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I am using the CAMS model output data to figure out the ground level ozone at a particular place. It is given in mass mixing ratio, and I want to convert to parts per billion volume mixing ratio (volume/volume).

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Shown above are ozone values from a model – basically the given values on the right beside the dates are in $\mathrm{kg} \cdot \mathrm{kg}^{-1}$. How can I convert them to ppbV?

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    $\begingroup$ For clarification: you are looking for "ppbV" (parts per billion with respect to volume) and not for "ppbM" (... with respect to mass)? Do you have some other parameters given? Is it a homework question? What did you do to find the answer on your own? $\endgroup$
    – daniel.heydebreck
    Feb 27, 2018 at 16:44
  • $\begingroup$ This is a VERY basic mathematical relationship unless I'm missing something, which I may be since you don't actually appear to ask a question in your question. $\endgroup$
    – Ash
    Feb 27, 2018 at 18:29
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    $\begingroup$ As @daniel.neumann wrote, we need some more specifics here in order to give a useful answer: do you simply want the parts per billion of mass (in which case it's trivial, as per Ash's current answer), or a molar fraction, or a volume fraction, or something else? I'm going to vote to close this question temporarily as "unclear what you're asking"; please edit it to add the necessary information, and I will vote to re-open. $\endgroup$
    – Pont
    Feb 27, 2018 at 19:30
  • $\begingroup$ @daniel.neumann Thank you for your response and my apologies for lacking clarity in my question! I am looking for ppbV. I shall explain what I'm trying to do. So I am using CAMS models' output data to figure out the ground level ozone at a particular place which is in mass mixing ratio and want to convert to volume mixing ratio/ volume itself. $\endgroup$
    – HalloweenKing
    Feb 28, 2018 at 2:19
  • $\begingroup$ @Pont Good Day Pont! Apologies for the question being ambiguous. Yes, I am looking at the scenario based on the volume aspect/volume fraction, in my case ppb, since I would be looking at the pollutant concentration rather than simply jot down the mass of the pollutant component. Thanks! $\endgroup$
    – HalloweenKing
    Feb 28, 2018 at 2:30

3 Answers 3

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So if you have a mass-mixing ratio, you effectively $\frac{ \text{kg pollutant}}{\text{kg dry air}}$. PPBV is parts per billion volume, or number of molecules of pollutant per billion molecules of dry air. Since not all particles weigh the same, you must use a conversion factor. Consider molar mass, which is the ratio of moles (a unit describing the number of molecules/photons/atoms) to mass. Ozone has a molar mass of 48 kg mol$^{-1}$. Dry air doesn't have a molar mass per se, but an effective molar mass may be computed by a weighted sum of the molar masses of the consitituent chemicals (or you can Google it). Afterwards, you may have to multiply by a billion.$$\therefore \frac{ \text{kg pollutant}}{\text{kg dry air}} \times\frac{\frac{\text{mols of pollutant}}{\text{kg of pollutant}}}{\frac{\text{mols of dry air}}{\text{kg of dry air}}}=\frac{\text{mols of pollutant}}{\text{mols of dry air}}$$

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    $\begingroup$ Thanks a ton Baroclini, this definitely answers my question precisely! $\endgroup$
    – HalloweenKing
    Mar 1, 2018 at 11:30
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1 part per billion is 1x10^-9 kilograms per kilogram so to convert a kilogram per kilogram ratio into a parts per billion figure divide it by 1x10^-9.

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  • $\begingroup$ What's the source of this information? $\endgroup$
    – Eevee
    Feb 27, 2018 at 18:10
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    $\begingroup$ @Imtherealsanic This is a very basic mathematical relationship, one most people should be able to manage in their head, what do you mean source? $\endgroup$
    – Ash
    Feb 27, 2018 at 18:15
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    $\begingroup$ I was going to ask you for a link to the article where you got the information provided in your answer, but instead I think I'll post an answer myself. $\endgroup$
    – Eevee
    Feb 27, 2018 at 18:22
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    $\begingroup$ I posted a similar answer, but deleted it when I realized there's more than one way to measure a part per billion: the questioner might want a molar fraction, for example, in which case the calculation is slightly more complex. I've commented on the question to request more information. $\endgroup$
    – Pont
    Feb 27, 2018 at 19:33
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    $\begingroup$ The asker has now clarified that they want a volume rathen than mass fraction. $\endgroup$
    – Pont
    Feb 28, 2018 at 7:02
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@BarocliniCplusplus's answer is correct. To convert Ozone (kg/kg) to (ppbv) you only need molar masses of dry air (28.9644 g/mol) and molar mass of Ozone (47.998 g/mol).

(Mass mixing ratio in ppb) = (28.9644 / 47.9982) * 1e9 * (Mass mixing ratio in kg/kg)

[Source: ECMWF webpage] [1]: https://confluence.ecmwf.int/pages/viewpage.action?pageId=153391710

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