.. _carbonstorage:

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Carbon Storage and Sequestration
********************************

Summary
=======

Terrestrial ecosystems, which store more carbon than the atmosphere, are vital to influencing carbon dioxide-driven climate change. The InVEST Carbon Storage and Sequestration model uses maps of land use along with stocks in four carbon pools (aboveground biomass, belowground biomass, soil, and dead organic matter) to estimate the amount of carbon stored in a landscape at baseline or the amount of carbon sequestered over time. Optionally, the market or social value of sequestered carbon, its annual rate of change, and a discount rate can be used to estimate the value of this ecosystem service to society. Limitations of the model include an oversimplified carbon cycle, an assumed linear change in carbon sequestration over time, and potentially inaccurate discounting rates.

.. note:: This carbon model is extremely simple. Its only inputs are four carbon pools and a land cover map. It provides a convenient way to map those carbon pool values to a land cover map, but DOES NOT include any biophysical complexities or dynamics like growing trees, evolving soil chemistry or incorporating the effects of changing temperature or precipitation over time. If you need to model anything more complex than static carbon pools and land cover maps, you will need to use a different carbon model.

Introduction
============

Ecosystems regulate Earth's climate by adding and removing greenhouse gases (GHGs) such as CO\ :sub:`2` from the atmosphere. Forests, grasslands, peat swamps, and other terrestrial ecosystems collectively *store* much more carbon than does the atmosphere (Lal 2002). By storing this carbon in wood, other biomass, and soil, ecosystems keep CO\ :sub:`2` out of the atmosphere, where it would contribute to climate change. Beyond just storing carbon, many systems also continue to accumulate it in plants and soil over time, thereby "sequestering" additional carbon each year. Disturbing these systems with fire, disease, or vegetation conversion (e.g., land use/land cover (LULC) conversion) can release large amounts of CO\ :sub:`2`. Other management changes, like forest restoration or alternative agricultural practices, can lead to the storage of large amounts of CO\ :sub:`2`. Therefore, the ways in which we manage terrestrial ecosystems are critical to regulating our climate.

Terrestrial-based carbon sequestration and storage is perhaps the most widely recognized of all ecosystem services (Stern 2007, IPCC 2006, Canadell and Raupach 2008, Capoor and Ambrosi 2008, Hamilton et al. 2008, Pagiola 2008). The social value of a sequestered ton of carbon is equal to the social damage avoided by not releasing the ton of carbon into the atmosphere (Tol 2005, Stern 2007). Calculations of social cost are complicated and controversial (see Weitzman 2007 and Nordhaus 2007b), but have resulted in value estimates that range from USD $9.55 to $84.55 per metric ton of CO\ :sub:`2` released into the atmosphere (Nordhaus 2007a and Stern 2007, respectively).

Managing landscapes for carbon storage and sequestration requires information about how much and where carbon is stored, how much carbon is sequestered or lost over time, and how shifts in land use affect the amount of carbon stored and sequestered over time. Since land managers must choose among sites for protection, harvest, or development, maps of carbon storage and sequestration are ideal for supporting decisions influencing these ecosystem services.

Such maps can support a range of decisions by governments, NGOs, and businesses. For example, governments can use them to identify opportunities to earn credits for reducing (carbon) emissions from deforestation and degradation (REDD). Knowing which parts of a landscape store the most carbon would help governments efficiently target incentives to landowners in exchange for forest conservation. Additionally, a conservation NGO may wish to invest in areas where high levels of biodiversity and carbon sequestration overlap (Nelson et al. 2008). A timber company may also want to maximize its returns from both timber production and REDD carbon credits (Plantinga and Birdsey 1994).

The Model
=========

Carbon storage on a land parcel largely depends on the sizes of four carbon pools: aboveground biomass, belowground biomass, soil, and dead organic matter. The InVEST Carbon Storage and Sequestration model aggregates the amount of carbon stored in these pools according to land use maps and classifications provided by the user. Aboveground biomass comprises all living plant material above the soil (e.g., bark, trunks, branches, leaves). Belowground biomass encompasses the living root systems of aboveground biomass. Soil organic matter is the organic component of soil, and represents the largest terrestrial carbon pool. Dead organic matter includes litter as well as lying and standing dead wood.

