Estimativa do erro de discretização analítico na solução de equações diferenciais utilizando o Método de Volumes Finitos

As análises de erros são conduzidas antes de qualquer projeto a ser desenvolvido. A necessidade do conhecimento do comportamento do erro numérico em malhas estruturadas e não-estruturadas surge com o aumento do uso destas malhas nos métodos de discretização. Desta forma, o objetivo deste trabalho foi criar uma metodologia para analisar os erros de discretização gerados através do truncamento na Série de Taylor, aplicados às equações de Poisson e de Advecção-Difusão estacionárias uni e bidimensionais, utilizando-se o Método de Volumes Finitos em malhas do tipo Voronoi. A escolha dessas equações se dá devido a sua grande utilização em testes de novos modelos matemáticos e função de interpolação. Foram usados os esquemas Central Difference Scheme (CDS) e Upwind Difference Scheme(UDS) nos termos advectivos. Verificou-se a influência do tipo de condição de contorno e a posição do ponto gerador do volume na solução numérica. Os resultados analíticos foram confrontados com resultados experimentais para dois tipos de malhas de Voronoi, uma malha cartesiana e outra triangular comprovando a influência da forma do volume finito na solução numérica obtida. Foi percebido no estudo que a discretização usando o esquema CDS tem erros menores do que a discretização usando o esquema UDS conforme literatura. Também se percebe a diferença nos erros em volumes vizinhos nas malhas triangulares o que faz com que não se tenha uma uniformidade nos gráficos dos erros estudados. Percebeu-se que as malhas cartesianas com nó no centróide do volume tem menor erro de discretização do que malhas triangulares. Mas o uso deste tipo de malha depende da geometria do problema estudado

Dynamics of the East Asian Summer Monsoon in Present and Future Climates

This thesis aims at enhancing our fundamental understanding of the East Asian summer monsoon (EASM), and mechanisms implicated in its climatology in present-day and warmer climates. We focus on the most prominent feature of the EASM, i.e., the so-called Meiyu-Baiu (MB), which is characterized by a well-defined, southwest to northeast elongated quasi-stationary rainfall band, spanning from eastern China to Japan and into the northwestern Pacific Ocean in June and July.

We begin with an observational study of the energetics of the MB front in present-day climate. Analyses of the moist static energy (MSE) budget of the MB front indicate that horizontal advection of moist enthalpy, primarily of dry enthalpy, sustains the front in a region of otherwise negative net energy input into the atmospheric column. A decomposition of the horizontal dry enthalpy advection into mean, transient, and stationary eddy fluxes identifies the longitudinal thermal gradient due to zonal asymmetries and the meridional stationary eddy velocity as the most influential factors determining the pattern of horizontal moist enthalpy advection. Numerical simulations in which the Tibetan Plateau (TP) is either retained or removed show that the TP influences the stationary enthalpy flux, and hence the MB front, primarily by changing the meridional stationary eddy velocity, with reinforced southerly wind on the northwestern flank of the north Pacific subtropical high (NPSH) over the MB region and northerly wind to its north. Changes in the longitudinal thermal gradient are mainly confined to the near downstream of the TP, with the resulting changes in zonal warm air advection having a lesser impact on the rainfall in the extended MB region.

Similar mechanisms are shown to be implicated in present climate simulations in the Couple Model Intercomparison Project - Phase 5 (CMIP5) models. We find that the spatial distribution of the EASM precipitation simulated by different models is highly correlated with the meridional stationary eddy velocity. The correlation becomes more robust when energy fluxes into the atmospheric column are considered, consistent with the observational analyses. The spread in the area-averaged rainfall amount can be partially explained by the spread in the simulated globally-averaged precipitation, with the rest primarily due to the lower-level meridional wind convergence. Clear relationships between precipitation and zonal and meridional eddy velocities are observed.

