Abstract. Large environmental simulation models are usually overparameterized with respect to given sets of observations. This results in poorly identifiable or nonidentifiable model parameters. For small models, plots of sensitivity functions have proven to be useful for the analysis of parameter identifiability. For models with many parameters, however, near-linear dependence of sensitivity functions can no longer be assessed graphically. In this paper a systematic approach for tackling the parameter identifiability problem of large models based on local sensitivity analysis is presented. The calculation of two identifiability measures that are easy to handle and interpret is suggested. The first accounts for the sensitivity of model results to single parameters, and the second accounts for the degree of near-linear dependence of sensitivity functions of parameter subsets. It is shown how these measures provide identifiability diagnosis for parameter subsets, how they are able to guide the selection of identifiable parameter subsets for parameter estimation, and how they facilitate the interpretation of the correlation matrix of the parameter estimate with respect to parameter identifiability. In addition, we show how potential bias of the parameter estimates, due to a priori fixing of some of the parameters, can be analyzed. Finally, two case studies are presented in order to illustrate the suggested approach.

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A survey over the capabilities of a new simulation and data analysis program for laboratory, technical and natural aquatic systems is given. In this program, the spatial configuration of a model system is represented by compartments, which are connected by links. The program allows the user to define an arbitrary number of substances to be modelled and it is extremely flexible in the formulation of transformation processes. It not only offers the possibility of performing simulations of the time evolution of the user-specified system, but it provides also methods for system identification (sensitivity analysis and automatic parameter estimation) and it allows us to estimate the uncertainty of calculated results. These features, together with the user-friendly interface, very much support scientist in analyzing their data. Three examples illustrate the capabilities of the program.

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The structure of human cortical bone evolves over multiple length scales from its basic constituents of collagen and hydroxyapatite at the nanoscale to osteonal structures at near-millimeter dimensions, which all provide the basis for its mechanical properties. To resist fracture, bone’s toughness is derived intrinsically through plasticity (e.g., fibrillar sliding) at structural scales typically below a micrometer and extrinsically (i.e., during crack growth) through mechanisms (e.g., crack deflection/bridging) generated at larger structural scales. Biological factors such as aging lead to a markedly increased fracture risk, which is often associated with an age-related loss in bone mass ( bone quantity ). However, we find that age-related structural changes can significantly degrade the fracture resistance ( bone quality ) over multiple length scales. Using in situ small-angle X-ray scattering and wide-angle X-ray diffraction to characterize submicrometer structural changes and synchrotron X-ray computed tomography and in situ fracture-toughness measurements in the scanning electron microscope to characterize effects at micrometer scales, we show how these age-related structural changes at differing size scales degrade both the intrinsic and extrinsic toughness of bone. Specifically, we attribute the loss in toughness to increased nonenzymatic collagen cross-linking, which suppresses plasticity at nanoscale dimensions, and to an increased osteonal density, which limits the potency of crack-bridging mechanisms at micrometer scales. The link between these processes is that the increased stiffness of the cross-linked collagen requires energy to be absorbed by “plastic” deformation at higher structural levels, which occurs by the process of microcracking.