Generalization of differential ray tracing by automatic differentiation of computational graphs.

Optical design relies on ray tracing to evaluate and optimize the performance of optical systems. Differential ray tracing, in which the ray properties are calculated together with their derivatives, has been shown to be of interest to improve the accuracy and speed of common optical design tasks. We present in this paper an algorithm capable of performing differential ray tracing in the general case. This algorithm is not constrained by a specific optical system geometry such as rotational symmetry or restricted to a set of surface definitions (e.g., conics, polynomial aspheres).

The importance of age-related decline in forest NPP for modeling regional carbon balances.

We show the implications of the commonly observed age-related decline in aboveground productivity of forests, and hence forest age structure, on the carbon dynamics of European forests in response to historical changes in environmental conditions. Size-dependent carbon allocation in trees to counteract increasing hydraulic resistance with tree height has been hypothesized to be responsible for this decline. Incorporated into a global terrestrial biosphere model (the Lund-Potsdam-Jena model, LPJ), this hypothesis improves the simulated increase in biomass with stand age. Application of the advanced model, including a generic representation of forest management in even-aged stands, for 77 European provinces shows that model-based estimates of biomass development with age compare favorably with inventory-based estimates for different tree species. Model estimates of biomass densities on province and country levels, and trends in growth increment along an annual mean temperature gradient are in broad agreement with inventory data. However, the level of agreement between modeled and inventory-based estimates varies markedly between countries and provinces. The model is able to reproduce the present-day age structure of forests and the ratio of biomass removals to increment on a European scale based on observed changes in climate, atmospheric CO2 concentration, forest area, and wood demand between 1948 and 2000. Vegetation in European forests is modeled to sequester carbon at a rate of 100 Tg C/yr, which corresponds well to forest inventory-based estimates.

Ecosystem service supply and vulnerability to global change in Europe.

Global change will alter the supply of ecosystem services that are vital for human well-being. To investigate ecosystem service supply during the 21st century, we used a range of ecosystem models and scenarios of climate and land-use change to conduct a Europe-wide assessment. Large changes in climate and land use typically resulted in large changes in ecosystem service supply. Some of these trends may be positive (for example, increases in forest area and productivity) or offer opportunities (for example, "surplus land" for agricultural extensification and bioenergy production). However, many changes increase vulnerability as a result of a decreasing supply of ecosystem services (for example, declining soil fertility, declining water availability, increasing risk of forest fires), especially in the Mediterranean and mountain regions.