.. _rst_Decomposition:
Decomposition
=================
Decomposition of fresh litter material into progressively more
recalcitrant forms of soil organic matter is represented in CLM is
defined as a cascade of :math:`{k}_{tras}` transformations between
:math:`{m}_{pool}` decomposing coarse woody debris (CWD), litter,
and soil organic matter (SOM) pools, each defined at
:math:`{n}_{lev}` vertical levels. CLM allows the user to define, at
compile time, between 2 contrasting hypotheses of decomposition as
embodied by two separate decomposition submodels: the CLM-CN pool
structure used in CLM4.0, or a second pool structure, characterized by
slower decomposition rates, based on the fCentury model (Parton et al.
1988). In addition, the user can choose, at compile time, whether to
allow :math:`{n}_{lev}` to equal 1, as in CLM4.0, or to equal the
number of soil levels used for the soil hydrological and thermal
calculations (see Section :numref:`Soil Layers` for soil layering).
.. _Figure Schematic of decomposition model in CLM:
.. figure:: CLM4_vertsoil_soilstruct_drawing.png
Schematic of decomposition model in CLM.
Model is structured to allow different representations of the soil C and
N decomposition cascade, as well as a vertically-explicit treatment of
soil biogeochemistry.
For the single-level model structure, the fundamental equation for
carbon balance of the decomposing pools is:
.. math::
:label: 21.1)
\frac{\partial C_{i} }{\partial t} =R_{i} +\sum _{j\ne i}\left(i-r_{j} \right)T_{ji} k_{j} C_{j} -k_{i} C_{i}
where :math:`{C}_{i}` is the carbon content of pool *i*,
:math:`{R}_{i}` are the carbon inputs from plant tissues directly to
pool *i* (only non-zero for CWD and litter pools), :math:`{k}_{i}`
is the decay constant of pool *i*; :math:`{T}_{ji}` is the fraction
of carbon directed from pool *j* to pool *i* with fraction
:math:`{r}_{j}` lost as a respiration flux along the way.
Adding the vertical dimension to the decomposing pools changes the
balance equation to the following:
.. math::
:label: 21.2)
\begin{array}{l} {\frac{\partial C_{i} (z)}{\partial t} =R_{i} (z)+\sum _{i\ne j}\left(1-r_{j} \right)T_{ji} k_{j} (z)C_{j} (z) -k_{i} (z)C_{i} (z)} \\ {+\frac{\partial }{\partial z} \left(D(z)\frac{\partial C_{i} }{\partial z} \right)+\frac{\partial }{\partial z} \left(A(z)C_{i} \right)} \end{array}
where :math:`{C}_{i}`\ (z) is now defined at each model level, and
in volumetric (gC m\ :sup:`-3`) rather than areal (gC m\ :sup:`-2`) units, along with :math:`{R}_{i}`\ (z) and
:math:`{k}_{j}`\ (z). In addition, vertical transport is handled by
the last two terms, for diffusive and advective transport. In the base
model, advective transport is set to zero, leaving only a diffusive flux
with diffusivity *D(z)* defined for all decomposing carbon and nitrogen
pools. Further discussion of the vertical distribution of carbon inputs
:math:`{R}_{i}`\ (z), vertical turnover times
:math:`{k}_{j}`\ (z), and vertical transport *D(z)* is below.
Discussion of the vertical model and analysis of both decomposition
structures is in :ref:`Koven et al. (2013) `.
.. _Figure Pool structure:
.. figure:: soil_C_pools_CN_century.png
Pool structure, transitions, respired fractions (numbers at
end of arrows), and turnover times (numbers in boxes) for the 2
alternate soil decomposition models included in CLM.
CLM-CN Pool Structure, Rate Constants and Parameters
---------------------------------------------------------
The CLM-CN structure in CLM45 uses three state variables for fresh
litter and four state variables for soil organic matter (SOM). The
masses of carbon and nitrogen in the live microbial community are not
modeled explicitly, but the activity of these organisms is represented
by decomposition fluxes transferring mass between the litter and SOM
pools, and heterotrophic respiration losses associated with these
transformations. The litter and SOM pools in CLM-CN are arranged as a
converging cascade (Figure 15.2), derived directly from the
implementation in Biome-BGC v4.1.2 (Thornton et al. 2002; Thornton and
Rosenbloom, 2005).
Model parameters are estimated based on a synthesis of microcosm
decomposition studies using radio-labeled substrates (Degens and
Sparling, 1996; Ladd et al. 1992; Martin et al. 1980; Mary et al. 1993;
Saggar et al. 1994; Sørensen, 1981; van Veen et al. 1984). Multiple
exponential models are fitted to data from the microcosm studies to
estimate exponential decay rates and respiration fractions (Thornton,
1998). The microcosm experiments used for parameterization were all
conducted at constant temperature and under moist conditions with
relatively high mineral nitrogen concentrations, and so the resulting
rate constants are assumed not limited by the availability of water or
mineral nitrogen. :numref:`Table Decomposition rate constants` lists the base decomposition rates for each
litter and SOM pool, as well as a base rate for physical fragmentation
for the coarse woody debris pool (CWD).
.. _Table Decomposition rate constants:
.. table:: Decomposition rate constants for litter and SOM pools, C:N ratios, and acceleration parameters for the CLM-CN decomposition pool structure.
