Building Transient MODFLOW Models

Governing Equation Ss = Storage coefficient Transient Component Ss = Storage coefficient Three types of storage coefficients are used with MODFLOW, depending on the layer type and flow package (BCF, LPF, or HUF): Specific storage Specific yield Storativity (BCF)

1 Change in water volume stored in a unit volume of the aquifer per unit change in head. Specific Storage 1 1 1

1 Change in water volume stored in a unit area of a confined aquifer per unit change in head. Storativity b 1 1

Volume of water lost due to gravity drainage 1 Specific Yield Volume of water lost due to gravity drainage H Change in water volume stored in a unit area of a unconfined aquifer per unit change in head. Approximately equal to saturated moisture content minus residual moisture content. 1 1

MODFLOW Storage Coeff.'s Storage parameters are entered in the flow package LPF, HUF, UPW Enter SS (specific storage) for all layers Enter SY (specific yield) for all “convertible” layers BCF Requires either a primary storage coefficient or both a primary and secondary storage coefficient Depends on Layer type

LPF Package Confined Convertible Specific Storage (1/L) Specific Yield (unitless) Note: Similar set of options for HUF and UPW packages

BCF Package Confined (0) Unconfined (1) Conf/Unconf (2) or (3) Primary Storage Coefficient (Storativity, 1/L) Unconfined (1) Primary Storage Coefficient (Sy) Conf/Unconf (2) or (3) Primary Storage Coefficient (Storativity) Secondary Storage Coefficient (Sy)

Defining Initial Conditions For steady state models: The initial conditions represent a “guess” at the starting heads and do not have a big impact on the solution. For transient model: The initial conditions represent the state of the aquifer at the beginning of the simulation Starting head values should be carefully selected Arbitrary head values or heads interpolated from observation wells should NOT be used OR the first stress period of the transient model should be steady state

Model-Generated Heads "Use of model-generated head values ensures that the initial head data and the model hydrologic inputs and parameters are consistent. If the field-measured head values were used as initial conditions, the model response in the early time steps would reflect not only the model stresses under study but also the adjustment of model head values to offset the lack of correspondence between model hydrologic inputs and parameters and the initial head values." Anderson & Woessner, Applied Ground Water Modeling

Example Water table lowers with time

Using Flat Water Table as Initial Condition

Using Steady State Solution as Initial Condition

Time Steps Must choose appropriate distribution of time step sizes Too short -> long simulation times, large solutions Too long -> model error Can calculate Dt or use trial and error Time Step Rule of Thumb for initial Dt where Dt = the time step increment S = storage coefficient a = representative cell dimension in x and y. T = transmissivity

Stress Periods & Time Steps Few stress periods, many time steps Few time steps, many stress periods

CHD Package Original method for defining specified heads works for static (steady state) heads only IBOUND Starting Heads Array CHD later added to allow for transient specified head boundary conditions Unlike most packages, values are specified at beginning and end of stress period

Managing Transient Data Types of Data GMS Strategy Transient model stresses River stage Recharge Pumping rates Transient observation well data Stress periods, time steps Transient solution data Define model reference time Define time units Enter all conceptual model data in date/time format Stress periods/solution time steps can be viewed/edited in either relative or date/time format

Model Reference Time Date/time corresponding to start of simulation 4/15/1994 12:00:00

Time Units Necessary for converting between date/time format and relative time Options Years Days Hours Minutes Seconds

Time Display Options Once reference time is defined, all time data in MODFLOW interface can be entered either in relative format (120.5) or date/time format (12/24/1990 0:0:0)

Date/Time Entry for Map Data Default entry mode is date/time Allows temporal data to be defined independently of time step discretization time units model start time

Discretization Algorithm MapMODFLOW Discretization Algorithm Temporal data values are automatically mapped to appropriate stress periods based on reference time and model units Stress periods should be sized to match changes in transient stresses Stress Period Area Under Curve Mean Value Time Series 0.0 5.0 10.0 15.0 20.0 25.0 30.0 40.0 Time Q

Time steps can be listed using the date/time format Post-Processing Time steps can be listed using the date/time format