TY  - JOUR
A1  - Gottwald, Georg A.
A1  - Reich, Sebastian
T1  - Supervised learning from noisy observations
BT  - Combining machine-learning techniques with data assimilation
JF  - Physica : D, Nonlinear phenomena
N2  - Data-driven prediction and physics-agnostic machine-learning methods have attracted increased interest in recent years achieving forecast horizons going well beyond those to be expected for chaotic dynamical systems. In a separate strand of research data-assimilation has been successfully used to optimally combine forecast models and their inherent uncertainty with incoming noisy observations. The key idea in our work here is to achieve increased forecast capabilities by judiciously combining machine-learning algorithms and data assimilation. We combine the physics-agnostic data -driven approach of random feature maps as a forecast model within an ensemble Kalman filter data assimilation procedure. The machine-learning model is learned sequentially by incorporating incoming noisy observations. We show that the obtained forecast model has remarkably good forecast skill while being computationally cheap once trained. Going beyond the task of forecasting, we show that our method can be used to generate reliable ensembles for probabilistic forecasting as well as to learn effective model closure in multi-scale systems. (C) 2021 Elsevier B.V. All rights reserved.
KW  - Data-driven modelling
KW  - Random feature maps
KW  - Data assimilation
Y1  - 2021
U6  - https://doi.org/10.1016/j.physd.2021.132911
SN  - 0167-2789
SN  - 1872-8022
VL  - 423
PB  - Elsevier
CY  - Amsterdam
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  - 
TY  - JOUR
A1  - Reich, Sebastian
T1  - A dynamical systems framework for intermittent data assimilation
JF  - BIT : numerical mathematics ; the leading applied mathematics journal for all computational mathematicians
N2  - We consider the problem of discrete time filtering (intermittent data assimilation) for differential equation models and discuss methods for its numerical approximation. The focus is on methods based on ensemble/particle techniques and on the ensemble Kalman filter technique in particular. We summarize as well as extend recent work on continuous ensemble Kalman filter formulations, which provide a concise dynamical systems formulation of the combined dynamics-assimilation problem. Possible extensions to fully nonlinear ensemble/particle based filters are also outlined using the framework of optimal transportation theory.
KW  - Data assimilation
KW  - Ensemble Kalman filter
KW  - Dynamical systems
KW  - Nonlinear filters
KW  - Optimal transportation
Y1  - 2011
U6  - https://doi.org/10.1007/s10543-010-0302-4
SN  - 0006-3835
VL  - 51
IS  - 1
SP  - 235
EP  - 249
PB  - Springer
CY  - Dordrecht
ER  -