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:
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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).
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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
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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.