conditions such as a different cultivar are facilitated by adjusting the relevant
parameters in the initialization (Haefner 2005).
2.2.4 Estimating Parameters
There are two acceptable general methods for parameter estimation:
1. Literature If the value of a parameter has been defined in research previously
published, then these data are a strong starting point. This source of parameters
is desirable because the research has been subjected to the rigors of peer review
and the results are available to everyone.
2. Measurement Experiments or observations need to be done by the person
constructing the model. Special research protocols need to be established and
executed to obtain information about the desired parameters. Careful statistical
analysis of the results is needed to obtain parameters. This method is timeconsuming, laborious, and expensive. Soltani et al. (2004, 2006) presented
examples of parameter estimation procedures related to different aspects of
crop growth and development.
Another method that is too frequently used for parameter estimation is ‘‘calibration’’ of parameters so that the final output of the overall models matches the
expected results. That is, the model is tested using different values for a specific
parameter, then values are chosen that provide the closest match to the observations of the major outputs. Adjustments in parameters to achieve closer matches
with observations by the complete model are difficult because it is not clear what
parameters need adjusting. A major problem is that parameter adjustments can
compensate each other and the parameters diverge from how the plant system
operates.
The major limitation of the ‘‘calibration’’ approach is that reduces the model to
an exercise in empirically fitting the model to the observations under a particular
set of circumstances. Parameters are adjusted to achieve end results rather than
relying on understanding about how the plants are performing and defining specific
functions for the individual processes.
Sometimes ‘‘calibration’’ is done be reserving a separate data set for the
calibration procedure. This approach does not overcome the basic empirical
problem in this approach. Success of ‘‘calibrated’’ parameters in matching a
second set of data only indicates success in splitting the two datasets, so that they
represent the same population of data. That is, success with a calibrated model
only assures that the calibration dataset were adequate to empirically math the
second set of data (Soltani and Sinclair 2012).
2 Mathematical Modeling of Biosystems
55
parameters in the initialization (Haefner 2005).
2.2.4 Estimating Parameters
There are two acceptable general methods for parameter estimation:
1. Literature If the value of a parameter has been defined in research previously
published, then these data are a strong starting point. This source of parameters
is desirable because the research has been subjected to the rigors of peer review
and the results are available to everyone.
2. Measurement Experiments or observations need to be done by the person
constructing the model. Special research protocols need to be established and
executed to obtain information about the desired parameters. Careful statistical
analysis of the results is needed to obtain parameters. This method is timeconsuming, laborious, and expensive. Soltani et al. (2004, 2006) presented
examples of parameter estimation procedures related to different aspects of
crop growth and development.
Another method that is too frequently used for parameter estimation is ‘‘calibration’’ of parameters so that the final output of the overall models matches the
expected results. That is, the model is tested using different values for a specific
parameter, then values are chosen that provide the closest match to the observations of the major outputs. Adjustments in parameters to achieve closer matches
with observations by the complete model are difficult because it is not clear what
parameters need adjusting. A major problem is that parameter adjustments can
compensate each other and the parameters diverge from how the plant system
operates.
The major limitation of the ‘‘calibration’’ approach is that reduces the model to
an exercise in empirically fitting the model to the observations under a particular
set of circumstances. Parameters are adjusted to achieve end results rather than
relying on understanding about how the plants are performing and defining specific
functions for the individual processes.
Sometimes ‘‘calibration’’ is done be reserving a separate data set for the
calibration procedure. This approach does not overcome the basic empirical
problem in this approach. Success of ‘‘calibrated’’ parameters in matching a
second set of data only indicates success in splitting the two datasets, so that they
represent the same population of data. That is, success with a calibrated model
only assures that the calibration dataset were adequate to empirically math the
second set of data (Soltani and Sinclair 2012).
2 Mathematical Modeling of Biosystems
55