Results

By the end of the data collection period, 6 of 24 strata representing 12.8 percent 

of FPA acres in the study had had only one unit harvested. Having no replicated 

observations in any stratum causes difficulties in stratum variance calculation, 

and causes statistical aliasing of main and interaction effects in the analysis of an 

experimental model. Therefore, the single observations from these six strata were 

dropped from the analysis, to guard also against the possibility that these single replicates might be unusual instances, that is, not truly representative of their respective strata. An additional nine strata representing 1.8 percent of the total acres 

could not be sampled for a lack of available harvest units. Ultimately, the analysis 

included nine strata accounting for 85.4 percent of the study acres. 

Transects—

In total, 511 transects were installed spread across 53 harvest units. Each transect 

record contains a list of large-fuel diameters and tallies for each fine-fuel survey. A 

single diameter value recorded on transect A, point 8 in FPA 2610223 was determined to be biologically infeasible and was removed from analysis. Scatter plots of 

residual versus predicted values for the linear model indicated by figure 2 describing residue production revealed heteroskedasticity among the data set (i.e., variance increased with predicted mean value). A boxplot of volume per acre by strata 

indicated a strong positive skew in the distribution. Constancy of variance and normally distributed data were requirements for the selected statistical analysis. A loge

transformation (Ln) of volumes sufficiently restored homoskedasticity and normalized distributions of transect and pile data sets. Figure 3 illustrates the before- and 

after-transformation variances and distributions of transect data. 

A type II ANOVA found ownership to significantly affect Ln-transformed 

residue volume production; an F-statistic of 2.078 on 1 and 50 degrees of freedom 

yielded a p-value of 0.1557 that was less than our desired type I error limit (0.2). 

Location, harvest type, and harvest method were not found to be significant factors. 

The updated linear model describing Ln-transformed transect data suggested in 

figure 2 indicates that public lands have a production rate of 1,588 ft3

 of biomass 

per harvested acre; nonpublic lands produce 1,155 ft3 of biomass per harvested 

acre. Both values have a variance of 4.23 in LN-space. Table 2 summarizes transect 

residue production.

Piles—

In total, 3,075 piles were measured across 55 sample units. Similar to transect data, 

pile data demonstrated heteroskedasticity and a positively skewed distribution by 

stratum transect and pile data sets (i.e., variance increased with predicted mean 

In total, 511 transects 

were installed spread 

across 53 harvest units 

and 3,075 piles were 

measured across 55 

sample units.
9

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

Figure 3—Skedacity and distribution of transect data. Top left: Natural-scale scatter plot of residual versus predicted values based on the 

production model described in figure 2; note the heteroskedasticity (nonconstant variance). Bottom left: LN-transformation of transect 

data yielding homoskedasticity (constant variance). Top right: Natural-scale boxplot of cubic-foot volumes of residue per acre by coded 

stratum; note the positive skew across strata. Bottom right: LN-transformation of transect data yielding normally distributed responses 

across strata.

value). A natural-log transformation (Ln) of volumes sufficiently restored homoskedasticity and a normalized distribution. Figure 4 illustrates the before- and -aftertransformation variances and distributions of pile data. 

A type II ANOVA found forest location, harvest type, ownership, and the interaction between intensity and ownership to be associated with different production 

rates. Results from the type II ANOVA on the updated linear model are detailed in 

table 3. A reduced set of eight strata (as harvest method is removed), with means 

ranging from 1.637 to 6.360 in LN-space and a variance of 1.067 in LN-space. A 

post-hoc pairwise comparison of strata means using the Tukey-Kramer method 
10

GENERAL TECHNICAL REPORT PNW-GTR-872

Table 2—Transected residue production metrics and confidence interval by 

ownership

	 Harvest	 Mean	 80% confidence

Ownership Acresa unitsb productionc interval

Public 21,065 18 1,588 1,403 , 1,797

Nonpublic 45,530 35 1,155 1,057 , 1,263

 Totald 66,595 53 1,292 1,283 , 1,301

a Acres reflect proportion of qualifying forest practice applications activity during the study period.

b

 Harvest units indicate sample size of stratum.

c

 Mean production and 80 percent interval values were calculated in LN-space but are reported in natural 

scale units (cubic foot/acre). Both public and nonpublic strata have a variance of 4.23 in LN-space. 

d

 Total mean production is weighted by acres; total variance was 0.0358 in LN-space.

