Los Angeles vs. Mono Lake: Introducing Mass Balance Modeling Using

a Controversial Environmental Issue

Greg Hancock, Dept. of GeologyCollege of William and Mary

Photo: Seth Hancock(no relation)

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 students3) Mostly B.S. Geology majors - sophomore to senior4) Student math is minimal (Calculus I at best); perhaps

introductory physics and chemistry5) Little to no experience with modeling or with MATLAB

The Mono Lake Assignment

1) Basics of mass conservation thinking2) Translation from idea to model construction3) Identifying and evaluating model assumptions4) Planning and troubleshooting numerical models5) Calibration and verification of a model6) Using models for prediction7) Presentation of modeling results

Goal is to introduce students to:

Four class sessions (two hours each), plus final presentation

Los Angeles and Mono Lake

LA

Mono Lake

SF

LA Aqueduct

Los Angeles Aqueduct in Context

1941: Los Angeles begins diverting water

1994: Court orderreduces diversion

Lake level falls nearly45’ in ~30 years

Mono Lake levels since 1995

Constructing a Mass Conservation Model

ΔS/Δt = i + ochange in storage/time = input/time + output/time

Water Balance Equation:ΔV/Δt = 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 expressions6) Translate to MATLAB expressions

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: 1937-1985Verification period: 1985-1995

Prediction of Future Lake LevelsUsing Monte Carlo Simulations

observed

mean – 2 std devmean – 1 std devMonte Carlo meanmean + 1 std dev

Student: Ben Zhang

Prediction of Future Lake Levels

Student: Ben Zhang

Prediction of Future Lake Levels

Student: Kira Holmes