Simulating rainfall time-series: how to account for statistical variability at multiple scales?

Daily rainfall is a complex signal exhibiting alternation of dry and wet states, seasonal fluctuations and an irregular behavior at multiple scales that cannot be preserved by stationary stochastic simulation models. In this paper, we try to investigate some of the strategies devoted to preserve these features by comparing two recent algorithms for stochastic rainfall simulation: the first one is the modified Markov model, belonging to the family of Markov-chain based techniques, which introduces non-stationarity in the chain parameters to preserve the long-term behavior of rainfall. The second technique is direct sampling, based on multiple-point statistics, which aims at simulating a complex statistical structure by reproducing the same data patterns found in a training data set. The two techniques are compared by first simulating a synthetic daily rainfall time-series showing a highly irregular alternation of two regimes and then a real rainfall data set. This comparison allows analyzing the efficiency of different elements characterizing the two techniques, such as the application of a variable time dependence, the adaptive kernel smoothing or the use of low-frequency rainfall covariates. The results suggest, under different data availability scenarios, which of these elements are more appropriate to represent the rainfall amount probability distribution at different scales, the annual seasonality, the dry-wet temporal pattern, and the persistence of the rainfall events.     

The probabilistic seismic hazard assessment of Germany—version 2016, considering the range of epistemic uncertainties and aleatory variability

The basic seismic load parameters for the upcoming national design regulation for DIN EN 1998-1/NA result from the reassessment of the seismic hazard supported by the German Institution for Civil Engineering (DIBt). This 2016 version of the national seismic hazard assessment for Germany is based on a comprehensive involvement of all accessible uncertainties in models and parameters and includes the provision of a rational framework for integrating ranges of epistemic uncertainties and aleatory variabilities in a comprehensive and transparent way. The developed seismic hazard model incorporates significant improvements over previous versions. It is based on updated and extended databases, it includes robust methods to evolve sets of models representing epistemic uncertainties, and a selection of the latest generation of ground motion prediction equations. The new earthquake model is presented here, which consists of a logic tree with 4040 end branches and essential innovations employed for a realistic approach. The output specifications were designed according to the user oriented needs as suggested by two review teams supervising the entire project. Seismic load parameters, for rock conditions of \(v_{S30}\) = 800 m/s, are calculated for three hazard levels (10, 5 and 2% probability of occurrence or exceedance within 50 years) and delivered in the form of uniform hazard spectra, within the spectral period range 0.02–3 s, and seismic hazard maps for peak ground acceleration, spectral response accelerations and for macroseismic intensities. Results are supplied as the mean, the median and the 84th percentile. A broad analysis of resulting uncertainties of calculated seismic load parameters is included. The stability of the hazard maps with respect to previous versions and the cross-border comparison is emphasized.     

The Wadden Sea in transition - consequences of sea level rise

The impact of sea level rise (SLR) on the future morphological development of the Wadden Sea (North Sea) is investigated by means of extensive process-resolving numerical simulations. A new sediment and morphodynamic module was implemented in the well-established 3D circulation model GETM. A number of different validations are presented, ranging from an idealized 1D channel over a semi-idealized 2D Wadden Sea basin to a fully coupled realistic 40-year hindcast without morphological amplification of the Sylt-Rømøbight, a semi-enclosed subsystem of the Wadden Sea. Based on the results of the hindcast, four distinct future scenarios covering the period 2010–2100 are simulated. While these scenarios differ in the strength of SLR and wind forcing, they also account for an expected increase of tidal range over the coming century. The results of the future projections indicate a transition from a tidal-flat-dominated system toward a lagoon-like system, in which large fractions of the Sylt-Rømøbight will remain permanently covered by water. This has potentially dramatic implications for the unique ecosystem of the Wadden Sea. Although the simulations also predict an increased accumulation of sediment in the back-barrier basin, this accumulation is far too weak to compensate for the rise in mean sea level.     

