.. _rst_Fire:
Fire
========
The fire parameterization in CLM contains four components: non-peat
fires outside cropland and tropical closed forests, agricultural fires
in cropland, deforestation fires in the tropical closed forests, and
peat fires (see :ref:`Li et al. 2012a `,
:ref:`Li et al. 2012b `, :ref:`Li et al. 2013 `,
:ref:`Li and Lawrence 2017 ` for details).
In this fire parameterization, burned area is affected by climate and
weather conditions, vegetation composition and structure, and human
activities. After burned area is calculated, we estimate the fire impact,
including biomass and peat burning, fire-induced vegetation mortality,
adjustment of the carbon and nitrogen (C/N) pools, and fire emissions.
.. _Non-peat fires outside cropland and tropical closed forest:
Non-peat fires outside cropland and tropical closed forest
---------------------------------------------------------------
Burned area in a grid cell, \ :math:`A_{b}` (km\ :sup:`2` s :sup:`-1`),
is determined by
.. math::
:label: 23.1
A_{b} =N_{f} a
where :math:`N_{f}` (count s\ :sup:`-1`) is fire
counts in the grid cell; :math:`a` (km\ :sup:`2`) is average fire
spread area of a fire.
.. _Fire counts:
Fire counts
^^^^^^^^^^^^^^^^^^
Fire counts :math:`N_{f}` is taken as
.. math::
:label: 23.2
N_{f} = N_{i} f_{b} f_{m} f_{se,o}
where :math:`N_{i}` ( count s\ :sup:`-1`) is the
number of ignition sources due to natural causes and human activities;
:math:`f_{b}` and :math:`f_{m}` (fractions) represent the availability
and combustibility of fuel, respectively; :math:`f_{se,o}` is the
fraction of anthropogenic and natural fires unsuppressed by humans and
related to the socioeconomic conditions.
:math:`N_{i}` (count s\ :sup:`-1`) is given as
.. math::
:label: 23.3
N_{i} = \left(I_{n} +I_{a} \right) A_{g}
where :math:`I_{n}` (count km\ :sup:`-2` s\ :sup:`-1`) and :math:`I_{a}`
(count km\ :sup:`-2` s\ :sup:`-1`) are the number of natural and anthropogenic
ignitions per km\ :sup:`2`, respectively; :math:`A_{g}` is the area of the
grid cell (km\ :sup:`2`). :math:`I_{n}` is estimated by
.. math::
:label: 23.4
I_{n} = \gamma \psi I_{l}
where :math:`\gamma` \ =0.22 is ignition efficiency of cloud-to-ground
lightning; :math:`\psi =\frac{1}{5.16+2.16\cos [3min(60,\lambda )]}` is the
cloud-to-ground lightning fraction and depends on the latitude
:math:`\lambda` (degrees) ; :math:`I_{l}` (flash km\ :sup:`-2` s\ :sup:`-1`) is
the total lightning flashes. :math:`I_{a}` is modeled as a monotonic
increasing function of population density:
.. math::
:label: 23.5
I_{a} =\frac{\alpha D_{P} k(D_{P} )}{n}
where :math:`\alpha =0.01` (count person\ :sup:`-1` mon\ :sup:`-1`) is the number of potential ignition sources by a
person per month; :math:`D_{P}` (person km\ :sup:`-2`) is the population density; :math:`k(D_{P} )=6.8D_{P} ^{-0.6}` represents anthropogenic ignition
potential as a function of human population density :math:`D_{P}` ; *n*
is the seconds in a month.
Fuel availability :math:`f_{b}` is given as
.. math::
:label: 23.6
f_{b} =\left\{\begin{array}{c}
{0} \\ {\frac{B_{ag} -B_{low} }{B_{up} -B_{low} } } \\ {1} \end{array}
\begin{array}{cc} {} & {} \end{array}\begin{array}{c} {B_{ag} B_{up} }
\end{array}\right\} \ ,
where :math:`B_{ag}` (g C m\ :sup:`-2`) is the biomass of combined leaf,
stem, litter, and woody debris pools; :math:`B_{low}` = 105 g C m :sup:`-2`
is the lower fuel threshold below which fire does not occur; :math:`B_{up}`
= 1050 g C m\ :sup:`-2` is the upper fuel threshold above which fire
occurrence is not limited by fuel availability.
Fuel combustibility :math:`f_{m}` is estimated by
.. math::
:label: 23.7
f_{m} = {f_{RH} f_{\beta}}, &\qquad T_{17cm} > T_{f}
where :math:`f_{RH}` and :math:`f_{\beta }` represent the dependence of
fuel combustibility on relative humidity :math:`RH` (%) and root-zone
soil moisture limitation :math:`\beta` (fraction); :math:`T_{17cm}` is
the temperature of the top 17 cm of soil (K) and :math:`T_{f}` is the
freezing temperature. :math:`f_{RH}` is a weighted average of real time
:math:`RH` (:math:`RH_{0}`) and 30-day running mean :math:`RH`
(:math:`RH_{30d}`):
.. math::
:label: 23.8
f_{RH} = (1-w) l_{RH_{0}} + wl_{RH_{30d}}
where weight :math:`w=\max [0,\min (1,\frac{B_{ag}-2500}{2500})]`,
:math:`l_{{RH}_{0}}=1-\max [0,\min (1,\frac{RH_{0}-30}{80-30})]`, and
:math:`l_{{RH}_{30d}}=1-\max [0.75,\min (1,\frac{RH_{30d}}{90})]`.
:math:`f_{\beta}` is given by
.. math::
:label: 23.9
f_{\beta } =\left\{\begin{array}{cccc}
{1} & {} & {} & {\beta\le \beta_{low} } \\ {\frac{\beta_{up} -\beta}{\beta_{up} -\beta_{low} } } & {} & {} & {\beta_{low} <\beta<\beta_{up} } \\
{0} & {} & {} & {\beta\ge \beta_{up} }
\end{array}\right\} \ ,
where :math:`\beta _{low}` \ =0.85 and :math:`\beta _{up}` \ =0.98 are the
lower and upper thresholds, respectively.
For scarcely populated regions (:math:`D_{p} \le 0.1` person
km :sup:`-2`), we assume that anthropogenic suppression on fire
occurrence is negligible, i.e., :math:`f_{se,o} =1.0`. In regions of
:math:`D_{p} >0.1` person km\ :sup:`-2`, we parameterize the
fraction of anthropogenic and natural fires unsuppressed by human
activities as
.. math::
:label: 23.10
f_{se,o} =f_{d} f_{e}
where :math:`{f}_{d}` and :math:`{f}_{e}` are the effects of the
demographic and economic conditions on fire occurrence. The demographic
influence on fire occurrence is
.. math::
:label: 23.11
f_{d} =0.01 + 0.98 \exp (-0.025D_{P} ).
For shrub and grass PFTs, the economic influence on fire occurrence is
parameterized as a function of Gross Domestic Product GDP (k 1995US$
capita\ :sup:`-1`):
.. math::
:label: 23.12
f_{e} =0.1+0.9\times \exp [-\pi (\frac{GDP}{8} )^{0.5} ]
which captures 73% of the observed MODIS fire counts with variable GDP
in regions where shrub and grass PFTs are dominant (fractional coverage
of shrub and grass PFTs :math:`>` 50%). In regions outside tropical
closed forests and dominated by trees (fractional coverage of tree PFTs
:math:`>` 50%), we use
.. math::
:label: 23.13
f_{e} =\left\{\begin{array}{c}
{0.39} \\ {0.79} \\ {1} \end{array}
\begin{array}{cc} {} & {} \end{array}\begin{array}{c} {GDP > 20 } \\
{ 8 < GDP \le 20 } \\ { GDP \le 8 }
\end{array}\right\} \ ,
to reproduce the relationship between MODIS fire counts and GDP.
