Walter Munk

Bio: Walter Munk is an academic researcher from University of California, San Diego. The author has contributed to research in topics: Internal wave & Ocean acoustic tomography. The author has an hindex of 61, co-authored 227 publications receiving 20000 citations. Previous affiliations of Walter Munk include Scripps Institution of Oceanography & University of California.

Measurement of the Roughness of the Sea Surface from Photographs of the Sun’s Glitter

Abstract: A method is developed for interpreting the statistics of the sun’s glitter on the sea surface in terms of the statistics of the slope distribution. The method consists of two principal phases: (1) of identifying, from geometric considerations, any point on the surface with the particular slope required for the reflection of the” sun’s rays toward the observer; and (2) of interpreting the average brightness of the sea surface in the vicinity of this point in terms of the frequency with which this particular slope occurs. The computation of the probability of large (and infrequent) slopes is limited by the disappearance of the glitter into a background consisting of (1) the sunlight scattered from particles beneath the sea surface, and (2) the skylight reflected by the sea surface.The method has been applied to aerial photographs taken under carefully chosen conditions in the Hawaiian area. Winds were measured from a vessel at the time and place of the aerial photographs, and cover a range from 1 to 14 m sec−1. The effect of surface slicks, laid by the vessel, are included in the study. A two-dimensional Gram-Charlier series is fitted to the data. As a first approximation the distribution is Gaussian and isotropic with respect to direction. The mean square slope (regardless of direction) increases linearly with the wind speed, reaching a value of (tan16°)2 for a wind speed of 14 m sec−1. The ratio of the up/ downwind to the crosswind component of mean square slope varies from 1.0 to 1.9. There is some up/downwind skewness which increases with increasing wind speed. As a result the most probable slope at high winds is not zero but a few degrees, with the azimuth of ascent pointing downwind. The measured peakedness which is barely above the limit of observational error, is such as to make the probability of very large and very small slopes greater than Gaussian. The effect of oil slicks covering an area of one-quarter square mile is to reduce the mean square slopes by a factor of two or three, to eliminate skewness, but to leave peakedness unchanged.

Space-Time Scales of Internal Waves' A Progress Report

Abstract: We present a revised model for the distribution of internal wave energy in wave number frequency space. The model is empirical, guided by the following measurements: moored spectra and moored coherences for horizontal and vertical separations (MS, MHC, MVC as functions of frequency), towed spectra and towed vertical and time-lagged coherences (TS, TVC, TLC as functions of horizontal wave number), and dropped spectra and dropped horizontal and lagged coherences (DS, DHC, DLC as functions of vertical wave number). Measurements are available for all but TLC and DHC. There is some indication of universality, suggesting perhaps a saturation limit.

On the wind-driven ocean circulation

Abstract: Streamlines of oceanic mass transport are derived from solutions to a vertically integrated vorticity equation which relates planetary vorticity, lateral stress curl, and the curl of the stress exerted by the winds on the sea surface. These solutions account for many of the gross features of the general ocean circulation, and some of its details, on the basis of the observed mean annual winds. The solution for zonal winds (section 3) gives the main gyres of the ocean circulation. The northern and southern boundaries of these gyres are the west wind drift, the equatorial currents, and equatorial counter-current. They are determined by the westerly winds, the trades, and the doldrums, respectively. For each gyre the solution gives the following observed features (from west to east): a concentrated current (e.g., the Gulf Stream), a countercurrent, boundary vortices (the Sargasso Sea), and a steady compensating drift. Using mean Atlantic zonal winds, the solution yields a transport for the Gulf Stre...

Efficient Inverse Modeling of Barotropic Ocean Tides

Abstract: A computationally efficient relocatable system for generalized inverse (GI) modeling of barotropic ocean tides is described. The GI penalty functional is minimized using a representer method, which requires repeated solution of the forward and adjoint linearized shallow water equations (SWEs). To make representer computations efficient, the SWEs are solved in the frequency domain by factoring the coefficient matrix for a finite-difference discretization of the second-order wave equation in elevation. Once this matrix is factored representers can be calculated rapidly. By retaining the first-order SWE system (defined in terms of both elevations and currents) in the definition of the discretized GI penalty functional, complete generality in the choice of dynamical error covariances is retained. This allows rational assumptions about errors in the SWE, with soft momentum balance constraints (e.g., to account for inaccurate parameterization of dissipation), but holds mass conservation constraints. Wh...

