# Forest Carbon Edge Effect

## Summary

The InVEST carbon edge effect model extends the approach of the InVEST carbon model to account for forest carbon stock degradation due to the creation of forest edges. It applies known relationships between carbon storage and distance from forest edge to calculate edge effects in carbon storage, and combines these estimates with carbon inventory data to construct the overall carbon map. The model for edge effects pertains to above-ground carbon only, because edge effects have not been documented for the other carbon pools (below-ground, soil and dead matter). For all other carbon pools, and for non-tropical forest classes, or if the model is run without edge effects, it follows the IPCC (2006) inventory approach to assigning carbon storage values by land cover class.

## Introduction

The effects of future land-use change on carbon storage or sequestration can be modeled by applying carbon storage estimates found in the literature for different habitat types to each habitat found in a landscape (e.g., Nelson et al. 2010). However, this approach assumes that all habitat is equivalent in its quality of carbon storage, regardless of where it occurs, despite the fact that there is substantial evidence that fragmentation can play a dramatic role in altering carbon storage and sequestration rates in tropical forests (Broadbent et al. 2008, Dantas et al 2011, Laurance et al. 1997, 2000, 2001, 2002). For example, core forest has been shown to store more than three times the carbon of edge forest in Brazilian Atlantic forests (Dantas et al. 2011). Chaplin-Kramer et al. (2015) investigated this pattern for the entire pantropics using remotely sensed data on biomass (Baccini et al 2012) and associated land cover (Friedl et al. 2011) and found a continuous relationship of carbon storage degrading gradually toward a forest edge, which varies substantially from region to region. This model accounts for these documented edge effects in tropical forests, assigning carbon storage based on the distance of a pixel to the nearest forest edge. This can improve the overall accuracy of carbon storage estimates by 20% relative to forest inventory approaches, and better captures the impacts of forest degradation from fragmentation, beyond merely the area of habitat lost.

## The Model

The InVEST carbon edge effect model is an update to the InVEST carbon model, which incorporates the degradation of carbon storage that occurs due to edge effects in tropical forests. The user designates which land cover classes are forest, and then the model uses pre-generated regression results to predict the carbon throughout a forest parcel based on its distance to the nearest forest edge. These results are combined with the carbon assigned to non-forest classes through traditional inventory methods (IPCC 2006) used in the InVEST carbon model, to generate a map of above-ground carbon storage for all land cover classes. The InVEST carbon edge effect model can be run to calculate only above ground carbon or all carbon pools, and it can be run with or without edge effects. It is important to note that the edge effects regression only pertains to above-ground carbon stocks because edge effects have only been detected for above-ground biomass. To include the other three carbon pools (below-ground, soil, and standing dead matter), carbon density (Mg/ha) should be included for each land cover class in the biophysical table.

Also note that the regression data does not cover all of the Earth. It may be useful to make sure that it covers your area of interest by bringing the regression model layer forest_carbon_edge_regression_model_parameters.shp (found in this model’s sample data) into a GIS and checking it against your study area. If the regression data does not cover your study area, you cannot use the model to calculate edge effects.

### How it works

This model follows the methodology described in Chaplin-Kramer et al. (2015), which constructs a series of regression models between forest biomass density (Mg/ha) and distance from forest edge (km) for 100 km x 100 km grid cells throughout the pantropics. In grid cells where the majority of pixels were from forest biomes, three candidate regression models are considered to represent the relationship between biomass density and distance to forest edge:

1. Asymptotic: \(\mathrm{\text{Biomass}} = \theta_{1} - \theta_{2} \cdot \mathrm{\exp}( - \theta_{3} \cdot \mathrm{\text{Distance}})\)

2. Logarithmic: \(\mathrm{\text{Biomass}} = \theta_{1} + \theta_{2} \cdot ln(\mathrm{\text{Distance}})\)

3. Linear: \(\mathrm{\text{Biomass}} = \theta_{1} + \theta_{2} \cdot \mathrm{\text{Distance}}\)

Then, for each grid cell, the candidate with the highest r2 value is used to best represent the relationship between density and distance to forest edge. Models (2) and (3) were deemed as suitable (and more simplistic) alternatives in cells where higher distances were generally not observed and as a result the forest core was not firmly established. In the vast majority of grid cells, model (1) was optimal.