Finally, the response of the EASM to greenhouse gas forcing is investigated at different time scales in CMIP5 model simulations. The reduction of radiative cooling and the increase in continental surface temperature occur much more rapidly than changes in sea surface temperatures (SSTs). Without changes in SSTs, the rainfall in the monsoon region decreases (increases) over ocean (land) in most models. On longer time scales, as SSTs increase, rainfall changes are opposite. The total response to atmospheric CO^2 forcing and subsequent SST warming is a large (modest) increase in rainfall over ocean (land) in the EASM region. Dynamic changes, in spite of significant contributions from the thermodynamic component, play an important role in setting up the spatial pattern of precipitation changes. Rainfall anomalies over East China are a direct consequence of local land-sea contrast, while changes in the larger-scale oceanic rainfall band are closely associated with the displacement of the larger-scale NPSH. Numerical simulations show that topography and SST patterns play an important role in rainfall changes in the EASM region.

Stationary Eddies and Zonal Variations of the Global Hydrological Cycle in a Changing Climate

This thesis advances our physical understanding of the sensitivity of the hydrological cycle to global warming. Specifically, it focuses on changes in the longitudinal (zonal) variation of precipitation minus evaporation (P - E), which is predominantly controlled by planetary-scale stationary eddies. By studying idealized general circulation model (GCM) experiments with zonally varying boundary conditions, this thesis examines the mechanisms controlling the strength of stationary-eddy circulations and their role in the hydrological cycle. The overarching goal of this research is to understand the cause of changes in regional P - E with global warming. An understanding of such changes can be useful for impact studies focusing on water availability, ecosystem management, and flood risk.

Based on a moisture-budget analysis of ERA-Interim data, we establish an approximation for zonally anomalous P - E in terms of surface moisture content and stationary-eddy vertical motion in the lower troposphere. Part of the success of this approximation comes from our finding that transient-eddy moisture fluxes partially cancel the effect of stationary-eddy moisture advection, allowing divergent circulations to dominate the moisture budget. The lower-tropospheric vertical motion is related to horizontal motion in stationary eddies by Sverdrup and Ekman balance. These moisture- and vorticity-budget balances also hold in idealized and comprehensive GCM simulations across a range of climates.

By examining climate changes in the idealized and comprehensive GCM simulations, we are able to show the utility of the vertical motion P - E approximation for splitting changes in zonally anomalous P - E into thermodynamic and dynamic components. Shifts in divergent stationary-eddy circulations dominate changes in zonally anomalous P - E. This limits the local utility of the "wet gets wetter, dry gets drier” idea, where existing P - E patterns are amplified with warming by the increase in atmospheric moisture content, with atmospheric circulations held fixed. The increase in atmospheric moisture content manifests instead in an increase in the amplitude of the zonally anomalous hydrological cycle as measured by the zonal variance of P - E. However, dynamic changes, particularly the slowdown of divergent stationary-eddy circulations, limit the strengthening of the zonally anomalous hydrological cycle. In certain idealized cases, dynamic changes are even strong enough to reverse the tendency towards "wet gets wetter, dry gets drier” with warming.

Motivated by the importance of stationary-eddy vertical velocities in the moisture budget analysis, we examine controls on the amplitude of stationary eddies across a wide range of climates in an idealized GCM with simple topographic and ocean-heating zonal asymmetries. An analysis of the thermodynamic equation in the vicinity of topographic forcing reveals the importance of on-slope surface winds, the midlatitude isentropic slope, and latent heating in setting the amplitude of stationary waves. The response of stationary eddies to climate change is determined primarily by the strength of zonal surface winds hitting the mountain. The sensitivity of stationary-eddies to this surface forcing increases with climate change as the slope of midlatitude isentropes decreases. However, latent heating also plays an important role in damping the stationary-eddy response, and this damping becomes stronger with warming as the atmospheric moisture content increases. We find that the response of tropical overturning circulations forced by ocean heat-flux convergence is described by changes in the vertical structure of moist static energy and deep convection. This is used to derive simple scalings for the Walker circulation strength that capture the monotonic decrease with warming found in our idealized simulations.

Through the work of this thesis, the advances made in understanding the amplitude of stationary-waves in a changing climate can be directly applied to better understand and predict changes in the zonally anomalous hydrological cycle.

