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Leibniz Institute for Science and Mathematics Education, Kiel

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  • Articles  (41)
  • 1
    Publication Date: 2018-03-16
    Description: Skillfully forecasting the intensity of flood events with advanced lead times is necessary for the issuing of flood warnings that subsequently provide adequate time for evacuations and infrastructural preparations. The ensemble mean is often used for deterministic guidance, but it is numerically demonstrated that the presence of large timing differences among ensemble members generates ensemble skewness that renders the ensemble mean an underestimate of the magnitude of an event. We show that one can associate to an ensemble forecast a complementary phase-aware ensemble forecast whose corresponding statistics are unaffected by timing differences among ensemble members. Corresponding to a phase-aware ensemble forecast is a phase-aware mean that remedies the magnitude underestimation problem of the ensemble mean. Uncertainty around the phase-aware mean is captured by phase-aware spread, which quantifies the spread of the magnitude of an event. We show that the uncertainty envelope associated with the phase-aware spread better preserves the structure of the individual ensemble member trajectories. The new methods were applied to storm surge reforecasts for Hurricanes Irene and Sandy at 13 stations located around the New York City metropolitan area. Consistent with theory, the phase-aware mean was found to be a better representation of storm surge magnitude than the ensemble mean. The phase-aware uncertainty envelopes around the phase-aware means were also found to depict the uncertainty of event magnitudes better than traditional uncertainty envelopes. The storm surge applications suggest that such methods should be incorporated into ensemble forecasting frameworks in which timing uncertainty is present, and thus a Matlab toolbox implementing the new methodology has been developed.
    Print ISSN: 0035-9009
    Electronic ISSN: 1477-870X
    Topics: Geography , Physics
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  • 2
    Publication Date: 2018-03-15
    Description: The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed. The aim is to investigate from a theoretical point of view the inefficiencies of this approach as observed in the application of the weakly-constrained 4D-Var algorithm in geosciences. Bounds on the eigenvalues of the preconditioned system matrix are provided. It highlights the interplay of the eigenstructures of both the model and weighting matrices: maintaining a low bound on the eigenvalues of the preconditioned system matrix requires an approximation error of the model matrix that compensates for the condition number of the weighting matrix. A low-dimension analytical example is given illustrating the resulting potential inefficiency of such preconditioners. Consequences of these results in the context of the state formulation of the weakly-constrained 4D-Var data assimilation problem are finally discussed. It is shown that the common approximations of the tangent linear model that maintain parallelization-in-time properties (identity or null matrix) can result in large bounds on the eigenvalues of the preconditioned matrix system.
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    Topics: Geography , Physics
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  • 3
    Publication Date: 2018-03-15
    Description: We present theoretical work directed toward improving our understanding of the mesoscale influence of deep convection on its tropospheric environment through forced gravity waves. From the linear, hydrostatic, non-rotating, incompressible equations, we find a two-dimensional analytical solution to prescribed heating in a stratified atmosphere, which is upwardly radiating from the troposphere when the domain lid is sufficiently high. We interrogate the spatial and temporal sensitivity of both the vertical velocity and potential temperature to different heating functions, considering both the near-field and remote responses to steady and pulsed heating. We find that the mesoscale tropospheric response to convection is significantly dependent on the upward radiation characteristics of the gravity waves, which are in turn dependent upon the temporal and spatial structure of the source, and the assumed stratification. We find a 50% reduction in tropospherically averaged vertical velocity when moving from a trapped (i.e. low lid) to upwardly-radiating (i.e. high lid) solution, but even with maximal upward radiation, we still observe significant tropospheric vertical velocities in the far-field 4 hours after heating ends. We quantify the errors associated with coarsening a 10 km wide heating to a 100 km grid (in the way a General Circulation Model (GCM) would), observing a 20% reduction in vertical velocity. The implications of these results for the parameterisation of convection in low-resolution numerical models are quantified and it is shown that the smoothing of heating over a grid-box leads to significant in grid-box tendencies, due to the erroneous rate of transfer of compensating subsidence to neighbouring regions. Further, we explore a simple time-dependent heating parameterisation that minimises error in a parent GCM grid box, albeit at the expense of increased error in the neighbourhood.
