1. Building Transient MODFLOW Models

2. 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)

3. 1
Change in water volume stored in a unit volume of the aquifer per unit change in head.
Specific Storage 1 1 1

4. 1
Change in water volume stored in a unit area of a confined aquifer per unit change in head.
Storativity b 1 1

5. Volume of water lost due to gravity drainage1
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

6. 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

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

8. 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)

9. 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

10. 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

11. Example
Water table lowers with time

12. Using Flat Water Table as Initial Condition

13. Using Steady State Solution as Initial Condition

14. 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

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

16. 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

17. 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

18. Model Reference Time Date/time corresponding to start of simulation
4/15/ :00:00

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

20. 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)

21. 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

22. 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

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