Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Fixes to methane Tech Note #2091

Merged
merged 6 commits into from
Sep 19, 2023
Merged
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
50 changes: 25 additions & 25 deletions doc/source/tech_note/Methane/CLM50_Tech_Note_Methane.rst
Original file line number Diff line number Diff line change
Expand Up @@ -66,15 +66,15 @@ phases:\ :math:`R = \epsilon _{a} +K_{H} \epsilon _{w}`, with
porosity, and partitioning coefficient for the species of interest,
respectively, and :math:`C` represents CH\ :sub:`4` or O\ :sub:`2` concentration with respect to water volume (mol m\ :sup:`-3`).

An analogous version of equation is concurrently solved for
An analogous version of equation :eq:`24.1` is concurrently solved for
O\ :sub:`2`, but with the following differences relative to
CH\ :sub:`4`: *P* = *E* = 0 (i.e., no production or ebullition),
and the oxidation sink includes the O\ :sub:`2` demanded by
methanotrophs, heterotroph decomposers, nitrifiers, and autotrophic root
respiration.

As currently implemented, each gridcell contains an inundated and a
non-inundated fraction. Therefore, equation is solved four times for
non-inundated fraction. Therefore, equation :eq:`24.1` is solved four times for
each gridcell and time step: in the inundated and non-inundated
fractions, and for CH\ :sub:`4` and O\ :sub:`2`. If desired,
the CH\ :sub:`4` and O\ :sub:`2` mass balance equation is
Expand Down Expand Up @@ -173,9 +173,9 @@ anoxic microsites above the water table, we apply the Arah and Stephen

\varphi =\frac{1}{1+\eta C_{O_{2} } } .

Here, :math:`\phi` is the factor by which production is inhibited
Here, :math:`\varphi` is the factor by which production is inhibited
above the water table (compared to production as calculated in equation
, :math:`C_{O_{2}}` (mol m\ :sup:`-3`) is the bulk soil oxygen
:eq:`24.2`, :math:`C_{O_{2}}` (mol m\ :sup:`-3`) is the bulk soil oxygen
concentration, and :math:`\eta` = 400 mol m\ :sup:`-3`.

The O\ :sub:`2` required to facilitate the vertically resolved
Expand Down Expand Up @@ -259,8 +259,8 @@ aqueous CH\ :sub:`4` concentration, and *p* is pressure.
The local pressure is calculated as the sum of the ambient pressure,
water pressure down to the local depth, and pressure from surface
ponding (if applicable). When the CH\ :sub:`4` partial pressure
exceeds 15% of the local pressure (Baird et al. 2004; Strack et al.
2006; Wania et al. 2010), bubbling occurs to remove CH\ :sub:`4`
exceeds 15% of the local pressure (:ref:`Baird et al. 2004<Bairdetal2004>`; :ref:`Strack et al.
2006<Stracketal2006>`; :ref:`Wania et al. 2010<Waniaetal2010>`), bubbling occurs to remove CH\ :sub:`4`
samsrabin marked this conversation as resolved.
Show resolved Hide resolved
to below this value, modified by the fraction of CH\ :sub:`4` in
the bubbles [taken as 57%; (:ref:`Kellner et al. 2006<Kellneretal2006>`;
:ref:`Wania et al. 2010<Waniaetal2010>`)].
Expand All @@ -286,14 +286,14 @@ The diffusive transport through aerenchyma (*A*, mol m\ :sup:`-2` s\ :sup:`-1`)

A=\frac{C\left(z\right)-C_{a} }{{\raise0.7ex\hbox{$ r_{L} z $}\!\mathord{\left/ {\vphantom {r_{L} z D}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ D $}} +r_{a} } pT\rho _{r} ,

where *D* is the free-air gas diffusion coefficient (m:sup:`2` s\ :sup:`-1`); *C(z)* (mol m\ :sup:`-3`) is the gaseous
where *D* is the free-air gas diffusion coefficient (m\ :sup:`2` s\ :sup:`-1`); *C(z)* (mol m\ :sup:`-3`) is the gaseous
concentration at depth *z* (m); :math:`r_{L}` is the ratio of root
length to depth; *p* is the porosity (-); *T* is specific aerenchyma
area (m:sup:`2` m\ :sup:`-2`); :math:`{r}_{a}` is the
area (m\ :sup:`2` m\ :sup:`-2`); :math:`{r}_{a}` is the
aerodynamic resistance between the surface and the atmospheric reference
height (s m:sup:`-1`); and :math:`\rho _{r}` is the rooting
height (s m\ :sup:`-1`); and :math:`\rho _{r}` is the rooting
density as a function of depth (-). The gaseous concentration is
calculated with Henry’s law as described in equation .
calculated with Henry’s law as described in equation :eq:`24.7`.
samsrabin marked this conversation as resolved.
Show resolved Hide resolved

