Towards lattice Boltzmann models for climate sciences : The GeLB programming language with applications

The complexity of Earth system models (ESMs) is continuously increasing a both quantitatively (higher spatio-temporal resolution for existing models) and qualitatively (accounting for additional processes). These trends are sustained by growing capabilities of computers and (equally important) by innovative algorithms. Better algorithms can lead to more accurate and/or more efficient numerical solutions. Efficiency attracted more attention during the last decade when, due to thermal limitations, the driving force behind increased computing performance has shifted from higher clock-frequencies (lower latencies) to more hardware parallelism (higher throughput). Not all numerical algorithms are suited for the new massively-parallel machines a some established approaches can reach plateaus in terms of performance scalability, which motivates ongoing research to find alternatives that thrive on the new hardware. In this thesis the potential of the lattice Boltzmann method (LBM) is analyzed, as a promising alternative for modeling processes relevant to ESMs . During the last two decades, this relatively new approach was successfully applied to many flow problems in engineering (simulation of multi-phase and multi-component flows, melting processes, flows in porous media, and direct numerical simulation (DNS) of turbulence). At the core of any LBM algorithm is a simplified physical landscape inspired by the kinetic theory of gases, with a mesoscopica particles which interact (collisions) and then propagate freely (streaming). This idealized dynamics (usually with local interactions) leads to algorithms which are particularly suited for parallel execution a a key property, which is also interesting for ESMs . However, the impact of LBM on Earth system models was small so far, due to limitations of the early LBM algorithms. The method deserves reconsideration, due to recent advances on improving its stability, a simplified implementation of accurate body-forces, and accurate simulation of thermal flows. This thesis adds two main contributions to this direction: (a) From a computer science (CS) / technical perspective, the new GeLB domain-specific language (DSL) is introduced, to facilitate testing and development of new LBM algorithms. By isolating many of the technical implementation side-issues away from the core physical algorithm, this new tool aims to counteract some of the a fragmentationa of the LBM research, by: (i) shortening the time to develop a parallel simulation from an algorithm idea, (ii) serving as a basis for objective comparisons of different physical algorithms, and by (iii) facilitating sharing of algorithms. (b) From a physical point of view, several flow-problems related to climate sciences are simulated, taking advantage of the recent progress in the LBM research literature. First, the Rayleigh-Benard ( RB ) problem is simulated (in 2D and 3D configurations). The evolution of the flow in this problem is driven by buoyancy forces which can trigger convection (similar to convection in the atmosphere, or to the intermittent bursts of deep-reaching convection, which significantly influence the composition and circulation of oceanic water-masses). As a last application, simulation results are shown for the wind-driven ocean circulation (WDOC) of an idealized barotropic ocean, to which one of the more recent LBM algorithms is applied for the first time (first with an idealized geometry, then with a realistic global land-mask)

A graphic method for depicting horizontal direction data on vertical outcrop photographs

Outcrop photographs which show two-dimensional representations of three-dimensionally dipping surfaces (e.g., bedding planes, cross-bed foresets) are commonly utilized in the description of sedimentary strata. In many instances, accurate depiction of the dip direction of such features is paramount for understanding their interpretation, and for visualizing the true form of three-dimensional bodies (e.g., conceptualizing the form of an architectural element in a cliff-face, preserved as a vertical slice that has been cut oblique to paleocurrent direction). However, as an outcrop photograph often presents information on a vertical plane and directional data refers to a horizontal plane, the accurate co-depiction of both sets of information may be challenging. There is presently no universal method for illustrating such measurements on outcrop photographs: techniques in common usage are often imprecise, and the lack of uniformity hinders comparison between different images. Here we present a method for accurately depicting horizontal direction data on vertical outcrop photographs which permits instant visualization of dip relative to the illustrated outcrop geometry. The method is simple to apply, does not compromise primary data, and is unobtrusive to other visual information within images; thus having utility across a broad spectrum of geological investigations

Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems

Simulating complex physical systems often involves solving partial differential equations (PDEs) with some closures due to the presence of multi-scale physics that cannot be fully resolved. Although the advancement of high performance computing has made resolving small-scale physics possible, such simulations are still very expensive. Therefore, reliable and accurate closure models for the unresolved physics remains an important requirement for many computational physics problems, e.g., turbulence simulation. Recently, several researchers have adopted generative adversarial networks (GANs), a novel paradigm of training machine learning models, to generate solutions of PDEs-governed complex systems without having to numerically solve these PDEs. However, GANs are known to be difficult in training and likely to converge to local minima, where the generated samples do not capture the true statistics of the training data. In this work, we present a statistical constrained generative adversarial network by enforcing constraints of covariance from the training data, which results in an improved machine-learning-based emulator to capture the statistics of the training data generated by solving fully resolved PDEs. We show that such a statistical regularization leads to better performance compared to standard GANs, measured by (1) the constrained model's ability to more faithfully emulate certain physical properties of the system and (2) the significantly reduced (by up to 80%) training time to reach the solution. We exemplify this approach on the Rayleigh-Bénard convection, a turbulent flow system that is an idealized model of the Earth's atmosphere. With the growth of high-fidelity simulation databases of physical systems, this work suggests great potential for being an alternative to the explicit modeling of closures or parameterizations for unresolved physics, which are known to be a major source of uncertainty in simulating multi-scale physical systems, e.g., turbulence or Earth's climate

Prostate Imaging Reporting and Data System score (PI-RADS) and Glutathione S-transferase P1 methylation status (GST-P1) in the diagnosis of prostate cancer patients with borderline PSA values

