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5eb8429
resolve issue #103: Example 1.7 typo
linniahawkins May 29, 2025
4062963
first update of the leaching doc
Oct 3, 2025
701256b
Merge branch 'master' into leaching-doc-update
jinmuluo Oct 3, 2025
41b4e10
Merge tag 'ctsm5.3.078' into merge-master-20251003
slevis-lmwg Oct 3, 2025
3d6713e
Merge pull request #3519 from slevis-lmwg/merge-master-20251003
slevis-lmwg Oct 3, 2025
6a9647b
Merge branch 'b4b-dev' into my_branch
ekluzek Oct 7, 2025
c383a15
Merge pull request #3193 from linniahawkins/my_branch
ekluzek Oct 7, 2025
63c0810
update of the citation
Oct 8, 2025
6faa26e
merge into master
Oct 8, 2025
69dbeed
Merge branch 'b4b-dev' into leaching-doc-update
samsrabin Oct 8, 2025
6a9894b
Merge pull request #3518 from jinmuluo/leaching-doc-update
samsrabin Oct 9, 2025
0072312
Add RC14_CANAIR as an output history variable, and change the hardcod…
ekluzek Sep 17, 2025
1ca9510
Revert back the sector change to the cmip6 version
ekluzek Oct 12, 2025
f5030fb
Set FC13/RC14 to spval so that zero's won't get averaged in
ekluzek Sep 18, 2025
d8c3f53
Only turn c13/c14 on by default for clm5_0 with BGC on and for CRUJRA…
ekluzek Oct 14, 2025
0bc6328
Add lnd_tuning_mode and ssp_rcp to the setting of use_c13/c14
ekluzek Oct 15, 2025
437537c
Set irrigate to .true. for clm6_0 and historical fixing #3527
ekluzek Oct 15, 2025
e1637a7
Merge pull request #3548 from ekluzek/rc14_canair
ekluzek Oct 15, 2025
f09dbb3
Merge tag 'ctsm5.3.079' into b4b-dev-merge-20251016
samsrabin Oct 16, 2025
ad53f9c
Update ChangeLog/Sum.
samsrabin Oct 17, 2025
5e4f2f0
Merge pull request #3553 from samsrabin/b4b-dev-merge-20251016
samsrabin Oct 17, 2025
1259356
Add a note that explains the c13/c14 settings in response to review
ekluzek Oct 22, 2025
1d5e990
Remove line not needed in response to review
ekluzek Oct 22, 2025
300c959
Merge remote-tracking branch 'escomp/master' into ciso_namelist_defau…
ekluzek Oct 22, 2025
27ee737
Apply suggestion from @ekluzek
ekluzek Oct 22, 2025
76fe4eb
Start updating change files
ekluzek Oct 22, 2025
8808a40
Merge branch 'ciso_namelist_default_changes' of github.com:ekluzek/CT…
ekluzek Oct 22, 2025
8faba54
A couple updates
ekluzek Oct 22, 2025
e1efc3c
Merge pull request #3549 from ekluzek/ciso_namelist_default_changes
ekluzek Oct 22, 2025
568ad66
Update to CMIP7 population density file for non-SSP cases
slevis-lmwg Oct 23, 2025
49c1cf3
Update ChangeLog/Sum
slevis-lmwg Oct 24, 2025
c05d112
Merge pull request #3563 from slevis-lmwg/upd_to_new_cmip7_popdens
slevis-lmwg Oct 24, 2025
1a3fe3f
Merge tag 'ctsm5.3.082' into upd_alpha54_to_082
slevis-lmwg Oct 27, 2025
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12 changes: 8 additions & 4 deletions bld/CLMBuildNamelist.pm
Original file line number Diff line number Diff line change
Expand Up @@ -3753,8 +3753,12 @@ sub setup_logic_c_isotope {
#
my ($opts, $nl_flags, $definition, $defaults, $nl) = @_;

