Satellite sea surface height (SSH) data over 1992-2012 are analyzed to study the spatial and temporal variability of sea level in the Red Sea. Empirical orthogonal functions (EOF) analysis suggests the remarkable seasonality of SSH in the Red Sea, and a significant correlation is found between SSH variation and seasonal wind cycle. A winding-angle based eddy identification algorithm is employed to derive the mesoscale eddy information from SSH data. Totally more than 5500 eddies are detected, belonging to 2583 eddy tracks. Statistics suggest that eddies generate over the entire Red Sea, with two regions in the central basin of high eddy frequency. 76% of the detected eddies have a radius ranging from 40km to 100km, of which both intensity and absolute vorticity decrease with eddy radius. The average eddy lifespan is about 5 weeks, and eddies with longer lifespan tend to have larger radius but less intensity. Different deformation rate exists between anticyclonic eddies (AEs) and cyclonic eddies (CEs), those eddies with higher intensity appear to be less deformed and more circular. Inspection of the 84 long-lived eddies suggests the AEs tend to move a little more northward than CEs. AE generation during summer is obviously lower than that during other seasons, while CE generation is higher during spring and summer. Other features of AEs and CEs are similar with both vorticity and intensity reaching the summer peaks in August and winter peaks in January. Inter-annual variability reveals that the eddies in the Red Sea are isolated from the global event. The eddy property tendencies are different from the south and north basin, both of which exhibit a two-year cycle. Showing a correlation coefficient of -0.91, Brunt–Väisälä frequency is negatively correlated with eddy kinetic energy (EKE), which results from AE activities in the high eddy frequency region. Climatological vertical velocity shear variation is identical with EKE except in the autumn, suggesting the vertical shear could convert the energy from baroclinic instability into eddy activity. Finally, numerical simulation results from the MIT general circulation model (MITgcm) are validated with previous studies and observations. The vertical structure of the simulated flux through Bab el Mandeb is successfully reproduced. Further validation with the 2010 cruise suggests that the thermocline occurs at ~200m, but the model vertical salinity gradient is lower than the observations. The model surface eddy variability is also examined, suggesting good agreement with satellite observations.

Baroclinic tides result from the interaction of barotropic tides with topography in stratified oceans. They play an important role in driving deep ocean mixing. In this research, investigations of the dynamics of baroclinic tides and internal solitary waves (ISWs) in the northern South China Sea (SCS) are conducted, mainly by means of the Massachusetts Institute of Technology general circulation model (MITgcm). Firstly, simulations of internal wave generation at the Luzon Strait (LS) are carried out. By conducting three-dimensional (3D), high-resolution experiments, it was found that the generated wave field features a multi-modal structure: large, pronounced ISWs of first mode (amplitude ~120 m) and second mode (amplitude ~120 m) were reproduced. The two north-south aligned ridges in the LS contribute together to the generation of the second mode ISWs, whereas the easternmost ridge of the two is responsible for the first mode ISWs. It was found that multiple generation mechanisms of internal waves could occur in this region, and overall it belongs to a mixed lee wave regime. A specific type of short internal waves arose during the 3D simulation. These ride on a second mode ISW with similar phase speed, trailing a first mode ISW. The short waves possess wavelengths of ~1.5 km and amplitudes of ~20 m, and only show up in the upper layer up to a depth of ~500 m. Scrutiny of the generation process showed that these short waves appear in two distinct regions and are produced due to two mechanisms, namely, the disintegration of an inclined baroclinic bore near the LS, and the overtaking of a second mode ISW in the deep water by a faster first mode ISW. Robust evidence has been sought from satellite imagery and by solving the theoretical Taylor-Goldstein Equation to verify their existence. The effects of superposition of multiple tidal harmonics (diurnal and semidiurnal) on the resultant ISW generation were investigated. It was first found that, by analyzing historical observational data, the occurrence of ISWs in the far-field always follow strong semidiurnal barotropic tidal peaks in the LS, regardless of whether it is the maximum for the diurnal or total tidal strength. However, modelling results of MITgcm and a linear internal tide generation model demonstrate that the diurnal tidal harmonics modulate the arrival time and amplitude of the propagating ISWs. Specifically, it leads to the emergence of the so-called A and B type ISWs and an alternation and transition between the two. Secondly, the shoaling process of ISWs in the northern SCS slope-shelf area is investigated. A series of two-dimensional (2D) experiments are set up to study the shoaling of a large-amplitude second mode concave ISW over a linear slope that resembles the SCS slope. Modelling results show that a strong transformation of the wave profile starts to take place when the wave is approaching the shelf break. A convex type wave is born at the trailing edge of the incident wave and gradually disintegrates into a group of ISWs due to the steepening of the rear wave profile. The frontal face of the wave gets flatter when travelling on the slope, but forms a steep structure right above the shelf break. However, this steep structure shows no tendency to evolve into an ISW: instead, it gets increasingly flat again while evolving on the shelf. The trailing convex wave packet travels faster and merges with the frontal concave wave. Finally, a wave packet with rank-ordered convex ISWs moves forward steadily on the shelf. Energy transfer to the ambient modes is evident, as both first mode and higher modes are clearly seen during and after the shoaling process. First mode ISW evolution is studied too by performing 3D, high-resolution experiments over the wide northern SCS slope and shelf area. It was found that the wave profiles change drastically near the shelf break and the Dongsha Atoll. In agreement with satellite imagery, the wavefront of the leading ISW becomes more spatially oblique with respect to its original orientation as it progresses westward due to the inclination of the slope in the topography. Wave disintegration is prominent in the shallow water zone, and wave polarity reverses near the turning point (at the 130 m isobath), which is consistent with the predictions of weakly nonlinear theory. A series of 2D experiments were set up to inspect the effects of rotation on the shoaling ISW. The results indicate that under the rotation, upon reaching the continental shelf, one shoaling ISW could disintegrate into one ISW packet and one secondary solibore that contains a number of rank-ordered waves with much shorter wavelength than an ISW. The secondary solibore is very pronounced in the northern portion of the northern SCS slope and shelf, but could hardly be discerned in the southern portion, which is consistent with the outcome of 3D simulations.

