<p>In fact, there are many chemical transport models which solve the radical chemistry without steady-state approximations. The equations are very stiff but can be integrated with suitable methods, usually implicit. Some approaches are discussed in <a href="http://www.mdpi.com/2073-4433/2/3/510" rel="nofollow noreferrer">this review</a>. The <a href="http://people.cs.vt.edu/~asandu/Software/Kpp/" rel="nofollow noreferrer">Kinetic Preprocessor</a>, mentioned in the comment, includes a set solvers for stiff systems and has become somewhat popular in atmospheric chemistry. Some models that use code generated by it (either by default or as an option) include <a href="http://wiki.seas.harvard.edu/geos-chem/index.php/KPP_solvers_FAQ" rel="nofollow noreferrer">GEOS-Chem</a> and <a href="https://ruc.noaa.gov/wrf/wrf-chem/wrf_tutorial_2015/WRF_CHEM_Chemistry.pdf" rel="nofollow noreferrer">WRF-Chem</a>. I used KPP to implement the CB4 chemical mechanism in <a href="http://silam.fmi.fi" rel="nofollow noreferrer">this air quality model</a>.</p>

<p>An approach like this is possible because of operator splitting, which means that the processes included in the model are solved as a sequence of uncoupled operations. For example, a model time step could consist of calling an explicit scheme for solving advection, then Crank-Nicolson for vertical diffusion, and then a Rosenbrock solver for chemical kinetics.</p>

CC BY-SA 3.0
2018-01-19T19:04:19.277Z
+1 Can you list which CTMs or provide resource that mentions how OH is treated? You say many CTMs...
f.thorpe
CC BY-SA 3.0
2018-01-23T19:35:16.087Z
I added a few links. Indeed such details are often quite hard find unless you go through the code.
jvir
CC BY-SA 3.0
2018-01-18T18:59:49.250Z
2018-01-23T21:34:40.417Z
2018-01-23T21:34:40.417Z
jvir
<p>The hydroxyl radical chemistry is not modeled explicitly in air quality models, so numerical stability is not an issue.  Instead, OH is held in pseudo-steady-state.  For instance, see <a href="https://www.cmascenter.org/cmaq/documentation/4.7.1/AQCHEM_NOTES.txt" rel="nofollow noreferrer">CMAQ's documentation</a> which states:</p>

<blockquote>
  <p>In CMAQ's gas phase, OH is assumed to be in pseudo-steady state, and it is not a transported species.  This is because hydroxyl radical reactions tend to be catalytic (e.g., consumption and production). In the aqueous phase chemistry, OH is absorbed by cloud water and in an open cloud model (i.e., the design approach currently employed), absorbed species (e.g., OH) would be replenished via gas-to-cloud partitioning. However, due to operator splitting, aqueous and gas-phase chemistry are not solved simultaneously. To account for this and other uncertainties in predicted OH aqueous phase concentrations (e.g., neglect of production reactions (H2O2 + hv -> 2 OH) not currently implemented in aqchem), a steady-state assumption for OH is adopted in the aqueous chemistry routine.</p>
</blockquote>

<p>Typically, if you are trying to model something like the hydroxyl radical, you would use a <a href="http://www.atmos-chem-phys.net/10/9705/2010/" rel="nofollow noreferrer">box-model like MECCA</a>, not a chemical transport model.</p>

CC BY-SA 3.0
2017-01-19T23:45:41.027Z
Is the same true for the kinetic preprocessor?
BarocliniCplusplus
CC BY-SA 3.0
2017-01-20T04:29:53.547Z
I'm not sure I understand your follow-up question.  You may want to post it as a separate question.
f.thorpe
CC BY-SA 3.0
2017-01-19T23:36:38.113Z
2017-01-19T23:36:38.113Z
f.thorpe
<p>Atmospheric mixing ratios of the hydroxyl radical have relatively short lifespans (on the order of microseconds). When modeling air quality or the weather, the time step is usually much larger than the the half life of hydroxyl. How is this computation numerically stable? Is the problem of numerical stability simply ignored?</p>

<atmosphere-modelling><numerical-modelling><atmospheric-chemistry><air-quality>
Does hydroxyl radical chemistry in air quality models create numerical stability problems?
BarocliniCplusplus
# Does hydroxyl radical chemistry in air quality models create numerical stability problems?

(Asked by: username_0 on 2017-01-19)

Atmospheric mixing ratios of the hydroxyl radical have relatively short lifespans (on the order of microseconds). When modeling air quality or the weather, the time step is usually much larger than the the half life of hydroxyl. How is this computation numerically stable? Is the problem of numerical stability simply ignored?

**Tags:** atmosphere-modelling, numerical-modelling, atmospheric-chemistry, air-quality


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## 2 answers

### Answer by username_2 on 2017-01-19. Score: 4 | Accepted answer

The hydroxyl radical chemistry is not modeled explicitly in air quality models, so numerical stability is not an issue. Instead, OH is held in pseudo-steady-state. For instance, see [CMAQ's documentation](https://www.cmascenter.org/cmaq/documentation/4.7.1/AQCHEM_NOTES.txt) which states:

> In CMAQ's gas phase, OH is assumed to be in pseudo-steady state, and it is not a transported species. This is because hydroxyl radical reactions tend to be catalytic (e.g., consumption and production). In the aqueous phase chemistry, OH is absorbed by cloud water and in an open cloud model (i.e., the design approach currently employed), absorbed species (e.g., OH) would be replenished via gas-to-cloud partitioning. However, due to operator splitting, aqueous and gas-phase chemistry are not solved simultaneously. To account for this and other uncertainties in predicted OH aqueous phase concentrations (e.g., neglect of production reactions (H2O2 + hv -> 2 OH) not currently implemented in aqchem), a steady-state assumption for OH is adopted in the aqueous chemistry routine.

Typically, if you are trying to model something like the hydroxyl radical, you would use a [box-model like MECCA](http://www.atmos-chem-phys.net/10/9705/2010/), not a chemical transport model.

> **Comments:**
> **username_0**: Is the same true for the kinetic preprocessor?  
> **username_2**: I'm not sure I understand your follow-up question.  You may want to post it as a separate question.  

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### Answer by username_1 on 2018-01-18. Score: 3

In fact, there are many chemical transport models which solve the radical chemistry without steady-state approximations. The equations are very stiff but can be integrated with suitable methods, usually implicit. Some approaches are discussed in [this review](http://www.mdpi.com/2073-4433/2/3/510). The [Kinetic Preprocessor](http://people.cs.vt.edu/~asandu/Software/Kpp/), mentioned in the comment, includes a set solvers for stiff systems and has become somewhat popular in atmospheric chemistry. Some models that use code generated by it (either by default or as an option) include [GEOS-Chem](http://wiki.seas.harvard.edu/geos-chem/index.php/KPP_solvers_FAQ) and [WRF-Chem](https://ruc.noaa.gov/wrf/wrf-chem/wrf_tutorial_2015/WRF_CHEM_Chemistry.pdf). I used KPP to implement the CB4 chemical mechanism in [this air quality model](http://silam.fmi.fi).

An approach like this is possible because of operator splitting, which means that the processes included in the model are solved as a sequence of uncoupled operations. For example, a model time step could consist of calling an explicit scheme for solving advection, then Crank-Nicolson for vertical diffusion, and then a Rosenbrock solver for chemical kinetics.

> **Comments:**
> **username_2**: +1 Can you list which CTMs or provide resource that mentions how OH is treated? You say many CTMs...  
> **username_1**: I added a few links. Indeed such details are often quite hard find unless you go through the code.  

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