Figure 4—Skedacity and distribution of pile data. Top left: Natural-scale scatter plot of residual versus predicted values based on the 

production model described in figure 2; note the heteroskedasticity (non-constant variance). Bottom left: LN-transformation of transect 

data yielding homoskedasticity (constant variance). Top right: Natural scale boxplot of cubic-foot volumes of residue per acre by coded 

stratum; note the positive skew across strata. Bottom right: LN-transformation of transect data yielding normally distributed responses 

across strata.
11

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

Table 3—Results of a four-way analysis of variance on piled residues

Sum of Degrees of Mean Calculated

Factora squares

b freedom squaresc F-statisticd P-valuee

Forest 4.114 1 4.114 3.9661 0.0524

location

Harvest 15.576 1 15.576 15.0162 0.0003

intensity

Ownership 8.695 1 8.695 8.3825 0.0058

Intensity: 3.837 1 3.837 3.6991 0.0606

ownership

Residuals 47.715 46 1.037

a

 Interactions between factors are indicated with a colon.

b Sum of squares (SS) calculation was performed by the open-source statistical package R (http://cran.r-project.

org) perform. Type II SS were used to account for unbalanced sampling among strata. 

c Mean square (MS) value for a factor is the quotient of SS and the degrees of freedom (DF), SS ÷ DF. 

d The calculated F-statistic is the quotient MSfactor ÷ MSresiduals, which are compared to critical F.20 (1,46) value to 

determine P-values.

e In this investigation, a P-value < 0.20 indicates significance.

Table 4—Piled residue production metrics and confidence interval by strata 

group

Strata Group Harvest Mean ft3/ac	 80% confidence

group acres units production interval (ft3/ac)

High 61,524 51 325 313 , 337

Low 4,538 4 65 58 , 75

 Total 66,062 55 307 306 , 307

Note: Strata groupings were identified using Tukey’s HSD test; group names reflect relative residue 

production rates. The high production group includes strata LwI

c

On, LwI

c

Op, LeI

c

On, and LwI

t

On. The low 

production group includes LeI

c

On, and LeI

t

On. Production estimates (and associated confidence intervals) 

were not available for strata LwI

t

Op and LeI

t

Op, as no data existed. Acres indicate stratum’s proportion of 

total activity during the study period; harvest units denote sample size across strata. Mean production and 

80 percent interval values were calculated in LN-space but reported in natural scale units (ft3/ac). Both high 

and low strata groups have a variance of 1.037 in LN-space. Total mean value is weighted by acres; total 

variance was 0.0025 in LN-space.

(Oehlert 2000) found that two distinct groups existed, where means between the 

groups could be distinguished from each other and means within a group could 

not be distinguished from one another. The first group consisted of strata LwI

c

O

p

, 

LwI

c

On, LeI

c

On, and LwI

t

On and was labeled “high” for its average production rate 

of 325 ft3 of residue per harvested acre. The second group included strata LeI

c

On

and LwI

t

O

p and was labeled “low” with an average production rate of 65 ft3 

per 

harvested acre. No data existed in strata LeI

t

O

p

 and LeI

t

On, and thus precluded 

production estimates, variance calculations, and the construction of confidence 

intervals. Production by group is summarized in table 4.
12

GENERAL TECHNICAL REPORT PNW-GTR-872

Discussion and Applications to Management

As timber harvest operations affect the production of residues, the economic conditions that affect timber production likely also affect residue production. Sampling 

was constrained by low timber prices, which resulted in an insufficient supply of 

units in strata with marginally higher cost harvest types and methods: thinning 

operations accounted for only 12.2 percent of the acres in the study, and cable-only 

methods accounted for 3.1 percent of the study acres. More than 100 FPAs representing these strata were included in the study, but less than 10 percent of the strata 

had been harvested. The labor required to install transects and census slash piles 

was higher than expected (2 man-days versus 1 expected); however, this did not 

affect the sampling matrix and all available units were sampled.

Initial exploration of transect and pile data revealed uneven variances and 

nonnormal distribution of production rates within strata. An LN transformation of 

transect and pile results sufficiently restored homoskedasticity and normality. A 

four-way Type II ANOVA found that forest ownership is a significant factor in scattered residue production—publicly owned lands yield 1,588 ft3

/ac, which is 433 ft3/

ac greater more than nonpublic lands (1,155 ft3/ac). A similar test on piled volumes 

found forest location, harvest type, ownership, and the interaction between intensity 

and ownership to be factors significantly affecting production. However, a comparison of the six strata means found that distinct production rates existed for only two 

groups: a “high”-yield group produced a mean of 325 ft3/ac; the “low” group yielded 

65 ft3/ac. Although no data existed for rigorous analysis of piled residue on east-side 

thinnings (LeI

t

), the reader may require production estimates. The linear model 

describing piled residue production indicated “low” production rates for both strata 

according to table 4. 

