Environmental Process Analysis, 2: Dynamic Steady States

Journal of Geoscience Education, Sep 2004 by Torgersen, T, Branco, B, Bean, J

ABSTRACT

Environmental analysis requires an understanding of processes that contribute to a system and the concept of dynamic balances. The Conservation of Mass (Heat) equation for a system determines whether (e.g.) concentration (heat) in the system will increase, decrease or remain constant. The rate at which change occurs in a system and the magnitude of that change are functions of the dynamic balance and the rate constants (residence times^sup -1^) for individual processes. We express this mass (heat) balance concept as a simplified algebraic expression ("IPOLA") and use it to evaluate the dynamics of systems. We present a classroom activity that can be accomplished in a short time with minimal cost to demonstrate these principles. Our experience suggests that this activity and the "IPOLA" equation build knowledge by developing a conceptual understanding of systems and their component processes.

INTRODUCTION

Many people perceive that net change in the environment around them is small over a lifetime (e.g., net climate change from increased CO2). This perception may lead to the erroneous conclusion that "nothing is changing" and the environment has an inherent resiliency that resists large change. However, environmental systems are governed by multiple individual processes that interact to produce a dynamic system. It is the balance or imbalance of inputs and production vs. outputs and losses that determine whether change will occur, in what direction and magnitude, and "how fast". These concepts are embodied in the equations for (1) Conservation of Mass, (2) Conservation of Energy and (3) Conservation of Momentum (e.g., Bird et al., 1960) that are the basis for most engineering and scientific analysis.

We describe here a classroom activity to learn the fundamentals of (environmental) process analysis, response times and dynamic steady states. The activity is designed to provide a progression of learning from the concrete to the abstract that is consistent with scientific inquiry (AAAS, 1990). The response time of the system under investigation (How long will it take to...? How fast will...?) is determined from direct observations of change, and is also calculated from measurements of the component processes contributing to the change. We apply equation (1) and have found that the acronym IPOLA can become a valuable mnemonic for students that prompts a methodological approach to complex problems. In its present configuration, the activity has been used primarily for second year university students although significant portions can be translated directly to the high school classroom. Our experience over the last decade with this activity shows that the analysis of real data generates a greater facility with the concepts of dynamic environmental systems than "plug-and-chug" problems from the textbook and imparts the physical meaning to numbers. The activity thus offers students an opportunity "to do and to talk science" (Abrams, 1998) and to engage in scientific inquiry that supports carry-over of principles to the real world.

BACKGROUND

For students with limited calculus, the concept of Conservation of Mass (Heat) balance is presented algebraically (equation 1) and students are familiarized with the concepts of residence times and reaction times (Torgersen et al., 2004). This laboratory activity is then conducted to investigate the individual components of a dynamic steady state (each term in IPOLA) and the time scale upon which a new dynamic steady state can be achieved given a change in the governing conditions. The questions to be addressed are:

1. What is a dynamic steady state?

2. How is a dynamic steady state maintained?

3. What parameters affect the dynamic steady state?

4. How is the rate of change from one dynamic steady state to another quantified in terms of the processes that contribute to the system?

5. How does one measure the components of a dynamic system and quantify their relative importance?

THE EXPERIMENT

Students construct an analog to a well mixed environmental system using a side-arm flask and a magnetically stirred hot plate (see Table 1, Figure 1 and www.mypond.uconn.edu for a complete experimental description; note especially cautions with regard to good experimental design and safety. We also suggest that the instructor conduct the experiment himself before conducting it with students.) The goals of this 1.5hr activity are to make measurements over time within the system in order to quantify the rate of change for the system and to explore the processes that control change. The experimental design is such that (1) contributions from each component part of the system heat balance can be investigated, (2) the response time of the system can be observed, and (3) the response time of the system can be evaluated from knowledge of the components. The principles for the quantification of the rate constant (λ) for change or the response time (τ =λ^sup -1^) for change generate knowledge that may then be applied to systems that cannot be explicitly observed (e.g., in naturally occurring environmental systems with large time and space scales). Questions that help students prepare for the activity include: