Parameterization of ocean wave-induced mixing processes for finite water depth

Three dimensional wave-induced mixing plays an important role in shallow water area. A quite direct approach through the Reynolds average upon characteristic length scale is proposed to parameterize the horizontal and vertical shallow water mixing. Comparison of finite depth case with infinite depth results indicates that the difference of the wave-induced mixing strength is evident. In the shallow water condition, the infinite water depth approximation overestimates the mixing strength in the lower layers. The nonzero horizontal wave-induced mixing presents anisotropic property near the shore. The Prandtl’s mixing length theory underestimated the wave-induced mixing in the previous studies.     

A model of ocean current flow and drifter motion

A minor generalization of the theory of random walk is used as a basis for a model of ocean current flow. The model is then applied in a computer simulation of drifter motion. The results of simulation indicate that the geometry of a coastline can have significant impact on the distribution of drifter landings.     

Evolving a Bayesian network model with information flow for time series interpolation of multiple ocean variables

Based on Bayesian network (BN) and information flow (IF), a new machine learning-based model named IFBN is put forward to interpolate missing time series of multiple ocean variables. An improved BN structural learning algorithm with IF is designed to mine causal relationships among ocean variables to build network structure. Nondirectional inference mechanism of BN is applied to achieve the synchronous interpolation of multiple missing time series. With the IFBN, all ocean variables are placed in a causal network visually, making full use of information about related variables to fill missing data. More importantly, the synchronous interpolation of multiple variables can avoid model retraining when interpolative objects change. Interpolation experiments show that IFBN has even better interpolation accuracy, effectiveness and stability than existing methods.     

Development of a regional ocean model for New Zealand

A regional ocean model with a horizontal resolution of 1/6° encompassing the New Zealand Exclusive Economic Zone is described. The regional model successfully downscaled solutions from a high resolution, global, coupled model HadCEM. Transport estimates from the global and regional models were compared with observations, and both models supported largely consistent, climatological mean solutions. The regional model used monthly mean forcing at the surface. Nevertheless, the regional model eddy kinetic energy (EKE) spatial patterns compared favourably with long‐term mean satellite altimetric estimates, although the modelled background EKE amplitudes were much lower than observed. A series of permanent eddies associated with the western boundary current system around the top of the North Island of New Zealand were reproduced, and an eddy adjacent to Norfolk Ridge was identified in both the global and regional models. The western boundary current system around the North Island of New Zealand and the associated eddies were the most sensitive components of the model solutions, being influenced by initial conditions, wind forcing, and the model domain size.     

Semi-Lagrangian methods for a finite element coastal ocean model

Coastal ocean hydrodynamic models are subject to a number of stability constraints. The most important of these are the Courant–Friedrichs–Levy (CFL) constraint on gravity waves, a Courant (Cr) number constraint on advection, and a time step constraint on the vertical component of viscous stresses. The model described here removes these constraints using a semi-implicit approximation in time and a semi-Lagrangian approximation for advection. The accuracy and efficiency of semi-Lagrangian methods depends crucially on the methods used to calculate trajectories and interpolate at the foot of the trajectory. The focus of this paper is on evaluation of several new and old semi-Langrangian methods. In particular, we compare 3 methods to calculate trajectories (Runge–Kutta (RK2), analytical integration (AN), power-series expansion (PS)) and 3 methods to interpolate (local linear (LL), global linear (GL), global quadratic (GQ)) on unstructured grids. The AN and PS methods are both efficient and accurate, and the latter can be expanded in a straightforward manner to treat time-dependent velocity. The GQ interpolation method provides a major step in introducing efficient and accurate semi-Lagrangian methods to unstructured grids.     

An eastward flow at lower middle latitudes derived from a three-layer model of a wind-driven ocean circulation

The steady state wind-driven circulation in an immiscible three-layer ocean bounded only by a meridional east coast and a flat bottom is studied. Particular attention is paid to the occurrence of internal modes of motions in the Sverdrup transports (Sverdrup, 1947). The thicknesses of the upper two layers are of the same order and are allowed to vary up to the same order as the layer thicknesses themselves. Frictional transfer of momentum across the interfaces and the frictional boundary layer at the east coast are neglected. An eastward flow is obtained in the uppermost layer at lower middle latitudes. Though the particular feature in the wind-stress distribution as revealed byYoshida andKidokoro (1967a, 1967b) is not taken into account, the results show good agreement with the observed flow pattern of the Subtropical Countercurrent. Beneath the Subtropical Countercurrent a westward flow is predicted. These flows exhibit an internal mode of motions associated with a subsurface thermal front.     

