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Increasing the efficiency of forest clearing estimation in the Legal Amazon using targeted sampling

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Sampling designs are commonly used to estimate deforestation in the humid tropics. In addition to deforestation estimates, sampling designs provide estimates of precision. In this study, precision and efficiency of two sampling designs estimating the loss of intact forest in the Brazilian Legal Amazon are quantified and compared. The systematic design, proposed for the UNFAO Forest Resource Assessment 2010, utilizes sample blocks at every degree Lat/Long intersection. The targeted design uses MODIS indicated deforestation for stratification and sample block allocation into areas of deforestation hotspots. PRODES data available for the entire study area were used to quantify per sample block deforestation, which allowed rigorous comparison of sampling designs. While the systematic design had error margins equal to 18% of the true value, the targeted design provided more precise estimates (within 11.5%) and required less than half of the samples used in the systematic design. The targeted design proposed here can provide effective and timely, annual estimates utilizing MODIS detected deforestation in combination with the existing PRODES methodology to interpret sample blocks. The implementation of the targeted design can make an important contribution to policy-support and assessments of policy effectiveness in the form of precise, cost effective, and timely annual deforestation estimates.
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A comparison of sampling designs for estimating deforestation from Landsat
imagery: A case study of the Brazilian Legal Amazon
Mark Broich
a,
, Stephen V. Stehman
b
, Matthew C. Hansen
a
, Peter Potapov
a
, Yosio E. Shimabukuro
c
a
Geographic Information Science Center of Excellence, South Dakota State University, Wecota Hall, Box 506B, Brookings, SD 57007, USA
b
State University of New York, College of Environmental Science and Forestry, Syracuse, NY 13210, USA
c
Brazilian National Institute for Space Research, INPE, Brazil
abstractarticle info
Article history:
Received 12 January 2009
Received in revised form 16 July 2009
Accepted 18 July 2009
Keywords:
MODIS
Design-based inference
PRODES
Humid tropics
FAO Forest Resource Assessment 2010
Three sampling designs simple random, stratied random, and systematic sampling are compared on
the basis of precision of estimated loss of intact humid tropical forest area in the Brazilian Legal Amazon from
2000 to 2005. MODIS-derived deforestation is used to partition the study area into strata to intensify
sampling within forest clearing hotspots. The precision of the estimator of deforestation area for each design
is calculated from a population of wall-to-wall PRODES deforestation data available for the study area. Both
systematic and stratied sampling yield smaller standard errors than simple random sampling, and the
stratied design has smaller standard errors than the systematic design at each sample size evaluated. The
results of this case study demonstrate the utility of a stratied design based on MODIS-derived deforestation
data to improve precision of the estimated loss of intact forest area as estimated from sampling Landsat
imagery.
© 2009 Elsevier Inc. All rights reserved.
1. Introduction
Quantication of tropical forest cover change is important for
forest resource management, biodiversity conservation, human
livelihoods, biogeochemical, climate and hydrologic cycle modeling,
and sustainability management (Avissar and Werth, 2005; Curran and
Trigg, 2006; FAO, 2005). International research organizations such as
the Global Observation of Forest and Land Cover Dynamics (GOFC-
GOLD, 2007) and the Global Climate Observing System (GCOS, 2004)
call for long-term monitoring of global forest cover change in support
of the United Nations Framework Convention on Climate Change
(UNFCCC, 2007). Providing robust, repeatable, cost effective, and
timely information on deforestation for tropical forests is still chal-
lenging, despite methodological advances and improved data avail-
ability. Both the methodology and results of efforts to estimate
tropical deforestation remain a matter of great importance and
controversy (Grainger, 2008; Kaiser, 2002; Kintisch, 2007).
1.1. Remote sensing methods for deforestation estimation
Since the early 1990s remotely sensed data have been used to
quantify deforestation area (DeFries et al., 2007). Coarse resolution
remote sensing data suchas those providedby the MODerate Resolution
Imaging Spectroradiometer (MODIS) are inadequate for direct estima-
tion of deforestation area (Morton et al., 2005) because most
deforestation occurs at subpixel scales (Hansen et al., 2008a). High
spatial resolution data sources such as Landsat allow for more accurate
quantication of deforestation area. High spatial resolution data are
employed by two different approaches: wall-to-wall mapping and
sampling.
