Estimating Forest Soil Carbon and Nitrogen Stocks with Double Sampling for Stratification C. H. Shaw* Natural Resources Canada Canadian Forest Service Northern Forestry Centre 5320 122 St. Edmonton, AB, Canada T6H 3S5
J. R. Boyle Forest Resources Oregon State Univ. 280 Peavy Hall Corvallis, OR 97331-5703
A. Y. Omule Agro Forestry Limited 1564 Granada Crescent Victoria, BC, Canada V8N 2B8
Precise and accurate estimation of C and N in forest soils is important for monitoring longterm site productivity and C stock changes. Obtaining such estimates remains a major challenge, however, especially because of high natural variability in the forest floor. Although most researchers have used simple random sampling (SRS) for within-plot soil sampling, double sampling for stratification (DSS) can be used to decrease costs, increase precision, and increase power. Estimates of C and N stocks based on DSS were compared with those estimated by SRS in the humus forms of Douglas-fir [Pseudotsuga menziesii (Mirb.) Franco] stands in the Cascade Mountains of Oregon. Generally, DSS was 1.34 to 5.11 times more efficient than SRS for total C, and 1.07 to 2.00 for total N. Coefficients of variation estimated from DSS were about one-half of those estimated by SRS and reported elsewhere in the literature. The cost for sampling using DSS was one-third to one-half of that for SRS, depending on the number of strata used. Costs were reduced because fewer samples were required using DSS to provide the same precision as SRS. The DSS design was more powerful than SRS and could detect smaller changes than SRS with the same number of samples. Results suggested that the most efficient design for total C would use two strata where samples were allocated proportional to variance rather than proportional to area. Overall, large gains in efficiency can be realized with a more complex within-plot sampling design, i.e., DSS, compared with SRS. Abbreviations: AWood, aboveground coarse woody debris; BWood, belowground coarse woody debris; CWD, coarse woody debris; DSS, double sampling for stratification; IMin, mineral soil inside the bole zone; IMinS, mineral soil plus stones inside the bole zone; OMin, mineral soil outside the bole zone; OMinS, mineral soil plus stones outside the bole zone; SRS, simple random sampling; TC, total carbon; TN, total nitrogen.
S
Freely available online through the author-supported open access option. Soil Sci. Soc. Am. J. 72:1611-1620 doi:10.2136/sssaj2007.0219 Received 13 June 2007. *Corresponding author (
[email protected]). © Soil Science Society of America 677 S. Segoe Rd. Madison WI 53711 USA All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher. SSSAJ: Volume 72: Number 6 • November–December 2008
that the required sample size is so large that it would be prohibitively expensive to conduct definitive studies (Lloyd and McKee, 1983). Although this challenge has always existed in forest soils research, it is particularly important for estimating C stocks and changes in C stocks for validation of predictive models and for project-level accounting of C for potential trading of C credits (Penman et al., 2003). Eberhardt and Thomas (1991) described eight classes of methods for ecological studies, which they divided into two groups: controlled experiments and observation of some uncontrolled process by sampling. These groups are similar to those distinguished by Hurlbert (1984) as manipulative and mensurative experiments, respectively. Proper estimation of C or N stocks depends more on the body of statistical theory for sampling that underlies the second group of methods, which were not discussed in detail by Hurlbert (1984), who referred the reader to textbooks by Cochran (1963) and Yates (1960) for advice. Gains in efficiency are achieved by controlling the allocation of observational effort in space and time. Even though progress in ecological research has been made by combining field observation with controlled experiments, the design of the observational stages is typically not rigorous (Eberhardt and Thomas, 1991). This may be especially true for forest soils research. Petersen and Calvin (1986) pointed out that few studies in soil science have been conducted on which sound sampling procedures can be based. They suggested that the costs of intensive studies have discouraged such work but that if progress
FOREST, RANGE & WILDLAND SOILS
oil C and N are “master variables” in determining soil fertility (Johnson and Curtis, 2001), and forest management practices may alter the status and dynamics of these elements in ways that influence the sustainability of long-term productivity (Gessel et al., 1990; Boyle and Powers, 2001). Yet in North American West Coast Douglas-fir and other forest ecosystems, estimation of C and N stocks in soils remains a challenge, largely because of high natural variability, especially in the forest floor (McNabb et al., 1986; Homann et al., 2001; Yanai et al., 2003). The inability to detect statistically significant differences in soils in relation to stand treatments or forest types is often attributed to high variances, and the most common conclusion is that sample size must be increased to maximize the power for statistical tests (McNabb et al., 1986; Homann et al., 2001; Yanai et al., 2003). Many researchers then conclude
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is to be made, investigations of different sampling plans are needed. They also stated that the sampling intensity needed to estimate some characteristics depends on the magnitude of variation; however, few data are available from which the magnitudes of sources of variation in soils may be estimated. In some instances, the variation within contiguous classification units is so great that it is not feasible to estimate differences among units with any satisfactory degree of precision (Petersen and Calvin, 1986). This problem is common in forest soil studies, for which within-plot variation often accounts for more than half of the total variation in the study (Homann et al., 2001). Estimates of high variability reported for forest soils often originate from studies that used within-plot sampling designs and statistical analyses for SRS (McNabb et al., 1986; Homann et al., 2001). Other sampling approaches, such as systematic or stratified random sampling, can be used to decrease costs or increase the precision of estimates relative to SRS with the same number of samples (Cochran, 1977). For ecological studies involving soils, stratification has been applied across large areas covering hundreds of hectares (e.g., by stand or ecotype in forestry and by soil mapping unit in agriculture) (Nortcliff, 1978; Penman et al., 2003). Plots (10–90 m2) are located within these strata, and soil samples (10–90 cm2) are taken