.. figure:: ./carbon_storage/CarbonStorage_carbon_pools.png

Figure 1. Four carbon pools included in the InVEST Carbon Storage model - Aboveground biomass, belowground biomass, soil and litter.

Using maps of LULC classes and the amount of carbon stored in carbon pools, this model estimates the net amount of carbon stored in a land parcel over time and the market value of the carbon sequestered in remaining stock. Limitations of the model include an oversimplified carbon cycle, an assumed linear change in carbon sequestration over time, and potentially inaccurate discounting rates. Biophysical conditions important for carbon sequestration such as photosynthesis rates and the presence of active soil organisms are also not included in the model.

How It Works
------------

The model maps carbon storage densities to LULC rasters which may include classess such as forest, pasture, or agricultural land. The model summarizes results into raster outputs of storage, sequestration, and value, as well as aggregate totals.

For each LULC type, the model requires an estimate of the amount of carbon in at least one of the four fundamental pools described above, given in metric tons per hectare (t/ha). If you have data for more than one pool, the modeled results will be more complete. The model simply applies these estimates to the LULC map to produce a map of carbon storage in the carbon pools included.

If you provide both a baseline and alternate LULC map, then the net change in carbon storage over time (sequestration and loss) and its social value can be calculated. To estimate this change in carbon sequestration over time, the model is simply applied to the baseline landscape and a real or projected alternate landscape, and the difference in storage is calculated, pixel by pixel.

Outputs of the model are expressed as metric tons (which is the same as megagrams) of carbon per hectare, and if desired, the value of sequestration in currency units per hectare. We strongly recommend using the social value of carbon sequestration if you are interested in expressing sequestration in monetary units. The social value of a sequestered ton of carbon is the social damage avoided by not releasing that ton of carbon into the atmosphere.

The valuation model estimates the economic value of sequestration and/or loss (not storage) as a function of the amount of carbon sequestered and/or lost, the monetary value of each unit of carbon, a monetary discount rate, and the change in the value of carbon sequestration over time. Thus, valuation can only be done in the carbon model if you have an alternate scenario. Valuation is applied to sequestration and/or loss, not storage, because market prices relate only to carbon sequestration or emissions. Discount rates are multipliers that typically reduce the value of carbon sequestration (or the cost of emissions) over time. The first type of discounting, the standard economic procedure of financial discounting, reflects the fact that people typically value immediate benefits more than future benefits due to uncertainty and assumed economic inflation over time. The second discount rate adjusts the social value of carbon sequestration or emissions over time. This value will change as the impact of carbon emissions on expected climate change-related damages changes. If we expect carbon sequestered today to have a greater impact on climate change mitigation than carbon sequestered in the future, this second discount rate should be positive. On the other hand, if we expect carbon sequestered today to have less of an impact on climate change mitigation than carbon sequestered in the future, this second discount rate should be negative.

The value of carbon sequestration over time for a given parcel *x* is:

.. math:: value\_seq_x=V\frac{s_x}{q-p}\sum^{q-p-1}_{t=0}\frac{1}{\left(1+\frac{r}{100}\right)^t\left(1+\frac{c}{100}\right)^t}
   :label: carbon_value

where

* :math:`V` is the price per metric ton of carbon

* :math:`s_x` is the amount of carbon, in metric tons, sequestered on parcel :math:`x`

