Sampling error distribution for the ensemble Kalman filter update step

In recent years, data assimilation techniques have been applied to an increasingly wider specter of problems. Monte Carlo variants of the Kalman filter, in particular, the ensemble Kalman filter (EnKF), have gained significant popularity. EnKF is used for a wide variety of applications, among them for updating reservoir simulation models. EnKF is a Monte Carlo method, and its reliability depends on the actual size of the sample. In applications, a moderately sized sample (40–100 members) is used for computational convenience. Problems due to the resulting Monte Carlo effects require a more thorough analysis of the EnKF. Earlier we presented a method for the assessment of the error emerging at the EnKF update step (Kovalenko et al., SIAM J Matrix Anal Appl, in press). A particular energy norm of the EnKF error after a single update step was studied. The energy norm used to assess the error is hard to interpret. In this paper, we derive the distribution of the Euclidean norm of the sampling error under the same assumptions as before, namely normality of the forecast distribution and negligibility of the observation error. The distribution depends on the ensemble size, the number and spatial arrangement of the observations, and the prior covariance. The distribution is used to study the error propagation in a single update step on several synthetic examples. The examples illustrate the changes in reliability of the EnKF, when the parameters governing the error distribution vary.     

Coal’s medium-run future under atmospheric greenhouse gas stabilization

We assess the future of coal under alternative climate stabilization regimes, investigating how the quantity and location of future coal production, trade and use depends upon five factors: the supply-side constraint of resource depletion, diversification and deepening of international trade, economic growth, trends in energy intensity, and the availability of coal-fired carbon-free electric generation technology (IGCC-CCS). Using the Phoenix computable general equilibrium model of the world economy, we find that coal is sensitive to demand-side assumptions about economic growth and energy-saving structural or technological change. In a 550 ppm stabilization emission tax scenario, the gobal coal industry initially declines sharply and then rebounds, in 2050 reaching roughly the same size as it is today—but only if IGCC-CCS is available by 2020. Under alternative stabilization regimes, IGCC-CCS penetration is a key influence on production and imports in major coal regions, where it interacts with extraction costs driven by the rate of depletion relative to trade partners.