Causal inference methods (CIMs) aim at identifying causal links from temporal dependencies found in time-series data. Using both synthetic data and real-time series from a karst system, we study and discuss the potential of four CIMs to reveal hydrological connections between variables in hydrological systems. Despite the ever-present risk of spurious hydrological connections, our results highlight that the nonlinear and multivariate CIM has a substantially lower false-positive rate.

Particle filters are becoming popular for state and parameter estimations in hydrology. The renewal of the ensemble (resampling) is crucial in preventing filter degeneration. We introduce a resampling method that uses the weighted covariance of the ensemble, which contains information between observed and unobserved dimensions, to generate new ensemble members. This allows us to estimate the state and parameters for a rough initial guess in a synthetic hydrological case with just 100 particles.

In this study electromagnetic induction (EMI) measurements were used to estimate soil salinity in an agriculture field irrigated with a drip irrigation system. Electromagnetic model parameters and uncertainty were estimated using adaptive Bayesian Markov chain Monte Carlo (MCMC). Application of the MCMC-based inversion to the synthetic and field measurements demonstrates that the parameters of the model can be well estimated for the saline soil as compared to the non-saline soil.

Applications of data assimilation (DA) arise in many fields of geosciences, perhaps most importantly in weather forecasting and hydrology. We want to investigate the roles of data assimilation methods and land surface models (LSMs) in joint estimation of states and parameters in the assimilation experiments. We find that all DA methods can improve prediction of states, and that differences between DA methods were limited but that the differences between LSMs were much larger.

Soil moisture is a major variable that affects regional climate, weather and hydrologic processes on the Earth's surface. In this study, real-world data of a network of cosmic-ray sensors were assimilated into a regional land surface model to improve model states and soil hydraulic parameters. The results show the potential of these networks for improving model states and parameters. It is suggested to widen the number of observed variables and to increase the number of estimated parameters.