Analytical methods for parameter-space delimination and application to shallow-lake phytoplankton-dynamics modeling

The first step in parameter estimation is to reduce the dimensionality of the problem by deriving estimates from independent experimentation and from the literature. In addition, insensitive parameters are either removed or fixed. In the remaining lower-dimensional problem, parameter-space delimitation is possible by analytical means. Three conjunctive methods are derived: period-average analysis, extremum analysis, and quasisteady-state analysis. The basic idea is to find conditions for the parameters that must be fulfilled in order to comply with average and extreme values in the observations. The approach is applied to the modeling of the phytoplankton dynamics of Lake Balaton. The analytical techniques prove to supply valuable insight into parameter interrelationships and model adequacy, and can serve as satisfactory substitutes for formal parameter-estimation techniques in the early stages of model development

What can systems and control theory do for agricultural science?

Abstract: While many professionals with a background in agricultural and bio-resource sciences work with models, only few have been exposed to systems and control theory. The purpose of this paper is to elucidate a selection of methods from systems theory that can be beneficial to quantitative agricultural science. The state space representation of a dynamical system is the corner stone in the mainstream of systems theory. It is not well known in agro-modelling that linearization followed by evaluation of eigenvalues and eigenvectors of the system matrix is useful to obtain dominant time constants and dominant directions in state space, and offers opportunities for science-based model reduction. The continuous state space description is also useful in deriving truly equivalent discrete time models, and clearly shows that parameters obtained with discrete models must be interpreted with care when transferred to another model code environment. Sensitivity analysis of dynamic models reveals that sensitivity is time and input dependent. Identifiability and sensitivity are essential notions in the design of informative experiments, and the idea of persistent excitation, leading to dynamic experiments rather than the usual static experiments can be very beneficial. A special branch of systems theory is control theory. Obviously, control plays an important part in agricultural and bio-systems engineering, but it is argued that also agronomists can profit from notions from the world of control, even if practical control options are restricted to alleviating growth limiting conditions, rather than true crop control. The most important is the idea of reducing uncertainty via feed-back. On the other hand, the systems and control community is challenged to do more to address the problems of real life, such as spatial variability, measurement delays, lacking data, environmental stochasticity, parameter variability, unavoidable model uncertainty, discrete phenomena, variable system structures, the interaction of technical ad living systems, and, indeed, the study of the functioning of life itself

Estimation of algal growth parameters from vertical primary production profiles

Phytoplankton maximum growth rate and the saturation light intensity, Is, can be estimated from vertical profiles of primary production by non-linear least-squares estimation. Solution through the normal equations leads to formulae which are relatively simple and easy to implement. The computation of confidence contours is demonstrated, and the results are contrasted to the confidence limits on the parameters individually. These can be quite misleading due to model non-linearity and correlation between parameter estimation.\ud \ud The procedure has been applied to primary production data from Lake Balaton, a shallow lake in Hungary. The growth rate-temperature relation is analysed by separating the parameters into two groups characteristic for “warm” and “cold” water phytoplankton, respectively. A bell-shaped curve is found for “cold” water communities, with an optimum at about 7–9°C, whereas the “warm” water phytoplankton exhibits a strong exponential dependency in the temperature range of interest (up to 25°C). Is also appears to be related to temperature except for the “cold” water group, where Is is essentially constant. However, a roughly linear relation with considerably less scatter is obtained when Is is plotted directly versus day-averaged solar radiation. This apparent fast adaptation is attributed to the extremely short turnover time in Lake Balaton. Maximum growth rates of 10–20 d−1 have been found for temperatures between 20 and 25°C. These results and a critical appraisal of available literature suggest that the common notion of maximum growth rates being in the order of 1–3 d−1 needs revision, at least for lakes with relatively high summer temperatures