The sampling design kept transects and pile measurements disjoint. Therefore, 

the total residue produced on a harvest unit was simply the sum of transect and 

pile production rates. The transect factor combines with the pile groupings to yield 

four combined production rates ranging from 1,478 ft3

/ac to 1,913 ft3/ac. The total 

acre-weighted mean production rate was 1,599 ft3/ac with an 80 percent confidence 

interval of (1,563, 1,636) ft3/ac. The combined results are summarized in table 5.

Applying the weighted mean production of 1,599 ft3/ac to an annual harvest 

of 33,364 acres yields a total annual residue production of 53,349,036 ft3 on the 

Olympic and Kitsap Peninsulas of Washington. If the bone-dry density of the wood 

is 24.18 lb/ft3, then total annual production can be expressed as 1,289,979,690, or 

644,989 bone-dry tons (BDTs). The reported harvest volume from the FPA survey 

was 1.67 billion board-feet, or 883 million board feet annually; therefore, approximately 3 BDTs of residue were produced for every 4 MBF of harvested timber.

As timber harvest 

operations affect 

the production of 

residues, the economic 

conditions that affect 

timber production 

likely also affect 

residue production. 
13

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

Table 5—Combined transected and piled residue production metrics and 

confidence intervals by strata group 

Distribution Productiond

Strata	 	 Harvest	 	 	 	 80% confidence

groupa Acresb unitsc Transect Piled Total interval

Highp 16,549 15 1,588 325 1,913 1,887 , 1,939

Highn 44,975 36 1,153 325 1,478 1,465 , 1,491

Low

p 4,538 4 1,588 65 1,653 1,610 , 1,697

 Totale 66,062 55 1,292 307 1,599 1,563 , 1,636

a Groups are the combination of transect (public/nonpublic) and pile (high/low) strata. Subscripts p and n 

indicate public and nonpublic ownership, respectively. Group HIGHp includes stratum LwI

c

Op; HIGHn

includes strata LwI

c

On, LeI

c

On, and LwI

t

On; LOWp includes strata LeI

c

Op and LwI

t

Op. b Acres indicate group’s proportion of total qualifying forest practice applications activity during the study 

period.

c Harvest units indicate group sample size. 

d Mean production and 80 percent confidence interval values were calculated in LN-space but reported in natural 

scale units (ft3/ac). As transect and pile sampling was disjoint (i.e., independent), variances were additive with 

covariance = 0; strata group variances are 4.270 in LN-space.

e Total mean values are weighted by acres; total variance is 0.445 in LN-space. 

Volume-to-Weight Ratios

Quantifying piled logging slash has long been important for smoke and fire 

management. However, the potential for offsite utilization of slash as a feedstock 

in energy production is driving interest in updated and improved production rate 

estimates. Howard (1978, 1981) and Hardy (1996) described and implemented 

methods for sampling scattered and piled residues. Few published studies have 

attempted to quantify the volume and mass of piled logging residues: Howard 

(1981), Hardy (1996), and Wright and Vihnanek (2009) all rely on the volume-toweight ratio developed by Little (1982)—a study based on measurements of nine 

slash piles from national forest harvest units in the Pacific Northwest harvested 

between 1979 and 1980. Significant changes in timber type and harvest methods 

have likely affected the composition of slash piles and warrant updated volume-toweight ratios—the objective of this brief investigation.

Methods

Twenty slash piles consisting primarily of branches and tops of harvested merchantable timber and excluding snags, downed logs, and stumps were made available for 

analysis across three harvest units located near Forks, Washington. These piles are 

not associated with harvest units or pile measurements mentioned previous to this 

section. Field procedures were conditioned on the manner in which logging residue 

was harvested and removed from the harvest site by our cooperator. The equipment 
14

GENERAL TECHNICAL REPORT PNW-GTR-872

and machinery used to gather, process, and transport residues precluded replicating 

directly Little’s (1982) methods; however, the objective remained to solve for mass 

using the general equation:

Mass = volume x density (1)

Volume—

Volume measurements were taken in two stages: (1) The first set of measurements were taken at the harvest site where slash piles were assigned one of 

the geometric shapes described by Hardy (1996) and the associated measurements to calculate gross residue volume (Vs

