Class 2.1

Projects

Model Classifications

The purpose of classification is to put like with the like (Gerritsen, 2000).

There is a number of criteria to classify models. Among others we may consider the following ones:

1. Form: in which form the model is presented?
   • Conceptual (verbal, descriptive) - only verbal descriptions are made. Examples:
     • A description of directions to my home: Take Road 5 for 5 miles East, then take a left to Main Street and follow through 2 lights. Take a right to Cedar Lane. My house is 3333 on the left. - This is a spatial model of my house location relative to a certain starting point. I describe the mental model of the route to my house in verbal terms.
     • A verbal portrait of a person: He is tall with red hair and green eyes, his cheeks are pale and his nose is pimpled. His left ear is larger than the right one and one of his front teeth is missing. - A static verbal model of a person's face.
     • Verbal description of somebody's behavior: When she wakes up in the morning, she is slow and sleepy until she has her first cup of coffee. After that she starts to move somewhat faster and has her bowl of cereal with the second cup of cofee. Only that brings her back to her normal pace of life. - A dynamic conditional verbal model.
     • A verbal description of a rainfall event: Rainfall occurs every now and then. If temperature is below 0^o(C) (32 F) the rain is called snow and it is accumulated as Snow or Ice on the terrain. Otherwise it comes in liquid form and part of it infiltrates into the subsurface layer and adds to the unsaturated storage underground. The rest stays on the surface as Surface Water. Go here for more.
   • Conceptual (diagrammatic) - in some cases a good drawing may cost a thousand words. Examples:

     • A diagram may explain your model even better than words.

     • A drawing or an image is also a model. In some cases it can offer much more information than the verbal description and may be also easier to understand and communicate among people. Also note that in some cases a diagram can exclude some of the uncertainties that may come from the verbal description. For example, the verbal model mentioned the left ear but did not specify whether it is the person's left ear or the person's left ear as seen by the observer. This ambiguity disappears when the image is offered.

     • Dynamic features can be included in an animation or a cartoon.
     • A conceptual model of the hydrologic cycle.
       
   • Physical - a reconstruction of the real object at a smaller scale. Examples:
     • Matchbox toy cars
     • Remember those mannequins they put in cars to crash them against a brick wall and see what happens to the passengers. Well, those are models of humans. They probably are no good to study the human IQ, but they reproduce certain features of a human body that are important to design car safety devices.
     • An airplane model in a wind tunnel
     • A fairly large (about 50 m long) model was created in the 70s to analyze currents in Lake Balaton (Hungary). Large fans blew air over the model and currents were measured and documented.
   • Formal (mathematical) - that is when equations and formulas reproduce the behavior of physical objects. Examples:
     • Q = m C (t₁ - t₂) - a model of heat emitted by a body of mass m, when cooling from temperature t₁ to temperature t₂. C is the heat capacity parameter.
     • Y = Y_o* 2^t/d a model of an exponentially growing population. Y_o - initial population, d - doubling time.
2. Time: how time is treated in the model.
   • Dynamic vs. Static. A Static model gives a snapshot of the reality. In Dynamic models time changes and so do the variables in the model. Examples:
     • A map is a static model. So is a photo.
     • A cartoon is a dynamic model.
     • Differential or difference equations are dynamic models.
   • Continuous vs. Discrete. Is time incremented step-wise in a dynamic model or is it assumed to change constantly, in infinitsimally small increments. Examples:
     • You may watch a toy car roll down a wedge. It will be a physical model with continuous time.
     • Generally speaking systems of differential equations represent continuous time models.
     • A difference equation is a discrete model. Time can change, but it is incremented in steps (1 minute, 1 day, 1 year, etc.)
     • A movie is a discrete model. Motion is achieved by viewing separate images, taken at certain intervals.
   • Stochastic vs. Deterministic. In a deterministic model the state of the system at the next time step is entirely defined by the state of the system at the current time step and the transfer functions used. In a stochastic model there may be several future states corresponding to the same current state. Each of these future states may occur with a certain probability.
3. Space: how space is treated in the model.
   • Spatial vs. Point (Box-models). A point model assumes that everything is homogenous in space. Either it looks at a specific locality or it considers averages over a certain area. A spatial model looks at spatial variability and considers spatially heterogenous processes and variables. Examples:
     • A demographic model of population growth in a city. All the population may be considered as a point variable, the spatial distribution is not of interest, only the total population over the area of the city is modelled.
     • A box model of a small lake. The lake is considered as a well mixed container, where spatial gradients are ignored and only the average concentrations of nutrients and biota are considered.
     • A model of spatial hydrology. See here.
   • Continuous vs. Discrete. Like time, space may be represented either as continuos or as a mosaic of uniform objects. Examples:
     • A painting vs. a mosaic. Both represent a spatial picture and both look quite similar from a distance. However at close observation one may see that smooth lines and color changes in a painting are substituted by discrete uniform elements in the mosaic, that change there color and shape in a stepwise manner.
     • Differential equations in partial derivatives are used for continuos formalizations.
     • Finite elements or difference schemes are used to formalize discrete models.
4. Structure: how is the model structure defined.
   • Empirical (black-box) vs. Process-based (simulation) models. In empirical models the output is linked to the input by some sort of a mathematical formula or physical device. The structure of the model is not important as long as the input signals are translated into the output ones properly. That is, as they are observed. These models are also called black-box models, because they operate as some closed devices on the way of the information flows.
     In process based models individual processes are analyzed and reproduced in the model. In any case we cannot go into all the details and cannot describe all the processes in all their complexity (it would not be a model then). Therefore a process based model may be considered as built out of numerous black boxes. The individual processes are still presented as closed devices or empirical formulas, however their interplay and feedbacks between them are taken into acocunt and analyzed.
   • Simple vs. Complex. Though qualitatively clear this distinction might turn out to be somewhat hard to quantify. It is usually defined by the goals of the model. Simple models are built to understand the system in general over long time intervals and large areas. Complex models are created for detailed studies of particular system functions. The increased structural complexity usually has to be compensated by smaller temporal and spatial resolutions.
5. Method: how the model is formulated and studied.
   • Analytic vs. Computer models. Mathematical models easily become too complex to be studied analytically. See Table.
6. Field related classification, e.g. in Ecology:
   • Population models - these are built to study the dynamics and structure of populations. A population is easily characterized by its size. That is probably why population ecology is probably the best formalized branch of ecology.
   • Individual (or agent) based models. These are built representing individual organisms as separate entities that operate in time and space. Click here for an example. Click here for another example. Or go here for a formal definition of the agent based approach. More on the SWARM project can be found here .
   • Ecosystem models attempt to represent the whole ecosystem, not just some components of it. Click here for an example of a wetland ecosystem model.

Exercises