Supporting Online Material for Achard (RE ) scheduled for 8/9/02 issue of Science

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Supporting Online Material for Achard (RE 1070656) scheduled for 8/9/02 issue of Science Materials and Methods

Overview

Forest cover change is calculated using a sample of 102 observations distributed throughout the tropical forest domain. The locations of the observations are selected using a stratified sampling scheme in order to reduce the variance of the estimator. The individual observations measure land cover areas at two dates using fine spatial resolution satellite imagery. The simplified land cover classes include three forest classes (“closed forest”, “open forest” and “plantations / forest regrowth” weighted as 100% forest cover), two composite classes with proportions of forest and non-forest cover (“fragmented forests” and “mosaics” weighted as 75% and 25% forest cover respectively) and three non-forest classes. As the satellite data do not always correspond to the two selected reference dates, June 1st 1990 and June 1st 1997, we use a linear interpolation to adjust all land cover change matrices of individual observations to these dates. The global or continental land cover change matrices are then calculated by the sum of each observation site matrix multiplied by its site selection probability for a given region. To reduce unforeseen bias in the selection process we use co-variable data to calibrate the selection probabilities in a two-step process. The total forest cover for the two reference dates is obtained by summation of the individual class contributions (class areas weighted by their class forest proportion) for each date.

Stratification and selection of 102 sample observations

When a spatial phenomenon, such as deforestation, is distributed in a non-homogeneous way, stratification reduces the variance of its estimation. As a starting point, the method uses the daily global imaging capabilities of a number of satellites to build up forest distribution baseline maps for the 3 tropical continents for the early 1990’s. These continental maps provide detail down to 1 km2 (S1-S3). Fast changing areas (“deforestation hot spots”) were then spatially delineated over these forest cover maps in conjunction with knowledge from forestry and environmental experts (8).

The resulting two information layers, forest and “hot spot” maps, provided a stratification framework for selecting 102 sample units around the tropics (Figure 1 of main paper) in a systematic manner with higher sampling probabilities for fast changing areas (S4). Stratum one, with the lowest sampling probability, includes samples with less than 10% forest cover and no hot spots. The sampling rate rises to a maximum in stratum five, which includes areas with more than 10% forest cover and more than 50% hot spot proportion.

The initial sampling grid is a tessellation of regular hexagons of 60 km spacing. All hexagons were assigned to one of the five strata. Then, 102 hexagons were systematically selected as sampling units with different sampling intensity for each stratum. The actual observation units were the Landsat TM image frames (full scenes or quarters of scene with 180 km and 90 km side lengths respectively) covering best the hexagonal sample units. Full scenes were selected for heterogeneous landscapes, and quarter scenes for homogeneous ones. The Landsat frame extents were clipped in order to avoid overlaps and therefore double sampling of identical areas. The sampling procedure is described in more details in S4.

The limitation of the observed area to the humid tropical domain only, and the higher intensity of the sampling on those forested areas where most of the deforestation takes place, were aimed at

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making the sampling scheme as efficient as possible and at reducing the variance of the change estimates, resulting in higher confidence. Such dedicated stratified statistical sampling scheme over the humid Tropics was expected to improve existing estimates of deforestation (S5).

Measuring forest change in the observation sites and interpolation to base-line years

Satellite images of fine spatial resolution (20m to 30 m) were selected over the 102 observation sites, from the best quality existing acquisitions and at two dates closest to our target years: 1990 and 1997. On-screen visual interpretations were carried out with a common standardised method by a network of 20 local institutions having an extensive knowledge of the local ecosystems’ conditions and of the change processes. A minimum mapping unit of 50 ha was applied and the change was interpreted in an interdependent manner, i.e. using both dates together. For each site the digital vectorized interpretations were used with a simplified legend of eight land cover classes to produce land cover change matrices. These matrices were linearly interpolated to two reference dates: 1st June 1990 and 1st June 1997.

