# Fire enhances forest degradation within forest edge zones in Africa

Zhe Zhao, Wei Li, Philippe Ciais, Maurizio Santoro, Oliver Cartus, Shushi Peng, Yi Yin, Chao Yue, Hui Yang, Le Yu, et al.

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Zhe Zhao, Wei Li, Philippe Ciais, Maurizio Santoro, Oliver Cartus, et al. Fire enhances forest degradation within forest edge zones in Africa. Nature Geoscience, 2021, 10.1038/s41561-021-00763-8. [https://doi.org/10.1038/s41561-021-00763-8](https://doi.org/10.1038/s41561-021-00763-8)

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# Fire enhances forest degradation within forest edge zones in Africa

Zhe Zhao<sup>1</sup>, Wei Li<sup>1,2</sup>✉, Philippe Ciais<sup>1,3,4</sup>, Maurizio Santoro<sup>1,5</sup>, Oliver Cartus<sup>5</sup>, Shushi Peng<sup>6</sup>, Yi Yin<sup>1,7</sup>, Chao Yue<sup>8</sup>, Hui Yang<sup>3</sup>, Le Yu<sup>1</sup>, Lei Zhu<sup>1</sup> and Jingmeng Wang<sup>1</sup>

African forests suffer from severe fragmentation that further causes forest degradation near forest edges. The impact of fires used for slash-and-burn on forest edge effects remains unclear. Here, using high-resolution satellite-based forest-cover and biomass datasets, we find that edge effects extend a median distance and an interquartile range of 0.11<sup>+0.06</sup><sub>-0.04</sub> km and 0.15<sup>+0.09</sup><sub>-0.05</sub> km into moist and dry forests, and biomass within the forest edge zones has a carbon deficit of 4.1 PgC. Fires occurred in 52% of the forest edges and increased the carbon deficit by 5.5<sup>+4.3</sup><sub>-2.9</sub> MgC ha<sup>-1</sup>, compared with non-fire edges, through both the direct impact of fires intruding into forests and the indirect impact of changes in the local atmospheric circulations increasing canopy dryness. If small-scale slash-and-burn practices continue, increased fragmentation during 2010-2100 will result in a carbon loss from edge effects of 0.54-4.6 PgC. Fragmentation-caused forest degradation could be avoided by implementing dedicated forest protection policies supported by satellite monitoring of forest edges.

Tropical forests are the largest stores of biomass carbon in terrestrial ecosystems<fnref n="1" /> but are exposed to anthropogenic disturbances causing deforestation and degradation²⁻<fnref n="4" /> and, during dry years, to fires⁵. Estimates of carbon losses from land-use and land-cover change (LULCC) and forest degradation in the tropics remain uncertain due to a lack of large-scale direct observations and the coarse resolution of satellite data, which means that small-scale disturbances cannot be captured<fnref n="6" />. Such small-scale features are common as tropical forests are experiencing extensive and growing fragmentation caused by diverse human activities such as logging, road development, cattle ranching and small-scale farming, which leads to small and irregularly shaped forest patches, increasing the area of forest edges⁷⁻⁹. From field studies¹⁰⁻¹² and by using remote-sensing data with relatively coarse resolution<fnref n="6" />,¹³, biomass carbon has been found to be lower within the forest edge zones than in the forest interior (edge effects) due to desiccating conditions and enhanced wind turbulence¹⁴,¹⁰. However, this type of disturbance and the consequent carbon loss are difficult to detect accurately without high-resolution data and have not been accurately accounted for in the tropical carbon budget.

The African forest is one of the most productive and high-biomass-density ecosystems in the world, but it is threatened by growing timber demands¹⁵ due to fast population growth. The rural population of Africa is expected to increase by 36% by 2050¹<fnref n="6" />, and the expansion of settlements, agriculture and timber harvesting could encroach on the forested areas¹⁷. In the central Congo basin over the past few decades, LULCC has shifted from large-scale industrial deforestation to clearing by smallholders for farming¹⁸, leading to severe forest fragmentation. Natural and human-induced forest fires (for example, associated with slash-and-burn agricultural practices) also lead to deforestation and forest degradation in Africa¹⁹. Precipitation, soil moisture and evapotranspiration are

reduced in the vicinity of burnt areas, which slows forest recovery and may enhance edge-induced carbon loss in adjacent remaining forest patches²⁰. Understanding the relationship between forest fires and edge degradation is crucial for assessing carbon loss and formulating appropriate forest protection measures.

In this article, we combine high-resolution remote-sensing datasets of forest cover²¹ and forest aboveground biomass (AGB)²²,²³ with burned-area data²⁴ to estimate the forest edge effects at fire and non-fire edges in each 0.25° grid cell across Africa (Methods). Forests were divided into moist and dry forests using the Moderate Resolution Imaging Spectroradiometer (MODIS) land-cover map²⁵. Two indicators were used to characterize edge effects on AGB, scale and magnitude (Extended Data Fig. 1). The scale parameter (km) is defined as the distance to edge at which AGB equals 90% of that of the interior forest. The magnitude parameter (%) is the relative difference in AGB between the edge and the interior of forests. We then estimated carbon deficit within forest edge zones (defined as forests with a distance to edge smaller than the scale in each grid cell) across Africa. We use the term ‘carbon deficit’ to represent the differences in AGB between forest edges and interior forests because the present edges include both long-established edges and recently created ones. The long-established edges reflect an equilibrium state of carbon stocks and do not result in any additional carbon flux exchanged with the atmosphere, while the recently created edges result in carbon loss from forest degradation within the new forest edge zones and represent an elusive component of global LULCC emissions. We further distinguished forest edges that have experienced fires from other non-fire edges using burned-area data²⁴ and analysed the impact of fires on edge effects and possible mechanisms. Finally, we predicted the additional carbon loss due to the newly created edges according to future deforestation scenarios.

