Modeling of the hydrological cycle in the integrated geophysical system

Hidrološki ciklus u integrisanom geofizičkom sistemu ima ulogu da simulira procese vezane za kopnene vode i međusobne interakcije komponenti klimatskog sistema koji opisuju kruženje vode u prirodi. Numerički modeli za prognozu vremena i simulaciju klime obuhvataju najveći deo ovih procesa i razvojem računarskih resursa postaju kompleksniji i prerastaju u modele za simulaciju celog geofizičkog sistema. Hidrološki ciklus u operativnim modelima nije zatvoren zbog nedostatka dinamičkog modela koji simulira kopneni oticaj vode. U ovom radu je predstavljen numerički model za simulaciju i prognozu površinskog oticaja koji direktno utiče na stanje podloge, što je donji granični uslov za atmosferske procese i prognozu vremena. Model je razvijen u skladu sa modelom za prognozu vremena poslednje generacije, NMMB, koji ima sposobnost da simulira procese od globalnih do lokalnih razmera. Testiranje numeričke ispravnosti nove komponente hidrološkog ciklusa kvalifikovalo ga je za povezivanje sa atmosferskim modelom. Povezani numerički model sa zatvorenim hidrološkim ciklusom otvara mogućnost za poboljšanje kvaliteta prognoza i klimatskih simulacija i uvodi nove prognostičke produkte koji mogu naći upotrebu u sistemima najava i upozorenja na ekstremne vremenske prilike. Upotreba ovakvog modela u operativnoj prognozi demonstrirana je na primeru simulacije majskih poplava 2014. godine u oblasti zapadnog Balkana. Povezani model je uspešno reprodukovao hidrološki ciklus ove vremenske nepogode, tj. intenzivne padavine, njihovo oticanje po površini i akumulaciju, uključujući njegovu interakciju sa podlogom i atmosferom, sve do porasta signala u rečnom toku, u skladu sa osmatranjimHydrological cycle in the integrated geophysical system simulates processes related to inland waters and interactions between the climate system components, that describes water cycle in its natural environment. Numerical models for weather forecast and climate simulations include majority of these processes and, following computer resource development, they are more complex and evolve into models of the integrated geophysical system. Hydrological cycle in operational numerical weather prediction models is not complete because dynamical overland water flow component is missing. Here is presented numerical model for simulation and forecast of the surface runoff, which has direct impact on land surface conditions and thereby lower boundary condition for atmospheric processes and weather forecast as well. The model is developed following numerical approach in the last generation weather forecast model, NMMB, which has the ability to simulate processes from global to local scales. Tests for numerical stability of the new hydrological cycle component justified its implementation within the atmospheric model. Coupled numerical model with complete water cycle opens new possibilities for quality increase in weather forecast and climate simulation, and introduces new prognostic products, which can be used in extreme weather warning system. Such model performance in operational forecast is demonstrated in case study of May 2014 flood event over west Balkans. Coupled model successfully simulated hydrological cycle in this extreme weather event with high precipitation, intense water surface runoff and accumulation, including its interaction with land surface and atmosphere, and at the end producing high signal in river discharge as observed

Method for efficient prevention of gravity wave decoupling on rectangular semi-staggered grids

Generation of short gravity wave noise often occurs on semi-staggered rectangular grids as a result of sub-grid decoupling when there is a strong forcing in the mass field. In this study a numerical scheme has been proposed to prevent the generation of the gravity wave decoupling. The proposed numerical method provides efficient communication between decoupled gravity wave finite-difference solutions by a simple averaging of a term in the height tendency in the continuity equation. The proposed method is tested using a shallow water sink model developed for the purpose of this study. It has been demonstrated that this method outperforms other existing approaches. The new scheme is time efficient, based on explicit time integration and can be easily implemented. The proposed method is applicable in hydrodynamic models specified on semi-staggered B or E grids

Variational multiscale stabilization of finite and spectral elements for dry and moist atmospheric problems