randomly within each plot. In such studies, stratification has been used to scale up estimates from the plot to the mapping unit, but this method has not been used to scale up from the sample to the plot, where a large proportion of the variability in forest soils occurs (McNabb et al., 1986; Homann et al., 2001). Although soil variability with depth can be addressed through sampling by soil horizon, within-plot lateral variability is not commonly considered, or selective sampling is used to avoid the problem (Fons and Klinka, 1998). The humus form, the focus of this study, is defined as “a group of soil horizons located at or near the surface of a pedon, which have formed from organic residues, either separate from, or intermixed with, mineral materials,” and it is related to site productivity (Green et al., 1993, p. 4). Because the humus form is a combination of the forest floor and the surface mineral A horizon, it often contains the highest proportion of variability of the entire soil profile (Petersen and Calvin, 1986). Green et al. (1993) described the humus form sampling unit as the smallest area that should be used to recognize, describe, and sample a humus form individual; they suggested lateral dimensions ranging from 20 by 20 cm to 50 by 50 cm. This study focused on the efficiency of the sampling design using data obtained in another study, which was undertaken to test hypotheses about humus form properties and soil fauna. This work directly responds to the concluding remarks of Yanai et al. (2003), who recommended that the full spectrum of spatially explicit sampling designs be explored and, furthermore, that studies should be able to discern patterns of change in forest floor mass across microsites and in relation to trees. Yanai et al. (2003) used power analysis calculations in a meta-analysis to compare the relative ability of different studies to detect a 20% change in mean forest floor C. They concluded that studies using paired samples were more powerful than those using independent (unpaired) samples. The power of a t-test measures the ability of the test to detect a difference between 1612
two means when a difference does exist, or the chance of not making a Type II error (Samuels 1989). The power of a test depends on many factors, including sample size (n) and the variability of the observations (Samuels 1989). Given adequate information about the parameter’s variability, a power analysis can be used to estimate n before designing a study. Although a larger n can increase power, some study designs are more powerful than others for the same n (Samuels 1989). Thus, a post hoc analysis of power can be used to compare the power of different sampling designs. We developed a DSS sampling design (Cochran, 1977; Lohr, 1999) for estimating total C and N in the humus form and compared statistics estimated from DSS with those estimated by SRS. Double sampling for stratification can be profitable if the gain in precision from the preliminary sampling more than offsets the loss in precision from the reduction in the size of the main sample (Cochran, 1977). It has been used to predict fuel loads in the forest floor of ponderosa pine (Pinus ponderosa P. Laws. ex C. Laws) forests (Fule and Covington, 1994). Double sampling for stratification is efficient when a response variable is heterogeneous, the preliminary sample can be assigned to meaningful strata on the basis of criteria correlated with the response variable, the preliminary sample is large enough that estimation of stratum proportions contributes little to the overall variance, and the value of increased precision resulting from stratification exceeds the cost of collecting the preliminary sample (Reinecke and Hartke, 2005). Using this approach, or alternate complex sampling designs, may be most valuable for projects requiring large investments in time and money such as long-term monitoring projects or large-scale surveys; or for estimation associated with high economic risk, such as estimates of soil C stocks and stock changes for potential offset trading systems. It is also clear, however, that any sampling method that increases precision and accuracy and therefore power for testing is beneficial for site-specific studies of a short duration where the ability to detect small changes is desirable or for studies where reducing the number of samples will reduce costs associated with specialized, high-cost analyses (e.g., isotopes).
MATERIALS AND METHODS Study Sites A study of forest soil properties (a mensurative study sensu Hurlbert, 1984) was undertaken in selected Douglas-fir forests of the Cascade Mountains in the Willamette National Forest, Oregon, to determine whether the humus forms (i.e., the O plus A horizons; Klinka et al., 1981; Green et al., 1993) could be used as indicators of resilience to disturbance from harvesting. Site types were defined by combinations of soil order and forest stand age (Table 1), and sites were selected to relate to other long-term forest research projects in the same general landscape. Plots on Inceptisol soils were located in the H.J. Andrews Experimental Forest, and plots on Ultisol soils were located to the south of the Andrews Forest, where second-growth stands were selected from the Morris Plots established in 1946 to 1952 to assess the long-term effects of burning on some forest ecosystems (Miller et al., 1989). Two plots were established in each of four site types, Ultisol old growth, Ultisol second growth, Inceptisol old growth, and Inceptisol second growth, for a total of eight plots (Table 1). On average, trees on the second-growth plots were 30 yr SSSAJ: Volume 72: Number 6 • November–December 2008
Table 1. Site characteristics of plots on Inceptisol and Ultisol soils located in the Willamette National Forest, Oregon, and sampled in 1990. Plot†
Slope
IOG (1) IOG (2) ISG (1) ISG (2) UOG (1)
% 18 17 14 18 21
UOG (2) USG (1) USG (2)
7 23 11
Aspect o
Elevation
Stand age
Year harvested
212 (SW) 300 (NW) 232 (SW) 296 (NW) 140 (SE)
m 870 970 870 960 680
yr ~350 ~350 22 32 ~350
NA‡ NA 1960 1953 NA
304 (NW) 16 (N) 318 (NW)
1090 570 1080
~350 35 34
NA 1946 1949
Post-harvest treatment
Broadcast burned and planted (1961, 1962) Broadcast burned and planted (1959)
Broadcast burned and natural regeneration Broadcast burned and natural regeneration
† IOG, Inceptisol old growth; ISG, Inceptisol second growth; UOG, Ultisol old growth; USG, Ultisol second growth. Numbers in parentheses indicate plot number. Soils were classified at the time of the study using the taxonomic system available at that time (Soil Survey Staff, 1975). Today, these soils would all be placed in the new Andisol Order (Soil Survey Staff, 2003) on the basis of having a common parent material with andic properties. ‡ NA, not applicable.
