Papers by Roland Potthast
Frontiers in Applied Mathematics and Statistics

Although the high amount of solar irradiance in the tropics is an advantage for a profitable PV p... more Although the high amount of solar irradiance in the tropics is an advantage for a profitable PV production, the local meteorological conditions induce a very high variability which is problematic for a safe and gainful injection into the power grid. This issue is even more critical in non-interconnected territories where network stability is an absolute necessity and the injection of PV power has to be limited. The basis for precise cloud evolution and subsequent irradiance forecasts are high quality atmospheric analyses for NWP. Geostationary meteorological satellites provide valuable observations of cloud properties with high spatio-temporal resolutions and allow a pertinent data assimilation. The shortcoming is that optical and thermal channels of satellite sensors do not provide cloud properties from inside clouds. Different existing data assimilation approaches aim at deriving atmospheric analyses with most realistic cloud features, utilising geostationary satellite observation...

European geosciences union general assembly, 2016
As an intermittent energy source, the injection of solar power into electricity grids requires ir... more As an intermittent energy source, the injection of solar power into electricity grids requires irradiance forecasting in order to ensure grid stability. On time scales of more than six hours ahead, numerical weather prediction (NWP) is recognized as the most appropriate solution. However, the current representation of clouds in NWP models is not sufficiently precise for an accurate forecast of solar irradiance at ground level. Dynamical downscaling does not necessarily increase the quality of irradiance forecasts. Furthermore, incorrectly simulated cloud evolution is often the cause of inaccurate atmospheric analyses. In non-interconnected tropical areas, the large amplitudes of solar irradiance variability provide abundant solar yield but present significant problems for grid safety. Irradiance forecasting is particularly important for solar power stakeholders in these regions where PV electricity penetration is increasing. At the same time, NWP is markedly more challenging in trop...
Bulletin of the American Meteorological Society, 2021

Quarterly Journal of the Royal Meteorological Society, 2020
A realistic simulation of the atmospheric boundary layer (ABL) depends on an accurate representat... more A realistic simulation of the atmospheric boundary layer (ABL) depends on an accurate representation of the land–atmosphere coupling. Land surface temperature (LST) plays an important role in this context and the assimilation of LST can lead to improved estimates of the boundary layer and its processes. We assimilated synthetic satellite LST retrievals derived from a nature run as truth into a fully coupled, state‐of‐the‐art land–atmosphere numeric weather prediction model. As assimilation system a local ensemble transform Kalman filter was used and the control vector was augmented by the soil temperature and humidity. To evaluate the concept of the augmented control vector, two‐day case‐studies with different control vector settings were conducted for clear‐sky periods in March and August 2017. These experiments with hourly LST assimilation were validated against the nature run and overall, the RMSE of atmospheric and soil temperature of the first‐guess (and analysis) were reduced....
Frontiers in Earth Science, 2020

Monthly Weather Review, 2019
Particle filters are well known in statistics. They have a long tradition in the framework of ens... more Particle filters are well known in statistics. They have a long tradition in the framework of ensemble data assimilation (EDA) as well as Markov chain Monte Carlo (MCMC) methods. A key challenge today is to employ such methods in a high-dimensional environment, since the naïve application of the classical particle filter usually leads to filter divergence or filter collapse when applied within the very high dimension of many practical assimilation problems (known as the curse of dimensionality). The goal of this work is to develop a localized adaptive particle filter (LAPF), which follows closely the idea of the classical MCMC or bootstrap-type particle filter, but overcomes the problems of collapse and divergence based on localization in the spirit of the local ensemble transform Kalman filter (LETKF) and adaptivity with an adaptive Gaussian resampling or rejuvenation scheme in ensemble space. The particle filter has been implemented in the data assimilation system for the global f...

Meteorologische Zeitschrift, 2018
Many research and societal applications such as surface solar irradiance assessment and forecasti... more Many research and societal applications such as surface solar irradiance assessment and forecasting require accurate short-term cloudiness forecasts at kilometre and hourly scales. Today limited-area numerical weather prediction models have the potential to provide such forecasts by simulating clouds at high spatial and temporal resolutions. However, the forecast performance during the first 12-24 h is strongly influenced by the accuracy of the cloud and thermodynamic analyses in the initial conditions. Geostationary meteorological satellites provide valuable observations that can be used in data assimilation for frequent cloud analysis determination. This paper provides an up-to-date review of the state of the art in cloud-related geostationary satellite data assimilation with limited-area models dedicated to improve cloudiness forecast performance. Research and operational studies have been reviewed by differentiating between satellite radiance and cloud property retrieval assimilation. This review gives insight into the best practices considering the large variety of limited-area models, data assimilation methods, satellite sensors and channels, cloud property retrieval products and various methodological challenges. Cloud analysis methods for regional models have become more sophisticated in recent years and are increasingly able to exploit observations from geostationary satellites. Important proofs of concept have been performed in this decade, paving the way for an optimal synergy of geostationary satellite data assimilation and convection-permitting limited-area model forecasts. At the same time, the increasing amount of channels of geostationary satellite instruments leads to more opportunities and challenges for data assimilation methods.

