.. _coastal-blue-carbon:

*******************
Coastal Blue Carbon
*******************

Summary
=======

Marine and terrestrial ecosystems help regulate Earth's climate by adding and
removing greenhouse gases (GHGs) such as carbon dioxide (CO\ :sub:`2`) to and
from the atmosphere.  Coastal marshes, mangroves, and seagrasses, in
particular, store large amounts of carbon in their sediments, leaves, and other
forms of biomass.  In addition to storing carbon, marine ecosystems continually
accumulate carbon in their sediments, creating large reservoirs of long-term
sequestered carbon. By storing and sequestering carbon, marine ecosystems keep
CO\ :sub:`2` out of the atmosphere where it would otherwise contribute to
climate change.

Management activities that change the cover of coastal vegetation, such as the
restoration of seagrass beds and the clearing of mangrove forests, change the
ability of coastal and marine areas to store and sequester carbon.

The InVEST Coastal Blue Carbon model attempts to predict the amount of carbon
stored and sequestered over a coastal zone at particular points in time due to
changes in land cover. Using an estimate of the monetary social value, or where
available, a market price for stored and sequestered carbon, the InVEST Coastal
Blue Carbon model also quantifies the marginal value of storage and
sequestration.

Results of the InVEST Coastal Blue Carbon model can be used to compare current
and future scenarios of carbon stock and net sequestration, as well as identify
locations within the landscape where degradation of coastal ecosystems should
be avoided and restoration of coastal ecosystems should be prioritized in order
to preserve and enhance these carbon storage and sequestration services.

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

This model makes use of a variety of information, including:

- The distribution and abundance of coastal vegetation
- Habitat-specific carbon stock data
- Impact characteristics of various land-cover disturbances to biomass and soil
  carbon stock pools to predict carbon emission rates
- Carbon accumulation rates to estimate carbon stock, net sequestration and
  value across a land or seascape
- Estimates of the monetary social value or market price of carbon

To quantify the value of carbon storage and sequestration, the model focuses on
changes in atmospheric carbon dioxide and other greenhouse gases as a result of
changes caused by human activities that can affect marine ecosystems which
store and sequester carbon.  Changes to the composition of the atmosphere have
wide-ranging effects on natural systems that can result in changes to
agricultural productivity, air quality, sea levels, and more.

The Model
=========

Modeling Considerations
-----------------------

Mapping and modeling changes in carbon storage and sequestration for coastal
and marine habitats can present challenges.  The types of spatial inputs and
available information about the carbon cycle vary by location.  Some study
areas have high-quality data available for a detailed analysis while other
locations do not have the information necessary to model changes in the
position and function of coastal vegetation.  Salt marsh, for example, is often
studied in the context of migration due to sea-level rise.  The combination of
natural (e.g. sea-level rise) and anthropogenic (e.g. salt marsh migration
blocked by roads) factors should be included in scenario maps and subsequent
carbon modeling where possible.  When exploring future land cover scenarios,
land cover map outputs produced by the SLAMM model (Sea Level Affecting Marshes
Model, developed by Warren Pinnacle) can be useful inputs to the InVEST Coastal
Blue Carbon model (Clougheet et al. 2010).  However, because not all sites have
the detailed elevation and habitat information required to run SLAMM, this
InVEST model provides a flexible approach that allows users to provide either
detailed land use/land cover maps or maps indicating the presence of coastal
and marine vegetation that can sequester carbon.


How it Works
------------

InVEST Coastal Blue Carbon models the carbon cycle through a bookkeeping-type
approach (Houghton, 2003). This approach simplifies the carbon cycle by
accounting for storage in three main pools (biomass, sediment carbon (i.e.
soil), and standing dead carbon (i.e. litter) see Figure 1).  Accumulation of
carbon in coastal habitats occurs primarily in sediments (Pendleton et al.,
2012).  The model requires users to provide maps of coastal ecosystems that
store carbon, such as mangroves and seagrasses.  Users must also provide data
on the amount of carbon stored in the three carbon pools and the rate of annual
carbon accumulation in the biomass and sediments. If local information is not
available, users can draw upon the global database of values for carbon stocks
and accumulation rates sourced from the peer-reviewed literature that is
included in the model.  If data from field studies or other local sources are
available, these values should be used instead of those in the global database.
The model requires land cover maps, which represent changes in human use
patterns in coastal areas or changes to sea level, to estimate the amount of
carbon lost or gained over a specified period of time.  The model quantifies
carbon storage across the land or seascape by summing the carbon stored in
these three carbon pools.

.. figure:: ./coastal_blue_carbon/BlueCarbon_carbon_pools.png

Figure 1. Three carbon pools for marine ecosystems included in the InVEST blue carbon model - Biomass (aboveground + belowground), soil and litter.

.. note::
        Several parameters are shared across most of the equations in the model:

        * :math:`t` is the timestep.  This model operates on an annual timescale, so
          :math:`t` represents the year represented by the timestep.

          * :math:`t_{baseline}` represents the year of the baseline landcover.

        * :math:`s` is the snapshot year.  This represents the year of any of
          the transition snapshots after the baseline year.
        * :math:`p` represents the carbon pool, generally biomass or soil.  The litter
          pool is considered only in the carbon accumulation calculations and is not
          affected by emissions.

        The model considers each grid cell :math:`x` independently, and has therefore
        been factored out of the equations described below.

.. note::
        Although this user's guide chapter refers to units in Megatonnes of
        CO2-equivalent per hectare, the model does no conversion of units
        whatsoever, and so any units representing the habitat-specific rate of
        accumulation or emissions, so long as they are consistent across all
        model inputs, may be used.


Carbon Storage
^^^^^^^^^^^^^^

Coastal blue carbon habitats can simply indicate the dominant vegetation type
(e.g., eelgrass, mangrove, etc), or they can be based on details that affect
pool storage values such as plant species, vegetation density, temperature
regime, or vegetation age (e.g., time since restoration or last major
disturbance).

For the sake of the carbon storage estimation, each coastal blue carbon habitat
is assumed to be in storage equilibrium at any point in time (accumulation of
carbon will be accounted for in the sequestration component of the model).

Carbon stocks :math:`S` for a given year :math:`t` and pool :math:`p` are
calculated by adding the net carbon sequestration for year :math:`t` to the
stocks available in the prior year :math:`t-1`.  Or, alternatively, by using
the initial stock values from the biophysical table,
:math:`S_{p,t_{baseline}}`.

.. math::
        S_{p,t} = \begin{Bmatrix}
                S_{p,t-1} + N_{p,t} & if & t > t_{baseline} \\
                S_{p,t_{baseline}} & if & t = t_{baseline}
        \end{Bmatrix}
        :label: cbc_stocks_pool

The carbon stocks for year :math:`t` represent the carbon stocks at the very
beginning of year :math:`t`.