add_default($opts, $nl_flags->{'inputdata_rootdir'}, $definition, $defaults, $nl, 'use_c13', 'bgc_mode'=>$nl_flags->{'bgc_mode'}, 'phys'=>$nl_flags->{'phys'});
add_default($opts, $nl_flags->{'inputdata_rootdir'}, $definition, $defaults, $nl, 'use_c14', 'bgc_mode'=>$nl_flags->{'bgc_mode'}, 'phys'=>$nl_flags->{'phys'});
add_default($opts, $nl_flags->{'inputdata_rootdir'}, $definition, $defaults, $nl, 'use_c13',
'bgc_mode'=>$nl_flags->{'bgc_mode'}, 'phys'=>$nl_flags->{'phys'},
'lnd_tuning_mode'=>$nl_flags->{'lnd_tuning_mode'}, ssp_rcp=>$nl_flags->{'ssp_rcp'} );
add_default($opts, $nl_flags->{'inputdata_rootdir'}, $definition, $defaults, $nl, 'use_c14',
'bgc_mode'=>$nl_flags->{'bgc_mode'}, 'phys'=>$nl_flags->{'phys'},
'lnd_tuning_mode'=>$nl_flags->{'lnd_tuning_mode'}, ssp_rcp=>$nl_flags->{'ssp_rcp'} );
my $use_c13 = $nl->get_value('use_c13');
my $use_c14 = $nl->get_value('use_c14');
if ( $nl_flags->{'bgc_mode'} ne "sp" && $nl_flags->{'bgc_mode'} ne "fates" ) {
Expand All @@ -3767,7 +3771,7 @@ sub setup_logic_c_isotope {
}
}
if ( &value_is_true($use_c14) ) {
add_default($opts, $nl_flags->{'inputdata_rootdir'}, $definition, $defaults, $nl, 'use_c14_bombspike', 'bgc_mode'=>$nl_flags->{'bgc_mode'}, 'phys'=>$nl_flags->{'phys'});
add_default($opts, $nl_flags->{'inputdata_rootdir'}, $definition, $defaults, $nl, 'use_c14_bombspike', 'use_c14'=>$use_c14 );
my $use_c14_bombspike = $nl->get_value('use_c14_bombspike');
if ( &value_is_true($use_c14_bombspike) ) {
add_default($opts, $nl_flags->{'inputdata_rootdir'}, $definition, $defaults, $nl, 'atm_c14_filename',
Expand All @@ -3781,7 +3785,7 @@ sub setup_logic_c_isotope {
}
}
if ( &value_is_true($use_c13) ) {
add_default($opts, $nl_flags->{'inputdata_rootdir'}, $definition, $defaults, $nl, 'use_c13_timeseries', 'bgc_mode'=>$nl_flags->{'bgc_mode'}, 'phys'=>$nl_flags->{'phys'});
add_default($opts, $nl_flags->{'inputdata_rootdir'}, $definition, $defaults, $nl, 'use_c13_timeseries', 'use_c13'=>$use_c13 );
my $use_c13_timeseries = $nl->get_value('use_c13_timeseries');
if ( &value_is_true($use_c13_timeseries) ) {
add_default($opts, $nl_flags->{'inputdata_rootdir'}, $definition, $defaults, $nl, 'atm_c13_filename',
Expand Down
28 changes: 19 additions & 9 deletions bld/namelist_files/namelist_defaults_ctsm.xml
Original file line number Diff line number Diff line change
Expand Up @@ -115,11 +115,22 @@ attributes from the config_cache.xml file (with keys converted to upper-case).
<use_c14>.false.</use_c14>
<use_c13_timeseries>.false.</use_c13_timeseries>
<use_c14_bombspike>.false.</use_c14_bombspike>

<use_c13 phys="clm6_0" bgc_mode="bgc" >.true.</use_c13>
<use_c14 phys="clm6_0" bgc_mode="bgc" >.true.</use_c14>
<use_c13_timeseries phys="clm6_0" bgc_mode="bgc" >.true.</use_c13_timeseries>
<use_c14_bombspike phys="clm6_0" bgc_mode="bgc" >.true.</use_c14_bombspike>
<!-- Turn timeseries on if Carbon isotopes are on -->
<use_c13_timeseries use_c13=".true.">.true.</use_c13_timeseries>
<use_c14_bombspike use_c14=".true.">.true.</use_c14_bombspike>

<!-- Turn Carbon isotopes on for clm6_0 physics with BGC on with CRUJRA or CAM7 forcing and for historical period-->
<!-- NOTE: Have Carbon isotopes off for older physics as those earlier versions were run that way.
They can only be on for BGC compsets (NOT SP or FATES).

