In two recent papers I have described the purposes, principles, and applications of spreadsheet modeling of Earth surface processes to undergraduate teaching (Locke, 1996, Geomorphology, 16, 251-258) and course-initiated research (Locke, 1995, Geomorphology, 14, 123-130). This page summarizes the teaching-related content of those papers; the research is discussed in attached papers on the glaciation of the northern Rocky Mountains of Montana, the Yellowstone region, and the Wind River Range of Wyoming.
Spreadsheets (Lotus1-2-3, ClarisWorks, Excel, Quattro Pro) are ubiquitous elements of software packages available on most personal and networked microcomputer systems. Their primary application is, of course, business/financial. As such they have the ability to hold and large numerical datasets and perform complex calculations, including statistical analyses. Thus, like standard scientific "black-box" models, they can perform calculations and generate output. More importantly, they have built-in graphical display capability. Thus they can also display graphics nested in the model which change as the variables or constants in the model change. Perhaps most importantly, the model is "transparent" in that simply clicking on a cell displays the cell contents as both formula and result. These three characteristics - availability, graphic display, and transparency - make spreadsheets the perfect tool for teaching undergraduates the principles of scientific numerical visualization and modeling.
As with most learning processes, spreadsheet modeling proceeds from exercises which emphasize the mechanics to those which emphasize the products. In the past I have required a computer literacy course as a prerequisite for the junior-level (Earth Science 307 - Principles of Geomorphology) course in which I use spreadsheet models. Now, in part in response to tightening of curricular credit-hour caps, I assume exposure to spreadsheeting.
The first computer lab serves to (re?)develop familiarity with the computer setting and the spreadsheet. The students load from the Web an Excel file containing several "pages" (screens) of instructions and only three columns of model! The exercise (which ostensibly focuses on scarp evolution) provides practice in data entry, block copy, modifying a graph, and of course, use of the "Help" utility. The actual model is a three-point running mean, which yields a surprisingly convincing rendition of a scarp evolving through time. Some students use the simplicity of the model to question the value of any model, others use it to suggest further refinements. The exercise can be completed within an hour of reserved teaching lab time, otherwise the students are released to general labs to complete the exercise - a graph showing change across time and a brief discussion of the inferred process.
The second lab looks the same as the first, but uses a more realistic means to get there - a transport function integrating "erodibility" and local slope. The transparent nature of the spreadsheet model is emphasized by the similarity in the graphical output, but the difference in the formula used. In addition to "growing" the model as they did the previous week, students are introduced to absolute cell references. They are also introduced to the concept of research by being required to articulate a hypothesis which can be "tested" through application of the model. Spreadsheet tools introduced include the Random Number Generator and conditional expressions. For example, they could test whether "repeated small offsets look the same as a single large offset". Of course, the "test" is only as good as the assumptions involved in the model. Some students are concerned by the lack of inclusion of extreme events, which can be a fertile discussion topic.
My third spreadsheet lab is a complex combination of "field", map, and literature-based work, and modeling. We take a virtual tour of an alluvial apron, collecting data on clast size and lithology. We then use a published algorithm to predict flood discharges of the mountain stream which formed the apron. The discharge and clast size data are used to constrain a digital model of an equilibrium transport-based longitudinal profile (Snow and Slingerland, 1987, Jour. Geol., 95, 15-33; Snow, 1991, Jour. Geol. Educ., 39, 227-229). Matching the modeled profile to the actual profile requires juggling of load caliber, erosion/deposition, and stream infiltration. Even working in teams of two or three, many students are unable to intuitively discern the steps required to "tame" the profile. Those who do, however, learn more about streams than would otherwise be possible in a junior-level, largely non-majors, class! The model itself is quite complex, involving conditional expressions.
The fourth (and frequently, final) spreadsheet lab is one in reconstructing past glaciation. The model (after Schilling and Hollin, 1981, in The Last Great Ice Sheets, Denton and Hughes (eds.), Wiley, New York, 207-220) is relatively simple. The application, however, is complex, involving the reconstruction of former glaciers generally poorly known in published work (see links above). The students each chose valleys or flowlines, and must determine the ice extent (from moraines) and ice divides (from the reconstructions). The accumulation of class data in a region (see the areas linked above) enables the students to conceptualize, and in some cases complete, a research project.
I have constructed an additional model on beach evolution, and have conceptualized models on mass wasting and eolian activity (as in cinder cone construction or loess deposition). The problem comes in trading off lab time for field trips and discussion against lab time for computer modeling. I have found the optimum mix at about 8 field trips to 4 models (in SW Montana in the fall) - others might find a different optimal mix depending on weather and field opportunities. Indeed - an entire course could be based on the principle!
For further information, including versions of the models discussed above, please contact me at the address below.