Net sequestration :math:`N_{p,t}` refers to the amount of carbon gained or lost
within year :math:`t`, and the state of the most recent transition determines
whether carbon is accumulating (positive net sequestration) or emitting
(negative net sequestration).  A single cell may *either* accumulate *or* emit
carbon; it is not possible to do both within a single timestep.  In this way,
the model assumes that a grid cell transitions completely from one habitat type
to another during a transition event.  The nature of sequestration
(accumulation or emission) will also remain consistent between
transition years on a given pixel.

Therefore, :math:`N_{p,t}` will be equal to one of these equations,
depending on the state of the most recent transition:

.. math::
        N_{p,t} = \begin{Bmatrix}
                -1 \cdot E_{p,t} & if & carbon\ is\ emitting \\
                A_{p,t} & if & carbon\ is\ accumulating
        \end{Bmatrix}
        :label: cbc_net_sequestration

The rate of accumulation :math:`A_{p,t}` is defined by the user in the
biophysical table for each landcover classification.  When a landcover class
transitions into an accumulation state, the rate of accumulation will reflect
the destination landcover class.

Note that emissions :math:`E_{p,t}` is calculated as a positive value, and the
:math:`-1` is needed to reflect a loss of carbon from the pool.

Note that the above only applies to the biomass and soil pools.  Litter stocks
are not subject to emissions, and so may only accumulate linearly according to
the rate defined by the user in the biophysical table:

.. math::
        S_{p_{litter},t} = S_{p_{litter},t_{baseline}} + (A_{p_{litter}} \cdot (t - t_{baseline}))
        :label: cbc_stocks_litter

Therefore, net sequestration for the litter pool, :math:`N_{p_{litter},t}` is
equivalent to :math:`A_{p_{litter}}`, which is defined by the user in the
biophysical table.  The rate of accumulation may change only when the landcover
class transitions to another class.

The model also calculates total stocks for each timestep year :math:`t`:

+ For the baseline year, total stock is simply the sum of all carbon stocks in all 3 pools, as defined by the user in the biohysical table:

.. math:: S_{t,total} = S_{t,p_{soil}} + S_{t,p_{biomass}} + S_{t,p_{litter}}
        :label: cbc_stocks_total_base_year

+ For each year between baseline+1 and the first snapshot transition, total stock is the stock from the previous year, plus accumulation:

.. math:: S_{t,total} = S_{t-1} + A_{t-1->t}
	:label: cbc_stocks_total_pre_snapshot

+ For years after the first snapshot transition, total stock is the stock from the previous year, plus accumulation during that year, minus emissions during that year caused by disturbance during the transition:

.. math:: S_{t,total} = S_{t-1} + A_{t-1->t} + E_{t-1->t}
	:label: cbc_stocks_total_post_snapshot

In practice, if accumulation or emission happens, for example, in the year 2030, they will start appearing in the carbon stock output in year 2031, not 2030, after there has been a year for carbon to be accumulated or emitted.

Carbon Accumulation
^^^^^^^^^^^^^^^^^^^

We model accumulation as the rate of carbon retained in the soil in organic
form after the first year of decomposition. In relation to the annual ecosystem
budget, this pool has not been remineralized, so it represents net
accumulation. This carbon is usually derived from belowground production, and
residence time can range from decades to millennia (Romero et al. 1994, Mateo
et al. 1997). This accumulation contributes to the development of carbon
"reservoirs" which are considered virtually permanent unless disturbed. Thus,
even in the absence of a land-use or land-cover change, carbon continues to be
sequestered naturally.

Loss of carbon from the soil pool (sediments) upon disturbance is more nuanced
than sequestration because different types of human uses and/or stasis may
cause varied disruption of the soils and the carbon stored below.  For example,
high impact activities such as the clearing of mangroves for a shrimp pond or
sediment dredging may result in a larger soil carbon disturbance than other
activities such as commercial fishing or oil exploration.  The impacts from
coastal development on carbon storage vary since some types of development may
involve paving over the soil, which often keeps a large percentage of the
carbon stored intact.  Alternatively, dredging could remove seagrasses and
disturb the sediments below, releasing carbon into the atmosphere.


Carbon Emissions
^^^^^^^^^^^^^^^^

When coastal ecosystems are degraded by human activities, the carbon stored in
the living plant material (above and below the ground) and the soil may be
emitted to the atmosphere. The magnitude of post-conversion CO\ :sub:`2`
release depends on the type of vegetation disturbed and the level of
disturbance. The type of disturbance will determine the amount of aboveground
biomass loss and depth to which the soil profile will be altered. The deeper
the effects of the disturbance, the more soil carbon that will be exposed to
oxygen, oxidized and consequently emitted in the form of CO\ :sub:`2`. Some
disturbances will only disturb the top soil layers while the deeper layers
remain inundated and their carbon intact.  Other disturbances may affect
several meters of the soil profile. To estimate the extent of the impact of
various disturbances, we classify disturbances into three categories of impact:
high, medium and low.  Examples of high impact disturbances include mangrove
conversion to shrimp farms and draining or diking salt marshes for conversion
to agriculture.  Low impact disturbance examples include recreational boating
or float home marinas.

Carbon emissions begin in a snapshot year where the landcover classification
underlying grid cell :math:`x` transitions into a state of low-, med-, or
high-impact disturbance.  In subsequent years, emissions continue until either
grid cell :math:`x` experiences another transition, or else the analysis year
is reached.  

The model uses an exponential decay function based on the user-defined
half-life :math:`H_{p}` of the carbon pool in question, as well as the volume of
disturbed carbon. In this case, :math:`s` represents the year of the transition, and
:math:`E_{p,t}` is the volume of carbon emitted from pool :math:`p` in year :math:`t`.

.. math:: E_{p,t} = D_{p,s} \cdot ({ 0.5 }^{ \frac { t-(s+1) }{ H_{p,s} } } - { 0.5 }^{ \frac { t-s }{ H_{p,s} } })
        :label: cbc_emissions

The volume of disturbed carbon :math:`D_{p,s}` represents the total volume of
carbon that will be released over time from the transition taking place on grid
cell :math:`x` in transition year :math:`s` as time :math:`t \rightarrow
\infty`.  This quantity is determined by the magnitude of the disturbance
:math:`M_{p,s}` (low- med- or high-impact), the stocks :math:`S` present at the
beginning of year :math:`s`, and the landcover transition undergone in year
:math:`s`:

.. math:: D_{p,s} = S_{p,s} \cdot M_{p,s}
        :label: cbc_disturbance_volume

The magnitude of the disturbance is determined by the transition matrix (low-,
med-, or high-impact), and specified as a percentage of carbon disturbed in the
Biophysical Table.  When a landcover classification undergoes a transition into
a state of emission, the disturbance magnitude will be taken from the source
landcover class.