Análise de erros da equação de advecção unidimensional no Método de Volumes Finitos

Uma análise utilizando a série de Taylor é apresentada para se estimar a priori os erros envolvidos na solução numérica da equação de advecção unidimensional com termo fonte, através do Método dos Volumes Finitos em uma malha do tipo uniforme e uma malha não uniforme. Também faz-se um estudo a posteriori para verificar a magnitude do erro de discretização e corroborar os resultados obtidos através da análise a priori. Por meio da técnica de solução manufaturada tem-se uma solução analítica para o problema, a qual facilita a análise dos resultados numéricos encontrados, e estuda-se ainda a influência das funções de interpolação UDS e CDS e do parâmetro u na solução numérica.

Hypoxic and low pH water in the nearshore marine environments of Monterey Bay, California: characterizing a decade of oxygen and pH, and drivers of variability.

A decade-long time series recorded in southern Monterey Bay, California demonstrates that the shallow, near-shore environment (17 m depth) is regularly inundated with pulses of cold, hypoxic and low pH water. During these episodes, oxygen can drop to biologically threatening levels, and pH levels were lower than expected. Weekly water chemistry monitoring revealed that the saturation state of aragonite (the more soluble form of calcium carbonate) was often below saturation and had a moderate positive relationship with pH, however, analytical and human error could be high. Pulses of hypoxia and low pH water with the greatest intensity arise at the onset of the spring upwelling season, and fluctuations are strongly semidurnal (tidal) and diurnal. Arrival of cold, hypoxic water on the inner shelf typically occurs 3 days after the arrival of a strong upwelling event and appears to be driven by upwelling modulated by internal tidal fluctuations. I found no relationship between the timing of low-oxygen events and the diel solar cycle nor with terrestrial nutrient input. These observations are consistent with advection of hypoxic water from the deep, offshore environment where water masses experience a general decline of temperature, oxygen and pH with depth, and inconsistent with biochemical forcing. Comparisons with concurrent temperature and oxygen time series taken ~20 km away at the head of the Monterey Canyon show similar patterns but even more intense hypoxic events due to stronger semidiurnal forcing there. Analysis of the durations of exposure to low oxygen levels establishes a framework for assessing the ecological relevance of these events. Increasing oceanic hypoxia and acidification of both surface and deep waters may increase the number, intensity, duration and spatial extent of future intrusions along the Pacific coast. Evaluation of the resiliency of nearshore ecosystems such as kelp forests, rocky reefs and sandy habitats, will require consideration of these events.

Onshore-offshore distribution and abundance of tuna larvae (Pisces: Scombridae: Thunnini) in near-reef waters of the Coral Sea

The on-offshore distributions of tuna larvae in near-reef waters of the Coral Sea, near Lizard Island (14°30ʹS, 145°27ʹE), Australia, were investigated during four cruises from November 1984 to February 1985 to test the hypothesis that larvae of these oceanic fishes are found in highest abundance near coral reefs. Oblique bongo net tows were made in five on-offshore blocks in the Coral Sea, ranging from 0–18.5 km offshore of the outer reefs of the Great Barrier Reef, as well as inside the Great Barrier Reef Lagoon. The smallest individuals (<3.2 mm SL) of the genus Thunnus could not be identified to species, and are referred to as Thunnus spp. We found species-specific distributional patterns. Thunnus spp. and T. alalunga (albacore) larvae were most abundant (up to 68 larvae/100 m2) in near-reef (0–5.5 km offshore) waters, whereas Katsuwonus pelamis (skipjack tuna) larvae increased in abundance in the offshore direction (up to 228 larvae/100 m2, 11.1–18.5 km offshore). Larvae of T. albacares (yellowfin tuna) and Euthynnus affinis (kawakawa) were relatively rare throughout the study region, and the patterns of their distributions were inconclusive. Few larvae of any tuna species were found in the lagoon. Size-frequency distributions revealed a greater proportion of small larvae inshore compared to offshore for K. pelamis and T. albacares. The absence of significant differences in size-frequency distributions for other species and during the other cruises was most likely due to the low numbers of larvae. Larval distributions probably resulted from a combination of patterns of spawning and vertical distribution, combined with wind-driven onshore advection and downwelling on the seaward side of the outer reefs.

Time-resolved volumetric measurement of fine-scale coherent structures in turbulence.