of age. Sites on Inceptisols had been broadcast burned and planted with Douglas-fir after harvesting; those on Ultisols had been broadcast burned and tree stands had been reestablished through natural regeneration. Old-growth stands selected to represent stands similar to those on the second-growth sites before burning were about 350 yr of age. Only plots with no evidence of recent human disturbance were selected, and plots within a soil order were selected to occur on sites relatively similar in elevation, topography, landform, slope, geologic parent material, and productivity (Site Classes II and III) (McArdle and Meyer, 1930; Table 1). Two standard soil pits were dug adjacent to each plot, one upslope and one downslope, and were used in describing and classifying the soil (Soil Survey Staff, 1975) and humus forms (Klinka et al., 1981) (Tables 2 and 3, Fig. 1). Each plot was 30 by 30 m, except for one plot with second growth on an Ultisol soil (Ultisol second-growth Plot 2), where a rectangular 32- by 24-m plot was used to avoid disturbance from old haul roads. The plot design included a 1-m buffer; the area used for scaling up plot-level estimates was 784 m2 (28 by 28 m) throughout, except for Ultisol second-growth Plot 2, where it was 660 m2 (30 by 22 m).
Double Sampling for Stratification Sampling Design The DSS design used in this study included two samplings. All samples were taken in the summer of 1990. First, a preliminary systematic sample was taken to estimate the proportion of each stratum in each plot, as follows. Within each plot, a 2- by 2-m grid was established with flagged stakes and grid points identified by row and column numbers (Fig. 1). Each grid point was classified into one of
six strata (described below), and the results were used to estimate the proportion of each stratum in each plot. These proportions were used to allocate the number of soil samples per plot to each stratum in each plot during the second sampling (the main sampling) (Cochran, 1977; Table 4). The total number of main soil samples to be obtained from a plot was initially estimated at three times the number of strata that were sufficiently large to be sampled. In some cases, one or more additional samples were taken in a stratum to ensure better agreement between the stratum proportions estimated from the preliminary sampling and those resulting from the main sampling. Sample points were randomly chosen from the grid points available within a stratum. Strata were defined by characteristics of the humus form composition and the environment that are thought to influence decomposition processes. Coarse woody debris (CWD, woody debris >2.5 cm in diameter) offers a unique habitat for primary and secondary decomposers (Ausmus, 1976; Spiers et al., 1986; Carpenter et al., 1988), and the microclimate surrounding the wood (Harmon et al., 1986; Harmon and Sexton, 1996) may differ depending on whether it is aboveground or belowground. Others have shown that pedogenesis and the quantity and types of soil fauna vary along a gradient radiating out from a tree bole (Crampton, 1982). The presence of CWD, its location in relation to the surface of the ground, and the proximity of a grid point to the bole or stump of a dominant or codominant tree were criteria used in determining four of the strata: (i) mineral soil inside the bole zone (IMin); (ii) mineral soil outside the bole zone (OMin); (iii) aboveground CWD (AWood); and (iv) belowground CWD (BWood).
Table 2. Example profile description for Inceptisol old growth Plot 1 located in the Willamette National Forest, Oregon, and described in 1990. The humus form classification would be Mineroleptomoder (Klinka et al., 1981). Horizon Oi–Oe Oa
Depth cm −8.0 to −7.0 −7.0 to 0.0
Description Clear wavy boundary; 0.5–2 cm thick Clear wavy boundary; 3–8 cm thick
A
0.0 to 5.0
10YR 2/2 (moist) very dark brown; sandy loam; 40% gravel; moderate fine medium and coarse granular; friable; abundant very fine and fine medium roots; gradual wavy boundary; 1.5–7.5 cm thick.
AB
5.0 to 19.0
10YR 3/4 (moist) dark yellowish brown; sandy loam; 25% gravel and 10% cobbles; medium subangular blocky to moderate fine and medium granular and medium subangular blocky; very friable; abundant very fine and fine and few medium roots; gradual wavy boundary; 10–16.5 cm thick.
B
19.0 to 40.5
7.5YR 3/4 (moist) dark brown; sandy loam; 35% gravel; very weak medium subangular blocky; loose; plentiful very fine and fine and few medium roots; gradual irregular boundary; 13–23 cm thick.
BC
40.5 to ≥60
10YR 3/6 (moist) dark yellowish brown; loamy sand; 40% gravel; very weak coarse subangular blocky; loose; plentiful very fine and fine and few medium roots.
SSSAJ: Volume 72: Number 6 • November–December 2008
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Table 3. Example profile description for Ultisol old growth Plot 1 located in the Willamette National Forest, Oregon, and described in 1990. The humus form classification would be Orthivermimull (Klinka et al., 1981). Horizon
Depth
Description
Oi-Oe
cm −1.5 to 0.0
A
0.0 to 13.0
10YR 3/4 (dry) dark yellowish brown and 10YR2/2(d) very dark brown; loam; 10% gravel; moderate fine granular; very friable; abundant very fine and plentiful fine and coarse roots; gradual irregular boundary; 7–15 cm thick.
AB
13.0 to 24.0
10YR 3/4 (moist) dark yellowish brown; loam; 10% gravel and 5% cobbles; moderate fine and medium granular; very friable; plentiful fine, very fine, and medium and few coarse roots; gradual wavy boundary; 8–15 cm thick.
B
24.0 to 48.0
C
48.0 to ≥90
Abrupt wavy boundary; 1–3 cm thick.
10YR 3/6 (moist) dark yellowish brown; clay loam; 5% gravel; very weak coarse subangular blocky; moderate medium and coarse granular and moderate fine subangular blocky; friable; few fine medium and coarse roots; clear wavy boundary; 22–26 cm thick. 10YR 4/4 (moist) dark yellowish brown; silt loam; 10% gravel; amorphous; very firm; few fine and medium roots.
