1. Boundary Conditions A steady state solution with all specified flux boundary conditions (including no flow) without specified head or head-dependent internal boundaries may not converge or will give a non-unique solution. Boundary conditions always influence a steady state solution but may not influence a transient solution. Initial conditions provide reference heads for transient solutions so that it may be appropriate to set all boundary conditions to flux conditions.

2. Boundary Conditions A specified head boundary acts as an infinite source or sink. Specified flux conditions allow calibration to hydraulic conductivity while specified head and no flow boundaries do not.

3. Types of Boundary Conditions 1.Specified head (including constant head) h = f (x,y,z,t) 2.Specified flux (including no flow)  h/  l = -q l /K l 3.Head-dependent conditions q = -K b (h b – h)/L Implementation in MODFLOW

4. Head Dependent Boundaries (e.g., MODFLOW’s River Package)

7. RBOT Gaining River Cell Q = C (h R – h ijk ) h ijk w m

9. RBOT Losing River Cell Q = C (h R – h ijk )

10. RBOT Losing River Cell Q = C (h R – h ijk )

11. RBOT Percolating River Cell Q = C (h R – RBOT)

12. Definitions Riverbed Conductance = (K v /m) wL Leakance = K v /m Resistance = m/K v K v = vertical hydraulic conductivity of riverbed sediments m = thickness of riverbed sediments w = width of the river L = length of the river within the cell

13. River with sandy bottom = 1 day Small stream with silty bottom = 1- 10 days Stream/lake in till = 100 days Resistance