Assignment:

Read handout titled "Modeling Agricultural Systems."

Modeling

modeling - the writing of equations to describe and predict the performance of a system both as functions of changes in inputs and as functions of the changes in the systems

Modeling Physical Systems

System relationships for physical systems are usually well known and in many instances classical solutions have been developed.

Process for modeling physical systems:

1. start with system components
2. identify and write equations for state variables
3. superimpose equations
4. change forcing function inputs to look at system response
5. change system parameters if desired

Problems associated with modeling biological systems as physical systems:

• Equations usually contain constants in physical systems. However, similar equations for biological systems have "constants" that are not actually constants but are functions of time.
• Biological systems often have growth and decay (more complex than physical systems).
• In addition to "constants" being functions of time, they are often also functions of environmental conditions for biological systems.
• For biological systems, "constants" are often assumed to be constant over short time periods. Thus, k=f(t). Short time steps are used in an attempt to provide accurate solutions.

Modeling Process

Model Development Steps

1. Identify and quantify objectives
2. Draw diagrams for a conceptual model
3. Formulate conceptual model
4. Write and debug computer code
5. Verify computer code
6. Validate concepts in model
7. Perform preliminary sensitivity analysis
8. Collect data to validate model
9. Complete sensitivity analysis
10. Publish model
11. Use model

Note the above process is iterative!

Model Development Steps

1. Identify and quantify objectives for model
   • more specific than for systems analysis objectives
   • what questions must the model be able to answer?
   • quantify time and space scales
   • quantify accuracy, sensitivity, etc.
   • determine level of detail needed
   • identify users
   • identify what output should/will look like
2. Draw diagrams for a conceptual model
   • Various diagraming techniques might be used
   • Draw diagram using charting/systems diagraming techniques
   • Determine solution "style" - type of model
3. Formulate conceptual model
   • Write equations relating system response to inputs and values of system parameters
   • Use diagram from previous step to assist with identifying/writing equations
   • Identify assumptions and provide appropriate support for these assumptions.
4. Write and debug computer code
   • Depends on equations written
   • May need to use heuristic (expert system) approach if you don't have concrete equations
   • Computer code should match equations and/or pictorial model
   • Never assume code is correct
5. Verify computer code
   • The intent of verification is to insure that the computer code accurately represents the conceptual model.
   • Use case studies
   • Problems identified may be in computer code
   • Problems identified may be in assumptions
     • rewrite equations
     • redo process
   • Note the differences between verifcation and validation
6. Validate concepts in model
   • Compare model results to experimental evidence
   • Validation is the process of testing the accuracy of a model with respect to the system being modeled
7. Perform preliminary sensitivity analysis
   • Contributions of changes in inputs to output
   • Contributions of changes in system changes to output
   • Sensitivity to assumptions
   • May allow elimination of some variables
8. Collect data to validate model
   • Use sensitivity analysis results of above step to determine what data is required and level of detail in data required. Will know what is important to measure and how often it must be measured.
   • Usually hope to come within 95% confidence interval. However, this is often difficult to accomplish with biological systems.
   • Validity is never absolute. Should state cases for which the model is valid.
9. Complete sensitivity analysis
   • Show what the model will do.
10. Publish model
    • Document code
    • Document conceptual model
    • Document sensitivity analysis
11. Use model

An example application of the above steps can be examined by selecting this link.