The bole zone was defined as a 1-m ring around the edge of the bole of a standing tree (or old stump) in the old-growth stands and around an old-growth stump in the second-growth stands. Only CWD that constituted a viable rooting medium for plants (i.e., Decay Classes IV and V [Sollins, 1982]) were used for strata AWood and BWood. Furthermore, only CWD with a minimum depth of 2.5 cm was used, and an estimate of “burial” was made to distinguish between AWood and BWood. If a grid point occurred where a sample could not be taken (e.g., a large rock at the surface, a living tree, or CWD Classes I–III), the point was shifted 0.5 m up the row. If once again a sample could not be taken, the grid point was not used. A total of 22 sampling grid points were shifted and the majority of these occurred on Inceptisol old-growth Plot 1 and Inceptisol second-growth Plot 1. The parent material in which the Inceptisols formed is characterized by a significant proportion of stones. The stones were large enough that they might have influenced development of the humus
form, so an additional two strata were included: (v) mineral soil and stones inside the bole zone (IMinS); and (vi) mineral soil and stones outside the bole zone (OMinS). Sampling of all strata was achieved for one set of plots of each site type. Because of limited funds and time, only the dominant strata in some of the second set of plots were sampled. Therefore, in some cases, grid points for the most similar strata were combined (Cochran, 1977) and then a random sample was taken from them accordingly (Table 4). Four horizon layers, the Oi–Oe, Oa, CWD, and A layers, were sampled, as each occurred at each sampling point. Initially, the CWD was classified separately from the Oa material, but macromorphological and micromorphological examination of the horizons revealed that the CWD represented a continuum of decomposition, the most decomposed of which would be classified as an Oa horizon; it was therefore decided to label the Oa and CWD as one horizon type, HCWD. Polyvinyl chloride cylinders (7.5-cm diameter and depth) were used to obtain semidisturbed samples for determination of bulk density (Db). After a core sample was removed, bulk samples from each horizon were collected for chemical analyses. If large stones prevented a Db sample with a core from being obtained, the sample was taken by extracting a 10- by 10-cm square at the surface along with multiple measurements of the sample’s thickness. In the laboratory, the core samples were gently removed from the cylinders and the thickness of each horizon was measured. The horizons were separated and dried to a constant weight at 105°C. If the mineral soil horizons contained stones, these were separated with a 2-mm sieve and their volumes and weights were estimated. The volume and weight of stones were subtracted from the volume and weight, respectively, of the original horizon sample to estimate Db (g cm–3) of the mineral soil corrected for the presence of stones. Bulk Oi–Oe and HCWD samples were air dried and ground through a Fig. 1. Double sampling for stratification sampling design for an individual plot. Wiley mill to pass through a 1-mm
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SSSAJ: Volume 72: Number 6 • November–December 2008
Table 4. Numbers of preliminary systematic samples (n = total, nh = by stratum) and main soil samples (m = total , mh = by stratum), and proportions estimated from each. Plots were located on Inceptisol and Ultisol soils in the Willamette National Forest, Oregon, and sampled in 1990. Plot†
Data type
Ultisol plots
Inceptisol plots‡ AWood BWood
OMin
IMin OMinS Total
OG (1)
Preliminary samples 21 74 39 22 39 Preliminary sample proportions 0.11 0.38 0.20 0.11 0.20 Main samples 2 6 4 2 2 Main sample proportions 0.13 0.38 0.25 0.13 0.13 OG (2) Preliminary samples 39 51 25 3 78 Preliminary sample proportions§ 0.20 0.26 0.13 0.01 0.40 Combined proportions§ 0.00 0.46 0.54 0.00 0.00 Main samples 0 5 7 0 0 Main sample proportions 0.00 0.42 0.58 0.00 0.00 SG (1) Preliminary samples 34 34 103 24 1 Preliminary sample proportions 0.17 0.17 0.53 0.12 0.01 Combined proportions§ N/A N/A N/A N/A N/A Main samples 2 2 6 2 0 Main sample proportions 0.17 0.17 0.50 0.17 0.00 SG (2) Preliminary samples 15 103 63 12 3 Preliminary sample proportions§ 0.08 0.52 0.32 0.06 0.02 Combined proportions§ 0.00 0.60 0.40 0.00 0.00 Main samples 0 6 4 0 0 Main sample proportions 0.00 0.60 0.40 0.00 0.00 † OG, old growth; SG, second growth. Numbers in parentheses indicate plot number.
AWood BWood
196 1 15 1 187 1 1 9 1 196 1 N/A 1 13 1 191 1 1 6
26 0.13 2 0.13 24 0.13 0.00 0 0.00 43 0.22 0.22 3 0.23 51 0.27 0.00 0 0.00
OMin
IMin
33 105 0.17 0.54 2 8 0.13 0.53 99 44 0.53 0.23 0.66 0.34 6 3 0.67 0.33 63 88 0.32 0.45 0.32 0.46 4 6 0.31 0.46 45 74 0.23 0.39 0.50 0.50 3 3 0.50 0.50
32 0.16 3 0.20 17 0.09 0.00 0 0.00 2 0.01 0.00 0 0.00 21 0.11 0.00 0 0.00
OMinS Total 0 0.00 0 0.00 3 0.02 0.00 0 0.00 0 0.00 0.00 0 0.00 0 0.00 0.00 0 0.00
196 1 15 1 187 1 1 9 1 196 1 1 13 1 191 1 1 6 1
‡ AWood, aboveground coarse woody debris; BWood, belowground coarse woody debris; OMin, mineral soil outside the bole zone; IMin, mineral soil inside the bole zone; OMinS, mineral soil with stones outside the bole zone. § Sample points in similar strata (AWood + BWood or OMin + IMin + OMinS) were combined to give combined proportions, which were used to determine the allocation of main samples taken in these cases.