1.1.1. Wall-to-wall mapping approaches
Operational approaches to map deforestation using wall-to-wall
high spatial resolution remote sensing imagery have been imple-
mented for several regions, including the Brazilian Legal Amazon
(INPE, 2008), India (Forest Survey of India, 2004), and Central Africa
(Hansen et al., 2008b). Exhaustive mapping methods face numerous
challenges. Persistent cloud cover and selective image acquisition (e.g.
following the Landsat Enhanced Thematic Mapper Plus Long-term
Acquisition Plan) reduces the availability of cloud-free high spatial
resolution imagery (Asner, 2001; Ju & Roy, 2008). High data volumes
and costs, and lengthy processing times impact the timeliness of
product generation and reporting. Operationalizing methods that
overcome these limitations are the focus of much deforestation
mapping research (Kintisch, 2007).
The Brazilian National Institute for Space Research (INPE)
Monitoring the Gross Deforestation in the Amazon Project (PRODES)
provides annual wall-to-wall deforestation maps of the Brazilian Legal
Amazon (BLA) (INPE, 2008). PRODES delineates deforestation from
Landsat data using a semi-automated interpretation approach (INPE,
Remote Sensing of Environment 113 (2009) 24482454
Corresponding author. Tel.: +1 605 688 6591.
E-mail address: Mark.Broich@sdstate.edu (M. Broich).
0034-4257/$ see front matter © 2009 Elsevier Inc. All rights reserved.
doi:10.1016/j.rse.2009.07.011
Contents lists available at ScienceDirect
Remote Sensing of Environment
journal homepage: www.elsevier.com/locate/rse
2008). The automated part of the approach generates a shade-fraction
image, which is based on a spectral mixture model, followed by image
segmentation, and unsupervised classication of the resulting poly-
gons (Shimabukuro et al., 1998). Analysts use photo-interpretation to
assign the clustered polygons to one of the following classes,
deforestation, old growth forest, clouds, hydrograph (water bodies
and ooded areas), or non-forest with a minimum polygon size of
6.25 ha. The resulting classication map product is provided annually
for the BLA at a spatial resolution of 120-m ×120-m (INPE, 2008). The
PRODES 2007 product consisted of 213 Landsat images (INPE, 2008)
requiring a large effort in data processing, storage, and analysis. Final
deforestation map products for the BLA are not available until several
months after initial acquisition of the Landsat imagery (INPE, 2008).
To overcome the reporting delay of the nal wall-to-wall PRODES
deforestation map, INPE provides an annual preliminary PRODES
estimate of deforestation for the BLA by mapping a subarea of the BLA.
The subarea consists of the Landsat images that contained approxi-
mately 90% of the deforestation mapped in the previous year (INPE,
2008). The preliminary PRODES is produced within three to four weeks
of image acquisition.
1.1.2. Sampling approaches
Sample-based approaches have the potential to reduce many of the
aforementioned constraints to quantifying deforestation with high
spatial resolution imagery. Because deforestation needs to be mapped
only for the portion of the study area sampled, sampling is a cost and
time efcient alternative if the objective is to estimate area of defor-
estation rather than to map deforestation. Moreover, sample-based
methods that use a probability sampling design provide a measure of
precision to quantify the uncertainty attributable to sampling and to
construct condence bounds for the area of deforestation.
Tucker and Townshend (2000) expressed concern that precise
deforestation estimates for individual countries could only be achieved
when using a very large random sample of entire Landsat images.
Czaplewski (2003) concluded thatthe high variance observed by Tucker
and Townshend (2000) was attributable to the small size of the study
area, and that sampling would provide adequate estimates for larger
regions permitting larger sample sizes. Alternative designs employing
sampling units smaller than entire Landsat images may yield more
precise estimates (Tucker and Townshend, 2000).Duveiller et al. (2008)
proposed that sampling efciency for deriving regional scale estimates
of forest cover change could be improved by using a large number of
small, systematically distributed image extracts. Even though the
population standard deviation (of the variable of interest) for smaller
sampling units typically will be greater than the population standard
deviation for larger units, for a xed total area sampled, a smaller
samplingunit usually will yield better precisionfor the estimator of area
because the larger sample size of smaller units compensates for their
greater standard deviation (Dunn & Harrison, 1993; Tomppo et al.,
2002; Stehman et al., 2005). Stehman et al. (2005) further suggested
that strategies incorporating stratied sampling, regression estimation,
or poststratied estimation could improve precision by taking advan-
tage of ancillary variables associated with forest clearing. Poststratied
estimation (Särndal et al., 1992, p. 265) has been shown to enhance
precision for estimating forest area (McRoberts et al., 2002, 2005)and
change in land-cover area (Stehman et al., 2005).