Extrapolation of site measurements to continental estimates

Land cover transitions were then estimated at continental and global levels using the interpolated change matrices. The set of individual site matrices for a given continent were integrated in a statistical calculation which takes into account each observation site’s selection probability. First, we considered that each observation site (full TM scene or quarter TM scene) is linked to a unique relative cluster of hexagonal sampling units (as sum of probabilities of the corresponding hexagons). As each observation site may include more than one stratum, we fall in a situation of unequal probability sampling rather than stratified sampling. The traditional unbiased estimator for an unequal probability sample is the Horwitz-Thomson estimator, also called π-estimator (S6). For any variable Y (any particular land cover transition type), the formula for the estimation of the total of Y is:

∑

= × = i i i i i i y d p y Yˆ_π

where yi = Measured value of variable Y in sample site i

di = Weight of sample site i (inverse of the sampling probability pi).

However, in our case we had (i) observation units (clipped Landsat frames) slightly different from their relative clusters of hexagonal sampling units and (ii) partially missing information (mainly due to cloud coverage) and non-random location shifting or replacement of a few sites in the sample (4 replacement sites in total). The average proportion of missing data (mainly clouds) inside the observed sites is 9%. This may introduce a bias in the estimator that must be corrected as far as possible. Two correction steps were applied to handle this situation of unequal

probability sampling: (i) correction of the initial probabilities of the clusters of hexagons to fit with the Landsat TM observation sites and (ii) calibration of the estimator using two proxies (or co-variables) available at regional scale. These two steps are described in the following section. Once these correction steps were performed the final change matrix was derived for each of the four different region (“Pan-Amazon and Central America”, “Brazil and the Guyanas”, “Africa”, and “Southeast Asia”), by summing by region the individual site’s change matrices, each multiplied by the new corrected/calibrated estimation weight wi.

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∑

× = i i i m w M

where M = Regional or global land cover change matrix

mi = Land cover change matrix for sample site i

wi = Corrected weight of sample site i .

The resulting regional land cover change matrices are shown in Table S2.

The total forest cover for each of the two reference dates is obtained by summation of the individual class areas (classes “closed forest”, “open forest”, “fragmented forest”, “plantations / forest regrowth” and “mosaics”), each weighted by their defined forest cover proportions, i.e. 100, 100, 75, 100 and 25 % respectively.

Correction and calibration of the site selection probabilities

Step 1. Due to the particular sampling method used, the original sampling probability of each sample site was proportional to the total land area of the tessellation hexagons that were

associated to the observation unit, and depended on the proportions of forest area (from the 1 km resolution maps) and hot spot area within these hexagons. The total area and the proportions of forest area and hot spot area in the observation units (clipped Landsat frames) are usually

different from the initial parameters. The first step corrected the initial sampling probabilities by applying the following linear ‘fitting’ model for each continent:

k k k k k k XL XH c XL XF b a XL p ₌ ₊ _× ₊ _× × 6 10

where : pk = Selection probability of site k

XLk = Total land area in site k

XFk = Forest area in site k (from the 1km resolution maps)

XHk = Hot spot area in site k

The parameters of the model (a, b and c) were determined for each continent from the data of the sample sites (clusters of hexagons), then applied to the data of the observation sites (TM

images).

Step 2. Potential bias can be corrected and precision can be improved by calibrating the estimator using one or more proxies (co-variables). We used two additional co-variables which are similar to the two main variables to be estimated (forest area and forest area change derived from the observation sites): forest area from the 1 km resolution forest maps and forest area change

derived from the hot spot proportion map and the regional hotness index (S5). Figure S1

demonstrates the appropriateness of using forest area from the 1 km resolution forest maps as a sampling co-variable for the estimation of forest cover from the 30m resolution maps.

We have selected the following approach (S7): Starting from the Horwitz-Thompson estimator, the calibration computes new weights wk as close as possible to observation sites weights dk (1/pk), such that the estimator applied to the two co-variables Xj (known for the whole

population) gives a result that coincides with the known total of the co-variables. Formulas of calculation of the calibrated weights are:

kj k k j j X w x TX = ˆ =

∑

× with

(

)

     

_∑

₋ k k k d w 2 min

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where: TXj = Total of the co-variable Xj

xkj = Value of the co-variable Xj in site k

dk = Weight of observation site k (1/pk )

wk = Calibrated weight of observation site k

The calibration was applied separately for the four continents/regions listed in Table S2.