<footnote n="1">¹Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing, China. ²Joint Center for Global Change Studies, Beijing, China. ³Laboratoire des Sciences du Climat et de l'Environnement (LSCE), CEA CNRS UVSQ, Gif Sur Yvette, France.</footnote>

<footnote n="4">⁴Climate and Atmosphere Research Center (CARE-C), The Cyprus Institute, Nicosia, Cyprus. ⁵Gamma Remote Sensing, Gümligen, Switzerland.</footnote>

<footnote n="6">⁶Sino-French Institute for Earth System Science, College of Urban and Environmental Sciences, Peking University, Beijing, China. ⁷Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA. ⁸State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Northwest A&F University, Yangling, China. ⁹e-mail: wli2019@tsinghua.edu.cn</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1 | Scales and magnitudes of forest edge effects in Africa.** a,d, Frequency distributions of scales (a) and magnitudes (d). b,c,e,f, Maps of scales (b,c) and magnitudes (e,f) for moist forest (b,e) and dry forest (c,f). Shading in a and d indicates the weighted interquartile ranges, and dashed lines indicate weighted medians. Grey areas in b,c,e,f indicate grid cells without detected edge effects (27% and 18% of all grid cells for moist and dry forests, respectively).</figcaption></figure>

## Edge effects in Africa

The scales of edge effects for moist and dry forests are $0.11_{-0.04}^{+0.06}$ km (median and interquartile range weighted by forest area) and $0.15_{-0.05}^{+0.09}$ km, and their magnitudes are $36_{-9}^{+10}$% and $54_{-11}^{+12}$%, respectively. Edge effects show a significantly longer scale and greater magnitude in dry forests than in moist forests (Fig. 1a,d, P<0.01). We detected more grid cells with an edge effect in dry forests (grid-cell number = 12,673, 82% of dry forests) than in moist forests (9,473, 73% of moist forests). Both moist and dry forests surrounding the Congo basin show edge effects (Extended Data Fig. 2) with higher scales and magnitudes than in other areas (Fig. 1). Large edge effects were also found in the dry forests of regions along the Guinean gulf (Côte d'Ivoire, Ghana and Togo). In Madagascar, magnitudes are generally large while scales are relatively small, especially for dry forests. Overall, within the forest edge zones in Africa, representing 34% of the total forest area (defined as tree cover >25%), total present AGB carbon deficit is 4.06 PgC ($16.1_{-5.9}^{+8.0}$ MgC ha$^{-1}$, median and interquartile range weighted by area of edge zones) (Table 1), partitioned into 3.4 PgC in the dry forests ($15.4_{-5.4}^{+8.0}$ MgC ha$^{-1}$ over $1.8 \times 10^8$ ha covering 29% of the forest areas) and 0.66 PgC in the moist forests ($19.1_{-7.4}^{+7.9}$ MgC ha$^{-1}$ over $3.3 \times 10^7$ ha covering 5% of the forest areas).

Our estimated scales of edge effects are within the range of previous field observations$^{9,26}$ (<0.3 km) but much smaller than those obtained using coarser-resolution remote-sensing data (500 m)$^{6,13}$ (0.8–2.7 km) (Supplementary Discussion 1). To assess the impact of data resolution, we aggregated both the forest map and the biomass map from 30 m to 500 m and recalculated the edge scales (Supplementary Discussion 1). The derived scales are 1.2 km for both dry and moist forests, confirming the overestimation of scales using coarse resolution data. Our estimated total carbon deficit due to edge effects (4.06 PgC) is close to the estimate by Brinck et al.$^{27}$ (3.56 PgC) using a fixed edge penetration distance and carbon loss

<table><caption>**Table 1 | Carbon deficit from edge effects, fire-increased carbon deficit and area with edge effects**</caption><thead><tr><th></th><th>Moist forest</th><th>Dry forest</th><th>Total</th></tr></thead><tbody><tr><td>Carbon deficit (PgC)</td><td>0.66</td><td>3.4</td><td>4.06</td></tr><tr><td>Density of carbon deficit (MgC ha<sup>-1</sup>)</td><td>19.1</td><td>15.4</td><td>16.1</td></tr><tr><td>Fire-increased carbon deficit (PgC)</td><td>0.077</td><td>0.82</td><td>0.90</td></tr><tr><td>Density of fire-increased carbon deficit (MgC ha<sup>-1</sup>)</td><td>3.8</td><td>6.4</td><td>5.5</td></tr><tr><td>Area with edge effects (ha)</td><td>3.3 × 10<sup>7</sup></td><td>1.8 × 10<sup>8</sup></td><td>2.1 × 10<sup>8</sup></td></tr></tbody></table>

Note that carbon deficit from edge effects includes fire-increased carbon deficit. The weighted medians of density of carbon deficit and density of fire-increased carbon deficit are shown in the table.

fraction in the forest edge zones. Our estimated carbon deficit represents 31% of the total AGB carbon storage within the forest edge zones in Africa, which is higher than previous field studies have found in the Amazon$^{10}$ (average deficit of 8.8% within 100 m of the forest edges), possibly due to their short term of experiments (10–17 years), larger forest fragments and relatively higher carbon density in the interior forests (Supplementary Discussion 1).

