Ground-water model calibration and uncertainty analysis

Course for Geologists and Engineers *by* Mary C. Hill, U.S. Geological
Survey

**Offered through CU-Boulder Civil, Environmental and Architectural
EngineeringDept., Fall 2000**

**Course Description:** Models are used extensively to evaluate
ground-water systems and to predict their response to such things as
changes in pumpage and proposed remediation efforts. Because many
aspects of ground-water systems are unknown, most models are calibrated.
Calibration commonly is achieved by trial and error alone, but these
methods provide less insight than is possible. This course teaches how
sensitivity analysis, nonlinear regression, and associated statistics
can be used to greatly improve how data is used to calibrate and test
ground-water models. For example, parameters that can not be estimated
accurately and uniquely with the available data can be quickly
identified. Parameter values that produce the best fit between simulated
and observed hydraulic heads, concentrations, and so on can be estimated
by nonlinear regression. Measures of prediction uncertainty and measures
of the importance of existing and potential observations are a natural
consequence of regression methods.

Prerequisites: Basic statistics, computer usage. Ideas are taught using
ground-water modeling but apply to any modeling; ground-water model
experience is useful but is not a prerequisite.

.

**Program Schedule:** Course participants will learn nonlinear
regression methods using the U.S. Geological Survey computer programs
MODFLOW-2000, an inverse ground-water flow model that is numerically
sophisticated but applies to limited situations; and UCODE, a universal
inverse code that can be used with any model. MT3DMS, a forward
ground-water transport program, also will be discussed in the course.
These public domain programs are well-documented, tested, and suitable
for complex field application.

Class hours will be from 12:30 to 1:45, Tuesday and Thursday, August 29
to Decedmber 14, room ECCE1B41. There is no class 10/5 and 11/23 because
of CU breaks. The dates of the classes are as follows:

+-------+-------+--------+--------+--------+--------+--------+--------+
| Class | Date  | Class  | Date   | Class  | Date   | Class  | Date   |
+-------+-------+--------+--------+--------+--------+--------+--------+
| 1     | 8/29  | 9      | 9/26   | 17     | 10/26  | 25     | 11/28  |
+-------+-------+--------+--------+--------+--------+--------+--------+
| 2     | 8/31  | 10     | 9/28   | 18     | 10/31  | 26     | 11/30  |
+-------+-------+--------+--------+--------+--------+--------+--------+
| 3     | 9/5   | 11     | 10/3   | 19     | 11/2   | 27     | 12/5   |
+-------+-------+--------+--------+--------+--------+--------+--------+
| 4     | 9/7   | 12     | 10/10  | 20     | 11/7   | 28     | 12/7   |
+-------+-------+--------+--------+--------+--------+--------+--------+
| 5     | 9/12  | 13     | 10/12  | 21     | 11/9   | 29     | 12/12  |
+-------+-------+--------+--------+--------+--------+--------+--------+
| 6     | 9/14  | 14     | 10/17  | 22     | 11/14  | 30     | 12/14  |
+-------+-------+--------+--------+--------+--------+--------+--------+
| 7     | 9/19  | 15     | 10/19  | 23     | 11/16  | Final  | 12/18  |
|       |       |        |        |        |        | exam   |        |
|       |       |        |        |        |        |        | 1:30-4 |
|       |       |        |        |        |        |        | pm     |
+-------+-------+--------+--------+--------+--------+--------+--------+
| 8     | 9/21  | 16     | 10/24  | 24     | 11/21  |        |        |
+-------+-------+--------+--------+--------+--------+--------+--------+

**Office hours and location:** Office hours will be Tuesday and
Thursday, 1:45-4:00. I will be available immediately after class at 1:45
the classroom, and shortly thereafter at my office at 3215 Marine St.,
Room E137

**Grades:** Homework, 25%; exams, 50%; class participation and
presentation, 25%. Except for mathematical proofs, homework must be
typed (if this is a problem, please see the instructor).

**Texts:** The main text for the course is a draft of the text book
"Methods and Guidelines for Effective Model Calibration" by Hill and
Tiedeman (M&G), and will be provided by the instructor. The text book
"Statistical methods in water resource" by Dennis R. Helsel and Robert
M. Hirsch needs to be purchased by the students. It is not available
through the book store. Documentation for the computer codes
MODFLOW-2000, UCODE, MODPATH, and MT3DMS will be provided by the
instructor. Copies of selected articles and reports will be provided by
the instructor.