The Deformational Response of a Viscoelastic Solid Earth Model Coupled to a Thermomechanical Ice Sheet Model

We apply a coupled thermomechanical ice sheet—self-gravitating viscoelastic solid Earth model (SGVEM), allowing for the dynamic exchange of ice thickness and bedrock deformation, in order to investigate the effect of viscoelastic deformation on ice dynamics and vice versa. In a synthetic glaciation scenario, we investigate the interaction between the ice sheet and the solid Earth deformation, the glacial-isostatic adjustment (GIA), accounting for an atmospheric forcing depending on the ice sheet surface altitude. We compare the results from the coupled model to runs with the common elastic lithosphere/relaxing asthenosphere (ELRA) model, where the lithosphere is represented by a thin plate and the mantle relaxes with one characteristic relaxation time, as well as to a rigid Earth without any deformation. We find that the deformational behaviour of the SGVEM on ice dynamics (i.e. stored ice volume, ice thickness and velocity field) is comparable to the ELRA for an optimal choice of the parameters in steady state, but exhibits differences in the transient behaviour. Beyond the ice sheet, in the region of peripheral forebulge, the differences in the transient surface deformation between ELRA and SGVEM are substantial, demonstrating the inadequacy of the ELRA model for interpreting constraints on GIA in the periphery of the ice sheet, such as sea-level indicators and GPS uplift rates.     

Forward induced seismic hazard assessment: application to a synthetic seismicity catalogue from hydraulic stimulation modelling

The M _w 3.2-induced seismic event in 2006 due to fluid injection at the Basel geothermal site in Switzerland was the starting point for an ongoing discussion in Europe on the potential risk of hydraulic stimulation in general. In particular, further development of mitigation strategies of induced seismic events of economic concern became a hot topic in geosciences and geoengineering. Here, we present a workflow to assess the hazard of induced seismicity in terms of occurrence rate of induced seismic events. The workflow is called Forward Induced Seismic Hazard Assessment (FISHA) as it combines the results of forward hydromechanical-numerical models with methods of time-dependent probabilistic seismic hazard assessment. To exemplify FISHA, we use simulations of four different fluid injection types with various injection parameters, i.e. injection rate, duration and style of injection. The hydromechanical-numerical model applied in this study represents a geothermal reservoir with preexisting fractures where a routine of viscous fluid flow in porous media is implemented from which flow and pressure driven failures of rock matrix and preexisting fractures are simulated, and corresponding seismic moment magnitudes are computed. The resulting synthetic catalogues of induced seismicity, including event location, occurrence time and magnitude, are used to calibrate the magnitude completeness M _c and the parameters a and b of the frequency-magnitude relation. These are used to estimate the time-dependent occurrence rate of induced seismic events for each fluid injection scenario. In contrast to other mitigation strategies that rely on real-time data or already obtained catalogues, we can perform various synthetic experiments with the same initial conditions. Thus, the advantage of FISHA is that it can quantify hazard from numerical experiments and recommend a priori a stimulation type that lowers the occurrence rate of induced seismic events. The FISHA workflow is rather general and not limited to the hydromechanical-numerical model used in this study and can therefore be applied to other fluid injection models.     

UV transit observations of EUV-heated expanded thermospheres of Earth-like exoplanets around M-stars: testing atmosphere evolution scenarios

The detection and investigation of EUV heated, extended and non-hydrostatic upper atmospheres around terrestrial exoplanets would provide important insights into the interaction of the host stars plasma environment as well as the evolution of Earth-type planets their atmospheres and possible magnetic environments. We discuss different scenarios where one can expect that Earth-like planets should experience non-hydrostatic upper atmosphere conditions so that dynamically outward flowing neutral atoms can interact with the stellar plasma flow so that huge hydrogen coronae and energetic neutral atoms (ENA) can be produced via charge exchange. By observing the size of the extended upper atmospheres and related ENA-clouds and by determining the velocities of the surrounding hydrogen atoms, conclusions can be drawn in respect to the origin of these features. Due to the large number of M-type stars in our neighbourhood and their long periods of strong and moderate stellar activity in comparison to G-stars, we expect that M-type stars represent the most promising candidates for the detection of hydrogen ENA-clouds and the subsequent study of the interaction between the host star and the planets?? upper atmosphere. We show that the low mass of M-type stars also makes them preferable targets to observe extended hydrogen clouds around terrestrial exoplanets with a mass as low as one Earth mass. Transit follow-up observations in the UV-range of terrestrial exoplanets around M-type stars with space observatories such as the World Space Observatory-UV (WSO-UV) would provide a unique opportunity to shed more light on the early evolution of Earth-like planets, including those of our own Solar System.     

