The defination of Hz

[zhangtianhao]

In website https://www.myroms.org/wiki/Vertical_S-coordinate, as the picture shown, in red circle 1, it says Hz=∂z/∂σ or Hz=Δz/Δσ. That means Hz is the slope of z-σ curve.

However, in red circle 2, it says that the sum of Hz is total water depth D. As for me, it means that Hz is layer thickness (the distance between two layer). That means Hz = Δz but not Δz/Δσ. And Then we get total water depth D=ΣHz.

I wonder if I misunderstand the defination of layer thickness Hz? Which definition is right? What is the relation between the Hz and total water depth D? Does D=ΣHz? Thanks!

Hoty

[kate]

Hz is the height of the vertical grid box, which you could call Hz=∂z/∂σ.
For consistency between the baroclinic and barotropic solutions, you also need D=ΣHz.

[zhangtianhao]

Hz is the height of the vertical grid box, which you could call Hz=∂z/∂σ.
For consistency between the baroclinic and barotropic solutions, you also need D=ΣHz.

Thanks, Kate!

I misunderstood the defination of Hz and now I get it. We can say that Hz is layer thickness in a physical sense.

Hoty