Second Simulation of the Satellite Signal in the Solar Spectrum, 6S: an overview

Abstract: Remote sensing from satellite or airborne platforms of land or sea surfaces in the visible and near infrared is strongly affected by the presence of the atmosphere along the path from Sun to target (surface) to sensor. This paper presents 6S (Second Simulation of the Satellite Signal in the Solar Spectrum), a computer code which can accurately simulate the above problems. The 6S code is an improved version of 5S (Simulation of the Satellite Signal in the Solar Spectrum), developed by the Laboratoire d'Optique Atmospherique ten years ago. The new version now permits calculations of near-nadir (down-looking) aircraft observations, accounting for target elevation, non lambertian surface conditions, and new absorbing species (CH/sub 4/, N/sub 2/O, CO). The computational accuracy for Rayleigh and aerosol scattering effects has been improved by the use of state-of-the-art approximations and implementation of the successive order of scattering (SOS) algorithm. The step size (resolution) used for spectral integration has been improved to 2.5 nm. The goal of this paper is not to provide a complete description of the methods used as that information is detailed in the 6S manual, but rather to illustrate the impact of the improvements between 5S and 6S by examining some typical remote sensing situations. Nevertheless, the 6S code has still limitations. It cannot handle spherical atmosphere and as a result, it cannot be used for limb observations. In addition, the decoupling the authors are using for absorption and scattering effects does not allow to use the code in presence of strong absorption bands.

The Paradox of the Plankton

Abstract: The problem that I wish to discuss in the present contribution is raised by the very paradoxical situation of the plankton, particularly the phytoplankton, of relatively large bodies of water. We know from laboratory experiments conducted by many workers over a long period of time (summary in Provasoli and Pintner, 1960) that most members of the phytoplankton are phototrophs, able to reproduce and build up populations in inorganic media containing a source of CO2, inorganic nitrogen, sulphur, and phosphorus compounds and a considerable number of other elements (Na, K, Mg, Ca, Si, Fe, Mn, B, C1, Cu, Zn, Mo, Co and V) most of which are required in small concentrations and not all of which are known to be required by all groups. In addition, a number of species are known which require one or more vitamins, namely thiamin, the cobalamines (B or related compounds), or biotin. The problem that is presented by the phytoplankton is essentially how it is possible for a number of species to coexist in a relatively isotropic or unstructured environment all competing for the same sorts of materials. The problem is particularly acute because there is adequate evidence from enrichment experiments that natural waters, at least in the summer, present an environment of striking nutrient deficiency, so that competition is likely to be extremely severe. According to the principle of competitive exclusion (Hardin, 1960) known by many names and developed over a long period of time by many investigators (see Rand, 1952; Udvardy, 1959; and Hardin, 1960, for historic reviews), we should expect that one species alone would outcompete all the others so that in a final equilibrium situation the assemblage would reduce to a population of a single species. The principle of competitive exclusion has recently been under attack from a number of quarters. Since the principle can be deduced mathematically from a relatively simple series of postulates, which with the ordinary postulates of mathematics can be regarded as forming an axiom system, it follows that if the objections to the principle in any cases are valid, some or all the biological axioms introduced are in these cases incorrect. Most objections to the principle appear to imply the belief that equilibrium under a given set of environmental conditions is never in practice obtained. Since the deduction of the principle implies an equilibrium system, if such sys-

Wavelet Methods for Time Series Analysis

Abstract: 1. Introduction to wavelets 2. Review of Fourier theory and filters 3. Orthonormal transforms of time series 4. The discrete wavelet transform 5. The maximal overlap discrete wavelet transform 6. The discrete wavelet packet transform 7. Random variables and stochastic processes 8. The wavelet variance 9. Analysis and synthesis of long memory processes 10. Wavelet-based signal estimation 11. Wavelet analysis of finite energy signals Appendix. Answers to embedded exercises References Author index Subject index.