The results of these regressions can be found in the carbon edge regression parameter shapefile (core_data/forest_carbon_edge_regression_model_parameters.shp) in the sample dataset that is provided for the InVEST carbon edge effect model.

For any forest pixel within the study region, the model calculates the distance of that pixel from forest edge then calculates biomass to a predefined number of nearest regression models which is then aggregated to a single result using a distance linear interpolation scheme. The model then converts biomass to carbon with a user provided conversion factor, defaulted to 0.47 (IPCC 2006). The user can designate the number of local models used in the interpolation scheme which is defaulted to 10 but can range anywhere from 1 (only closest point) to 2313 (every regression model on the planet). Note that only those regression models that fall within 500km of the study area will be used, so the actual number of models averaged may be fewer. A selection of 1 may result in artificially large differences in carbon when moving from one pixel to the next where they fall in different regression grid cells. The higher the number of regression grid cells selected, the smoother the transition from one pixel to the next. The user may wish to select the number of grid cells overlapping the entire study region in order to eliminate any artifacts of model selection. This can be determined by examining the intermediate_outputs/local_carbon_shape.shp geometry overlaid on the area of interest. The linear interpolation scheme for biomass b on pixel p is given below:

\[b_{p} = \frac{\sum_{i \in n}\frac{1}{d_{i}}{b_{i}^{'}}_{}}{\sum\frac{1}{d_{i}}}\]

Where

- \(b_{p}\) is the interpolated biomass on pixel p

- n is the number of nearest models to interpolate from, a value provided by the user

- i is the ith nearest biomass model from pixel p

- di is the distance from pixel p to the centroid of the ith biomass model.

The carbon calculated for non-forest classes follows the methodology from the InVEST carbon model, assigning values based on forest carbon inventory data designated in the biophysical table. The carbon maps following this inventory approach and the edge effects approach are merged into the final carbon map, such that the forest land covers exhibit edge effects and all other land covers will not.

## Limitations and Simplifications

Edge effect data are only provided for tropical regions. To see if it overlaps your study area, bring the sample data layer core_data/forest_carbon_edge_regression_model_parameters.shp into a GIS. If the regression data does not cover your study area, you cannot use the model to calculate edge effects.

Edge effect data are only provided for above-ground carbon. If you want to include below-ground, soil or dead matter in the calculations, you can provide these data per land use class in the carbon pool table.

The default edge effect data that are provided with the model are pre-generated, and have a resolution of 100 km x 100 km. If you want to use different edge effect data, or a different resolution, you will need to create these data yourself, outside of the model.

## Data Needs

Note that all spatial inputs must be in the same projected coordinate system and in linear meter units.

- workspace (directory, required): The folder where all the model’s output files will be written. If this folder does not exist, it will be created. If data already exists in the folder, it will be overwritten.

- file suffix (text, optional): Suffix that will be appended to all output file names. Useful to differentiate between model runs.

- land use/land cover (raster, required): Map of land use/land cover codes. Each land use/land cover type must be assigned a unique integer code. All values in this raster must have corresponding entries in the Biophysical Table.

- biophysical table (CSV, required): A table mapping each LULC code from the LULC map to biophysical data for that LULC class.

  > Columns:

  > - lucode (integer, required): LULC codes from the LULC raster. Each code must be a unique integer.

  > - is_tropical_forest (true/false): Enter 1 if the LULC class is tropical forest, 0 if it is not tropical forest.

  > - c_above (number, units: t/ha, required): Carbon density value for the aboveground carbon pool.

  > - c_below (number, units: t/ha, conditionally required): Carbon density value for the belowground carbon pool. Required if calculating all pools.

  > - c_soil (number, units: t/ha, conditionally required): Carbon density value for the soil carbon pool. Required if calculating all pools.

  > - c_dead (number, units: t/ha, conditionally required): Carbon density value for the dead matter carbon pool. Required if calculating all pools.