+--------------------------+------------------------------------------------+-----------------------------------------------+---------------+-----------------------------------------+
| | Biome-BGC | CLM-CN | | |
+==========================+================================================+===============================================+===============+=========================================+
| | :math:`{k}_{disc1}`\ (d\ :sup:`-1`) | :math:`{k}_{disc2}` (hr\ :sup:`-1`) | *C:N ratio* | Acceleration term (:math:`{a}_{i}`) |
+--------------------------+------------------------------------------------+-----------------------------------------------+---------------+-----------------------------------------+
| :math:`{k}_{Lit1}` | 0.7 | 0.04892 | - | 1 |
+--------------------------+------------------------------------------------+-----------------------------------------------+---------------+-----------------------------------------+
| :math:`{k}_{Lit2}` | 0.07 | 0.00302 | - | 1 |
+--------------------------+------------------------------------------------+-----------------------------------------------+---------------+-----------------------------------------+
| :math:`{k}_{Lit3}` | 0.014 | 0.00059 | - | 1 |
+--------------------------+------------------------------------------------+-----------------------------------------------+---------------+-----------------------------------------+
| :math:`{k}_{SOM1}` | 0.07 | 0.00302 | 12 | 1 |
+--------------------------+------------------------------------------------+-----------------------------------------------+---------------+-----------------------------------------+
| :math:`{k}_{SOM2}` | 0.014 | 0.00059 | 12 | 1 |
+--------------------------+------------------------------------------------+-----------------------------------------------+---------------+-----------------------------------------+
| :math:`{k}_{SOM3}` | 0.0014 | 0.00006 | 10 | 5 |
+--------------------------+------------------------------------------------+-----------------------------------------------+---------------+-----------------------------------------+
| :math:`{k}_{SOM4}` | 0.0001 | 0.000004 | 10 | 70 |
+--------------------------+------------------------------------------------+-----------------------------------------------+---------------+-----------------------------------------+
| :math:`{k}_{CWD}` | 0.001 | 0.00004 | - | 1 |
+--------------------------+------------------------------------------------+-----------------------------------------------+---------------+-----------------------------------------+
The first column of :numref:`Table Decomposition rate constants` gives the rates as used for the Biome-BGC
model, which uses a discrete-time model with a daily timestep. The
second column of :numref:`Table Decomposition rate constants` shows the rates transformed for a one-hour
discrete timestep typical of CLM-CN. The transformation is based on the
conversion of the initial discrete-time value (:math:`{k}_{disc1}`)
first to a continuous time value (:math:`{k}_{cont}`), then to the
new discrete-time value with a different timestep
(:math:`{k}_{disc2}`) , following Olson (1963):
.. math::
:label: ZEqnNum608251
k_{cont} =-\log \left(1-k_{disc1} \right)
.. math::
:label: ZEqnNum772630
k_{disc2} =1-\exp \left(-k_{cont} \frac{\Delta t_{2} }{\Delta t_{1} } \right)
where :math:`\Delta`\ :math:`{t}_{1}` (s) and
:math:`\Delta`\ t\ :sub:`2` (s) are the time steps of the
initial and new discrete-time models, respectively.
Respiration fractions are parameterized for decomposition fluxes out of
each litter and SOM pool. The respiration fraction (*rf*, unitless) is
the fraction of the decomposition carbon flux leaving one of the litter
or SOM pools that is released as CO\ :sub:`2` due to heterotrophic
respiration. Respiration fractions and exponential decay rates are
estimated simultaneously from the results of microcosm decomposition
experiments (Thornton, 1998). The same values are used in CLM-CN and
Biome-BGC (:numref:`Table Respiration fractions for litter and SOM pools`).
.. _Table Respiration fractions for litter and SOM pools:
.. table:: Respiration fractions for litter and SOM pools
+---------------------------+-----------------------+
| Pool | *rf* |
+===========================+=======================+
| :math:`{rf}_{Lit1}` | 0.39 |
+---------------------------+-----------------------+
| :math:`{rf}_{Lit2}` | 0.55 |
+---------------------------+-----------------------+
| :math:`{rf}_{Lit3}` | 0.29 |
+---------------------------+-----------------------+
| :math:`{rf}_{SOM1}` | 0.28 |
+---------------------------+-----------------------+
| :math:`{rf}_{SOM2}` | 0.46 |
+---------------------------+-----------------------+
| :math:`{rf}_{SOM3}` | 0.55 |
+---------------------------+-----------------------+
| :math:`{rf}_{SOM4}` | :math:`{1.0}^{a}` |
+---------------------------+-----------------------+
:sup:`a`:math:`{}^{a}` The respiration fraction for pool SOM4 is 1.0 by
definition: since there is no pool downstream of SOM4, the entire carbon
flux leaving this pool is assumed to be respired as CO\ :sub:`2`.
Century-based Pool Structure, Rate Constants and Parameters
----------------------------------------------------------------
The Century-based decomposition cascade is, like CLM-CN, a first-order
decay model; the two structures differ in the number of pools, the
connections between those pools, the turnover times of the pools, and
the respired fraction during each transition (Figure 15.2). The turnover
times are different for the Century-based pool structure, following
those described in Parton et al. (1988) (:numref:`Table Turnover times`).
.. _Table Turnover times:
.. table:: Turnover times, C:N ratios, and acceleration parameters for the Century-based decomposition cascade.
+------------+------------------------+-------------+-------------------------------------------+
| | Turnover time (year) | C:N ratio | Acceleration term (:math:`{a}_{i}`) |
+============+========================+=============+===========================================+
| CWD | 4.1 | - | 1 |
+------------+------------------------+-------------+-------------------------------------------+
| Litter 1 | 0.066 | - | 1 |
+------------+------------------------+-------------+-------------------------------------------+
| Litter 2 | 0.25 | - | 1 |
+------------+------------------------+-------------+-------------------------------------------+
| Litter 3 | 0.25 | - | 1 |
+------------+------------------------+-------------+-------------------------------------------+
| SOM 1 | 0.17 | 8 | 1 |
+------------+------------------------+-------------+-------------------------------------------+
| SOM 2 | 6.1 | 11 | 15 |
+------------+------------------------+-------------+-------------------------------------------+
| SOM 3 | 270 | 11 | 675 |
+------------+------------------------+-------------+-------------------------------------------+
Likewise, values for the respiration fraction of Century-based structure are in :numref:`Table Respiration fractions for Century-based structure`.