* :math:`q` is the alternate year

* :math:`p` is the baseline year

* :math:`r` is the yearly market discount rate for the carbon price

* :math:`c` is the yearly rate of change in the price of carbon

Limitations and Simplifications
===============================

The model simplifies the carbon cycle which allows it to run with relatively little information, but also leads to important limitations. For example, the model assumes that none of the LULC types in the landscape are gaining or losing carbon over time. Instead it is assumed that all LULC types are at some fixed storage level equal to the average of measured storage levels within that LULC type. Under this assumption, the only changes in carbon storage over time are due to changes from one LULC type to another. Therefore, any pixel that does not change its LULC type will have a sequestration value of 0 over time. In reality, many areas are recovering from past land use or are undergoing natural succession. The problem can be addressed by dividing LULC types into age classes (essentially adding more LULC types), such as three ages of forest. Then, parcels can move from one age class to the other in scenarios and change their carbon storage values as a result.

A second limitation is that because the model relies on carbon storage estimates for each LULC type, the results are only as detailed and reliable as the LULC classification used and carbon pool values supplied. Carbon storage clearly differs among LULC types (e.g., tropical forest vs. open woodland), but often there can also be significant variation within an LULC type. For example, carbon storage within a "tropical moist forest" is affected by temperature, elevation, rainfall, and the number of years since a major disturbance (e.g., clear-cut or forest fire). The variety of carbon storage values within coarsely defined LULC types can be partly recovered by using an LULC classification system and related carbon pool table which stratifies coarsely defined LULC types with relevant environmental and management variables. For example, forest LULC types can be stratified by elevation, climate bands or time intervals since a major disturbance. Of course, this more detailed approach requires data describing the amount of carbon stored in each of the carbon pools for each of the finer LULC classes.

Another limitation of the model is that it does not capture carbon that moves from one pool to another. For example, if trees in a forest die due to disease, much of the carbon stored in aboveground biomass becomes carbon stored in other (dead) organic material. Also, when trees are harvested from a forest, branches, stems, bark, etc. are left as slash on the ground. The model assumes that the carbon in wood slash "instantly" enters the atmosphere.

Finally, while most sequestration follows a nonlinear path such that carbon is sequestered at a higher rate in the first few years and a lower rate in subsequent years, the model's valuation of carbon sequestration assumes a linear change in carbon storage over time. Due to discounting, the assumption of a constant rate of change will tend to undervalue sequestered carbon, as a nonlinear path of sequestration is more socially valuable than is a linear path (Figure 1).

.. figure:: ./carbon_storage/carbon_envelope.jpg
   :align: center
   :figwidth: 500px

*Figure 1: The model assumes a linear change in carbon storage (the solid line), while the actual path to the year "T"'s carbon storage level may be non-linear (like the dotted line). In this case "t" indicates the year of the baseline landscape and "T" the year of the alternate landscape. With positive discounting, the value of the modeled path (the solid line) is less valuable than the actual path. Therefore, if sequestration paths tend to follow the dotted line, the model will undervalue sequestered carbon.*

Data Needs
==========

.. note:: All spatial inputs must be in the same projected coordinate system and in linear meter units.

.. note:: If you are including an alternate LULC, this raster must have a pixel size that is *exactly the same* as the baseline LULC raster.

.. note:: All carbon data should be for elemental carbon, not CO\ :sub:`2`.

- :investspec:`carbon lulc_bas_path`

- :investspec:`carbon lulc_bas_year`

- :investspec:`carbon calc_sequestration`

- :investspec:`carbon lulc_alt_path`

- :investspec:`carbon lulc_alt_year`

- :investspec:`carbon carbon_pools_path` Values must be provided for all carbon pools, and for all LULC classes, none may be left blank. If information on some carbon pools is not available, pools can be estimated from other pools, or omitted by leaving all values for the pool equal to 0.
   Columns:

   - :investspec:`carbon carbon_pools_path.columns.lucode`
   - :investspec:`carbon carbon_pools_path.columns.c_above`
   - :investspec:`carbon carbon_pools_path.columns.c_below`
   - :investspec:`carbon carbon_pools_path.columns.c_soil`
   - :investspec:`carbon carbon_pools_path.columns.c_dead`

   *Example:* Hypothetical study with five LULC classes. Class 1 (Forest) contains the most carbon in all pools. In this example, carbon stored in above- and below-ground biomass differs strongly among land use classes, but carbon stored in soil varies less dramatically. Values are in metric tons/hectare (t/ha).

