Data assimilation in integrated hydrological modeling using ensemble Kalman filtering:evaluating the effect of ensemble size and localization on filter performance

Groundwater head and stream discharge is assimilated using the ensemble transform Kalman filter in an integrated hydrological model with the aim of studying the relationship between the filter performance and the ensemble size. In an attempt to reduce the required number of ensemble members, an adaptive localization method is used. The performance of the adaptive localization method is compared to the more common distance-based localization. The relationship between filter performance in terms of hydraulic head and discharge error and the number of ensemble members is investigated for varying numbers and spatial distributions of groundwater head observations and with or without discharge assimilation and parameter estimation. The study shows that (1) more ensemble members are needed when fewer groundwater head observations are assimilated, and (2) assimilating discharge observations and estimating parameters requires a much larger ensemble size than just assimilating groundwater head observations. However, the required ensemble size can be greatly reduced with the use of adaptive localization, which by far outperforms distance-based localization. The study is conducted using synthetic data only

Geostatistical inference using crosshole ground-penetrating radar

High-resolution tomographic images obtained from crosshole geophysical measurements have the potential to provide valuable information about the geostatistical properties of unsaturated-zone hydrologic-state va riables such as moisture content. Under drained or quasi-steady-state conditions, the moisture content will reflect the variation of the physical properties of the subsurface, which determine the flow patterns in the unsaturated zone. Deterministic least-squares inversion of crosshole groundpenetrating-radar GPR traveltimes result in smooth, minimumvariance estimates of the subsurface radar wave velocity structure, which may diminish the utility of these images for geostatistical inference. We have used a linearized stochastic inversion technique to infer the geostatistical properties of the subsurface radar wave velocity distribution using crosshole GPR traveltimes directly. Expanding on a previous study, we have determined that it is possible to obtain estimates of global variance and mean velocity values of the subsurface as well as the correlation lengths describing the subsurface velocity structures. Accurate estimation of the global variance is crucial if stochastic realizations of the subsurface are used to evaluate the uncertainty of the inversion estimate. We have explored the full potential of the geostatistical inference method using several synthetic models of varying correlation structures and have tested the influence of different assumptions concerning the choice of covariance function and data noise level. In addition, we have tested the methodology on traveltime data collected at a field site in Denmark. There, inferred correlation structures indicate that structural differences exist between two areas located approximately 10 m apart, an observation confirmed by a GPR reflection profile. Furthermore, the inferred values of the subsurface global variance and the mean velocity have been corroborated with moisturecontent measurements, obtained gravimetrically from samples collected at the field site

Coherent photon assisted cotunneling in a Coulomb blockade device

We study cotunneling in a double junction Coulomb blockade device under the influence of time dependent potentials. It is shown that the ac-bias leads to photon assisted cotunneling which in some cases may dominate the transport. We derive a general non-perturbative expression for the tunneling current in the presence of oscillating potentials and give a perturbative expression for the photon assisted cotunneling current.Comment: Replaced with a longer paper which includes a non-perturbative calculation. 13 pages with 1 figure. To be published in Physical Review