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This article shows that increasing the observation variance at small scalescan reduce the ensemble size required to avoid collapse in particle filteringof spatially-extended dynamics and improve the resulting uncertaintyquantification at large scales. Particle filter weights depend on how wellensemble members agree with observations, and collapse occurs when a fewensemble members receive most of the weight. Collapse causes catastrophicvariance underestimation. Increasing small-scale variance in the observationerror model reduces the incidence of collapse by de-emphasizing small-scaledifferences between the ensemble members and the observations. Doing so smoothsthe posterior mean, though it does not smooth the individual ensemble members.Two options for implementing the proposed observation error model aredescribed. Taking discretized elliptic differential operators as an observationerror covariance matrix provides the desired property of a spectrum that growsin the approach to small scales. This choice also introduces structureexploitable by scalable computation techniques, including multigrid solvers andmultiresolution approximations to the corresponding integral operator.Alternatively the observations can be smoothed and then assimilated under theassumption of independent errors, which is equivalent to assuming large errorsat small scales. The method is demonstrated on a linear stochastic partialdifferential equation, where it significantly reduces the occurrence ofparticle filter collapse while maintaining accuracy. It also improvescontinuous ranked probability scores by as much as 25%, indicating that theweighted ensemble more accurately represents the true distribution. The methodis compatible with other techniques for improving the performance of particlefilters.

Improving particle filter performance by smoothing observations