When wind blows over a stratified lake an interface tilt is often generated, and internal waves usually appear after the wind stops. Internal waves in lakes are studied in many literatures, but most assume a hydrostatic pressure balance. In this thesis we discuss the internal Poincare waves and Kelvin waves in a rotating, continuously stratified, flat-bottom, circular lake with fully nonlinear and non-hydrostatic effects. An analytical solution is derived for the linearized system and it provides initial conditions used in the MIT General Circulation Model (MITgcm). This model is chosen due to its non-hydrostatic capability. Both Poincare waves and Kelvin waves are considered. The analytical solution of the linear system is verified numerically when the wave amplitude is small. As the wave amplitude increases the waves become more nonlinear. Poincare waves steepen and generate solitary-like waves with shorter wavelengths, but most of the energy contained in these waves is transferred back and forth between the parent wave and the solitary-like waves. Kelvin waves, on the other hand, steepen and lose their energy to solitary-like waves. The appearance of the solitary-like waves is not absolutely clear and higher resolution is required to clear up the details of this process. This conclusion agrees with de la Fuente et al (2008) who discussed the internal waves in a two-layer model. Moreover, in the Kelvin waves case, unexpected small waves are generated at the side boundaries and travel inwards. The wave amplitude and wavelength of these spurious waves become smaller as the horizontal resolution increases. One possible reason to explain these waves is the use of square grids to approximate the circular lake.

When wind blows over a stratified lake an interface tilt is often generated, and internal waves usually appear after the wind stops. Internal waves in lakes are studied in many literatures, but most assume a hydrostatic pressure balance. In this thesis we discuss the internal Poincare waves and Kelvin waves in a rotating, continuously stratified, flat-bottom, circular lake with fully nonlinear and non-hydrostatic effects. An analytical solution is derived for the linearized system and it provides initial conditions used in the MIT General Circulation Model (MITgcm). This model is chosen due to its non-hydrostatic capability. Both Poincare waves and Kelvin waves are considered. The analytical solution of the linear system is verified numerically when the wave amplitude is small. As the wave amplitude increases the waves become more nonlinear. Poincare waves steepen and generate solitary-like waves with shorter wavelengths, but most of the energy contained in these waves is transferred back and forth between the parent wave and the solitary-like waves. Kelvin waves, on the other hand, steepen and lose their energy to solitary-like waves. The appearance of the solitary-like waves is not absolutely clear and higher resolution is required to clear up the details of this process. This conclusion agrees with de la Fuente et al (2008) who discussed the internal waves in a two-layer model. Moreover, in the Kelvin waves case, unexpected small waves are generated at the side boundaries and travel inwards. The wave amplitude and wavelength of these spurious waves become smaller as the horizontal resolution increases. One possible reason to explain these waves is the use of square grids to approximate the circular lake.

