Slab temperatures control melting in subduction zones, what controls slab temperature?

1. By working with a simple analog, students will develop understanding for how two key factors control the flow of beads from one space to another: a) slope and b) material property of the inclined bead roller.
2. By working in groups, students develop an intuition for how math is used to represent the bead flow data they have generated, specifically relating physical processes like bead flux to the concept of gradient and the mathematical representation of gradient.
3. Students will develop an understanding of Fouriers Law for heat flow by developing their own, similar, laws for representing the results from their bead flow experiments and reflecting on how this fits with the thermal analogy (flux, gradient, material property). By relating back to heat flow, students will solidify their understanding of the relationship between a written description of flux-gradient-property to the appropriate math descriptions.
4. Students will reflect on transitioning results from bead activity to heat flow generally to heat flow in subduction zones. Students will reflect on basic temperature patterns, and temperature gradients in different regions of subduction zones. Discuss qualitatively and semi-quantitatively expected heat flow levels in each area.
5. Students will learn a key second phase for describing thermal evolution of subduction zones, the concept of conservation of energy (temperature). The concept is introduced for describing subduction zones as a great number of mini-volumes (called parcels). Students use a second stage of bead flow activity to understand how bead numbers change through time based on bead flows through different sides of the parcel.
6. Following the reflection step for bead flow to heat flow done after the 1st activity, students reflect on how their 2nd activity represents "conservation of beads" parcel by parcel, and how this relates to an analogous law for conservation of temperature in mantle parcels. Where does the analogy work, or break down, and why?
7. Armed with the knowledge and intuition for conservation of thermal energy, students explore how parcels will evolve as they move at different rates through different portions of a subduction zone. The guided focus is on the slab wedge interface, from the point where mantle and slab parcels come together down to an approximate depth of melting (e.g. depth of 150 km or so). Students reflect on how changes in dip angle, subduction rate and temperature gradient between wedge and slab influence the change in temperature through time for a slab surface parcel. Students may achieve this goal through discussion or running the bead activity.
8. An overarching goals is for students to hone skills for working in a group, and being a good teammate in setting up and carrying out activities. This includes assigning different jobs and recording, summarizing and presenting data, and making sure all team members grasp concepts.

A central goal of SUBFAC section of Margins is to connect surface observations made in subduction zones to Earth's internal processes. This requires better linkages between geological data sets and the geodynamic models used in predicting circulation and thermal evolution of the mantle wedge. This module involves a hands-on, exploration-based approach for learning about heat conduction and advection that does not require significant math or physics background prerequisites. This can be added to any course covering basic subduction processes to the chemical recycling through subduction zones, and related melt generation models. One potential lead in to this activity is following any lecture discussing how slab and/or wedge temperatures, or pressure-temperature paths, influence the geological signal (e.g., melt production, metamorphic petrology/igneous petrology, seismic signal of slabs).

Instructors can provide an introduction to the activity on using bead flow to represent heat flow and have groups of student run the activity, summarize findings and explore additional controlling parameters in a single class period. Additional modules are included to tie the results and new intuition for heat flow to real subduction zones using a) a homework assignment to place their results into a subduction zone setting or b) an additional activity to develop ideas on heat advection, relative to conduction in subduction zone settings.

Student background. The activity does not assume any specific level of post high school mathematics. Students should be able to work effectively in groups, assigning tasks within the activity and in representing results.

Overview powerpoint for bead flow to heat flow exercise (PowerPoint 2007 (.pptx) 522kB Sep20 13). An introductory powerpoint presents a very broad overview on the importance of thermal processes in subduction zones, and many other natural systems, for controlling the production of melt in the mantle wedge, chemical transport through arcs and the characteristics of geological formations recorded at Earth's surface. To provide motivations (and context) the point is stressed that there is a need for greater communication between geoscientists developing geologic data sets in subduction zones and the qualitative dynamical process models from these data sets, and the more quantitative geodynamic models of subduction. To underscore this point, there is a summary provided for the very wide range in slab geotherms that are reported in the scientific literature. What leads to such diversity in predicted geothermal?

Before launching into a discussion of conductive versus advective heat transfer, and the conservation law for temperatures in subduction zones, we begin the module with a hands on activity where bead flow is an analog for heat flow. Students will explore the relationship between bead flow and three key parameters (material property, rise, run (e.g. slope)). Students are first given specific instructions for experimental setup, with a given slope and surface type for the bead roller guide. Data are collected and summarized, and compared with results of other teams. Students then discuss other options for parameters, and explore these through additional experiments. Finally, students are asked to write down a relationship between bead flow and the parameters they explored, first in english and then with math. This is compared with Fouriers Law for heat flow.

This is phase 1 of the conductive heat transfer activity. Phase 2 is to put this into context of an actual system, and work towards an understanding of the conservation law for temperature, again using beads. We start with developing the idea of how a conservation law for heat flow through a wall would look by focusing on a small mini-volume of the wall, called a parcel. Since we have developed identical laws for heat flow and bead flow from phase 1, we will explore the conservation law using our bead flow activity.

Phase 2 involves two bead flow setups with a receptacle in between for representing the parcel. One setup provides beads to the parcel, the other draws beads from the parcel. Separate teams work each bead flow setup, choosing their own slope. The activity is run while monitoring the accumulation or decrease in beads within the parcel through time. Teams compare results and explore different parameter combinations. Teams once again describe with words what is controlling bead numbers in time within the parcel. Then they develop their own math law for the words. This is compared with same problem where heat is flowing instead of beads, and is compared with the conservation law for temperature in parcels.

To end class, a game that reinforces the concept is run. The parcel (bead container) is placed in the middle of a table. Four bead roller guides are placed around the parcel, each one leading out from four of the parcel sides. Four volunteers are asked to produce a slope with their bead roller (without actually sending beads down the roller guide) and hold that position. The class is asked if the pattern will lead to bead accumulation or bead decrease with time in the parcel. They are asked to vote with their height. If there is no change assume a squat. If there is accumulation, stand up straight. If there is a bead decrease in time, sit down. Once they get the hang of it, have the 4 volunteers change their slope, re-assess. Increase the speed of changes and voting cycles to make it fun. The final task for the class is to ask groups how they would modify their math law from phase 2, for how bead numbers change with time in the parcel depending on the pattern in the slopes. This introduces a change from a 1-D bead flow law to a 2-D bead flow conservation law. As above, the bead flow analogy is always related back to heat flow.

A good homework assignment to tie the activity back to subduction zones is to use the knowledge gained from the class and combine it with a cross section of temperature patterns expected in a subduction zone. Ask students to (theoretically) place their 2-D conservation activity setup at a few sites in the subduction zone. Substituting height slopes for the bead example to temperature gradients (slopes) for the temperature case, have them decide what the heat flow rates into and out of the parcels are expected to be. They should be prepared to talk about if each area has thermal gradients where temperature (in place of beads) is expected to increase, decrease or stay the same with time. Just as with the beads, the students should be able to tell (in a relative sense) something about the rate of change of temperature in the different parcel locations. When going over this in class, it can be fun to have different teams give each other locations in the subduction cross section and work through the resulting heat flows, differences in heat flows through all sides of the parcel and expected temperature change in time.

In classes where this has been used, typically each group presents a written summary of their work and an oral summary to the rest of the class. We often allow other groups to select the person to present from group that has the floor. This ensures that all group members participate in the group learning process. Having each group rate each others performance has also proven effective.

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