What is a Model

A model is a simplified representation of the real world

There are two types of models

· Conceptual

· Mathematical

Conceptual Models

What are they?

· Qualitative, usually based on graphs

· Represent important system:

· components

· processes

· linkages

· Interactions

When should they be used?

· As an initial step –

· For hypothesis testing

· For mathematical model development

· As a framework –

· For future monitoring, research, and management actions at a site

· Design field sampling and monitoring programs

· Ensure that all important system attributes are measured

· Determine causes of environmental problems

· Identify system linkages and possible cause and effect relationships

· Identify potential conflicts among management objectives

· Anticipate the full range of possible system responses to management actions

· Including potential negative effects

Mathematical Models

What are they?

· Mathematical equations that translate a conceptual understanding of a system or process into quantitative terms (Reckhow and Chapra 1983)

How are they used?

· Diagnosis

· E.g., What is the cause of reduced water clarity in a lake?

· Prediction

· E.g., How long will it take for lake water quality to improve, once controls are in place?

Categories of Mathematical Models

Type
Empirical Based on data analysis	Mechanistic Mathematical descriptions based on theory
Time Factor
Static or steady-state Time-independent	Dynamic Describe or predict system behavior over time
Treatment of Data Uncertainty and Variability
Deterministic Do not address data variability	Stochastic Address variability/uncertainty

When should you not use a model?

· If you do not understand the problem or system well enough to express it in concise, quantitative terms

· If the model has not been tested and verified for situations and conditions similar to your resource

It is important to understand model:

· Structure

· Assumptions

· Limitations