maxhbalsmeier
New member
Hi,
I just started with WRF. I implemented the deep atmosphere into the ICON-IAP model, so I checked wether the deep atmospehre is implemented into the ARW solver. I found that replacing the functional determinant of spherical coordinates according to
sqrt(g) = r^2*cos(latitude) -> a^2*cos(latitutde),
where a is the mean Earth radius, is sufficient to consistently derive the shallow atmosphere approximation (compare https://rmets.onlinelibrary.wiley.com/doi/abs/10.1256/qj.04.49 , they do not show this in detail, but go into the same direction). Otherwise you will run into inconsistencies concerning spurious divergences and/or vorticities (numerically small but aviodable). In my view the shallow atmosphere has four implications:
1.) radius and related grid properties (faces, volumes, depending on the model formulation) independant on height
2.) non-traditional Coriolis components neglected
3.) gravity independant on height
4.) metric terms ~ uw/r, vw/r neglected
I can show You detailed derivations if You like.
From a look into the documentation and the code, ARW is a deep solver in terms of aspects 2.) and 4.), but still makes approximations 1.) and 3.).
Would it be appreciated if I sat down and implemented a height-dependant gravity as well as height-dependant grid properties into the code? Since I only just begin with WRF, this would take some time.
Cheers
Max
I just started with WRF. I implemented the deep atmosphere into the ICON-IAP model, so I checked wether the deep atmospehre is implemented into the ARW solver. I found that replacing the functional determinant of spherical coordinates according to
sqrt(g) = r^2*cos(latitude) -> a^2*cos(latitutde),
where a is the mean Earth radius, is sufficient to consistently derive the shallow atmosphere approximation (compare https://rmets.onlinelibrary.wiley.com/doi/abs/10.1256/qj.04.49 , they do not show this in detail, but go into the same direction). Otherwise you will run into inconsistencies concerning spurious divergences and/or vorticities (numerically small but aviodable). In my view the shallow atmosphere has four implications:
1.) radius and related grid properties (faces, volumes, depending on the model formulation) independant on height
2.) non-traditional Coriolis components neglected
3.) gravity independant on height
4.) metric terms ~ uw/r, vw/r neglected
I can show You detailed derivations if You like.
From a look into the documentation and the code, ARW is a deep solver in terms of aspects 2.) and 4.), but still makes approximations 1.) and 3.).
Would it be appreciated if I sat down and implemented a height-dependant gravity as well as height-dependant grid properties into the code? Since I only just begin with WRF, this would take some time.
Cheers
Max