Mälaren är en mycket viktig dricksvattentäkt för många människor. I den här studien utreds riskfaktorersom kan påverka råvattenkvaliteten i Mälaren och sedan relateras dessa till hydrodynamiskmodellering av Mälaren. Hydrodynamisk modellering är ett modernt verktyg som kan simulera vattnets rörelse och tar hänsyn till många hydrodynamiska och meteorologiska drivvariabler. Modellerkan användas för att till exempel förutse transport av punktutsläpp och beräkna när och vilken koncentration som kommer till ett vattenverks intag. Beställaren av detta projekt är Norrvatten, en dricksvattenproducent som är intresserad av utvecklingsmöjligheterna hos oceanografen Göran Broströms tillämpning av den hydrodynamiska modellen MITgcm. Norrvatten använder sig idag av en modell vid namn MIKE 3 FM skapad av DHI. De är intresserade av vilken utveckling av MITgcm som skulle behövas för att den ska uppnå liknande kvalitetskrav som deras nuvarande modell gör. I en litteraturstudie samlades information om Mälarens fysikaliska, biologiska, kemiska förutsättningar samt information om hydrodynamisk modellering, för att göra en analys kring Mälarens råvattenkvalitet såväl som modellering av Mälaren. Genom kvalitativa intervjuer med Göran Broström angående MITgcm samt Helene Ejhed, uppströmsansvarig på Norrvatten som ofta använder MIKE 3 FM var det möjligt att ingående analysera modellerna utifrån såväl drivdata som modellernas övergripande kapaciteter. Utöver analys från intervjuerna gjordes en körning av Göran Broströms tillämpning av MITgcm. Resultaten visade att de största riskerna gällande Mälarens råvattenkvalitet är oljeutsläpp från närliggande farleder och patogener som släpps ut från reningsverk. Jämförelsen mellan MIKE 3 FM och MITgcm etablerade många likheter mellan modellerna, även om vissa variabler skilde sig åt, såsom in- och utflöden, ytvågor och nederbörd. Förslag på en ordning som Göran Broströms modell kan byggas ut på presenteras i form av en prioriteringspyramid. Validering av modellen visade sigvara ett viktigt första steg i utvecklingen samt att förbättra interaktionsdesignen. Utveckling av modellen skulle resultera i vissa kostnader för Norrvatten. Vidare studier behöver bidra med en större förståelse över den tillämpning Broström gjort av MITgcm samt jämförelser med flera modeller.

This thesis presents our efforts to build an operational ensemble forecasting system for the Red Sea, based on the Data Research Testbed (DART) package for ensemble data assimilation and the Massachusetts Institute of Technology general circulation ocean model (MITgcm) for forecasting. The Red Sea DART-MITgcm system efficiently integrates all the ensemble members in parallel, while accommodating different ensemble assimilation schemes. The promising ensemble adjustment Kalman filter (EAKF), designed to avoid manipulating the gigantic covariance matrices involved in the ensemble assimilation process, possesses relevant features required for an operational setting. The need for more efficient filtering schemes to implement a high resolution assimilation system for the Red Sea and to handle large ensembles for proper description of the assimilation statistics prompted the design and implementation of new filtering approaches. Making the most of our world-class supercomputer, Shaheen, we first pushed the system limits by designing a fault-tolerant scheduler extension that allowed us to test for the first time a fully realistic and high resolution 1000 ensemble members ocean ensemble assimilation system. In an operational setting, however, timely forecasts are of essence, and running large ensembles, albeit preferable and desirable, is not sustainable. New schemes aiming at lowering the computational burden while preserving reliable assimilation results, were developed. The ensemble Optimal Interpolation (EnOI) algorithm requires only a single model integration in the forecast step, using a static ensemble of preselected members for assimilation, and is therefore computationally significantly cheaper than the EAKF. To account for the strong seasonal variability of the Red Sea circulation, an EnOI with seasonally-varying ensembles (SEnOI) was first implemented. To better handle intra-seasonal variabilities and enhance the developed seasonal EnOI system, an automatic procedure to adaptively select the ensemble members through the assimilation cycles was then introduced. Finally, an efficient Hybrid scheme combining the dynamical flow-dependent covariance of the EAKF and a static covariance of the EnOI was proposed and successfully tested in the Red Sea. The developed Hybrid ensemble data assimilation system will form the basis of the first operational Red Sea forecasting system that is currently being implemented to support Saudi Aramco operations in this basin.