The Forest Resources Assessment 1990, the Global Forest Resources
Assessment 2000 (FAO, 1996, 2001), and Achard et al. (2002) employed
stratied sampling to estimate forest cover and deforestation. The
remote sensing Forest Resources Assessment surveys of FAO for 1990
and 2000 were based on a stratied design (FAO, 1996) that used
predicted rates of deforestation (FAO, 1993) to allocate more samples
into strata with greater expected deforestation. Achard et al. (2002)
used expert opinion to construct strata and determine sampling rates.
For the FAO Forest Resource Assessment 2010 (FRA 2010) the proposed
design is a systematic sample of 10-km× 10-km blocks located where
whole degree lines of latitude and longitude intersect (Ridder, 2007).
Duveiller et al. (2008) evaluated the costand precision of this systematic
design for Central Africa using 10-km× 10-km sampling units and
Landsat image extracts to estimate forest area change, as well as a more
intensive systematic design with sample blocks located at the intersec-
tions of the half-degree lines of latitude and longitude.
Hansen et al. (2008a) developed a stratied sampling design to
estimate deforestation for the pan-humid tropical forest biome
between 2000 and 2005. The humid tropical forest biome was
stratied using MODIS-derived deforestation data. Deforestation per
sample block was quantied using pairs of expert interpreted Landsat
image extracts. Hansen et al. (2008a) also used a regression estimator
with MODIS-derived deforestation as an ancillary variable to further
improve precision. Hansen et al.'s (2008a) pan-humid tropical defor-
estation estimates achieved precision comparable to that obtained by
FAO (2001) and Achard et al. (2002) even though the proportion of
area sampled by Hansen et al. (2008a) was much smaller than the
proportion sampled in these other studies.
Although stratied sampling has been recommended for operational
assessment of global and regional deforestation rates in the tropics
(Mayaux et al., 2005, p. 382) and implemented in several studies (Achard
et al., 2002; FAO, 1996, 2001; Hansen et al., 2008a), there has been limited
evaluation of stratied sampling for this specic application. Tomppo et
al. (2002) examined the potential gain in precision achievable using
stratied sampling for a simulated population of forest cover change.
Tucker and Townshend (2000) evaluated the precision of estimated area
of deforestation for simple random sampling from a complete coverage
population of Landsat-mapped deforestation, but their study did not
include an assessment of stratied sampling. Our case study extends
these previous studies by evaluating stratied, systematic, and simple
random sampling applied to a real population of Landsat-mapped loss of
intact forest area, the PRODES deforestation map of the BLA.
1.2. Study area: Brazilian Legal Amazon
The area chosen for this study is the humid tropical forest biome
within the BLA. The forest of the Amazon Basin is of great interest as it is
one of the world's most important bioregions, harboring a rich array of
plants and animal species and offering a wealth of goods and services to
society(Foley et al., 2007). The largest portion of the Amazon Basin is
situated inside the BLA. The majority of deforestation in the BLA took
place since the early 1970sand the cumulative deforestation until 1999
was estimated to be 547,000 km
2
(INPE, 2008), an area about the size of
France (Fearnside, 2005). Over the past 10 years the average estimated
annual clearing area was approximately 18,400 km
2
with the estimated
values of individual years ranging from approximately 11,500 km
2
to
approximately 27,400 km
2
(INPE, 2008). Forest loss in the BLA, mainly
caused by large scale agricultural clearing activities, is concentrated in
the arc of deforestationalong the southern and eastern forest edges,
while a vast interior remains intact (Fearnside, 2005).
Within the humid tropical forest biome inside the BLA, the study
area was restricted to the region mapped by INPE's (2008) PRODES
between 2000 and 2005. This region of approximately 3.2 million km
2
featured wall-to-wall PRODES-mapped deforestation (http://www.
obt.inpe.br/prodes/index.html) and complete cover ancillary infor-
mation in the form of annual MODIS-derived deforestation data
(Hansen et al., 2008c). The concentration of major deforestation
hotspots (Hansen et al., 2008a) and the availability of spatially explicit
PRODES and MODIS-derived deforestation data for the entire study
area make this region an opportune testing ground for the comparison
of sampling designs. The PRODES model quanties loss of the
remaining intact forest area (old growth forest) of the BLA (INPE,
2008), but does not include the clearing of regrowth forests. We
dened our study area to be the aggregate area of PRODES-mapped
forest, PRODES-mapped deforestation identied within the 2000 to
2005 interval, and PRODES-mapped cloud coverage (Fig. 1). Areas
2449M. Broich et al. / Remote Sensing of Environment 113 (2009) 24482454
where deforestation could not clearly be attributed to the 2000 to
2005 interval due to cloud cover were excluded. PRODES also maps
regions of savannas. Because these regions are outside of the humid
tropical forest biome, they were excluded. While important from a
forest monitoring point of view, area of clearing of regrowth forest
(Neeff et al., 2006) and area of selectively logged forest (Asner et al.,
2005) were not taken into account and only loss of intact forest area
was considered in this study.
