Closure of the hyperbolic system of equations (1)–(2) is obtained from the geometry of cross sections – by providing a functional relationship between the cross-sectional area A and the surface elevation ζ at each position x. For example, for a rectangular cross section, with constant channel width B and channel bed elevation z b, the cross sectional area is: A = B (ζ − z b) = B h. The instantaneous water depth is h (x, t) = ζ(x, t) − z b (x), with z b (x) the bed level (i.e. elevation of the lowest point in the bed above datum, see the cross-section figure). For non-moving channel walls the cross-sectional area A in equation (1) can be written as: A ( x , t ) = ∫ ∫ 0 h ( x , t ) b ( x , h ′ ) d h ′ , with b (x, h) the effective width of the channel cross section at location x when the fluid depth is h – so b (x, h) = B (x) for rectangular channels.