The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Geophysical fluid dynamics.

Internal oceanic waves are subsurface gravity waves that can be enormous and travel thousands of kilometres before breaking but they are difficult to study; here observations of such waves in the South China Sea reveal their formation mechanism, extreme turbulence, relationship to the Kuroshio Current and energy budget. Internal waves are the underwater version of more familiar surface waves. They can be enormous and travel thousands of kilometres before breaking. The South China Sea is known to be home to the largest internal waves in the world's oceans, but their size, generation mechanisms and role in the regional energy budget are unknown. Matthew Alford and colleagues now present the results from the IWISE observational campaign and reveal that internal waves more than 200 metres high break in the South China Sea and create turbulence that is orders of magnitude larger than in the open ocean, and that wave formation is influenced by the Kuroshio current. These results now allow for a complete energy budget of the South China Sea, and for a more accurate incorporation of internal waves into climate models. Internal gravity waves, the subsurface analogue of the familiar surface gravity waves that break on beaches, are ubiquitous in the ocean. Because of their strong vertical and horizontal currents, and the turbulent mixing caused by their breaking, they affect a panoply of ocean processes, such as the supply of nutrients for photosynthesis1, sediment and pollutant transport2 and acoustic transmission3; they also pose hazards for man-made structures in the ocean4. Generated primarily by the wind and the tides, internal waves can travel thousands of kilometres from their sources before breaking5, making it challenging to observe them and to include them in numerical climate models, which are sensitive to their effects6,7. For over a decade, studies8,9,10,11 have targeted the South China Sea, where the oceans’ most powerful known internal waves are generated in the Luzon Strait and steepen dramatically as they propagate west. Confusion has persisted regarding their mechanism of generation, variability and energy budget, however, owing to the lack of in situ data from the Luzon Strait, where extreme flow conditions make measurements difficult. Here we use new observations and numerical models to (1) show that the waves begin as sinusoidal disturbances rather than arising from sharp hydraulic phenomena, (2) reveal the existence of >200-metre-high breaking internal waves in the region of generation that give rise to turbulence levels >10,000 times that in the open ocean, (3) determine that the Kuroshio western boundary current noticeably refracts the internal wave field emanating from the Luzon Strait, and (4) demonstrate a factor-of-two agreement between modelled and observed energy fluxes, which allows us to produce an observationally supported energy budget of the region. Together, these findings give a cradle-to-grave picture of internal waves on a basin scale, which will support further improvements of their representation in numerical climate predictions.

/pdf/the-formation-and-fate-of-internal-waves-in-the-south-china-4lmce4xjug.pdf

The formation and fate of internal waves in the South China Sea

If model parameterizations of unresolved physics, such as the variety of upper ocean mixing processes, are to hold over the large range of time and space scales of importance to climate, they must be strongly physically based. Observations, theories, and models of oceanic vertical mixing are surveyed. Two distinct regimes are identified: ocean mixing in the boundary layer near the surface under a variety of surface forcing conditions (stabilizing, destabilizing, and wind driven), and mixing in the ocean interior due to internal waves, shear instability, and double diffusion (arising from the different molecular diffusion rates of heat and salt). Mixing schemes commonly applied to the upper ocean are shown not to contain some potentially important boundary layer physics. Therefore a new parameterization of oceanic boundary layer mixing is developed to accommodate some of this physics. It includes a scheme for determining the boundary layer depth h, where the turbulent contribution to the vertical shear of a bulk Richardson number is parameterized. Expressions for diffusivity and nonlocal transport throughout the boundary layer are given. The diffusivity is formulated to agree with similarity theory of turbulence in the surface layer and is subject to the conditions that both it and its vertical gradient match the interior values at h. This nonlocal “K profile parameterization” (KPP) is then verified and compared to alternatives, including its atmospheric counterparts. Its most important feature is shown to be the capability of the boundary layer to penetrate well into a stable thermocline in both convective and wind-driven situations. The diffusivities of the aforementioned three interior mixing processes are modeled as constants, functions of a gradient Richardson number (a measure of the relative importance of stratification to destabilizing shear), and functions of the double-diffusion density ratio, Rρ. Oceanic simulations of convective penetration, wind deepening, and diurnal cycling are used to determine appropriate values for various model parameters as weak functions of vertical resolution. Annual cycle simulations at ocean weather station Papa for 1961 and 1969–1974 are used to test the complete suite of parameterizations. Model and observed temperatures at all depths are shown to agree very well into September, after which systematic advective cooling in the ocean produces expected differences. It is argued that this cooling and a steady salt advection into the model are needed to balance the net annual surface heating and freshwater input. With these advections, good multiyear simulations of temperature and salinity can be achieved. These results and KPP simulations of the diurnal cycle at the Long-Term Upper Ocean Study (LOTUS) site are compared with the results of other models. It is demonstrated that the KPP model exchanges properties between the mixed layer and thermocline in a manner consistent with observations, and at least as well or better than alternatives.

Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization

[1] A composite time series (1993–2000) of sea surface height anomaly from several satellites is used to identify eddies in the South China Sea (SCS). The eddy lifetime, radius, strength, and straight-line travel distance are estimated. Altogether 58 anticyclonic eddies and 28 cyclonic eddies are identified for this period. They are grouped into four geographical zones according to known eddy generation mechanisms, and their statistics are discussed accordingly. Our geographical classification is a useful first step in gaining an overview of their generation.

/pdf/mesoscale-eddies-in-the-south-china-sea-observed-with-eogqaltsnm.pdf

Mesoscale eddies in the South China Sea observed with altimeter data

A method to estimate the forces exerted by internal solitons on cylindrical piles

https://pure.hw.ac.uk/ws/files/25140027/Zhao_Ning_Zou_BreakWater_WEC_Review_FinalAccepted_OE2019.pdf

Hybrid floating breakwater-WEC system: A review

Internal solitary waves (ISWs) are the nonlinear large amplitude waves existing in the oceanic pycnocline. They are very active in the northern South China Sea (SCS). With more and more remote sensing data, in situ observational data and the development of the numerical simulation technology, a number of studies on the characteristics, the source site, the generation, and evolution of the ISWs in the SCS are reported. In this paper, earlier studies on the ISWs in the SCS are summarized and some problems worthy of study are put forward.

An Overview of Internal Solitary Waves in the South China Sea

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2018JC014054

Shuqun Cai

Papers

A method to estimate the forces exerted by internal solitons on cylindrical piles

Hybrid floating breakwater-WEC system: A review

An Overview of Internal Solitary Waves in the South China Sea

A New Assessment of Mesoscale Eddies in the South China Sea: Surface Features, Three-Dimensional Structures, and Thermohaline Transports

A simple estimation of the force exerted by internal solitons on cylindrical piles