We present full volumetric (three-dimensional) time-resolved (+one-dimensional) measurements of the velocity field in a large water mixing tank, allowing us to assess spatial and temporal rotational energy (enstrophy) and turbulent energy dissipation intermittency. In agreement with previous studies, highly intermittent behavior is observed, with intense coherent flow structures clustering in the periphery of larger vortices. However, further to previous work the full volumetric measurements allow us to separate out the effects of advection from other effects, elucidating not only their topology but also the evolution of these intense events, through the local balance of stretching and diffusion. These findings contribute toward a better understanding of the intermittency phenomenon, which should pave the way for more accurate models of the small-scale motions based on an understanding of the underlying flow physics.

Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations. © 2012 Society for Industrial and Applied Mathematics.

Application of the characteristic CIP method to a shallow water model on the sphere

Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directly using a semi-Lagrangian advection scheme instead of the semi-implicit method in a shallow water model, to avoid expensive matrix inversions. Adoption of the semi-Lagrangian scheme renders the numerical model always stable for any Courant number, and which saves CPU time. To illustrate the efficiency of the characteristic constrained interpolation profile (CIP) method, some numerical results are shown for idealized test cases on a sphere in the Yin-Yang grid system.

A model study on carbon cycle and phytoplankton dynamical processes in the Bohai Sea

The carbon cycle of lower trophic level in the Bohai Sea is studied with a three-dimension-al biological and physical coupled model. The influences of the processes (including horizontal advection,river nutrient load, active transport etc. ) on the phytoplankton biomass and its evolution are estimated.The Bohai Sea is a weak sink of the CO2 in the atmosphere. During the cycle, 13.7% of the gross pro-duction of the phytoplankton enter the higher trophic level and 76.8 % of it are consumed by the respira-tion itself. The nutrient reproduction comes mainly from the internal biogeochemical loop and the rem-ineralization is an important mechanism of the nutrient transfer from organic form to inorganic. Horizon-tal advection decreases the total biomass and the eutrophication in some sea areas. Change in the nutrientload of a river can only adjust the local system near its estuary. Controlling the input of the nutrient,which limits the alga growth, can be very useful in lessening the phytoplankton biomass.

Geophysical signatures associated with fluid flow and gas hydrate occurrence in a tectonically quiescent sequence, Qiongdongnan Basin, South China Sea

Interpretation of high-resolution two-dimensional (2D) and three-dimensional (3D) seismic data collected in the Qiongdongnan Basin, South China Sea reveals the presence of polygonal faults, pockmarks, gas chimneys and slope failure in strata of Pliocene and younger age. The gas chimneys are characterized by low-amplitude reflections, acoustic turbidity and low P-wave velocity indicating fluid expulsion pathways. Coherence time slices show that the polygonal faults are restricted to sediments with moderate-amplitude, continuous reflections. Gas hydrates are identified in seismic data by the presence of bottom simulating reflectors (BSRs), which have high amplitude, reverse polarity and are subparallel to seafloor. Mud diapirism and mounded structures have variable geometry and a great diversity regarding the origin of the fluid and the parent beds. The gas chimneys, mud diapirism, polygonal faults and a seismic facies-change facilitate the upward migration of thermogenic fluids from underlying sediments. Fluids can be temporarily trapped below the gas hydrate stability zone, but fluid advection may cause gas hydrate dissociation and affect the thickness of gas hydrate zone. The fluid accumulation leads to the generation of excess pore fluids that release along faults, forming pockmarks and mud volcanoes on the seafloor. These features are indicators of fluid flow in a tectonically-quiescent sequence, Qiongdongnan Basin. Geofluids (2010) 10, 351-368.

Characteristics and flux of settling particulate matter in neritic waters: The southern Yellow Sea and the East China Sea

