where A, I 1 and I 2 are functions of the channel geometry, described in the terms of the channel width B (σ, x). Here σ is the height above the lowest point in the cross section at location x, see the cross-section figure. So σ is the height above the bed level z b (x) (of the lowest point in the cross section): A ( σ σ , x ) = ∫ ∫ 0 σ σ B ( σ σ ′ , x ) d σ σ ′ , I 1 ( σ σ , x ) = ∫ ∫ 0 σ σ ( σ σ − − σ σ ′ ) B ( σ σ ′ ′ , x ) d σ σ ′ and I 2 ( σ σ , x ) = ∫ ∫ 0 σ σ ( σ σ − − σ σ ′ ) ∂ ∂ B ( σ σ ′ , x ) ∂ ∂ x d σ σ ′ .