## Fire impacts on edge effects

We defined forest edges with at least one fire event during 2004–2009 as fire-related edges. We found that the scales are higher in fire-related edges in most grid cells (Fig. 2a,b). Fires increase scales by $0.09_{-0.06}^{+0.14}$ km over 72% of forested grid cells in moist forests and by $0.06_{-0.03}^{+0.09}$ km over 63% of forested grid cells in dry forests. The patterns of fire impact on the magnitude parameter are similar
<figure><img src="image_4.png" /><figcaption>b. ΔScale, dry forest</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>c. ΔMagnitude, moist forest</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>d. ΔMagnitude, dry forest</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>e. Moist forest</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>f. Dry forest</figcaption></figure>

<figure><img src="image_9.png" /></figure>

ΔScale (km)

-0.50 -0.25 0 0.25 0.50

**Fig. 2 | Difference of forest edge effects at fire and non-fire edges for moist and dry forests and Δscale change with Δβ and fire distance.**

**a,b.** ΔScale (fire minus non-fire) for moist forest (a) and dry forest (b). **c,d.** ΔMagnitude for moist forest (c) and dry forest (d). **e,f.** ΔScale change with Δβ and fire distance for moist forest (e) and dry forest (f). The differences in edge effects (Δscale and Δmagnitude) are regarded as the fire impacts on edge effects. Numbers in **e** and **f** are the total number of 0.25° grid cells located in each Δβ and fire distance interval. Only grid cells with successfully fitted curves at both fire and non-fire edges and with available β at both fire and non-fire edges are shown.

to those observed for the scale of edges. Fires increase the magnitudes by $14^{+16}_{-8}\%$ and $10^{+8}_{-5}\%$ in 70% and 61% of the grid cells in moist and dry forests, respectively (Fig. 2c,d). Fires increase the carbon deficit arising from edge effects by 0.90 PgC ($5.5^{+4.3}_{-2.9} \text{ MgC ha}^{-1}$, median and interquartile range weighted by area of fire-related edge zones) at fire-related edges, accounting for 22% of the total carbon deficit (Table 1). Most of the fire-related increased carbon deficit occurs in dry forests (0.82 PgC, $6.4^{+4.4}_{-2.9} \text{ MgC ha}^{-1}$) rather than in moist forests (0.077 PgC, $3.8^{+3.2}_{-1.7} \text{ MgC ha}^{-1}$) (Table 1).

Two mechanisms relating to fire impact on edge effects were identified: direct fire intrusion into forests and indirect changes in local atmospheric circulations and canopy dryness. The first mechanism was studied through the distance that fires burn into a forest (fire distance) and the second through the difference in Bowen ratio ($\beta$) between fire and non-fire edges (Δ$\beta$), where $\beta$ is the ratio between sensible and latent heat fluxes$^{28,29}$ (Methods). The value of $\beta$ for different pixel types follows the order moist forest < dry forest < non-fire edge < fire edge, and the difference between fire and non-fire edges is significant at the 0.01 confidence level (Extended

Data Fig. 3). For moist forests, the partial correlation coefficients of Δscale with Δ$\beta$ and fire distance are similar (0.26 and 0.18, respectively, both $P<0.01$, Fig. 2e), indicating that fires influence the scale of edge effects through both direct and indirect impacts. For dry forests, although Δscale is significantly correlated with Δ$\beta$ and fire distance (both $P<0.01$), the partial correlation coefficient of Δscale with fire distance (0.39) is much higher than that of Δscale with Δ$\beta$ (0.04), indicating that the scale of edge effects is controlled more by direct impacts than by indirect impacts (Fig. 2f).

## Future carbon loss under different scenarios

Future deforestation will result in not only carbon emissions from forest loss but also additional carbon loss from forest degradation in newly created edge zones. We used forecasts of African deforestation areas in 2100 obtained from two representative concentration pathways (RCPs) (gross forest loss area = $1.2 \times 10^7 \text{ ha}$ and $9.7 \times 10^7 \text{ ha}$ in RCP 2.6 and RCP 8.5, respectively)$^{30}$ and designed four scenarios of forest pixel (30 m) loss in each 0.25° grid cell (Extended Data Fig. 4): (1) all pixels starting from current forest edges are deforested from the perimeter inwards until the target deforestation area is achieved, and thus new edges are created (S-1); (2) small forest patches are cleared first to minimize new forest edges (S-2); (3) pixels in the forest interiors are preferentially deforested (S-3); (4) pixels are deforested randomly, maximizing the area of new forest edges (S-4). The additional carbon loss from edge effects was estimated for each scenario by comparing present-day AGB with calculated AGB using the new distance to the edges in 2100, assuming AGB densities to be unchanged in the future (Methods).

