Unit 6: Hydrologic Balance and Climate Change

On completing this module, students are expected to be able to:

• Create a model of a lake chain using topographic data to derive depth-area-volume relationships for each lake and if-then-else logical statements to determine whether a lake has reached its overflow point given various runoff and evaporation scenarios.
• Demonstrate the impact of changing boundary conditions (in this case, lake reservoir geometries) on system behavior.
• Predict and assess how reservoir response time affects the ability of the lake chain to record climatic variations occurring over different periods of time (e.g. orbital to centennial-scale cycles).

This unit is intended to be used in a three- to four-hour class period that meets once a week. It can be used as part of this modeling course or it can be adapted as a lab exercise for courses in paleoclimatology or geomorphology. For this module, students should come to class prepared to take a short quiz on the assigned reading. Thereafter they will be led through a series of prompts designed to help them create and experiment with a number of simple models using the iconographic box modeling software STELLA (see https://www.iseesystems.com/store/products/ for different options for purchasing student or computer lab licenses of STELLA or for downloading a trial version). Students should have access to Microsoft Excel or similar spreadsheet software to allow them to graph and create best-fit polynomials and power law equations to depth-area-volume data for each lake in the Owens River chain.

For those learning to use STELLA, we suggest the online "play-along" tutorials from isee systems. You can find them here: isee Systems Tutorials.

In preparation for the exercise, students should read the following: Unit 6 Student Reading.

For advanced courses, instructors may also wish to have students read and present on Menking and Anderson reading (Acrobat (PDF) 2.8MB Dec9 14). This is a chapter from Kirsten Menking's 1995 doctoral dissertation at the University of California, Santa Cruz (Paleoclimatic Reconstructions from Owens Lake Core OL-92, Southeastern California).

Students should take the following quiz prior to coming to class to ensure they have done the assigned reading: Lake hydrologic balance reading quiz (Microsoft Word 2007 (.docx) 51kB Aug11 16). An answer key for the reading quiz can be found here:

Lake hydrologic balance reading quiz answer key -- private instructor-only file

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In class, students should be provided with the exercise found here: Owens River chain exercise (Microsoft Word 2007 (.docx) 36kB Dec3 16).

An answer key for the exercise can be found here:

Owens River chain answer key -- private instructor-only file

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Students will need to generate polynomial relationships between lake volume, surface area, and depth in order to determine whether each lake in the chain has reached its overflow threshold and in order to determine the amount of water lost to evaporation. The following Excel file contains the data they need to create these relationships: Hypsometry data (Excel 73kB Dec9 14). For Owens Lake, a power law relationship works best for the area/volume relationship. The other lakes are best fit with second- or third-order polynomials. See the answer key for the equations used in the STELLA model provided here.

Instructors can download a version of the STELLA lake chain model by clicking on this link: Owens Lake chain STELLA model (Stella Model (v10 .stmx) 27kB Aug11 16). The model was created using STELLA Professional and should open on any subsequent version of STELLA. If you are using an earlier version of STELLA, the complete model graphic and equations can be found in the answer key so that you can reconstruct the model yourself.

We generally post the readings and assignments for students to an LMS site (e.g. Moodle, Blackboard, Canvas). Students can open the assignment in Microsoft Word on the same computer they are using to construct the STELLA model and then answer the questions by typing directly into the document. Students can either print a paper copy to hand in to the instructor or email their modified file to the instructor. It is straightforward to copy graphs and model graphics out of STELLA and to paste them into Word. Simply select the items to be copied, hit copy in STELLA, and paste into Word. There is no need to export graphics to jpg.

We teach the course in a three- to four-hour block once a week because we have found that models require a lot of uninterrupted time to construct. If students have a 50- or 75-minute class period several times a week, they spend at least 20 minutes of subsequent class periods trying to figure out where they were in the exercise at the beginning of the week. This is not a good use of time, hence the recommended three- to four-hour class session once per week. However, we also know that sustaining attention for this length of time can be difficult. We therefore recommend allowing students the freedom to take breaks throughout the modeling session to get snacks or coffee.

A typical 4-hour class session might be broken up into the following sections:

• 20-minute discussion of the reading to ensure all the students are familiar with the mathematics behind the model
• 1.5 to 2 hours to build the model
• 1.5 hours to conduct experiments

For instructors who have more limited contact hours with their students, we suggest that the model construction parts of this exercise be assigned as a pre-lab to be handed in a day or two before class along with the completed STELLA model itself. This would allow the instructor to determine whether students' models are working correctly and to provide feedback to address errors in construction, omissions in documentation, problems with unit conversions, and inappropriately sized time steps that might lead to spurious model behavior. Class time could then be devoted to running experiments and analyzing the results. If access to STELLA outside of class time is impossible due to computer lab scheduling or to financial constraints that prevent students from purchasing their own STELLA licenses, students could be asked to create a pencil and paper sketch of what their model should look like, annotated with equations and then sent to the instructor in advance of class for feedback. This should facilitate a faster model construction time during the limited class hours.

Answers to exercise questions are located in the answer key for this unit (see Description and Teaching Materials section above). Instructors may download an assessment rubric for the modeling exercise here: Assessment rubric (Microsoft Word 2007 (.docx) 121kB Jan8 15). Rather than assign a point value to every question in the exercise, we employ a holistic approach that determines the extent to which a student has correctly built the model, supplied appropriate documentation of equations and units, thoroughly answered questions throughout the assignment, and provided appropriately labeled graphs and figures in answering questions.

This exercise is based on the following references (see also student reading for Unit 6):

Menking, K.M., and Anderson, R.S., 1995, "A Model of Runoff, Evaporation, and Overspill in the Owens River System of Lakes, Eastern California," in Menking, K.M., PhD dissertation, University of California, Santa Cruz, p. 40–107.

Phillips, F.M., 2008, "Geological and Hydrological History of the Paleo-Owens River Drainage since the Late Miocene," in Reheis, M.C., Hershler, R., and Miller, D.M., eds., Late Cenozoic Drainage History of the Southwestern Great Basin and Lower Colorado River Region: Geologic and Biotic Perspectives, Geological Society of America Special Paper 439, p. 115–150.

Smith, G.I., Bischoff, J.L., and Bradbury, J.P., 1997, "Synthesis of the paleoclimatic record from Owens Lake core OL-92," in Smith, G.I., and Bischoff, J.L., eds., An 800,000-Year Paleoclimatic Record from Core OL-92, Owens Lake, Southeast California: Boulder, Colorado, Geological Society of America Special Paper 317, p. 143–160.

Smith, G.I., and Street-Perrot, F.A., 1983, "Pluvial Lakes in the Western United States," in Wright, H.E., Jr., ed., Late Quaternary Environments of the United States. Minneapolis, University of Minnesota Press, p. 190–211.

An additional web resource includes:

• Owens Lake: To Dust Bowl and Back? by Bob Harrington, PhD, Inyo County Water District.