National-scale estimation of gross forest aboveground carbon loss: a case study of the Democratic Republic of the Congo

Recent advances in remote sensing enable the mapping and monitoring of carbon stocks without relying on extensive in situ measurements. The Democratic Republic of the Congo (DRC) is among the countries where national forest inventories (NFI) are either non-existent or out of date. Here we demonstrate a method for estimating national-scale gross forest aboveground carbon (AGC) loss and associated uncertainties using remotely sensed-derived forest cover loss and biomass carbon density data. Lidar data were used as a surrogate for NFI plot measurements to estimate carbon stocks and AGC loss based on forest type and activity data derived using time-series multispectral imagery. Specifically, DRC forest type and loss from the FACET (Forêts d’Afrique Centrale Evaluées par Télédétection) product, created using Landsat data, were related to carbon data derived from the Geoscience Laser Altimeter System (GLAS). Validation data for FACET forest area loss were created at a 30-m spatial resolution and compared to the 60-m spatial resolution FACET map. We produced two gross AGC loss estimates for the DRC for the last decade (2000–2010): a map-scale estimate (53.3 ± 9.8 Tg C yr−1) accounting for whole-pixel classification errors in the 60-m resolution FACET forest cover change product, and a sub-grid estimate (72.1 ± 12.7 Tg C yr−1) that took into account 60-m cells that experienced partial forest loss. Our sub-grid forest cover and AGC loss estimates, which included smaller-scale forest disturbances, exceed published assessments. Results raise the issue of scale in forest cover change mapping and validation, and subsequent impacts on remotely sensed carbon stock change estimation, particularly for smallholder dominated systems such as the DRC.


Introduction
The United Nations Reducing Emissions from Deforestation and forest Degradation (UN-REDD) program seeks to Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. compensate developing countries for avoiding emissions due to likely future forest clearing and logging (Houghton 2012) through the emerging REDD+ mechanism. The success of REDD+ will be defined by confirmed reductions in rates of deforestation and forest degradation. A program requirement is the capability to accurately map and monitor changes in forest carbon by estimating gross emissions as a function of area of forest loss and density of carbon stocks within areas of forest loss. National forest inventories (NFIs) could provide detailed and comprehensive information to produce national-scale carbon stock and change estimates. However, NFIs have not been established in many developing countries that participate in the UN-REDD program (Romijn et al 2012). The United Nations Food and Agriculture Organization (FAO) and the UN-REDD are working on the general guidelines for implementing multi-objective NFIs in these countries (UN-REDD 2011). Meanwhile, alternative methods of national-scale carbon stocks assessment independent of the availability of systematically collected ground-based forest inventory data are being investigated and prototyped (GOFC-GOLD 2010). Goetz et al (2009) provided an overview of the satellite-based methods of mapping and monitoring carbon stocks, and identified three general approaches: 'stratify and multiply' (SM), when a single carbon density value is assigned to each land cover type; 'combine and assign' (CA), extending the SM approach by adding various ancillary spatial data layers; and 'direct remote sensing' (DR) approach, aimed to derive the carbon stock estimates from machine learning algorithms based on satellite observations and other detailed spatial data coupled with field measurements. The last approach requires acquisition and processing of large volumes of data to produce a national-scale carbon stock or loss estimate. The first approach, SM, also referred to as the 'biome-average approach' , is relatively easy to implement using a limited set of published data available at low or no cost. Although this approach is fairly generalized, in that it does not capture finer-scale spatial heterogeneity of carbon stocks, the accuracy of the estimates can be increased via data refinements and overlays with other data sets in a CA approach.