) were recorded. (2) A residue 

pile was subsequently processed into hog fuel and taken to an intermediate 

location where a second set of volume measurements were taken. Processed 

residue piles produced numerous truck loads of hog fuel. At the second location, a front-end loader was used to reconstitute a complete pile from the 

truck loads of hog fuel arriving from the harvest site. Piles were constructed 

with a circular footprint such that the radius of the pile could be derived from 

a direct measurement of its circumference. Pile heights were recorded from 

a distance of 100 ft from the pile center using a clinometer with precision 

to 0.5 percent. The shape of the curve illustrated in figure 5 is given by the 

equation:

y = {[cos((π x x) ÷ r) + 1] ÷ 2} x h (2)

Where r is the derived radius of the pile and h is its height and x ranges from –r to 

r; equation (2) scales a cosine curve to an amplitude of h and a half-period of r. The 

volume (Vh

) of the solid (pile) formed by rotating equation (2) about the y-axis is 

given by:

Vh = [(π2

 - 4) x h x r

2

] ÷ 2π (3)

The hog fuel pile contains the same quantity of solid wood as the original slash pile, 

only with less air. If we let f() represent the relationship of piled hog fuel volume 

(Vh

) to the volume of the original slash pile (Vs), then volume in equation (1) can be 

written as:

Volume = f(Vs

) (4)

And by substitution, (1) becomes:

Mass = f(Vs

) x density
15

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

Density—

We are interested in quantifying the solid wood component of a hog fuel pile. 

However, other pile components must be properly accounted for in order 

to isolate the bone-dry mass of wood: air and water (in the form of wood 

moisture content). A modified version of Glass and Zelinka’s (2010) formula 

provides an alternate version of equation (1), expanding density to more completely account for these pile elements:

Density = [1 – a] x [1 + x] x [Gb x Ρb] (5)

where:

a = air proportion in pile,

x = moisture content of pile,

Gb = specific gravity of wood in pile, and

Ρb = specific gravity of water (62.43 lbs/ft3).

To estimate the distribution of parameters of a, x, and Gb for each pile, five 

samples of hog fuel were drawn from each hog fuel pile and removed for further 

analysis. For each sample, four measurements were taken in the following order: 

Figure 5—Processed hog fuel pile with profile curve estimate. The function describing the curve 

(in green) is given by the equation: y = {[Cos((π × x) ÷ r) + 1] ÷ 2} × h. Where r is the half-period 

of the curve (y-axis to endpoint) and was derived from a direct measurement of circumference; h 

was the height measured from 100 distance from the center using a clinometer. 

Jason Cross
16

GENERAL TECHNICAL REPORT PNW-GTR-872

green mass of sample (M

g

); green volume of the sample with air (Vg+a); 4 green 

volume of sample without air (V

g

); 5 and bone-dry mass of sample (Md). 6 The values 

of variables a, x, and Gb were calculated and recorded.7

Results

Volume—

The set of 20 gross pile volumes ranged from 5,243 ft3 to 99,452 ft3; hog fuel pile 

volumes ranged from 2,549 ft3 to 21,674 ft3. A model relating hog fuel pile volumes 

to slash pile volumes as a straight line through the origin—matching Little’s (1982) 

methods—was applied to the data and yielded a slope of 0.3324. However, a plot of 

residual versus fitted values indicated that the relationship was not linear: Figure 6

details the negative-trend among residual values. A subsequent model relating hog 

fuel pile volume as a function of the square root of slash pile volume yielded a coefficient of 92.18 and intercept of -4,468 with an adjusted R2

 of 0.9317. Figure 7 overlays the fitted curve on the volume data. Substituting the regression coefficient for 

volume in equation (4) yields the following:

Vh = 92.18Vs

1⁄2 – 4,468 (4a)

Density—

For each set of pile samples, the mean and variance were calculated for a, x, and 

Gb

. Air space (a) had a range of (0.5811, 0.6649), with a mean and stratified variance estimate of (0.6230, 5.32E-04). Moisture content ranged over (0.727, 1.4231), 

with a mean and stratified variance estimate of (1.0528, 7.67E-03). Specific gravity 

had a range of [0.36, 0.421] with a mean and stratified variance estimate of (0.3874, 

2.25E-04). Equation (5) can be updated with Pb and the mean values for a, x, and 

Gb:

Density = [1 – 0.6230] x [1 + 1.0528] x [62.43 lbs/ft3

 x 0.3874] (5a)

This can be simplified to:

Density = 18.72 (lbs/ft3) (5b)

When moisture content is 105.28 percent; however, when bone-dry calculations are 

desired (i.e., when x = 0), equation (5a) becomes:

Bone-dry density = [1 – 0.6230] x [62.43 lbs/ft3

 x 0.3874] (5c)

4

 Sample placed in a 4L graduated cylinder, permeable plunger used to compress samples 

with uniform pressure.

