@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}
}
@misc{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 = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {627},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41874},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-418743},
  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{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}
}
@misc{AcevedoReichCubasch2015,
  author    = {Acevedo, Walter and Reich, Sebastian and Cubasch, Ulrich},
  title     = {Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  volume    = {46},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {892},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43636},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436363},
  pages     = {1909 -- 1920},
  year      = {2015},
  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}
}
@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}
}
@article{AizingerKornGiorgettaetal.2015,
  author    = {Aizinger, Vadym and Korn, Peter and Giorgetta, Marco and Reich, Sebastian},
  title     = {Large-scale turbulence modelling via alpha-regularisation for atmospheric simulations},
  series = {Journal of turbulence},
  volume    = {16},
  journal   = {Journal of turbulence},
  number    = {4},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1468-5248},
  doi       = {10.1080/14685248.2014.991443},
  pages     = {367 -- 391},
  year      = {2015},
  abstract  = {We study the possibility of obtaining a computational turbulence model by means of non-dissipative regularisation of the compressible atmospheric equations for climate-type applications. We use an -regularisation (Lagrangian averaging) of the atmospheric equations. For the hydrostatic and compressible atmospheric equations discretised using a finite volume method on unstructured grids, deterministic and non-deterministic numerical experiments are conducted to compare the individual solutions and the statistics of the regularised equations to those of the original model. The impact of the regularisation parameter is investigated. Our results confirm the principal compatibility of -regularisation with atmospheric dynamics and encourage further investigations within atmospheric model including complex physical parametrisations.},
  language  = {en}
}
@article{AkhmatskayaBouRabeeReich2009,
  author    = {Akhmatskaya, Elena and Bou-Rabee, Nawaf and Reich, Sebastian},
  title     = {A comparison of generalized hybrid Monte Carlo methods with and without momentum flip},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2008.12.014},
  year      = {2009},
  abstract  = {The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.},
  language  = {en}
}
@article{AkhmatskayaBouRabeeReich2009,
  author    = {Akhmatskaya, Elena and Bou-Rabee, Nawaf and Reich, Sebastian},
  title     = {Erratum to "A comparison of generalized hybrid Monte Carlo methods with and without momentum flip" [J. Comput. Phys. 228 (2009), S. 2256 - 2265]},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2009.06.039},
  year      = {2009},
  abstract  = {The generalized hybrid Monte Carlo (GHMC) method combines Metropolis corrected constant energy simulations with a partial random refreshment step in the particle momenta. The standard detailed balance condition requires that momenta are negated upon rejection of a molecular dynamics proposal step. The implication is a trajectory reversal upon rejection, which is undesirable when interpreting GHMC as thermostated molecular dynamics. We show that a modified detailed balance condition can be used to implement GHMC without momentum flips. The same modification can be applied to the generalized shadow hybrid Monte Carlo (GSHMC) method. Numerical results indicate that GHMC/GSHMC implementations with momentum flip display a favorable behavior in terms of sampling efficiency, i.e., the traditional GHMC/GSHMC implementations with momentum flip got the advantage of a higher acceptance rate and faster decorrelation of Monte Carlo samples. The difference is more pronounced for GHMC. We also numerically investigate the behavior of the GHMC method as a Langevin-type thermostat. We find that the GHMC method without momentum flip interferes less with the underlying stochastic molecular dynamics in terms of autocorrelation functions and it to be preferred over the GHMC method with momentum flip. The same finding applies to GSHMC.},
  language  = {en}
}
@article{AmezcuaIdeKalnayetal.2014,
  author    = {Amezcua, Javier and Ide, Kayo and Kalnay, Eugenia and Reich, Sebastian},
  title     = {Ensemble transform Kalman-Bucy filters},
  series = {Quarterly journal of the Royal Meteorological Society},
  volume    = {140},
  journal   = {Quarterly journal of the Royal Meteorological Society},
  number    = {680},
  publisher = {Wiley-Blackwell},
  address   = {Hoboken},
  issn      = {0035-9009},
  doi       = {10.1002/qj.2186},
  pages     = {995 -- 1004},
  year      = {2014},
  abstract  = {Two recent works have adapted the Kalman-Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman-Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.},
  language  = {en}
}
@article{AsgarimehrWickertReich2018,
  author    = {Asgarimehr, Milad and Wickert, Jens and Reich, Sebastian},
  title     = {TDS-1 GNSS Reflectometry},
  series = {IEEE journal of selected topics in applied earth observations and remote sensing},
  volume    = {11},
  journal   = {IEEE journal of selected topics in applied earth observations and remote sensing},
  number    = {11},
  publisher = {Inst. of Electr. and Electronics Engineers},
  address   = {Piscataway},
  issn      = {1939-1404},
  doi       = {10.1109/JSTARS.2018.2873241},
  pages     = {4534 -- 4541},
  year      = {2018},
  abstract  = {This study presents the development and a systematic evaluation study of GNSS reflectometry wind speeds. After establishing a wind speed retrieval algorithm, UK TechDemoSat-1 (TDS-1) derived winds, from May 2015 to July 2017, are compared to the Advanced Scatterometer (ASCAT). ERA-Interim wind fields of the European Centre for Medium-range Weather Forecasts (ECMWF) and in situ observation from Tropical Atmosphere Ocean buoy array in the Pacific are taken as reference. One-year averaged TDS-1 global winds demonstrate small differences with ECMWF in a majority of areas as well as discuss under- and overestimations. The pioneering TDS-1 winds demonstrate a root-mean-squared error (RMSE) and bias of 2.77 and -0.33 m/s, which are comparable to the RMSE and bias derived by ASCAT winds, as large as 2.31 and 0.25 m/s, respectively. Using buoys measurements as reference, RMSE and bias of 2.23 and -0.03 m/s for TDS-1 as well as 1.40 and -0.68 m/s for ASCAT are obtained. Utilizing rain microwave-infrared estimates of the Tropical Rainfall Measuring Mission, rain-affected observation of both ASCAT and TDS-1 are collected and evaluated. Although ASCAT winds show a significant performance degradation resulting in an RMSE and bias of 3.16 and 1.03 m/s, respectively, during rain condition, TDS-1 shows a more reliable performance with an RMSE and bias of 2.94 and -0.21 m/s, respectively, which indicates the promising capability of GNSS forward scattering for wind retrievals during rain. A decrease in TDS-1-derived bistatic radar cross sections during rain events, at weak winds, is also demonstrated.},
  language  = {en}
}