Many countries are currently dealing with the COVID-19 epidemic and are searching for an exit strategy such that life in society can return to normal. To support this search, computational models are used to predict the spread of the virus and to assess the efficacy of policy measures before actual implementation. The model output has to be interpreted carefully though, as computational models are subject to uncertainties. These can stem from, e.g., limited knowledge about input parameters values or from the intrinsic stochastic nature of some computational models. They lead to uncertainties in the model predictions, raising the question what distribution of values the model produces for key indicators of the severity of the epidemic. Here we show how to tackle this question using techniques for uncertainty quantification and sensitivity analysis. We assess the uncertainties and sensitivities of four exit strategies implemented in an agent-based transmission model with geographical stratification. The exit strategies are termed Flattening the Curve, Contact Tracing, Intermittent Lockdown and Phased Opening. We consider two key indicators of the ability of exit strategies to avoid catastrophic health care overload: the maximum number of prevalent cases in intensive care (IC), and the total number of IC patient-days in excess of IC bed capacity. Our results show that uncertainties not directly related to the exit strategies are secondary, although they should still be considered in comprehensive analysis intended to inform policy makers. The sensitivity analysis discloses the crucial role of the intervention uptake by the population and of the capability to trace infected individuals. Finally, we explore the existence of a safe operating space. For Intermittent Lockdown we find only a small region in the model parameter space where the key indicators of the model stay within safe bounds, whereas this region is larger for the other exit strategies.

Multi-scale systems, such as the climate system, the atmosphere, and the ocean, are hard to understand and predict due to their intrinsic nonlinearities and chaotic behavior. Here, we apply a physics-consistent machine learning method, the multi-resolution dynamic mode decomposition (mrDMD), to oceanographic data. mrDMD allows a systematic decomposition of high-dimensional data sets into time-scale dependent modes of variability. We find that mrDMD is able to systematically decompose sea surface temperature and sea surface height fields into dynamically meaningful patterns on different time scales. In particular, we find that mrDMD is able to identify varying annual cycle modes and is able to extract El Nino–Southern Oscillation events as transient phenomena. mrDMD is also able to extract propagating meanders related to the intensity and position of the Gulf Stream and Kuroshio currents. While mrDMD systematically identifies mean state changes similarly well compared to other methods, such as empirical orthogonal function decomposition, it also provides information about the dynamically propagating eddy component of the flow. Furthermore, these dynamical modes can also become progressively less important as time progresses in a specific time period, making them also state dependent.

In this study we aim to present the successful development of an energy conserving conceptual stochastic climate model based on the inviscid 2-layer Quasi-Geostrophic (QG) equations. The stochastic terms have been systematically derived and introduced in such away that the total energy is conserved. In this proof of concept studywe give particular emphasis to the numerical aspects of energy conservation in a highdimensional complex stochastic system andwe analyzewhat kind of assumptions regarding the noise should be considered in order to obtain physical meaningful results. Our results show that the stochastic model conserves energy to an accuracy of about 0.5% of the total energy; this level of accuracy is not affected by the introduction of the noise, but is mainly due to the level of accuracy of the deterministic discretization of the QG model. Furthermore, our results demonstrate that spatially correlated noise is necessary for the conservation of energy and the preservation of important statistical properties, while using spatially uncorrelated noise violates energy conservation and gives unphysical results. A dynamically consistent spatial covariance structure is determined through Empirical Orthogonal Functions (EOFs). We find that only a small number of EOFs is needed to get good results with respect to energy conservation, autocorrelation functions, PDFs and eddy length scale when comparing a deterministic control simulation on a 512 × 512 grid to a stochastic simulation on a 128 × 128 grid. Our stochastic approach has the potential to seamlessly be implemented in comprehensive weather and climate prediction models.

Stochastic parameterizations are increasingly being used in climate modeling to represent subgrid scale processes. While different parameterizations are being developed considering different aspects of the physical phenomena, less attention is given to technical and numerical aspects. In particular, Empirical Orthogonal Functions (EOFs) are employed when a spatial structure is required. Here, we provide evidence they might not be the most suitable choice. By applying an energy consistent parameterization to the 2‐layer Quasi‐Geostrophic (QG) model, we investigate the model sensitivity to a priori assumptions made on the parameterization. In particular, we consider here two methods to prescribe the spatial covariance of the noise. First, by using climatological variability patterns provided by EOFs, second, by using time‐varying dynamics‐adapted Koopman modes, approximated by Dynamic Mode Decomposition (DMD). The performance of the two methods are analyzed through numerical simulations of the stochastic system on a coarse spatial resolution and the outcomes compared to a high‐resolution simulation of the original deterministic system. The comparison reveals that the DMD based noise covariance scheme outperforms the EOF based. The use of EOFs leads to a significant increase of the ensemble spread and to a meridional misplacement of the bi‐modal eddy kinetic energy (EKE) distribution. Conversely, using DMDs, the ensemble spread is confined, the meridional propagation of the zonal jet stream is accurately captured and the total variance of the system is improved. Our results highlight the importance of the systematic design of stochastic parameterizations with dynamically adapted spatial correlations, rather than relying on statistical spatial patterns

The total quantity and energy delivered through a gas grid is calculated using simple formulæ that sum the increments measured at regular time intervals. These calculations are described in international standards (e.g., ISO 15112 and EN 1776) and guidelines (e.g., OIML R140). These guidelines recommend that the associated measurement uncertainty is evaluated assuming the measurement results to be mutually independent. This assumption leads to the underestimation of the measurement uncertainty. To address the growing concern among transmission and distribution system operators, the underlying assumptions of these uncertainty evaluations are revisited and reworked to be more adequate. The dependence of measurement results coming from, e.g., the same flow meter and gas chromatograph will be assessed for correlations, as well as other effects, such as the effect of the chosen mathematical approximation of the totalisation integral and fluctuations in the flow rate and gas quality. In this paper, an outline is given for improvements that can be implemented in the measurement models to render them more responsive to the error structure of the measurement data, temporal effects in these data, and the fluctuations in the gas quality and gas quantity. By impact assessment using a simple scenario involving the injection of (renewable) hydrogen into a natural gas grid, it is shown that these improvements lead to a substantive difference. This preliminary work demonstrates that correlations occur both in the instrumental measurement uncertainty and due to temporal effects in the gas grid. To obtain a fit-for-purpose uncertainty budget for custody transfer and grid balancing, it is key to enhance the current models and standards accordingly.