  Parameter estimation has a high importance in the geosciences. The ensemble
Kalman filter (EnKF) allows parameter estimation for large, time-dependent
systems. For large systems, the EnKF is applied using small ensembles, which
may lead to spurious correlations and, ultimately, to filter divergence. We
present a thorough evaluation of the pilot point ensemble Kalman filter
(PP-EnKF), a variant of the ensemble Kalman filter for parameter estimation. In
this evaluation, we explicitly state the update equations of the PP-EnKF,
discuss the differences of this update equation compared to the update
equations of similar EnKF methods, and perform an extensive performance
comparison. The performance of the PP-EnKF is tested and compared to the
performance of seven other EnKF methods in two model setups, a tracer setup and
a well setup. In both setups, the PP-EnKF performs well, ranking better than
the classical EnKF. For the tracer setup, the PP-EnKF ranks third out of eight
methods. At the same time, the PP-EnKF yields estimates of the ensemble
variance that are close to EnKF results from a very large-ensemble reference,
suggesting that it is not affected by underestimation of the ensemble variance.
In a comparison of the ensemble variances, the PP-EnKF ranks first and third
out of eight methods. Additionally, for the well model and ensemble size 50,
the PP-EnKF yields correlation structures significantly closer to a reference
than the classical EnKF, an indication of the method's skill to suppress
spurious correlations for small ensemble sizes.
