Carbon storage and sequestration

How much carbon does a landscape hold, and how much would it lose if the forest at its edges became pasture? In this tutorial you will build InVEST's carbon model in Terraflux, node by node, on the landscape of Ribeirão Claro: first the carbon stored in 2020, pool by pool, then the change to a scenario of 2040, then the value of that change with a price and a discount rate. At the end you will know where the carbon is, which conversions lose most of it, how much the answer depends on the numbers in the table and on the discount rate, and what to report.

The idea#

Plants take carbon dioxide from the air and keep the carbon in their wood, roots and leaves; part of it moves into the litter, the dead wood and the soil. Land use decides how much stays: a hectare of mature tropical forest can hold well over a hundred tons of carbon in its trees alone, a hectare of pasture only a few, although its soil may still hold a lot. Converting one into the other sends the difference to the atmosphere; restoring the forest slowly takes it back. Carbon storage is the amount a landscape holds now; sequestration (in InVEST's sense) is the change of that amount between two maps.

InVEST's carbon model is the simplest of all its models, and that is its strength. It follows the bookkeeping of the IPCC's guidelines for national inventories (IPCC, 2006): every land use class has a typical carbon density, in tons of carbon per hectare, in each of four pools:

The densities are averages for a class: the model assumes that every hectare of "forest" holds the same carbon, whatever its age or its neighbours, and that a class neither gains nor loses carbon over time.

A cell of forest holds \(140 + 35 + 95 + 12 = 282\) t C / ha in this tutorial's table; the same cell as pasture holds \(3 + 6 + 60 + 0.5 = 69.5\). Clearing it loses \(212.5\) t C / ha, or \(212.5 \times 0.09 = 19.1\) tons of carbon for the cell, about 70 tons of CO₂ (multiply carbon by 44/12 = 3.67 to get CO₂).

What the change is worth#

A ton of carbon kept out of the atmosphere avoids damages: InVEST's guide (Natural Capital Alliance, 2026) recommends valuing it at the social cost of carbon, an estimate of those damages per additional ton emitted, rather than at a market price. The change between the two maps happens over the years between them; InVEST spreads it evenly over those years and discounts each year's share to the present.

With a price of 50 per ton, \(r = 5\), \(c = 0\) and \(n = 20\) years (2020 to 2040), the factor \(\frac{P}{n}\sum\dots\) is \(2.5 \times 13.085 = 32.71\): the cleared cell above is worth \(-212.5 \times 32.71 = -6\,952\) per hectare.

When to use it#

• Scenarios of land use: the carbon a development plan would emit, the carbon a restoration plan would recover, as tons and as money.
• Carbon beside other services and species. Nelson et al. (2008) modelled payments to the landowners of the Willamette Basin (Oregon): payments for carbon raised carbon sequestration but did little for the conservation of species, payments for species did not raise carbon, and no policy came close to what the landscape could provide for both.
• Mapping where carbon is, to prioritize protection or to check a REDD+ baseline with a simple, transparent method.

What it is not for: the model does not grow forests. A restored forest gets the density of its class at once, and an old forest and a young one hold the same carbon unless you give them different classes. It knows nothing of fire, harvest or the time soil carbon takes to change. For carbon from a continuous map (tree cover or canopy height instead of classes), use raster.calc; for the uncertainty of the densities, see Monte Carlo uncertainty.

What you need#

• A land use map (the baseline), projected in metres, with integer class codes. Here lulc_2020.tif of Ribeirão Claro (download: ribeirao-claro.zip).
• A table of carbon pools, a CSV file with the columns lucode, c_above, c_below, c_soil and c_dead, in tons of carbon per hectare (InVEST writes Mg C / ha: a megagram is a ton). Every class of the maps must have a row. Where do the numbers come from? Ideally from forest inventories and soil samples in your study area; otherwise from the IPCC's default values for your climate zone (IPCC, 2006) or from regional studies. The values used here are illustrative:

• A future land use map (optional), on the same grid: here lulc_2040.tif.
• For the valuation (optional): a price per ton of carbon, a discount rate, the change of the price, and the years of the two maps.

Build the model#

Step 1: the carbon stored#

format = "terraflux/1"

[[nodes]]
id = "lulc"
op = "raster.read"
params = { path = "lulc_2020.tif" }
note = "Baseline land use, 30 m, UTM 23S."

[[nodes]]
id = "pools"
op = "table.read"
params = { path = "carbon_pools.csv" }
note = "t C / ha in four pools, by class."

[[nodes]]
id = "carbon"
op = "services.carbon"
inputs = { lulc = "lulc.raster", pools = "pools.table" }

[[plots]]
id = "show"
title = "Carbon stored, t C / ha"
layers = [{ from = "carbon.storage" }]

The carbon node gives:

• storage: the carbon of each cell, t C / ha (InVEST's c_storage_bas);
• pools: a stack (several maps on one grid, each with a name) of the four pools, its layers named c_above, c_below, c_soil and c_dead;
• totals: a table of one row with the landscape's tons of carbon in the column baseline.

Cells with no land use have no carbon (no value), and are not counted.

Step 2: a future map#

Add a second raster.read with path = lulc_2040.tif and connect it to the input future. The node now also gives storage_future and pools_future (the same maps for 2040), change (2040 minus 2020, per hectare) and, in totals, the columns alternate (the tons of 2040) and change.

format = "terraflux/1"

[[nodes]]
id = "lulc"
op = "raster.read"
params = { path = "lulc_2020.tif" }

[[nodes]]
id = "future"
op = "raster.read"
params = { path = "lulc_2040.tif" }
note = "The scenario of 2040, same grid."

