Modeling Geochemical Cycles Nelson Eby Department of Environmental, Earth & Atmospheric Sciences University of Massachusetts Lowell, MA

Introduction The use of box models to describe the cycling of various elements and chemical species through the lithosphere - hydrosphere - atmosphere - biosphere was pioneered by Garrels, McKenzie, and Hunt (1975). Over the past 30 years a variety of models have been developed to characterize these cycles. Such models are useful in assessing the impact of changes in the release or uptake of various species on the concentrations of these elements and species in various reservoirs. 1

A simple box model for the hydrologic cycle 2

The basic assumption in using box models is that the system is in a steady state, that is the rates of addition and removal (flux) of substances from the various reservoirs are in equilibrium - the concentration of the substance in the various reservoirs remains constant. Given a steady state one can calculate the residence time for a particular substance in a particular reservoir. Residence time is defined as the average length of time a particular substance will reside in a reservoir. 3

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6 Pre-human cycle for mercury. Reservoir masses in 10 8 g. Fluxes in 10 8 g y -1. From Garrels et al. (1975)

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Exponential approach of mercury concentration in the atmospheric reservoir to a new equilibrium value calculated from a first-order kinetics model. 8

9 In a sense the traditional steady-state box models are static, that is they do not show the various cause-and- effect feedbacks that can occur between the different reservoirs. Berner (1999) proposed a different approach using an interactive model that shows the various cause-and-effect feedbacks.

10 Traditional box model for the long-term carbon cycle. From Berner (1999)

11 Cause-and-effect feedback diagram for the long-term carbon cycle. Arrows originate at causes and end at effects. Arrows with the small concentric circles represent inverse responses. Arrows without concentric circles represent direct responses. From Berner (1999)

12 We can look at subcycles in the diagram to see if they have positive or negative feedbacks. If the subcycle contains an even number of concentric circles the the feedback is positive. If the subcycle contains an odd number of concentric circles the feedback is negative. Positive feedbacks lead to an amplification of an initial increase or decrease, and negative feedbacks lead to a dampening of the initial increase or decrease.

13 For example, consider the subcycle B-L-G which has an odd number of concentric circles. In this cycle, increasing CO 2 leads to a warmer and wetter climate with a concomitant increase in the weathering of Ca-Mg silicates. This increase in weathering leads to an increase in the uptake of CO 2, a negative feedback. Hence, this cycle tends to dampen increases in CO 2.

14 Using the cause-and-effect feedback diagram for carbon, for each of the following determine if they are positive or negative feedback cycles. 1. N-S-G 2. A-H-Q-C 3. D-E-C 4. D-F-P-Q-C 5. D-F-M 6. B-J-P-Q-R

15 References Berner, R. A., A new look at the long-term carbon cycle. GSA Today 9, 11, 1-6. Eby, G. N., Principles of Environmental Geochemistry. Pacific Grove, CA: Brooks/Cole, 510 pp. Garrels, R. M., Mackenzie, F. T., and Hunt, C., Chemical Cycles and the Global Environment: Assessing Human Influences. Los Altos, CA: William Kaufmann, Inc., 206 pp.