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    Topics: Geography , Physics
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  • 4
    Publication Date: 2018-03-15
    Description: This study explores the dynamic processes on intraseasonal timescales responsible for the devastating floods over the Yangtze Basin during June–August 1998. Wavelet analysis suggests that the unusual double Meiyu episodes over the south of the middle and lower reaches of the Yangtze River valley (SMLY) depended on the 25–60-day intraseasonal oscillation (ISO), which has an anomalous ascending branch over the SMLY and descending branch south of 20°N over eastern China. This vertical–meridional cell was not only regulated by the tropical ISO over the Asian summer monsoon region but also modulated by the mid-latitude ISO in the upper troposphere. The intraseasonal Rossby wave train along the Asian westerly jet, presenting as the anomalous anticyclone over the Tibetan Plateau (TP) sandwiched between anomalous cyclones in the upstream and downstream areas, tended to trigger another reversed vertical–meridional cell with updraft over the SMLY and downdraft to the north through vorticity advection. The phase-lock of these ascending branches over the SMLY produced the double Meiyu episodes. The duration of the SMLY flooding was also associated with the interactions between tropical and mid-latitude ISOs. During the first wet episode, as the tropical ISO-related upper-level divergent flows propagated northward to the southwestern TP, they tended to anchor the anticyclone over the TP through their interaction with the mid-latitude rotational circulation. This favored persistent ascent over the SMLY, and thus the prolonged Meiyu episode in June. In contrast, the northward propagation was confined to the central Bay of Bengal in July, leading to a short Meiyu episode.
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  • 5
    Publication Date: 2018-03-15
    Description: A new grid system on a sphere is proposed that allows for straightforward implementation of both spherical-harmonics-based spectral methods and gridpoint-based multigrid methods. The latitudinal gridpoints in the new grid are equidistant and spectral transforms in the latitudinal direction are performed using Clenshaw-Curtis quadrature. The spectral transforms with this new grid and quadrature are shown to be exact within the machine precision provided that the grid truncation is such that there are at least 2 N + 1 latitudinal gridpoints for the total truncation wavenumber of N . The new grid and quadrature is implemented and tested on a shallow-water equations model and the hydrostatic dry dynamical core of the global NWP model JMA-GSM. The integration results obtained with the new quadrature are shown to be almost identical to those obtained with the conventional Gaussian quadrature on Gaussian grid. Only minor code changes are required to adapt any Gaussian-based spectral models to employ the proposed quadrature.
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  • 6
    Publication Date: 2018-03-15
    Description: In this paper we propose finite volume schemes for solving the inviscid and viscous quasi-geostrophic equations on coastal-conforming unstructured primal-dual meshes. Several approaches for enforcing the boundary conditions are also explored along with these schemes. The pure transport part in these schemes are shown to conserve the potential vorticity along fluid paths in an averaged sense, and conserve the potential enstrophy up to the time truncation errors. Numerical tests based on the centroidal Voronoi-Delaunay meshes are performed to confirm these properties, and to distinguish the dynamical behaviors of these schemes. Finally some potential applications of these schemes in different situations are discussed.
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  • 7
    Publication Date: 2018-03-09
    Description: Verification in the presence of observation errors is approached form the Bayesian point of view. Like data assimilation (DA), Bayesian verification is shown to have a robust foundation established by Bayesian inference. Together, DA and Bayesian verification form two difference levels of Bayesian inference. Evaluation of a model is equivalent to inference on the plausibility of this model given observations. Relative performances between different models are measured by ratios of posterior plausibilities, which becomes ratios of likelihoods in case of no prior information. These ratios are called the Bayes factors and are the standard verification method in Bayesian model comparison. Since verification scores are used intensively in numerical weather prediction, the verification scores derived from likelihoods are proposed to replace the Bayes factors in Bayesian verification. With two requirements that the verification scores are both strictly proper and local, the logarithm score, i.e. log-likelihood, and its linear transformation are shown to be the unique class. Log-likelihoods in Bayesian verification are determined by the form of forecast probability distributions from models. The empirical form is preferable since its flexibility in incorporating not only observation errors but also other uncertainties in observation biases or observation error variances into calculation to obtain closed forms for log-likelihoods. When applied for observations with Gaussian errors, the logarithm score induces the weighted mean squared error which is non-dimensional and can be used for both univariate and multivariate observations. The most interesting application of Bayesian verification is to offer a new explanation for rank histograms and quantify the flatness of rank histograms by a metric which turns out to be the Kullback-Leibler divergence between the rank distribution observed in reality and a uniform rank distribution. It is worthy of note that the two very different metrics come from the logarithm score.