[[nodes]]
id = "pools"
op = "table.read"
params = { path = "carbon_pools.csv" }

[[nodes]]
id = "carbon"
op = "services.carbon"
inputs = { lulc = "lulc.raster", pools = "pools.table", future = "future.raster" }

[[plots]]
id = "show"
title = "Change, t C / ha"
layers = [{ from = "carbon.change" }]

Step 3: the value of the change#

Select the carbon node and fill five settings in the Node pane: price (50, in your currency per ton of carbon), discount_rate (5, percent per year), rate_change (0, percent per year), year (2020) and future_year (2040). The node now gives the map npv, the net present value of each hectare's change, and the column npv of totals. The valuation needs the future map, and the future year must come after the baseline year: otherwise the node stops and says why.

format = "terraflux/1"

[[nodes]]
id = "lulc"
op = "raster.read"
params = { path = "lulc_2020.tif" }

[[nodes]]
id = "future"
op = "raster.read"
params = { path = "lulc_2040.tif" }

[[nodes]]
id = "pools"
op = "table.read"
params = { path = "carbon_pools.csv" }

[[nodes]]
id = "carbon"
op = "services.carbon"
inputs = { lulc = "lulc.raster", pools = "pools.table", future = "future.raster" }
params = { price = 50, discount_rate = 5, rate_change = 0, year = 2020, future_year = 2040 }
note = "A price per ton of carbon, 5% a year, 20 years."

[[nodes]]
id = "totals"
op = "table.write"
inputs = { table = "carbon.totals" }
params = { path = "carbon_totals.csv" }

The same from the command line, with the model saved as carbon.toml in the folder of the data:

terraflux run carbon.toml --out results

Read the results#

Where the carbon is#

Enlarge

The map has only six values, one per class: it is the land use map seen through the table. All of its information is in the table and in the areas of the classes, which is why the totals by class are worth a look:

What the scenario changes#

2020

2040

Enlarge

The totals table holds the landscape's numbers:

Which conversions cause the loss? Cross the two land use maps with the change map:

This is the kind of table to report: it says which decisions matter. Here the riparian restoration does not compensate the clearing, because it restores a quarter of the area and every hectare restored gains about what a hectare cleared loses.

Settings that change the answer#

The discount rate#

The net present value depends strongly on the discount rate and on the change of the price. The chart below comes from running the full model with each pair of rates:

With no discounting and no change of the price, the value is simply the price times the change (50 times 112,020 t = 5.6 million). Every percent of discount rate lowers it. The choice is an ethical one (how much the future counts), so report the rate and show the answer for a few.

The numbers in the table#

The densities are the model's only parameters, and some are much more uncertain than others. Soil carbon under pasture, for example, varies widely with the age and management of the pasture. Move it from 40 to 95 t C / ha and watch what happens:

Enlarge

PlaySoil carbon of pasture (t C / ha)

Why does the change move the other way (more loss with more soil carbon in pasture)? Pasture both receives forest (where more soil carbon in pasture means a smaller loss) and gives way to cropland, the town, plantations and restored forest (where it means a larger loss or a smaller gain). In this scenario 532 ha of forest become pasture but 700 ha of pasture become something else, so the second effect wins. The general lesson: test the densities of the classes involved in the conversions, and expect storage and change to respond differently. To propagate the uncertainty of all the densities at once, run the model many times with values drawn from their ranges (Monte Carlo uncertainty).

Common pitfalls#

• Carbon or CO₂. InVEST's tables are in tons of carbon, and its price is per ton of carbon. Prices of the social cost of carbon are often per ton of CO₂: multiply them by 3.67 before using them as price.
• Biomass or carbon. Forest inventories often give dry biomass; carbon is roughly half of it (the IPCC's default carbon fraction is 0.47 for wood). Dividing or not makes a factor of two.
• Instant change. A forest restored in 2040 holds 282 t C / ha in this model, although real regrowth would take decades to get there. Make young forest its own class if the timing matters.
• Soil carbon changes slowly. The model moves the whole soil pool at once when a class changes; field data suggest soil carbon takes years to decades to settle.
• Cells without a value. A cell that is missing in either map has no change and no value, and is not counted: compare totals only over the cells both maps have.
• Years in the wrong order. future_year before year stops the model; equal years too (there is no time to spread the change over).

Going further#

• Habitat quality and rarity, the next part: the same landscape seen as habitat.
• Ecosystem service models: the ideas for the landscape and the series' models together.
• Monte Carlo uncertainty to carry the uncertainty of the densities into the totals.
• Several benefits and trade-offs for carbon beside biodiversity in a restoration plan.
• The operator's reference: services.carbon.

References#

• IPCC. (2006). 2006 IPCC Guidelines for National Greenhouse Gas Inventories, Volume 4: Agriculture, Forestry and Other Land Use (H. S. Eggleston, L. Buendia, K. Miwa, T. Ngara, & K. Tanabe, Eds.). Institute for Global Environmental Strategies.
• Natural Capital Alliance. (2026). InVEST 3.20.2 User's Guide: Carbon storage and sequestration. https://storage.googleapis.com/releases.naturalcapitalproject.org/invest-userguide/latest/en/carbonstorage.html
• Nelson, E., Polasky, S., Lewis, D. J., Plantinga, A. J., Lonsdorf, E., White, D., Bael, D., & Lawler, J. J. (2008). Efficiency of incentives to jointly increase carbon sequestration and species conservation on a landscape. Proceedings of the National Academy of Sciences, 105(28), 9471–9476. https://doi.org/10.1073/pnas.0706178105