Primitive Equation Modelling ofPlankton Ecosystems
379
18.2 Primitive equation modelling
The concept of primitive equations originated with Galileo (1638), who showed
how the basic Laws of Nature could be established by reproducible laboratory
experiments. This new approach to science swept away the intuitive, but false, laws
propagated by Aristotle. It provided a sound scientific basis for modem physics.
Applications of primitive equations for simulating natural phenomena began with
Newton's study of gravity. In the last century they were used to simulate increasingly complex systems in nature and engineering. The primitive equations of real
systems are often non-linear, which prevents analytical solutions. Richardson
(1910) showed how to integrate non-linear equations numerically, and he went on
to publish a scheme for numerical weather forecasting, which is now in operational
use. Richardson's (1922) method of modelling complex physical systems by integrating a primitive equation model has become standard practice in physics and
engineering. It is the method used to simulate ocean circulation, and it has an
important role to play in biological oceanography.
18.2.1 Credibility and Verification
Primitive equation (PE) models have scientific credibility because they are based
on reproducible laboratory experiments. Whenever possible, credibility is bolstered
by verification. This is done by the Ecological Turing Test (see 18.17), which compares features of the ecosystem, as they are described by two data sets generated
respectively by mathematical simulation and observation. In practice this kind of
formal verification is very difficult. It sets high standards for both simulation and
the observations. In biologic al oceanography it is rare to obtain adequate observations for proper verification of models.
Until recently, models have not been sufficiently comprehensive to create simulations suitable for true verification. Consider, for example, Sverdrup's (1953)
model oflight-limited growth during the spring bIoom, which has had an enormous
impact on biologic al oceanographers (Platt et al 1994). Although we believe the
scientific idea behind Sverdrup's model, it cannot be verified because its equations
describe the seasonal variation of only two processes, light and turbulence: it omits
other processes which influence the increase of phytoplankton biomass during the
spring bloom: nutrient limitation, grazing and diumal variation. Verification
demands comprehensive simulation of the ecosystem in winter (Woods & Barkmann 1994).
It is not enough to claim credibility by noting similarities between a pair of time
series from observation and simulation: verification is about differences, not similarities. And no comparison is valid without explicit treatment of the uncertainties
in each description of the chosen feature of the ecosystem (18.17 & 18.18). The
near impossibility of formally verifying plankton ecology models puts the onus for
credibility on model design. Confidence acquired by using primitive equations is
particularly important.
379
18.2 Primitive equation modelling
The concept of primitive equations originated with Galileo (1638), who showed
how the basic Laws of Nature could be established by reproducible laboratory
experiments. This new approach to science swept away the intuitive, but false, laws
propagated by Aristotle. It provided a sound scientific basis for modem physics.
Applications of primitive equations for simulating natural phenomena began with
Newton's study of gravity. In the last century they were used to simulate increasingly complex systems in nature and engineering. The primitive equations of real
systems are often non-linear, which prevents analytical solutions. Richardson
(1910) showed how to integrate non-linear equations numerically, and he went on
to publish a scheme for numerical weather forecasting, which is now in operational
use. Richardson's (1922) method of modelling complex physical systems by integrating a primitive equation model has become standard practice in physics and
engineering. It is the method used to simulate ocean circulation, and it has an
important role to play in biological oceanography.
18.2.1 Credibility and Verification
Primitive equation (PE) models have scientific credibility because they are based
on reproducible laboratory experiments. Whenever possible, credibility is bolstered
by verification. This is done by the Ecological Turing Test (see 18.17), which compares features of the ecosystem, as they are described by two data sets generated
respectively by mathematical simulation and observation. In practice this kind of
formal verification is very difficult. It sets high standards for both simulation and
the observations. In biologic al oceanography it is rare to obtain adequate observations for proper verification of models.
Until recently, models have not been sufficiently comprehensive to create simulations suitable for true verification. Consider, for example, Sverdrup's (1953)
model oflight-limited growth during the spring bIoom, which has had an enormous
impact on biologic al oceanographers (Platt et al 1994). Although we believe the
scientific idea behind Sverdrup's model, it cannot be verified because its equations
describe the seasonal variation of only two processes, light and turbulence: it omits
other processes which influence the increase of phytoplankton biomass during the
spring bloom: nutrient limitation, grazing and diumal variation. Verification
demands comprehensive simulation of the ecosystem in winter (Woods & Barkmann 1994).
It is not enough to claim credibility by noting similarities between a pair of time
series from observation and simulation: verification is about differences, not similarities. And no comparison is valid without explicit treatment of the uncertainties
in each description of the chosen feature of the ecosystem (18.17 & 18.18). The
near impossibility of formally verifying plankton ecology models puts the onus for
credibility on model design. Confidence acquired by using primitive equations is
particularly important.