  We extended the multilevel Monte of Carlo (MLMC) approach to simulation of
groundwater flow in porous media by incorporating direct measurements of medium
properties. Numerical simulations of Waste Isolation Pilot Plant (WIPP)
repository in southeastern New Mexico are performed to test the performance of
the conditional MLMC technique. The log-transmissivity of WIPP site is modeled
as the conditional random fields which honor exact field values at a few
locations. The conditional random fields are generated through the modified
circulant embedding methods in (Dietrich and Newsam, 1996). We also study
effects of a combination of the conditional MLMC accompanied by antithetic
variates. The main quantity of interest is the time of radionuclides travelling
from the center of repository to the site boundary. Numerical examples are
presented to demonstrate the cost-effectiveness of the multilevel approach in
comparison to the standard Monte Carlo (MC) simulation.