For a national-level aboveground carbon (AGC) loss assessment, SM approaches require a national-scale land cover change dataset (activity data in the IPCC terminology IPCC 2006) and mean AGC density estimates for each land cover type (IPCC emission factors, here referred to as carbon data). Modifying the basic IPCC equation used to calculate carbon emissions (IPCC 2006, vol 1, chapter 1.2), the equation to estimate gross AGC loss within a study region or a country is the following: where AD i (activity data) denotes the change in the extent of a given land cover type i, and CD i (carbon data) represents average vegetation carbon content per land cover type. Carbon data that are required for the national-scale AGC loss assessments in an SM approach could be derived from field inventory data (e.g. tree DBH and height measurements) converted to aboveground biomass using allometric equations (e.g. for tropical forests-from Brown 1997 andChave et al 2005) or existing databases and maps of biomass carbon density (e.g. Zheng et al 2013, Gibbs 2006, FAO 2010, Malhi et al 2006. Alternatively, biomass carbon content can be mapped using multi-source lidar and radar data that are capable to capture vertical tree canopy structure Dubayah 2011, Treuhaft et al 2009). Several regional and global-scale carbon stock maps have been created recently using the synergy of field measurements, optical, lidar and radar remotely sensed data (Saatchi et al 2011. Another approach, presented here, is to calibrate lidar data using co-located field measurements . In this approach, a model is derived to convert lidar waveforms into biomass estimates. The derived model is then extrapolated to a much larger population of lidar shots, providing a biomass database for assigning carbon density values to mapped forest cover types. For REDD+ countries, deforestation is likely to be the key category for greenhouse gas emissions estimates. A good practice for these countries is to use at least IPCC Tier two or three level assessments for this category of emissions, which implies reporting uncertainties (Maniatis and Mollicone 2010). AGC stock and loss uncertainty estimates are also crucial if these datasets are to be used as inputs to carbon cycle and biosphere models. However, published land cover change datasets that may be used as activity data often lack key accuracy assessment information (e.g. description of sampling design, original error matrix, area of each map category, etc) that would permit error-adjusted estimates of the change area (Olofsson et al 2013). The objectives of our analyses are: (i) to illustrate the process of activity data accuracy assessment on the national level, applicable when using already published land cover data or when creating a new data set, (ii) to integrate uncertainties from activity and carbon data in a national-level forest AGC loss estimate.
In this study, we implemented a SM ('stratify and multiply') approach for assessing gross forest AGC loss in the Democratic Republic of the Congo (DRC), where forest cover change is dominated by smallholder land use and industrial selective logging (Laporte et al 2007). Due to the aftermath of two civil wars, persistent political unrest and lack of infrastructure, the DRC does not collect NFI data required for ground-based estimates of AGC stock and its change. Our approach employs the best available activity and carbon data at the national scale-forest extent and loss maps derived from Landsat imagery  and AGC estimates derived from GLAS-based canopy vertical structure metrics . Results include new estimates of error-adjusted area of forest cover loss between 2000 and 2010, gross AGC loss, and associated uncertainties.

Activity data
To estimate the area of forest loss, we used Landsat-based year 2000 forest cover and 2000-2010 forest cover loss data from the Forêts d'Afrique Centrale Evaluées par Télédétection (FACET) product, available online (ftp:// congo.iluci.org/FACET/DRC/). FACET data processing and mapping methodology are described in Potapov et al (2012). The FACET dataset provides forest cover and gross forest cover loss for three forest types: primary humid tropical forests, defined as mature humid tropical forest with canopy cover >60%; secondary forests, defined as regrowing forest with canopy cover >60%; and woodlands, defined as forested areas with canopy cover 30-60%. The spatial resolution of FACET data is 60 m per pixel. We further separated these three forest types into terra firma (dryland) and wetland sub-classes using the DRC wetland map of Bwangoy et al (2010), resulting in six forest types in total. FACET forest cover loss was attributed to these new forest classes (figure 1). In this manner, the different carbon content of the antecedent forest cover could be directly related to disturbance dynamics in terra firma and wetland forested ecosystems. In this research, we conduct an explicit statistical validation of FACET forest cover loss for each of these forest types and derive the error-adjusted estimate of changed area based on the validation sample.

