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    Global Heat Uptake by Inland Waters
    (Hoboken, NJ [u.a.] : Wiley, 2020) Vanderkelen, I.; van Lipzig, N.P.M.; Lawrence, D.M.; Droppers, B.; Golub, M.; Gosling, S.N.; Janssen, A.B.G.; Marcé, R.; Schmied, H.M.; Perroud, M.; Pierson, D.; Pokhrel, Y.; Satoh, Y.; Schewe, J.; Seneviratne, S.I.; Stepanenko, V.M.; Tan, Z.; Woolway, R.I.; Thiery, W.P
    Heat uptake is a key variable for understanding the Earth system response to greenhouse gas forcing. Despite the importance of this heat budget, heat uptake by inland waters has so far not been quantified. Here we use a unique combination of global-scale lake models, global hydrological models and Earth system models to quantify global heat uptake by natural lakes, reservoirs, and rivers. The total net heat uptake by inland waters amounts to 2.6 ± 3.2 ×1020 J over the period 1900–2020, corresponding to 3.6% of the energy stored on land. The overall uptake is dominated by natural lakes (111.7%), followed by reservoir warming (2.3%). Rivers contribute negatively (-14%) due to a decreasing water volume. The thermal energy of water stored in artificial reservoirs exceeds inland water heat uptake by a factor ∼10.4. This first quantification underlines that the heat uptake by inland waters is relatively small, but non-negligible. ©2020. The Authors.
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    Memory equations as reduced Markov processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Stephan, Artur; Stephan, Holger
    A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with such a memory equation, we give an explicit construction of the corresponding Markov process. From a physical point of view the Markov process can be understood as the change of the type of some quasiparticles along one-way loops. Typically, the arising Markov process does not have the detailed balance property. The method leads to a more realisitc modeling of memory equations. Moreover, it carries over the large number of investigation tools for Markov processes to memory equations, like the calculation of the equilibrium state, the asymptotic behavior and so on. The method can be used for an approximative solution of some degenerate memory equations like delay differential equations.