.. _Average spread area of a fire:
Average spread area of a fire
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Fire fighting capacity depends on socioeconomic conditions and affects
fire spread area. Due to a lack of observations, we consider the
socioeconomic impact on the average burned area rather than separately
on fire spread rate and fire duration:
.. math::
:label: 23.14
a=a^{*} F_{se}
where :math:`a^{*}` is the average burned area of a fire without
anthropogenic suppression and :math:`F_{se}` is the socioeconomic
effect on fire spread area.
Average burned area of a fire without anthropogenic suppression is
assumed elliptical in shape with the wind direction along the major axis
and the point of ignition at one of the foci. According to the area
formula for an ellipse, average burned area of a fire can be represented
as:
.. math::
:label: 23.15
a^{*} =\pi \frac{l}{2} \frac{w}{2} \times 10^{-6} =\frac{\pi u_{p}^{2} \tau ^{2} }{4L_{B} } (1+\frac{1}{H_{B} } )^{2} \times 10^{-6}
where :math:`u_{p}` (m s\ :sup:`-1`) is the fire spread rate in the
downwind direction; :math:`\tau` (s) is average fire duration; :math:`L_{B}`
and :math:`H_{B}` are length-to-breadth ratio and head-to-back ratio of
the ellipse; 10 :sup:`-6` converts m :sup:`2` to km :sup:`2`.
According to :ref:`Arora and Boer (2005)`,
.. math::
:label: 23.16
L_{B} =1.0+10.0[1-\exp (-0.06W)]
where :math:`W`\ (m s\ :sup:`-1`) is the wind speed. According to
the mathematical properties of the ellipse, the head-to-back ratio
:math:`H_{B}` is
.. math::
:label: 23.17
H_{B} =\frac{u_{p} }{u_{b} } =\frac{L_{B} +(L_{B} ^{2} -1)^{0.5} }{L_{B} -(L_{B} ^{2} -1)^{0.5} } .
The fire spread rate in the downwind direction is represented as
.. math::
:label: 23.18
u_{p} =u_{\max } C_{m} g(W)
(:ref:`Arora and Boer, 2005`), where :math:`u_{\max }`
(m s\ :sup:`-1`) is the PFT-dependent average maximum fire spread
rate in natural vegetation regions; :math:`C_{m} =\sqrt{f_{m}}` and :math:`g(W)`
represent the dependence of :math:`u_{p}` on fuel wetness and wind
speed :math:`W`, respectively. :math:`u_{\max }` is set to 0.33
m s :sup:`-1`\ for grass PFTs, 0.28 m s :sup:`-1` for shrub PFTs, 0.26
m s\ :sup:`-1` for needleleaf tree PFTs, and 0.25 m s\ :sup:`-1` for
other tree PFTs. :math:`g(W)` is derived from the mathematical properties
of the ellipse and equation :eq:`23.16` and :eq:`23.17`.
.. math::
:label: 23.19
g(W)=\frac{2L_{B} }{1+\frac{1}{H_{B} } } g(0).
Since g(\ *W*)=1.0, and \ :math:`L_{B}` and :math:`H_{B}` are at their
maxima \ :math:`L_{B} ^{\max } =11.0` and \ :math:`H_{B} ^{\max } =482.0`
when :math:`W\to \infty` , g(0) can be derived as
.. math::
:label: 23.20
g(0)=\frac{1+\frac{1}{H_{B} ^{\max } } }{2L_{B} ^{\max } } =0.05.
In the absence of globally gridded data on barriers to fire (e.g.
rivers, lakes, roads, firebreaks) and human fire-fighting efforts,
average fire duration is simply assumed equal to 1 which is the observed
2001–2004 mean persistence of most fires in the world
(:ref:`Giglio et al. 2006 `).