Magnitude and Timing of Loss
""""""""""""""""""""""""""""

We model the release of carbon from the biomass and soil pools by estimating
the fraction of carbon lost from each pool's total stock at the time of
disturbance.  The fraction of carbon lost is determined by the original coastal
blue carbon habitat and the level of impact resulting from the disturbance (see
Table 1).

The InVEST Coastal Blue Carbon model allows users to provide details on the
level of disturbance that occurs during a transition from a coastal blue carbon
habitat to a non-coastal blue carbon habitat.  This information can be provided
to the model through a preprocessor tool and further clarified with an input
transition table.

In general, carbon stock pools emit carbon at different rates: most emissions
from the biomass pool take place within the first year, whereas emissions from
the soil pool may take much longer. The model assigns exponential decay
functions and half-life values to the biomass and soil carbon pools of each
habitat type (Table 1; Murray et al. 2011).

..
  This table is so annoying to edit by hand.  If you really need to edit by hand, find the widest monitor you can and make the text super small
  Also, FYI, the | | syntax allows for line breaks within a table cell.

+-----------------------------------+-----------------------------------+------------------------------------------------------------------------------------+------------------------------------------------------------------+---------------------------+
| **Rank**                          | Salt marshes                      | Mangroves                                                                          | Seagrasses                                                       | Other vegetation          |
+===================================+===================================+====================================================================================+==================================================================+===========================+
| **% carbon loss from biomass**    | | LI/MI: 50% biomass loss (1)     | | LI/MI: 50% biomass loss (1)                                                      | | LI/MI: 50% biomass loss (1)                                    | Use literature/field data |
|                                   | | HI: 100% biomass loss           | | HI: 100% biomass loss                                                            | | HI: 100% biomass loss                                          |                           |
+-----------------------------------+-----------------------------------+------------------------------------------------------------------------------------+------------------------------------------------------------------+---------------------------+
| **% carbon loss from soil**       | | LI: 30% loss (1)                | | LI: 30% loss (1)                                                                 | | LI/MI: top 10% washes away, bottom 90% decomposes in place (2) | Use literature/field data |
|                                   | | MI/HI: 100% loss (3)            | | MI: 50% loss (1)                                                                 | | HI: top 50% washes away, bottom 50% decomposes in place (2)    |                           |
|                                   |                                   | | HI: 66% loss (up to 1.5 m depth) (1)                                             |                                                                  |                           |
+-----------------------------------+-----------------------------------+------------------------------------------------------------------------------------+------------------------------------------------------------------+---------------------------+
| **Rate of decay (over 25 years)** | | Biomass half-life: 6 months (2) | | Biomass half-life: 15 years, but assume 75% is released immediately from burning | | Biomass half-life: 100 days (2)                                | Use literature/field data |
|                                   | | Soil half-life: 7.5 years (2)   | | Soil half-life 7.5 years (2)                                                     | | Soil half-life: 1 year (2)                                     |                           |
+-----------------------------------+-----------------------------------+------------------------------------------------------------------------------------+------------------------------------------------------------------+---------------------------+
| **Methane emissions**             | 1.85 T CO2/ha/yr (4)              | 0.4 T CO2/ha/yr                                                                    | Negligible                                                       | Use literature/field data |
+-----------------------------------+-----------------------------------+------------------------------------------------------------------------------------+------------------------------------------------------------------+---------------------------+

Table 1: Percent carbon loss and habitat-specific decay rates as a result of **low (LI), medium (MI) and high (HI) impact** activities disturbing salt marsh, mangrove, and seagrass ecosystems.  These default values can be adjusted by modifying the input CSV tables.

References (numbers in parentheses above):

1. Donato, D. C., Kauffman, J. B., Murdiyarso, D., Kurnianto, S., Stidham, M., & Kanninen, M. (2011). Mangroves among the most carbon-rich forests in the tropics. Nature Geoscience, 4(5), 293-297.
2. Murray, B. C., Pendleton, L., Jenkins, W. A., & Sifleet, S. (2011). Green payments for blue carbon: Economic incentives for protecting threatened coastal habitats. Nicholas Institute for Environmental Policy Solutions, Report NI, 11, 04.
3. Crooks, S., Herr, D., Tamelander, J., Laffoley, D., & Vandever, J. (2011). Mitigating climate change through restoration and management of coastal wetlands and near-shore marine ecosystems: challenges and opportunities. Environment Department Paper, 121, 2011-009.
4. Krithika, K., Purvaja, R., & Ramesh, R. (2008). Fluxes of methane and nitrous oxide from an Indian mangrove. Current Science (00113891), 94(2).


Valuation of Net Sequestered Carbon
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The valuation option for the blue carbon model estimates the economic value of
sequestration (not storage) as a function of the amount of carbon sequestered,
the monetary value of each ton of sequestered carbon, a discount rate, and the
change in the value of carbon sequestration over time. The value of sequestered
carbon is dependent on who is making the decision to change carbon emissions
and falls into two categories: social and private. If changes in carbon
emissions are due to public policy, such as zoning coastal areas for
development, then decision-makers should weigh the benefits of development
against the social losses from carbon emissions. Because local carbon emissions
affect the atmosphere on a global scale, the social cost of carbon (SCC) is
commonly calculated at a global scale (USIWGSCC, 2010). Efforts to calculate
the social cost of carbon have relied on multiple integrated assessment models
such as FUND (http://www.fund-model.org/), PAGE (Hope, 2011), DICE and RICE
(https://sites.google.com/site/williamdnordhaus/dice-rice). The US Interagency
Working Group on the Social Cost of Carbon has synthesized the results of some
of these models and gives guidance for the appropriate SCC through time for
three different discount rates (USIWGSCC, 2010; 2013). If your research
questions lead you to a social cost of carbon approach, it is strongly
recommended to consult this guidance. The most relevant considerations for
applying SCC valuation based on the USIWGSCC approach in InVEST are the
following:

 * The discount rate that you choose for your application must be one of the
   three options in the report (2.5%, 3%, or 5%). In the context of policy
   analysis, discount rates reflect society's time preferences. For a primer on
   social discount rates, see Baumol (1968).
 * Since the damages incurred from carbon emissions occur beyond the date of
   their initial release into the atmosphere, the damages from emissions in any
   one period are the sum of future damages, discounted back to that point. For
   example, to calculate the SCC for emissions in 2030, the present value (in
   2030) of the sum of future damages (2030 onward) is needed. This means that
   the SCC in any future period is a function of the discount rate, and
   therefore, a consistent discount rate should be used throughout the
   analysis. There are different SCC schedules (price list) for different
   discount rates. Your choice of an appropriate discount rate for your context
   will, therefore, determine the appropriate SCC schedule choice.

