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

The sensitivity of sonic anemometer-derived stress estimates to the tilt of the anemometer is investigated. The largest stress errors are shown to occur for unstable stratification (z/L<0) and deep convective boundary layers. Three methods for determining the tilt angles relative to a mean streamline coordinate system and for computing the tilt-corrected stresses are then compared. The most commonly used method, involving a double rotation of the anemometers' axes, is shown to result in significant run-to-run stress errors due to the sampling uncertainty of the mean vertical velocity. An alternative method, requiring a triple rotation of the anemometer axes, is shown to result in even greater run-to-run stress errors due to the combined sampling errors of the mean vertical velocity and the cross-wind stress. For measurements over the sea where the cross-stream stress is important, the double rotation method is shown to overestimate the surface stress, due to the uncorrected lateral tilt component. A third method, using a planar fit technique, isshown to reduce the run-to-run stress errors due to sampling effects, and provides an unbiased estimate of the lateral stress.

Sonic anemometer tilt correction algorithms

Most implementations of genetic algorithms experience sampling bias and are unnecessarily inefficient. This paper reviews various sampling algorithms proposed in the literature and offers two new algorithms of reduced bias and increased efficiency. An empirical analysis of bias is then presented.

Reducing bias and inefficiency in the selection algorithm

Tools for quality assessment of surface-based flux measurements

A tendency to erect ever more wind turbines can be observed in order to reduce the environmental consequences of electric power generation. As a result of this, in the near future, wind turbines may start to influence the behavior of electric power systems by interacting with conventional generation and loads. Therefore, wind turbine models that can be integrated into power system simulation software are needed. In this contribution, a model that can be used to represent all types of variable speed wind turbines in power system dynamics simulations is presented. First, the modeling approach is commented upon and models of the subsystems of which a variable speed wind turbine consists are discussed. Then, some results obtained after incorporation of the model in PSS/E, a widely used power system dynamics simulation software package, are presented and compared with measurements.

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General model for representing variable speed wind turbines in power system dynamics simulations

Presents, in a single volume, an up-to-date summary of the current knowledge of the statistical characteristics of atmospheric turbulence and an introduction to the methods required to apply these statistics to practical engineering problems. Covers basic physics and statistics, statistical properties emphasizing their behavior close to the ground, and applications for engineers.

Atmospheric Turbulence: Models and Methods for Engineering Applications

A set of conditions which justify the application of the Boussinesq approximation to compressible fluids is developed. Two cases are found and compared. In the first, in which the vertical scale of the motion can be of the same order of magnitude as the scale height of the medium, the perturbation momentum must be nondivergent and the effects of perturbations of pressure appear in several places. In the other case, where the vertical scale of the motion is much less than the scale height, the perturbation velocities are non-divergent and the perturbation pressure appears only in the pressure gradient force. The approximate equations lead to linearized equations controlling the stability of wave motion which are formally equivalent to those for the same problem in the flow of a stratified medium which is incompressible in the sense that the flow is solenoidal. Thus, a variety of results about such motions are made applicable to the problems of convection and gravity wave motion in the atmosphere. ...

Approximate Equations of Motion for Gases and Liquids

Clear air turbulence: a mystery may be unfolding.

Expanding capabilities an new requirements for atmospheric information services create an exciting new era with economic and political challenge and a need for clear priorities.

Opportunities and priorities in a new era for weather and climate services

Publisher Summary The concept of available potential energy is founded upon the principle of conservation of mass and the idealization that flows, which conserve specific entropy, may exist Under these conditions, the sum of the internal, potential, and kinetic energies is a constant, and; therefore, a state of the atmosphere, which possesses a minimum of total potential energy will likewise have a maximum of kinetic energy The purpose of this chapter to: (1) Develop the theory of available potential energy and its rate of change rigorously and exactly, and thereby clarify the roles of convection, hydrostatic departures, static stability, and diabatic processes (2) Investigate the relationships between the concepts of available potential energy, static stability, and entropy, and investigate contributions to available energy under various circumstances (3) Demonstrate that the methods of the calculus of variations provide an economical method of obtaining exact results in available energy theory (4) Propose an application of variational techniques, which offer considerable intuitive insight and the possibility of analytic and numerical attacks on the problem of why the atmosphere chooses the modes of circulation it does (5) Illustrate the role of available potential energy in maintaining the circulation in the context of the proposed theory of the control of the general circulation Studies of energy transformations in general and those involving available potential energy in particular, can never yield information about the control of the circulation unless they are coupled with a dynamic theory By themselves, such studies are of necessity diagnostic and kinematic, and can yield only a detailed understanding of the mechanisms by which energy is conserved The discovery and application of variational and integral techniques in atmospheric research is just beginning, but their success in other fields is sufficient guarantee that their exploitation will dispel many mysteries

John A. Dutton

Papers

Atmospheric Turbulence: Models and Methods for Engineering Applications

Approximate Equations of Motion for Gases and Liquids

Clear air turbulence: a mystery may be unfolding.

Opportunities and priorities in a new era for weather and climate services

The Theory of Available Potential Energy and a Variational Approach to Atmospheric Energetics