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:
 start with system components
 identify and write equations for state variables
 superimpose equations
 change forcing function inputs to look at system response
 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
Recall that modeling is one of the steps in the
methodology of systems analysis
and begins once the project (systems analysis) objectives
have been defined.
The model steps are similar to the steps followed
in the methodology of systems analysis but include
more detail.
The following steps are usually followed in model development:
 Identify and quantify objectives
 Draw diagrams for a conceptual model
 Formulate conceptual model
 Write and debug computer code
 Verify computer code
 Validate concepts in model
 Perform preliminary sensitivity analysis
 Collect data to validate model
 Complete sensitivity analysis
 Publish model
 Use model
Note the above process is iterative!
Model Development Steps
 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

Draw diagrams for a conceptual model
 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.
 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
 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
 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
 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
 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.
 Complete sensitivity analysis
 Show what the model will do.
 Publish model
 Document code
 Document conceptual model
 Document sensitivity analysis
 Use model
An example application of the above steps can be examined
by selecting this link.