Also, we configured the defaults the following ways:
- On only for CRUJRA2024 or CAM7 forcing because that is how the CESM3.0 clm6_0 simulations were run
- In contrast to above, it's turned off for other forcing options as we haven't run simulations with those configurations
- It's also only turned on for Historical periods and NOT future scenarios because we don't have CMIP7 data for them -->
<use_c13 phys="clm6_0" bgc_mode="bgc" lnd_tuning_mode="clm6_0_CRUJRA2024" ssp_rcp="hist">.true.</use_c13>
<use_c14 phys="clm6_0" bgc_mode="bgc" lnd_tuning_mode="clm6_0_CRUJRA2024" ssp_rcp="hist">.true.</use_c14>
<use_c13 phys="clm6_0" bgc_mode="bgc" lnd_tuning_mode="clm6_0_cam7.0" ssp_rcp="hist">.true.</use_c13>
<use_c14 phys="clm6_0" bgc_mode="bgc" lnd_tuning_mode="clm6_0_cam7.0" ssp_rcp="hist">.true.</use_c14>

<!-- Carbon isotope concentration files -->
<atm_c13_filename use_c13=".true." use_c13_timeseries=".true." ssp_rcp="hist" >lnd/clm2/isotopes/atm_delta_C13_CMIP6_1850-2015_yearly_v2.0_c190528.nc</atm_c13_filename>
Expand All @@ -141,6 +152,7 @@ attributes from the config_cache.xml file (with keys converted to upper-case).
<!-- Irrigation default (Note, the use-cases also set this) -->
<irrigate >.false.</irrigate>
<irrigate use_cndv=".false." sim_year_range="1850-2100">.true.</irrigate>
<irrigate phys="clm6_0" use_cndv=".false." sim_year_range="1850-2000">.true.</irrigate>
<irrigate phys="clm4_5" use_cndv=".false." sim_year_range="1850-2100">.false.</irrigate>

<!-- Saturation excess runoff for crops -->
Expand Down Expand Up @@ -2282,8 +2294,7 @@ lnd/clm2/surfdata_esmf/NEON/ctsm5.3.0/surfdata_1x1_NEON_TOOL_hist_2000_78pfts_c2
<stream_year_first_popdens use_fates=".true." sim_year="constant" sim_year_range="1000-1004" >2000</stream_year_first_popdens>
<stream_year_last_popdens use_fates=".true." sim_year="constant" sim_year_range="1000-1004" >2000</stream_year_last_popdens>

<stream_fldfilename_popdens hgrid="0.5x0.5" use_cn=".true." phys="clm6_0" >lnd/clm2/firedata/clmforc.Li_2025_CMIP7_SSP3CMIP6_hdm_0.5x0.5_simyr1850-2100_c250717.nc</stream_fldfilename_popdens>
<stream_fldfilename_popdens hgrid="0.5x0.5" use_cn=".true." >lnd/clm2/firedata/clmforc.Li_2017_HYDEv3.2_CMIP6_hdm_0.5x0.5_AVHRR_simyr1850-2016_c180202.nc</stream_fldfilename_popdens>
<stream_fldfilename_popdens hgrid="0.5x0.5" use_cn=".true." >lnd/clm2/firedata/clmforc.Li_2025_CMIP7_hdm_0.5x0.5_simyr1850-2025_c251013.nc</stream_fldfilename_popdens>
<stream_fldfilename_popdens hgrid="0.5x0.5" use_cn=".true." ssp_rcp="SSP1-1.9" >lnd/clm2/firedata/clmforc.Li_2018_SSP1_CMIP6_hdm_0.5x0.5_AVHRR_simyr1850-2100_c181205.nc
</stream_fldfilename_popdens>
<stream_fldfilename_popdens hgrid="0.5x0.5" use_cn=".true." ssp_rcp="SSP1-2.6" >lnd/clm2/firedata/clmforc.Li_2018_SSP1_CMIP6_hdm_0.5x0.5_AVHRR_simyr1850-2100_c181205.nc
Expand All @@ -2301,8 +2312,7 @@ lnd/clm2/surfdata_esmf/NEON/ctsm5.3.0/surfdata_1x1_NEON_TOOL_hist_2000_78pfts_c2
<stream_fldfilename_popdens hgrid="0.5x0.5" use_cn=".true." ssp_rcp="SSP5-3.4" >lnd/clm2/firedata/clmforc.Li_2018_SSP5_CMIP6_hdm_0.5x0.5_AVHRR_simyr1850-2100_c181205.nc
</stream_fldfilename_popdens>