.. _Table Respiration fractions for Century-based structure:
.. table:: Respiration fractions for litter and SOM pools for Century-based structure
+---------------------------+----------+
| Pool | *rf* |
+===========================+==========+
| :math:`{rf}_{Lit1}` | 0.55 |
+---------------------------+----------+
| :math:`{rf}_{Lit2}` | 0.5 |
+---------------------------+----------+
| :math:`{rf}_{Lit3}` | 0.5 |
+---------------------------+----------+
| :math:`{rf}_{SOM1}` | f(txt) |
+---------------------------+----------+
| :math:`{rf}_{SOM2}` | 0.55 |
+---------------------------+----------+
| :math:`{rf}_{SOM3}` | 0.55 |
+---------------------------+----------+
Environmental modifiers on decomposition rate
--------------------------------------------------
These base rates are modified on each timestep by functions of the
current soil environment. For the single-level model, there are two rate
modifiers, temperature (:math:`{r}_{tsoil}`, unitless) and moisture
(:math:`{r}_{water}`, unitless), both of which are calculated using
the average environmental conditions of the top five model levels (top
29 cm of soil column). For the vertically-resolved model, two additional
environmental modifiers are calculated beyond the temperature and
moisture limitations: an oxygen scalar (:math:`{r}_{oxygen}`,
unitless), and a depth scalar (:math:`{r}_{depth}`, unitless).
The Temperature scalar :math:`{r}_{tsoil}` is calculated in CLM
using a :math:`{Q}_{10}` approach, with :math:`{Q}_{10} = 1.5`.
.. math::
:label: 21.5)
r_{tsoil} =Q_{10} ^{\left(\frac{T_{soil,\, j} -T_{ref} }{10} \right)}
where *j* is the soil layer index, :math:`{T}_{soil,j}` (K) is the
temperature of soil level *j*. The reference temperature :math:`{T}_{ref}` = 25C.
The rate scalar for soil water potential (:math:`{r}_{water}`,
unitless) is calculated using a relationship from Andrén and Paustian
(1987) and supported by additional data in Orchard and Cook (1983):
.. math::
:label: 21.6)
r_{water} =\sum _{j=1}^{5}\left\{\begin{array}{l} {0\qquad {\rm for\; }\Psi _{j} <\Psi _{\min } } \\ {\frac{\log \left({\Psi _{\min } \mathord{\left/ {\vphantom {\Psi _{\min } \Psi _{j} }} \right. \kern-\nulldelimiterspace} \Psi _{j} } \right)}{\log \left({\Psi _{\min } \mathord{\left/ {\vphantom {\Psi _{\min } \Psi _{\max } }} \right. \kern-\nulldelimiterspace} \Psi _{\max } } \right)} w_{soil,\, j} \qquad {\rm for\; }\Psi _{\min } \le \Psi _{j} \le \Psi _{\max } } \\ {1\qquad {\rm for\; }\Psi _{j} >\Psi _{\max } \qquad \qquad } \end{array}\right\}
where :math:`{\Psi}_{j}` is the soil water potential in
layer *j*, :math:`{\Psi}_{min}` is a lower limit for soil
water potential control on decomposition rate (in CLM5, this was
changed from a default value of -10 MPa used in CLM4.5 and earlier to a
default value of -2.5 MPa). :math:`{\Psi}_{max,j}` (MPa) is the soil
moisture at which decomposition proceeds at a moisture-unlimited
rate. The default value of :math:`{\Psi}_{max,j}` for CLM5 is updated
from a saturated value used in CLM4.5 and earlier, to a value
nominally at field capacity, with a value of -0.002 MPa
For frozen soils, the bulk of the rapid dropoff in decomposition with
decreasing temperature is due to the moisture limitation, since matric
potential is limited by temperature in the supercooled water formulation
of Niu and Yang (2006),
.. math::
:label: 21.8)
\psi \left(T\right)=-\frac{L_{f} \left(T-T_{f} \right)}{10^{3} T}
An additional frozen decomposition limitation can be specified using a
‘frozen Q\ :sub:`10`' following :ref:`Koven et al. (2011) `, however the
default value of this is the same as the unfrozen Q\ :sub:`10`
value, and therefore the basic hypothesis is that frozen respiration is
limited by liquid water availability, and can be modeled following the
same approach as thawed but dry soils.
An additional rate scalar, :math:`{r}_{oxygen}` is enabled when the
CH\ :sub:`4` submodel is used (set equal to 1 for the single layer
model or when the CH\ :sub:`4` submodel is disabled). This limits
decomposition when there is insufficient molecular oxygen to satisfy
stoichiometric demand (1 mol O\ :sub:`2` consumed per mol
CO\ :sub:`2` produced) from heterotrophic decomposers, and supply
from diffusion through soil layers (unsaturated and saturated) or
aerenchyma (Chapter 19). A minimum value of :math:`{r}_{oxygen}` is
set at 0.2, with the assumption that oxygen within organic tissues can
supply the necessary stoichiometric demand at this rate. This value lies
between estimates of 0.025–0.1 (Frolking et al. 2001), and 0.35 (Wania
et al. 2009); the large range of these estimates poses a large
unresolved uncertainty.