The typology and flux of settling particulate matter (SPM) were investigated based on sediment trap sampling at six typical stations in the Yellow Sea and the East China Sea. The settling particulate matter in the neritic seas was sorted into three categories, lithogenic particles, living organisms, and particle aggregates. The mass of individual organisms is an important portion of particulate matter in the neritic waters. The aggregates contain six types, mucus aggregates, fecal pellets, diatom aggregates, silicoflagellate aggregates, tintinnids, and miscellaneous aggregates, of which the silicoflagellate aggregates and tintinnids are the most abundant in the Yellow Sea and the East China Sea. High particle fluxes, such as 215 to 874 g m(-2). day(-1) SPM in the bottom layer, were found at three stations where the water was well mixed, and the maximum flux was detected in the boundary area between the Yellow Sea and the East China Sea, where a wide nepheloid layer was present. Hence, particle flux in neritic waters can be easily shifted by water turbulence. The net vertical flux (123 to 961 mg C day(-1)), the contribution of lateral advection to resuspension flux (5 to 76%), and the particulate organic carbon export ratio (18 to 60%) were estimated for the other three stations where the water was stratified. The highest values were all found in the upwelling area off the Zhejiang coast, suggesting that the area of high productivity provides a high net vertical flux of SPM. (C) 2010 Elsevier Ltd. All rights reserved.

Effect of low-frequency Rossby wave on thermal structure of the upper southwestern tropical Indian Ocean

We investigate the influence of low-frequency Rossby waves on the thermal structure of the upper southwestern tropical Indian Ocean (SWTIO) using Argo profiles, satellite altimetric data, sea surface temperature, wind field data and the theory of linear vertical normal mode decomposition. Our results show that the SWTIO is generally dominated by the first baroclinic mode motion. As strong downwelling Rossby waves reach the SWTIO, the contribution of the second baroclinic mode motion in this region can be increased mainly because of the reduction in the vertical stratification of the upper layer above thermocline, and the enhancement in the vertical stratification of the lower layer under thermocline also contributes to it. The vertical displacement of each isothermal is enlarged and the thermal structure of the upper level is modulated, which is indicative of strong vertical mixing. However, the cold Rossby waves increase the vertical stratification of the upper level, restricting the variability related to the second baroclinic mode. On the other hand, during decaying phase of warm Rossby waves, Ekman upwelling and advection processes associated with the surface cyclonic wind circulation can restrain the downwelling processes, carrying the relatively colder water to the near-surface, which results in an out-of-phase phenomenon between sea surface temperature anomaly (SSTA) and sea surface height anomaly (SSHA) in the SWTIO.

Modeling vertical heat transport in the wave affected surface layer of the ocean

In considering the vertical heat transport problems in the upper ocean, the flat upper boundary approximation for the free surface and the horizontal homogenous hypothesis are usually applied. However, due to the existence of the wave motion, the application of this approximation may result in some errors to the solar irradiation since it decays quickly in respect to the actual thickness of the water layer below the surface; on the other hand, due to the fluctuation of the water layer depth, it is improper to neglect the effects of the horizontal advection and turbulent diffusion since they also contribute to the vertical heat transport. A new model is constructed in this study to reflect these effects. The corresponding numerical simulations show that the wave motion may remarkably accelerate the vertical heat transferring process and the variation of the temperature in the wave affected layer appears in an oscillating manner.

An N-shape thermal front in the western South Yellow Sea in winter

An N-shape thermal front in the western South Yellow Sea (YS) in winter was detected using Advanced Very High Resolution Radiation (AVHRR) Sea Surface Temperature data and in-situ observations with a merged front-detecting method. The front, which exists from late October through early March, consists of western and eastern wings extending roughly along the northeast-southwest isobaths with a southeastward middle segment across the 20-50 m isobaths. There are north and south inflexions connecting the middle segment with the western and eastern wings, respectively. The middle segment gradually moves southwestward from November through February with its length increasing from 62 km to 107 km and the southern inflexion moving from 36.2A degrees N to 35.3A degrees N. A cold tongue is found to coexist with the N-shape front, and is carried by the coastal jet penetrating southward from the tip of the Shandong Peninsula into the western South YS as revealed by a numerical simulation. After departing from the coast, the jet flows as an anti-cyclonic recirculation below 10 m depth, trapping warmer water originally carried by the compensating Yellow Sea Warm Current (YSWC). A northwestward flowing branch of the YSWC is also found on the lowest level south of the front. The N-shape front initially forms between the cold tongue and warm water involved in the subsurface anti-cyclonical recirculation and extends upwards to the surface through vertical advection and mixing. Correlation analyses reveal that northerly and easterly winds tend to be favorable to the formation and extension of the N-shape front probably through strengthening of the coastal jet and shifting the YSWC pathway eastward, respectively.