Past exam of the mathematics and the environment and mathematical physiology course of the University of Oxford / 2009 / A / 1 / iii

Hydrostatic pressure at the entrance is $p_w=p_{\mathrm{ref}}+{\rho }_{w}gh$, with a constant reference pressure. Therefore $N=p_i-p_{\mathrm{ref}}-{\rho }_{w}gh$, and constant overburden pressure givesA filling lake raises water pressure and lowers effective pressure, reducing material creep closure. A draining lake has the reverse effect. These signs supply the pressure feedback in the coupled drainage model.