<stream_fldfilename_popdens hgrid="0.5x0.5" use_fates=".true." phys="clm6_0" >lnd/clm2/firedata/clmforc.Li_2025_CMIP7_SSP3CMIP6_hdm_0.5x0.5_simyr1850-2100_c250717.nc</stream_fldfilename_popdens>
<stream_fldfilename_popdens hgrid="0.5x0.5" use_fates=".true." >lnd/clm2/firedata/clmforc.Li_2017_HYDEv3.2_CMIP6_hdm_0.5x0.5_AVHRR_simyr1850-2016_c180202.nc</stream_fldfilename_popdens>
<stream_fldfilename_popdens hgrid="0.5x0.5" use_fates=".true." >lnd/clm2/firedata/clmforc.Li_2025_CMIP7_hdm_0.5x0.5_simyr1850-2025_c251013.nc</stream_fldfilename_popdens>
<stream_fldfilename_popdens hgrid="0.5x0.5" use_fates=".true." ssp_rcp="SSP1-1.9" >lnd/clm2/firedata/clmforc.Li_2018_SSP1_CMIP6_hdm_0.5x0.5_AVHRR_simyr1850-2100_c181205.nc
</stream_fldfilename_popdens>
<stream_fldfilename_popdens hgrid="0.5x0.5" use_fates=".true." ssp_rcp="SSP1-2.6" >lnd/clm2/firedata/clmforc.Li_2018_SSP1_CMIP6_hdm_0.5x0.5_AVHRR_simyr1850-2100_c181205.nc
Expand Down
227 changes: 227 additions & 0 deletions doc/ChangeLog
Original file line number Diff line number Diff line change
@@ -1,4 +1,231 @@
===============================================================
Tag name: ctsm5.3.082
Originator(s): slevis (Samuel Levis,UCAR/TSS,303-665-1310)
Date: Fri 24 Oct 2025 11:17:41 AM MDT
One-line Summary: Update to CMIP7 population density file for non-SSP cases

Purpose and description of changes
----------------------------------

Update two lines in namelist_defaults_ctsm.xml.

Significant changes to scientifically-supported configurations
--------------------------------------------------------------

Does this tag change answers significantly for any of the following physics configurations?
(Details of any changes will be given in the "Answer changes" section below.)

[Put an [X] in the box for any configuration with significant answer changes.]

[ ] clm6_0

[ ] clm5_0

[ ] ctsm5_0-nwp

[ ] clm4_5


Bugs fixed
----------
List of CTSM issues fixed (include CTSM Issue # and description) [one per line]:
Resolves #3545 Update to official CMIP7 pop. density data

Notes of particular relevance for users
---------------------------------------
Changes made to namelist defaults (e.g., changed parameter values):
Updated pop. density file for non-SSP cases.

Changes to the datasets (e.g., parameter, surface or initial files):
Updated pop. density file for non-SSP cases.

Testing summary:
----------------
[PASS means all tests PASS; OK means tests PASS other than expected fails.]

regular tests (aux_clm: https://github.com/ESCOMP/CTSM/wiki/System-Testing-Guide#pre-merge-system-testing):

derecho ----- OK
izumi ------- OK

Answer changes
--------------

Changes answers relative to baseline: Yes

Summarize any changes to answers, i.e.,
- what code configurations: non-SSP
- what platforms/compilers: all
- nature of change: larger than roundoff/same climate

Other details
-------------
Pull Requests that document the changes (include PR ids):
https://github.com/ESCOMP/ctsm/pull/3563

===============================================================
===============================================================
Tag name: ctsm5.3.081
Originator(s): erik (Erik Kluzek,UCAR/TSS,303-497-1326)
Date: Wed 22 Oct 2025 05:31:52 PM MDT
One-line Summary: Change defaults for when Carbon isotopes are turned on, and turn on irrigate for Sp/Bgc cases for clm6_0 historical transient cases

Purpose and description of changes
----------------------------------

Only turn C13/C14 for clm6_0 and BGC, and also require the DATM forcing to be CRUJRA2024 or CAM7 and for the historical period. So for example SSP compsets won't have C13/C14 on, single point compsets won't, or for using older forcing (like CAM6, or GSWP3v1, Qian, or CRUv7). Also whenever use_c13 or use_c14 is on turn on the corresponding time series file.

Also change default for irrigate to on for historical SP/BGC cases.


Significant changes to scientifically-supported configurations
--------------------------------------------------------------

Does this tag change answers significantly for any of the following physics configurations?
(Details of any changes will be given in the "Answer changes" section below.)

[Put an [X] in the box for any configuration with significant answer changes.]

