How to explain IPR ZADV?

Hi everyone,
When I used the IPR module of CMAQ5.5 to analyze the formation of PM2.5, I encountered a very confusing problem.
Assume the modle CCTM_PA(file) PM25 ZADV is -6.17, does it mean PM2.5 concentration lose 6.17 ugm-3 by ZADV process?

Second question is how ZADV be caculated in CMAQ? Where can I find the formula?

Third question is can I use W_VEL and z-direction PM2.5 concentration to explain ZADV?
IF W_VEL>0, (dPM2.5/dz)<0, it means ZADV < 0, and PM2.5 will decrease(first explain).
But if I used diffusion equation(only focus ZADV), then dPM2.5/dt = - W * (dPM2.5/dz), the same as above, W_VEL>0, dPM2.5/dz<0, and I got (dPM2.5/dt)>0, which is different from first exlpain. How to explain the negative sign on the right side?

I would appreciate any guidance or feedback on this issue.

Process analysis results are computed by difference before and after the call to a given process. Look for the calls to PA_UPDATE_PROC in sciproc.F.

You may also be interested in the budget tool. See Chapter 9 of the User Guide.

In your equation dPM2.5/dt = -W * (dPM2.5/dz), if W is negative then -W is positive, so if dPM2.5/dz < 0 then dPM2.5/dt < 0. There is no inconsistency here.

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Thank you for your reply!

However, I’m still confused, so I’ve provided some data to help with the discussion:

  1. The first figure shows daily Wwind from the first layer to the 20th layer. We can see that on 04/06, 04/07, and 04/08, the values are positive (W > 0), while on 04/09, the values are negative (W < 0).
  2. The second figure shows the daily PM2.5 concentration from the first layer to the 20th layer. We can observe that on 04/06, 04/07, 04/08, and 04/09, the concentration decreases from bottom to top (dPM2.5/dz < 0).
  3. The third figure presents the IPR output. We can see that ZADV on 04/06, 04/07, 04/08, and 04/09 is negative, which implies dPM2.5/dt < 0 at Miaoli station. Is that correct?

However, when I apply the diffusion equation:
dPM2.5/dt=−W∗(dPM2.5/dz)dPM2.5/dt = - W * (dPM2.5/dz)dPM2.5/dt=−W∗(dPM2.5/dz)
(considering only ZADV), I find that on 04/06, 04/07, and 04/08, W > 0 and dPM2.5/dz < 0, which results in dPM2.5/dt > 0. This seems to contradict the earlier conclusion.

If I made any mistakes at any step, please let me know.
Thank you!



@brucelee,

I think you are conflating the outputs of IPR with the actual advective flux calculations used to update the mass in a grid cell at each time step.

As @cgnolte said, IPR only gives the the difference in values before and after a process call. When looking at advection (transfer of matter from one grid cell to another), to me it doesn’t make much sense to look at just advection in one direction. Remember advection in CMAQ is a 3-D process happening as the sum of all three directions:

\Large \frac{\partial \rho}{\partial t} + \frac{\partial \rho u}{\partial x} + \frac{\partial \rho v}{\partial y} + \frac{\partial \rho w}{\partial z} = 0

So to get a sense of how much matter was transferred into or out of the cell via the bulk flow, you would add the three terms (in other words this would tell you how mass changed due to 3D advection within a cell over that timestep).

In this case, its not possible to recreate the actual advective flux at each step because you don’t have the output at each sync step since presumably you have the output at the hourly marks only, making it very hard to recover the exact output from IPR.

The basic equation that our code is following is shown above, with the solution of the equation being achieved using time-splitting (Yanenko, 1971) into 1-D dimensional equations.

Essentially each 1-D component will solve the following equation (consider x-direction for example):

\Large c_i^{n+1} = c_i^{n} - \frac{\Delta t}{\Delta x}(F_{i+1/2}^{n} - F_{i-1/2}^{n})

Where \Large c_i^{n+1} represents the mass of cell i, at time n+1, and \Large F_{i+1/2}^{n} is the flux (mass times velocity) at one grid face (in this case since considering the X direction – this would be the right cell face).

What you have in the output is the cell averaged value at the middle of a grid cell, however, what’s needed is the flux at the grid face. There are several ways of approximating the flux – the method that CMAQ chooses is the Piecewise Parabolic Method (PPM; Colella and Woodward, 1984).

Hopefully this helps!

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