**COURSE OUTLINE** (**HW:** homework due next class except as noted;
exercises are from M&G except as noted)

**Class Topic**

(1) Ground-water management problem used for class exercises. The
    weighted least-squares objective function as a measure of model fit.
    Relevant ground-water flow and observation capabilities of
    MODFLOW-2000. **HW:** exercises 1-4, extended as described in class.
    (due class 3)

(2) MODFLOW-2000, continued. Discuss graphical interfaces. **HW:** Read
    H&H sections 9.1 to 9.4.

(3) Motivation and methods for model calibration. Model calibration
    using nonlinear regression. Basics of linear regression. **HW:** H&H
    exercise 9.1, extended as described in class. Read H&H section 9.5.

(4) More basics of linear regression. **HW:** More extensions of H&H
    exercise 9.1. Read H&H sections 11.1, to 11.4 and 11.5.2.

(5) Multiple linear regression. **HW:** H&H 11.1, with computer output
    provided, and exercise on the variance of the sum of two random,
    normally distributed numbers.

(6) Parameters in ground-water problems. Additive parameters. **HW:**
    exercises 5 (include optional exercises).

(7) Calculate sensitivities with MODFLOW-2000 using the
    sensitivity-equation sensitivities or with UCODE using the
    perturbation method. Parallel computing. PEST. Evaluate data and
    parameters using dimensionless, composite, and one-percent scaled
    sensitivities. **HW:** exercises 6.

(8) Objective-function surfaces. Effect of parameter correlation and
    insensitivity. **HW:** exercise 7.

(9) Multiple nonlinear regression. Modified Gauss-Newton optimization.
    Use a two-parameter version of the test problem to investigate how
    the modified Gauss-Newton method works. **HW:** Derive the
    Gauss-Newton equation. Exercise 7. Attempt regression in exercise
    8b.

(10) Prior information. Statistical and graphical evaluation of model
     fit. **HW:** Study the simple test cases in Poeter and Hill (1996)
     and Poeter and Hill (1997); exercise 8c, 8d, 9, 10. Use UCODE
     generated data sets to plot the objective function for pairs of
     parameters from the steady-state class problem to study why the
     prior information was needed in exercise 8.

(11) Calculate measures of parameter uncertainty and correlation.
     **HW:** exercises 11.

(12) Test for model nonlinearity. **HW:** exercise 12.

(13) Predictions and prediction uncertainty. Evauate potential new
     observations. **HW:** exercises 13-14.

(14) Review session. **HW:** read D'Agnese and others (1999) (due class
     16)

(15) ....Midterm exam....

(16) Field example: Modeling the Death Valley regional flow system.
     **HW:** Prepare idea for class presentation (due class 19)

(17) Using hydrogeologic data to constrain ground-water model
     development, methods and examples -- Dr. Claudia C. Faunt

(18) \[optional\] Model calibration and evaluation using transient
     observations. **HW:** exercises 15-22 (due class 19).

(19) **Assign student presentations.** **HW:** Read Christensen and
     Cooley (1999)

(20) Model nonlinearity and its effect on sensitivity analysis,
     regression, and uncertainty analysis -- Dr. Richard L. Cooley,
     guest lecture

(21) Objective function design. **HW:** read Mehl and Hill (1999).

(22) Calibrate with concentration data from a laboratory experiment
     using UCODE, MODFLOW, and different solution methods from MT3DMS --
     Mr. Steffen Mehl. **HW:** read Barlebo and others (1998).

(23) Calibrate with heads alone, and heads and with concentrations in
     the Grindsted landfill site, Denmark. **HW:** read Sanford and
     others (2004, USGS SRIR 03-4286)

(24) Calibrate with age dates using UCODE and MODPATH in the Rio Grande
     basin. **HW:** read Tiedeman and others (1997, GW) Due: First draft
     of project. First regression attempt. Sens, model fit. HW: Hill +
     (1998, GW)

     **More applications of the methods and guidelines**

(25) Characterizing a fractured rock ground-water system in Mirror Lake,
     New Hampshire; investigation of regression using a synthetic test
     case. **HW:** read Tiedeman and Gorelick (1993, WRR)

(26) Optimal remediation strategies under parameter uncertainty in
     Michigan. **HW:** Read Anderman and Hill (1999, WRR)

(27) Presentation and investigation of a multistage optimization method
     for ground-water transport problems

(28) **Student presentations**

(29) **Student presentations**

(30) Upcoming developments for MODFLOW-2000 and UCODE. Review session