Objectives. The objective of this study was to evaluate the potential use of Prostate Imaging – Reporting and Data System version 2 (PI-RADS) in combination with Glutathione S-transferase P1 (GST-P1) expression for an improved diagnosis of prostate cancer, in patients with inconclusive values of prostate-specific antigen (PSA). Materials and Methods. The study was conducted on 80 patients for whom PSA values were evaluated and were found to be inconclusive (4-10 ng/ml). These patients underwent imagistic evaluation (PI-RADS), followed by transurethral prostate biopsy, with the evaluation of GST-P1 expression and histopathological examination (for diagnosis confirmation). Results. By combining the results of PI-RADS and GST-P1 the capacity of the tests to correctly identify healthy subjects, with an area under curve of 0,832 (95% CI 0.732–0.907), with a sensitivity of 73,25% and a specificity of 77,78%. Conclusions. PI-RADS lesions and GST-P1 methylation testing when PSA levels are in a “grey zone”, provide a better specificity and sensitivity by comparison through single testing. Testing patients with inconclusive PSA levels allows for a more accurate diagnosis and less over-diagnosis by non-invasive procedures, such as repeated biopsies

Zu Gitter-Boltzmann-Modellen für die Klimawissenschaften : Die GeLB-Programmiersprache mit Anwendungen

The complexity of Earth system models (ESMs) is continuously increasing a both quantitatively (higher spatio-temporal resolution for existing models) and qualitatively (accounting for additional processes). These trends are sustained by growing capabilities of computers and (equally important) by innovative algorithms. Better algorithms can lead to more accurate and/or more efficient numerical solutions. Efficiency attracted more attention during the last decade when, due to thermal limitations, the driving force behind increased computing performance has shifted from higher clock-frequencies (lower latencies) to more hardware parallelism (higher throughput). Not all numerical algorithms are suited for the new massively-parallel machines a some established approaches can reach plateaus in terms of performance scalability, which motivates ongoing research to find alternatives that thrive on the new hardware. In this thesis the potential of the lattice Boltzmann method (LBM) is analyzed, as a promising alternative for modeling processes relevant to ESMs . During the last two decades, this relatively new approach was successfully applied to many flow problems in engineering (simulation of multi-phase and multi-component flows, melting processes, flows in porous media, and direct numerical simulation (DNS) of turbulence). At the core of any LBM algorithm is a simplified physical landscape inspired by the kinetic theory of gases, with a mesoscopica particles which interact (collisions) and then propagate freely (streaming). This idealized dynamics (usually with local interactions) leads to algorithms which are particularly suited for parallel execution a a key property, which is also interesting for ESMs . However, the impact of LBM on Earth system models was small so far, due to limitations of the early LBM algorithms. The method deserves reconsideration, due to recent advances on improving its stability, a simplified implementation of accurate body-forces, and accurate simulation of thermal flows. This thesis adds two main contributions to this direction: (a) From a computer science (CS) / technical perspective, the new GeLB domain-specific language (DSL) is introduced, to facilitate testing and development of new LBM algorithms. By isolating many of the technical implementation side-issues away from the core physical algorithm, this new tool aims to counteract some of the a fragmentationa of the LBM research, by: (i) shortening the time to develop a parallel simulation from an algorithm idea, (ii) serving as a basis for objective comparisons of different physical algorithms, and by (iii) facilitating sharing of algorithms. (b) From a physical point of view, several flow-problems related to climate sciences are simulated, taking advantage of the recent progress in the LBM research literature. First, the Rayleigh-Benard ( RB ) problem is simulated (in 2D and 3D configurations). The evolution of the flow in this problem is driven by buoyancy forces which can trigger convection (similar to convection in the atmosphere, or to the intermittent bursts of deep-reaching convection, which significantly influence the composition and circulation of oceanic water-masses). As a last application, simulation results are shown for the wind-driven ocean circulation (WDOC) of an idealized barotropic ocean, to which one of the more recent LBM algorithms is applied for the first time (first with an idealized geometry, then with a realistic global land-mask)

Introduction to Modern Fortran for Earth System Sciences

This work provides a short "getting started" guide to Fortran 90/95. The main target audience consists of newcomers to the field of numerical computation within Earth system sciences (students, researchers or scientific programmers). Furthermore, readers accustomed to other programming languages may also benefit from this work, by discovering how some programming techniques they are familiar with map to Fortran 95

Trends and Correlation Estimation in Climate Sciences: Effects of Timescale Errors

Trend describes time-dependence in the first moment of a stochastic process, and correlation measures the linear relation between two random variables. Accurately estimating the trend and correlation, including uncertainties, from climate time series data in the uni- and bivariate domain, respectively, allows first-order insights into the geophysical process that generated the data. Timescale errors, ubiquitious in paleoclimatology, where archives are sampled for proxy measurements and dated, poses a problem to the estimation. Statistical science and the various applied research fields, including geophysics, have almost completely ignored this problem due to its theoretical almost-intractability. However, computational adaptations or replacements of traditional error formulas have become technically feasible. This contribution gives a short overview of such an adaptation package, bootstrap resampling combined with parametric timescale simulation. We study linear regression, parametric change-point models and nonparametric smoothing for trend estimation. We introduce pairwise-moving block bootstrap resampling for correlation estimation. Both methods share robustness against autocorrelation and non-Gaussian distributional shape. We shortly touch computing-intensive calibration of bootstrap confidence intervals and consider options to parallelize the related computer code. Following examples serve not only to illustrate the methods but tell own climate stories: (1) the search for climate drivers of the Agulhas Current on recent timescales, (2) the comparison of three stalagmite-based proxy series of regional, western German climate over the later part of the Holocene, and (3) trends and transitions in benthic oxygen isotope time series from the Cenozoic. Financial support by Deutsche Forschungsgemeinschaft (FOR 668, FOR 1070, MU 1595/4-1) and the European Commission (MC ITN 238512, MC ITN 289447) is acknowledged