Carbon data
Mean AGC density values for each of the forest types were derived from GLAS-based biomass estimates. Baccini et al (2012) developed a statistical model to predict AGC densities observed in the field using GLAS lidar energy metrics in order to estimate biomass per 65 m diameter GLAS shot. The model was based on nearly 300 field sites located in 12 countries across the tropics. GLAS-predicted AGC explained 83% of variance in the field-measured carbon density at the GLAS-footprint scale with a standard error of 22.6 Mg C ha −1 . For this study, we employed the GLAS-derived biomass data as if they were field inventory data and did not incorporate this model uncertainty in downstream calculations. After screening GLAS data for noise and filtering for slope (≤10 • ), 371 458 AGC-estimated GLAS shots for the years 2004-2008 (figure 2) were analyzed together with the combined FACET forest cover and DRC wetland maps to calculate mean AGC density values for the six target forest classes. Only shots within the forested areas that did not experience forest cover loss between 2000 and 2010 according to FACET were used for these calculations. The use of a large number of GLAS-estimated biomass values to calculate biome-average AGC densities helps avoid biases often inherent in estimates based on the compilation of point-based field measurements (i.e. paucity of sites over large areas, inadequate stratification to capture variability, and other factors that limit their spatial representativeness).

Validation data
For the purposes of activity data validation, namely the uncertainty estimation for the FACET forest cover loss, we used all available original L1T Landsat images for years 2000 and 2010 available at no charge from USGS archives (http://glovis.usgs.gov/) and annual Landsat composites for circa , 2005. Year 2005 composite images helped identify forest cover loss in the early 2000s that might be difficult to detect in 2010 Landsat images due to rapid vegetation regeneration in the tropics.
In addition to the use of Landsat images for the validation (reference) classification, we also employed visual interpretation of very high spatial resolution images available for the study region through Google Earth TM and through a partnership between NASA and NGA that provides access to unclassified commercial high spatial resolution satellite data from NGA archives for NASA Earth Science Investigators (http://cad4nasa.gsfc.nasa.gov/). A total of 1689 high resolution images from multispectral and panchromatic sensors (Ikonos, WorldView-1, WorldView-2, Quickbird, Orbview-5) for 2008-2011 time interval were used for the visual assessment of validation samples. In total, 503 out of a final 1061 validation samples had at least one matching high resolution image available between 2000 and 2013, either from Google Earth TM or from the NGA archive. These images facilitated the forest cover loss validation, providing information about forest cover type on date 1 (2000) or date 2 (2010).

Uncertainties from activity data
The key objective of activity data validation is to estimate error-adjusted area of forest cover loss for each forest type and to quantify its uncertainty. Error-adjusted area estimation uses validation sample data to adjust area of forest cover loss due to classification errors (including omission errors and excluding commission errors) present in the map product (Olofsson et al 2013). The choice of sampling design is determined by this objective, as well as by feasibility issues and time constraints.
3.1.1. Sampling design and sample size.
The target activity data class, forest cover loss, is relatively small compared with the unchanged forest areas; the sampling design should increase the sample representation of this rare class in order to achieve a precise estimate of forest cover loss accuracy (Khorram 1999). Moreover, our objective is forest type-specific loss area estimation and its accuracy; stratified random sampling is an appropriate choice in this case (Stehman 2009).
Initially, two strata within each forest type class were considered: 'no loss' (forests, undisturbed between 2000 and 2010) and 'loss' (2000-2010 forest cover loss). However, sufficient estimation of loss omission error within the large 'no loss' stratum requires special attention. Given a simple 'loss' and 'no loss' stratification, rates of false negatives (change omission errors) could be poorly characterized (Khorram 1999). Furthermore, the FACET national-scale forest cover loss product is likely to be conservative, i.e. omitting forest cover loss in comparison to committing forest loss. To address this issue we identified an additional 'probable loss' stratum within each forest type class. This stratum was constructed to target omitted forest cover loss in order to improve the loss area estimate for the AGC loss calculation. We define the 'probable loss' stratum as a 1-km radius circular region around forest cover loss, assuming that omission of loss is likely to occur in proximity to mapped loss. The choice of the 1-km wide 'probable loss' stratum is supported by the evidence that increased tree mortality in temperate and tropical forests is generally observed up to 1 km from the forest edge (Broadbent et al 2008).