(∑ x ) = m
mesh sieve. Bulk mineral soil samples were air dried and ground to pass through a 2-mm sieve. Total C for all samples was determined by oxidation at 1300°C in an O2 stream followed by infrared CO2 detection (LECO carbon determinator, LECO Corp., St. Joseph, MI). The Oi–Oe and HCWD samples were digested according to the method described by Parkinson and Allen (1975), and Kjeldahl N was determined according to the method of Bremner and Mulvaney (1982). Nitrogen in the digests was determined with an autoanalyzer (Technicon Industrial Systems, 1977). Total C (g cm−2) for each horizon was calculated as TC =
C(%) DbTh 100
[1]
where TC is the total C in a horizon (g cm−2), Db is bulk density (g cm−3), and Th is horizon thickness (cm). The same equation was used for total N (TN), substituting TN for TC and N percentage for C percentage. Total C or N per unit ground surface area for the humus form at the sampling point was calculated as the sum of total C or N for all humus form horizon layers at that point.
Statistical Analyses Means, variances of the means, and CVs for TC and TN were estimated using separate equations for SRS and for DSS to allow comparison of the relative effectiveness of the two approaches. Even though the samples were taken in the field using a DSS design, the equations for SRS could be used with these data because DSS with proportional allocation approximates SRS (Cochran, 1977, p. 136). Means (g cm−2), variances of the means ([g cm−2]2), and CVs (%) for TC and TN based on SRS were estimated using (Lohr, 1999) SSSAJ: Volume 72: Number 6 • November–December 2008
xSRS
vxSRS
[2]
i =1 i
m
s2 = m
[3]
with
s
2
(x − x ) = ∑ i SRS (m − 1) i =1
2
m
CVSRS =
s2 xSRS
100
[4]
where xi is the total C or total N of a main sample, m is the number of main samples taken in a plot, xSRS is the mean of xi based on SRS, v x SRS is the variance of xSRS , s2 is the sample variance, and CVSRS is the CV based on SRS. Means (g cm−2), variances of the means ([g cm−2]2), and CVs for TC and TN based on DSS were estimated using (Lohr 1999)
nh xh h =1 n
[5]
nh − 1 nh sh2 1 H nh 2 + ∑ (xh − xDSS ) n − 1 h =1 n h =1 n − 1 n mh
[6]
H
xDSS = ∑ H
vxDSS = ∑ CVDSS =
∑
H 2 h =1 h
xDSS
s
100
[7]
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Table 5. The mean and variance of the mean for total C and total N for each stratum† and plot. AWood
Plot‡
IOG (1)
Mean
Variance
Mean
Variance
Mean
Variance
g cm−2
(g cm−2)2
g cm−2
(g cm−2)2
g cm−2 (g cm−2)2 Total C
g cm−2
(g cm−2)2
g cm−2
(g cm−2)2
0.86
0.17980
0.41
0.01475
0.45
0.00472
0.34
0.21860
0.88
0.04249
0.0104
0.00002609
0.0134
0.00000657
0.0110
0.00000380
0.0320
0.00010920
0.02361
1.44
0.00284
UOG (2) 0.98
0.00420
USG(2) IOG(1) IOG(2) ISG(1) ISG(2) UOG(1) UOG(2) USG(1) USG(2)
OMinS
Variance
0.74
USG(1)
IMin
Mean
ISG (2) UOG (1)
OMin
Variance
IOG (2) ISG (1)
BWood
Mean
0.0066
0.00001095
0.0113
0.00000038
0.0388
0.00000564
0.0234
0.00000409
0.82
0.01964
0.42
0.00357
0.28
0.00084
0.20
0.00403
0.72
0.04167
0.36
0.02020
0.97
0.02692
0.70
0.05535
1.59
0.016924
0.96
0.08356
1.23
0.011396
0.95
0.02789 0.01571
0.90
0.00656
0.45
0.68
0.08061
0.46
0.0155 0.0257 0.0144 0.0248 0.0457 0.0342 0.0254 0.0141
0.00000319 0.00008382 0.00000004 0.00001379 0.00000606 0.00000872 0.00000700 0.00000753
0.00686 Total N 0.0106 0.00001000 0.0125 0.00000785 0.114 0.00002717 0.0201 0.00002469 0.385 0.00008000 0.0276 0.00001064 0.0214 0.00002398 0.0136 0.00000331
† AWood, aboveground coarse woody debris; BWood, belowground coarse woody debris; OMin, mineral soil outside the bole zone; IMin, mineral soil inside the bole zone; OMinS, mineral soil with stones outside the bole zone. ‡ IOG, Inceptisol old growth; ISG, Inceptisol second growth. Numbers in parentheses indicate plot number.