Estimation of variance and accuracy assessment

As the usual variance estimator is not applicable because of the adjustment calibration, we adopted a re-sampling (bootstrap) approach to estimate the variance. For each bootstrap

replicate, the calibration of the site probabilities is re-computed and the variance of the obtained estimations gives an estimate of the estimator variance. The variance was estimated separately for the four continents/regions.

Risks of bias can come from the sampling and estimation scheme or from the procedure to measure the transition matrix in each sampling site (image-interpretation). The main risk of bias in the sampling scheme is the existence of missing or replacement sites and missing data for specific areas inside the sample sites with persistent cloud cover. For partially missing data inside a site, we assume that the change rate in the missing areas is similar to the change rate in the areas with data of the same site. To reduce the bias due to replacement sites (4 sites in total), we have applied the calibration estimator described above. Possible inaccuracy in the 1 km forest map or in the hot spot areas make the sampling and the calibration less efficient (higher variance in the estimates), but do not introduce any significant bias in the area change estimates.

The possible bias from the image-interpretation of the satellite images over the 102 observation sites has been assessed by an independent image-interpretation “consistency assessment” performed on a sub-sample of the data set. The re-examination of one or two sub-samples covering (in total) 5 % of the interpreted area in each sample site was carried out by a single expert. For each sub-sample the polygons covering 100 dots were re-interpreted in an independent and consistent way. The consistency represents the fraction of agreed polygon interpretations to the total number of polygons. The resulting interpretation consistency has been estimated to some 93% globally for 10 aggregated land cover classes (closed forest, open forest, fragmented forest, plantations, forest regrowth, mosaics, natural non forest, agriculture, non vegetated, water) with the following continental distribution: 96% for Latin America, 88% for Africa and 92% for Southeast Asia. For the forest cover change estimations, the global

consistency was estimated to some 91% with 96% for Latin America, 82% for Africa and 90% for Southeast Asia. A comparison of the forest area and forest area change has been made between the two interpretations (original and re-interpreted) using the sum of entire sub-sample dataset, which gives an indication of a possible source of bias. The relative difference in the

forest area ranges from -1.9% to 0.0% for closed forest or total forest classes respectively, and

the relative difference in the forest area change ranges from –1.7% to –8.4% respectively. The same independent consistency assessment allowed an assessment of the thematic accuracy by re-interpretation over the 100 dots (i.e. not polygons). The re-interpreted results show that 89.7% of the sample dots correspond to the class of the polygon. In addition 9.7% of the sample dots fall in one of the two composite classes: “fragmented forest” or “mosaics”. The “fragmented forest” class contains 78% forested dots with 22 % non-forested dots, while the “mosaics” class contains 30% forested dots, which confirms its definition of 10 – 40% forest cover. Hence

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together with pure class assignments there is a 99.4 % correspondence between dot interpretation and polygon assignment.

The confidence intervals presented in Table 1 and Table 4 of the main paper represent the statistical sampling accuracy. The consistency assessment accuracy is not included as it does not correspond to a real ground truth validation and is only indicative. The confidence range

corresponds to two standard deviations to the mean (standard error) and represents therefore 95% of the confidence range. The relative variances (standard deviation) are then 2.4% for the global forest cover estimate (from 3.3% to 5.5% for continental estimates) and 13% for the global forest cover change estimate (from 19% to 28% for continental estimates).

References and Notes

S1. F. Achard, C. Estreguil, Remote Sens. Environ. 54, 198 (1995).

S2. H. D. Eva, A. Glinni, P. Janvier, C. Blair-Myers, Vegetation Map of South America, Scale

1/5M (European Commission, Luxembourg, 1999).

S3. P. Mayaux,, T. Richards, E. Janodet, J. Biogeogr. 26, 353 (1999).

S4. T. S. Richards, J. Gallego, F. Achard, Int. J. Remote Sens. 21, 1473 (2000).