A total of 18 strata were analyzed: 'loss', 'probable loss', and 'no loss' for each of the six forest types (terra firma and wetland primary forests, terra firma and wetland secondary forests, terra firma and wetland woodlands). Allocation of samples among these strata should effectively address our validation objective (see section 3.1) of minimizing standard errors (SEs) of error-adjusted estimators of forest cover loss area (Stehman 2012).
When considering allocation of samples among forest types, we examined both the area of forest type and the area of our target class (forest loss) within each forest type. Proportional allocation of samples among forest types based on the forest type area would lead to small sample sizes from secondary forest, woodlands and wetland forests: almost half of all samples in this case fall into the dense forest class (table 1). Although forest cover loss in dense forests that have high biodiversity and other high-value ecosystem services is important to estimate correctly, the majority of mapped forest cover loss occurred in secondary forests. However, allocation of samples based on the forest cover loss area leads to the majority of samples being located in secondary forests. In order to find a compromise between preserving a sufficient number of samples in the strategically important dense forest class while adequately representing the relatively small classes with high proportional forest cover change (secondary forest, woodlands), we implemented an arbitrary allocation that was close to proportional by forest type area, but adjusted for forest loss area (table 1).
The sample size allocation to the three strata within each forest type was determined as follows. Because it is equally important for our primary validation objective (estimation of forest loss area for each forest type based on an error matrix) to account for committed and omitted loss area, we addressed the need to account for omission errors by creating the separate 'probable loss' strata within the original 'no loss' class. Therefore, when allocating samples among loss strata, we chose to have an allocation closer to equal, which helped to target errors of commission (Stehman 2012) among the 'no loss', 'probable loss' and 'loss' strata. A total sample size of 1000 was projected as feasible to be visually interpreted by expert analysts. We imposed the condition that a sample size greater than 50 was required for the major forest types (primary, secondary forests, woodlands, wetland primary forests), the allocation of sample size per stratum (the sampling unit is one 60-m FACET pixel) was implemented as shown in table 2.
For the chosen sample allocation we calculated SEs of the estimated area of change using hypothetical omission and commission error rates in order to confirm that the chosen allocation would not lead to inflated standard errors. We compared our arbitrary allocation to proportional among forest allocation with equal and proportional allocation among loss strata and found that the arbitrary allocation performed as well or better than the other options. The equation used to calculate SEs of the estimated area of change for each forest type is similar to equation (3) from Olofsson et al (2013). However, after the assignment of reference values to the samples during expert validation, we found out that the 'probable loss' stratum contributed 35% of the total variance in primary forest, 50% of the variance in secondary forest, and 20% of the variance in woodlands. Additional random samples were added to the 'probable loss' stratum of terra firma primary, secondary forests and woodlands (20, 30 and 10 samples respectively) in order to minimize the total SE of the loss area estimate.
3.1.2. Estimating area of forest loss and its uncertainty. Visual interpretation of validation samples was performed at a 30-m spatial resolution, enabling map-scale and sub-grid error assessments (FACET was made at a 60 m spatial resolution  using resampled 30-m Landsat time-series imagery). We produced two forest loss area estimates for the DRC for the last decade (2000-2010): a map-scale estimate accounting for whole-pixel classification errors in the 60-m resolution FACET forest cover change product, and a sub-grid estimate that took into account 60-m cells that experienced partial forest loss (table 3). For the map-scale estimate we treated a 60-m validation pixel as 'loss' only if the reference forest loss fraction detected using 30-m Landsat and/or high spatial resolution was ≥75% of pixel area. For the sub-grid estimate, three gradations of reference loss fraction per pixel were used: 1 (loss) with reference loss ≥75% of pixel area; 0.5 (mixed pixels) with reference loss between 75% and 25%; and 0 (no loss) otherwise (figure 3). When the sampling strata and map classes being validated are the same, equations (2)-(4) from Olofsson et al (2013) should be used to calculate error-adjusted area of forest cover loss and its standard error based on a validation confusion matrix. In our case, there was a mismatch between sampling strata ('no loss', 'probable loss', 'loss') and map classes ('loss' and 'no loss') within each forest cover type arising from the attempt to target omitted forest cover loss by creating the additional 'probable loss' stratum. Based on sampling theory (Cochran 1977), the following equation was employed to produce an unbiased estimator of the area of forest cover loss within each of the forest cover types when validation strata and map classes do not match (Stehman 2013, in review where A tot -total area of the forest cover type; y u = 0.5 or 1 if pixel u (or it's half) is in reference class 'forest cover loss', and y u = 0 otherwise; y h = u∈h y u n h , the sample-mean of the y u values in stratum h; n h -sample size in stratum h; N h -number of pixels in stratum h; N-total number of pixels within the forest cover type.