Journal of Computational and Applied Mathematics, 2018
Multiscale approaches are very popular for example for solving partial differential equations and... more Multiscale approaches are very popular for example for solving partial differential equations and in many applied fields dealing with phenomena which take place on different levels of detail. The broad idea of a multiscale approach is to decompose your problem into different scales or levels and to use these decompositions either for constructing appropriate approximations or to solve smaller problems on each of these levels, leading to increased stability or increased efficiency. The idea of sequential multiscale is to first solve the problem in a large-scale subspace and then successively move to finer scale spaces. Our goal is to analyse the sequential multiscale approach applied to an inversion or state estimation problem. We work in a generic setup given by a Hilbert space environment. We work out the analysis both for an unregularized and a regularized sequential multiscale inversion. In general the sequential multiscale approach is not equivalent to a full solution, but we show that under appropriate assumptions we obtain convergence of an iterative sequential multiscale version of the method. For the regularized case we develop a strategy to appropriately adapt the regularization when an iterative approach is taken. We demonstrate the validity of the iterative sequential multiscale approach by testing the method on an integral equation as it appears for atmospheric temperature retrieval from infrared satellite radiances.

Frontiers in Applied Mathematics and Statistics, 2018
Data assimilation permits to compute optimal forecasts in high-dimensional systems as, e.g., in w... more Data assimilation permits to compute optimal forecasts in high-dimensional systems as, e.g., in weather forecasting. Typically such forecasts are spatially distributed time series of system variables. We hypothesize that such forecasts are not optimal if the major interest does not lie in the temporal evolution of system variables but in time series composites or features. For instance, in neuroscience spectral features of neural activity are the primary functional elements. The present work proposes a data assimilation framework for forecasts of time-frequency distributions. The framework comprises the ensemble Kalman filter and a detailed statistical ensemble verification. The performance of the framework is evaluated for a simulated FitzHugh-Nagumo model, various measurement noise levels and for in situ-, nonlocal and speed observations. We discover a resonance effect in forecast errors between forecast time and frequencies in observations.

Quarterly Journal of the Royal Meteorological Society, 2017
Representation, representativity, representativeness error, forward interpolation error, forward ... more Representation, representativity, representativeness error, forward interpolation error, forward model error, observation‐operator error, aggregation error and sampling error are all terms used to refer to components of observation error in the context of data assimilation. This article is an attempt to consolidate the terminology that has been used in the earth sciences literature and was suggested at a European Space Agency workshop held in Reading in April 2014. We review the state of the art and, through examples, motivate the terminology. In addition to a theoretical framework, examples from application areas of satellite data assimilation, ocean reanalysis and atmospheric chemistry data assimilation are provided. Diagnosing representation‐error statistics as well as their use in state‐of‐the‐art data assimilation systems is discussed within a consistent framework.

Quarterly Journal of the Royal Meteorological Society, 2016
An ensemble data assimilation system for 3D radar reflectivity data is introduced for the convect... more An ensemble data assimilation system for 3D radar reflectivity data is introduced for the convection‐permitting numerical weather prediction model of the COnsortium for Small‐scale MOdelling (COSMO) based on the Kilometre‐scale ENsemble Data Assimilation system (KENDA), developed by Deutscher Wetterdienst and its partners. KENDA provides a state‐of‐the‐art ensemble data assimilation system on the convective scale for operational data assimilation and forecasting based on the Local Ensemble Transform Kalman Filter (LETKF). In this study, the Efficient Modular VOlume RADar Operator is applied for the assimilation of radar reflectivity data to improve short‐term predictions of precipitation. Both deterministic and ensemble forecasts have been carried out. A case‐study shows that the assimilation of 3D radar reflectivity data clearly improves precipitation location in the analysis and significantly improves forecasts for lead times up to 4 h, as quantified by the Brier Score and the Con...

Kilometre‐scale ensemble data assimilation for the COSMO model (KENDA)
Quarterly Journal of the Royal Meteorological Society, 2016
An ensemble Kalman filter for convective‐scale data assimilation (KENDA) has been developed for t... more An ensemble Kalman filter for convective‐scale data assimilation (KENDA) has been developed for the COnsortium for Small‐scale MOdelling (COSMO) model. The KENDA system comprises a local ensemble transform Kalman filter (LETKF) and a deterministic analysis based on the Kalman gain for the analysis ensemble mean. The KENDA software suite includes tools for adaptive localization, multiplicative covariance inflation, relaxation to prior perturbations and adaptive observation errors. In the version introduced here, conventional data (radiosonde, aircraft, wind profiler, surface station data) are assimilated. Latent heat nudging of radar precipitation has also been added to the KENDA system to be applied to the deterministic analysis only or additionally to all ensemble members. The performance of different system components is investigated in a quasi‐operational setting using a basic cycling environment (BACY) for a period of six days with 24 h forecasts. For this period and an addition...