Based on the ranges reported in :ref:`Colmer (2003)<Colmer2003>`, we have chosen
baseline aerenchyma porosity values of 0.3 for grass and crop PFTs and 0.1 for
Expand All @@ -310,7 +310,7 @@ m\ :sup:`-2` s\ :sup:`-1`); *R* is the aerenchyma radius
belowground fraction of annual NPP; and the 0.22 factor represents the
amount of C per tiller. O\ :sub:`2` can also diffuse in from the
atmosphere to the soil layer via the reverse of the same pathway, with
the same representation as Equation but with the gas diffusivity of
the same representation as Equation :eq:`24.8` but with the gas diffusivity of
oxygen.

CLM also simulates the direct emission of CH\ :sub:`4` from leaves
Expand Down Expand Up @@ -358,7 +358,7 @@ potential and :math:`{P}_{c} = -2.4 \times {10}^{5}` mm.
Reactive Transport Solution
--------------------------------

The solution to equation is solved in several sequential steps: resolve
The solution to equation :eq:`24.11` is solved in several sequential steps: resolve
competition for CH\ :sub:`4` and O\ :sub:`2` (section
:numref:`Competition for CH4and O2`); add the ebullition flux into the
layer directly above the water
Expand Down Expand Up @@ -416,7 +416,7 @@ Aqueous and Gaseous Diffusion

For gaseous diffusion, we adopted the temperature dependence of
molecular free-air diffusion coefficients (:math:`{D}_{0}`
(m:sup:`2` s\ :sup:`-1`)) as described by
(m\ :sup:`2` s\ :sup:`-1`)) as described by
:ref:`Lerman (1979) <Lerman1979>` and applied by
:ref:`Wania et al. (2010)<Waniaetal2010>`
(:numref:`Table Temperature dependence of aqueous and gaseous diffusion`).
Expand All @@ -426,7 +426,7 @@ molecular free-air diffusion coefficients (:math:`{D}_{0}`
.. table:: Temperature dependence of aqueous and gaseous diffusion coefficients for CH\ :sub:`4` and O\ :sub:`2`

+----------------------------------------------------------+----------------------------------------------------------+--------------------------------------------------------+
| :math:`{D}_{0}` (m\ :sup:`2` s\ :sup:`-1`) | CH\ :sub:`4` | O\ :sub:`2` |
| :math:`{D}_{0}` (cm\ :sup:`2` s\ :sup:`-1`) | CH\ :sub:`4` | O\ :sub:`2` |
Copy link
Contributor

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

I'm assuming you checked these units with the code?

Copy link
Collaborator Author

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Yep! The constants are set here, where the correct units are given in the comment:
https://github.com/samsrabin/CTSM/blob/7ae1372c0c39747ba71ae399cd2c5964e72f917d/src/main/clm_varcon.F90#L244-L247

When they're used, they're multiplied by 1e-4 to convert D0 from cm2/s to m2/s:
https://github.com/samsrabin/CTSM/blob/7ae1372c0c39747ba71ae399cd2c5964e72f917d/src/soilbiogeochem/SoilBiogeochemNitrifDenitrifMod.F90#L400

However, it looks like the table is missing a digit. Will add.

+==========================================================+==========================================================+========================================================+
| Aqueous | 0.9798 + 0.02986\ *T* + 0.0004381\ *T*\ :sup:`2` | 1.172+ 0.03443\ *T* + 0.0005048\ *T*\ :sup:`2` |
+----------------------------------------------------------+----------------------------------------------------------+--------------------------------------------------------+
Expand All @@ -437,7 +437,7 @@ Gaseous diffusivity in soils also depends on the molecular diffusivity,
soil structure, porosity, and organic matter content.
:ref:`Moldrup et al. (2003)<Moldrupetal2003>`, using observations across a
range of unsaturated mineral soils, showed that the relationship between
effective diffusivity (:math:`D_{e}` (m:sup:`2` s\ :sup:`-1`)) and soil
effective diffusivity (:math:`D_{e}` (m\ :sup:`2` s\ :sup:`-1`)) and soil
properties can be represented as:

.. math::
Expand All @@ -457,8 +457,8 @@ measurements more closely in unsaturated peat soils:

