Introduce 2nd order Tdry integration into ropp_apps_utils.f90

[Ian Culverwell]

SUBROUTINE ropp_apps_calc_tdry in ropp_apps/common/ropp_apps_utils.f90 uses simple Euler forward method to calculate dry temperature. The attached contains a second order method (explicit midpoint), which is slightly more accurate (differences in Tdry <~ 0.5K) and slightly more expensive. Note that the resulting differences in PBLH are <~ 0.1m, ie negligible. Nonetheless, we may choose to implement this scheme at ROPP9.0.

[Ian Culverwell]

ropp_apps_utils.f90

[Ian Culverwell]

For the record, the 2nd order pblh_tdry - 1st order pblh_tdry for the 438 profiles on 20130401/00Z satisfies:

-1.20947 < pblh_tdry_diff (in m) (avg = -0.0312037) < 0.16626.

And the 2nd strongest says

-0.340088 < pblh_tdry2_diff (in m) (avg = -0.0101814 ) < 0.756348.  

So really very small impact overall.

[Ian Culverwell]

Can generate suprisingly large (20 K) differences high up in Tdry in the test example, ropp_apps/data/ropp_apps_pblh_test.nc, but these are mostly due to the use of a more accurate estimate of dlogN/dz at the top. it makes a very small difference to the PBLH, and to the temperature at the PBLH, so accept the change.

Code changes implemented at r4747 (and r4750).

Supporting documentation changes made at r4749.

[Ian Culverwell]

Closing ticket.