1.3. Objectives
The primary objective was to compare the precision of simple
random, s tratied (using MODIS-derived deforestation), and systematic
samplingfor estimating deforestationwithin the BLA between2000 and
2005, with the complete coverage PRODES-mapped deforestation data
serving as the population of interest. To provide a broader context for
our sampling design comparisons, we compared the standard errors
obtained from our sampling designs applied to the BLA population to
those reported from several studies in which a sampling approach was
implemented to provide an actual estimate of deforestation for areas
within the tropics (see Section 3.3). The design-based inference
framework will be used throughout. In design-based inference, the
population of interest is regarded as a xed set of elements and the
attributes of each element of the population are regarded as xed, not
random, q uantities (Särndal et al. , 1992). Wewill apply the Gregoire and
Valentine (2008, p. 19) denition that An estimator is an algebraic
expression that one evaluates with the data from the sample in order to
provide a quantitative estimate of the target parameter.
2. Methods
2.1. Data
The evaluation of the sampling designs was based on comparing
the standard errors (precision) of estimates of deforested area for
each sampling design applied to a known population of deforestation.
This population was constructed from the wall-to-wall PRODES map,
a photo-interpretation product with 120-m× 120-m pixel size. We
translated the PRODES class of each pixel into either deforestation or
no-change. PRODES pixels that had been interpreted as deforestation
by the PRODES analysts between 2000 and 2005 were marked as
deforestation and pixels with other PRODES classes were labeled as
no-change. The BLA study area was partitioned into 11,630 blocks
each measuring 18.5-km×18.5-km. Within each block, the area of
deforestation was calculated as the area of all 120-m × 120-m pixels
labeled as deforestation. The target parameter of our sampling design
comparison is the total area of PRODES deforestation between 2000
and 2005 for the study region, 108,637 km
2
. The PRODES deforesta-
tion data represent only the loss of intact forest area (old growth
forest) so the target parameter does not include area of humid tropical
forest cover change due to degradation, regeneration, afforestation,
regrowth, or clearing of regrowth.
The accuracy of PRODES relative to a ground determination of
deforestation is not known. Therefore, our analysis does not take into
account the potential bias in the PRODES area of deforestation
attributable to classication error relative to ground data. The sample-
based estimators evaluated are unbiased estimators of the area of
PRODES deforestation, but are not necessarily unbiased estimators of
deforestation as it would be determined from ground data rather than
satellite data. Further, our standard error comparisons do not take into
account variability attributable to measurement error (Särndal et al.,
1992, Chapter 16) such as mislabeling by the PRODES analysts because
the information to quantify this component of variability does not exist.
2.2. BLA-stratied design
The stratication of the BLA was based on MODIS-derived
deforestation data, more specically, a 500-m× 500-m MODIS 2000
to 2005 deforestation probability layer covering the entire study area.
The annual deforestation probability per 500-m ×500-m pixel derived
from the MODIS imagery was obtained using a generic classication
tree model (Hansen et al., 2008c). A 50% threshold was applied to the
maximum annual deforestation probability of each MODIS pixel
between 2000 and 2005. Pixels with probability 50% were classied
as deforested while pixels with probability b50% were classied as not
deforested. Our denition of MODIS-derived deforestation is a per
pixel decrease in tree canopy cover to less than 25% within the intact
forest according to PRODES. This denition was best met when
applying the 50% deforestation probability threshold, which repre-
sented a compromise between a greater deforestation probability
threshold that would have likely missed smaller patches of deforesta-
tion, and a smaller deforestation probability threshold that may have
been plagued by unacceptably high commission errors of deforesta-
tion. The percentage of pixels agged as deforested was calculated per
18.5-km× 18.5-km block to provide an indication of blocks where
deforestation was likely to have occurred. MODIS-derived deforesta-
tion represented the same time interval as the PRODES-mapped
deforestation data but was produced independently.
The stratication based on the MODIS-derived deforestation
values was implemented by dening stratum boundaries using the
DaleniusHodges rule (Cochran, 1977, p. 129; Tomppo et al., 2002).
The resulting low, medium, high, and very high deforestation strata
were dened as 01%, N17%, N721%, and N21100% MODIS-derived
deforestation per block, respectively (Fig. 1). The number of strata
was initially set to four, consistent with Cochran's (1977, p. 132134)
recommendation that it is seldom protable to increase the number of
strata beyond six. The sample sizes were allocated to the four strata i)
proportionally and ii) based on Neyman optimal allocation (Cochran,
1977, p. 99). The optimal allocation was determined using per-
stratum variances of the percent MODIS-derived deforestation of all
blocks within each stratum.