D_{e} =D_{0} \frac{\theta _{a} ^{{\raise0.7ex\hbox{$ 10 $}\!\mathord{\left/ {\vphantom {10 3}} \right. \kern-\nulldelimiterspace}\!\lower0.7ex\hbox{$ 3 $}} } }{\theta _{s} ^{2} }

In CLM, we applied equation for soils with zero organic matter content
and equation for soils with more than 130 kg m\ :sup:`-3` organic
In CLM, we applied equation :eq:`24.12` for soils with zero organic matter content
and equation :eq:`24.13` for soils with more than 130 kg m\ :sup:`-3` organic
matter content. A linear interpolation between these two limits is
applied for soils with SOM content below 130 kg m\ :sup:`-3`. For
aqueous diffusion in the saturated part of the soil column, we applied
Expand Down Expand Up @@ -518,10 +518,10 @@ a zero flux gradient at the bottom of the soil column.
Crank-Nicholson Solution
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Equation is solved using a Crank-Nicholson solution
(:ref:`Press et al. 1992<Pressetal1992>`),
Equation :eq:`24.1` is solved using a Crank-Nicholson solution
(:ref:`Press et al., 1992<Pressetal1992>`),
which combines fully explicit and implicit representations of the mass
balance. The fully explicit decomposition of equation can be written as
balance. The fully explicit decomposition of equation :eq:`24.1` can be written as

.. math::
:label: 24.15
Expand All @@ -535,11 +535,11 @@ and :math:`S_{j}^{n}` is the net source at time step *n* and position
*j*, i.e.,
:math:`S_{j}^{n} =P\left(j,n\right)-E\left(j,n\right)-A\left(j,n\right)-O\left(j,n\right)`.
The diffusivity coefficients are calculated as harmonic means of values
from the adjacent cells. Equation is solved for gaseous and aqueous
from the adjacent cells. Equation :eq:`24.15` is solved for gaseous and aqueous
concentrations above and below the water table, respectively. The *R*
term ensure the total mass balance in both phases is properly accounted
for. An analogous relationship can be generated for the fully implicit
case by replacing *n* by *n+1* on the *C* and *S* terms of equation .
case by replacing *n* by *n+1* on the *C* and *S* terms of equation :eq:`24.15`.
Using an average of the fully implicit and fully explicit relationships
gives:

Expand All @@ -548,14 +548,14 @@ gives:

\begin{array}{l} {-\frac{1}{2\Delta x_{j} } \frac{D_{m1}^{} }{\Delta x_{m1}^{} } C_{j-1}^{n+1} +\left[\frac{R_{j}^{n+1} }{\Delta t} +\frac{1}{2\Delta x_{j} } \left(\frac{D_{p1}^{} }{\Delta x_{p1}^{} } +\frac{D_{m1}^{} }{\Delta x_{m1}^{} } \right)\right]C_{j}^{n+1} -\frac{1}{2\Delta x_{j} } \frac{D_{p1}^{} }{\Delta x_{p1}^{} } C_{j+1}^{n+1} =} \\ {\frac{R_{j}^{n} }{\Delta t} +\frac{1}{2\Delta x_{j} } \left[\frac{D_{p1}^{} }{\Delta x_{p1}^{} } \left(C_{j+1}^{n} -C_{j}^{n} \right)-\frac{D_{m1}^{} }{\Delta x_{m1}^{} } \left(C_{j}^{n} -C_{j-1}^{n} \right)\right]+\frac{1}{2} \left[S_{j}^{n} +S_{j}^{n+1} \right]} \end{array},

Equation is solved with a standard tridiagonal solver, i.e.:
Equation :eq:`24.16` is solved with a standard tridiagonal solver, i.e.:

.. math::
:label: 24.17

aC_{j-1}^{n+1} +bC_{j}^{n+1} +cC_{j+1}^{n+1} =r,

with coefficients specified in equation .
with coefficients specified in equation :eq:`24.16`.

Two methane balance checks are performed at each timestep to insure that
the diffusion solution and the time-varying aggregation over inundated
Expand Down Expand Up @@ -599,7 +599,7 @@ Inundated Fraction Prediction
----------------------------------

A simplified dynamic representation of spatial inundation
based on recent work by :ref:`Prigent et al. (2007)<Prigentetal2007>` is used. Prigent et al. (2007) described a
based on recent work by :ref:`Prigent et al. (2007)<Prigentetal2007>` is used. :ref:`Prigent et al. (2007)<Prigentetal2007>` described a
multi-satellite approach to estimate the global monthly inundated
fraction (:math:`{F}_{i}`) over an equal area grid
(0.25 :math:`\circ` \ :math:`\times`\ 0.25\ :math:`\circ` at the equator)
Expand Down
Loading