An alternative to SCC is the market value of carbon credits approach. If the
decision-maker is a private entity, such as an individual or a corporation,
they may be able to monetize their land use decisions via carbon credits.
Markets for carbon are currently operating across several geographies and new
markets are taking hold in Australia, California, and Quebec (World Bank,
2012). These markets set a cap on total emissions of carbon and require that
emitters purchase carbon credits to offset any emissions. Conservation efforts
that increase sequestration can be leveraged as a means to offset carbon
emissions and therefore sequestered carbon can potentially be monetized at the
price established in a carbon credit market. The means for monetizing carbon
offsets depends critically on the specific rules of each market, and therefore
it is important to determine whether or not your research context allows for
the sale of sequestration credits into a carbon market. It is also important to
note that the idiosyncrasies of market design drive carbon credit prices
observed in the market and therefore prices do not necessarily reflect the
social damages from carbon.

For further detail and discussion on the Social Cost of Carbon,
refer to https://www.carbonbrief.org/qa-social-cost-carbon.

Net present value :math:`V` is calculated for each snapshot year :math:`s`
after the baseline year, extending out to the final analysis year.

.. math:: V = \sum_{t=0}^{T} \frac{p_t (S_t - S_{t-1})}{(1+d)^t}
        :label: cbc_net_present_value

where

 * :math:`V` is the net present value of carbon sequestration
 * :math:`T` is the number of years between :math:`t_{baseline}` and the
   snapshot year :math:`s`.  If an analysis year is provided beyond the final
   snapshot year, this will be used in addition to the snapshot years.
 * :math:`p_t` is the price per ton of carbon at timestep :math:`t`
 * :math:`S_t` represents the total carbon stock at timestep :math:`t`, summed
   across the soil and biomass pools.
 * :math:`d` is the discount rate


.. note::
        The most recent carbon price table used for federal policy making in the
        United States can be found at https://www.epa.gov/sites/production/files/2016-12/documents/sc_co2_tsd_august_2016.pdf.
        For a discussion on why these methods are currently used in the US
        and what has happened since 2016, see the discussion at
        https://www.gao.gov/assets/710/707776.pdf.

        The sample price tables that come with the latest version of InVEST
        are based on 2016 carbon price estimates from the US Environmental
        Protection Agency from the 2016 publication linked above.  These tables
        are in USD from the year 2007, which is consistent with USIWGSCC estimates.

	Any currency may be used.


Identifying LULC Transitions with the Preprocessor
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The land use / land cover (LULC) maps provide snapshots of a changing landscape
and are the inputs that drive carbon accumulation and emissions in the model.
The user must first produce a set of coastal and marine habitat maps via a land
change model (e.g., SLAMM), a scenario assessment tool, or manual GIS
processing.  The user must then input the LULC maps into the model with an
associated year so that the appropriate source and destination transitions may
be determined.

The preprocessor tool compares LULC classes across the maps to identify the set
of all LULC transitions that occur.  The tool then generates a
transition matrix that indicates whether a transition occurs between two
habitats (e.g. salt marsh to developed dry land) and whether carbon
accumulates, is disturbed, or remains unchanged once that transition occurs.
The nature of carbon accumulation or disturbance is determined according to whether
the landcover is transitioning to and/or from a coastal blue carbon habitat:

- Other LULC Class :math:`\Rightarrow` Coastal Blue Carbon Habitat (*Carbon Accumulation* in Succeeding Years of Transition Event Until Next Bounding Year)

- Coastal Blue Carbon Habitat :math:`\Rightarrow` Coastal Blue Carbon Habitat (*Carbon Accumulation* in Succeeding Years of Transition Event Until Next Bounding Year)

- Coastal Blue Carbon Habitat :math:`\Rightarrow` Other LULC Class (*Carbon Disturbance* in Succeeding Years of Transition Event Until End of Time Series Forecast)

- Other LULC Class :math:`\Rightarrow` Other LULC Class (*No Carbon Change* in Succeeding Years of Transition Event Until Next Bounding Year)

This transition matrix produced by the coastal blue carbon preprocessor, and
**subsequently edited by the user**, allows the model to identify where human
activities and natural events disturb carbon stored by vegetation.   If a
transition from one LULC class to another does not occur during any of the time
steps, the cell will be left blank.  For cells in the matrix where transitions
occur, the tool will populate a cell with 'accum' in the cases where a
non-coastal blue carbon habitat transitions to a coastal blue carbon habitat or
a coastal blue carbon habitat transitions to another coastal blue carbon
habitat, 'disturb' in the case where a coastal blue carbon habitat transitions
to a non-coastal blue carbon habitat, or 'NCC' (for "no carbon change") in the
case where a non-coastal blue carbon habitat transitions to another non-coastal
blue carbon habitat.  For example, if a salt marsh pixel in :math:`s_{0}` is
converted to developed dry land in :math:`s_{1}` then the cell will be
populated with 'disturb'.  On the other hand, if a mangrove remains a mangrove
over this same time period then this cell in the matrix will be populated with
'accum'.  It is likely that a mangrove that remains a mangrove will accumulate
carbon in its soil and biomass.

The user will then need to modify the 'disturb' cells with either
'low-impact-disturb', 'med-impact-disturb' or 'high-impact-disturb' depending
on the level of disturbance that occurs as the transition occurs between LULC
types. This gives the user more fine-grained control over emissions due to
disturbance.   For example, rather than provide only one development type in an
LULC map, a user can separate out the type into two development types and
update the transition matrix accordingly so that the model can more accurately
quantify and map changes in carbon as a result of natural and anthropogenic
factors.  Similarly, different species of mangroves may accumulate soil carbon
at different rates.  If this information is known, it can improve the accuracy
of the model to provide this species distinction (two different classes in the
LULC input maps) and then the associated accumulation rates in the Biophysical
Table.


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

In the absence of detailed knowledge on the dynamics of the carbon cycle in
coastal and marine systems, we take the simplest accounting approach and draw
on published carbon stock datasets from neighboring coastlines.  We use carbon
estimates from the most extensive and up-to-date published global datasets of
carbon storage and accumulation rates (e.g., Fourqurean et al. 2012 & Silfeet
et al. 2011).