The standard error of the error-adjusted estimate of the forest cover loss is: , the sample variance for stratum h. A 95% confidence interval (assuming normal distribution) is:Â An example of the forest cover loss area estimation for terra firma primary forests (map-scale estimate) is presented in 3.2. Uncertainties from carbon data Table 5 presents the mean and population standard deviation (STD) derived from the number of GLAS shots per forest type. Using the SM ('stratify and multiply') approach we assigned a single mean AGC density value to each of the forest type classes to estimate gross AGC loss. To quantify the uncertainty of this estimate, we employed the standard deviation of the sample-mean's estimate of a population mean, the standard error of the mean (SEM). According to the central limit theorem, the distribution of sample estimates of the mean is normally distributed, enabling us to calculate the 95% confidence interval (CI) of mean AGC density estimates as ±1.96SEM. Table 5 shows mean AGC densities of our target forests classes along with their 95% CIs.

Combination of the uncertainties
When calculating AGC loss for each forest type using equation (1), uncertainty comes both from activity data (in our case-forest cover loss) and emission factors (carbon data). In order to combine uncertainties from these quantities, the multiplication approach from the recent IPCC Guidelines for National Greenhouse Gas Inventories (IPCC 2006, vol 1, chapter 3, p 28, equation (3.1)) was used: where U total is the percentage uncertainty in the product of the quantities (half the 95% confidence interval divided by the total and expressed as a percentage). U i is the percentage uncertainties associated with each of the quantities.
When calculating total gross AGC loss within the DRC (summing AGC loss values for all forest types), the addition and subtraction approach from the IPCC Guidelines (IPCC 2006, vol 1, chapter 3, p 28, equation (3.2)) was used to estimate the uncertainty of the resulting quantity: where U total is the percentage uncertainty in the sum of the quantities (half the 95% confidence interval divided by the total and expressed as percentage); x i and U i are the uncertain quantities and percentage uncertainties associated with them.
Thus, the overall uncertainty of gross AGC loss estimate for the entire DRC is: where numbers (1-n) stand for the six forest cover types.

Results
Applying the approach of adjustment for the classification errors described in section 3, we produced estimates of forest cover loss within target DRC forest classes (table 6). Error-adjustment significantly increased estimated areas of forest loss in terra firma forest classes (primary, secondary forests and woodlands); omission errors prevailed over commission errors (figure 4). In the wetland forests and woodlands, on the contrary, more loss was committed in the map product; error-adjusted loss area estimates were smaller than those prior to adjustment. SE was highest in wetland secondary forests and terra firma woodlands. High uncertainty in the wetland secondary forests is associated with it being the smallest and spatially discontinuous class. Woodland is a challenging forest type to map and monitor due to the gradients of tree canopy cover and seasonality as well as the comparatively uneven intensity of disturbance events, all of which contributes to larger SEs.
To compare AGC density estimates for our target forest classes with published estimates, we calculated average AGC densities within the 6 DRC forest types using available spatially explicit vegetation carbon density products , Saatchi et al 2011, Kindermann et al 2008 and compared them with the GLAS-based estimates of the current study ( figure 5). This comparison provides a general understanding of how well our current estimates correspond to existing knowledge. Examination of figure 5 shows that GLAS-based AGC density estimates are generally higher than those modeled using optical remotely sensed data , Saatchi et al 2011, probably because of spatial averaging (Goetz and Dubayah 2011, Zolkos et     Sub-grid gross AGC loss estimates were 20-50% higher than map-scale ones for the major terra firma forests (primary, secondary forests and woodlands) and nearly equal for the less widespread wetland forests (table 7, figures 6(b) and (c)).