   ====== ================== ======= ======= ====== ======
   lucode LULC_name          C_above C_below C_soil C_dead
   ====== ================== ======= ======= ====== ======
   1      Forest              140     70      35     12
   2      Coffee              65      40      25     6
   3      Pasture/grass       15      35      30     4
   4      Shrub/undergrowth   30      30      30     13
   5      Open/urban          5       5       15     2
   ====== ================== ======= ======= ====== ======

- :investspec:`carbon do_valuation`

- :investspec:`carbon price_per_metric_ton_of_c` This is :math:`V` in equation :eq:`carbon_value`. Price given in currency (any currency) per metric ton of elemental carbon (not CO\ :sub:`2`). For applications interested in estimating the total value of carbon sequestration, we recommend value estimates based on damage costs associated with the release of an additional ton of carbon - the social cost of carbon (SCC). Stern (2007), Tol (2009), and Nordhaus (2007a) present estimates of SCC. For example, two SCC estimates we have used from Tol (2009) are $66 and $130 (in 2010 US dollars) (Polasky et al. 2010).

- :investspec:`carbon discount_rate` This is :math:`r` in equation :eq:`carbon_value`. One default value is 7% per year, which is one of the market discount rates recommended by the U.S. government for cost-benefit evaluation of environmental projects. However, this rate will depend on the country and landscape being evaluated, and should be selected based on local requirements. Philosophical arguments have been made for using a lower discount rate when modeling climate change related dynamics, which users may consider using. If the rate is set equal to 0% then monetary values are not discounted.

- :investspec:`carbon rate_change` This is :math:`c` in equation :eq:`carbon_value`. This adjusts the value of sequestered carbon as the impact of emissions on expected climate change-related damages changes over time.

  Setting this rate greater than 0% suggests that the societal value of carbon sequestered in the future is less than the value of carbon sequestered now. It has been widely argued that GHG emissions need to be curtailed immediately to avoid crossing a GHG atmospheric concentration threshold that would lead to a 3 degree Celsius or greater change in global average temperature by 2105. Some argue that such a temperature change would lead to major disruptions in economies across the world (Stern et al. 2006). Therefore, any mitigation in GHG emissions that occurs many years from now may have no effect on whether or not this crucial concentration threshold is passed. If this is the case, C sequestration in the far future would be relatively worthless and a carbon discount rate greater than zero is warranted.


Interpreting Results
====================

.. note:: As of InVEST 3.15.0, the raster results of the Carbon model are given as values *per hectare*.

* **[Workspace]** folder:

	* **Parameter log**: Each time the model is run, a text (.txt) file will be created in the Workspace. The file will list the parameter values and output messages for that run and will be named according to the service, the date and time. When contacting NatCap about errors in a model run, please include the parameter log.

	* **carbon_report_[Suffix].html:** A summary of a model run, including visualizations of key outputs, tables of calculated results, and information about model inputs. The report can be accessed in the Workbench or opened with any web browser. For an example, see the `Sample Carbon Report <https://storage.googleapis.com/releases.naturalcapitalproject.org/invest-reports/latest/carbon_report_willamette.html>`_, generated by running the Carbon model with the Carbon sample data.

	* **c_storage_bas_[Suffix].tif/c_storage_alt_[Suffix].tif**: Rasters showing the amount of carbon stored for the baseline and alternate scenarios. It is a sum of all of the carbon pools provided by the biophysical table. Units are metric tons per hectare.

	* **c_change_bas_alt_[Suffix].tif**: Raster showing the difference in carbon stored between the alternate landscape and the baseline landscape. The values are in metric tons per hectare. In this map some values may be negative and some positive. Positive values indicate sequestered carbon, negative values indicate carbon that was lost.