Lastly, a possible explicit depth dependence, :math:`{r}_{depth}`,
(set equal to 1 for the single layer model) can be applied to soil C
decomposition rates to account for processes other than temperature,
moisture, and anoxia that can limit decomposition. This depth dependence
of decomposition was shown by Jenkinson and Coleman (2008) to be an
important term in fitting total C and 14C profiles, and implies that
unresolved processes, such as priming effects, microscale anoxia, soil
mineral surface and/or aggregate stabilization may be important in
controlling the fate of carbon at depth :ref:`Koven et al. (2013) `. CLM
includes these unresolved depth controls via an exponential decrease in
the soil turnover time with depth:
.. math::
:label: 21.9)
r_{depth} =\exp \left(-\frac{z}{z_{\tau } } \right)
where :math:`{z}_{\tau}` is the e-folding depth for decomposition. For
CLM4.5, the default value of this was 0.5m. For CLM5, this has been
changed to a default value of 10m, which effectively means that
intrinsic decomposition rates may proceed as quickly at depth as at the surface.
The combined decomposition rate scalar (:math:`{r}_{total}`,unitless) is:
.. math::
:label: 21.10)
r_{total} =r_{tsoil} r_{water} r_{oxygen} r_{depth} .
N-limitation of Decomposition Fluxes
-----------------------------------------
Decomposition rates can also be limited by the availability of mineral
nitrogen, but calculation of this limitation depends on first estimating
the potential rates of decomposition, assuming an unlimited mineral
nitrogen supply. The general case is described here first, referring to
a generic decomposition flux from an “upstream” pool (*u*) to a
“downstream” pool (*d*), with an intervening loss due to respiration.
The potential carbon flux out of the upstream pool
(:math:`{CF}_{pot,u}`, gC m\ :sup:`-2` s\ :sup:`-1`) is:
.. math::
:label: 21.11)
CF_{pot,\, u} =CS_{u} k_{u}
where :math:`{CS}_{u}` (gC m\ :sup:`-2`) is the initial mass
in the upstream pool and :math:`{k}_{u}` is the decay rate constant
(s:sup:`-1`) for the upstream pool, adjusted for temperature and
moisture conditions. Depending on the C:N ratios of the upstream and
downstream pools and the amount of carbon lost in the transformation due
to respiration (the respiration fraction), the execution of this
potential carbon flux can generate either a source or a sink of new
mineral nitrogen
(:math:`{NF}_{pot\_min,u}`\ :math:`{}_{\rightarrow}`\ :math:`{}_{d}`, gN m\ :sup:`-2` s\ :sup:`-1`). The governing equation
(Thornton and Rosenbloom, 2005) is:
.. math::
:label: 21.12)
NF_{pot\_ min,\, u\to d} =\frac{CF_{pot,\, u} \left(1-rf_{u} -\frac{CN_{d} }{CN_{u} } \right)}{CN_{d} }
where :math:`{rf}_{u}` is the respiration fraction for fluxes
leaving the upstream pool, :math:`{CN}_{u}` and :math:`{CN}_{d}`
are the C:N ratios for upstream and downstream pools, respectively.
Negative values of
:math:`{NF}_{pot\_min,u}`\ :math:`{}_{\rightarrow}`\ :math:`{}_{d}`
indicate that the decomposition flux results in a source of new mineral
nitrogen, while positive values indicate that the potential
decomposition flux results in a sink (demand) for mineral nitrogen.
Following from the general case, potential carbon fluxes leaving
individual pools in the decomposition cascade, for the example of the
CLM-CN pool structure, are given as:
.. math::
:label: 21.13)
CF_{pot,\, Lit1} ={CS_{Lit1} k_{Lit1} r_{total} \mathord{\left/ {\vphantom {CS_{Lit1} k_{Lit1} r_{total} \Delta t}} \right. \kern-\nulldelimiterspace} \Delta t}
.. math::
:label: 21.14)
CF_{pot,\, Lit2} ={CS_{Lit2} k_{Lit2} r_{total} \mathord{\left/ {\vphantom {CS_{Lit2} k_{Lit2} r_{total} \Delta t}} \right. \kern-\nulldelimiterspace} \Delta t}
.. math::
:label: 21.15)
CF_{pot,\, Lit3} ={CS_{Lit3} k_{Lit3} r_{total} \mathord{\left/ {\vphantom {CS_{Lit3} k_{Lit3} r_{total} \Delta t}} \right. \kern-\nulldelimiterspace} \Delta t}
.. math::
:label: 21.16)
CF_{pot,\, SOM1} ={CS_{SOM1} k_{SOM1} r_{total} \mathord{\left/ {\vphantom {CS_{SOM1} k_{SOM1} r_{total} \Delta t}} \right. \kern-\nulldelimiterspace} \Delta t}
.. math::
:label: 21.17)
CF_{pot,\, SOM2} ={CS_{SOM2} k_{SOM2} r_{total} \mathord{\left/ {\vphantom {CS_{SOM2} k_{SOM2} r_{total} \Delta t}} \right. \kern-\nulldelimiterspace} \Delta t}
.. math::
:label: 21.18)
CF_{pot,\, SOM3} ={CS_{SOM3} k_{SOM3} r_{total} \mathord{\left/ {\vphantom {CS_{SOM3} k_{SOM3} r_{total} \Delta t}} \right. \kern-\nulldelimiterspace} \Delta t}
.. math::
:label: 21.19)
CF_{pot,\, SOM4} ={CS_{SOM4} k_{SOM4} r_{total} \mathord{\left/ {\vphantom {CS_{SOM4} k_{SOM4} r_{total} \Delta t}} \right. \kern-\nulldelimiterspace} \Delta t}