The estimated carbon loss varies across the scenarios (Fig. 3). Under RCP 2.6, the total carbon losses (deforestation carbon emission + additional edge loss) are 1.8, 1.7, 2.1 and 4.1 PgC for S-1, S-2, S-3 and S-4 (moist + dry forests), accounting for 3.9–9.5% of the current forest biomass. The carbon losses from deforestation follow the order S-2 < S-1 < S-4 < S-3 for moist forests (dark grey bars in Fig. 3a), while there is little difference between the various scenarios for dry forests (light grey bars in Fig. 3a). Newly created edges induce an additional carbon loss from edge effects. In both moist and dry forests, the random deforestation scenario (S-4) leads to the highest additional carbon loss from edge effects (1.92 PgC, moist + dry forests, yellow bars in Fig. 3a), while the other three scenarios have lower carbon losses of 0.57, 0.54 and 0.57 PgC (S-1, S-2 and S-3, respectively).

The total carbon loss under RCP 8.5 is greater than that under RCP 2.6, due mainly to the larger deforestation area. The total carbon losses of deforestation and edge effects are 10.6, 10.6, 12.1 and 14.2 PgC for S-1, S-2, S-3 and S-4, respectively (Fig. 3b) under RCP 8.5, representing 24.5–32.8% of the current forest biomass. The ranking of carbon losses in the four scenarios is the same for RCP 8.5 and RCP 2.6. Additional carbon losses from edge effects are 0.84, 0.80, 0.97 and 3.14 PgC for S-1, S-2, S-3 and S-4, respectively.

We also calculated the additional carbon loss from edge effects in an extreme case where all edges would experience fires (Methods). Compared with the reference scenarios without fire occurrence (yellow bars in Fig. 3), this sensitivity test leads to 56–198% greater edge carbon losses (red bars in Fig. 3) in the moist forests and 30–70% larger losses in the dry forests.

## Implications and uncertainties

Edge effects are stronger in dry forests than in moist forests. Moist forests generally occur in regions with higher precipitation and soil moisture than regions where dry forests occur$^{31}$. Therefore, there are more fire-related edges in dry forests than in moist forests, together with more tree burning or tree mortality due to desiccating conditions (for example, higher vapour-pressure deficit). The percentages of forest edges experiencing fires are 24% for moist forests and 55% for dry forests. In addition, the edge scales of moist forests are controlled by both direct and indirect fire impacts, while the scales
<figure><img src="image_10.png" /><figcaption>**Fig. 3** | Future carbon loss due to forest edge effects and deforestation in different scenarios under RCP 2.6 and RCP 8.5. a, RCP 2.6. b, RCP 8.5. Dark colours indicate moist forests; light colours indicate dry forests. Note that the x-axis scales are different for the two plots.</figcaption></figure>

of dry forests are predominately attributed to direct fire impacts. A possible reason for this difference is that the evapotranspiration of dry forests is lower than that of moist forests³², making the moisture gradient between dry forests and edges smaller, resulting in less moisture loss due to local atmospheric circulations (Extended Data Fig. 5). Nevertheless, fires would enhance the forest edge effects and release more carbon to the atmosphere. In fact, fires are widely used in land management practices such as slash-and-burn agriculture³³. Our study shows that, regardless of the low cost and efficiency of this agricultural practice, it will lead to more-severe forest degradation. Therefore, slash-and-burn practices should be controlled in future land and fire management policy making.

In addition to fire, other disturbance types (for example, agriculture, construction and logging) may influence edge effects in Africa. We thus analysed the differences in edge effects across different disturbance types in the Congo basin³⁴. Forests with disturbances other than fire have smaller edge effects than forests without disturbances (Supplementary Discussion 2 and Supplementary Fig. 1), probably because the disturbances occurred during 2000–2010 and the edge forests did not reach the equilibrium. In fact, the edge effects are smaller for forests with edges created after 2000 than for those with edges created before 2000 (Supplementary Discussion 2 and Supplementary Table 1), implying a non-equilibrium state. The carbon deficit from edge effects in the forests with new edges thus may be underestimated. Some forests in Africa are already severely fragmented with a large number of small forest patches⁷. The overall impact of present fragmentation on edge effects is relatively small at the grid-cell level (Supplementary Discussion 2 and Supplementary Fig. 2). However, more activities such as mining, road building and small-scale farming in the future would cause severe damage to the intact forests and large carbon losses from edge effects (like S-3 and S-4).

The AGB map may present underestimates when AGB > 250 Mg ha⁻¹ (ref. ²²), which could impact our estimation of edge effects, especially for the moist forests with high biomass densities. In fact, moist- and dry-forest pixels (30 m × 30 m) with AGB > 250 Mg ha⁻¹ account for 32% and 3%, respectively, of all forest pixels in the grid cells where edge effects were detected (Extended Data Fig. 6). We thus corrected the AGB bias in these forest pixels on the basis of the field observation data (Extended Data Fig. 7) and then estimated the resultant edge effects. The corresponding scales are 0.13<sup>+0.07</sup><sub>-0.04</sub> km and 0.16<sup>+0.10</sup><sub>-0.06</sub> km for moist and dry forests, respectively, and the magnitudes are 47<sup>+11</sup><sub>-11</sub>% and 56<sup>+12</sup><sub>-11</sub>%, which are similar to the results based on the original data (0.11<sup>+0.06</sup><sub>-0.04</sub> km and 0.15<sup>+0.09</sup><sub>-0.05</sub> km, 36<sup>+10</sup><sub>-9</sub>% and 54<sup>+12</sup><sub>-11</sub>%), reflecting the small impacts of AGB underestimation on our results at the continental scale. Spatial variability of AGB may be large at a 30 m scale in mature forests even without disturbances³⁵. Indeed, the coefficient of variation of AGB in the interior forests is 34% and 37% for moist and dry forest, respectively (Supplementary Fig. 3). This natural variability may impact the edge-effect curve fitting, reflected by the relatively low R² (Supplementary Fig. 4). However, it may have limited impact on the estimation of edge area, which was determined by the distance to edge (rather than the AGB) of a large number of forest pixels on the basis of the scale in each 0.25° grid cell (Supplementary Discussion 3). The median of R² is 0.05 and 0.1, and the maximum R² is 0.8 and 0.71 for moist and dry forests, respectively. The relatively low R² is possibly caused by the large numbers of 30 m forest pixels in each grid cell (generally >1 × 10⁵) and the high natural variability of forest AGB³⁵. Similar to Chaplin-Kramer et al.⁶, we also found a higher value of R² in grid cells with larger edge effects (Supplementary Fig. 4).

