Earth Science and Geography
Modeling U-Series Concordia/Discordia Using STELLA part of Rates and Time:GSA Activity Posters
U-Series dating techniques are widely used to determine the absolute ages of some of Earth's oldest rocks, but the concordia/discordia diagram can be quite difficult for students to grasp. In particular, the fact that differing amounts of lead and uranium loss from minerals such as zircon can be used to determine not only the original formation age, but also the time of metamorphism of a rock like granite, is a challenging concept. Making use of previous workers' web-published excercises on radiometric decay, I have produced a STELLA-based lab exercise to develop students' understanding of this important chronologic technique. Students create models of the two isotopic decay systems, 238U --> 206Pb and 235U --> 207Pb, and run these models for 4.5 billion years to create the concordia diagram. They then carry out experiments in which they "add" or "remove" varying amounts of lead or uranium in simulation of metamorphism. The uranium-lead ratios at the end of the simulation allow the discordia line to be plotted on top of the concordia diagram and the ages of original crystallization and metamorphism to be determined from the points of intersection of the two lines. In the course of the lab, students are introduced to the concepts of exponential decay and secular equilibrium as well as modeling concepts such as the creation of if-then statements.
Daisyworld Model part of Cutting Edge:Complex Systems:Teaching Activities
In this exercise, students recreate the classic Daisyworld model of Watson and Lovelock (1983). Daisyworld is a planet covered by two species of daisy, one white and one black, whose growth is determined by temperature, and whose albedo influences that temperature. The planet experiences a steady increase in solar luminosity, impacting the temperature and the populations of black and white daisies over time. The growth and die-off of the different daisy species results in a stabilization of planetary temperature for some time, despite the increasing solar luminosity.
Modeling Earth's Energy Balance part of Cutting Edge:Complex Systems:Teaching Activities
In this exercise, students use the STELLA box modeling software to determine Earth's temperature based on incoming solar radiation and outgoing terrestrial radiation. Starting with a simple black body model, the exercise gradually adds complexity by incorporating albedo, then a 1-layer atmosphere, then a 2-layer atmosphere, and finally a complex atmosphere with latent and sensible heat fluxes. With each step, students compare the modeled surface temperature to Earth's actual surface temperature, thereby providing a check on how well each increasingly complex model captures the physics of the actual system.
Daisyworld Lab part of Quantitative Skills:Activity Collection
Students explore Daisyworld, a model of a self-regulating system incorporating positive and negative feedbacks. Daisyworld is a planet on which black and white daisies are the only things growing. The model explores the effect of a steadily increasing solar luminosity on the daisy populations and the resulting planetary temperature. The growth function for the daisies allows them to modulate the planet's temperature for many years, warming it early on as radiation absorbing black daisies grow, and cooling it later as reflective white daisies grow. Eventually, the solar luminosity increases beyond the daisies' capability to modulate the temperature and they die out, leading to a rapid rise in the planetary temperature. Daisyworld was conceived of by Andrew Watson and James Lovelock to illustrate how life might in part have been responsible for regulating Earth's temperature as the Sun's luminosity increased over time. This exercise guides students through some of the mathematics behind the modeling, and uses STELLA or Fortran 90 code.
Radioactive Decay and Geochronology part of Quantitative Skills:Activity Collection
Students create a STELLA model of the radioactive decay process. They then learn how the special radioactive series 238U - 206Pb and 237U - 205Pb can be used to determine both the time when a rock initially crystallized and when it underwent a recrystallization, even when the sample being dated was not a closed system.
Temperature Profiles in Permafrost part of Quantitative Skills:Activity Collection
Students create a STELLA model of heat flow in the outer km of Earth's crust and then perform experiments to change the air temperature variable in an attempt to replicate the findings of Lachenbruch and Marshall (1986). These workers used inflections in the geothermal gradient of Alaskan permafrost to search for evidence of recent climatic change.
Lake Level Changes in the Arid West part of Quantitative Skills:Activity Collection
Many basins in the arid West today contain small lakes, but also contain shoreline deposits that indicate these lakes were once much larger. In this lab students explore the impact of changes in climate on the level of lakes in the Owens River system. These lakes, which were separated by bedrock sills and which were fed by runoff from the eastern flank of the Sierra Nevada mountains in California, were headed by Owens Lake. When Owens Lake filled to its maximum level, it overflowed into the China Lake Basin, which in turn overflowed into Searles Lake. During particularly wet periods in the geologic past Searles overflowed into Panamint Lake, which ultimately overflowed into Manly Lake in Death Valley. Students use the STELLA modeling software to see what combinations of runoff and evaporation might have led to Pleistocene lake level oscillations.
Modeling Earth's Temperature part of Quantitative Skills:Activity Collection
Students use the STELLA program to create hierarchies of models of increasing complexity to understand the absorption of solar energy by the Earth and its radiation of that energy back to space. They first assume that Earth is a perfect black body lacking an atmosphere, then move on to incorporate the fact that Earth reflects much of the solar radiation incident upon it, and later incorporate the fact that Earth has an atmosphere. Each time they build onto the model students evaluate the output and compare it to actual Earth surface conditions to see how well each model refinement captures the reality of the physics of heat absorption, exchange, and emission. A second lab asks students to take their STELLA model of an Earth with a two-layer atmosphere and code it into fortran.
Landscape Diffusion Lab part of Quantitative Skills:Activity Collection
Students create a STELLA model of two marine terrace platforms separated in elevation by a cliff. They use the hillslope flux equation to simulate the change in the cliff face over time as diffusive processes tear it down. This modeling project is based on a problem of great geomorphological interest: how landscapes evolve over time in response to processes such as raindrop impacts, the annual cycle of freeze-thaw, tree throw, and the action of burrowing animals. All of these diffusive processes act to move soils and sediments from topographic high points to low points.
Global Phosphorus Cycle part of Quantitative Skills:Activity Collection
This exercise guides students through creating and modifying a STELLA model of the global phosphorus cycle to test the behavior of phosphorus reservoirs in a number of scenarios. Students build a steady state system and then modify it to explore anthropogenic changes to the system, including the addition of phosphorus-rich fertilizers to the land surface and the shut down of ocean circulation due to global climate change. Other scenarios include an increase in plate tectonic rates, increased insoluble weathering due to glaciation, and changes in the planet's plant populations. The exercise includes the use of STELLA and Fortran 90 code.
Modeling the Earth part of Cutting Edge:Complex Systems:Workshop 2010:Participant Essays
Kirsten Menking, Vassar College The class in which my students acquire the most hands-on experience with complex systems is my senior seminar on numerical modeling, entitled Modeling the Earth. This course ...