Slight modification in orographic gravity wave drag (OGWD) scheme

[rhaesung]

This modification is from @JongilHan66

Description:

1. The reference height (href) in the OGWD (Orographic Gravity Wave Drag) scheme is a critical parameter that significantly influences the strength of OGWD. Currently, href is defined as the maximum of the maximum subgrid orographic elevation (Omax) and twice the standard deviation of subgrid orography (sigma), i.e.,
   href = max(Omax, 2*sigma).

   In the proposed modification, this is changed to:
   href = max(Omax, 2*sigma, hpbl),
   where hpbl is the planetary boundary layer height.

   The inclusion of hpbl in determining href is informed by prior studies on the OGWD scheme:

   href = hpbl (Kim and Arakawa, 1995)
   href = 2* sigma (Kim and Doyle, 2005)
   href = max(2*sigma, hpbl) (Hong et al., 2005)

2. The modified href not only improves the 500mb height anomaly correlation, but it also helps to reduce too strong wintertime polar vortex in the upper stratosphere, where hr5a01 is the control run and hr5a12 is same as the control run but with the modified href.

[mdtoyNOAA]

Modifying 'href' to include the height of the PBL makes sense for the orographic gravity wave drag. However, I don't agree with the modification of hmax by adding line 2003: hmax(i) = max(hmax(i),hpbl(i))
'hmax' is the maximum subgrid terrain height assumed for blocking. No blocking can physically occur above this assumed height, but the addition of line 2003 means that the blocking height can exceed the terrain height if the boundary layer height exceeds the subgrid terrain height, which is not an uncommon scenario.
In Choi and Hong (2015), equation 6, H (which corresponds to href) is defined as the "maximum height of the actual subgrid orography within each grid box". I think 'href' should maintain this definition and not be influenced by the boundary layer height.

[JongilHan66]

Modifying 'href' to include the height of the PBL makes sense for the orographic gravity wave drag. However, I don't agree with the modification of hmax by adding line 2003: hmax(i) = max(hmax(i),hpbl(i)) 'hmax' is the maximum subgrid terrain height assumed for blocking. No blocking can physically occur above this assumed height, but the addition of line 2003 means that the blocking height can exceed the terrain height if the boundary layer height exceeds the subgrid terrain height, which is not an uncommon scenario. In Choi and Hong (2015), equation 6, H (which corresponds to href) is defined as the "maximum height of the actual subgrid orography within each grid box". I think 'href' should maintain this definition and not be influenced by the boundary layer height.

@mdtoyNOAA how about hmax=max(hmax,hpbl) for orographic GWD, and introducing a new variable, 'hbmax', for blocking and using hbmax with hbmax=max(elvmax, zlowtop) for blocking?

[mdtoyNOAA]

Modifying 'href' to include the height of the PBL makes sense for the orographic gravity wave drag. However, I don't agree with the modification of hmax by adding line 2003: hmax(i) = max(hmax(i),hpbl(i)) 'hmax' is the maximum subgrid terrain height assumed for blocking. No blocking can physically occur above this assumed height, but the addition of line 2003 means that the blocking height can exceed the terrain height if the boundary layer height exceeds the subgrid terrain height, which is not an uncommon scenario. In Choi and Hong (2015), equation 6, H (which corresponds to href) is defined as the "maximum height of the actual subgrid orography within each grid box". I think 'href' should maintain this definition and not be influenced by the boundary layer height.

@mdtoyNOAA how about hmax=max(hmax,hpbl) for orographic GWD, and introducing a new variable, 'hbmax', for blocking and using hbmax with hbmax=max(elvmax, zlowtop) for blocking?

@JongilHan66 I think that will work.