5

 Same graduated cylinder filled to top of permeable plunger with water; quantity of water 

subtracted from Vg+a. 6

 104 °C for 48 hours.

7

 a = [(Vg+a - V

g

) ÷ Vg+a]; x = [(Mg - Md) ÷ Md]; Gb = [(Md ÷ V

g

) ÷ 62.43].
17

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

Figure 6—Plot of residual versus fitted values for the linear model Vh ~ Vs + 0. The equation of 

the dotted trendline is y = -0.2211X + 3,458.

Figure 7—Hog fuel pile volume versus slash pile volume with regression line. The function 

describing the regression line is 92.18Vs

1/2 – 4,468.
18

GENERAL TECHNICAL REPORT PNW-GTR-872

As both a and Gb are unitless, equation (5c) can be simplified to:

Bone-dry density = 9.05 lbs/ft3 (5d)

Discussion and Applications to Management

Equations (4a) and (5d) can be substituted into equation (1) to yield:

Bone-dry mass = (92.18Vs

1⁄2 – 4,468) x 9.05 lbs/ft3 (1a)

where bone-dry mass is in pounds. Equation (1a) is only meaningful for slash piles 

greater than 2,350 ft3

. The implication of the negative intercept is that processing 

(grinding) slash piles sufficiently small in size yields negligible amounts of hog 

fuel; or at least volumes that cannot be estimated with the geometric solid indicated by equation (3). In situations where it is necessary to estimate Vh

 yielded by 

very small slash piles, it may be reasonable to use the slope from the linear model 

(0.3324), which had an adjusted R2 of 0.94, although it should be noted that this 

estimator is based on only 19 piles, as one pile highly leveraged the estimate and 

was ejected using Quenouilles jackknife (Cochoran 1977).

The nonlinear relationship between volumes of slash and hog fuel piles suggests 

that increasingly larger increments of slash volume are required to yield a constant 

increment of hog fuel. This may be explained by the onsite operational methods: As 

slash is piled for processing, the pile diameter is limited by the length of the loader’s 

boom arm. To concentrate material as much as possible—so that the maximum 

amount of slash can be processed without moving the grinder—the loader will 

grow the pile in height, with more material in the center. The result is a breakdown 

between the actual shape of very large slash piles and the necessity of selecting a 

shape from a discrete list that is measurable. The selection of a parabolic solid may 

be the best fit, but the slash is concentrated down the center and around the bottom, 

with more air space in the outer mid-section of the solid. A nonlinear relationship 

may also explain Little’s (1982) data plot, although the lack of large-volume slash 

piles makes it difficult to state with certitude that a similar residual pattern exists.

Note that with respect to pile composition, the average green specific-gravities 

of Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco), western hemlock (Tsuga 

heterophylla (Raf.) Sarg.), Sitka spruce (Picea sitchensis (Bong.) Carriere), and 

western redcedar (Thuja plicata Donn ex D. Don) are 0.53, 0.46, 0.35, and 0.32, 

respectively. Given that the mean specific gravity among the 20 piles was 0.38 and 

that moisture content was sufficient to ensure mean or higher values, there was 

likely a significant component of western redcedar in the piles; based on these 

values and the observed ranges, there were likely significant components of Sitka 
19

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

spruce and western redcedar in the piles. Pure Douglas-fir stands or stands composed mostly of fir and hemlock would have higher specific gravities, and therefore 

yield higher bone-dry masses for the same volumes.

Supply Curves

Interest in using biomass to produce energy is increasing. In April 2011, House 

Bill 1422 authorized the Washington State Department of Natural Resources to 

develop aviation fuels from forest biomass. Previously in 2006, Washington voters 

approved Ballot Initiative 937, requiring large utilities to obtain at least 15 percent 

of their electricity from new renewable resources, including biomass. Where and 

how biomass will be utilized will depend, in part, on the available supply and cost 

of delivery.

Supply curves describe the behavior of average unit cost as cumulative supply 

increases. Kerstetter and Lyons (2001) demonstrated a straightforward methodology 

for constructing supply curves for logging and agricultural residues in Washington, 

Oregon, and Idaho: Factor analyses of site production, in-woods cost of recovery, 

and transportation cost to specified delivery center, where the delivered price is the 

sum of recovery and transportation factors.