In this thesis the finite and spectral element methods (FEM and SEM, respectively) applied to problems in atmospheric simulations are explored through the common thread of Variational Multiscale Stabilization (VMS). This effort is justified by three main reasons. (i) the recognized need for new solvers that can efficiently execute on massively parallel architectures ¿a spreading framework in most fields of computational physics in which numerical weather prediction (NWP) occupies a prominent position. Element-based methods (e.g. FEM, SEM, discontinuous Galerkin) have important advantages in parallel code development; (ii) the inherent flexibility of these methods with respect to the geometry of the grid makes them a great candidate for dynamically adaptive atmospheric codes; and (iii) the localized diffusion provided by VMS represents an improvement in the accurate solution of multi-physics problems where artificial diffusion may fail. Its application to atmospheric simulations is a novel approach within a field of research that is still open. First, FEM and VMS are described and derived for the solution of stratified low Mach number flows in the context of dry atmospheric dynamics. The validity of the method to simulate stratified flows is assessed using standard two- and three-dimensional benchmarks accepted by NWP practitioners. The problems include thermal and gravity driven simulations. It will be shown that stability is retained in the regimes of interest and a numerical comparison against results from the the literature will be discussed. Second, the ability of VMS to stabilize the FEM solution of advection-dominated problems (i.e. Euler and transport equations) is taken further by the implementation of VMS as a stabilizing tool for high-order spectral elements with advection-diffusion problems. To the author¿s knowledge, this is an original contribution to the literature of high order spectral elements involved with transport in the atmosphere. The problem of monotonicity-preserving high order methods is addressed by combining VMS-stabilized SEM with a discontinuity capturing technique. This is an alternative to classical filters to treat the Gibbs oscillations that characterize high-order schemes. To conclude, a microphysics scheme is implemented within the finite element Euler solver, as a first step toward realistic atmospheric simulations. Kessler microphysics is used to simulate the formation of warm, precipitating clouds. This last part combines the solution of the Euler equations for stratified flows with the solution of a system of transport equations for three classes of water: water vapor, cloud water, and rain. The method is verified using idealized two- and three-dimensional storm simulations.En esta tesis los métodos de elementos finitos y espectrales (FEM - finite element method y SEM- spectral element method, respectivamente), aplicados a los problemas de simulaciones atmosféricas, se exploran a través del método de estabilización conocidocomo Variational Multiscale Stabilization (VMS). Tres razones fundamentales justifican este esfuerzo: (i) la necesidad de tener nuevos métodos de solución de las ecuaciones diferenciales a las derivadas parciales usando máquinas paralelas de gran escala –un entorno en expansión en muchos campos de la mecánica computacional, dentro de la cual la predicción numérica de la dinámica atmosférica (NWP-numerical weather prediction)representa una aplicación importante. Métodos del tipo basado en elementos(por ejemplo, FEM, SEM, Galerkin discontinuo) presentan grandes ventajas en el desarrollo de códigos paralelos; (ii) la flexibilidad intrínseca de tales métodos respecto a lageometría de la malla computacional hace que esos métodos sean los candidatos ideales para códigos atmosféricos con mallas adaptativas; y (iii) la difusión localizada que VMSintroduce representa una mejora en las soluciones de problemas con física compleja en los cuales la difusión artificial clásica no funcionaría. La aplicación de FEM o SEM con VMS a problemas de simulaciones atmosféricas es una estrategia innovadora en un campo de investigación abierto. En primera instancia, FEM y VMS vienen descritos y derivados para la solución de flujos estratificados a bajo número de Mach en el contexto de la dinámica atmosférica. La validez del método para simular flujos estratificados es verificada por medio de test estándar aceptado por la comunidad dentro del campo deNWP. Los test incluyen simulaciones de flujos térmicos con efectos de gravedad. Se demostrará que la estabilidad del método numérico se preserva dentro de los regímenesde interés y se discutirá una comparación numérica de los resultados frente a aquellos hallados en la literatura. En segunda instancia, la capacidad de VMS para estabilizarmétodos FEM en problemas de advección dominante (i.e. ecuaciones de Euler y ecuaciones de transporte) se implementa además en la solución a elementos espectrales de alto orden en problemas de advección-difusión. Hasta donde el autor sabe, esta es una contribución original a la literatura de métodos basados en elementos espectrales en problemas de transporte atmosférico. El problema de monotonicidad con métodos de alto orden es tratado mediante la combinación de SEM+VMS con una técnica de shockcapturing para un mejor tratamiento de las discontinuidades. Esta es una alternativa a los filtros que normalmente se aplican a SEM para eilminar las oscilaciones de Gibbsque caracterizan las soluciones de alto orden. Como último punto, se implementa un esquema de humedad acoplado con el núcleo en elementos finitos; este es un primer paso hacia simulaciones atmosféricas más realistas. La microfísica de Kessler se emplea para simular la formación de nubes y tormentas cálidas (warm clouds: no permite la formación de hielo). Esta última parte combina la solución de las ecuaciones de Eulerpara atmósferas estratificadas con la solución de un sistema de ecuaciones de transporte de tres estados de agua: vapor, nubes y lluvia. La calidad del método es verificadautilizando simulaciones de tormenta en dos y tres dimensiones