  > Example Biophysical Table (data for Brazil):

  > lucode | is_tropical_forest | c_above | c_below | c_soil | c_dead | Description
  > --- | --- | --- | --- | --- | --- | ---
  > 0 | 0 | 0 | 0 | 0 | 0 | Water
  > 1 | 1 | n/a | 16.8 | 60 | 14.4 | Evergreen Needleleaf forest
  > 2 | 1 | n/a | 22.4 | 60 | 19.2 | Evergreen Broadleaf forest
  > 3 | 1 | n/a | 12.8 | 60 | 11 | Deciduous Needleleaf forest
  > 4 | 1 | n/a | 15.6 | 60 | 13.4 | Deciduous Broadleaf forest
  > 5 | 1 | n/a | 14.1 | 60 | 12.1 | Mixed Forest
  > 6 | 0 | 10.5 | 6.7 | 60.1 | 1.3 | Closed Shrublands
  > 7 | 0 | 4.5 | 7.3 | 65.5 | 1.1 | Open Shrublands
  > 8 | 0 | 20.1 | 23.6 | 151.4 | 2.6 | Woody Savannas
  > 9 | 0 | 4.4 | 7.1 | 211 | 1.5 | Savannas
  > 10 | 0 | 3 | 7.9 | 71 | 0.9 | Grasslands
  > 12 | 0 | 0.25 | 0.5 | 50.8 | 2.4 | Croplands
  > 13 | 0 | 0 | 0 | 0 | 0 | Urban and Built-up
  > 16 | 0 | 0 | 0 | 0 | 0 | Barren or sparsely vegetated

  > Sources for c_above data:

  > Closed shrublands, open shrublands, grasslands: Miranda, Sabrina do Couto, et al. Regional variations in biomass distribution in Brazilian savanna woodland. Biotropica 46.2 (2014): 125-138.

  > Woody savannas, savanna: Saatchi, Susan S., et al. Distribution of aboveground live biomass in the Amazon basin. Global Change Biology 13.4 (2007): 816-837.

  > Croplands: Fearnside, Philip M. Greenhouse gases from deforestation in Brazilian Amazonia: net committed emissions. Climatic Change 35.3 (1997): 321-360.

- carbon pools to calculate (option, required): Which carbon pools to consider.

  > Values must be one of the following text strings:

  > - ”aboveground only”: Only use the aboveground pool in the carbon pool calculation.

  > - ”all”: Use all pools (aboveground, belowground, soil, and dead matter) in the carbon pool calculation.

- compute forest edge effects (true/false): Account for forest edge effects on aboveground carbon.

  If selected, the model uses the Chaplin-Kramer et al. method to account for above ground carbon stocks in tropical forest types indicated by a ‘1’ in the ‘is_tropical_forest’ field in the biophysical table.

- global regression models (vector, polygon/multipolygon, conditionally required): Map storing the optimal regression model for each tropical subregion and the corresponding theta parameters for that regression equation. Default data is provided. Required if Compute Forest Edge Effects is selected.

  This input is provided in the sample data and need not be altered unless you have run a separate regression for your region and have better or updated information. The provided shapefile was derived from a pantropical analysis of the relationship between forest biomass and distance from forest edge (Chaplin-Kramer et al. 2015).

  > Note that the regression data does not cover all of the Earth. It may be useful to make sure that it covers your area of interest by bringing the regression model layer forest_carbon_edge_regression_model_parameters.shp (found in this model’s sample data) into a GIS and checking it against your study area. If the regression data does not cover your study area, you cannot use the model to calculate edge effects.

- number of points to average (integer, units: unitless, conditionally required): Number of closest regression models that are used when calculating the total biomass. Each local model is linearly weighted by distance such that the pixel’s biomass is a function of each of these points with the closest point having the largest effect. Must be greater than 0. Required if Compute Forest Edge Effects is selected.

  Default value is 10. Higher values smooth the variation in the edge effect detected in the different grid cells (seen in the carbon edge regression parameter shapefile) to a greater degree.

- forest edge biomass to carbon conversion factor (ratio, conditionally required): Proportion of forest edge biomass that is elemental carbon. Required if Compute Forest Edge Effects is selected.

  Default value is 0.47 (according to IPCC 2006). This pertains to the edge-effects regression parameters only; all values in the Biophysical Table should already be in terms of carbon, not biomass.

- area of interest (vector, polygon/multipolygon, optional): A map of areas over which to aggregate and summarize the final results.

  Note that the regression data does not cover all of the Earth. It may be useful to make sure that it covers your area of interest by bringing the regression model layer forest_carbon_edge_regression_model_parameters.shp (found in this model’s sample data) into the GIS and checking it against your study area. If the regression data does not cover your study area, you cannot use the model to calculate edge effects.