Fig. 1. Study area in Brazil, South America: PRODES-mapped area (20002005) within
the humid tropical forest biome in the Brazilian Legal Amazon (BLA). The study area
was partitioned into blocks (18.5-km × 18.5-km) that were assigned to four deforesta-
tion strata (shown as green, yellow, orange, and red) based on MODIS-derived
deforestation.
2450 M. Broich et al. / Remote Sensing of Environment 113 (2009) 24482454
To evaluate whether further renement of the stratication would
lead to additional improvement in precision, two strata were created
within the low deforestation stratum. The rationale for this sub-
straticationwas the recognition that small patches of deforestation
would be difcult to detect from the MODIS imagery resulting in the
low deforestation stratum containing some blocks that had more
extensive clearing. This would diminish the advantage of grouping the
blocks into strata that were supposed to possess relatively similar
magnitudes of deforestation. Consequently, the low deforestation
stratum was subdivided into a virtually no deforestationstratum
and a some deforestationstratum using criteria described by
Hansen et al. (2008a) to create similar substrata in their pan-tropical
sampling design. These criteria included information from the Intact
Forest Landscapes project (IFL; Potapov et al., 2008), MODIS-derived
deforestation (Hansen et al., 2008c), and percent forest cover of each
block (Hansen et al., 2003). The sample sizes allocated to the ve
strata were determined by Neyman optimal allocation.
2.3. Systematic design
The systematic sampling design evaluated is based on the design
proposed for FRA 2010 (Mayaux et al., 2005; Ridder, 2007) in which
sample blocks are located where whole degree lines of latitude and
longitude intersect (systematic one-degree grid design). A more
intensive systematic sampling design, in which sample blocks are
located where half-degree lines of latitude and longitude intersect
(systematic half-degree grid design) was also evaluated. Whereas the
systematic design proposed for the FRA 2010 and tested by Duveiller
et al. (2008) for Central Africa uses 10-km× 10-km blocks, our
precision evaluation retained the 18.5-km ×18.5-km sample blocks to
maintain comparability with the stratied design of Hansen et al.
(2008a). The relative performance of the sampling designs in terms of
the precision of the estimator of deforested area should be consistent
for the two sample block sizes.
2.4. Comparing precision among designs
Because the PRODES-mapped area of Landsat-derived loss of intact
forest is available for all blocks in the population making up the BLA, it
is possible to calculate the exact standard errors for each sampling
design, simple random, stratied, and systematic (Table 1). In the
design-based inference framework (Särndal et al., 1992), these
standard errors represent the degree to which the estimates vary
over the set of all possible samples that could be realized for a
particular sampling design. For simple random sampling, the standard
error of the estimated total area of deforestation is
SE ˆ
Y

=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
N21n=NðÞS2=n
qð1Þ
where Y
̂
is the estimator of total deforestation area, Nis the number of
blocks in the population, nis the sample size, and S
2
is the population
variance of the per block area of PRODES-mapped deforestation. For
stratied random sampling the standard error is given by
SE ˆ
Y

=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
X
H
h=1
N2
h1nh=Nh
ðÞS2
h=nh
v
u
u
tð2Þ
where N
h
and n
h
are the number of blocks in the population and sample
for stratum h,S
h
2
is the stratum-specic population variance of the per
block area of PRODES-mapped deforestation, and His the number of
strata. The standard error was calculated for both the optimal and
proportional allocation cases of the stratied design to separate the
effects of stratication and sample allocation. The standard error for
proportional allocation also approximates the standard error of
poststratied estimation (Cochran, 1977).
The systematic sampling designs were evaluated for the xed
partition of the BLA intothe population of blocks. For this xed partition,
therewereanite number of possible systematic sample realizations.
The systematic designs were implemented by selecting every 6th block
in the NorthSouth and EastWest directions to represent the
systematic one-degree grid design and every 3rd block in both
directions to represent the systematic half-degree grid design. This
resulted in 36 and 9 possible sample realizations, respectively. The
standard errors of the systematic one-degree and half-degree grid
designs were then calculated from this set of all possible sample
realizations, with the standard error given by
SE
ˆ
Y

=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1=K
ðÞ
X
K
k=1
ˆ
YkY

2
v
u
u
tð3Þ
where Kis the number of possible sample realizations, Ŷ
k
is the
PRODES-mapped deforestation area estimated from the kth realiza-
tion, and Yis the population total (i.e. true) PRODES-mapped defor-
estation, Y=108,637 km
2
.
