Kathryn E. Lenz

Simulating the growth response of aspen to elevated ozone: a mechanistic approach to scaling a leaf-level model of ozone effects on photosynthesis to a complex canopy architecture

Predicting ozone-induced reduction of carbon sequestration of forests under elevated tropospheric ozone concentrations requires robust mechanistic leaf-level models, scaled up to whole tree and stand level. As ozone effects depend on genotype, the ability to predict these effects on forest carbon cycling via competitive response between genotypes will also be required. This study tests a process-based model that predicts the relative effects of ozone on the photosynthetic rate and growth of an ozone-sensitive aspen clone, as a first step in simulating the competitive response of genotypes to atmospheric and climate change. The resulting composite model simulated the relative above ground growth response of ozone-sensitive aspen clone 259 exposed to square wave variation in ozone concentration. This included a greater effect on stem diameter than on stem height, earlier leaf abscission, and reduced stem and leaf dry matter production at the end of the growing season. Further development of the model to reduce predictive uncertainty is discussed.

When is a controllerH∞-optimal?

This paper examines conditions under which a given single input, single output, linear time invariant control system isH∞-optimal with respect to weighted combinations of its sensitivity function and its complementary sensitivity function. The specific weighting functions considered are defined in terms of the given plant and nominal controller. This paper shows that a large class of practical controllers areH∞-optimal, including typical stable controllers.

Analysis of a Farquhar-von Caemmerer-Berry leaf-level photosynthetic rate model for Populus tremuloides in the context of modeling and measurement limitations

The balance of mechanistic detail with mathematical simplicity contributes to the broad use of the Farquhar, von Caemmerer and Berry (FvCB) photosynthetic rate model. Here the FvCB model was coupled with a stomatal conductance model to form an [A,g(s)] model, and parameterized for mature Populus tremuloides leaves under varying CO(2) and temperature levels. Data were selected to be within typical forest light, CO(2) and temperature ranges, reducing artifacts associated with data collected at extreme values. The error between model-predicted photosynthetic rate (A) and A data was measured in three ways and found to be up to three times greater for each of two independent data sets than for a base-line evaluation using parameterization data. The evaluation methods used here apply to comparisons of model validation results among data sets varying in number and distribution of data, as well as to performance comparisons of [A,g(s)] models differing in internal-process components.

Characterizing optimal solutions to weighted mixed sensitivity problems

Optimal weighted mixed sensitivity designs for single-input/single-output, linear, time-invariant systems are characterized by qualitative properties. Conditions for optimality based on flatness of the objective function and the relative numbers of closed right half-plane poles and zeros of the plant and optimal controller are examined.

Simulating the growth response of aspen to elevated ozone: A mechanistic approach from leaf-level photosynthesis to complex architecture

Abstract Predicting ozone-induced reduction of carbon sequestration of forests under elevated tropospheric ozone concentrations requires robust mechanistic leaf-level models, scaled up to whole tree and stand level. As ozone effects depend on genotype, the ability to predict these effects on forest carbon cycling via competitive response between genotypes will also be required. This study tests a process-based model that predicts the relative effects of ozone on the photosynthetic rate and growth of an ozone-sensitive aspen clone, as a first step in simulating the competitive response of genotypes to atmospheric and climate change. The resulting composite model simulated the relative above ground growth response of ozone-sensitive aspen clone 259 exposed to square wave variation in ozone concentration. This included a greater effect on stem diameter than on stem height, earlier leaf abscission, and reduced stem and leaf dry matter production at the end of the growing season. Further development of the model to reduce predictive uncertainty is discussed.

Weights determine stability of sensitivity-optimal controllers

Abstract It is shown that the weight determines the stability of the H ∞ -optimal controller for weighted sensitivity minimization problems for a large class of scalar plants and weights. Necessary and sufficient interpolation conditions on the weight are given in order for the optimal controller to be stable. An easily evaluated formula for the optimal controller is provided when the interpolation conditions are met. It is also shown that for many scalar plants it is possible to choose the weights for weighted mixed sensitivity minimization so that the optimal controller is stable and minimum-phase.