## Interpreting Results

Note

As of InVEST 3.15.0, the raster results of the Forest Carbon Edge Effect model are given as values per hectare.

### Final Results

- Parameter log. Each time the model is run, a text (.txt) file will appear in the Workspace. The file will list the parameter values for that run and will be named according to the service, date, and time. Please include the parameter log when contacting NatCap about errors in a model run.

- carbon_map_[Suffix].tif. A map of carbon stock, with the amount in forest derived from the regression based on distance to forest edge, and the amount in non-forest classes according to the biophysical table. Units are metric tons per hectare (t/ha).

- aggregated_carbon_stocks_[Suffix].shp: If service areas of interest are provided by the user, this output shapefile summarizes the total carbon (column c_sum) and mean carbon per hectare (column c_ha_mean) in the area defined by polygons. Values are in metric tons (t).

### Intermediate Results

- intermediate_outputs\c_above_carbon_stocks_[Suffix].tif.

    Carbon stored in the aboveground biomass carbon pool.

- intermediate_outputs\c_below_carbon_stocks_[Suffix].tif.

    Carbon stored in the belowground biomass carbon pool.

- intermediate_outputs\c_dead_carbon_stocks_[Suffix].tif. Carbon

    stored in the dead matter biomass carbon pool.

- intermediate_outputs\c_soil_carbon_stocks_[Suffix].tif. Carbon

    stored in the soil biomass carbon pool.

- intermediate_outputs\local_carbon_shape.shp. The regression

    parameters reprojected to match your study area.

- intermediate_outputs\edge_distance_[Suffix].tif. The distance

    of each forest pixel to the nearest forest edge

- intermediate_outputs\tropical_forest_edge_carbon_stocks_[Suffix].tif.

    A map of carbon in the forest only, according to the regression method

## Appendix: Data Sources

### Land Use/Land Cover

### Carbon Pools

## References

Baccini, A., S. J. Goetz, W. S. Walker, N. T. Laporte, M. Sun, D. Sulla-Menashe, J. Hackler, P. S. A. Beck, R. Dubayah, M. A. Friedl, S. Samanta, and R. A. Houghton. 2012. Estimated carbon dioxide emissions from tropical deforestation improved by carbon-density maps. Nature Climate Change 2:182–185.

Chaplin-Kramer, R., I. Ramler, R. Sharp, N. M. Haddad, J. S. Gerber, P. C. West, L. Mandle, P. Engstrom, A. Baccini, S. Sim, C. Mueller, and H. King. (2015). Degradation in carbon stocks near tropical forest edges. Nature Communications.

Dantas de Paula, M., Alves-Costa, C., Tabarelli, M., 2011. Carbon storage in a fragmented landscape of Atlantic forest: the role played by edge-affected habitats and emergent trees. Tropical Conservation Science 4, 349–358.

Friedl, M. A., D. Sulla-Menashe, B. Tan, A. Schneider, N. Ramankutty, A. Sibley, and X. Huang. 2010. MODIS Collection 5 global land cover: Algorithm refinements and characterization of new datasets. Remote Sensing of Environment 114:168–182.

Intergovernmental Panel on Climate Change (IPCC). 2006. IPCC Guidelines for National Greenhouse Gas Inventories. Volume 4: Agriculture, Forestry and Other Land Use.

Laurance, W. F., 1997. Biomass Collapse in Amazonian Forest Fragments. Science 278, 1117–1118.

Laurance, W.F., 2000. Do edge effects occur over large spatial scales? Trends in ecology & evolution 15, 134–135.

Laurance, William F., Williamson, G.B., 2001. Positive Feedbacks among Forest Fragmentation, Drought, and Climate Change in the Amazon. Conservation Biology 15, 1529–1535.

Laurance, W., Lovejoy, T., Vasconcelos, H., Bruna, E., Didham, R., Stouffer, P., Gascon, C., Bierregaard, R., Laurance, S., Sampaio, E., 2002. Ecosystem decay of Amazonian forest fragments: a 22-year investigation. Conservation Biology 16, 605–618.

Nelson, E., et al. 2010. Projecting global land-use change and its effect on ecosystem service provision and biodiversity with simple models. PLOS One 5: e14327