 * We assume all meaningful storage, accumulation and emission in case of
   impact occurs in the biomass and soil pools.
 * We ignore increases in stock and accumulation with growth and aging of
   habitats.
 * We assume that carbon is stored and accumulated linearly through time
   between transitions.
 * We assume that, after a disturbance event occurs, the disturbed carbon is
   emitted over time at an exponential decay rate.
 * We assume that some human activities that may degrade coastal ecosystems do
   not disturb carbon in the sediments.
 * We assume that landcover transitions happen instantaneously and completely
   in the first moment of the year in which the transition occurs.


Data Needs and Running the Model
================================

Because the Coastal Blue Carbon model relies upon the specific transitions from
one landcover to another, an optional preprocessor has been provided to make it
easier to identify the landcover transitions that take place on the lanscape
and the nature of those transitions. The outputs of this preprocessor, if
used, must then be edited by the user to indicate the magnitude of disturbances
before being used as an input to the main model. The inputs for both the
preprocessor and the main model are described here.

Step 1. Preprocessing - Coastal Blue Carbon Preprocessor
--------------------------------------------------------

The preprocessor tool compares LULC classes across snapshot years in
chronological order to identify the set of all LULC transitions that occur.
From this set, the preprocessor generates a transition matrix that indicates
whether a transition occurs between two habitats (e.g. salt marsh to developed
dry land) and whether carbon accumulates, is disturbed, or remains unchanged
once that transition occurs. It also produces a template biophysical table for
the user to fill in with information quantifying carbon change due to LULC
transitions. This table must be further edited by the user, and the edited
table is a required input to the main Coastal Blue Carbon model. See the
*Identifying LULC Transitions with the Preprocessor* section above for more
information.

Inputs
^^^^^^

- :investspec:`coastal_blue_carbon.preprocessor workspace_dir`

- :investspec:`coastal_blue_carbon.preprocessor results_suffix`

- :investspec:`coastal_blue_carbon.preprocessor landcover_snapshot_csv`

  Columns:

  - :investspec:`coastal_blue_carbon.preprocessor landcover_snapshot_csv.columns.snapshot_year`
  - :investspec:`coastal_blue_carbon.preprocessor landcover_snapshot_csv.columns.raster_path` The paths may be either absolute or relative to the location of the snapshots table itself.

- :investspec:`coastal_blue_carbon.preprocessor lulc_lookup_table_path`

  Columns:

  - :investspec:`coastal_blue_carbon.preprocessor lulc_lookup_table_path.columns.lucode`
  - :investspec:`coastal_blue_carbon.preprocessor lulc_lookup_table_path.columns.lulc-class`
  - :investspec:`coastal_blue_carbon.preprocessor lulc_lookup_table_path.columns.is_coastal_blue_carbon_habitat`


Outputs
^^^^^^^

Output files for the preprocessor are located in the folder
**Workspace/outputs_preprocessor**. "Suffix" in the following file names refers
to the optional user-defined Suffix input to the model.

- **Parameter log**: Each time the model is run, a text (.txt) file will be
  created in the main Workspace folder. 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 this parameter log.

- **transitions_[Suffix].csv**: CSV (.csv, Comma Separated Value) format table,
  which is a transition matrix indicating whether disturbance or accumulation
  occurs in a transition from one LULC class to another.  If the cell is left
  blank, then no transition of that kind occurs between the input Land Use/Land
  Cover Rasters.  The left-most column (*lulc-class*) represents the source
  LULC class, and the top row (<lulc1>, <lulc2>...) represents the destination
  LULC classes. Depending on the transition type, a cell will be pre-populated
  with one of the following: empty if no such transition occurs, 'NCC' (for no
  carbon change), 'accum' (for accumulation) or 'disturb' (for disturbance).
  You must edit the 'disturb' cells with the degree to which disturbance occurs
  due to the LULC change.  This is done by changing 'disturb' to either
  'low-impact-disturb', 'med-impact-disturb', or 'high-impact-disturb'.

 The edited table is used as input to the main Coastal Blue Carbon model as the
 **LULC Transition Effect of Carbon Table**.

  ==========  ========  ========  ===
  lulc-class  <lulc1>   <lulc2>   ...
  ==========  ========  ========  ===
  <lulc1>     <string>  <string>  ...
  <lulc2>     <string>  <string>  ...
  ...         ...       ...       ...
  ==========  ========  ========  ===


- **carbon_pool_transient_template_[Suffix].csv**: CSV (.csv, Comma Separated
  Value) format table, mapping each LULC type to impact and accumulation
  information. You must fill in all columns of this table except the
  'lulc-class' and 'lucode' columns, which will be pre-populated by the model.
  See *Step 2. The Main Model* for more information. Accumulation units are
  (Megatonnes of CO\ :sub:`2` e/ha-yr), half-life is in integer years, and
  disturbance is in integer percent.

 The edited table is used as input to the main Coastal Blue Carbon model as the **Biophysical Table**.

  ==========  ==========  ===============  ============  ==============  =================  ==========================  ==========================  ===========================  ===========================  ==============  =======================  =======================  ========================  ========================  ==========================
  lucode      lulc-class  biomass-initial  soil-initial  litter-initial  biomass-half-life  biomass-low-impact-disturb  biomass-med-impact-disturb  biomass-high-impact-disturb  biomass-yearly-accumulation  soil-half-life  soil-low-impact-disturb  soil-med-impact-disturb  soil-high-impact-disturb  soil-yearly-accumulation  litter-yearly-accumulation
  ==========  ==========  ===============  ============  ==============  =================  ==========================  ==========================  ===========================  ===========================  ==============  =======================  =======================  ========================  ========================  ==========================
  <int>       <lulc1>
  <int>       <lulc2>
  ...         ...
  ==========  ==========  ===============  ============  ==============  =================  ==========================  ==========================  ===========================  ===========================  ==============  =======================  =======================  ========================  ========================  ==========================


- **aligned_lulc_[year]_[Suffix].tif**: Rasters that are the result of aligning
  all of the input LULC rasters with each other.  All rasters are resampled to
  the minimum resolution of the input rasters and cropped to the intersection
  of their bounding boxes.  Any resampling needed is done using
  nearest-neighbor interpolation.  You generally don't need to do anything with
  these files.


Step 2. The Main Model - Coastal Blue Carbon
--------------------------------------------

The main Coastal Blue Carbon model calculates carbon stock and sequestration
over time, based on the transition and carbon pool information generated by the
preprocessor and edited by the user. It can also calculate the value of
sequestration if economic data is provided.

Inputs
^^^^^^

- :investspec:`coastal_blue_carbon.coastal_blue_carbon workspace_dir`

- :investspec:`coastal_blue_carbon.coastal_blue_carbon results_suffix`

- :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path` A template of this table is produced by
  the preprocessor (described above), and is also included with the sample data for the model.