where n is the number of sample points in the preliminary systematic sample, h represents the stratum, nh is the number of sample points in the preliminary sample assigned to stratum h, H is the total number of strata, mh is the sample size for the main sample in stratum h, xh is the mean from the main sample in stratum h, sh2 is the variance from the main sample in stratum h, xDSS is the mean of xi based on DSS, vxDSS is the variance of xDSS based on DSS, CVDSS is the CV based on DSS, and xi is the total C or total N of a main sample. Individual strata means ( xh ) and variances (sh2) were estimated using
xh
∑ =
xhi
[7a]
mh
mh
s =∑ 2 h
mh i =1
(xhi − xh )
i =1
2
mh − 1
[7b]
where xhi is the total C or total N of the main sample in stratum h, and mh is the number of main samples in stratum h. The design effects (Deff) and effective sample sizes (neff) were calculated to assess the efficiency of DSS relative to that of SRS (Cochran, 1977; Lohr, 1999, p. 239–242):
Deff =
vxSRS vxDSS
[8]
neff = Deff m
[9]
When Deff > 1, DSS is judged more efficient than SRS (Cochran, 1977, p. 136); neff is the number of simple random samples that would provide equal precision (Lohr, 1999, p. 239–242). Power analysis calculations were performed to estimate the sample size required to detect a 10 or 20% change in the mean with SRS or DSS. These estimates were done for a two-sided test with α = 1616
0.05 and β = 0.75 using the SYSTAT (Version 10) statistical software (Systat Software, San Jose, CA) to arrive at estimates directly comparable to Yanai et al. (2003). A complete assessment of the efficiency of the DSS design relative to that of the SRS design should include an assessment of their relative costs. Estimated sampling costs were based on the following assumptions: (i) travel to and from the sampling site, US$100 d−1; (ii) two workers completing a preliminary systematic sampling in 4 h at US$20 h−1 = US$160 per preliminary systematic sampling; (iii) two workers taking 16 main samples in a day at US$20 per sample = $320; and (iv) analysis of Db and C and N percentages at $15 per analytical sample, with an average of three horizons (analytical samples) per sample = $45 per sample for analysis.
RESULTS The AWood, BWood, and OMin strata were the most common strata on all Ultisol and Inceptisol plots (Table 4). In addition, there was a substantial proportion of IMin on some Ultisol plots and of OMinS on some Inceptisol plots. Proportions of the AWood stratum ranged from 0.08 to 0.27; for BWood, from 0.17 to 0.53; for OMin, from 0.13 to 0.54; for IMin, from 0.01 to 0.16; and for OMinS, from 0.00 to 0.40 (Table 4). Means for TC differed between strata within each plot (Table 5) and were generally higher for woody strata (AWood and BWood), ranging in value from 0.28 to 1.59 g cm−2, than for mineral strata (OMin, IMin, OMinS), which ranged in value from 0.20 to 0.96 g cm−2. Means for TN between strata did not differ as much as for TC and the range in values was similar for woody (0.0066– 0.0457 g cm−2) and mineral (0.0106–0.0385 g cm−2) strata (Table 5). Plot means for TC and TN estimated with the equations for DSS and SRS were, as expected, similar (Table 6). Variances of the means estimated with DSS were, in all cases except one (Ultisol second-growth Plot 2), smaller than SSSAJ: Volume 72: Number 6 • November–December 2008
Table 6. Estimates of the plot means and variances of the means for total C and total N in the humus form based on simple random sampling (SRS) and double sampling for stratification (DSS). Total C Plot† DSS IOG (1) IOG (2) ISG (1) ISG (2) UOG (1) UOG (2) USG (1) USG (2)
Total N
Mean — g cm−2 — 0.624 0.230 0.482 0.861 1.115 1.137 0.710 0.568
Variance SRS 0.627 0.230 0.479 0.860 1.113 1.141 0.710 0.552
DSS
Mean SRS
—— (g cm−2)2 —— 0.00194 0.00397 0.00019 0.00037 0.00221 0.00422 0.00388 0.00519 0.00608 0.00825 0.00217 0.00390 0.00108 0.00551 0.00721 0.00634
DSS
Variance SRS
—— g cm−2 —— 0.01256 0.01287 0.01806 0.01801 0.01188 0.01185 0.02292 0.02291 0.03867 0.03826 0.03192 0.03201 0.02331 0.02329 0.01410 0.01383
DSS
SRS
——— (g cm−2)2 ——— 0.0000006 0.0000011 0.0000038 0.0000071 0.0000013 0.0000012 0.0000018 0.0000022 0.0000040 0.0000043 0.0000011 0.0000021 0.0000011 0.0000012 0.0000008 0.0000006
† IOG, Inceptisol Old Growth; ISG, Inceptisol Second Growth; UOG, Ultisol Old Growth; USG, Ultisol Second Growth. Numbers in parentheses indicate plot number.
those estimated by SRS for TC and for all except two (Ultisol the number of samples required to detect a 20% change in the second-growth Plot 2 and Inceptisol second-growth Plot 1) for mean for TC ranged from 5 to 50 for DSS and from 8 to 78 TN (Table 6). Consequently values for Deff were generally >1 for SRS. The number of samples required using DSS was, on (Table 7), so we conclude that the DSS design was generally average, about half that required using SRS (Table 8). These effective in reducing the estimate of the variance relative to results clearly show that DSS is more powerful than SRS, and SRS. Where DSS was more efficient than SRS, values for Deff in some cases (Ultisol old-growth Plot 2 and Ultisol secondranged from 1.34 to 5.11 for TC and 1.07 to 2.00 for TN growth Plot 1) can be used to detect changes in the mean as (Table 7). In these cases using DSS provided greater precision low as 10% using relatively small numbers of samples. for the same sample size (Cochran, 1977). Values for Deff were Estimates of costs associated with the two sampling generally greater for TC than TN on most plots, which indidesigns (Table 9) to detect a 20% change in the mean illustrate cates that DSS worked better at improving the precision of the relative cost effectiveness of the DSS design. To obtain the estimates for TC than TN (Table 7). This may be attributed to same level of precision with SRS as with DSS, the cost per using as the criteria for stratification factors that covary more plot was higher using SRS (US$815–5570) than using DSS strongly with C than with N (i.e., humus form properties and (US$715–3550). The reduction in cost per plot ranged from site environment). 12 to 71%, where the highest reduction was associated with The CVs for each plot and sampling strategy were calcuthe highest Deff of 5.11 (Tables 7 and 9). The exception was lated to facilitate comparison of results from this study with Ultisol second-growth Plot 2 where Deff was 1, ISG (2) 10 1.34 13 26.5 15.8 1.19 12 20.3 13.0 ranged from 13 to 66 for TC and from 12 to UOG (1) 15 1.36 20 32.6 15.5 1.07 16 21.6 13.2 27 for TN; only 6 to 16 samples were required UOG (2) 9 1.80 16 16.4 8.5 2.00 18 13.6 7.0 for DSS (Table 7). USG (1) 13 5.11 66 37.5 9.1 1.11 14 17.1 10.5 Where Deff was >1, estimates of the num- USG (2) 6 0.88 5 38.2 26.0 0.73 4 14.9 11.8 ber of samples required to detect a 10 or 20% † IOG, Inceptisol old growth; ISG, Inceptisol second growth; UOG, Ultisol old growth; USG, Ultisol second growth. Numbers in parentheses indicate plot number. change in the mean for TC or TN were lower for DSS than for SRS (Table 8). Estimates for ‡ m, main sample size using DSS. SSSAJ: Volume 72: Number 6 • November–December 2008
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Table 8. Number of samples required to detect a 20 or 10% change in the mean for total C and total N in the humus form based on simple random sampling (SRS) and double sampling for stratification (DSS).
