State updating in a distributed hydrological model by ensemble Kalman filtering with error estimation

For flood simulation in small- and medium-sized catchments, discharge observations may be used to update model states of a distributed hydrological model to improve performance. The ensemble Kalman filter (EnKF) has been widely used for hydrological assimilation due to its relative simplicity and robustness. An advantage of the EnKF is that it is easy to include different sources of uncertainty, therefore the choice of error model is crucial for the application of the EnKF assimilation. This paper describes an EnKF assimilation scheme for estimating error models using the maximum a posteriori estimation method (MAP). We test this scheme in two small and medium-sized catchments in China with different characteristics, and in addition compared the performance differences under two kinds of rainfall forcing. We show that MAP is beneficial in specifying error models and providing reliable ensemble spread. The assimilation scheme can effectively ameliorate the degradation of distributed hydrological model performance due to uncalibrated model parameters and/or poor quality of input data

Dendrite initiation and propagation in lithium metal solid-state batteries

All-solid-state batteries with a Li anode and ceramic electrolyte have the potential to deliver a step change in performance compared with today’s Li-ion batteries. However, Li dendrites (filaments) form on charging at practical rates and penetrate the ceramic electrolyte, leading to short circuit and cell failure. Previous models of dendrite penetration have generally focused on a single process for dendrite initiation and propagation, with Li driving the crack at its tip. Here we show that initiation and propagation are separate processes. Initiation arises from Li deposition into subsurface pores, by means of microcracks that connect the pores to the surface. Once filled, further charging builds pressure in the pores owing to the slow extrusion of Li (viscoplastic flow) back to the surface, leading to cracking. By contrast, dendrite propagation occurs by wedge opening, with Li driving the dry crack from the rear, not the tip. Whereas initiation is determined by the local (microscopic) fracture strength at the grain boundaries, the pore size, pore population density and current density, propagation depends on the (macroscopic) fracture toughness of the ceramic, the length of the Li dendrite (filament) that partially occupies the dry crack, current density, stack pressure and the charge capacity accessed during each cycle. Lower stack pressures suppress propagation, markedly extending the number of cycles before short circuit in cells in which dendrites have initiated