where the factor (1/:math:`\Delta`\ *t*) is included because the rate
constant is calculated for the entire timestep (Eqs. and ), but the
convention is to express all fluxes on a per-second basis. Potential
mineral nitrogen fluxes associated with these decomposition steps are,
again for the example of the CLM-CN pool structure (the CENTURY
structure will be similar but without the different terminal step):
.. math::
:label: ZEqnNum934998
NF_{pot\_ min,\, Lit1\to SOM1} ={CF_{pot,\, Lit1} \left(1-rf_{Lit1} -\frac{CN_{SOM1} }{CN_{Lit1} } \right)\mathord{\left/ {\vphantom {CF_{pot,\, Lit1} \left(1-rf_{Lit1} -\frac{CN_{SOM1} }{CN_{Lit1} } \right) CN_{SOM1} }} \right. \kern-\nulldelimiterspace} CN_{SOM1} }
.. math::
:label: 21.21)
NF_{pot\_ min,\, Lit2\to SOM2} ={CF_{pot,\, Lit2} \left(1-rf_{Lit2} -\frac{CN_{SOM2} }{CN_{Lit2} } \right)\mathord{\left/ {\vphantom {CF_{pot,\, Lit2} \left(1-rf_{Lit2} -\frac{CN_{SOM2} }{CN_{Lit2} } \right) CN_{SOM2} }} \right. \kern-\nulldelimiterspace} CN_{SOM2} }
.. math::
:label: 21.22)
NF_{pot\_ min,\, Lit3\to SOM3} ={CF_{pot,\, Lit3} \left(1-rf_{Lit3} -\frac{CN_{SOM3} }{CN_{Lit3} } \right)\mathord{\left/ {\vphantom {CF_{pot,\, Lit3} \left(1-rf_{Lit3} -\frac{CN_{SOM3} }{CN_{Lit3} } \right) CN_{SOM3} }} \right. \kern-\nulldelimiterspace} CN_{SOM3} }
.. math::
:label: 21.23)
NF_{pot\_ min,\, SOM1\to SOM2} ={CF_{pot,\, SOM1} \left(1-rf_{SOM1} -\frac{CN_{SOM2} }{CN_{SOM1} } \right)\mathord{\left/ {\vphantom {CF_{pot,\, SOM1} \left(1-rf_{SOM1} -\frac{CN_{SOM2} }{CN_{SOM1} } \right) CN_{SOM2} }} \right. \kern-\nulldelimiterspace} CN_{SOM2} }
.. math::
:label: 21.24)
NF_{pot\_ min,\, SOM2\to SOM3} ={CF_{pot,\, SOM2} \left(1-rf_{SOM2} -\frac{CN_{SOM3} }{CN_{SOM2} } \right)\mathord{\left/ {\vphantom {CF_{pot,\, SOM2} \left(1-rf_{SOM2} -\frac{CN_{SOM3} }{CN_{SOM2} } \right) CN_{SOM3} }} \right. \kern-\nulldelimiterspace} CN_{SOM3} }
.. math::
:label: 21.25)
NF_{pot\_ min,\, SOM3\to SOM4} ={CF_{pot,\, SOM3} \left(1-rf_{SOM3} -\frac{CN_{SOM4} }{CN_{SOM3} } \right)\mathord{\left/ {\vphantom {CF_{pot,\, SOM3} \left(1-rf_{SOM3} -\frac{CN_{SOM4} }{CN_{SOM3} } \right) CN_{SOM4} }} \right. \kern-\nulldelimiterspace} CN_{SOM4} }
.. math::
:label: ZEqnNum473594
NF_{pot\_ min,\, SOM4} =-{CF_{pot,\, SOM4} \mathord{\left/ {\vphantom {CF_{pot,\, SOM4} CN_{SOM4} }} \right. \kern-\nulldelimiterspace} CN_{SOM4} }
where the special form of Eq. arises because there is no SOM pool
downstream of SOM4 in the converging cascade: all carbon fluxes leaving
that pool are assumed to be in the form of respired CO\ :sub:`2`,
and all nitrogen fluxes leaving that pool are assumed to be sources of
new mineral nitrogen.
Steps in the decomposition cascade that result in release of new mineral
nitrogen (mineralization fluxes) are allowed to proceed at their
potential rates, without modification for nitrogen availability. Steps
that result in an uptake of mineral nitrogen (immobilization fluxes) are
subject to rate limitation, depending on the availability of mineral
nitrogen, the total immobilization demand, and the total demand for soil
mineral nitrogen to support new plant growth. The potential mineral
nitrogen fluxes from Eqs. - are evaluated, summing all the positive
fluxes to generate the total potential nitrogen immobilization flux
(:math:`{NF}_{immob\_demand}`, gN m\ :sup:`-2` s\ :sup:`-1`), and summing absolute values of all the negative
fluxes to generate the total nitrogen mineralization flux
(:math:`{NF}_{gross\_nmin}`, gN m\ :sup:`-2` s\ :sup:`-1`). Since :math:`{NF}_{griss\_nmin}` is a source of
new mineral nitrogen to the soil mineral nitrogen pool it is not limited
by the availability of soil mineral nitrogen, and is therefore an actual
as opposed to a potential flux.
N Competition between plant uptake and soil immobilization fluxes
----------------------------------------------------------------------
Once :math:`{NF}_{immob\_demand }` and :math:`{NF}_{nit\_demand }` for each layer *j* are known, the competition between plant and microbial nitrogen demand can be resolved. Mineral nitrogen in
the soil pool (:math:`{NS}_{sminn}`, gN m\ :sup:`-2`) at the
beginning of the timestep is considered the available supply.
Here, the :math:`{NF}_{plant\_demand}` is the theoretical maximum demand for nitrogen by plants to meet the entire carbon uptake given an N cost of zero (and therefore represents the upper bound on N requirements). N uptake costs that are
:math:`>` 0 imply that the plant will take up less N that it demands, ultimately. However, given the heuristic nature of the N competition algorithm, this discrepancy is not explicitly resolved here.