As with the socioeconomic influence on fire occurrence, we assume that
the socioeconomic influence on fire spreading is negligible in regions
of :math:`D_{p} \le 0.1` person km\ :sup:`-2`, i.e.,
:math:`F_{se} = 1.0`. In regions of :math:`D_{p} >0.1` person
km\ :sup:`-2`, we parameterize such socioeconomic influence as:
.. math::
:label: 23.21
F_{se} =F_{d} F_{e}
where :math:`{F}_{d}` and :math:`{F}_{e}` are
effects of the demographic and economic conditions on the average spread
area of a fire, and are identified by maximizing the explained
variability of the GFED3 burned area fraction with both socioeconomic
indices in grid cells with various dominant vegetation types. For shrub
and grass PFTs, the demographic impact factor is
.. math::
:label: 23.22
F_{d} =0.2+0.8\times \exp [-\pi (\frac{D_{p} }{450} )^{0.5} ]
and the economic impact factor is
.. math::
:label: 23.23
F_{e} =0.2+0.8\times \exp (-\pi \frac{GDP}{7} ).
For tree PFTs outside tropical closed forests, the demographic and
economic impact factors are given as
.. math::
:label: 23.24
F_{d} =0.4+0.6\times \exp (-\pi \frac{D_{p} }{125} )
and
.. math::
:label: 23.25
F_{e} =\left\{\begin{array}{cc}
{0.62,} & {GDP>20} \\ {0.83,} & {8` that shows the
2001-2009 average contribution of cropland fires is 4.7% of the total
global burned area.
The socioeconomic factor :math:`f_{se}` is given as follows:
.. math::
:label: 23.31
f_{se} =f_{d} f_{e} .
Here
.. math::
:label: 23.32
f_{d} =0.04+0.96\times \exp [-\pi (\frac{D_{p} }{350} )^{0.5} ]
and
.. math::
:label: 23.33
f_{e} =0.01+0.99\times \exp (-\pi \frac{GDP}{10} )
are the effects of population density and GDP on burned area, derived
in a similar way to equation :eq:`23.32` and :eq:`23.33`. :math:`f_{t}`
is set to 1 at the first time step during the climatological peak month
for agricultural fires (:ref:`van der Werf et al. 2010 `);
:math:`{f}_{t}` is set to 0 otherwise. Peak
month in this dataset correlates with the month after harvesting or the
month before planting. In CLM we use this dataset the same way whether
the CROP option is active or not, without regard to the CROP option’s
simulated planting and harvesting dates.
In the post-fire region, fire impact is parameterized similar to section
:numref:`Fire impact` but with combustion completeness factors and tissue
mortality factors for crop PFTs
(:numref:`Table PFT-specific combustion completeness and fire mortality factors`).
.. _Deforestation fires:
Deforestation fires
------------------------
CLM focuses on deforestation fires in tropical closed forests. Tropical
closed forests are defined as grid cells with tropical tree (BET and BDT tropical)
coverage :math:`>` 60% according to the FAO classification. Deforestation fires
are defined as fires caused by deforestation, including escaped
deforestation fires, termed degradation fires. Deforestation and
degradation fires are assumed to occur outside of cropland areas in
these grid cells. Burned area is controlled by the deforestation rate
and climate:
.. math::
:label: 23.34
A_{b} = b \ f_{lu} f_{cli,d} f_{b} A_{g}
where :math:`b` (s\ :sup:`-1`) is a global constant;
:math:`f_{lu}` (fraction) represents the effect of decreasing
fractional coverage of tree PFTs derived from land use data;
:math:`f_{cli,d}` (fraction) represents the effect of climate
conditions on the burned area.
Constants :math:`b` and :math:`{f}_{lu}` are calibrated
based on observations and reanalysis datasets in the Amazon rainforest
(tropical closed forests within 15.5 :sup:`o` S :math:`\text{-}` 10.5
:sup:`o` N, 30.5 :sup:`o` W :math:`\text{-}` 91 :sup:`o` W).
:math:`b` = 0.033 d\ :sup:`-1` and :math:`f_{lu}` is defined as
.. math::
:label: 23.35
f_{lu} = \max (0.0005,0.19D-0.001)
where :math:`D` (yr\ :sup:`-1`) is the annual loss of tree cover
based on CLM land use and land cover change data.