[ ] clm6_0

[ ] clm5_0

[ ] ctsm5_0-nwp

[ ] clm4_5


Bugs fixed
----------

List of CTSM issues fixed (include CTSM Issue # and description) [one per line]:
Fixes #3527 -- irrigation settings for control vs historical cases
Fixes #3551 -- Turn on relevent Carbon isotope time-series when use_c13/c14 is on
Some work on #3346 -- CMIP7 Carbon isotope data

Notes of particular relevance for users
---------------------------------------

Caveats for users (e.g., need to interpolate initial conditions):
This just changes the defaults for when Carbon isotopes are turned on, to make it less often
Users can still turn it on by hand for the cases that they want.

Changes made to namelist defaults (e.g., changed parameter values):
Carbon isotope timeseries files are turned on whenever use_c13/use_c14 is turned on so it uses
the historical
Turn irrigate on for clm6_0 historical
Carbon isotopes only turned on by default for clm6_0 when CRUJRA2024 or CAM7 forcing is used
and only for historical cases and not SSP's

Testing summary: regular
----------------
[PASS means all tests PASS; OK means tests PASS other than expected fails.]

build-namelist tests (if CLMBuildNamelist.pm has changed):

derecho - OK (differences in namelists are all as expected)

python testing (if python code has changed; see instructions in python/README.md; document testing done):

derecho - PASS

regular tests (aux_clm: https://github.com/ESCOMP/CTSM/wiki/System-Testing-Guide#pre-merge-system-testing):

derecho ----- OK
izumi ------- OK

If the tag used for baseline comparisons was NOT the previous tag, note that here: previous


Answer changes
--------------

Changes answers relative to baseline: HistClm60 compsets and tests with the ciso testmod

Summarize any changes to answers, i.e.,
- what code configurations: HistClm60Sp/HistClm60Bgc now with irriage on
cases with use_c13/use_c14 now have c13/c14 isotope timeseries files on
- what platforms/compilers: all
- nature of change (roundoff; larger than roundoff/same climate; new climate):
Carbon Isotopes -- are diagnostic and only change fields on history files
Cases that now have C13/C14 isotopes on now use timeseries files rather
than the default pre-industrial so change answers for C13/C14 fields
Irrigate turned on for HistClm60Bgc/HistClm60Sp compsets will change answers

Other details
-------------

Pull Requests that document the changes (include PR ids):
(https://github.com/ESCOMP/ctsm/pull)

https://github.com/ESCOMP/CTSM/pull/3549

===============================================================
===============================================================
Tag name: ctsm5.3.080
Originator(s): samrabin (Sam Rabin, UCAR/TSS)
Date: Thu Oct 16 13:41:08 MDT 2025
One-line Summary: Merge b4b-dev to master

Purpose and description of changes
----------------------------------

Merge b4b-dev to master. Includes these PRs:
- [ESCOMP/CTSM Pull Request #3193: resolve issue #103: Example 1.7 typo by linniahawkins](https://github.com/ESCOMP/CTSM/pull/3193)
- [ESCOMP/CTSM Pull Request #3518: Update of the leaching doc by jinmuluo](https://github.com/ESCOMP/CTSM/pull/3518)
- [ESCOMP/CTSM Pull Request #3548: Finishing adding RC14_CANAIR history output by ekluzek](https://github.com/ESCOMP/CTSM/pull/3548)

Significant changes to scientifically-supported configurations
--------------------------------------------------------------

Does this tag change answers significantly for any of the following physics configurations?
(Details of any changes will be given in the "Answer changes" section below.)

[Put an [X] in the box for any configuration with significant answer changes.]

[ ] clm6_0

[ ] clm5_0

[ ] ctsm5_0-nwp

[ ] clm4_5


Bugs fixed
----------

List of CTSM issues fixed in the included PRs:
- [ESCOMP/CTSM Issue #103: Example 1.7 typo](https://github.com/ESCOMP/CTSM/issues/103)
- [ESCOMP/CTSM Issue #3488: Add RC14_CANAIR as optional to history output so that C14 time series data can be verified](https://github.com/ESCOMP/CTSM/issues/3488)
- [ESCOMP/CTSM Issue #3490: Change history averaging of RC13_CANAIR and RC14_CANAIR so that zero's aren't averaged in](https://github.com/ESCOMP/CTSM/issues/3490)


Notes of particular relevance for users
---------------------------------------

Changes to documentation:
- Updated leaching documentation
- Typo fix


Testing summary:
----------------

regular tests (aux_clm: https://github.com/ESCOMP/CTSM/wiki/System-Testing-Guide#pre-merge-system-testing):

derecho ----- OK
izumi ------- OK


Other details
-------------

Pull Requests that document the changes (include PR ids):
- [ESCOMP/CTSM Pull Request #3553: b4b-dev merge 2025-10-16 by samsrabin](https://github.com/ESCOMP/CTSM/pull/3553)