The purpose of this analysis is to use a similar methodology and construct 

updated supply curves for delivery centers on Washington’s Olympic and Kitsap 

Peninsulas: Aberdeen, Forks, Port Angeles, Port Townsend, and Shelton.

Methods

Residue production—

The production study described the criteria for residue-producing parcels on the 

Olympic and Kitsap Peninsulas: Timberlands greater than 15 ac excluding federal 

and tribal lands; also excluded were single-tree sales, right-of-way, and salvage 

operations. The Washington State Forestland Database (Rogers and Cooke 2010) 

delineated 1,963,352 ac within the study area meeting these criteria; total harvest 

acreage over the 2-year study period (66,729) suggests an annualized harvest rate of 

1.7 percent. Using the Forestland Database, parcels were directly stratified by forest 

location and ownership type factors, and aggregated by 10-minute delivery interval 

to a specific delivery center. Harvest intensity was imposed on each location/ownership group in the same proportion as table 1. Harvest method was not considered 

as it was not found to be associated with distinct production rates. The acreage in 

each forest location, harvest intensity, and ownership type stratum within a delivery 

interval was assigned its corresponding residue production rate from table 5. 

Pure Douglas-fir 

stands or stands 

composed mostly of 

fir and hemlock would 

have higher specific 

gravities, and therefore 

yield higher bone-dry 

masses for the same 

volumes.
20

GENERAL TECHNICAL REPORT PNW-GTR-872

To illustrate, there are 15,016 ac of timberland between 10 and 20 minutes of 

delivery time from Port Angeles, of which 5,069 ac is located on the west side of 

the Olympic Peninsula and has public ownership (LwO

p

). According to table 1, 87.9 

percent (4,410 ac) of LwO

p lands were clearcut, of which approximately 1.7 percent 

(75 ac) would be expected to be harvested in a given year. The average residue 

produced per clearcut acre of public land on the west side of the Olympic Peninsula 

(LwI

c

O

p

) is 1,913 ft3 (see table 5), yielding a total of 143,000 ft3. Applying a bonedry density of 24.18 lbs/ft3

, this volume is equivalent to 1,729 BDTs. These calculations were repeated for each stratum for each delivery interval for each delivery 

center. 

In woods recovery costs—

Recovery operations consist of one or two loaders that gather material about the 

harvest unit, their operators, and a grinder located near a road. Current operational 

procedures apply a base processing rate around $35/BDT that covers labor, capital, 

and a small margin.8

 A fuel surcharge is applied at the rate of 1 percent of the base 

rate for every 10 cent increase in the price of diesel fuel.9

Transportation—

Parcels were aggregated into 10-minute intervals of delivery time;10 however, transportation also includes load and unload times, and the return trip. Han (2011) estimated the loading and unloading times at around 30 minutes each. Total transportation costs are the sum of loading, unloading, and twice the interval time; an hourly 

base transportation rate of $65 was found to represent the region. A fuel surcharge 

is applied in the same manner as for recovery operations. Assuming a full truck 

load is 29 green tons of hog fuel at 53 percent moisture (see x, in the “Volume-toweight ratios” section), transportation cost is calculated at $1.59/BDT/10-minute 

interval.

8

 Both Port Townsend Paper Corporation and Hermann Brothers Logging and Construction, Inc. collaborated with the Olympic Natural Resources Center on this project and 

agreed to share information. Consequently, we were able to capture costs and procedures 

that reflect current operations.

9

 The U.S. Energy Information Administration posts regional on-highway diesel fuel prices 

each week. The base price on which a surcharge is calculated is $1.21 from March 21, 1994. 

Therefore if diesel prices post at $4.21 for a given week, then a 30 percent surcharge is 

applied to the base rate.

10 Transportation time estimates were derived from a combination of Environmental 

Systems Research Institute’s Streetmap North America 2010 that has speed limits for 

interstates, highways, urban roads, and surface streets. The transportation layer from the 

Washington State DNR was used for all other roads, with an assumed average speed of 15 

mph. Aggregations were constructed within the Washington State Forestland Database.
21

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

Supply Curves

Supply curves were developed for Aberdeen, Forks, Port Angeles, Port Townsend, 

and Shelton. Price represents the cumulative average delivered base price; cumulative supply is denoted in MBDTs. The length of the curve represents total accessible 

biomass within 180 minutes (one-way) delivery time. Residue production within 

delivery intervals will differ with the distribution of stratified factors; costs are 

expected to remain constant within a delivery interval—marginal increases reflect 

increased distance. Aggregate supply curves are presented in figure 8 for comparison purposes, followed by individual curves in figures 9 through 13.

