  Ensemble smoother (ES) has been widely used in inverse modeling of hydrologic
systems. However, for problems where the distribution of model parameters is
multimodal, using ES directly would be problematic. One popular solution is to
use a clustering algorithm to identify each mode and update the clusters with
ES separately. However, this strategy may not be very efficient when the
dimension of parameter space is high or the number of modes is large.
Alternatively, we propose in this paper a very simple and efficient algorithm,
i.e., the iterative local updating ensemble smoother (ILUES), to explore
multimodal distributions of model parameters in nonlinear hydrologic systems.
The ILUES algorithm works by updating local ensembles of each sample with ES to
explore possible multimodal distributions. To achieve satisfactory data matches
in nonlinear problems, we adopt an iterative form of ES to assimilate the
measurements multiple times. Numerical cases involving nonlinearity and
multimodality are tested to illustrate the performance of the proposed method.
It is shown that overall the ILUES algorithm can well quantify the parametric
uncertainties of complex hydrologic models, no matter whether the multimodal
distribution exists.