There are also uncertainties in the forest-cover map (Supplementary Discussion 3). For example, a previous study found that the forest-cover data did not separate plantations from native forests and thus may overestimate forest areas and underestimate forest loss in regions with plantations³⁶. We thus calculated the edge effects separately for plantations and native forests in grid cells with plantations (Supplementary Fig. 5) using a planted-forest map³⁷. The edge effects for plantations are smaller than those for native forests (Supplementary Fig. 6 and Supplementary Discussion 3). The fire data used in this study is relatively coarse (250 m), which introduces uncertainties in the identification of fire edges and forest pixels with fire intrusion (Extended Data Fig. 8). Future products providing high-resolution time series of burned areas (for example, using Sentinel-2 Multi Spectral Instrument as input) will help improve fire pixel detection³⁸. In addition, we tested other edge-effect fitting models and found similar edge effects to the original model (Supplementary Discussion 3 and Supplementary Table 2).

Using high-resolution satellite data, we better captured the edge effects at the continental scale in Africa, which are consistent with the field observations. The analysis of fire impacts on edge effects also helps in understanding the mechanisms driving forest degradation in the forest edge zone, and fire will play an important role in determining the carbon loss through edge effects in future deforestation scenarios. Our study demonstrates that long-term, high-resolution datasets of land-cover, biomass, fire and climatic variables are important for accurately estimating forest degradation and monitoring forest dynamics and, hence, for supporting forest management and forest protection policy making. It is also important that dynamic global vegetation models implement forest edge effects to accurately simulate forest degradation and, thus, the terrestrial carbon cycle.

Online content

Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of
author contributions and competing interests; and statements of
data and code availability are available at https://doi.org/10.1038/
s41561-021-00763-8.

Received: 12 December 2020; Accepted: 11 May 2021;
Published online: 5 July 2021

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## Methods

**Edge effects estimation.** To quantify the AGB deficit in the edge zones of forests, we combined forest-cover maps (30 m) (ref. 21) and the full-resolution GlobBiomass AGB map (resampled from 25 m to 30 m) (ref. 22,23). Because the GlobBiomass estimates are representative of the year circa 2010, we overlaid this data on the corresponding forest map with a 25% tree-cover threshold from Hansen et al. 21. We used the latest version of the forest-cover and loss data of Hansen et al. 21 (v1.7).

We first calculated the distance to edge *d* in kilometres from the nearest non-forest 30 m pixel. Then, the pixel-level AGB (Mg ha⁻¹) was related to *d* across all pixels within the 0.25°×0.25° grid cells by fitting equation (1), following Chaplin-Kramer et al.⁶:

$$ \text{AGB} (d) = \theta_1 - \theta_2 e^{-d \theta_3} \quad (1) $$

Where $\theta_1$, $\theta_2$ and $\theta_3$ are fitted parameters. Each edge-effect curve thus represents an average relationship in each grid cell. Two indicators were used to characterize the scale and magnitude of edges (Extended Data Fig. 1). Scale (km) is the distance at which AGB equals a given percentage, *p* = 90%, of the asymptotic AGB in the interior forests. Magnitude (%) is the relative difference of AGB between the edges and the interior forest, with edge AGB being estimated for *d* = 0.015 km (half the pixel length) to avoid negative values in the intercept at *d* = 0 due to uncertainty in the fitting routine. Forest edge zone was defined as forest pixels (30 m × 30 m) with a distance to edge smaller than the scale from the fitted edge-effect curve in each 0.25° grid cell. We used only forest pixels with a distance to edge <5 km in the edge curve fitting since the observed edge-effect scale is much smaller (~100–300 m (refs. 9,26)); forest pixels with a distance >5 km contribute little to the estimates of scale and magnitude and were thus excluded from our analyses. Model fitting was performed using the nlsLM function in R.

We grouped forest pixels into moist and dry forests using MODIS land-cover maps (MCD12Q1 version 6, 500 m)²⁵. Moist forests comprise evergreen broadleaf forests, deciduous broadleaf forests and mixed forests, while dry forests comprise savannas and woody savannas. The edge-effect curve (EEC, equation (1), Extended Data Fig. 1) was fitted separately for moist and dry forests to avoid the fitting biases induced by the biomass gradient between these two forest types. We excluded grid cells with unrealistic results ($\theta_1$ > 1,000, $\theta_2$ < 0, $\theta_3$ < 0, AGB (0) < 0) and grid cells that failed to be fitted (no convergence within the maximum number of iterations, which was set as 100). As a result, 27% of the moist-forest grid cells and 18% of the dry-forest grid cells (mainly interior forests that do not have edge effects) were excluded.

