LCLUC_training.org

Atmospheric chemistry with a focus on ozone and hands-on modeling

Lecture 1

Goals - I

Introduce concepts of atmospheric chemistry

• Today it’s all about ozone
• Primary/secondary pollutants
• Emission (briefly)
• Photochemistry (more detail)
• Box model exercise

Goals - II

Run first numerical simulation of a chemical system

• Simple photochemical system
• Conditions to produce ozone production

Code is available here

You can clone the code using git via

git clone git@gitlab.com:ptg21/LCLUC_presentation.git

Who is this course for?

My goal is to introduce atmospheric chemistry with a focus on tropospheric ozone and other secondary pollutants.

I won’t discuss the chemistry in detail but will summarise the relevant reactions. It gets complex towards the end.

The goal is to use these reactions to study how ozone levels respond to other pollutants.

Our focus is on rates of production of ozone during the day.

For the purpose of this course, everything is a pollutant.

Tricks of the trade

Mostly think about processes in terms of their characteristic timescales

• How fast is ozone formed?
• How fast is transport out of the planetary boundary layer?
• How does this compare with transport times?

What are the important species?

• Ozone
• NO₂
• Aldehydes
• Oxidants such as OH, NO₃
• Key species such as O¹D

General comments on atmospheric pollution

Air pollution is a global problem

Biogenic emissions are also important

Typical levels of atmospheric constituents

Pollutant	Concentration	Lifetime / yr
CH4	1700 ppbv	10
H2	500 ppbv	4
CO	40-200 ppbv	0.2
O3	20-120 ppbv	0.05
OH	0.1 pptv	0.1s

1 ppbv = 10^-9

1 pptv = 10^-12

US EPA Air Quality Index levels of pollutants

Pollutant	Low	Moderate	UFSG	Unhealthy
Ozone	0-54	55-70	71-85	86-105
NO2	0-53	54-100	101-360	186-304
CO	0-4.4	4.5-9.4	9.5-12.4	12.5-15.4

Levels are in ppbv

Air quality index

\vspace{-0.1in}

\begin{eqnarray*} I & = & \frac{(I_high - I_low)}{(C_high-C_low)} (C - C_low) + I_low \end{eqnarray*}

$I$ and $C$ are the instantaneous index and concentrations, $I_high, I_low$ are index breakpoints, $C_high, C_low$ are concentration breakpoints.

Primary and secondary pollutants

Primary Emitted directly into the atmosphere (usually at the surface)

• Nitric oxide, NO
• Volatile organic compounds such as methane, CO
  • Biogenic VOCs suc as isoprene, terpenes, formaldehyde (HCHO)
  • Anthropogenic VOCs such as benzene, gasoline
• Primary aerosol such as soot
• SO₂

Secondary Made in the atmosphere by oxidation

• Ozone, O₃
• NO₂
• Formaldehyde (HCHO)

Quantitative treatment of chemical processes

Emission and loss - Timescales in atmospheric chemistry

Considering the atmosphere as a whole, or some air-mass within in it, we could write an equation describing the rate of change (‘tendency’) of a species.

Prognostic equation for species X, with concentration $x$

\vspace{-0.1in} \begin{eqnarray*} \frac{dx}{dt} &=& R -k x \end{eqnarray*}

where R is the (constant) rate of emission of X and k is a constant

We now have a first-order linear differential equation, which can be solved to give

\vspace{-0.1in} \begin{eqnarray*} x(t) &=& \frac{R}{k_1}\big(1-exp (-k_1 t)\big) \end{eqnarray*}

System has a characteristic time, $τ = 1/k$

Time dependence of X

Time dependence for constant emission rate and first-order loss.

The rate law

Basic points

• Rate is defined as change in concentration per unit time
• Natural unit of concentration in air quality modelling:
  • concentration: molecules per cm^3 gas so units are cm$^-3$
  • rate: cm$^-3$ s$^-1$
• Law of Mass Action - Double the concentration = Double the rate

NO + O₃ = NO₂ + O₂

• The rate of change of NO can be expressed as

\vspace{-0.1in} \begin{eqnarray*} \frac{d [NO]}{dt} &=& -k_1[NO][O_3] \end{eqnarray*}

• Similarly, $\frac{d[NO_2]}{dt} = k_1[NO][O_3]$

Photochemistry

Photochemistry <<oxidation>>

• Molecules absorb photons and the chemical bonds are broken - photolysis

\vspace{-0.1in}

\begin{eqnarray*} \mathrm{NO}_2 + hv → \mathrm{NO} + \mathrm{O} \end{eqnarray*}

• Rate of photolysis depends on number of photons of the correct wavelength.