The sample sizes evaluated were 150, 325, and 1310 representing
1.29%, 2.79% and 11.26% of the BLA study area. The larger two sample
sizes were determined by the systematic one-degree and half-degree
grid designs. The sample size of 150 was evaluated to determine if the
stratied design could achieve precision comparable to the systematic
designs at a much smaller sample size and therefore considerably
lower cost.
3. Results
3.1. Distribution of sample blocks
The expected distribution of the sample blocks among the strata is
shown in Table 2. Strata differed in their proportions of area of the
study region covered, and percent PRODES-mapped deforestation.
The low deforestation stratum made up 74% of the BLA study area and
included 8% of the deforested area. The optimally allocated stratied
sampling design allocated 26% of the sample blocks into this stratum.
The very high deforestation stratum contained 30% of the deforested
area, made up 3% of the study area, and received 25% of the sample
blocks (Table 2). For comparison purposes, the expected distribution
of the systematically sampled blocks among the BLA strata is also
shown in Table 2. Because systematic sampling is an equal probability
sampling design, the sample size within any subgroup (e.g.,
deforestation stratum) will be proportional to the area representation
of that subgroup. The results shown in Table 2 reect the expected
outcome that an effective stratication with optimal allocation will
increase the sampling intensity within regions of anticipated forest
Table 1
Overview of sampling designs evaluated.
Design Number
of strata
Number of
sample blocks
Simple random sampling. n/a 150; 325; 1310
Stratied random sampling with strata based on
percent MODIS-derived deforestation per block
and i) proportional and ii) optimal allocation
used to determine sample sizes per stratum.
4 150; 325; 1310
Same as optimally allocated design above but with low
deforestation stratum subdivided into two substrata.
5 150; 325; 1310
Systematic design in which sample blocks are located
where whole degree lines of latitude and longitude
intersect (systematic one-degree grid design).
n/a 325
Systematic design in which sample blocks are located
where half-degree lines of latitude and longitude
intersect (systematic half-degree grid design).
n/a 1310
2451M. Broich et al. / Remote Sensing of Environment 113 (2009) 24482454
clearing (deforestation hotspots), and decrease the sampling intensity
in the large, supposedly unchanged, and homogeneous forest interior.
3.2. Comparing precision of the estimated area of deforestation
The 4-strata design with optimal allocation had the smallest
standard errors followed by the 4-strata design with proportional
allocation and the systematic design, with the simple random design
having the largest standard errors (Table 3). The comparison of designs
can also be based on relative efciency, dened as the variance of simple
random sampling divided by the varianceachieved by stratied random
or systematic sampling of equivalent sample size. The relative
efciencies of the systematic designs were 1.6 for the one-degree grid
and 2.8 for the half-degree grid. The relative efciencies of the 4-strata
designs were about 5.8 for proportional allocation and 9.9 for optimal
allocation, indicating that implementing optimal allocation was advan-
tageous relative to proportional allocation and to poststratied estima-
tion. Thestandard error forthe optimally allocated 4-strata designwith a
sample size of 325 was only slightly greater than the standard error of
the systematic half-degree grid design with a sample size of 1310.
Comparing the two stratied options with optimal allocation, the 5-
strata design that included substratication of the low deforestation
stratum did not show a large reduction in standard error relative to the
4-strata design (Table 3). The design comparison can also be framed by
calculating the number of sample blocks required by the stratied
design to achieve the standard errors of the systematic one-degree and
half-degree grid designs. The optimally allocated 4-strata design would
require 55 sample blocks to achieve the same standard error as the
systematic sample of 325 blocks, and 375 sample blocks to achieve the
same standard error as the systematic sample of 1310 blocks.
3.3. Comparing precision with previous sampling studies
To place the results of our sampling design comparisons into the
context of other deforestation studies, we compared the standard errors
calculated from our sampling designs applied to the BLA population to
the standard errors estimated from several studies in which a sampling
approach was implemented to provide an actual estimate of deforesta-
tion for the tropics (Table 4). For all studies mentioned in Table 4,
deforestation for each sampling unit was derived from Landsat imagery.
Of the study areas listed, the BLA had the greatest annual rate of
deforestation (as calculated from the PRODES-mapped deforestation
area). The annual area deforested reported in these studies represents a
small percentage of the total area of each study region. The standard
errors of the estimated annual deforestation rates range from 0.02% to
0.08%. The standard errors achieved by the systematic designs and the
stratied design (four strata with optimal allocation) within the BLA
were within the range of standard errors reported by previous studies.
In particular, the stratied design applied to the BLA achieved a low
standard error despite sampling a smaller proportion of area (1.29%)
relative to the other studies with the exception of Hansen et al. (2008a).
