TY  - JOUR
A1  - Gregory, A.
A1  - Cotter, C. J.
A1  - Reich, Sebastian
T1  - MULTILEVEL ENSEMBLE TRANSFORM PARTICLE FILTERING
JF  - SIAM journal on scientific computing
N2  - This paper extends the multilevel Monte Carlo variance reduction technique to nonlinear filtering. In particular, multilevel Monte Carlo is applied to a certain variant of the particle filter, the ensemble transform particle filter (EPTF). A key aspect is the use of optimal transport methods to re-establish correlation between coarse and fine ensembles after resampling; this controls the variance of the estimator. Numerical examples present a proof of concept of the effectiveness of the proposed method, demonstrating significant computational cost reductions (relative to the single-level ETPF counterpart) in the propagation of ensembles.
KW  - multilevel Monte Carlo
KW  - sequential data assimilation
KW  - optimal transport
Y1  - 2016
U6  - https://doi.org/10.1137/15M1038232
SN  - 1064-8275
SN  - 1095-7197
VL  - 38
SP  - A1317
EP  - A1338
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Acevedo, Walter
A1  - Reich, Sebastian
A1  - Cubasch, Ulrich
T1  - Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques
JF  - Climate dynamics : observational, theoretical and computational research on the climate system
N2  - 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.
KW  - Proxy forward modeling
KW  - Data assimilation
KW  - Fuzzy logic
KW  - Ensemble Kalman filter
KW  - Paleoclimate reconstruction
Y1  - 2016
U6  - https://doi.org/10.1007/s00382-015-2683-1
SN  - 0930-7575
SN  - 1432-0894
VL  - 46
SP  - 1909
EP  - 1920
PB  - Springer
CY  - New York
ER  -