Differences between these estimates are mostly associated with the 'loss' and 'probable loss' strata, particularly in regions where primary and secondary forest loss predominate. There are no significant differences in the forests and woodlands of the 'no loss' strata ( figure 6(d)). For the whole of the DRC, the sub-grid AGC loss estimate was 35% higher than the map-scale estimate (table 7).
The comparison of gross forest cover loss and gross AGC rates from this study with published estimates is presented in table 8. We report annual forest cover loss rates separately for primary and secondary forests, excluding woodlands (table 8) to best match the definition of forests employed in the most recent regional sample-based forest cover loss estimate by Ernst et al (2013) (all tropical moist forests, excluding woodland savannahs and tropical dry forests).

Discussion
The results reported in table 8 need to be considered in the context of inconsistencies in methodologies, definitions, and areas of analysis (a direct consequence of the differences in the definitions of forest and woodlands). Our map-scale 2000-2010 annual forest cover loss estimate within dense forests (0.35% ± 0.03%) agrees well with the estimates of Ernst et al (2013) for the first half of the decade (0.32% ± 0.05%) and of Hansen et al (2013) for 2000-2012 (0.34%). Our map-scale estimate also falls within the confidence interval of the global sample-based estimate of Hansen et al (2010), but is significantly higher than the FACET map-based estimate without error-adjustment . The sub-grid estimate, accounting for the finer-scale forest disturbance, is 30-40% higher than published estimates for the DRC, and points to the difficulty of mapping forest change in a landscape where smallholder shifting cultivation predominates. For example, FACET forest cover loss has a mean patch area of 1.4 ha . While patch size is not the same as field size, it is worth noting that typical shifting cultivation practices in the tropics employ field sizes well under 1 ha (Aweto 2013). The quantification of such change is challenging and represented by the comparatively large presence of mixed pixels in the FACET data. The difference of two methodologically consistent loss area estimates based on input data of different resolutions (60-m FACET and 30-m Hansen et al 2013, table 8) prior to error-adjustment illustrates the issue: the 30-m product depicts 1.5 times more change than the 60-m one. Any binary (yes/no) change map will have scale-dependent omission errors. These 'cryptic disturbances' have been reported to add more than 50% of forest cover loss  (2012) Forests + woodlands 23 to existing Landsat-scale forest disturbance classifications for the Amazon Basin (Asner et al 2005). Table 8 reflects a second type of omission error related to algorithmic and/or data limitations. Estimates of forest loss derived at a 30-m spatial resolution, particularly the Hansen et al (2013) and Ernst et al (2013) products, have comparable gross forest cover loss rates, 0.34% and 0.32% ± 0.05%. However, the 30-m validation estimate is 0.47% ± 0.04%. Large area mapping algorithms are often conservatively implemented in attempting to avoid commission error. For validation, the determination of loss/no loss is performed independently per sample and is free of this consideration. Differences between the Hansen et al (2013) 30-m map and the Ernst et al (2013) 30-m sample estimates could be due to this fact. However, the estimate of Ernst et al (2013) was also sample based. The additional loss found in our validation effort compared to Ernst et al (2013), while partially due to the use of very high spatial resolution data for a portion of the reference samples, is not easily explained and may be more related to definitional differences or other methodological factors. In summary, the difference between the 60-m FACET loss rates of 0.22% and 0.25% and the 30-m loss rates of 0.34% and 0.32% is most likely related to the differing scales of measurement. The difference between the 30-m loss rates of 0.34% and 0.32% and the validation rate of 0.47% is most likely related to limitations in mapping versus sampling or to other methodological factors. The discrepancy between map-scale and sub-grid estimates emphasizes the issue of scale in change area estimation for smallholder dominated landscapes like the DRC.
