Models Mean Different Things to Different People

Scientific Modeling 101

What are models?

The latest in a line of cars? Tiny trains steaming through miniature landscapes? Long mathematical equations full of unpronounceable symbols? Colorful boxes of different shapes and sizes connected by lots of arrows?

Models are all these things, and more: Fundamentally, they are what we think the world around us - from cars and trains to water supply and ecosystems - looks like, or what we think it should look like. All of us are modelers: we construct our own mental models of the world around us, what it looks like, and how it works. We also share our mental models with others in conversation and writing, through drawings or sculptures, and sometimes with mathematics. Each of us constructs and shares our models with a unique set of mental and communication tools provided to us by our upbringing, education, and surroundings. And each of us uses our own mental models to make decisions about how to act in the world, from which car or clothes to buy to how we manage water supplies and ecosystems.

Few of us, however, realize that while “all decisions are based on models . . . all models are wrong,” as pointed out by the systems modeler John Sterman (2002). This is because all models are abstract simplifications of the real world. This means that all models have limitations; none of us ever sees or understands the world in its entirety, as it really is. As simplifications, models are necessarily incomplete, incorrect, or simply wrong. On the other hand, George Box, a pioneering statistician, said that while “all models are wrong, some are useful,” (1979).


“Models are useful if we ask the right questions.”

--Chris Enright, Delta Science Program


“Models are useful if we are clear about their limitations and remain open to alternative models that might be just as good or better,” says Anke Mueller-Solger, Interagency Ecological Program Lead Scientist with the Delta Stewardship Council. “Models are useful if we ask the right questions,” adds Chris Enright, Senior Water Resources Engineer with the Delta Science Program. “The questions we ask must match model capability. Where models and their supporting data match the spatial and temporal scale of the process we want to know about, models can be very useful.”

In the Delta Plan, models are considered useful tools that help “formalize and apply current scientific understanding, develop expectations, assess the likelihood of success, and identify tradeoffs associated with different management actions.” The Delta Plan also mentions different types of models - “conceptual, statistical, physical, decision support, or simulation” and how they might be used to achieve the Plan’s goals and objectives: “Models link the objectives to the proposed actions and clarify why an intended action is expected to result in meeting its objectives. Models provide a road map for testing hypotheses through statements that describe the expected outcome of an action.”

All types of models mentioned in the Delta Plan have a long tradition in the Delta.

Most familiar - and often not even recognized as “real” models - are conceptual models. They are narrative or graphical descriptions of what we know about how a system, such as the Delta, looks and works. They also show gaps in our knowledge and help articulate hypotheses that can be tested scientifically.

Recent conceptual models developed specifically for the Delta include a comprehensive suite of models developed as part of the Delta Regional Ecosystem Restoration Implementation Plan (DRERIP). The DRERIP models were designed to aid in the identification and evaluation of ecosystem restoration actions in the Delta, and include both ecosystem models (process, habitat, and stressor), and species life history models. Another set of conceptual models was developed to plan the IEP’s Pelagic Organism Decline (POD) investigations and to synthesize the POD results into “stories” about what may have happened.

The Delta also has a rich history of various types of quantitative models. Quantitative models tell stories with numbers (quantities) instead of words or graphics, although results can be graphically displayed and talked about. All quantitative models use mathematical equations. Two common types of quantitative models are:

  • Statistical Models - These models use statistical techniques to explore, characterize, and explain observed quantitative data patterns and relationships among different kinds of data. For example, they are used to estimate statistics such as averages. They can also be used to estimate probable future observations from relationships based on past observations and the uncertainty associated with model estimates. Statistical models are commonly used to analyze long-term monitoring data. For instance, a group of scientists working at the National Center for Ecological Analysis and Synthesis in Santa Barbara, California, used a variety of classical and modern statistical modeling tools to explore long-term monitoring data in search for the reasons for the POD.

  • Numerical Simulation Models - These models are used to explore and simulate how variables change over time either individually or in response to changes in other variables. The stories told by these types of models are more about dynamic processes than about long-term trends. Meteorologists use complex simulation models of atmospheric conditions for weather projections. Those tools allow them to predict rain, wind and temperature days in advance, or even the paths of hurricanes. In the Bay-Delta, simulation models can be used to predict water motion and “transport” of materials such as salt, contaminants and larval fish. Simulating water motion amounts to solving equations on the computer that assure that both the amount and momentum of water are “conserved.” That is, no water is lost or found and if it’s in motion, it stays in motion until stopped by gravity or friction. Using a computer, the equations are solved at pre-defined locations on a grid that approximates the three-dimensional shape of the estuary. The better the approximation (by the fineness of the grid) the more refined or complex the question addressed by the model can be, although highly complex models can take many hours to run even on a powerful and fast computer.

Today’s sophisticated simulation models would not be possible without modern computers. But the need for good simulations of water movements through the estuary preceded computers. This is why, in 1957, the U.S. Army Corps of Engineers constructed the 1.5 acre “San Francisco Bay Model” (Bay Model) in Sausalito. Reminiscent of a model train track, this three-dimensional working hydraulic model complete with water is a miniature version of the entire estuary. It was used from 1958-2000 to simulate and study water flows and tides through the estuary. Today, the Bay Model is no longer used for scientific purposes. It continues, however, to be a very useful model - it now teaches school children and the public about what the estuary looks like and how water moves through it. It’s an educational and fun model - more educational, and perhaps, even more fun than a model train track.

As discussed above, models are abstract simplifications of the real world-what we think the world around us looks like, or should look like. Models take many forms including conceptual, statistical, physical, decision support, or simulation and are useful tools that provide a road map for testing hypotheses.