Applications to Management

Recovery and transportation—

Much effort has been devoted in other analyses to precisely quantify the cost of 

recovery. Although piece size, yarding method, and yarding distance most certainly 

affect the delivered cost of a BDT, the precision achieved in accounting methods 

belies operational realities: once material is processed and in a van, it becomes

impossible to dissect the load into constituent costs. This presents an auditing

problem for buyers and inefficiencies in the field. The simplicity achieved with a 

base rate also reflects the compromise that is being struck with landowners for access. Direct pay to landowners is essentially forgone (≤ $4 BDT) in exchange for 

operations that cover an entire unit. Landowners realize a gain in reduced (or even 

Figure 8—Supply curves for all delivery centers. BTD = bone dry ton. MBDT = 

thousand bone dry tons.
22

GENERAL TECHNICAL REPORT PNW-GTR-872

Figure 9—Aberdeen supply curve. BTD = bone dry ton. MBDT = thousand bone dry tons.

Figure 10—Forks supply curve. BTD = bone dry ton. MBDT = thousand bone dry tons.
23

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

Figure 11—Port Angeles supply curve. BTD = bone dry ton. MBDT = thousand bone dry tons.

Figure 12—Port Townsend supply curve. BTD = bone dry ton. MBDT = thousand bone dry tons.
24

GENERAL TECHNICAL REPORT PNW-GTR-872

Figure 13—Shelton supply curve. BTD = bone dry ton. MBDT = thousand bone dry tons.

perhaps eliminated) site preparation, fire, and smoke management costs and concerns. Therefore, operators agree to take material from the entire unit—even if 

some of the unit’s slash would not otherwise be economical to extract—in exchange 

for permission to remove residues. A single rate for recovery operations will reflect 

this compromise; purchasers understand that in order to access the low-cost residues, they must be willing to purchase some quantity at a higher cost.

Supply—

Forks is the most competitive delivery center up to approximately 50 MBDT; 

equivalent to roughly 6 megawatt-years of power.11 Aberdeen, Forks, and Shelton 

demonstrate relatively similar behavior up to 250 MBDT, beyond which delivery to 

Forks is noticeably more expensive and to Aberdeen noticeably less. Port Angeles 

and Port Townsend are at a decided disadvantage with respect to total quantity of 

biomass accessible and average price; however, barge delivery of hog fuel from outside sources is possible at both locations, but accounting for any such sources was

11 The average energy value of piled residue in the study was about 9,000 BTUs per 

bone-dry pound (Howard 1988). Therefore, one BDT is equivalent to 5.3 megawatt hours 

(MWH) of energy. The U.S. Department of Energy estimates 75 percent combustion 

efficiency, and 40 percent generation efficiency (http://www.ornl.gov), resulting in 1.6 

MWH of electricity per BDT of biomass that may be rounded conservatively to 1 MWH. If 

one megawatt year consists of approximately 8,000 MWH, then total electrical production 

from biomass can be calculated by dividing the available supply (BDT) by 8,000.
25

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

was beyond the scope of this investigation. Aberdeen has access to the greatest 

quantities of logging residue at the lowest average price; both Aberdeen and Shelton 

are likely to have access to additional residues in Thurston, Lewis, and Pacific 

Counties (not included here), counties that would increase their overall supply and 

competitiveness. Listed below (in decreasing order) is the annual quantity of hog 

fuel available to each delivery center at an average cost of $50/BDT:

1. Aberdeen (410 MBDT/year)

2. Shelton (320 MBDT/year)

3. Forks (280 MBDT/year)

4. Port Angeles (110 MBDT/year)

5. Port Townsend (100 MBDT/year)

The average price for each supply curve represents the base recovery and 

transportation rate, on which a fuel surcharge must be levied. The effect of the 

surcharge is to shift each curve up, but does not affect the shape or relative position 

of each curve.

Conclusion

The investigation of the quantity of slash produced by timber harvest operations for 

calendar years 2008 and 2009 included 975 FPAs accounting for 66,729 ac of land 

on the Olympic and Kitsap Peninsulas of Washington. In total, nearly 30 mi of transect surveys and a census of more than 3,000 slash piles isolated mean production 

within 3 percent of the mean production rate of 1,599 ft3/ac, with 80 percent confidence. Four factors were thought to be associated with difference slash production 

rates: forest location, ownership type, harvest intensity, and harvest method. For 

slash measured by transects, only ownership type was associated with different production rates. Public lands produced an average of 1,588 ft3

/ac compared with 1,155 

ft3/ac on nonpublic lands. Several factors were associated with different production 

rates for pile residues: forest location, harvest intensity, ownership type, and the 

interaction between intensity and ownership. Further analysis found two distinct 

levels of piled residue production ranging from 65 ft3/ac to 325 ft3/ac.