The approach for validating activity data employed in this study is relatively straightforward and easy to implement. The method allows for the generation of error-adjusted loss area estimates from the existing land cover and vegetation maps. This approach does not require large volumes of data processing and is therefore not limited by computational facilities. The use of open access medium-and high resolution imagery for map product validation (USGS Landsat archive, Google Earth TM high resolution imagery) allows defining reference values of validation samples without in situ measurements. Despite its advantages, the method is sensitive to sampling design and the associated decision of how to allocate the sample size among validation strata. For the strata and sample size allocation implemented in this study, the decisions were advantageous; for the four largest forest types, the reduction in standard error attributable to the stratification was substantial. Specifically, the gain in precision due to stratification can be computed from the sample data (Cochran 1977, section 5A.11) as the ratio of the standard error that would have been obtained from simple random sampling to the standard error obtained from the stratified design implemented (same sample size for both designs). For the four largest forest types, these ratios were 1.42 for primary forest, 1.10 for secondary forest, 1.32 for woodlands, and 23.21 for wetland primary forest (the latter estimate is likely inflated by the fact that two of the three strata had 0% forest loss). The methodology is also highly dependent on the knowledge base of the remote sensing experts performing visual interpretation of validation samples. Finally, it is a function of the quality of the reference imagery and the resulting clarity or conversely ambiguity in assigning change per validation sample. The map-scale and sub-grid estimates reflect the importance of this issue.
A further consideration in assessing the results concerns the reference data and the potential volatility of the samplebased estimate itself. Table 4 illustrates this issue. The 'loss' stratum records 60 of 63 samples as having experienced terra firma primary forest cover loss, representing 905 574 ha of error-adjusted forest loss area. For the 'probable loss' stratum, 1 of 90 samples was interpreted as having experienced forest cover loss. Due to the much larger size of this stratum, this one sample accounts for an estimated 224 635 ha of error-adjusted forest loss area, or fully 20% of terra firma primary forest cover loss. Without the use of the 'probable loss' stratum and the inclusion of this single sample of commission error, results would indicate a slight underestimate of terra firma forest cover loss. Validation studies should formally consider likely regions of false negatives of forest change in developing stratified sampling methods for error-adjusted area estimation. The validity of the sample-based estimate is a function of many factors, including the vagaries of any individual sample data set used in creating the error-adjusted estimates.
Estimates of carbon density derived using different methods can vary considerably within the same region (Houghton et al 2001), introducing uncertainty to the carbon loss estimation. However, recent published estimates of carbon loss from deforestation differ primarily due to major disagreements in the quantification of the areal extent of forest cover loss (Pan et al 2011, Harris et al 2012. The DRC gross AGC loss estimates from the current study (map-scale and sub-grid) are 2 to 3 times higher than the biomass carbon loss (total carbon, above-and belowground) estimate of Harris et al (2012) (table 8) (table 8). Harris et al (2012) reported a 90% carbon loss prediction interval for the DRC, based on a Monte Carlo approach: 16-32 Tg C yr −1 ; our current DRC gross AGC loss estimates, map-scale (53.3 Tg C yr −1 ) and sub-grid (72.1 Tg C yr −1 ), are not within this interval.
In our analysis, DRC gross forest AGC loss assessment consists only of stand-replacement forest disturbance that can be observed at the mapping scale and in reference data. However, forest degradation processes that do not lead to the complete loss of tree canopy or cause small-scale canopy openings, and can be detected only in the field or using dense series of sub-meter remotely sensed data may result in significant AGC loss at the national scale (IPCC 2003, Schoene et al 2007. One possible approach to assess the loss of biomass from these disturbances could be based on monitoring changes in the area of intact forest landscapes (Potapov et al 2008) and assigning an AGC loss value to the forests that have undergone the transition from intact primary to primary degraded and secondary forests (Margono et al 2012, Zhuravleva et al 2013. For countries such as the DRC, where large-scale agro-industrial forest disturbance is largely absent, the question of scale and its impact on AGC loss due to deforestation and degradation remains an important line of scientific inquiry. We employed GLAS-based AGC estimates as a proxy for the ground-based NFI data. There are some known issues and limitations concerning the estimation of biomass from GLAS metrics. For example, GLAS-estimated vegetation heights often used in AGC models have on average 2-3-m error when compared with USDA Forest Inventory and Analysis (FIA) and other field-measured heights (Pflugmacher et al 2008, Lefsky et al 2005, Sun et al 2008. GLAS-derived biomass estimates are also known to be affected by the season of data acquisition and terrain slope (Sun et al 2008). In total, GLAS-based AGC models explain from 73% (Lefsky et al 2005, Pflugmacher et al 2008 to 83% (current study; Baccini et al 2012) of the variance in field-estimated biomass. Regional forest inventory data are required to calibrate and validate the current forest type GLAS-based estimates. Additional field data collection could further refine the estimates but, unfortunately, GLAS observations are not available after 2009, posing a near-term challenge for improved AGC mapping and monitoring beyond the current models. As part of the process of establishing an NFI for the DRC continues, other sources of remotely sensed data characterizing vegetation vertical structure, such as airborne lidar or spaceborne radar data, can bridge the gap until systematic spaceborne lidar measurements become available to the scientific and REDD+ implementation communities.

