# Mode median diameter and mode standard deviation in CMAQ?

I want to calculate the UFP number so I need Mode median diameter and mode standard deviation but I do not know where to get them.
How can I calculate mode median diameter and mode standard deviation in CMAQ?
Should I turn on a specific option?

In the FAQ, there is an answer about calculating PM2.5 or PM1.

It says to understand these calculations, evaluate the species definition file that is available for each mechanism. For example for the cb6r3_ae7_aq mechanism, examine the following file.

and

From the following article:
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2001JD001410

[14] Based upon the near source observations reported by Whitby [1978], we have chosen values of 0.3 μm for the geometric mean mass diameter D gv and 2.0 for the geometric standard deviation σg for the accumulation mode. The corresponding values for the Aitken mode are 0.03 μm and 1.7, and those for the coarse mode are 6 μm and 2.2.

I know how to calculate PM2.5 and PM1 by using combine tool
But what I want to know is UFP Particulate Number Concentration (PNC)
To calculate PNC, I want to know the geometric mean mass diameter and standard deviation.
→ Both numbers are fixed numbers in CMAQ or can I get them in CMAQ?

where Dg is the mode median diameter in 𝜇m
𝜎g is the mode standard deviation
N is the total number particles in the mode
subscripts i (Aitken) and j (accumulation)
Erf = gauss error function

The fixed values that you requested were sourced from the article listed in my earlier reply.

[14] Based upon the near source observations reported by Whitby [1978] , we have chosen values of 0.3 μm for the geometric mean mass diameter D gv and 2.0 for the geometric standard deviation σg for the accumulation mode. The corresponding values for the Aitken mode are 0.03 μm and 1.7, and those for the coarse mode are 6 μm and 2.2.
I’ve created the following table with the information from the quote in the paper, if that helps.

Aerosol Mode geometric mean mass diameter (micrometer) standard deviation
accumulation .3 2
aiken .03 1.7
coarse 6 2.2

I am confused about Standard Deviation
If you see APMDIAG file, there is STDEV for each mode.
One of paper I read the number of mean and STD are different.

Hello,

You are on the right track with the equation you posted. Simply use the STDEVXXX and WET_DGXXX for each mode from the APMDIAG file as you guessed and plug them into the equation for UFP number.

Keep in mind that the parameters from ACONC and APMDIAG are hourly averages, so there may unfortunately be some inconsistencies in extreme cases, but it should be a minor issue.

In the next CMAQ release, you will have the option to output UFP number directly from the model and skip this post-processing step.

Best wishes,
Ben Murphy

Thank you for your response. I think I have almost reached the goal.

Q 1-1. I found the geometric mean diameter. Should I use WET, not DRY right?

Q 1-2. Where can I get the description of APMDIAG result? because I tried to find CMAQ manual but I was not able to find it.

Q 2. Is there any code for the equation ? I have no idea to make a code for that equation.

Best regards,
Hyeongseok

Hi Hyeongseok,

1. Yes, you should use wet diameter, unless you are comparing to measurements that dry the particles first.
2. Hm, I don’t quite know what you meant by a description of an APMDIAG result. Here is some general information about APMDIAG: CMAQ/CMAQ_UG_ch07_model_outputs.md at main · USEPA/CMAQ · GitHub
3. Here’s a snapshot of some code I use in CMAQ to calculate number between two diameters (D_ST1 and D_ST2). This needs to be done for each mode.

Cheers,
Ben

1 Like

Hello Ben,

Thank you for helping me a lot with UFP.

My replies are
1. I understand it

2. I meant that I know there is a description for APMDIAG broadly but not variable by variable.
e.g.,
DGACC_DRY (um) # dry diameter geometric accumulation mode
DGACC_WET (um) # wet diameter geometric accumulation mode
DGATKN_WET (um) # wet diameter geometric aitken mode

3-1. Should I put this code to aero_subs.F lines 2823 ?

3-2. Is it possible to apply it to combine_script as well?
because I want to use DGN, XXLSG, D_ST1, and D_ST2 manually.
using this table and observation data.

3-3. Possible to get the scripts?

Best regards,
Hyeongseok

Hi Hyeongseok,
Very happy to help!

1. Great!

2. Hm, I thought we had posted that in the userguide but I can not find it either. Please let me know which variables you would like descriptions for and I can help out.

3-1. You can experiment with that, but I wouldn’t recommend it unless you have a lot of time and curiosity on your hands. You’ll need to add ultrafine number (or any integrated number you want to consider) to the output list and make sure a lot of infrastructure is hooked correctly. I think post-processing will be a lot easier.

3-2. Unfortunately you cannot apply it to the combine script because it does not accept error functions. I may be misunderstanding your goals, but I don’t think the table of parameters will be very helpful to you here because you have access to the time-varying parameters so you can calculate the time-varying integrated number concentrations.

3-3. That algorithm is implemented in aero_subs (exactly as you suggested above). But I would recommend implementing in a Fortran, R, or Python script and post-processing your existing output data.

Best wishes,
Ben

1 Like

Hi again,

@hogrefe.christian just reminded me that you can actually access error functions in COMBINE. Please see documentation here: CMAQ/POST/combine at main · USEPA/CMAQ · GitHub

So I think you could implement this algorithm in a SpecDef file and have COMBINE process the integrated number for you.

Cheers,
Ben

3 Likes

Thank you so much!
I think I got the UFP number by using combine scripts.

Here is minor typo in your script electricla → electrical