The very small standard error and small proportion of sampled area
reported in Hansen et al. (2008a) is partly attributable to the use of
poststraticationand regression estimation and therefore is not entirely
the result of the choice of sampling design.
4. Discussion
The standard errors reported for the Previous Studiesin Table 4
are based on the sample realized for each study, and therefore these
estimated standard errors are subject to sampling variability (i.e. a
different sample would yield a different estimate of the standard
error). In contrast, because the PRODES-mapped area of deforestation
is known for the entire study area, the standard errors reported for
each sampling design applied to the BLA study region are exact or true
standard errors. Thus the availability of the complete coverage PRODES
data permits a unique opportunity to carry out an ideal assessment of
different sampling designs because it permits comparing designs on
the basis of the true standard errors of the estimators, not just on
estimated standard errors from a single sample. Our comparison of
designs follows methodology similar to that employed by Tucker and
Townshend (2000) and Tomppo et al. (2002) which were also based
on known populations of complete coverage Landsat-mapped defor-
estation data.
The BLA-stratied design employing MODIS-derived deforestation
to form the strata and to determine the Neyman optimal sample
allocation resultedin smaller standard errors (better precision) than the
simple random design and also the systematic design using a one-
degree sample grid. Stratication and optimal allocation both con-
tributed to the smaller standard error as demonstrated by the
comparison of simple random sampling, stratied sampling with
proportional allocation, and stratied sampling with optimal allocation
(Table 3). The BLA-stratied, optimally allocated design using 150
sample blocks was almost three times more precise as the simple
random design using the same number of sample blocks and the
standard error for this stratied design using 325 sample blocks was
only slightly greater than that of the systematic design with a sample of
1310 blocks (thesystematic half-degree grid design).The BLA-stratied,
Table 2
Distribution of the sample blocks to the BLA strata, percentage of study area, and deforestation within each stratum. The strata were constructed based on MODIS-derived
deforestation and substratied based on criteria described by Hansen et al. (2008a).
Table 3
Standard errors of the estimator of PRODES-mapped deforestation area 20002005
expressed as percent of the study area; the target parameter of total area deforested is
108,637 km
2
or 2.73% of the study area.
Design Number of sample blocks
n=150 n=325 n=1310
Simple random sampling 0.48 0.32 0.15
Systematic n/a 0.25 0.09
BLA 4 strata (proportional allocation) 0.20 0.13 0.06
BLA 4 strata (optimal allocation) 0.15 0.10 0.05
BLA 5 strata (substratied) 0.14 0.10 0.04
2452 M. Broich et al. / Remote Sensing of Environment 113 (2009) 24482454
optimally allocated design effectively targeted sampling resources to
the high and very high deforestation strata where the majority of the
PRODES-mapped deforestation occurred (Table 2). In contrast, a large
proportion of the sample blocks in the systematic designs were located
in regionswhere only a small fraction of the total deforestation occurred
(Table 2). The targeted allocation of sampling effort to deforestation
hotspotsevidently translated into improved precision (smaller
standard error) for the stratied design relative to the simple random
and systematic designs. Further partitioning of the low deforestation
stratum into two substrata provided only minor improvement in
precision (Table 3). This indicates that the generic MODIS-derived low
deforestation stratum had already effectively identied most blocks
with little deforestation (Table 2).
The success of the stratication employed in the BLA study region is
attributable to the ability of the MODIS 500-m× 500-m product to
detect the large agro-industrial clearings thatdominate deforestation in
the BLA (Fearnside, 2005; Hansen et al., 2008c). Accordingly, the same
methodology should be effective in other regions undergoing rapid
agro-industrial scale clearing, such as Insular Southeast Asia. A forth-
coming MODIS deforestation product with 250-m× 250-m spatial
resolution will likely be more sensitive to small clearing events that
are currently only detectable with sensors that have at least Landsat-
scale spatial resolution (30-m× 30-m). This impending annual dataset
holds potential for further rening the stratied sampling design to
permit application of the approach to Central Africa, where small scale
clearings make up the majority of the deforestation area (Hansen et al.,
2008b). Such small scale deforestation cannot be readily identied by
the currently available MODIS 500-m× 500-m product, so the improve-
ment in precision achievedby stratication and optimal allocation using
the MODIS 500-m× 500-m product in the BLA would not necessarily
extend to Central Africa. The MODIS 250-m× 250-m product will need
to be evaluated to determine if it is effective for stratication and
optimal allocation in Central Africa.
