Analysis of plant root systems is difficult under field conditions, especially root systems of adult trees, which are large and complex and include fine absorbing roots as well as conducting coarse roots. Although coarse roots can be visualized by several methods, there are technical difficulties with root quantification. The method presented here focuses on the quantification of absorbing root surfaces through an electrical (the modified earth impedance) method. It is based on the experimentally verified fact that an applied electric current flows from the roots to the soil (or vice versa) through the same interfacial areas and predominantly in the same way as water (water solution of minerals or nutrients) flows from the soil to the tree. Based on the different conductivities of tree tissues and soil, the interfacial area, which represents the absorbing root surfaces (or root absorption zones), can be calculated. Only the theoretical description of the method is presented in this paper: the experimental verification of the method under field conditions is presented in the accompanying paper.

We validated, by means of allometric relationships and root severing experiments, the modified earth impedance method developed for measuring absorbing root surfaces. For the allometric studies, a series of 350 small and large trees of six broadleaf and coniferous species in several experimental sites was examined. We found a good linear ln-ln fit between absorbing root surface area and basal area (or stem cross-sectional area at the root collar in seedlings) over a range of stem diameters from 0.5-55 cm. The absorbing root surface area also changed consistently with crown projected area and the root-accessed area (territory) of the tree. At the whole-tree level, absorbing root surface area reached about 70 times that of basal area and 40% of crown projected area, or roughly 1/3 of the root-accessed area in Norway spruce (in this species, the ratio was relatively larger in small trees and smaller in large trees). The absorbing root surfaces of mechanically severed parts of Norway spruce root systems changed in about the same proportions as the geometrically determined parts of the severed root systems. These results are promising and support field applications of the method in biological and ecological studies.

Till 2020 the predominant key success factors of battery development have been overwhelmingly energy density, power density, lifetime, safety, and costs per kWh. That is why there is a high expectation on energy storage systems such as lithium-air (Li-O2) and lithium-sulfur (Li-S) systems, especially for mobile applications. These systems have high theoretical specific energy densities compared to conventional Li-ion systems. If the challenges such as practical implementation, low energy efficiency, and cycle life are handled, these systems could provide an interesting energy source for EVs. However, various raw materials are increasingly under critical discussion. Though only 3 wt% of metallic lithium is present in a modern Li-ion cell, absolute high amounts of lithium demand will rise due to the fast-growing market for traction and stationary batteries. Moreover, many lithium sources are not available without compromising environmental aspects. Therefore, there is a growing focus on alternative technologies such as Na-ion and Zn-ion batteries. On a view of Na-ion batteries, especially the combination with carbons derived from food waste as negative electrodes may generate a promising overall cost structure, though energy densities are not as favorable as for Li-ion batteries. Within the scope of this work, the future potential of sodium-based batteries will be discussed in view of sustainability and abundance vs. maximization of electric performance. The major directions of cathode materials development are reviewed and the tendency towards designing high-performance systems is discussed. This paper provides an outlook on the potential of sodium-based batteries in the future battery market of mobile and stationary applications.

This paper examines the predictive power of five linear hedonic pricing models for the residential market with varying levels of complexity in their spatial and temporal structures. Unlike similar studies, we extend the out-of-sample forecast evaluation to one-day-ahead predictions with a rolling estimation window, which is a reasonable setting for many practical applications. We show that the in-sample fit and cross-validation prediction accuracy improve significantly when we account for spatial heterogeneity. In particular, for one-dayahead forecasts, the spatiotemporal autoregressive (STAR) model demonstrates its superiority over model specifications with alternating spatial and temporal heterogeneity and dependence structures. In addition, sub-market fixed effects, constructed on the basis of statistical TREE methods, improve the results of predefined local rental markets further.