Viscous ΛCDM universe models

We explore flat ΛCDM models with bulk viscosity, and study the role of the bulk viscosity in the evolution of these universe models. The dynamical equations for these models are obtained and solved for some cases of bulk viscosity. We obtain differential equations for the Hubble parameter H and the energy density of dark matter ρ _m , for which we give analytical solutions for some cases and for the general case we give a numerical solution. Also we calculate the statefinder parameters for these models and display them in the s–r-plane.     

Modelling Freshwater Resources at the Global Scale: Challenges and Prospects

Quantification of spatially and temporally resolved water flows and water storage variations for all land areas of the globe is required to assess water resources, water scarcity and flood hazards, and to understand the Earth system. This quantification is done with the help of global hydrological models (GHMs). What are the challenges and prospects in the development and application of GHMs? Seven important challenges are presented. (1) Data scarcity makes quantification of human water use difficult even though significant progress has been achieved in the last decade. (2) Uncertainty of meteorological input data strongly affects model outputs. (3) The reaction of vegetation to changing climate and CO₂ concentrations is uncertain and not taken into account in most GHMs that serve to estimate climate change impacts. (4) Reasons for discrepant responses of GHMs to changing climate have yet to be identified. (5) More accurate estimates of monthly time series of water availability and use are needed to provide good indicators of water scarcity. (6) Integration of gradient-based groundwater modelling into GHMs is necessary for a better simulation of groundwater–surface water interactions and capillary rise. (7) Detection and attribution of human interference with freshwater systems by using GHMs are constrained by data of insufficient quality but also GHM uncertainty itself. Regarding prospects for progress, we propose to decrease the uncertainty of GHM output by making better use of in situ and remotely sensed observations of output variables such as river discharge or total water storage variations by multi-criteria validation, calibration or data assimilation. Finally, we present an initiative that works towards the vision of hyperresolution global hydrological modelling where GHM outputs would be provided at a 1-km resolution with reasonable accuracy.     

The future of the western Baltic Sea: two possible scenarios

Globally coupled climate models are generally capable of reproducing the observed trends in the globally averaged atmospheric temperature. However, the global models do not perform as well on regional scales. Here, we present results from four 100-year, high-resolution ocean model experiments (resolution less than 1 km) for the western Baltic Sea. The forcing is taken from a regional atmospheric model and a regional ocean model, imbedded into two global greenhouse gas emission scenarios, A1B and B1, for the period of 2000 to 2100 with each two realisations. Two control runs from 1960 to 2000 are used for validation. For both scenarios, the results show a warming with an increase of 0.5–2.5 K at the sea surface and 0.7–2.8 K below 40 m. The simulations further indicate a decrease in salinity by 1.5–2 practical salinity units. The increase in water temperature leads to a prolongation of heat waves based on present-day thresholds. This amounts to a doubling or even tripling of the heat wave duration. The simulations show a decrease in inflow events (barotropic/baroclinic), which will affect the deepwater generation and ventilation of the central Baltic Sea. The high spatial resolution allows us to diagnose the inflow events and the mechanism that will cause future changes. The reduction in barotropic inflow events correlates well with the increase in westerly winds. The changes in the baroclinic inflows can be consistently explained by the reduction of calm wind periods and thus a weakening of the necessary stratification in the western Baltic Sea and the Danish Straits.