  Columns:

  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.lucode`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.lulc-class`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.biomass-initial`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.soil-initial`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.litter-initial`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.biomass-half-life`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.biomass-low-impact-disturb`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.biomass-med-impact-disturb`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.biomass-high-impact-disturb`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.biomass-yearly-accumulation`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.soil-half-life`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.soil-low-impact-disturb`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.soil-med-impact-disturb`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.soil-high-impact-disturb`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.soil-yearly-accumulation`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon biophysical_table_path.columns.litter-yearly-accumulation` This will generally be ``0``, but can be adjusted if needed.

- :investspec:`coastal_blue_carbon.coastal_blue_carbon landcover_transitions_table`
  The Coastal Blue Carbon preprocessor exists to help create this table for you. You must edit the ``transitions_[suffix].csv`` preprocessor output as described in *Step 1 Preprocessing Outputs* before it can be used by the main model.

  Columns:

  - :investspec:`coastal_blue_carbon.coastal_blue_carbon landcover_transitions_table.columns.lulc-class`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon landcover_transitions_table.columns.[LULC CODE]`

- :investspec:`coastal_blue_carbon.coastal_blue_carbon landcover_snapshot_csv` The raster with the earliest chronological year will be used as the baseline raster. If rasters provided in this table have different extents or resolutions, they will be resampled to the minimum resolution of the set of rasters, and clipped to the intersection of all of the bounding boxes. All rasters provided in this table must be in a projected coordinate system with units in meters.

  Columns:

  - :investspec:`coastal_blue_carbon.coastal_blue_carbon landcover_snapshot_csv.columns.snapshot_year`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon landcover_snapshot_csv.columns.raster_path`

- :investspec:`coastal_blue_carbon.coastal_blue_carbon analysis_year`

- :investspec:`coastal_blue_carbon.coastal_blue_carbon do_economic_analysis`


 The value of carbon sequestration over time is given by:

 * **Value of a sequestered ton of carbon**: This user's guide assumes carbon
   is measured in tons of CO\ :sub:`2`. If you have prices in terms of tons of
   elemental carbon, these need to be converted to prices per ton of CO\
   :sub:`2`. This requires dividing the price by a factor of 3.67 to reflect
   the difference in the atomic mass between CO\ :sub:`2` and elemental carbon.
   Again, this value can be input using a price schedule over the appropriate
   time horizon, or by supplying a base year carbon price and an annual rate of
   inflation. Any currency may be used, as long as it is consistent across all valuation inputs.

 * **Discount rate**: (:math:`d` in the net present value equation), which
   reflects time preferences for immediate benefits over future benefits. If
   the rate is set equal to 0% then monetary values are not discounted.

 If the **Calculate Net Present Value of Sequestered Carbon** box is checked, you must also provide the following valuation information.

 - :investspec:`coastal_blue_carbon.coastal_blue_carbon use_price_table`

 - :investspec:`coastal_blue_carbon.coastal_blue_carbon price` May be any currency, as long as it is consistent across valuation inputs.

 - :investspec:`coastal_blue_carbon.coastal_blue_carbon inflation_rate`

 - :investspec:`coastal_blue_carbon.coastal_blue_carbon price_table_path` This table can be used in place of the Price and Interest Rate inputs.

  Columns:

  - :investspec:`coastal_blue_carbon.coastal_blue_carbon price_table_path.columns.year`
  - :investspec:`coastal_blue_carbon.coastal_blue_carbon price_table_path.columns.price`

 - :investspec:`coastal_blue_carbon.coastal_blue_carbon discount_rate`

Outputs
^^^^^^^
- **Parameter log**: Each time the model is run, a text (.txt) file will be
  created in the main Workspace folder. 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 this parameter log.

**Workspace/outputs**

- **carbon-accumulation-between-[year]-and-[year][Suffix].tif**. Amount of
  carbon accumulated between the two specified years. Units: Megatonnes CO\
  :sub:`2` e per Hectare

- **carbon-emissions-between-[year]-and-[year][Suffix].tif**. Amount of carbon
  lost to disturbance between the two specified years. Units: Megatonnes CO\
  :sub:`2` e per Hectare

- **carbon-stock-at-[year][Suffix].tif**. For the first baseline year, stock = (Sum of the 3 initial carbon pools from the biophysical table). For each year between baseline+1 and first snapshot transition, stock = (stock from previous year + accumulation) for the specified year. For years after the first snapshot transition, stock = (stock from previous year + accumulation - emissions). Note that emissions and accumulation will only be reflected in the output for the year after they begin. Units: Megatonnes CO\ :sub:`2` e per Hectare

- **total-net-carbon-sequestion-between-[year]-and-[year][Suffix].tif**. Total carbon
  sequestration between the two specified years, based on accumulation minus
  emissions during that time period. Units: Megatonnes CO\ :sub:`2` e per
  Hectare

- **total-net-carbon-sequestration[Suffix].tif**. Total carbon sequestration
  over the whole time period between the Baseline and either the latest
  Snapshot Year or the Analysis Year, based on accumulation minus emissions.
  Units: Megatonnes CO\ :sub:`2` e per Hectare

- **net-present-value[Suffix].tif**. Monetary value of carbon sequestration.
  Units: (Currency of provided Prices) per Hectare


**Workspace/intermediate**

This folder contains input rasters that have all been resampled and aligned to
the same bounding box, as intermediate steps in the modeling process.
Generally, you don't need to do anything with these files.

- **stocks-[pool]-[year][suffix].tif** - the carbon stocks available at the
  Beginning of the year noted in the filename.  Units: Megatonnes CO2E per hectare

- **accumulation-[pool]-[year][suffix].tif** - the spatial distribution of
  rates of carbon accumulation in the given pool at the given year.  Years will
  represent the snapshot years in which the accumulation raster takes effect.
  Units: Megatonnes CO2E per hectare.

- **halflife-[pool]-[year][suffix].tif** - a raster of the spatial distribution
  of the half-lives of carbon in the pool mentioned at the given snapshot year.
  Units: years.

- **disturbance-magnitude-[pool]-[year][suffix].tif** - the magnitude of
  disturbance in the given pool in the given snapshot year.
  Units: 0-1, the percentage of carbon disturbed.

- **disturbance-volume-[pool]-[year][suffix].tif** - the volume of the carbon
  disturbed in the snapshot year.  This is a function of the carbon stocks at
  the year prior and the disturbance magnitude in the given snapshot year.  See
  :eq:`cbc_disturbance_volume`  Units: Megatonnes CO2E per hectare.

