@article{AcevedoDeWiljesReich2017,
  author    = {Acevedo, Walter and De Wiljes, Jana and Reich, Sebastian},
  title     = {Second-order accurate ensemble transform particle filters},
  series = {SIAM journal on scientific computing},
  volume    = {39},
  journal   = {SIAM journal on scientific computing},
  number    = {5},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  issn      = {1064-8275},
  doi       = {10.1137/16M1095184},
  pages     = {A1834 -- A1850},
  year      = {2017},
  abstract  = {Particle filters (also called sequential Monte Carlo methods) are widely used for state and parameter estimation problems in the context of nonlinear evolution equations. The recently proposed ensemble transform particle filter (ETPF) [S. Reich, SIAM T. Sci. Comput., 35, (2013), pp. A2013-A2014[ replaces the resampling step of a standard particle filter by a linear transformation which allows for a hybridization of particle filters with ensemble Kalman filters and renders the resulting hybrid filters applicable to spatially extended systems. However, the linear transformation step is computationally expensive and leads to an underestimation of the ensemble spread for small and moderate ensemble sizes. Here we address both of these shortcomings by developing second order accurate extensions of the ETPF. These extensions allow one in particular to replace the exact solution of a linear transport problem by its Sinkhorn approximation. It is also demonstrated that the nonlinear ensemble transform filter arises as a special case of our general framework. We illustrate the performance of the second-order accurate filters for the chaotic Lorenz-63 and Lorenz-96 models and a dynamic scene-viewing model. The numerical results for the Lorenz-63 and Lorenz-96 models demonstrate that significant accuracy improvements can be achieved in comparison to a standard ensemble Kalman filter and the ETPF for small to moderate ensemble sizes. The numerical results for the scene-viewing model reveal, on the other hand, that second-order corrections can lead to statistically inconsistent samples from the posterior parameter distribution.},
  language  = {en}
}
@article{AcevedoFallahReichetal.2017,
  author    = {Acevedo, Walter and Fallah, Bijan and Reich, Sebastian and Cubasch, Ulrich},
  title     = {Assimilation of pseudo-tree-ring-width observations into an atmospheric general circulation model},
  series = {Climate of the past : an interactive open access journal of the European Geosciences Union},
  volume    = {13},
  journal   = {Climate of the past : an interactive open access journal of the European Geosciences Union},
  publisher = {Copernicus},
  address   = {G{\"o}ttingen},
  issn      = {1814-9324},
  doi       = {10.5194/cp-13-545-2017},
  pages     = {545 -- 557},
  year      = {2017},
  abstract  = {Paleoclimate data assimilation (DA) is a promising technique to systematically combine the information from climate model simulations and proxy records. Here, we investigate the assimilation of tree-ring-width (TRW) chronologies into an atmospheric global climate model using ensemble Kalman filter (EnKF) techniques and a process-based tree-growth forward model as an observation operator. Our results, within a perfect-model experiment setting, indicate that the "online DA" approach did not outperform the "off-line" one, despite its considerable additional implementation complexity. On the other hand, it was observed that the nonlinear response of tree growth to surface temperature and soil moisture does deteriorate the operation of the time-averaged EnKF methodology. Moreover, for the first time we show that this skill loss appears significantly sensitive to the structure of the growth rate function, used to represent the principle of limiting factors (PLF) within the forward model. In general, our experiments showed that the error reduction achieved by assimilating pseudo-TRW chronologies is modulated by the magnitude of the yearly internal variability in themodel. This result might help the dendrochronology community to optimize their sampling efforts.},
  language  = {en}
}
@article{AcevedoReichCubasch2016,
  author    = {Acevedo, Walter and Reich, Sebastian and Cubasch, Ulrich},
  title     = {Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques},
  series = {Climate dynamics : observational, theoretical and computational research on the climate system},
  volume    = {46},
  journal   = {Climate dynamics : observational, theoretical and computational research on the climate system},
  publisher = {Springer},
  address   = {New York},
  issn      = {0930-7575},
  doi       = {10.1007/s00382-015-2683-1},
  pages     = {1909 -- 1920},
  year      = {2016},
  abstract  = {This paper investigates the applicability of the Vaganov-Shashkin-Lite (VSL) forward model for tree-ring-width chronologies as observation operator within a proxy data assimilation (DA) setting. Based on the principle of limiting factors, VSL combines temperature and moisture time series in a nonlinear fashion to obtain simulated TRW chronologies. When used as observation operator, this modelling approach implies three compounding, challenging features: (1) time averaging, (2) "switching recording" of 2 variables and (3) bounded response windows leading to "thresholded response". We generate pseudo-TRW observations from a chaotic 2-scale dynamical system, used as a cartoon of the atmosphere-land system, and attempt to assimilate them via ensemble Kalman filtering techniques. Results within our simplified setting reveal that VSL's nonlinearities may lead to considerable loss of assimilation skill, as compared to the utilization of a time-averaged (TA) linear observation operator. In order to understand this undesired effect, we embed VSL's formulation into the framework of fuzzy logic (FL) theory, which thereby exposes multiple representations of the principle of limiting factors. DA experiments employing three alternative growth rate functions disclose a strong link between the lack of smoothness of the growth rate function and the loss of optimality in the estimate of the TA state. Accordingly, VSL's performance as observation operator can be enhanced by resorting to smoother FL representations of the principle of limiting factors. This finding fosters new interpretations of tree-ring-growth limitation processes.},
  language  = {en}
}