The three-dimensional (3D) baroclinic response of Cayuga Lake to surface wind forcing was investigated using the fully nonhydrostatic MITgcm. The model was validated against observed temperature data using a hydrostatic 450 m (horizontal) grid and both qualitative and quantitative methods. The model correctly reproduces the basin-scale dynamics (e.g., seiche with horizontal mode-one period T1 = 80 h) with a basin-wide root-mean-square error of 1.9 C. Nonlinear internal surges were visualized to evolve due to (i) a wind-induced locally downwelled thermocline (wind duration Twind < T1/4), (ii) a basin-scale wind-induced upwelled thermocline (Twind > T1/4), (iii) internal hydraulic jumps (IHJs). Results from a 113 m grid and field observations were used to characterize the basin-scale internal wave field according to composite Froude number (G2), Wedderburn number (WN), and Lake number (LN). The typical Cayuga Lake response is a surge when ~ 1 < WN (LN) < ~ 2-12 and a surge with emergent nonlinear internal waves (NLIWs) when WN or LN < ~ 2, in agreement with published laboratory studies. An observed shock front was simulated to be an IHJ, occurring at mid-basin during strong winds when WN < 0.8. This is the first simulation of a mid-basin seiche-induced IHJ due to super critical conditions (G2 > 1) in a lake. The topographic-induced IHJs were also shown to form when the surges interact with a sill-contraction topographic feature. Both high-resolution hydrostatic and nonhydrostatic models were used to investigate the evolution, propagation and shoaling of NLIWs at medium lake-scale. A nonhydrostatic 22 m grid with lepticity λ ~ 1 ensures minimal numerical relative to physical dispersion, qualitatively reproducing observed dispersive NLIWs using ~ 2.3E+8 grid cells. Solitary waves evolve with almost unchanged wavelengths upon grid refinement from 40 m (λ ~ 2) to 22 m; suggesting model convergence to the correct solution. Corresponding hydrostatic grids were shown to produce a packet of narrower spurious solitary-like motions with different wavelengths, representing a balance between nonlinear steepening and numerical dispersion. Local gyre-like patterns and secondary transverse NLIW packets were visualized to result from wave-topography interaction, suggesting that NLIW propagation in long narrow lakes, where the bottom topography has irregularities is fundamentally 3D. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2012-12-14 12:45:21.727

The barotropic tide dissipates a well established estimate of 2.5 TW of energy at the M2 frequency. Bottom topography is responsible for part of this dissipation, and the generation of the internal tide is also partly responsible. The fate of this energy is largely described by a cascade from large scales to small scales by non-linear wave-wave interactions where it gets dissipated. This thesis aims to investigate how the presence of mesoscale eddies (vortices) in the ocean affect the internal tide. Previous work has looked at the interaction of the barotropic tide with eddies. Krauss (1999) found that the interaction can produce a modulated internal tide, however a scaling analysis suggests that the effect may not be as strong as reported. The MITgcm is used to simulate internal wave generation by barotropic flow over topography and comparisons are made with Dr. Lamb's IGW model. Baroclinic eddies are analytically prescribed and then geostrophically adjusted also using the MITgcm. Finally, the two are combined, and the internal tide field is analysed with and without the presence of eddies of various magnitude and length scales. The results of this investigation do not find a strong transfer of energy between modes; the modal distribution of energy in the internal tide remains the same when an eddy is added. However, focusing and shadow beams of internal waves are produced in the wake of an eddy as the internal waves pass through it. The beams show very strong variations in intensity, vertically integrated energy flux can reduce almost to zero in the shadow regions and increase more than double in the focusing regions. Modal decomposition of the horizontal flow field reveals that mode 2 and 3 waves are most strongly affected by the eddies and contribute strongly to the formation of the beams. Mode 1 appears to be less affected by the eddy. The larger wavelength and faster group velocity of mode 1 supports the notion that the eddy interacts with it less.

The barotropic tide dissipates a well established estimate of 2.5 TW of energy at the M2 frequency. Bottom topography is responsible for part of this dissipation, and the generation of the internal tide is also partly responsible. The fate of this energy is largely described by a cascade from large scales to small scales by non-linear wave-wave interactions where it gets dissipated. This thesis aims to investigate how the presence of mesoscale eddies (vortices) in the ocean affect the internal tide. Previous work has looked at the interaction of the barotropic tide with eddies. Krauss (1999) found that the interaction can produce a modulated internal tide, however a scaling analysis suggests that the effect may not be as strong as reported. The MITgcm is used to simulate internal wave generation by barotropic flow over topography and comparisons are made with Dr. Lamb's IGW model. Baroclinic eddies are analytically prescribed and then geostrophically adjusted also using the MITgcm. Finally, the two are combined, and the internal tide field is analysed with and without the presence of eddies of various magnitude and length scales. The results of this investigation do not find a strong transfer of energy between modes; the modal distribution of energy in the internal tide remains the same when an eddy is added. However, focusing and shadow beams of internal waves are produced in the wake of an eddy as the internal waves pass through it. The beams show very strong variations in intensity, vertically integrated energy flux can reduce almost to zero in the shadow regions and increase more than double in the focusing regions. Modal decomposition of the horizontal flow field reveals that mode 2 and 3 waves are most strongly affected by the eddies and contribute strongly to the formation of the beams. Mode 1 appears to be less affected by the eddy. The larger wavelength and faster group velocity of mode 1 supports the notion that the eddy interacts with it less.