Monthly Weather Review, 2022
We investigate the assimilation of nowcasted information into a classical data assimilation cycle... more We investigate the assimilation of nowcasted information into a classical data assimilation cycle. As a reference setup, we employ the assimilation of standard observations such as direct observations of particular variables into a forecasting system. The pure advective movement extrapolation of observations as a simple nowcasting (NWC) is usually much better for the first minutes to hours, until outperformed by numerical weather prediction (NWP) based on data assimilation. Can nowcasted information be used in the data assimilation cycle? We study both an oscillator model and the Lorenz 63 model with assimilation based on the localized ensemble transform Kalman filter (LETKF). We investigate and provide a mathematical framework for the assimilation of nowcasted information, approximated as a local tendency, into the LETKF in each assimilation step. In particular, we derive and discuss adequate observation error and background uncertainty covariance matrices and interpret the assimil...

SIAM Journal on Applied Dynamical Systems, 2021
In this study, we develop model bias estimators based on an asymptotic expansion of the model dyn... more In this study, we develop model bias estimators based on an asymptotic expansion of the model dynamics for small time scales and small perturbations in a model parameter, and then use the estimators to improve the performance of a data assimilation system. We employ the well-known Lorenz (1963) model so that we can study all aspects of the dynamical system and model bias estimators in a detailed way that would not be possible with a full physics numerical weather prediction model. In particular, we first work out the asymptotics of the Lorenz model for small changes in one of its parameters and then use statistics from cycled data assimilation experiments to demonstrate that the asymptotics accurately represent the behavior of the model and that the coefficients of the nonlinear asymptotical expansion can be reasonably estimated by solving a least squares minimization problem. In data assimilation, the background error covariance matrix usually estimates the uncertainty of the model background, which is then used along with the observation error covariance matrix to produce an updated analysis. If the uncertainty of the model background is strongly influenced by time-dependent model biases, then the development of nonlinear bias estimators that also vary with time could improve the performance of the assimilation system and the accuracy of the updated analysis. We demonstrate this improvement through the combination of a constant background error covariance matrix with a dynamically-varying matrix computed using the model bias estimators. Numerical tests using the Lorenz (1963) model illustrate the feasibility of the approach and show that it leads to clear improvements in the analysis and forecast accuracy.
The convergence proof of the no-response test for localizing an inclusion

Cognitive computation such as e.g. language processing, is conventionally regarded as Turing comp... more Cognitive computation such as e.g. language processing, is conventionally regarded as Turing computation, and Turing machines can be uniquely implemented as nonlinear dynamical systems using generalized shifts and subsequent G\"odel encoding of the symbolic repertoire. The resulting nonlinear dynamical automata (NDA) are piecewise affine-linear maps acting on the unit square that is partitioned into rectangular domains. Iterating a single point, i.e. a microstate, by the dynamics yields a trajectory of, in principle, infinitely many points scattered through phase space. Therefore, the NDAs microstate dynamics does not necessarily terminate in contrast to its counterpart, the symbolic dynamics obtained from the rectangular partition. In order to regain the proper symbolic interpretation, one has to prepare ensembles of randomly distributed microstates with rectangular supports. Only the resulting macrostate evolution corresponds then to the original Turing machine computation. H...

SIAM Journal on Applied Mathematics, 2006
For a nonlocally perturbed half-space we consider the scattering of time-harmonic acoustic waves.... more For a nonlocally perturbed half-space we consider the scattering of time-harmonic acoustic waves. A second kind boundary integral equation formulation is proposed for the sound-soft case, based on a standard ansatz as a combined single-and double-layer potential but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Due to the unboundedness of the surface, the integral operators are noncompact. In contrast to the two-dimensional case, the integral operators are also strongly singular, due to the slow decay at infinity of the fundamental solution of the three-dimensional Helmholtz equation. In the case when the surface is sufficiently smooth (Lyapunov) we show that the integral operators are nevertheless bounded as operators on L 2 (Γ) and on L 2 (Γ) ∩ BC(Γ) and that the operators depend continuously in norm on the wave number and on Γ. We further show that for mild roughness, i.e., a surface Γ which does not differ too much from a plane, the boundary integral equation is uniquely solvable in the space L 2 (Γ) ∩ BC(Γ) and the scattering problem has a unique solution which satisfies a limiting absorption principle in the case of real wave number.
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Papers by Roland Potthast