documentation for averaging #1056
Conversation
|
Once this is all written out, it is obvious, but there seems to always be confusion about what is an ice average versus a cell average, when to multiply or divide by ice area when time averaging, what to do with various kinds of tracers, etc, so I think this documentation could be useful to users and developers. It's more detailed than necessary, but some of the confusion is because those details aren't always clear (e.g. sum(a_n) = 1 when summed over the whole grid cell and the grid cell areas cancel, which obfuscates the units). @dabail10 I did not attempt to insert the 'intrinsic' and 'extrinsic' labels, but we could if it's helpful. I hope these definitions are indeed what SIMIP recommends! I'm sure you'll all point out typos and other errors... |
There was a problem hiding this comment.
This look useful - thanks @eclare108213 !
Is it worth having a seperate page now for history output ? (Although this content is a bit more general - its true for all cases of averaging of quantities right ?)
| \bar{V}_{i} = {\int_t \int_{cell} \int_{0}^{h} g(\mathbf{X},t) \, dz \, d\mathbf{X} \, dt \over \int_{t} dt} | ||
| \sim {\sum_{\Delta t} \sum_{n=1}^{ncat} h_n \, a_n \, A \, \Delta t \over N \, \Delta t} | ||
| = {A \over N} \sum_{\Delta t} \sum_{n=1}^{ncat} h_n \, a_n | ||
There was a problem hiding this comment.
I think v and V need a definition ?
| \sim \frac{ \sum_{n=1}^{ncat} T_n \, a_n \, }{ \sum_{n=1}^{ncat} a_n} | ||
| then the ice-averaged quantity must be multiplied by the ice area to return it to the cell-averaged quantity (assuming | ||
| a value of zero in open water) before being accumulated in time and divided once again by the ice area: |
There was a problem hiding this comment.
a value of zero in open water) before being accumulated in time and divided once again by the ice area:
I think this line needs a bit more introduction - its not clear why we are now talking about accumulating in time?
3 participants
Mathematical description of various averages in space and time
@eclare108213
No changes to code, only documentation. See section 4.9.3 in https://cice-consortium-cice--1056.org.readthedocs.build/en/1056/developer_guide/dg_other.html.
There is a great deal of confusion about how various history variables are time-averaged, e.g. SIMIP history output implementation #1038, Fixes for sitemptop, sitempbot, and sitempsnic. #1054. This PR attempts to clarify the situation. These averages are also relevant for conservative coupling.