An updated analysis of slash piles found significantly less wood per unit 

volume than previous estimates, likely owing to changes in forest types and harvest 

methods between studies. The bone-dry mass (in pounds) of wood in a pile of slash 

was related to its gross volume (Vs

) with the equation: bone dry mass = (92.18Vs

1⁄2 

– 4,468) x 9.05 lb/ft3. This equation reflects the specific gravities (i.e., the types 

and mix of species) in the sampled piles, and the moisture content at the time of 

sampling. As species and moistures differ among piles, so will this relationship.

An updated analysis 

of slash piles found 

significantly less wood 

per unit volume than 

previous estimates, 

likely owing to changes 

in forest types and 

harvest methods 

between studies.
26

GENERAL TECHNICAL REPORT PNW-GTR-872

Supply curves that detail the quantity available to, and average unit price on, 

delivery were constructed for the cities of Aberdeen, Forks, Port Angeles, Port 

Townsend, and Shelton. The in-woods costs for processing slash and transportation 

were asserted at $35/BDT and $65/hour, respectively. This resulted in a delivered 

cost of $1.59/BDT/10-minute delivery interval one way. Aberdeen was found 

to have access to the greatest quantity of slash (600 MBDT/year), and had 

more than four times the quantity available for delivery (410 MBDT/year) 

than Port Townsend (100 MBDT/year) at an average price of $50/BDT. Forks 

was found to have the lowest average unit price for the first 50 MBDT/year, 

at $43.64/BDT; a quantity that could produce approximately 6 MW of power. 

The deliverable quantities were based on harvest rates for 2008 and 2009, 

and would be expected to increase and decrease as harvest rates change.

Acknowledgments

The research team for the production study and updated volume-to-weight ratios 

included principal investigator Eric Turnblom, associate professor at the University 

of Washington, College of the Environment, School of Environmental and Forest 

Sciences; Jason Cross, research coordinator for the University of Washington’s 

Olympic Natural Resources Center (ONRC); John Calhoun, director of the Olympic 

Natural Resources Center. The research team for the supply curves also included 

Gregory Ettl, director of the Center for Sustainable Forestry at Pack Forest; Jeff 

Comnick, research scientist at the ONRC.

Jeff McGinley of Pacific Forest Management in Forks, Washington, helped 

secure landowners’ permissions to access harvest units and collect field data; Reed 

Wendel, Aaron Brooks, and Scott Jamieson, all from Pacific Forest Management, 

collected field data. Rebecca Gentry of ONRC conducted the laboratory analyses 

of hog fuel samples. Updated volume-to-weight ratios would not have been possible without the cooperation of Bill Hermann of Hermann Brothers Logging in 

Port Angeles, Washington. His willingness to alter production methods allowed for 

measurements that could not otherwise be taken. George Cave of Port Townsend 

Paper provided insight into the methods for developing supply curves that tempered 

a desire for precision with operational realities. 

This work was made possible with funding from the Restoration Silviculture 

Initiative—a partnership between the University of Washington’s ONRC and the 

U.S. Forest Service’s Pacific Northwest Research Station. The expanded scope of 

the analysis was made possible by additional funding from the Northwest Clean 

Energy Application Center and Washington State University. This report represents 

the conclusion and fulfillment of the following contracts: 09-CA-11261991-010 

(PNW), 09-CA-11261991-007 (PNW), DE-FG02-97ER41020 (WSU).
27

Biomass Production on the Olympic and Kitsap Peninsulas, Washington

Metric Equivalents

When you know:	 Multiply by:	 To find:

Inches (in) 2.54 Centimeters

Feet (ft) .305 Meters

Miles (mi) 1.609 Kilometers

Miles per hour (mph) .447 Meters per second

Acres (ac) .405 Hectares

Cubic feet (ft3

) .0283 Cubic meters

Pounds (lb) .454 Kilograms

Pounds per acre (lb/ac) 1.12 Kilograms per hectare

Tons (ton) 907 Kilograms

Degrees Celsius (C) 1.8 °C + 32 Degrees Fahrenheit

Cubic feet per acre (ft3/ac) .07 Cubic meters per hectare

Pounds per cubic foot (lb/ft3) 16.02 Kilograms per cubic meter

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