The effect of climate on deforestation fires is parameterized as:
.. math::
:label: 23.36
\begin{array}{ll}
f_{cli,d} \quad = & \quad \max \left[0,\min (1,\frac{b_{2} -P_{60d} }{b_{2} } )\right]^{0.5} \times \\
& \quad \max \left[0,\min (1,\frac{b_{3} -P_{10d} }{b_{3} } )\right]^{0.5} \times \\
& \quad \max \left[0,\min (1,\frac{0.25-P}{0.25} )\right]
\end{array}
where :math:`P` (mm d :sup:`-1`) is instantaneous precipitation, while
:math:`P_{60d}` (mm d\ :sup:`-1`) and :math:`P_{10d}` (mm d :sup:`-1`)
are 60-day and 10-day running means of precipitation, respectively;
:math:`b_{2}` (mm d :sup:`-1`) and :math:`b_{3}` (mm d :sup:`-1`) are
the grid-cell dependent thresholds of :math:`P_{60d}` and :math:`P_{10d}` ;
0.25 mm d :sup:`-1` is the maximum precipitation rate for drizzle.
:ref:`Le Page et al. (2010) ` analyzed the relationship
between large-scale deforestation fire counts and precipitation during 2003
:math:`\text{-}`\ 2006 in southern Amazonia where tropical evergreen trees
(BET Tropical) are dominant. Figure 2 in
:ref:`Le Page et al. (2010) ` showed that fires generally
occurred if both :math:`P_{60d}` and :math:`P_{10d}` were less than about
4.0 mm d :sup:`-1`, and fires occurred more frequently in a drier environment.
Based on the 30-yr (1985 to 2004) precipitation data in
:ref:`Qian et al. (2006) `. The climatological precipitation
of dry months (P < 4.0 mm d :sup:`-1`) in a year over tropical deciduous
tree (BDT Tropical) dominated regions is 46% of that over BET Tropical
dominated regions, so we set the PFT-dependent thresholds of :math:`P_{60d}`
and :math:`P_{10d}` as 4.0 mm d :sup:`-1` for BET Tropical and 1.8 mm d
:sup:`-1` (= 4.0 mm d :sup:`-1` :math:`\times` 46%) for BDT Tropical, and
:math:`b`\ :sub:`2` and :math:`b`\ :sub:`3` are the average of thresholds
of BET Tropical and BDT Tropical weighted bytheir coverage.
The post-fire area due to deforestation is not limited to land-type
conversion regions. In the tree-reduced region, the maximum fire carbon
emissions are assumed to be 80% of the total conversion flux. According
to the fraction of conversion flux for tropical trees in the
tree-reduced region (60%) assigned by CLM4-CN, to reach the maximum fire
carbon emissions in a conversion region requires burning this region
about twice when we set PFT-dependent combustion completeness factors to
about 0.3 for stem [the mean of 0.2\ :math:`{-}`\ 0.4 used in
:ref:`van der Werf et al. (2010) `. Therefore, when
the burned area calculated from equation :eq:`23.36` is
no more than twice the tree-reduced area, we assume no escaped fires
outside the land-type conversion region, and the fire-related fraction
of the total conversion flux is estimated as
:math:`\frac{A_{b} /A_{g} }{2D}` . Otherwise, 80% of the total
conversion flux is assumed to be fire carbon emissions, and the biomass
combustion and vegetation mortality outside the tree-reduced regions
with an area fraction of :math:`\frac{A_{b} }{A_{g} } -2D` are set as in
section :numref:`Fire impact`.