Estimates for CVs based on SRS in this study were similar to those previously reported. The CVs based on DSS in this study were about Total C Total N half of those estimated by SRS and values for Deff Plot† 20% change 10% change 20% change 10% change were generally >1, indicating that DSS resulted in DSS SRS DSS SRS DSS SRS DSS SRS greater precision than SRS. The increase in preIOG (1) 29 58 112 226 24 38 93 147 cision from DSS resulted in lower estimates for IOG (2) 16 31 61 118 50 93 196 366 study costs, and with DSS a smaller change in ISG (1) 41 78 161 308 75 37 296 144 stocks could be detected with the same number ISG (2) 20 26 74 99 13 16 49 60 of samples. For verification of C stock estimates UOG (1) 27 36 104 140 15 17 57 63 for offset trading, the development of sampling UOG (2) 7 11 22 39 5 8 15 27 designs that improve the precision as well as the USG (1) 11 51 40 199 11 12 38 41 accuracy of the estimates of mean total C stocks USG (2) 46 40 178 157 10 12 35 43 is critical. It is very possible that projects will † IOG, Inceptisol old growth; ISG, Inceptisol second growth; UOG, Ultisol old growth; be established that are small enough that samUSG, Ultisol second growth. Numbers in parentheses indicate plot number. pling will not involve the establishment of plots and that sampling designs more complex than be expected from a sampling design more complex than SRS SRS will be used to improve estimates of means for C stocks. (Lohr, 1999). Plot means for TC and TN estimated with the Comparative studies can also benefit from increased precision equations for DSS and SRS were, as expected, similar (Table of the estimate for the within-plot component of the total 6); however, the DSS sample estimate was expected to be more variance. The within-plot component is often not considered representative than what might have been estimated if an SRS important under the assumption that between-plot variances was taken in the field. This is because a stratified sample is are very high relative to within-plot variances. This assumpmore representative when the population is highly heterogetion may be valid only for some forest ecosystems. Yanai et neous and the sample size is small (Lohr, 1999). Obtaining a al. (2003) published variances for both within and between representative sample to estimate the plot mean is important plots from nine studies. Calculation of the contribution of the to all types of forest soil studies. Comparative studies in forest within-plot variance to the total variance for the nine studies soils research often involve the installation of plots where the showed that it was low for forest ecosystems in the northeastdesired strategy is to have as many plots as are economically ern United States (0.3–3.3%) but higher for coastal ecosystems feasible to increase inference space, while taking few samples in the northwestern United States and Canada (3.0–28.5%). within the plot. When few samples are taken within the plot, Homann et al. (2001) concluded that within-plot variance can however, the estimate of the mean will probably have low account for more than half of the total variance in the West accuracy relative to what could be achieved with a within-plot Coast systems they studied. Thus, sampling designs that are stratified design. Estimates of the mean for the plot with lower able to increase the precision as well as accuracy of the estimate accuracy may then contribute to poor estimation of the variof the mean of a plot will increase the overall efficiency of a ance between plots. Therefore, even in designed experiments study design for comparative studies. or comparative studies with a large number of plots, gains in Stratification is expected to improve the precision of estiprecision for the overall study can result from improved accumates provided the means of the strata are different, which is racy of the estimate for the plot mean. the case for all plots for TC and for most plots for TN (Table 5), Table 9. Estimates of costs and time for sampling and analysis using double sampling for stratification (DSS) and simple random sampling (SRS) to detect a 20% change in the mean for total C (TC) and total N (TN). For simplicity, sample size was based on TC only, as the sample size using DSS (m) or the estimated effective sample size if SRS were used (neff) was generally greater for TC than for TN. Parameter
Plot† IOG (1)
IOG (2)
ISG (1)
ISG (2)
UOG (1)
UOG (2)
USG (1)
USG (2)
Total
DSS (TC and TN) 29 16 41 20 27 7 11 46 197 m Sampling time with two workers, d 2.5 1.5 3.0 2.0 2.0 1.0 1.5 3.5 17.0 Preliminary sampling cost, US$ 160 160 160 160 160 160 160 160 1,280 Travel cost, US$ 300 200 300 200 200 100 200 400 1,900 Sampling + analysis cost, US$ 1885 1040 2665 1300 1755 455 715 2990 12,805 Total cost per plot, US$ 2345 1400 3125 1660 2115 715 1075 3550 15,785 SRS (TC and TN) 58 31 78 26 36 11 51 40 331 neff Sampling time with two workers, d 3.5 2.0 5.0 1.5 2.5 1.0 3.5 2.5 21.5 Travel cost, US$ 400 200 500 200 300 100 400 300 2,400 Sampling + analysis cost, US$ 3770 2015 5070 1690 2340 715 3315 2600 21,515 Total cost per plot, US$ 4170 2215 5570 1890 2640 815 3715 2900 23,915 Reduction in cost, % 44 37 44 12 20 12 71 −22 33 † IOG, Inceptisol old growth; ISG, Inceptisol second growth; UOG, Ultisol old growth; USG, Ultisol second growth. Numbers in parentheses indicate plot number. 1618
