Monotone conservative strategies in data assimilation

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This work describes the implementation of strong stability preserving time integration techniques in the stochastic context, where a particle filter (with jittering, tempering, conditional systematic resampling) is employed on non monotonic data for the nonlinear stochastic compressible advection equation. In the presence non positive data, it was possible to produce a positive ensemble naturally from the forward model, this was found to improve forecasting skill scores.