.. _Peat fires:
Peat fires
---------------
The burned area due to peat fires is given as :math:`{A}_{b}`:
.. math::
:label: 23.37
A_{b} = c \ f_{cli,p} f_{peat} (1 - f_{sat} ) A_{g}
where :math:`c` (s\ :sup:`-1`) is a constant; :math:`f_{cli,p}` represents
the effect of climate on the burned area; :math:`f_{peat}` is the fractional
coverage of peatland in the grid cell; and :math:`f_{sat}` is the fraction
of the grid cell with a water table at the surface or higher. :math:`c` = 0.17
:math:`\times` 10 :sup:`-3` hr\ :sup:`-1` for tropical peat fires and
:math:`c` = 0.9 :math:`\times` 10 :sup:`-5` hr :sup:`-1` for boreal peat fires
are derived using an inverse method, by matching simulations to earlier
studies: about 2.4 Mha peatland was burned over Indonesia in 1997
(:ref:`Page et al. 2002 `) and the average burned area of peat
fires in Western Canada was 0.2 Mha yr :sup:`-1` for 1980-1999
(:ref:`Turetsky et al. 2004 `).
For tropical peat fires, :math:`f_{cli,p}` is set as a function of
long-term precipitation :math:`P_{60d}` :
.. math::
:label: 23.38
f_{cli,p} = \ max \left[0,\min \left(1,\frac{4-P_{60d} }{4} \right)\right]^{2} .
For boreal peat fires, :math:`f_{cli,p}` is set to
.. math::
:label: 23.39
f_{cli,p} = \exp (-\pi \frac{\theta _{17cm} }{0.3} )\cdot \max [0,\min (1,\frac{T_{17cm} -T_{f} }{10} )]
where :math:`\theta _{17cm}` is the wetness of the top 17 cm of soil.
Peat fires lead to peat burning and the combustion and mortality of
vegetation over peatlands. For tropical peat fires, based on
:ref:`Page et al. (2002) `, about 6% of the peat carbon loss
from stored carbon is caused by 33.9% of the peatland burned. Carbon emissions
due to peat burning (g C m\ :sup:`-2` s\ :sup:`-1`) are therefore set as the
product of 6%/33.9%, burned area fraction of peat fire (s\ :sup:`-1`), and
soil organic carbon (g C m\ :sup:`-2`). For boreal peat fires, the carbon
emissions due to peat burning are set as 2.2 kg C m\ :sup:`-2` \ peat fire
area (:ref:`Turetsky et al. 2002 `). Biomass combustion
and vegetation mortality in post-fire peatlands are set the same as section
:numref:`Fire impact` for non-crop PFTs and as section
:numref:`Agricultural fires` for crops PFTs.
.. _Fire trace gas and aerosol emissions:
Fire trace gas and aerosol emissions
-------------------------------------
CESM2 is the first Earth system model that can model the full coupling
among fire, fire emissions, land, and atmosphere. CLM5, as the land
component of CESM2, calculates the surface trace gas and aerosol emissions
due to fire and fire emission heights, as the inputs of atmospheric
chemistry model and aerosol model.
Emissions for trace gas and aerosol species x and the j-th PFT, :math:`E_{x,j}`
(g species s\ :sup:`-1`), are given by
.. math::
:label: 23.40
E_{x,j} = EF_{x,j}\frac{\phi _{j} }{[C]}.
Here, :math:`EF_{x,j}` (g species (g dm)\ :sup:`-1`) is PFT-dependent emission
factor scaled from biome-level values (Li et al., in prep, also used for FireMIP
fire emissions data) by Dr. Val Martin and Dr. Li. :math:`[C]` = 0.5
(g C (g dm)\ :sup:`-1`) is a conversion factor from dry matter to carbon.
Emission height is PFT-dependent: 4.3 km for needleleaf tree PFTs, 3 km for other
boreal and temperate tree PFTs, 2.5 km for tropical tree PFTs, 2 km for shrub
PFTs, and 1 km for grass and crop PFTs. These values are compiled from earlier
studies by Dr. Val Martin.
.. _Table PFT-specific combustion completeness and fire mortality factors:
.. table:: PFT-specific combustion completeness and fire mortality factors.
