Types of Boundary Conditions 1 Specified head including

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

Versions of MODFLOW 88/96 MODFLOW 2000 MODFLOW 2005

required MODFLOW 88/96 Packages required head dependent BCs 1 is required & PCG 2

RIVER Package Field setting Representation in the model

hb= h. R = head in the river q = -Kb (hb – h)/b Head Dependent Boundaries MODFLOW’s River Package

m w Q = conductance x change in head

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

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

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

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

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

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

Head Dependent Boundaries in MODFLOW 88/96 Q = C h • River Package • Drain Package • General Head Boundary (GHB) Package • ET Package

River Package Q = C (h. R – hijk) where C =Kv. Lw/m

Drain Package

Drain Package Q = C (hijk-d) where d = head in the drain. Q = 0 if hijk<d

General Head Boundary Package Boundary cell L h Q= C (h. B-h) C = K A /L h. B

Evapotranspiration (EVT) Package …to be discussed later, when we do the Final Project

GHB L Q = C (h. B - h) C = Conductance = K A/L K is the hydraulic conductivity of the aquifer between the model and the lake; A is the area of the boundary cell, perpendicular to flow. h. B

• Streamflow Package (Prudic 1989)- see p. 127 A&W Allows for dynamic interchange of groundwater and streamflow; solves for stream stage. Manning’s Equation: d = (Q n / C w S 1/2)3/5 n is Manning’s Roughness coefficient New MODFLOW Package available in MODFLOW 2000. • Streamflow Routing Package (Prudic 2004) Q

Estimating Manning’s n http: //www. engineering. usu. edu/classes/cee/5470/wsp 2339. pdf

• Lake Package – Available in MODFLOW 2000 (Cheng and Anderson, GW, 1993) (Council, 1998) (Merritt and Konikow, 2000) Solves for lake levels Other packages: • Wetland Module (Restrepo et al. , GW, 1998) • MODBRANCH (Swain, 1993)

Lake (LAK) Package Change in Storage = Outflow - Inflow Change in lake level = Change in Storage/Area

Head Dependent Boundaries in original MODFLOW 88/96 Q = C h • River Package • Drain Package • General Head Boundary (GHB) Package • ET Package Prudic’s 1989 Streamflow Package and a few other packages have since been added to MODFLOW 88/96 and are available when running MODFLOW 88/96 in Groundwater Vistas.