Regarding T2 and T2MEAN calculation: explaining bias between diagnostics

[Arty]

Hello,

I am currently working with the wrfout* and wrfxtrm* files and have encountered a significant issue related to the computation of T2 and T2MEAN. Despite reviewing the relevant directories, particularly within the Physics modules, and consulting the User's Guide as well as searching GitHub, I have not found any clear explanation regarding how T2 and T2MEAN are computed.

One concerning observation is that I am seeing an average temperature difference of approximately -1.1°C between T2 from the wrfout* files and T2MEAN in the wrfxtrm* files. This difference appears to be quite consistent across the entire domain, regardless of whether it is over ocean or land. This bias seems large, and I am struggling to understand its cause.

Could anyone provide insight into how T2 and T2MEAN are calculated in these files, or offer any explanations as to why this bias might be occurring in my simulations?

Thank you for your help.

 

[Ming Chen]

T2 is diagnosed based on similarity theory. Please see the code module_sf_sfcdiags.F, in which you can find its calculation:

T2(I,J) = TSK(I,J) - HFX(I,J)/(RHO*CP*CHS2(I,J))

T2MEAN is mean T2 during the interval of diagnostic output ( output_diagnostics = 1)

T2 is instantaneous and T2MEAN is time-average. They should not be same.

 

[Arty]

T2 is diagnosed based on similarity theory. Please see the code module_sf_sfcdiags.F, in which you can find its calculation:

T2(I,J) = TSK(I,J) - HFX(I,J)/(RHO*CP*CHS2(I,J))

T2MEAN is mean T2 during the interval of diagnostic output ( output_diagnostics = 1)

T2 is instantaneous and T2MEAN is time-average. They should not be same.

Thank you, Ming, for your input.

I am aware that T2MEAN represents the average of all the intermediate timesteps within the hourly output. However, I’m still curious about the persistent -1.1°C bias I’ve observed.

For additional context, my simulation focuses on climate modeling over the island of Tahiti in the South Pacific Ocean, with a finer domain resolution of 2.333 km. What’s particularly puzzling is that this bias remains relatively constant both over time (throughout my 35-month simulation) and across the entire domain. Since any temporal variations should have been smoothed out by the averaging process, I find this result quite unusual. Please see the details below.

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mean = -1.110938 ;
mean = -1.110967 ;
mean = -1.114687 ;
mean = -1.116371 ;
mean = -1.118445 ;
mean = -1.118346 ;
mean = -1.118211 ;
mean = -1.115408 ;
mean = -1.113776 ;
mean = -1.113368 ;
mean = -1.112928 ;
mean = -1.112652 ;
mean = -1.112268 ;
mean = -1.113387 ;
mean = -1.11675 ;
mean = -1.119222 ;
mean = -1.119186 ;
mean = -1.119925 ;
mean = -1.119378 ;
mean = -1.117571 ;
mean = -1.115998 ;
mean = -1.113726 ;
mean = -1.111723 ;
mean = -1.109729 ;
mean = -1.109065 ;
mean = -1.113164 ;
mean = -1.116117 ;
mean = -1.117814 ;
mean = -1.119994 ;
mean = -1.118929 ;
mean = -1.121866 ;
mean = -1.116948 ;

I initially began investigating this after noticing a +1.5°C bias in comparison to in-situ measurements and ERA5 data across the 16 tested configurations, where the model is forced by NCEP2 reanalysis. Given these findings, I am wondering if it might be more appropriate to use the T2 variable instead of T2MEAN, as T2 seems to align more closely with the observed and reanalyzed values.

I appreciate any further insights you may have regarding this issue.

 

[Arty]

Dear @Ming Chen,

First of all, I wish you a happy and successful New Year!

If you don’t mind, I am still working on the above issue and believe you might have some valuable insights to help me better understand and identify the root cause of the discrepancy.

Thank you very much in advance for your support.

 

[Arty]

Hi @Ming Chen ,

I hope you’re doing well. I’m following up on our previous discussion regarding the T2 vs. T2MEAN bias issue. I’d greatly appreciate any further insights you might have on this matter when you have a chance.

Thank you so much for your time and help!

 

[Ming Chen]

Hi Arty,

I am sorry to get back to you so late, partly because I was out of office for a sick leave.

T2 bias is common in WRF simulations, especially when the model resolution is high (for example, 2.3km in your case). We usually recommend to correct T2 bias by:

(1) set slope_rad = 1 and topo_shading = 1
(2) correct T2 based on difference between model terrain height and elevation of observation stations
(3) turn on objective analysis , ---- however, this option only works for mall-area simulation with high-density and high-quality in-situ observations.

Some people also develop post-process package to correct the bias in the simulation.

 

[Arty]

Hi Arty,

I am sorry to get back to you so late, partly because I was out of office for a sick leave.

T2 bias is common in WRF simulations, especially when the model resolution is high (for example, 2.3km in your case). We usually recommend to correct T2 bias by:

(1) set slope_rad = 1 and topo_shading = 1
(2) correct T2 based on difference between model terrain height and elevation of observation stations
(3) turn on objective analysis , ---- however, this option only works for mall-area simulation with high-density and high-quality in-situ observations.

Some people also develop post-process package to correct the bias in the simulation.

Thank you so much, Ming, for all the valuable insights—I learned a lot. I was only familiar with the terrain height correction (which I haven't implemented yet). Unfortunately, I won't be able to re-run my 25-year simulation, but all these suggestions will be very helpful for future work.

That said, I’m still curious about why T2 and T2MEAN show such consistent biases across space and time. In any case, I will use T2 instead of T2MEAN, as it aligns more closely with observations.

I apologize for insisting earlier, and I’m sorry to hear about your sick leave.