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