Extending the general evaluation of sampling designs to other
complete coverage forest loss datasets would be invaluable to gauge
the general utility of MODIS-guided (stratied) sampling under a variety
of deforestation scenarios (i.e. different rates and spatial patterns of
deforestation). Further, evaluating a broader range of deforestation
scenarios will provide better understanding for choosing strata and
sample size allocations that produce more precise estimates of
deforestation. The comparison of sampling designs presented here was
based exclusively on the criterion of precision, which is readily
quantiable. Other criteria such as ease of implementation and familiarity
to foresters and policymakers may favor systematic sampling, whereas
the criterion of unbiased estimation of variance would favor stratied
random sampling. All of these criteria may be factored into the nal
choice of sampling design. Our evaluation of the different sampling
designs also focused only on the case in which the objective is to estimate
area of deforestation for a single time interval. Comparing different
sampling designs and different stratication options for long-term forest
monitoring that would include several time intervals and more than one
target variable (e.g., area of deforestation, afforestation, and degradation)
would be another useful extension of this research.
5. Conclusions
A sampling design employing MODIS-derived deforestation for
strata construction and sample allocation provided more precise
estimates of PRODES-mapped 20002005 deforestation in the BLA
than both simple random and systematic sampling as the MODIS signal
allowed efcient targeting of deforestation hotspots. Moreover, the
small standard errors reported in Table 4 suggest that sampling of
Landsat imagery is capable of producing estimates of deforested area
with adequate precision. These results serve tocounterbalance the poor
performance of simple random sampling observed by Tucker and
Townshend(2000). The latter result continuesto exert an unduly strong
inuence on opinion; for example, Grainger (2008) questioned the
reliability of all sample-based estimates of deforestation principally on
the basis of Tucker and Townshend's (2000) study. As pointed out by
Stehman et al. (2005),theTucker and Townshend (2000) result should
be taken as a strong caution that if deforestation is spatially
concentrated within one or a few Landsat images (i.e. an extremely
large area of forest clearing occurs in a single Landsat image), a simple
random sample of Landsat images will not yield a precise estimate
unless the sample size is large. Precise estimates based on smaller
sample sizes may be achievable if sampling units smaller than Landsat
images are employed and if stratied sampling is implemented to take
advantage of ancillary information related to deforestation. The
standard errors obtained for the systematic and stratied designs
applied to the BLA study area help dispel the claim that sampling cannot
be used to precisely estimate deforestation. The stratied sampling
design taking advantage of MODIS-derived deforestation demonstrates
the effectiveness of a well designed sampling approach. To fulll the
need for more effective monitoring of tropical deforestation as
advocated by DeFries et al. (2007), sampling approaches merit
consideration as a timely, cost-effective component of a monitoring
Table 4
Precision of sample-based estimates of tropical deforestation.
Source Target population Design % of area sampled Sample unit
(sample size)
Annual deforestation
rate
Standard error
of deforestation
rate
Previous studies
FAO (2001) Net deforestation in world's
tropical forests 19902000
Stratied 10% of world's
tropical forests
Landsat images (117) 0.52% of 1990 forest area 0.08%
Achard et al. (2002) Gross deforestation in evergreen
and seasonal forests of the tropical
humid bioclimatic zone 199097
Stratied 6.5% of humid
forest domain
Landsat images and
quarter images (100)
0.30% of study area 0.04%
Hansen et al. (2008a) Gross deforestation in humid tropical
forest biome 200005
Stratied (with
poststratied and
regression estimators)
0.21% of study area 18.5-km× 18.5-km
blocks (183)
0.28% of study area 0.02%
Duveiller et al. (2008) Gross deforestation in moist tropical
forest of Central Africa 19902000
Systematic 2.25% of forest
domain
10-km×10-km
blocks (390)
0.21% of the study area 0.05%
BLA study
BLA design four strata Loss of intact forest area in the
humid tropics of the BLA 200005
Stratied 1.29% of study area 18.5-km× 18.5-km
blocks (150)
0.55% of study area 0.03%
Systematic one-degree
grid design
As above Systematic 2.79% of study area As above (325) As above 0.05%
Systematic half-degree
grid design
As above Systematic 11.26% of study area As above (1310) As above 0.02%
2453M. Broich et al. / Remote Sensing of Environment 113 (2009) 24482454
strategy. The results of our case study for the BLA contribute to a
growing body of evidence supporting the important contribution of
sampling to tropical deforestation monitoring.
Acknowledgments
We thank four anonymous reviewers for their helpful comments
leading to major improvements in the manuscript. Funding from the
National Aeronautics and Space Administration supported this
research under grant NNG06GD95G managed under the NASA Land
Cover Land Use Change program (manager: Dr. Garik Gutman).
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