Modeling in Environmental Science and Management: Understanding Different Types of Models, Study notes of Environmental Science

Download Modeling in Environmental Science and Management: Understanding Different Types of Models and more Study notes Environmental Science in PDF only on Docsity! ESM 232: Model Types January 8, 2004 NOTE: Read Chapters 1-2 in Modeling in Natural Resource Management. 1 Broad classes of models Broadly, models in environmental science and management can be: 1. Conceptual - a set of ideas 2. Verbal - translate into words, or 3. Mathematical - translate words into equations 1.1 Example Suppose you work for the California Department of Fish and Game and you are responsible for making a recommendation about the daily bag limit of mallard ducks harvested in Cal- ifornia next year. One relationship in which you might be interested is how this year’s pop- ulation and harvest will affect next year’s population. (1) Draw CONCEPTUAL MODEL. (2) VERBAL MODEL of this system might sound something like this, “The population of adult ducks is reduced on a one-to-one basis by the harvest of adult ducks. The larger is the resulting population, the larger will be the next year’s population (ceteris paribus), but there are likely diminishing returns in this growth process. And a MATHEMATICAL MODEL might look like the following: Y (t) = X(t)−H(t) (1) X(t + 1) = f(Y (t)) (2) where Y (t) is the breeding population of mallard ducks in year t, H(t) is the harvest of mallard ducks in year t, X(t) is the population of adult ducks prior to harvest in year t, and the function f(Y ) determines the “growth” of the population, where f ′(Y ) > 0 and f ′′(Y ) < 0. Equation 1 reflects the first part of the verbal statement. Equation 2 reflects the second part of the verbal statement. We can add complexity to each type of model (e.g. temperature affecting biological productivity). 2 What kind of models should we use? The type of model for a particular application should always be driven by the questions or hypotheses that will be analyzed using the model. Often times, developing a mathematical 1 model is unnecessary. Simply developing a clear conceptual model and a more refined verbal model is sufficient for determining the answer to a question. However, many complex environmental problems cannot be solved with conceptual models alone. The process of developing a mathematical model can be extremely helpful in clarifying the thought process. It forces the modeler (you) to think clearly about the important processes and relationship that govern important features of the problem. Our focus here will be on the sorts of environmental problems that require some type of mathematical model for their solution. And of course, different environmental problems require different kinds of mathematical models. In the next section we will consider a general classification of mathematical models. 3 A classification of mathematical models Successful model development always begins with a question or hypothesis, and the model complexity and scale should match those of the question. At that point, a number of decisions must be made about the type of mathematical model the researcher will develop. Below is a general classification of six such decisions that must be confronted in model design. Most models in environmental science and management will embody one branch of each dichotomy on the list below. For example, the duck harvest model above is a dynamic, deterministic, analytical, structural, predictive model. 1. Static vs. Dynamic: Does the action occur at one point in time or over time? (a) (Static) What is the globally averaged surface temperature of Earth? (b) (Dynamic) In 1991 19,000 gallons of the pesticide metam sodium spilled into the Upper Sacramento River. What will be the consequences of this spill for aquatic invertebrates over time? 2. Deterministic vs. Stochastic: Are the important processes random or can they be viewed as non-random? Note that it is usually a good idea to develop a deterministic model first and then to add randomness. (a) (Deterministic) How much carbon is released when one hectare of Amazon rain- forest is burned? (b) (Stochastic) What will be the high-water level on Mission Creek in February? 3. Empirical vs. Analytical: Is the model driven by data or are the results general to a class of problems? (a) (Empirical) Are bacteria counts higher near sewage outfalls, ceteris paribus? (b) (Analytical) If OPEC is dissolved, will carbon emissions decrease? 4. Structural vs. Reduced-Form (also called Mechanistic vs. Phenomenological): Are the underlying processes modeled explicitly or are we working with equations that con- dense them into a simple framework? (a) If we are interested in how much sediment is carried into Lake Powell, we could model the interrelationships between geomorphology, hydrology, and climate (Structural) or we could, for example simply model a relationship between annual precipitation and sediment load (reduced-form). 2