\vspace{-0.1in} \begin{eqnarray*} \frac{d[\mathrm{NO}_2]}{dt} &=& - J [\mathrm{NO}_2] \end{eqnarray*}

J depends on molecule and flux of photons (hence: time of day, lat, lon, cloud cover). Units of J are s^-1

Example: NO2

Example: NO2

First example: the NO/NO₂ interconversion by ozone

NO₂/NO ‘Photostationary state’ - our first chemical model

Using the reactions already given,

\vspace{-0.1in}

\begin{eqnarray*} \mathrm{NO} + \mathrm{O}_3 & → & \mathrm{NO}_2 + \mathrm{O}_2
\mathrm{NO}_2 + hv &→& \mathrm{NO} + \mathrm{O}\ \mathrm{O}_2 + \mathrm{O} &→ & \mathrm{O}_3\ \end{eqnarray*}

\vspace{-0.15in}

we can write rates of change for each species

\vspace{-0.1in} \begin{eqnarray*} \frac{d[\mathrm{NO}_2]}{dt} &=& - J_1 [\mathrm{NO}_2] + k_3\mathrm{[NO]}\mathrm{[O}_3]
\frac{d[\mathrm{NO]}}{dt} &=& J_1 [\mathrm{NO}_2] - k_3\mathrm{[NO]} \mathrm{[O}_3] \ \frac{d\mathrm{[O]}}{dt} &=& - k_2 [\mathrm{O}][\mathrm{O}_2] + J_1 [\mathrm{NO}_2] \ \frac{d\mathrm{[O}_3]}{dt} &=& k_2 [\mathrm{O}][\mathrm{O}_2] - k_3 \mathrm{[NO]} \mathrm{[O}_3] \end{eqnarray*}

A set of coupled differential equations results!

How to proceed - I

What is our mechanism going to do?

column one

• We can see that NO and ozone make NO2
• NO2 makes NO and O, and O makes O3
• so NO2 regenerates the NO and O3
• This is an active equilibrium - NO and NO2 interconvert, consuming/releasing ozone as they do so.

As we shall see in L2, this equilibrium is crucial.

column two

How to proceed - II

• So we expect our equations to solve to an equilibrium with zero net rate of change
• There exists a wealth of literature on the solution of these stiff differential equations (lifetimes of each species vary by many orders of magnitude, resulting in small timesteps).
• In our example, the lifetime of O is very short, set by k_2[O2], while that of NO2 is determined by J and can be much longer.
• Step forward our numerical (‘box’) model…

Box models

Box models

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• Box models represent a single representative area of the atmosphere.
• Notionally 1cm^3 in volume
• Can be connected to the ground via emission/deposition.
• Could also be chosen to represent the free troposphere.
• Need to supply photolysis rates, emissions

column two

Anatomy of a box model - I

column one

• Box models need a chemical mechanism.
• The literature can supply these, or you can write your own.
• You then code up the mechanism as a differential for each species, in terms of other species’ concentrations and other inputs.

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Anatomy of a box model - II

column one

• Implementation in the language of your choice
• You need an integrator for the differential equations.
• There are good ones already implemented, so don’t write your own!
• Typically you supply initial conditions, C0, functions for the tendency of each species,$f$, a timestep (dt) and an end point (tend).

column two

Practical one

End of lecture 1

Getting started

• Open RStudio or R
• Look at \tt kinetics-box-model-pss.R

in the src folder.

• What do equations describe?
• What do you expect to happen?

\color{red} Any Pythonistas in the audience?

\color{red} Anyone not got the software installed?

Practical one

Run the simulation

• source("kinetics-box-model-pss.R")

Do the results make sense?

• If so: get a coffee!
• If not: shout out!

Coffee break

Recap of the first hour

Begun to think about putting together a chemical mechanism

First model looked at the NO / NO₂ / O₃ interconversion reactions

Lecture 2

Box models in the literature

Box models in recent literature

Box models are great for process-based studies and the box can be as big as you like

column one

file:figures/isotope_box_model.png

column two

file:figures/edwards.png

Can focus on processes of interest, parameterize other processes (e.g. mixing), build up complexity as required.

Goals of lecture 2

Goals of lecture 2

Introduce ozone formation reactions

• Photochemical oxidant, OH, formation
• Peroxy radicals introduction

Run a box model describing ozone formation

• Conceptual overview of a box model
• Implementing air quality into a box model

Our mechanism

Our mechanism is rather complex - the CO and NO emissions interact with sunlight and water vapour

\begin{eqnarray*} \mathrm{NO}_2 + hv & → & \mathrm{NO} + \mathrm{O}
\mathrm{O}_2 + \mathrm{O} & → & \mathrm{O}_3 \ \mathrm{NO} + \mathrm{O}_3 &→ & \mathrm{NO}_2 + \mathrm{O}_2 \ \mathrm{O}_3 + hv & → & \mathrm{O}_2 + \mathrm{O1D} \ \mathrm{O1D} + \mathrm{H}_2\mathrm{O} & → & 2 \mathrm{OH} \ \mathrm{O1D} + \mathrm{N}_2 / \mathrm{O}_2 & → & \mathrm{O} + \mathrm{N}_2 / \mathrm{O}_2 \ \mathrm{OH} + \color{red} \mathrm{CO} \color{black} + \mathrm{O}_2 & → & \mathrm{HO}_2 + \mathrm{CO}_2 \ \color{red} \mathrm{NO} \color{black} + \mathrm{HO}_2 &→ & \mathrm{OH} + \mathrm{NO}_2 \end{eqnarray*}

Primary species coloured in \color{red} red

Some general points

VOCs such as CO are degraded by reaction with OH

\vspace{-0.15in} \begin{eqnarray*} \mathrm{OH} + \mathrm{CO} +\mathrm{O}_2 & → & \mathrm{HO}_2 + \mathrm{CO}_2 \end{eqnarray*} and HO₂ (a class of ‘peroxy’) radicals are produced.

NO2 is produced additionally via reaction of peroxy radicals with NO

\vspace{-0.15in} \begin{eqnarray*} \mathrm{NO} + \mathrm{HO}_2 &→ & \mathrm{OH} + \mathrm{NO}_2 \end{eqnarray*}

NO2 photolysis leads to O3

\vspace{-0.15in} \begin{eqnarray*} \mathrm{NO}_2 + hv & → & \mathrm{NO} + \mathrm{O}
\mathrm{O}_2 + \mathrm{O} & → & \mathrm{O}_3 \end{eqnarray*}

Implementation in a box model

As a series of tendencies

dNO2 = -J1*NO2   + k3*NO*O3 + k8*HO2*NO - k9*OH*NO2 +
	        k13*OH*HONO2

dNO  =  J1*NO2   - k3*O3*NO - k8*HO2*NO 

dO3  =  k2*O     - k3*NO*O3 - J4*O3

dO   =  J1*NO2   - k2*O  + k5*O1D*M

dOH  =  2.k6*O1D*H2O - k7*OH*CO + k8*HO2*NO +
	        k11*HO2*O3 - k12*OH*O3 - k9*OH*NO2  

dHO2 =  k7*OH*CO - k8*HO2*NO - k11*HO2*O3 +
	        k12*OH*O3 - k14*HO2*HO2 

dCO  = -k7*OH*CO 

dO1D =  J4*O3    - k5*O1D*M     - k6*O1D*H2O

dHONO2 = k9*OH*NO2 - k13*OH*HONO2

Formation of OH

Formation of OH from ozone and water vapour

The photochemical oxidant, OH, is formed from ozone and water vapour.

\vspace{-0.15in} \begin{eqnarray*} \mathrm{O}_3 + hv & → & \mathrm{O}_2 + \mathrm{O1D}
\mathrm{O1D} + \mathrm{H}_2\mathrm{O} & → & 2\color{red} \mathrm{OH} \ \mathrm{O1D} + \mathrm{N}_2 / \mathrm{O}_2 & → & \mathrm{O} + \mathrm{N}_2 / \mathrm{O}_2 \end{eqnarray*}

Via excited state oxygen atoms - the O1D species.