S5. R. L. Czaplewski, On Sampling for Estimating Global Tropical Deforestation (FAO, Rome, 2002).

S6. W. Cochran, Sampling Techniques (Wiley, New York, 1977). S7. J. C. Deville, C. E. Särndal, J. Am. Stat. Assoc. 87, 376 (1992).

Fig. S1. Forest cover measurements derived from fine spatial resolution (30 m) satellite imagery

versus forest cover measurements from coarse spatial resolution (1 km) satellite imagery over the 102 samples for the year 1990. Scales are in thousand hectares.

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Table 1. Main regional forest types included and excluded in the study.

Included forest types

Bioclimatic domain

Latin America Africa Southeast Asia

Humid Evergreen lowland

forest Evergreen mountain forest Semi-evergreen forest Heath forest (Caatingas)

Varzea / swamp forest and swamp forest with palms Coniferous Mangrove Evergreen lowland forest Evergreen mountain forest

Semi- evergreen forest Swamp forest Mangrove Evergreen lowland forest Evergreen mountain forest Semi-evergreen forest Moist mixed deciduous forest

Heath forest Coniferous

Swamp and peat swamp forests

Mangrove

Dry Mixed deciduous forest

Dry dipterocarp forest Excluded forest types

Bioclimatic domain

Latin America Africa Southeast Asia

Dry Deciduous forest

Woodland (Cerradão, Cerrado, Chaco) Deciduous forest Woodland savanna Tree savanna Deciduous forest of south eastern India

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Table S2. Forest cover changes in the humid tropics from 1990 to 1997 by continent.

Africa

1997 Forest classes Non-forest classes Forest cover

Closed Open Fragmented Plant/regrow Mosaics Natural Agriculture Unvegetated in 1990

1990 cover weight 100 100 75 100 25 0 0 0 per class total

Closed 100 154.8 1.9 0.8 0.3 1.5 0.9 1.4 0.0 162 Forest Open 100 0.6 26.7 0.3 0.0 0.4 0.2 0.2 0.0 28 classes Fragmented 75 0.2 0.0 5.1 0.0 0.1 0.3 0.5 0.0 5 Plant/regrow 100 0.0 0.0 0.0 0.4 0.0 0.0 0.1 0.0 1 Non Mosaics 25 0.1 0.1 0.0 0.0 8.9 1.8 0.7 0.1 3 forest Natural 0 0.0 0.0 0.0 0.0 1.3 89.7 1.5 0.5 0 classes Agriculture 0 0.2 0.0 0.0 0.0 0.2 0.2 30.4 0.0 0 Unvegetated 0 0.0 0.0 0.0 0.0 0.0 0.3 0.1 3.6 0 198

Forest in per class 156 29 5 1 3 0 0 0

cover 1997 total 193

Southeast Asia

cover 1997 total 270

Pan-Amazon & Central America

cover 1997 total 243

Brazil & Guyanas

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Note 1: All area figures are in million hectares.

Note 2: The forest class definitions were made according to those applied by the FAO Forest Resource Assessment Exercise (11) using two parameters: tree cover (canopy density within a forest stand) and forest proportion (stand density within the mapping unit). An area assigned to one of the forest classes has a forest proportion of more than 40% in which the forest stands have a tree cover of more than 10%. When the forest proportion is at least 70 %, the area is

considered “closed forest” if the tree cover is more than 40%, and “open forest” if between 10 and 40%. When the forest proportion is between 40 and 70%, the area is defined as “fragmented forest”. “Plantations / forest regrowth” are grouped as natural forest. Referring to the non-forest classes: “Mosaics” are defined as containing a non-forest proportion between 10 and 40%. Other “Natural Vegetation” such as shrub or grassland, but also “agriculture” land may still contain a forest proportion or a tree cover up to 10 %.

Note 3: For forest cover calculation we applied forest proportion “weights” per class as determined by an independent post-assessment of the observation site results (8). The “Total

forest cover” estimates in 1990 and in 1997 are derived by the addition per class of the weighted