Bifurcation analysis of 3D ocean flows using a parallel fully-implicit ocean model

To understand the physics and dynamics of the ocean circulation, techniques of numerical bifurcation theory such as continuation methods have proved to be useful. Up to now these techniques have been applied to models with relatively few degrees of freedom such as multi-layer quasi-geostrophic and shallow-water models and relatively low-resolution (e.g., 4° horizontal resolution) primitive equation models. In this paper, we present a new approach in which continuation methods are combined with parallel numerical linear system solvers. With this implementation, we show that it is possible to compute steady states versus parameters (and perform fully implicit time integration) of primitive equation ocean models with up to a few million degrees of freedom.     

Quasi-isopycnic layer model for large-scale ocean circulation

A hydrothermodynamic model of a multilayer ocean, incorporating the upper mixed layer (UML) is described. The model is based on a system of primitive equations integrated within each layer. All layers are assumed to be horizontally-inhomogeneous, however, the density in each thermocline layer changes within the limits determineda priori by the prescribed basic stratification. It is assumed that the layers may outcrop. Results of the numerical experiment on subduction simulation (downwelling of UML waters toward the main thermocline layers) are given.Translated by V. Puchkin.     

An ocean model for climate variability studies

Models of the time dependent ocean circulation can be simplified considerably by filtering out all short term, small scale motions which are unimportant for climatic processes. For time scales large compared with a day and space scales large compared with the internal Rossby radius of deformation (～50 km), the currents in most of the interior ocean can be determined diagnostically as quasi-equilibrium fields, so that only the salinity and temperature fields need be treated prognostically.Regions of closed f/h contours, however, represent exceptions. Here trapped vorticity gyres exist as free flow solutions without external forcing, and in the presence of forcing the barotropic velocity field must therefore be determined prognostically through a potential vorticity equation for the gyres.Lateral boundary layers and the equatorial regions also require separate treatment. These were not considered specifically, but it is suggested that integrated (parametrical) models analogous in structure to mixed-layer models or the integrated boundary layer models of aerodynamics may be the most appropriate technique for coupling these regions to the interior ocean in a comprehensive ocean model suitable for climate studies.A coupled multi-region model of the global ocean circulation based on these scale considerations could be sufficiently cost-effective to permit systematic investigation of the role of the oceanic heat storage and transport in climate variability studies over a wide spectrum of space and time scales.The analysis of the seasonal variations of the interior ocean circulation represents a simple example in which the filtered model yields considerably simpler and more readily interpretable results than a fully three-dimensional, unfiltered model.     

A reduced grid for a parallel global ocean general circulation model

A limitation of many global climate models with explicit finite-difference numerics is the timestep restriction caused by the decrease in cell size associated with the convergence of meridians near the poles. To keep the longitudinal width of model cells as uniform as possible, we apply a “reduced” grid to a three-dimensional primitive equation ocean-climate model. With this grid the number of cells in the longitudinal direction is reduced at high latitudes. The grid consists of subgrids which interact at interfaces along their northern and southern boundaries, where the resolution changes by a factor of three. We extend the finite-difference techniques to these interfaces, focusing on the conservation required to perform long time integrations, while preserving the staggered spatial arrangement of variables and the numerics used on subgrids. The common alternative used to reduce the timestep restriction caused by the spherical grid is the filtering of high-frequency modes from the high-latitude solution. The reduced grid allows an increased timestep while eliminating the need for filtering and reduces execution time per model step by roughly 20%. We implement the reduced grid model for parallel computer architectures with two-dimensional domain decomposition and message passing, with speedup results similar to those of the original model. We present results of model runs showing small effects on the solution and sizable improvements to the execution time.     