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and optimal when the variances of the means of the strata are equal. In these data, the strata variances are not equal and have influenced the estimated vxDSS and therefore Deff. When variances are unequal, the precision of estimates can be improved by allocating samples proportional to variance rather than proportional to area (used in this study) (Cochran, 1977). The effect of allocation by area when variances are unequal can be illustrated by comparing the estimates for TC for Ultisol second-growth Plot 1 with the highest Deff (5.11) with those for Ultisol second-growth Plot 2 with the lowest Deff (0.88) (Table 7). For Plot 1, means for the three strata were different and the allocation of samples proportional to area was similar to what would be desired if samples were allocated proportional to variance (i.e., more samples were allocated to the stratum OMin with the highest variance; Table 4). The result was a significant reduction in the estimate of the variance using DSS and a high Deff. For Plot 2, the means of the strata were different (Table 5) and the allocation proportional to area resulted in an equal number of samples being taken from each stratum (Table 4). The variance for BWood was substantially greater than for OMin (Table 5), however, and this resulted in a vx DSS > vxSRS for this plot (Table 6). Estimation in this case would probably have improved if more samples were allocated to BWood with the high variance. The data presented here came from a study with several objectives that included comparison of domains (between strata). Therefore, more strata were used than would necessarily lead to the most precise estimate of the mean for the whole plot. In plots where more than two strata were sampled, the means estimated for AWood and BWood were often similar, and the means for OMin, IMin, and OMinS were also similar. Combining AWood with BWood into one stratum and OMin, IMin, and OMinS into a second stratum resulted in a significant increase in Deff, especially for TC. For example, reducing to two strata for Ultisol old-growth Plot 1 increased the Deff from 1.36 to 5.3 and for Ultisol second-growth Plot 2 increased the Deff from 5.11 to 7.10. For TN, the increase in Deff was large for Ultisol old-growth Plot 1 (from 1.07 to 3.80) but negligible for Ultisol second-growth Plot 1 (from 1.11 to 1.14). When strata were combined to give two strata for all plots, the values for Deff were >1 for every plot. If the number of strata were reduced to two, the study would take 6.5 d less and cost 52% less than with SRS. These results indicate that the greatest efficiency for estimates at the plot level would have been achieved if only two strata were used: one for humus forms dominated by woody materials (AWood and BWood combined) and one for humus forms originating from other types of litter (OMin, IMin, and OMinS) combined. The focus of this study was the humus form and criteria for stratification were related to properties of the humus form considered important to the variables being measured (TC and TN) in the ecosystem under investigation. The criteria for stratification and the number of strata will change depending on the ecosystem and variables under consideration and a priori knowledge. For example, in boreal forests where bryophytes and lichens are a significant component of the forest floor, stratification could be based on the presence or absence of bryophyte or lichen patches. Pedodiversity in northeastern hardwood forests, characterized by pits and mounds, presence SSSAJ: Volume 72: Number 6 • November–December 2008
or absence of gaps, and influences of individual tree species, was found to have significant effects on soil chemical properties (Scharenbroch and Bockheim, 2007). Therefore, these characteristics could be used to define strata in northeastern hardwood ecosystems.
CONCLUSIONS Results from this study have demonstrated that a DSS sampling design is more efficient than SRS for estimation of TC and to a lesser degree TN, at least in forest soils in ecosystems similar to those used here. This is because it yields greater precision and accuracy than SRS for the same number of samples. An alternate stratification scheme, where strata are defined on properties that covary more with total N than total C, would be expected to perform better for total N estimation. The cost of achieving the same level of precision for total C with SRS would be about double that of DSS because of the large number of samples that would be required and the costs associated with their collection and analysis. Generally, the DSS design is more powerful than SRS and permits a scientist to detect smaller changes than would be the case with SRS with the same number of samples. Results showed that efficiency was greatest when only two strata, one for humus forms dominated by woody materials (AWood and BWood combined) and one for humus forms originating from other types of litter (OMin, IMin, and OMinS) combined, were used. Compared with SRS, the estimated total cost for this study was 33% less using DSS and 52% less if only two strata were used. Further gains may have been realized if samples were allocated proportional to variance rather than proportional to area, because the variances of strata means were not equal. The gains in precision, accuracy, and power of a study overall from using DSS, or potentially other sampling designs that are more complex than SRS, are relevant to both designed and observational studies and for estimation of C stocks and C stock changes for potential offset trading systems. Gains are expected to be greatest for forest types where the within-plot variance component is a high proportion of the total variance, as is often the case in West Coast Douglas-fir forest ecosystems. The sampling design described here can be modified to estimate TC or TN in ecosystem types, experimental units, or sampling units other than the ones described in this study. For example, a stand-level study would use a larger grid size (or transects) for estimation of proportions and subsequent sampling. It can also be adapted for estimation of soil variables other than C or N. The primary consideration is to study a well-defined population and to take full advantage of existing knowledge of that population so that it can be fully stratified using criteria relevant to the variables under consideration. ACKNOWLEDGMENTS We appreciate the patient and thorough assistance provided by Duane McCoy in the field. Conversations about statistical details with Cindy Shaw’s colleagues Ilka Bauer, Markus Thormann, and Ted Nason proved invaluable. We thank Mike Apps, Werner Kurz, Jag Bhatti, Ed Banfield, and Brenda Laishley at the Canadian Forest Service for personal, professional, and technical support. Funding for this research was provided by the College of Forestry, Oregon State University.
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