The hypothetical plant nitrogen demand from the soil mineral pool is distributed between layers in proportion to the profile of available mineral N:
.. math::
:label: 21.291
NF_{plant\_ demand,j} = NF_{plant\_ demand} NS_{sminn\_ j} / \sum _{j=1}^{nj}NS_{sminn,j}
Plants first compete for ammonia (NH4). For each soil layer (*j*), we calculate the total NH4 demand as:
.. math::
:label: 21.292
NF_{total\_ demand_nh4,j} = NF_{immob\_ demand,j} + NF_{immob\_ demand,j} + NF_{nit\_ demand,j}
where
If :math:`{NF}_{total\_demand,j}`\ :math:`\Delta`\ *t* :math:`<`
:math:`{NS}_{sminn,j}`, then the available pool is large enough to
meet both the maximum plant and microbial demand, then immobilization proceeds at the maximum rate.
.. math::
:label: 21.29)
f_{immob\_demand,j} = 1.0
where :math:`{f}_{immob\_demand,j}` is the fraction of potential immobilization demand that can be met given current supply of mineral nitrogen in this layer. We also set the actual nitrification flux to be the same as the potential flux (:math:`NF_{nit}` = :math:`NF_{nit\_ demand}`).
If :math:`{NF}_{total\_demand,j}`\ :math:`\Delta`\ *t*
:math:`\mathrm{\ge}` :math:`{NS}_{sminn,j}`, then there is not enough
mineral nitrogen to meet the combined demands for plant growth and
heterotrophic immobilization, immobilization is reduced proportional to the discrepancy, by :math:`f_{immob\_ demand,j}`, where
.. math::
:label: 21.30)
f_{immob\_ demand,j} = \frac{NS_{sminn,j} }{\Delta t\, NF_{total\_ demand,j} }
The N available to the FUN model for plant uptake (:math:`{NF}_ {plant\_ avail\_ sminn}` (gN m\ :sup:`-2`), which determines both the cost of N uptake, and the absolute limit on the N which is available for acquisition, is calculated as the total mineralized pool minus the actual immobilized flux:
.. math::
:label: 21.311)
NF_{plant\_ avail\_ sminn,j} = NS_{sminn,j} - f_{immob\_demand} NF_{immob\_ demand,j}
This treatment of competition for nitrogen as a limiting resource is
referred to a demand-based competition, where the fraction of the
available resource that eventually flows to a particular process depends
on the demand from that process in comparison to the total demand from
all processes. Processes expressing a greater demand acquire a larger
vfraction of the available resource.
Final Decomposition Fluxes
-------------------------------
With :math:`{f}_{immob\_demand}` known, final decomposition fluxes
can be calculated. Actual carbon fluxes leaving the individual litter
and SOM pools, again for the example of the CLM-CN pool structure (the
CENTURY structure will be similar but, again without the different
terminal step), are calculated as:
.. math::
:label: 21.32)
CF_{Lit1} =\left\{\begin{array}{l} {CF_{pot,\, Lit1} f_{immob\_ demand} \qquad {\rm for\; }NF_{pot\_ min,\, Lit1\to SOM1} >0} \\ {CF_{pot,\, Lit1} \qquad {\rm for\; }NF_{pot\_ min,\, Lit1\to SOM1} \le 0} \end{array}\right\}
.. math::
:label: 21.33)
CF_{Lit2} =\left\{\begin{array}{l} {CF_{pot,\, Lit2} f_{immob\_ demand} \qquad {\rm for\; }NF_{pot\_ min,\, Lit2\to SOM2} >0} \\ {CF_{pot,\, Lit2} \qquad {\rm for\; }NF_{pot\_ min,\, Lit2\to SOM2} \le 0} \end{array}\right\}
.. math::
:label: 21.34)
CF_{Lit3} =\left\{\begin{array}{l} {CF_{pot,\, Lit3} f_{immob\_ demand} \qquad {\rm for\; }NF_{pot\_ min,\, Lit3\to SOM3} >0} \\ {CF_{pot,\, Lit3} \qquad {\rm for\; }NF_{pot\_ min,\, Lit3\to SOM3} \le 0} \end{array}\right\}
.. math::
:label: 21.35)
CF_{SOM1} =\left\{\begin{array}{l} {CF_{pot,\, SOM1} f_{immob\_ demand} \qquad {\rm for\; }NF_{pot\_ min,\, SOM1\to SOM2} >0} \\ {CF_{pot,\, SOM1} \qquad {\rm for\; }NF_{pot\_ min,\, SOM1\to SOM2} \le 0} \end{array}\right\}
.. math::
:label: 21.36)
CF_{SOM2} =\left\{\begin{array}{l} {CF_{pot,\, SOM2} f_{immob\_ demand} \qquad {\rm for\; }NF_{pot\_ min,\, SOM2\to SOM3} >0} \\ {CF_{pot,\, SOM2} \qquad {\rm for\; }NF_{pot\_ min,\, SOM2\to SOM3} \le 0} \end{array}\right\}
.. math::
:label: 21.37)
CF_{SOM3} =\left\{\begin{array}{l} {CF_{pot,\, SOM3} f_{immob\_ demand} \qquad {\rm for\; }NF_{pot\_ min,\, SOM3\to SOM4} >0} \\ {CF_{pot,\, SOM3} \qquad {\rm for\; }NF_{pot\_ min,\, SOM3\to SOM4} \le 0} \end{array}\right\}
.. math::
:label: 21.38)
CF_{SOM4} =CF_{pot,\, SOM4}
Heterotrophic respiration fluxes (losses of carbon as
CO\ :sub:`2` to the atmosphere) are:
.. math::
:label: 21.39)
CF_{Lit1,\, HR} =CF_{Lit1} rf_{Lit1}
.. math::
:label: 21.40)
CF_{Lit2,\, HR} =CF_{Lit2} rf_{Lit2}
.. math::
:label: 21.41)
CF_{Lit3,\, HR} =CF_{Lit3} rf_{Lit3}
.. math::
:label: 21.42)
CF_{SOM1,\, HR} =CF_{SOM1} rf_{SOM1}
