Can I expect an exact mass conservation based on CAM output

[FuchengY]

What version of the code are you using?
CESM 2.1.5 on Derecho

Have you made any changes to files in the source tree?
No.

Describe every step you took leading up to the problem:
Diagnose half-hourly output of F2000 (FV, 2deg)

Describe your problem or question:

Hi,

I am doing some simple calculation using half-hourly output of U,V,PS,PRECT,LHFLX to verify the conservation of mass in model.

I selected a small domain (~10degx10deg) over the North Pacific Ocean during Jan to Feb (about 50 days), computed the divergence of vertically integrated mass flux, and compared it with the change of total mass (PS/g). The mass on each grid and each level is calculated based on PS, hyai, and hybi on each timestep, and cos lat is considered when calculating the flux and area average. All values are calculated in per unit area.

As shown in the first figure, it is clear that the surface pressure decreases when the flow diverge and vise versa. Moisture processes given by precipitation (1000*PRECT as kg/s) and surface latent flux (LHFLX/2.3e6 as kg/s) make little change to the mass convergence. However, after integrating the mass convergence from the first timestep and comparing it with the change of PS with respect to the first timestep, a significant departure happens as shown in the second figure. The total mass increases by about 120 kg in 50 days while the mass change due to mass convergence is over 600 kg.

I know that bias may occur due to various reasons, such as if the value is on the edge or center of grid. But I am wondering if an exact mass conservation can be expected in CAM output or my calculation is the correct way to verify the mass conservation.

Thanks

Fucheng

 

[pel]

Hi Fucheng,

The mass budget in CAM-FV should be closed, but there are some complications to be aware of. I would start by looking at global budgets so you don’t have to worry about lateral transport of water in and out of a particular region.

In CAM-FV the surface pressure includes dry air and water vapor only; PS does not include the weight of condensates (cloud ice, cloud liquid, rain, graupel).

Aside: in CAM7 the condensates are included in PS when using MPAS or the SE dycore.

PRECT, on the other hand, encompasses all forms of water in the atmosphere (water vapor + condensates) that leave the atmosphere through precipitation (rain, snow, hail, …). You must also take into account EVAP (evaporation), which is the total water flux into the atmosphere from the surface. The change of water vapor, cloud ice, cloud liquid, rain, and graupel should match PRECT − EVAP globally. The mass of condensates should be a small term in the global budget.

So if you look at the global change in PS compared to PRECT − EVAP, the terms should only approximately match, as you are not including condensates.

Sampling error: When doing budgets, one has to be careful with sampling (i.e., where in the time loop the fields you are outputting are taken from). The sampling error gradually reduces if you run long enough.

Regional analysis: You can then repeat the above for a regional analysis, in which case you will need to include the lateral transport of water in and out of the region.

Hope that helps,

Peter

 

[FuchengY]

Hi Fucheng,

The mass budget in CAM-FV should be closed, but there are some complications to be aware of. I would start by looking at global budgets so you don’t have to worry about lateral transport of water in and out of a particular region.

In CAM-FV the surface pressure includes dry air and water vapor only; PS does not include the weight of condensates (cloud ice, cloud liquid, rain, graupel).

Aside: in CAM7 the condensates are included in PS when using MPAS or the SE dycore.

PRECT, on the other hand, encompasses all forms of water in the atmosphere (water vapor + condensates) that leave the atmosphere through precipitation (rain, snow, hail, …). You must also take into account EVAP (evaporation), which is the total water flux into the atmosphere from the surface. The change of water vapor, cloud ice, cloud liquid, rain, and graupel should match PRECT − EVAP globally. The mass of condensates should be a small term in the global budget.

So if you look at the global change in PS compared to PRECT − EVAP, the terms should only approximately match, as you are not including condensates.

Sampling error: When doing budgets, one has to be careful with sampling (i.e., where in the time loop the fields you are outputting are taken from). The sampling error gradually reduces if you run long enough.

Regional analysis: You can then repeat the above for a regional analysis, in which case you will need to include the lateral transport of water in and out of the region.

Hope that helps,

Peter

Hi Peter,

Thank you for your reply.

I read the paper, Lin and Rood (1997), which is the main reference for the FV dycore in CAM. The design of this scheme is more complex than I had initially expected. The dynamics are cycled eight times within a single timestep, and the conversions of U and V between different grid schemes are not simple averages. I suspect these aspects may introduce biases when diagnosing the mass budget from model output, even though mass is conserved in CAM-FV.

Thanks
Fucheng