These are distinct from the ground state oxygen atoms, O, produced by NO2 photolysis.

The photochemical oxidant OH is reactive towards VOCs. This species initiates the photochemical degradation of VOCs and in the presence of NO will produce ozone.

Reaction of photochemical oxidant, OH, with VOCs to produce ozone

Reaction of photochemical oxidant, OH, with VOCs

Able to react with CO and with other VOC via the H atoms, and so initiate photo-degradation.

\vspace{-0.15in} \begin{eqnarray*} \mathrm{OH} + \mathrm{CO} +\mathrm{O}_2 & → & \color{red} \mathrm{HO}_2 \color{black} + \mathrm{CO}_2
\ \mathrm{OH} + \mathrm{CH}_4 & → & \mathrm{H}_2\mathrm{O} + \color{red} \mathrm{CH}_3\mathrm{O}_2 \ \end{eqnarray*}

Once produced, these peroxy radicals oxidize NO to NO2 and ozone is produced.

\vspace{-0.15in} \begin{eqnarray*} \mathrm{NO} + \mathrm{HO}_2 &→ & \mathrm{OH} + \mathrm{NO}_2
\mathrm{NO}_2 + hv & → & \mathrm{NO} + \mathrm{O} \ \mathrm{O}_2 + \mathrm{O} & → & \mathrm{O}_3 \end{eqnarray*}

Without the HO₂ the NO reacts with ozone to produce NO2, which recreates the ozone. No net ozone production!!

Conclusions

Conclusions

If you have an air mass with NO, VOC (here CO) and sunlight you can expect ozone formation.

The amount of ozone formed also depends on H₂O, number of photons (sunlight).

You can calculate the rate at which ozone is being formed.

Without these ozone will be destroyed

Ozone in model world

Practical 2

Practical 2

• Open RStudio or R
• Look at \tt kinetics-box-model-ozone.R

in the src folder.

• What do equations describe?
• What do you expect to happen?

\color{red} Any Pythonistas in the audience?

Practical 2

Run the simulation

• source("kinetics-box-model-ozone.R")
• Can you shift the atmosphere from ozone destruction to ozone production?
• How?

Conclusions/next steps

Next steps

Hand coding the tendency functions gets tedious and can be error-prone.

• Automatic code generation is possible
• See KPP, the Kinetic Pre-Processor
• Generates F77, F90, C, Matlab code which you compile and run (or run within Matlab)
• This has been incorporated into DSMACC

This is an excellent model but its usage requires good Shell and compiler skills.

It’s easy to show that J values are key to the chemistry

• Consider using a verifiable radiative transfer model such as TUV (Tropospheric Ultraviolet and Visible TUV model)

Conclusion

This is the end of the ‘planned part’

Thank you for your attention

Any questions?

Any suggestions?

Useful links

http://acmg.seas.harvard.edu/education.html

particularly

http://acmg.seas.harvard.edu/education.html#mmac

Supplementary material

Emissions and deposition

Emission of primary pollutants

Emissions into a boundary layer - dimensional analysis

• Emissions per unit surface area:
  • Flux $E$ has units of (molecules) per unit of surface area per unit time (cm^-2 s^-1)
• Into a well-mixed layer of height $h$ (cm)

Rate equation

• A rate of change of $E/h$

\vspace{-0.1in} \begin{eqnarray*} \frac{d[NO]}{dt} &=& E_NO/h \end{eqnarray*} has the correct dimensions (cm^-3 s^-1)

Dry deposition at the surface

• Flux depends on concentration in gas phase above surface and on the reactivity of the surface
• Flux has units of (molecules) per unit of surface area per unit time (cm^-2 s^-1)

\vspace{-0.1in} \begin{eqnarray*} \mathrm{Flux} &\propto& C[O_3] \end{eqnarray*}

• Units of C are therefore cm s^-1, a ‘velocity’, $v$, dependent on surface type

\vspace{-0.1in} \begin{eqnarray*} \frac{d[O_3]}{dt} &=& - \frac{v}{h}[O_3] = - k_1 [O₃] \end{eqnarray*}

column one

column two