TY - GEN A1 - Asgarimehr, Milad A1 - Wickert, Jens A1 - Reich, Sebastian T1 - Evaluating impact of rain attenuation on space-borne GNSS Reflectometry wind speeds T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - The novel space-borne Global Navigation Satellite System Reflectometry (GNSS-R) technique has recently shown promise in monitoring the ocean state and surface wind speed with high spatial coverage and unprecedented sampling rate. The L-band signals of GNSS are structurally able to provide a higher quality of observations from areas covered by dense clouds and under intense precipitation, compared to those signals at higher frequencies from conventional ocean scatterometers. As a result, studying the inner core of cyclones and improvement of severe weather forecasting and cyclone tracking have turned into the main objectives of GNSS-R satellite missions such as Cyclone Global Navigation Satellite System (CYGNSS). Nevertheless, the rain attenuation impact on GNSS-R wind speed products is not yet well documented. Evaluating the rain attenuation effects on this technique is significant since a small change in the GNSS-R can potentially cause a considerable bias in the resultant wind products at intense wind speeds. Based on both empirical evidence and theory, wind speed is inversely proportional to derived bistatic radar cross section with a natural logarithmic relation, which introduces high condition numbers (similar to ill-posed conditions) at the inversions to high wind speeds. This paper presents an evaluation of the rain signal attenuation impact on the bistatic radar cross section and the derived wind speed. This study is conducted simulating GNSS-R delay-Doppler maps at different rain rates and reflection geometries, considering that an empirical data analysis at extreme wind intensities and rain rates is impossible due to the insufficient number of observations from these severe conditions. Finally, the study demonstrates that at a wind speed of 30 m/s and incidence angle of 30 degrees, rain at rates of 10, 15, and 20 mm/h might cause overestimation as large as approximate to 0.65 m/s (2%), 1.00 m/s (3%), and 1.3 m/s (4%), respectively, which are still smaller than the CYGNSS required uncertainty threshold. The simulations are conducted in a pessimistic condition (severe continuous rainfall below the freezing height and over the entire glistening zone) and the bias is expected to be smaller in size in real environments. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1132 KW - GNSS Reflectometry KW - wind speed KW - rain effect KW - rain attenuation KW - DDM simulation Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473441 SN - 1866-8372 IS - 1132 ER - TY - GEN A1 - Nüsken, Nikolas A1 - Reich, Sebastian A1 - Rozdeba, Paul J. T1 - State and parameter estimation from observed signal increments T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean–Vlasov equations as the starting point to derive ensemble Kalman–Bucy filter algorithms for combined state and parameter estimation. We demonstrate their performance through a series of increasingly complex multi-scale model systems. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 916 KW - parameter estimation KW - continuous-time data assimilation KW - ensemble Kalman filter KW - correlated noise KW - multi-scale diffusion processes Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-442609 SN - 1866-8372 IS - 916 ER - TY - GEN A1 - Acevedo, Walter A1 - Reich, Sebastian A1 - Cubasch, Ulrich T1 - Towards the assimilation of tree-ring-width records using ensemble Kalman filtering techniques T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 892 KW - proxy forward modeling KW - data assimilation KW - fuzzy logic KW - ensemble Kalman filter KW - paleoclimate reconstruction Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436363 SN - 1866-8372 VL - 46 IS - 892 SP - 1909 EP - 1920 ER - TY - GEN A1 - Acevedo, Walter A1 - Fallah, Bijan A1 - Reich, Sebastian A1 - Cubasch, Ulrich T1 - Assimilation of pseudo-tree-ring-width observations into an atmospheric general circulation model T2 - Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 627 KW - high resolution paleoclimatology KW - sparse proxy data KW - climate reconstructions KW - limiting factors KW - Kalman filter KW - co-limitation KW - ensemble KW - variability KW - reanalysis KW - framework Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-418743 SN - 1866-8372 IS - 627 SP - 545 EP - 557 ER - TY - GEN A1 - Reich, Sebastian T1 - Algebrodifferentialgleichungen und Vektorfelder auf Mannigfaltigkeiten N2 - In diesem Beitrag wird der Zusammenhang zwischen Algebrodifferentialgleichungen (ADGL) und Vektorfeldern auf Mannigfaltigkeiten untersucht. Dazu wird zunächst der Begriff der regulären ADGL eingeführt, wobei unter eirter regulären ADGL eine ADGL verstanden wird, deren Lösungsmenge identisch mit der Lösungsmenge eines Vektorfeldes ist. Ausgehend von bekannten Aussagen über die Lösungsmenge eines Vektorfeldes werden analoge Aussagen für die Lösungsmenge einer regulären ADGL abgeleitet. Es wird eine Reduktionsmethode angegeben, die auf ein Kriterium für die Begularität einer ADGL und auf die Definition des Index einer nichtlinearen ADGL führt. Außerdem wird gezeigt, daß beliebige Vektorfelder durch reguläre ADGL so realisiert werden können, daß die Lösungsmenge des Vektorfeldes mit der der realisierenden ADGL identisch ist. Abschließend werden die für autonome ADGL gewonnenen Aussagen auf den Fall der nichtautonomen ADGL übertragen. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 160 Y1 - 1980 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-47290 ER - TY - GEN A1 - Reich, Sebastian T1 - On the local qualitative behavior of differential-algebraic equations N2 - A theoretical famework for the investigation of the qualitative behavior of differential-algebraic equations (DAEs) near an equilibrium point is established. The key notion of our approach is the notion of regularity. A DAE is called regular locally around an equilibrium point if there is a unique vector field such that the solutions of the DAE and the vector field are in one-to-one correspondence in a neighborhood of this equili Drium point. Sufficient conditions for the regularity of an equilibrium point are stated. This in turn allows us to translate several local results, as formulated for vector fields, to DAEs that are regular locally around a g: ven equilibrium point (e.g. Local Stable and Unstable Manifold Theorem, Hopf theorem). It is important that ihese theorems are stated in terms of the given problem and not in terms of the corresponding vector field. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 159 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46739 ER - TY - GEN A1 - Reich, Sebastian T1 - On an existence and uniqueness theory for nonlinear differential-algebraic equations N2 - An existence and uniqueness theory is developed for general nonlinear and nonautonomous differential-algebraic equations (DAEs) by exploiting their underlying differential-geometric structure. A DAE is called regular if there is a unique nonautonomous vector field such that the solutions of the DAE and the solutions of the vector field are in one-to-one correspondence. Sufficient conditions for regularity of a DAE are derived in terms of constrained manifolds. Based on this differential-geometric characterization, existence and uniqueness results are stated for regular DAEs. Furthermore, our not ons are compared with techniques frequently used in the literature such as index and solvability. The results are illustrated in detail by means of a simple circuit example. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 158 Y1 - 1991 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46706 ER - TY - GEN A1 - Reich, Sebastian T1 - On a geometrical interpretation of differential-algebraic equations N2 - The subject of this paper is the relation of differential-algebraic equations (DAEs) to vector fields on manifolds. For that reason, we introduce the notion of a regular DAE as a DAE to which a vector field uniquely corresponds. Furthermore, a technique is described which yields a family of manifolds for a given DAE. This socalled family of constraint manifolds allows in turn the formulation of sufficient conditions for the regularity of a DAE. and the definition of the index of a regular DAE. We also state a method for the reduction of higher-index DAEs to lowsr-index ones that can be solved without introducing additional constants of integration. Finally, the notion of realizability of a given vector field by a regular DAE is introduced, and it is shown that any vector field can be realized by a regular DAE. Throughout this paper the problem of path-tracing is discussed as an illustration of the mathematical phenomena. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 157 Y1 - 1990 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46683 ER - TY - GEN A1 - Reich, Sebastian T1 - Differential-algebraic equations and applications in circuit theory N2 - Technical and physical systems, especially electronic circuits, are frequently modeled as a system of differential and nonlinear implicit equations. In the literature such systems of equations are called differentialalgebraic equations (DAEs). It turns out that the numerical and analytical properties of a DAE depend on an integer called the index of the problem. For example, the well-known BDF method of Gear can be applied, in general, to a DAE only if the index does not exceed one. In this paper we give a geometric interpretation of higherindex DAEs and indicate problems arising in connection with such DAEs by means of several examples. N2 - Die mathematische Modellierung technisch physikalischer Systeme wie elektrische Netzwerke, führt häufig auf ein System von Differentialgleichungen und nichtlinearen impliziten Gleichungen sogenannten Algebrodifferentialgleichungen (ADGL). Es zeigt sich, daß die numerischen und analytischen Eigenschaften von ADGL durch den Index des Problems charakterisiert werden können. Insbesondere können die bekannten Integrationsformeln von Gear im allgemeinen nur auf ADGL mit dem Index eins angewendet werden. In diesem Beitrag wird eine geometrische Interpretation von ADGL mit einem höheren Index gegeben sowie auf Probleme im Zusammenhang mit derartigen ADGL an Hand verschiedener Beispiele hingewiesen. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 156 Y1 - 1992 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-46646 ER - TY - GEN A1 - Reich, Sebastian T1 - Momentum conserving symplectic integrators N2 - In this paper, we show that symplectic partitioned Runge-Kutta methods conserve momentum maps corresponding to linear symmetry groups acting on the phase space of Hamiltonian differential equations by extended point transformation. We also generalize this result to constrained systems and show how this conservation property relates to the symplectic integration of Lie-Poisson systems on certain submanifolds of the general matrix group GL(n). T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 044 Y1 - 1994 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-16824 ER -