===============================================================
===============================================================
Tag name: ctsm5.3.079
Originator(s): samrabin (Sam Rabin, UCAR/TSS)
Date: Mon Oct 6 21:41:11 MDT 2025
Expand Down
3 changes: 3 additions & 0 deletions doc/ChangeSum
Original file line number Diff line number Diff line change
@@ -1,5 +1,8 @@
Tag Who Date Summary
============================================================================================================================
ctsm5.3.082 slevis 10/24/2025 Update to CMIP7 population density file for non-SSP cases
ctsm5.3.081 erik 10/22/2025 Change defaults for when Carbon isotopes are turned on, and turn on irrigate for Sp/Bgc cases for clm6_0 historical transient cases
ctsm5.3.080 samrabin 10/16/2025 Merge b4b-dev to master
ctsm5.3.079 samrabin 10/06/2025 Update submodules to match versions in cesm3_0_alpha07e
ctsm5.3.078 slevis 10/03/2025 Merge b4b-dev to master
ctsm5.3.077 rgknox 10/02/2025 Adjustment of timestep albedo filtering with FATES
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -133,6 +133,45 @@ where :math:`{WS}_{tot\_soil}` (kgH\ :sub:`2`\ O m\ :sup:`-2`) is the total mass

NF_{leached} =\min \left(NF_{leached} ,\frac{NS_{sminn} sf}{\Delta t} \right).

Alternative way of evaluating the Leaching Losses of Nitrogen
--------------------------------------------------------------

The previous leaching mechanism is not designed for describing the vertical transport of :math:`{NO}_{3}^{-}` in soil, an alternative way to evaluate the vertical convective, diffusive, and dispersive of dissolved :math:`{NO}_{3}^{-}` in soil is provided in (:ref:`Luo et al. 2025 <Luoetal2025>`).
To obtain the vertical profile of soil mineral N after vertical movement of each timestep, the vertical transport equation is summarized in :eq:`22.20`.

.. math::
:label: 22.20

\frac{\partial NS_{sminn}}{\partial t} = \frac{\partial J}{\partial z} + S

where :math:`NS_{sminn} (gN m^{-3})` is the soil :math:`{NO}_{3}^{-}` concentration in each layer, :math:`J (gN m^{-2} s^{-1})` is the different vertical transport terms (:math:`J_{convective}, J_{diffusive}, J_{dispersive}`) between two soil layers, and :math:`S` is the sources or sinks fluxes.
Different transport terms are explained below

.. math::
:label: 22.21

J_{convective} = sf \frac{SN_{sminn}q_{out}}{\theta}

where :math:`q_{out} (mH_{2}Os^{-1})` is the darcy flow of water, :math:`\theta (m^3H_{2}O m^{-3}soil)` is the soil water content.

.. math::
:label: 22.22

J_{diffusive} = -D_{aq} \frac{\theta^{7/3}}{\phi^{2}} \frac{\partial SN_{sminn}}{ \partial z}

where :math:`\partial SN_{sminn}/ \partial z` is the concentration gradient, :math:`D_{aq}` is the nitrate aqueous diffusion coefficient which is taken as :math:`1.7*10^{-9} m^{2}s^{-1}`, and :math:`\phi (m^3m^{-3})` is soil porosity.

.. math::
:label: 22.23

J_{dispersive} = -D_{dis} \frac{\theta^{7/3}}{\phi^{2}} \frac{\partial SN_{sminn}}{ \partial z}

where :math:`D_{dis}` is the dispersion coefficient, which equal to :math:`L_{dis} q_{out} \theta ^{-1}`, for simplicity reasons, :math:`L_{dis}` is taken as 0.1 meter.

Finally, the classical convective-diffusion algorithm described in (:ref:`Patankar.2018 <Patankaretal2018>`) is used to discrete and solve the :math:`{NO}_{3}^{-}` vertical transport :eq:`22.20` in soils.
The advantage of this leaching mechanism is the soil :math:`{NO}_{3}^{-}` is able to move vertically (both upward or downward) with soil water movement, the mass of :math:`{NO}_{3}^{-}` reaches bedrock layer is finally taken as the :math:`NF_{leached}`.


Losses of Nitrogen Due to Fire
-----------------------------------

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