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  • 8
    Publication Date: 2018-03-09
    Description: Atmospheric mountain flows produced when the incoming wind is small near the surface and continuously increases with altitude are evaluated with models of increasing complexity. All models confirm that foehn can be produced by a mountain gravity wave critical level mechanism, where the critical level is located below the surface. This mechanism does not involve humidity, upper level wave breaking, upstream blocking, downward wave reflections or hydraulic control as often suggested by popular theories. The first model used is a theoretical model which combines linear gravity wave dynamics with a nonlinear boundary condition: in this model the wave breaking does not feedback onto the dynamics by construction. Partial linear waves reflection are also minimized by using smooth profiles of the incident wind and a uniform stratification N 2 = cte, and can even be suppressed when the incident wind shear is also constant, U z = cst. The second model is a numerical mesoscale model (Weather Research and Forecast), and we show that it predicts mountain wave fields that can be reproduced by the theoretical model, provided that we specify an adequate boundary layer depth in the theoretical model.
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  • 9
    Publication Date: 2018-03-09
    Description: This study presents turbulence kinetic energy (TKE) budget terms above tall, deciduous walnut canopy in the wintertime stable boundary layer (SBL) and makes a comparison to well-known results of horizontally-homogeneous and flat (HHF) terrain. Turbulence measurements performed at five levels above the canopy height (approximately h =18 m) enable the investigation of joint effect of the roughness sublayer (RSL) and the transition layer on the TKE budget terms. Each term of the TKE budget is investigated within the framework of local similarity theory. Kolomogorov’s similarity hypothesis assumes local isotropy within the inertial subrange. Thoroughly testing the local isotropy hypothesis for the present data set results in a ratio of the horizontal spectral densities ( S v / S u ) approaching 4/3 , while the ratio of the vertical to the longitudinal spectral density ( S w / S u ) is less than the canonical value of 4/3 (even less than 1) for all levels indicating anisotropic turbulence even at very small scales above the canopy. As a consequence, estimated values of TKE dissipation rate ( ε ) from the vertical component are smaller than those obtained from the horizontal velocity components. This finding has a direct influence on the applicability of classical Kansas spectral models valid for HHF terrain as well as on the budget of wind variances. Additionally, the behavior of the non-dimensional gradient of mean wind speed is tested with regard to conformity to z -less scaling requirements (i.e., linear dependence on stability). It is confirmed that a stability threshold (such as Rf  〉 0.25 , where Rf is the flux Richardson number) is a stronger determinant of z -less behavior than the existence of a well-defined inertial subrange - opposite to observations in the SBL over ideal flat surfaces. Finally, the local equilibrium between the production and destruction of TKE within the RSL and transition layer is analyzed.
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  • 10
    Publication Date: 2018-02-27
    Description: Mediterranean cyclones with tropical-like characteristics such as spiral cloud coverage and a central cloud-free ‘eye’ are referred as medicanes. These systems have been analyzed due to their relation with high impact weather. In previous studies, the identification of medicanes is typically performed subjectively, using satellite pictures, but also objectively through three-dimensional diagnosis of a warm core and an axisymmetric structure. Despite the presence of these characteristics, it is still unclear if medicanes present dynamical similarities with tropical cyclones. We analyse the (thermo-)dynamics of a recognized medicane that occurred in December 2005 by applying different diagnostics to a high resolution simulation. These diagnostics are focused on the intensification, dynamical structure and water budget of this representative case, aiming to highlight extratropical and tropical cyclone characteristics. Three stages in the medicane life-cycle are identified: In stage I, a potential vorticity (PV) streamer reaches the Mediterranean, triggering deep convection and deepening the medicane’s central surface pressure due to diabatic heating. When lowest central pressure intensity is reached (stage II), the medicane presents a warm-core and axisymmetric structure. However, convection is rather weak and the PV streamer evolves into a cut-off system that contributes to the deepening of the medicane’s surface pressure. Finally, stage III corresponds to the decay phase where the medicane tends to weaken and to lose its axisymmetric structure. Our results highlight the detrimental role of deep convection prior to medicanes mature stage, as well as the possibility of positive or negative feedback of upper tropospheric dynamics on their central surface pressure. In addition, we show that medicanes’ warm core might be achieved due to fronts seclusion, while the “eye" formation is associated with dry air intrusions. Our analysis suggests that medicanes are hybrid systems combining both characteristics of tropical and extratropical cyclones and thus they plausibly correspond to subtropical cyclones.
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