We also aggregated the Hansen forest map and the GlobBiomass AGB map to 500 m, to test the impact of resolution on the edge effects, and compared our results with Chaplin-Kramer et al.⁶, who used the MODIS forest map (500 m) (ref. 25) and AGB data with a coarser resolution (500 m) (ref. 2). When aggregating the Hansen forest map, 500 m pixels with >50% 30 m Hansen forest pixels (tree cover >25%) were set as forest pixels. The GlobBiomass AGB map was aggregated by averaging 30 m GlobBiomass pixels in each 500 m pixel. The magnitude at *d* = 0.232 km (half pixel length) is calculated to compare with the magnitude from Chaplin-Kramer et al.⁶.

As a sensitivity test, we also used the AGB map over Africa (25 m) from Bouvet et al.³⁹ instead of the GlobBiomass map to calculate edge effects. We found that the scales were smaller, with values of 0.09⁻⁰.⁰⁰⁰⁷ km for moist forests and 0.10⁻⁰.⁰⁰⁰³ km for dry forests, because the approach used by Bouvet et al.³⁹ allows for estimating only AGB < 85 Mg ha⁻¹ and does not provide density in higher-biomass systems.

**Fire impacts on edge effects.** Fires that occur at forest edges generally intrude into forest patches. Here, we examined two possible mechanisms through which fire impacts forest edge effects on AGB. The first (direct) mechanism is that fire intrudes into forest patches and decreases carbon stocks by the burning of trees and understories (Extended Data Fig. 5). The second (indirect) mechanism is that nearby fire leads to a lower canopy moisture in the remaining forest fragments, in contrast to other disturbances leading to edges (Extended Data Fig. 5). Fire-related forest edges are generally hotter and drier and have a higher Bowen ratio ($\beta$), equation (1)) than non-fire edges. These conditions enhance the local atmospheric circulation, which draws down canopy moisture⁴⁰,⁴¹ and may also decrease precipitation in the forest patches and lead to higher tree mortality⁴².

Forest edges were separated into fire-related (Extended Data Fig. 5; anthropogenic and natural fires) and non-fire categories, the latter related to large-scale tree mortality or logging. We used forest pixels with fire-related edges as forests influenced by fires. We used the FireCCI burned-area dataset, based on MODIS data (250 m) (ref. 25), to identify fire edges for each 30 m pixel. Note that natural and anthropogenic fires were not separated in our analyses. Fire edges were defined as pixels that had at least one fire event during the period 2004–2009, and non-fire edges were defined as pixels that either had never had a fire or had already recovered from the last fire before 2004. As shown in Extended Data Fig. 8 and Supplementary Methods, forest pixels for moist forests in the same grid cell were separated into fire and non-fire edges (MF and MN) according to their nearest edge types. EEC was fitted separately for each edge type (EEC_MF and EEC_MN). Differences in the indicators (Δscale and Δmagnitude) derived from two EECs (EEC_MF and EEC_MN) were calculated. The same process was followed for dry

forests (separated into DF and DN). Only grid cells with successfully fitted curves for both fire- and non-fire-edge forests (57% of the total for moist forests and 70% for dry forests) were used in the analysis.

The fire distance was used as an indicator of the direct impact of fires on edge effects. The median of the distances that fire burns into forests of forest pixels with fire edges (MF and DF) was used for each 0.25° grid cell (Extended Data Fig. 8 and Supplementary Methods).

We used $\beta$ to reflect environmental conditions at the forest edges. $\beta$ is defined as the ratio of sensible heat (H, W m⁻²) and latent heat (LE, W m⁻², equation (2)):

$$ \beta = \frac{H}{LE} = \frac{R_n - LE - G}{LE} \quad (2) $$

H was calculated from the mass balance between surface net radiation ($R_n$, W m⁻²), LE and ground heat flux (G, W m⁻²) from satellite datasets. $R_n$ is from CERES EBAF 4.0 (1°, monthly)²⁸ and LE is from MOD16A2 (500 m, 8 days)²⁹. Because G is negligible over a long timescale, we simply used mean $R_n$ and LE during 2004–2009 to calculate $\beta$. We averaged $\beta$ values over fire and non-fire edges separately in the same 0.25° grid cell (Extended Data Fig. 8) and examined their difference. The difference ($\Delta\beta$, fire minus non-fire) was used as a proxy for the indirect impact of fires on edge effects.

Partial correlations of Δscale with Δ$\beta$ and fire distance were calculated to investigate the relative importance of direct and indirect impacts of fires on scales. Because magnitude reflects only the difference in biomass between forests near edges (0.015 km) and the forest interiors, magnitude is unrelated to fire distance. Fires at the edges may both increase $\beta$ and burn trees near the edges, so it is difficult to separate the direct and indirect impacts. As expected, the partial correlation coefficients of Δmagnitude with Δ$\beta$ and fire distance are very small (even negative) for fire distance (–0.05 and –0.03 for moist and dry forests, respectively). Therefore, we did not analyse the direct and indirect fire impacts on magnitude here.