.. math::
:label: 21.43)
CF_{SOM2,\, HR} =CF_{SOM2} rf_{SOM2}
.. math::
:label: 21.44)
CF_{SOM3,\, HR} =CF_{SOM3} rf_{SOM3}
.. math::
:label: 21.45)
CF_{SOM4,\, HR} =CF_{SOM4} rf_{SOM4}
Transfers of carbon from upstream to downstream pools in the
decomposition cascade are given as:
.. math::
:label: 21.46)
CF_{Lit1,\, SOM1} =CF_{Lit1} \left(1-rf_{Lit1} \right)
.. math::
:label: 21.47)
CF_{Lit2,\, SOM2} =CF_{Lit2} \left(1-rf_{Lit2} \right)
.. math::
:label: 21.48)
CF_{Lit3,\, SOM3} =CF_{Lit3} \left(1-rf_{Lit3} \right)
.. math::
:label: 21.49)
CF_{SOM1,\, SOM2} =CF_{SOM1} \left(1-rf_{SOM1} \right)
.. math::
:label: 21.50)
CF_{SOM2,\, SOM3} =CF_{SOM2} \left(1-rf_{SOM2} \right)
.. math::
:label: 21.51)
CF_{SOM3,\, SOM4} =CF_{SOM3} \left(1-rf_{SOM3} \right)
In accounting for the fluxes of nitrogen between pools in the
decomposition cascade and associated fluxes to or from the soil mineral
nitrogen pool, the model first calculates a flux of nitrogen from an
upstream pool to a downstream pool, then calculates a flux either from
the soil mineral nitrogen pool to the downstream pool (immobilization)
or from the downstream pool to the soil mineral nitrogen pool
(mineralization). Transfers of nitrogen from upstream to downstream
pools in the decomposition cascade are given as:
.. math::
:label: 21.52)
NF_{Lit1,\, SOM1} ={CF_{Lit1} \mathord{\left/ {\vphantom {CF_{Lit1} CN_{Lit1} }} \right. \kern-\nulldelimiterspace} CN_{Lit1} }
.. math::
:label: 21.53)
NF_{Lit2,\, SOM2} ={CF_{Lit2} \mathord{\left/ {\vphantom {CF_{Lit2} CN_{Lit2} }} \right. \kern-\nulldelimiterspace} CN_{Lit2} }
.. math::
:label: 21.54)
NF_{Lit3,\, SOM3} ={CF_{Lit3} \mathord{\left/ {\vphantom {CF_{Lit3} CN_{Lit3} }} \right. \kern-\nulldelimiterspace} CN_{Lit3} }
.. math::
:label: 21.55)
NF_{SOM1,\, SOM2} ={CF_{SOM1} \mathord{\left/ {\vphantom {CF_{SOM1} CN_{SOM1} }} \right. \kern-\nulldelimiterspace} CN_{SOM1} }
.. math::
:label: 21.56)
NF_{SOM2,\, SOM3} ={CF_{SOM2} \mathord{\left/ {\vphantom {CF_{SOM2} CN_{SOM2} }} \right. \kern-\nulldelimiterspace} CN_{SOM2} }
.. math::
:label: 21.57)
NF_{SOM3,\, SOM4} ={CF_{SOM3} \mathord{\left/ {\vphantom {CF_{SOM3} CN_{SOM3} }} \right. \kern-\nulldelimiterspace} CN_{SOM3} }
Corresponding fluxes to or from the soil mineral nitrogen pool depend on
whether the decomposition step is an immobilization flux or a
mineralization flux:
.. math::
:label: 21.58)
NF_{sminn,\, Lit1\to SOM1} =\left\{\begin{array}{l} {NF_{pot\_ min,\, Lit1\to SOM1} f_{immob\_ demand} \qquad {\rm for\; }NF_{pot\_ min,\, Lit1\to SOM1} >0} \\ {NF_{pot\_ min,\, Lit1\to SOM1} \qquad {\rm for\; }NF_{pot\_ min,\, Lit1\to SOM1} \le 0} \end{array}\right\}
.. math::
:label: 21.59)
NF_{sminn,\, Lit2\to SOM2} =\left\{\begin{array}{l} {NF_{pot\_ min,\, Lit2\to SOM2} f_{immob\_ demand} \qquad {\rm for\; }NF_{pot\_ min,\, Lit2\to SOM2} >0} \\ {NF_{pot\_ min,\, Lit2\to SOM2} \qquad {\rm for\; }NF_{pot\_ min,\, Lit2\to SOM2} \le 0} \end{array}\right\}
.. math::
:label: 21.60)
NF_{sminn,\, Lit3\to SOM3} =\left\{\begin{array}{l} {NF_{pot\_ min,\, Lit3\to SOM3} f_{immob\_ demand} \qquad {\rm for\; }NF_{pot\_ min,\, Lit3\to SOM3} >0} \\ {NF_{pot\_ min,\, Lit3\to SOM3} \qquad {\rm for\; }NF_{pot\_ min,\, Lit3\to SOM3} \le 0} \end{array}\right\}
.. math::
:label: 21.61)
NF_{sminn,SOM1\to SOM2} =\left\{\begin{array}{l} {NF_{pot\_ min,\, SOM1\to SOM2} f_{immob\_ demand} \qquad {\rm for\; }NF_{pot\_ min,\, SOM1\to SOM2} >0} \\ {NF_{pot\_ min,\, SOM1\to SOM2} \qquad {\rm for\; }NF_{pot\_ min,\, SOM1\to SOM2} \le 0} \end{array}\right\}
.. math::
:label: 21.62)
NF_{sminn,SOM2\to SOM3} =\left\{\begin{array}{l} {NF_{pot\_ min,\, SOM2\to SOM3} f_{immob\_ demand} \qquad {\rm for\; }NF_{pot\_ min,\, SOM2\to SOM3} >0} \\ {NF_{pot\_ min,\, SOM2\to SOM3} \qquad {\rm for\; }NF_{pot\_ min,\, SOM2\to SOM3} \le 0} \end{array}\right\}
.. math::
:label: 21.63)
NF_{sminn,SOM3\to SOM4} =\left\{\begin{array}{l} {NF_{pot\_ min,\, SOM3\to SOM4} f_{immob\_ demand} \qquad {\rm for\; }NF_{pot\_ min,\, SOM3\to SOM4} >0} \\ {NF_{pot\_ min,\, SOM3\to SOM4} \qquad {\rm for\; }NF_{pot\_ min,\, SOM3\to SOM4} \le 0} \end{array}\right\}
.. math::
:label: 21.64)
NF_{sminn,\, SOM4} =NF_{pot\_ min,\, SOM4}
Vertical Distribution and Transport of Decomposing C and N pools
---------------------------------------------------------------------
Additional terms are needed to calculate the vertically-resolved soil C
and N budget: the initial vertical distribution of C and N from PFTs
delivered to the litter and CWD pools, and the vertical transport of C
and N pools.