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| PFT | *CC*\ :sub:`leaf` | *CC*\ :sub:`stem` | *CC*\ :sub:`root` | *CC*\ :sub:`ts` | *M*\ :sub:`leaf` | *M*\ :sub:`livestem,1` | *M*\ :sub:`deadstem` | *M*\ :sub:`root` | *M*\ :sub:`ts` | *M*\ :sub:`livestem,2` | :math:`\xi`\ :sub:`j` |
+==================================+===========================+===========================+===========================+=========================+==========================+==============================+==============================+==========================+========================+==============================+=================================+
| NET Temperate | 0.80 | 0.30 | 0.00 | 0.50 | 0.80 | 0.15 | 0.15 | 0.15 | 0.50 | 0.35 | 0.15 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| NET Boreal | 0.80 | 0.30 | 0.00 | 0.50 | 0.80 | 0.15 | 0.15 | 0.15 | 0.50 | 0.35 | 0.15 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| NDT Boreal | 0.80 | 0.30 | 0.00 | 0.50 | 0.80 | 0.15 | 0.15 | 0.15 | 0.50 | 0.35 | 0.15 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| BET Tropical | 0.80 | 0.27 | 0.00 | 0.45 | 0.80 | 0.13 | 0.13 | 0.13 | 0.45 | 0.32 | 0.13 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| BET Temperate | 0.80 | 0.27 | 0.00 | 0.45 | 0.80 | 0.13 | 0.13 | 0.13 | 0.45 | 0.32 | 0.13 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| BDT Tropical | 0.80 | 0.27 | 0.00 | 0.45 | 0.80 | 0.10 | 0.10 | 0.10 | 0.35 | 0.25 | 0.10 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| BDT Temperate | 0.80 | 0.27 | 0.00 | 0.45 | 0.80 | 0.10 | 0.10 | 0.10 | 0.35 | 0.25 | 0.10 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| BDT Boreal | 0.80 | 0.27 | 0.00 | 0.45 | 0.80 | 0.13 | 0.13 | 0.13 | 0.45 | 0.32 | 0.13 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| BES Temperate | 0.80 | 0.35 | 0.00 | 0.55 | 0.80 | 0.17 | 0.17 | 0.17 | 0.55 | 0.38 | 0.17 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| BDS Temperate | 0.80 | 0.35 | 0.00 | 0.55 | 0.80 | 0.17 | 0.17 | 0.17 | 0.55 | 0.38 | 0.17 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| BDS Boreal | 0.80 | 0.35 | 0.00 | 0.55 | 0.80 | 0.17 | 0.17 | 0.17 | 0.55 | 0.38 | 0.17 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| C\ :sub:`3` Grass Arctic | 0.80 | 0.80 | 0.00 | 0.80 | 0.80 | 0.20 | 0.20 | 0.20 | 0.80 | 0.60 | 0.20 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| C\ :sub:`3` Grass | 0.80 | 0.80 | 0.00 | 0.80 | 0.80 | 0.20 | 0.20 | 0.20 | 0.80 | 0.60 | 0.20 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| C\ :sub:`4` Grass | 0.80 | 0.80 | 0.00 | 0.80 | 0.80 | 0.20 | 0.20 | 0.20 | 0.80 | 0.60 | 0.20 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
| Crop | 0.80 | 0.80 | 0.00 | 0.80 | 0.80 | 0.20 | 0.20 | 0.20 | 0.80 | 0.60 | 0.20 |
+----------------------------------+---------------------------+---------------------------+---------------------------+-------------------------+--------------------------+------------------------------+------------------------------+--------------------------+------------------------+------------------------------+---------------------------------+
Leaves (:math:`CC_{leaf}` ), stems (:math:`CC_{stem}` ),
roots (:math:`CC_{root}` ) , and transfer and storage carbon
(:math:`CC_{ts}` ); mortality factors for leaves
(:math:`M_{leaf}` ), live stems (:math:`M_{livestem,1}` ),
dead stems (:math:`M_{deadstem}` ), roots
(:math:`M_{root}` ), and transfer and storage carbon
(:math:`M_{ts}` ) related to the carbon transfers from these pools
to litter pool; mortality factors for live stems
(:math:`M_{livestem,2}` ) related to the carbon transfer from live
stems to dead stems; whole-plant mortality factor (:math:`\xi _{j}` ).