	* **npv_alt_[Suffix].tif**: Raster showing the economic value of carbon sequestered between the baseline and the alternate landscape dates. The units are in currency per hectare.

    * **raster_values_summary_[Suffix].csv**: CSV summarizing the total values, units, and filenames of the output rasters.

* **[Workspace]\\intermediate_outputs** folder:

	* **c_above_[Suffix].tif**: Raster of aboveground carbon values, mapped from the Carbon Pools table to the LULC. Units are metric tons per hectare.
	* **c_below_[Suffix].tif**: Raster of belowground carbon values, mapped from the Carbon Pools table to the LULC. Units are metric tons per hectare.
	* **c_dead_[Suffix].tif**: Raster of dead carbon values, mapped from the Carbon Pools table to the LULC. Units are metric tons per hectare.
	* **c_soil_[Suffix].tif**: Raster of soil carbon values, mapped from the Carbon Pools table to the LULC. Units are metric tons per hectare.

Appendix: Data Sources
======================

:ref:`Land Use/Land Cover <lulc>`
---------------------------------

:ref:`Carbon Pools <carbon_pools>`
----------------------------------

Carbon Price and Discount Rates
-------------------------------

Recent estimates suggest that the social cost of carbon (SCC), or the marginal damage associated with the release of an additional metric ton of C into the atmosphere, ranges from $32 per metric ton of C (Nordhaus 2007a) to $326 per metric ton of C (Stern 2007) in 2010 US dollars. The value of this damage can also be considered the monetary benefit of an avoided release. Tol (2009) provides a comprehensive survey of SCC estimates, reporting median values of $66 and $130 per metric ton in 2010 US dollars (values differ because of different assumptions regarding discounting of time). Other estimates can be found in Murphy et al. (2004), Stainforth et al. (2005), and Hope (2006).

An alternative method for measuring the cost of an emission of a metric ton of C is to set the cost equal to the least cost alternative for sequestering that ton. The next best alternative currently is to capture and store the C emitted from utility plants. According to Socolow (2005) and Socolow and Pacala (2007), the cost of this technology per metric ton captured and stored is approximately $100.

Finally, while we do not recommend this approach, market prices can be used to set the price of sequestered carbon. We do not recommend the use of market prices because they usually only apply to "additional" carbon sequestration; sequestration above and beyond some baseline sequestration rate. Further, carbon credit values from carbon markets are largely a function of various carbon credit market rules and regulations and do not necessarily reflect the benefit to society of a sequestered ton of carbon. Therefore, correct use of market prices would require estimating a baseline rate for the landscape of interest, mapping additional sequestration, and then determining which additional sequestration is eligible for credits according to market rules and regulations.

We discount the value of future payments for carbon sequestration to reflect society's preference for payments that occur sooner rather than later. The U.S. Office of Management and Budget recommends a 7% per annum market discount rate for US-based projects (OMB 1992). Discount rates vary for other parts of the world. Canada and New Zealand recommend 10% for their projects (Abusah and de Bruyn 2007). It is best to look for the recommended discount rate for your country.

Some economists believe that a market or consumption discount rate of 7% to 12% is too high when dealing with the climate change analysis. Because climate change has the potential to severely disrupt economies in the future, the preference of society to consume today at the expense of both climate stability in the future and future generations' economic opportunities is seen as unethical by some (Cline 1992, Stern 2007). According to this argument, analyses of the effects of climate change on society and policies designed to reduce climate change should use low discount rates to encourage greater GHG emission mitigation and therefore compensate for the potentially severe damages incurred by future generations (e.g., r = 0.014 in Stern (2007)). Recent government policies in several countries have supported the use of a very low discount rate for certain long-term projects (Abusah and de Bruyn 2007).

The carbon discount rate, which reflects the greater climatic impact of carbon sequestered immediately over carbon sequestered in the future, is discussed in Adams et al. (1999), Plantinga et al. (1999), Feng 2005, and Nelson et al. (2008).

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