For initial vertical inputs, CLM uses separate profiles for aboveground
(leaf, stem) and belowground (root) inputs. Aboveground inputs are given
a single exponential with default e-folding depth = 0.1m. Belowground
inputs are distributed according to rooting profiles with default values
based on the Jackson et al. (1996) exponential parameterization.
Vertical mixing is accomplished by an advection-diffusion equation. The
goal of this is to consider slow, soild- and adsorbed-phase transport
due to bioturbation, cryoturbation, and erosion. Faster aqueous-phase
transport is not included in CLM, but has been developed as part of the
CLM-BeTR suite of parameterizations (Tang and Riley 2013). The default
value of the advection term is 0 cm/yr, such that transport is purely
diffusive. Diffusive transport differs in rate between permafrost soils
(where cryoturbation is the dominant transport term) and non-permafrost
soils (where bioturbation dominates). For permafrost soils, a
parameterization based on that of :ref:`Koven et al. (2009) ` is used: the
diffusivity parameter is constant through the active layer, and
decreases linearly from the base of the active layer to zero at a set
depth (default 3m); the default permafrost diffusivity is 5
cm\ :sup:`2`/yr. For non-permafrost soils, the default diffusivity
is 1 cm\ :sup:`2`/yr.
Model Equilibration and its Acceleration
-----------------------------------------
For transient experiments, it is usually assumed that the carbon cycle
is starting from a point of relatively close equilibrium, i.e. that
productivity is balanced by ecosystem carbon losses through
respiratory and disturbance pathways. In order to satisfy this
assumption, the model is generally run until the productivity and loss
terms find a stable long-term equilibrium; at this point the model is
considered 'spun up'.
Because of the coupling between the slowest SOM pools and productivity
through N downregulation of photosynthesis, equilibration of the model
for initialization purposes will take an extremely long time in the
standard mode. This is particularly true for the CENTURY-based
decomposition cascade, which includes a passive pool. In order to
rapidly equilibrate the model, a modified version of the “accelerated
decomposition” :ref:`(Thornton and Rosenbloon, 2005) ` is used. The fundamental
idea of this approach is to allow fluxes between the various pools (both
turnover-defined and vertically-defined fluxes) adjust rapidly, while
keeping the pool sizes themselves small so that they can fill quickly.
To do this, the base decomposition rate :math:`{k}_{i}` for each
pool *i* is accelerated by a term :math:`{a}_{i}` such that the slow
pools are collapsed onto an approximately annual timescale :ref:`Koven et al. (2013) `. Accelerating the pools beyond this timescale distorts the
seasonal and/or diurnal cycles of decomposition and N mineralization,
thus leading to a substantially different ecosystem productivity than
the full model. For the vertical model, the vertical transport terms are
also accelerated by the same term :math:`{a}_{i}`, as is the
radioactive decay when :math:`{}^{14}`\ C is enabled, following the same
principle of keeping fluxes between pools (or fluxes lost to decay)
close to the full model while keeping the pools sizes small. When
leaving the accelerated decomposition mode, the concentration of C and N
in pools that had been accelerated are multiplied by the same term
:math:`{a}_{i}`, to bring the model into approximate equilibrium.
Note that in CLM, the model can also transition into accelerated
decomposition mode from the standard mode (by dividing the pools by
:math:`{a}_{i}`), and that the transitions into and out of
accelerated decomposition mode are handled automatically by CLM upon
loading from restart files (which preserve information about the mode of
the model when restart files were written).
The base acceleration terms for the two decomposition cascades are shown in
Tables 15.1 and 15.3. In addition to the base terms, CLM5 also
includes a geographic term to the acceleration in order to apply
larger values to high-latitude systems, where decomposition rates are
particularly slow and thus equilibration can take significantly longer
than in temperate or tropical climates. This geographic term takes
the form of a logistic equation, where :math:`{a}_{i}` is equal to the
product of the base acceleration term and :math:`{a}_{l}` below:
.. math::
:label: 21.65)
a_l = 1 + 50 / \left ( 1 + exp \left (-0.1 * (abs(latitude) -
60 ) \right ) \right )