**Carbon deficit due to edge effects.** To estimate the AGB deficit from edges, we assumed that forest pixels in the edge zones should have the same AGB as the interior forests in each grid cell if there were no edge effects. We used asymptotic AGB values from the fitted curve with $d \to \infty$ (equation (1) and Extended Data Fig. 1) as the AGB of the interior forests. The difference between interior AGB and actual AGB within the edge zones is the carbon deficit due to edge effects. We also tried AGB fitting by using equation (1), rather than the observed AGB for forest pixels in the forest edge zones, and the results showed no significant difference. AGB was converted from a dry matter unit (Mg) to a carbon unit (MgC) by multiplying by a factor of 0.5.

For a forest pixel with a fire edge, the corresponding assumed non-fire AGB is calculated using its distance to edge (*d*) and the fitted EEC for non-fire edge in the same 0.25° grid cell. The difference between observed AGB and non-fire AGB is defined as the fire-increased carbon deficit. If an EEC for fire edge is successfully fitted in one grid cell but the EEC for a non-fire edge failed, we searched the nearest grid cell with a successfully fitted EEC for a non-fire edge and used this curve to calculate the non-fire AGB. For grid cells with a failed fitted EEC for a fire edge, the fire-increased carbon deficit was set to 0.

**Future carbon loss due to forest edge effects.** The deforestation fraction between 2015 and 2100 for two RCPs (RCP 2.6 and RCP 8.5) was derived from the Land-Use Harmonization (LUH2 v2f) dataset (0.25°) (ref. 30). We focused only on grid cells with forest loss. To match the deforestation fraction in each grid cell, we created four scenarios (Extended Data Fig. 4): (1) pixels in the forest edge zones are deforested from the outer edge inwards until the target deforestation area is achieved, and thus new edges created (S-1); (2) small forest patches are cleared first, to minimize the creation of new forest edges (S-2), and if the area of small patches cannot satisfy the target deforestation area, forests in the edge zones are cleared as in S-1; (3) pixels of interior forest (with largest *d*) are deforested first (S-3); (4) pixels are deforested randomly to maximize newly created forest edges (S-4). S-4 is the ideal scenario only for sensitivity analysis. For each scenario, we calculated carbon loss from deforestation using present-day (2010) observed AGB in the deforestation pixels. The carbon loss from edge effects, due to the newly created edges, for each remaining forest pixel was estimated by comparing the present-day observed AGB with the calculated AGB from EEC using the new distance *d* in 2100. We assumed two extreme cases for new edges: all experiencing fires or none experiencing fires. Therefore, both fire and non-fire EEC were used. The fire-increased carbon loss is the difference between the results obtained from using the fire EEC and results from using the non-fire EEC.

## Data availability

The 30 m forest-cover map (v1.7) from Hansen et al.²¹ can be downloaded from https://earthenginepartners.appspot.com/science-2013-global-forest/download_v1.7.html. The 25 m full-resolution GlobBiomass map for Africa from Santoro et al.²³ can be downloaded from https://zenodo.org/record/4725667. The global and official 100 m GlobBiomass map²² can be downloaded from http://globbiomass.org/products/global-mapping or https://doi.pangaea.de/10.1594/PANGAEA.894711.
The fire data from FireCCI²⁴ can be downloaded from https://doi.org/10.5285/58f00d8814064b79a0c49662ad3af537. Source data are provided with this paper.

## Code availability

All additional computer codes are available from the corresponding author on request.

## References

39. Bouvet, A. et al. An above-ground biomass map of African savannas and woodlands at 25 m resolution derived from ALOS PALSAR. *Remote Sens. Environ.* **206**, 156–173 (2018).

40. Laurance, S. G. W. Responses of understory rain forest birds to road edges in central Amazonia. *Ecol. Appl.* **14**, 1344–1357 (2004).

41. Cochrane, M. A. & Laurance, W. F. Synergisms among fire, land use, and climate change in the Amazon. *AMBIO* **37**, 522–527 (2008).

42. Khanna, J., Medvigy, D., Fueglistaler, S. & Walko, R. Regional dry-season climate changes due to three decades of Amazonian deforestation. *Nat. Clim. Change* **7**, 200–204 (2017).

43. Brienen, R. J. W. et al. Long-term decline of the Amazon carbon sink. *Nature* **519**, 344–348 (2015).

## Acknowledgements

This study was supported by the National Key R&D Program of China (no. 2019YFA0606604, to W.L.). The authors also acknowledge funding from the ANR CLAND Convergence Institute (16-CONV-0003, to P.C.), the European Space Agency (ESA) within the CCI Biomass project (contract 4000123662/18/I-NB, to P.C.), the

National Natural Science Foundation of China (grant no. 41971132 and grant no. U20A2090, to C.Y.), the Strategic Priority Research Program of Chinese Academy of Sciences (grant no. XDB40020305, to C.Y.) and the National Key Scientific and Technological Infrastructure project 'Earth System Science Numerical Simulator Facility' (EarthLab, to L.Y.). The global AGB dataset was generated as part of the European Space Agency (ESA) Data User Element (DUE) GlobBiomass project (ESRIN contract no. 4000113100/14/I-NB).

## Author contributions

W.L. designed the research. Z.Z. performed analysis. M.S. and O.C. processed the biomass map data. Z.Z. and W.L. drafted the paper. All authors contributed to the interpretation of the results and to the text.

## Competing interests

The authors declare no competing interests.

