1. Los Angeles vs. Mono Lake:
Introducing Mass Balance Modeling
Using a Controversial Environmental
Issue
Greg Hancock, Dept. of Geology
College of William and Mary
Photo: Seth Hancock
(no relation)

2. Course and Student Context
GEOL427: Introduction to Modeling in the
Earth Sciences
1) Two-credit hour course, meets once/week for two hours
2) Limit of 11 students
3) Mostly B.S. Geology majors - sophomore to senior
4) Student math is minimal (Calculus I at best); perhaps
introductory physics and chemistry
5) Little to no experience with modeling or with MATLAB

3. The Mono Lake Assignment
1) Basics of mass conservation thinking
2) Translation from idea to model construction
3) Identifying and evaluating model assumptions
4) Planning and troubleshooting numerical models
5) Calibration and verification of a model
6) Using models for prediction
7) Presentation of modeling results
Goal is to introduce students to:
Four class sessions (two hours each), plus final presentation

4. Los Angeles and
Mono Lake
LA
Mono Lake
SF
LA Aqueduct

5. Los Angeles Aqueduct in
Context

6. 1941: Los Angeles begins
diverting water
1994: Court order
reduces diversion
Lake level falls nearly
45’ in ~30 years

7. Mono Lake levels since 1995

8. Constructing a Mass Conservation Model
S/ t =Δ Δ i + o
change in storage/time = input/time + output/time
Water Balance Equation:
V/ t =Δ Δ Q + P + ET + SR + G + D
Steps to construct of our model:
1) What are the questions?
2) What is the relevant
reservoir?
3) What quantity will be
conserved?
Practice: college enrollment, sodas in a vending machine, carboy volume
4) Construct a stock and flow diagram
5) Translate to numerical expressions
6) Translate to MATLAB expressions

9. Calibrating and Verification of the
Mass Conservation Model
A wealth of data collected from 1937 to present…
Annual measurements for:
precipitation, stream flow, evapotranspiration,
diversions, lake elevation/lake area/lake volume
Calibration period: 1937-1985
Verification period: 1985-1995

10. Prediction of Future Lake Levels
Using Monte Carlo Simulations
observed
mean – 2 std dev
mean – 1 std dev
Monte Carlo mean
mean + 1 std dev
Student: Ben Zhang

11. Prediction of Future Lake Levels
Student: Ben Zhang

12. Prediction of Future Lake Levels
Student:
Kira Holmes