- **year-of-latest-disturbance-[pool]-[year][suffix].tif** - each cell
  indicates the most recent year in which the cell underwent a landcover
  transition.

- **aligned-lulc-[snapshot type]-[year][suffix].tif** - the snapshot landcover
  raster of the given year, aligned to the intersection of the bounding boxes
  of all snapshot rasters, and with consistent cell sizes.  The cell size of
  the aligned landcover rasters is the minimum of the incoming cell sizes.

- **net-sequestration-[pool]-[year][suffix].tif** - the net sequestration in
  the given pool in the given year.  See :eq:`cbc_net_sequestration`
  Units: Megatonnes CO2E per hectare.

- **total-carbon-stocks-[year][suffix].tif** - the sum of the stocks present
  across all three carbon pool at the given year. Units: Megatonnes CO2E per
  Hectare.


Advanced Usage: Spatially-explicit Biophysical Parameters
---------------------------------------------------------

While the Coastal Blue Carbon's preprocessor and main model user interfaces are
helpful for most cases that can be classified into various landcover types, an
advanced user may desire to provide spatially explicit maps of carbon
half-lives, rates of accumulation, and other biophysical parameters to the
model.  This is not possible through the User Interface, but is available as a
python function that provides lower-level access to the model's timeseries
analysis.  Use of this advanced functionality requires a substantial amount of
data preprocessing and has much more complex data requirements.  Please see the
model's source code on github for details:
https://github.com/natcap/invest/blob/main/src/natcap/invest/coastal_blue_carbon/coastal_blue_carbon.py


Example Use-Case
================

Freeport, Texas
---------------

Summary
^^^^^^^

Over the next 100 years, the US Gulf coast has been identified as susceptible to rising sea levels.  The use of the InVEST blue carbon model serves to identify potential changes in the standing stock of carbon in coastal vegetation that sequester carbon.  This approach in Freeport, TX was made possible with rich and resolute elevation and LULC datasets.  We used a 10-meter DEM with sub-meter vertical accuracy to model marsh migration and loss over time as a result of sea level rise (SLR) using Warren Pinnacle's SLAMM (Sea Level Affected Marsh Model).  Outputs from SLAMM serve as inputs to the InVEST Coastal Blue Carbon model which permits the tool to map, measure, and value carbon sequestration and emissions resulting from changes to coastal land cover over a 94-year period.

The Sea Level Affecting Marshes Model (SLAMM: http://www.warrenpinnacle.com/prof/SLAMM/) models changes in the distribution of 27 different coastal wetland habitat types in response to sea-level rise.  The model relies on the relationship between tidal elevation and coastal wetland habitat type, coupled with information on slope, land use, erosion and accretion to predict changes or loss of habitat.  SLAMM outputs future habitat maps for user-defined time steps and sea-level rise scenarios. These future habitat maps can be utilized with InVEST service models to evaluate resultant changes in ecosystem services under various sea-level rise scenarios (e.g. 1 meter SLR by 2100).

For example, SLAMM was used to quantify differences in carbon sequestration over a range of sea-level rise projections in Galveston Bay, Texas, USA.  First, SLAMM was used to map changes in the distribution of coastal wetland habitat over time under different sea-level rise projections.  Then, the InVEST Coastal Blue Carbon model was used to evaluate changes in carbon sequestration associated with predicted changes in habitat type.  The 27 land-cover classes modeled by SLAMM were condensed into a subset relevant to carbon sequestration and converted from ASCII to raster format for use with InVEST.  SLAMM results produced LULC maps of future alternative scenarios over 25-year time slices beginning in 2006 and ending in 2100.  The following figure depicts 2006 LULC and a table of disaggregated land class types.

.. figure:: ./coastal_blue_carbon/freeport_LULC_2006.png

Figure CS1. Current (2006) LULC map of Freeport, Texas

Carbon stored in the sediment ('soil' pool) was the focus of this analysis.  The vast majority of carbon is sequestered in this pool by coastal and marine vegetation.  See the case study limitations for additional information.  To produce maps of carbon storage at the different 25-year time steps, we used the model to perform a simple "look-up" to determine the amount of carbon per 10-by-10 meter pixel based on known storage rates from sampling in the Freeport area (Chmura et al. 2003).

Next, we provide the InVEST model with a transition matrix in order to identify the amount of carbon gained or lost over each 25-year time step.  Annual accumulation rates in the salt marsh were also obtained from Chmura et al. (2003).  When analyzing the time period from 2025 to 2050, we assume :math:`t_{2}` = 2025 and :math:`t_{3}` = 2050.  We identify all the possible transitions that will result in either accumulation or loss of carbon.  The model compares the two LULC maps (:math:`t_{2}` and :math:`t_{3}`) to identify any pixel transitions from one land cover type to another.  We apply these transformations to the standing stock of carbon which is the running carbon tally at :math:`t_{2}` (2025).  Once these adjustments are complete, we have a new map of standing carbon for :math:`t_{3}` (2050).  We repeat this step for the next time period where :math:`t_{3}` = 2050 and :math:`t_{4}` = 2075.  This process was repeated until 2100.  The model produces spatially explicit depictions of net sequestration over time as well as summaries of net gain/emission of carbon for the two scenarios at each 25-year time step.  This information was used to determine during which time period for each scenario the rising seas and resulting marsh migration led to net emissions for the study site and the entire Freeport area.

+------------------------------------------+----------------------------+-------------------------+
| Time Period                              | Scenario #1: No Management | Scenario #2: High Green |
+==========================================+============================+=========================+
|  2006-2025 (:math:`t_{1}`-:math:`t_{2}`) | +4,031,180                 | +4,172,370              |
+------------------------------------------+----------------------------+-------------------------+
|  2025-2050 (:math:`t_{2}`-:math:`t_{3}`) | -1,170,580                 | +684,276                |
+------------------------------------------+----------------------------+-------------------------+
|  2050-2075 (:math:`t_{3}`-:math:`t_{4}`) | -7,403,690                 | -5,525,100              |
+------------------------------------------+----------------------------+-------------------------+
|  2075-2100 (:math:`t_{4}`-:math:`t_{5}`) | -7,609,020                 | -8,663,600              |
+------------------------------------------+----------------------------+-------------------------+
|  100-Year Total:                         | -12,152,100                | -9,332,050              |
+------------------------------------------+----------------------------+-------------------------+

Table CS1. Carbon sequestration and emissions for each 25-year time period for the two scenarios of the entire Freeport study area.


.. figure:: ./coastal_blue_carbon/freeport_2006_2010.png

Figure CS2. Carbon emissions (red) and sequestration (blue) from 2006 to 2100 for the two scenarios and a subset of the Freeport study area.