## Additional information

**Extended data** is available for this paper at https://doi.org/10.1038/s41561-021-00763-8.

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s41561-021-00763-8.

**Correspondence and requests for materials** should be addressed to W.L.

**Peer review information** *Nature Geoscience* thanks Rico Fischer and other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Xujia Jiang.

**Reprints and permissions information** is available at www.nature.com/reprints.
<figure><img src="image_11.png" /></figure>

**Extended Data Fig. 1** | Schematic of edge effects characterization. Scale of the edge effects is the distance (km) where the biomass equals *p* % of the estimated biomass of interior forest (*p*=90 in this study). Magnitude is the difference (%) of biomass between interior forest and forest edge. We used *d* km away from the edge in practice to avoid negatives due to bad fittings. *d*=0.015 km is used in this study and *d*=0.232 km is used for the comparison with Chaplin-Kramer et al. (Supplementary Discussion 1).
a Moist forest

<figure><img src="image_12.png" /></figure>

b Dry forest

<figure><img src="image_13.png" /></figure>

c Frequency distribution

<figure><img src="image_14.png" /></figure>

**Extended Data Fig. 2** | Average tree cover of all forest pixels in each grid cell. Shading in (c) indicates the interquartile ranges, and dashed lines indicate medians.
<figure><img src="image_15.png" /></figure>

**Extended Data Fig. 3** | Frequency distributions of Δβ and β for different types of pixels across Africa. a, Δβ is calculated as β at fire edge minus β at non-fire edge. b, β for different types of pixels (moist forest, dry forest, fire edge, non-fire edge). Shading in (a) indicates the weighted interquartile range, and the dashed line indicates the weighted median. Δβ > 0 was found in 66% of the grid cells. The order of β for different pixel types is: moist forest < dry forest < non-fire edge < fire edge.
<figure><img src="image_16.png" /></figure>

**Extended Data Fig. 4** | Different scenarios of forest pixel (30 m) loss during the period 2010-2100. Deforestation fraction between 2015 and 2100 for RCP2.6 and RCP8.5, derived from LUH2 v2f (0.25°), was used as an approximation to deforestation fraction between 2010 and 2100 for each grid cell. We only focused on grid cells with forest loss, and the gross forest loss area in Africa is the sum of the forest loss areas of these grid cells. We created four scenarios to match the deforestation fraction in each grid cell: (1) all pixels starting from current forest edges are deforested from the outer edge inwards until the target deforestation area is achieved, and thus new edges are created (S-1); (2) small forest patches are cleared first to minimize new forest edges (S-2); (3) pixels in the interior of forest are preferentially deforested (S-3); (4) pixels are deforested randomly, maximizing the area of new forest edges (S-4).
<figure><img src="image_17.png" /></figure>

**Extended Data Fig. 5** | Local circulation that draws moisture from the forest edge zone to the edge. The Schematic is adapted from Laurance *et al.* (2011)¹⁴. Edge effects result from local circulations that draw down moisture due to the gradient of *β* between forest edges and nearby forest patches. Fire-related edges have even higher *β* than non-fire edges, which enhances local circulations and edge effects. Two possible ways of fire influencing edge effects were defined: direct impact, i.e. direct burning of trees and understories, and indirect impact, i.e., fire-enhanced *β* at fire-edges compared to non-fire edges. The frequency distributions of *β* in the forest edge zone and at different edges are shown in Fig. E3.
<figure><img src="image_18.png" /><figcaption>b Dry forests</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>c Moist forests</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>d Dry forests</figcaption></figure>

<figure><img src="image_21.png" /></figure>

**Extended Data Fig. 6** | Fraction of forest pixels with AGB > 250 Mg ha⁻¹. **a–b**, Frequency distributions of forest pixel (30 m × 30 m) AGB. Only 0.25° grids where edge effects were successfully detected were used. **c–d**, The fraction of forest pixels with AGB > 250 Mg ha⁻¹ in each 0.25° grids where edge effects were successfully detected. Shading area in (**a**) and (**b**) indicates the interquartile ranges, and dashed lines indicate the medians.
<figure><img src="image_22.png" /></figure>

**Extended Data Fig. 7** | AGB bias of the GlobBiomass map at different AGB levels. Data of the solid line is from Supplementary Fig. S8 in Santoro *et al.* (2020)$^{22}$, and data of the dots is based on field observations in the Amazon from Bienen *et al.* (2015)$^{43}$. The field plot data in the Amazon were aggregated at each interval of 5 Mg ha$^{-1}$, and the dots and error bars indicate means and standard deviations of GlobBiomass AGB in each 5 Mg ha$^{-1}$ intervals.
<figure><img src="image_23.png" /></figure>

nonfire edge

fire edge

Forests with nonfire edge (MN, DN)

Forest with fire edge but no fire intrusion (MF_N, DF_N)

Forest with fire edge and fire intrusion (MF_F, DF_F)

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>

**Extended Data Fig. 8** | Schematic of different types of forests and edges. Hierarchical structure of pixels is described in Supplementary Methods. β values were averaged over fire- and non-fire edges separately in the same 0.25° grid cell, and Δβ (fire minus non-fire) was used as indicator of indirect fire impact on edge effects. The fire distance was used as an indicator of the direct impact of fires on edge effects. The median distance that fire burns into forests of forest pixels with fire edges (MF and DF) was used for each 0.25° grid cell.