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