The effects of chaotic advection in a three-layer ocean model

A three-layer model of an inviscid incompressible fluid is considered in a quasigeostrophic approximation within the concept of background currents. A singular topographic obstacle yields the formation of a vortical motion in the layers. It is always present in the lower layer, while in the upper and middle layers it can be observed only at certain velocities of the external flows. Three current functions describing a singular topographic flow in the lower layer and two regular flows in the upper layer are obtained. In case of a nonstationary harmonic perturbation of the external flow, chaotic particle transport is possible in these flows. This paper analyzes the chaotic properties of this model. Depending on the type of unperturbed frequency curves of the fluid particle revolution is determined by the model parameters (stratification) and the incident flow, the patterns of the chaotic transport will substantially differ. Two of the limiting dependences of the revolution frequency are determined, namely, the dependence for a singular vortex and that for a regular vortex with the smallest area. Other dependences are intermediate ones. Two limiting types of revolution frequencies determine the two different scenarios of chaotic advection.     

Long-period topographic trapped waves in a two-layer ocean with basic flow

The characteristics of free topographic trapped waves are investigated numerically for a two-layer model with basic flow, which is uniform, geostrophically balanced motion flowing parallel to the coast. Six modes are identified for this model with depth variations. They are external and internal Kelvin modes, a topographic Rossby mode, and additional three modes. The two of the additional modes are interesting. The first one is a quasi-geostrophic surface-trapped mode, while the second one is a quasi-geostrophic bottom-trapped mode. It is suggested that baroclinic instability takes place when these two modes take a resonance coupling each other.     

A 3-D model for ocean waves over a Columb-damping poroelastic seabed

The evaluation of the wave-induced seabed instability in the vicinity of a breakwater is particularly important for coastal and geotechnical engineers involved in the design of coastal structures. In this paper, an analytical solution for three-dimensional short-crested wave-induced seabed instability in a Coulomb-damping porous seabed is derived. The partial wave reflection and self-weight of breakwater are also considered in the new solution. Based on the analytical solution, we examine (1) the wave-induced soil response at different location; (2) the maximum liquefaction and shear failure depth in coarse and fine sand; (3) the effects of reflection coefficients; and (4) the added stresses due to the self-weight of the breakwater.     

Collocation numerical model for synoptic eddy evolution in the ocean

A quasi-geostrophic model for synoptic eddy evolution in a confined oceanic area is examined. The numerical scheme is based on the combination of spline collocation, splitting, and Fourier series expansion by the dynamic operator's eigenfunctions over the vertical. The functions and their derivatives are approximated with cubic splines in a basis constituted by B-spline functions. A series of experiments focusing on eddy transformation were conducted. The acquired data confirmed the inference regarding the oscillatory nature of the energy exchange between the primary eddy and the secondary ones and showed how vortical formations affect the currents. The evidence obtained indicates that, vertically, the pattern of eddy propagation is complicated.Translated by Vladimir A. Puchkin.     

Efficient identification of ocean thermodynamics in a physical/biogeochemical ocean model with an iterative Importance Sampling method

Efficient identification of parameters in numerical models remains a computationally demanding problem. Here we present an iterative Importance Sampling approach and demonstrate its application to estimating parameters that control the heat uptake efficiency of a physical/biogeochemical ocean model coupled to a simple atmosphere. The algorithm has similarities to a previously-developed ensemble Kalman filtering (EnKF) method applied to similar problems, but is more flexible and powerful in the case of nonlinear models and non-Gaussian uncertainties. The method is somewhat more computationally demanding than the EnKF but may be preferred in cases where the approximations that the EnKF relies upon are unsound. Our results suggest that the three-dimensional structure of ocean tracer fields may act as a useful constraint on ocean mixing and consequently the heat uptake of the climate system under anthropogenic forcing.     

The effect of ocean tides on a climate model simulation

We implemented an explicit forcing of the complete lunisolar tides into an ocean model which is part of a coupled atmosphere–hydrology–ocean–sea ice model. An ensemble of experiments with this climate model shows that the model is significantly affected by the induced tidal mixing and nonlinear interactions of tides with low frequency motion. The largest changes occur in the North Atlantic where the ocean current system gets changed on large scales. In particular, the pathway of the North Atlantic Current is modified resulting in improved sea surface temperature fields compared to the non-tidal run. These modifications are accompanied by a more realistic simulation of the convection in the Labrador Sea. The modification of sea surface temperature in the North Atlantic region leads to heat flux changes of up to 50 W/m². The climate simulations indicate that an improvement of the North Atlantic Current has implications for the simulation of the Western European Climate, with amplified temperature trends between 1950 and 2000, which are closer to the observed trends.