Conclusion
We applied a method of error-adjustment of forest cover loss area to produce a national-scale gross forest AGC loss estimate for the DRC based on a published forest cover loss dataset. We employed field-calibrated GLAS lidar-derived biomass carbon densities as a substitute for NFI data, which do not exist for the territory of the DRC. Two realizations of the resulting DRC gross AGC loss estimate, map-scale and sub-grid, were produced. The sub-grid AGC loss estimate accounted for disturbances finer than the map grid scale of 60 m and was higher than published estimates, highlighting issues of scale and spatial averaging in AGC estimation. Omitted disturbances were largely related to smallholder agriculture land cover change, the detection of which is scaledependent. For the FACET product, the input Landsat imagery were averaged to 60 m and then classified, leading to the estimated scale-related omission error. Other processing steps can lead to change omission, either through the algorithm itself, for example image segmentation, post-processing of the output classification, or the application of a minimum mapping unit. In Brazil, where agro-industrial land conversion results in large forest disturbances, the Brazilian Space Agency's PRODES product 6.25 ha minimum mapping unit (the equivalent of approximately 69 Landsat pixels) (INPE 2012), provides a viable deforestation monitoring approach. However, a 6.25 ha minimum mapping unit for the DRC would omit the majority of change. For heterogeneous landscapes with change dynamics at or finer than the resolution of Landsat data, higher spatial resolution imagery to directly map such changes, or indirect methods to delimit degraded areas and subsequently relate to in situ measurements, are required.
Our study also illustrates the importance of reference forest state in assessing carbon dynamics, as with the primary, secondary and woodland forest types presented here. The Brazilian PRODES product, the current standard for national-scale forest monitoring, quantifies only the loss of primary forest in the Legal Amazon. While reducing primary humid tropical forest loss is the main focus of climate mitigation strategies such as REDD+, other forest types and even trees outside of forests will be part of national carbon accounting schemes. Our study underscored the importance of monitoring other forest dynamics, as we found AGC loss in secondary forests to be 140% that of primary forests. The reuse of secondary forests remains a challenge to carbon monitoring and the development of appropriate strategies for reducing emissions, but monitoring all relevant forest types and dynamics is required as national-scale programs are developed and implemented. REDD+ mechanisms will rely on accurate mapping and monitoring of AGC (Houghton et al 2010). However, scientific, technical and operational aspects of AGC mapping and monitoring are still in their infancy. Results from this study have significant implications for policy initiatives like REDD+. It is clear that the spatial scale of forest change characterization, reference information on forest type and carbon stock, and sample representativeness, can all dramatically impact AGC loss estimation. For example, considering change at a 30 m validation scale, an extra 35% of AGC loss was estimated compared to the 60-m spatial scale; terra firma secondary forest cover loss accounted for 40% more AGC loss than that of terra firma primary forest loss; a single validation sample added 20% to map-scale terra firma primary forest cover loss area. The volatility of results within this study indicates the DRC to be a challenging environment for quantifying changes to forest carbon stocks, with implications for other countries as well. Eventual national monitoring systems will need to demonstrate spatio-temporal consistency given the various factors that impact AGC loss estimation. While absolute accuracies may differ due to some of the aforementioned factors, relative consistency for any particular set of observations and spatial scale should be achievable and implementable. Demonstrating such consistency will be a proof of readiness for REDD+ monitoring.