The following is table summarizing how the main inputs, where they were obtained and how they were used in the model:

 
| Input                                      | Source                                           | Use in the InVEST blue carbon model                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |
 
| DEM                                        | USGS                                             | DEM was needed to produce the future LULC maps using the SLAMM tool.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |
 
| Land use / land cover (LULC)               | USGS/NOAA                                        | Salt marshes store carbon in biomass and soils.  We utilized maps showing the current distribution of salt marshes to establish a baseline coverage of marshes from which we estimate aboveground biomass and soil carbon.                                                                                                                                                                                                                                                                                                                                                                                                        |
 
| Carbon stock in salt marsh systems         | Natural Capital Alliance literature review       | Carbon storage was calculated by summing the carbon stored in biomass and sediments.  Carbon stocks were calculated for all of the areas of functional salt marsh in the study region (Chmura et al. 2003).                                                                                                                                                                                                                                                                                                                                                                                                                       |
 
| Social value of carbon in 2006 US $        | USIWGSCC 2010                                    | The "social cost of carbon" (SCC) is an estimate of the monetized damages associated with an incremental increase in carbon emissions in a given year.  It is intended to include (but is not limited to) changes in net agricultural productivity, human health, property damages from increased flood risk, and the value of ecosystem services.  The social cost of carbon is useful for allowing institutions to incorporate the social benefits of reducing carbon dioxide (CO\ :sub:`2`) emissions into cost benefit analyses of management actions that have small, or "marginal," impacts on cumulative global emissions. |
 
| Discount rate                              | USIWGSCC 2010                                    | This discount rate reflects society's preferences for short run versus long term consumption.  Since carbon dioxide emissions are long-lived, subsequent damages occur over many years.  We use the discount rate to adjust the stream of future damages to its present value in the year when the emissions were changed.                                                                                                                                                                                                                                                                                                        |
 

Table CS2. Input summary table for using InVEST blue carbon model in Freeport, Texas

Limitations
^^^^^^^^^^^

* This analysis did not model change in carbon resulting from growth or loss of aboveground biomass of coastal and marine vegetation.

* While the spatial resolution of the LULC maps produced by SLAMM was very high (10 meters), the temporal resolution provided by SLAMM was quite coarse (25-year time steps).  The carbon cycle is a dynamic process.  By analyzing change over 25-year time periods, we ignore any changes that are not present at the start and end of each time step.


.. _cbc-global-database:

Appendix: Global Database of Carbon Values
==========================================

If local information on carbon stocks and accumulation rates are not available,
users may wish to draw on the global database of values for carbon stocks and
accumulation rates that is included with the InVEST CBC model sample data, and
is available for download here:
https://bitbucket.org/natcap/invest-sample-data/src/master/CoastalBlueCarbon/inputs/BlueCarbon_GlobalDB.xls
Note that if data from field studies or other local sources are available,
these values should be used instead of those in this global database.

This excel spreadsheet includes sheets for carbon stocks and accumulation rates
for saltmarshes, seagrass and mangroves across biomass and soil pools and also
carbon accumulation rates.  Carbon biomass stocks are provided in units of
Tons of CO2e/ha, and carbon accumulation rates are provided in units of Tons of
CO2e/ha per year.

Note that in the ``SaltMarshSoil`` sheet, the ``T_CO2e_ha`` column is
calculated from the ``gC_cm3`` column (representing grams of carbon/cubic
centimeter)` using the equation:

.. math::

   T\_CO2e\_ha = \frac{(gC\_cm^3) \cdot 10^6 \cdot 10^4 \cdot 44}{12*10^6}

Which converts from grams of elemental carbon per cubic centimeter to tons of CO2 per hectare.



References
==========

Baumol, W. J. (1968). On the social rate of discount. The American Economic Review, 788-802.

Bouillon, S., Borges, A. V., Castañeda-Moya, E., Diele, K., Dittmar, T., Duke, N. C., ... & Twilley, R. R. (2008). Mangrove production and carbon sinks: a revision of global budget estimates. Global Biogeochemical Cycles, 22(2).

Chmura, G. L., Anisfeld, S. C., Cahoon, D. R., & Lynch, J. C. (2003). Global carbon sequestration in tidal, saline wetland soils. Global biogeochemical cycles, 17(4).

Clough, J. S., Park, R., and Fuller, R. (2010). "SLAMM 6 beta Technical Documentation."  Available
at http://warrenpinnacle.com/prof/SLAMM.

Fourqurean, J. W., Duarte, C. M., Kennedy, H., Marbà, N., Holmer, M., Mateo, M. A., ... & Serrano, O. (2012). Seagrass ecosystems as a globally significant carbon stock. Nature Geoscience, 5(7), 505-509.

Hope, Chris. (2011) "The PAGE09 Integrated Assessment Model: A Technical Description." Cambridge Judge Business School Working Paper No. 4/2011 (April). Available at https://www.jbs.cam.ac.uk/wp-content/uploads/2020/08/wp1104.pdf.

Houghton, R. A. (2003). Revised estimates of the annual net flux of carbon to the atmosphere from changes in land use and land management 1850–2000. Tellus B, 55(2), 378-390.

Pendleton, L., Donato, D. C., Murray, B. C., Crooks, S., Jenkins, W. A., Sifleet, S., ... & Baldera, A. (2012). Estimating global “blue carbon” emissions from conversion and degradation of vegetated coastal ecosystems. PLoS One, 7(9), e43542.

Rosenthal, A., Arkema, K., Verutes, G., Bood, N., Cantor, D., Fish, M., Griffin, R., and Panuncio, M. (In press). Identification and valuation of adaptation options in coastal-marine ecosystems: Test case from Placencia, Belize. Washington, DC: InterAmerican Development Bank. Technical Report.

Sifleet, S., Pendleton, L., and B. Murray. (2011). State of the Science on Coastal Blue Carbon. Nicholas Institute Report, 1-43.

United States, Interagency Working Group on Social Costs of Carbon. (2010) "Technical Support Document: Social Cost of Carbon for Regulatory Impact Analysis Under Executive Order 12866." Available at https://www.epa.gov/sites/production/files/2016-12/documents/scc_tsd_2010.pdf.

United States, Interagency Working Group on Social Costs of Carbon. (2013) "Technical Update of the Social Cost of Carbon for Regulatory Impact Analysis Under Executive Order 12866." Available at https://environblog.jenner.com/files/technical-update-of-the-social-cost-of-carbon-for-regulatory-impact-analysis-under-executive-order-12866.pdf.

World Bank. (2012). State and Trends of the Carbon Market 2012. Washington DC: The World Bank, 133.
