Search Results

You are looking at 1 - 6 of 6 items for

  • Author or Editor: S. Hasselmann x
  • Refine by Access: All Content x
Clear All Modify Search
S. Hasselmann
and
K. Hasselmann

Abstract

A more efficient method of computing the nonlinear transfer in a surface wave spectrum is developed which is symmetrical with respect to all wavenumbers of the resonant interaction quadruplets. This enables a large number of computations to be carried out, as required for investigations of the spectral energy balance or the development of parameterizations. New results are presented for finite-depth surface waves. By filtering out regions in interaction phase space, the assumptions involved in the narrow-peak and local-interaction approx-imations are investigated. Both approximations are found to be useful but are generally not sufficiently accurate to replace exact computations or provide adequate parameterizations for wave models.

Full access
G. J. Komen
,
S. Hasselmann
, and
K. Hasselmann

Abstract

We consider the energy transfer equation for well-developed ocean waves under the influence of wind, and study the conditions for the existence of an equilibrium solution in which wind input, wave-wave interaction and dissipation balance each other. For the wind input we take the parameterization proposed by Snyder and others, which was based on their measurements in the Bight of Abaco and which agrees with Miles's theory. The wave-wave interaction is computed with an algorithm given recently by S. Hasselmann and others. The dissipation is less well-known, but we will make the general assumption that it is quasi-linear in the wave spectrum with a factor coefficient depending only on frequency and integral spectral parameters. In the first part of this paper we investigate whether the assumption that the equilibrium spectrum exits and is given by the Pierson-Moskowitz spectrum with a standard type of angular distribution leads to a reasonable dissipation function. We find that this is not the case. Even if one balances the total rate of change for each frequency (which is possible), a strong angular imbalance remains. Thus the assumed source terms are not consistent with this type of asymptotic spectrum. In the second part of the paper we choose a different approach. We assume that the dissipation is given and perform numerical experiments simulating fetch-limited growth, to see under which conditions a stationary solution can be reached. For the dissipation we take K. Haseelmann's form with two unknown parameters. From our analysis it follows that for a certain range of values of these parameters, a quasi-equilibrium solution results. We estimate the relation between dissipation parameters and asymptotic growth rates. For equilibrium spectra, the input, dissipation and nonlinear-transfer source functions are all significant in the energy-containing range of the spectrum. The energy balance proposed by Zakharov and Filonenko in 1966 and Kitaigorodskii in 1983, in which dissipation is assumed to be significant only at high frequencies, yields a spectrum that grows too rapidly and does not approach equilibrium. One of our equilibrium solutions has a one-dimensional spectrum that lies close to the Pierson-Moskowitz spectrum. However, the angular distribution differs in some important features from standard spreading functions. The energy balance of this equilibrium spectrum is analysed in detail.

Full access
I. R. Young
,
S. Hasselmann
, and
K. Hasselmann

Abstract

The response of a wind-sea spectrum to a step function change in wind direction is investigated theoretically for a sequence of direction changes ranging from 30° to 180°, in increments of 30°. Two spectral energy balance models are used: the model EXACT-NL, in which the nonlinear transfer is represented exactly, and the model 3G-WAM, in which the nonlinear transfer is approximated by the discrete interaction parameterization. In both modes the input and dissipation source functions are taken from the energy balance proposed by Komen et al. The operational model 3G-WAM reproduces fairly closely the EXACT-NL results. For wind direction changes less than 60°, the wind-sea direction adjusts smoothly. The high-frequency components relax more rapidly to the new wind direction than the low-frequency components. The computed relaxation rates are generally consistent with the analysis of measured directional spectra by D.E. Hasselman et al. and Allender et al. However, the relaxation rate is found to be a function of wind speed as well as frequency. For wind direction changes greater than 60°, a second, independent wind-sea spectrum is generated in the new wind direction, while the old wind-sea gradually decays as swell.

Full access
S. Hasselmann
,
K. Hasselmann
,
J. H. Allender
, and
T. P. Barnett

Abstract

Four different parameterizations of the nonlinear energy transfer S nl in a surface wave spectrum are in investigated. Two parameterizations are based on a relatively small number of parameters and are useful primarily for application in parametrical or hybrid wave models. In the first parameterization, shape-distortion parameters are introduced to relate the distribution S nl for different values of the peak-enhancement parameter γ. The second parameterization is based on an EOF expansion of a set of S nl computed for a number of different spectral distributions. The remaining two parameterizations represent operator forms that contain the same number of free parameters as used to describe he wave spectrum. Such parameterizations with a matched number of input and output parameters are required for numerical stability in high-resolution discrete spectral models. A cubic, fourth-order diffusion-operator expression derived by a local-interaction expansion is found to be useful for understanding many of the properties of S nl , but is regarded as too inaccurate in detail for application in most wave models. The best results are achieved with a discrete-interaction operator parameterization, in which a single interaction configuration, together with its mirror image (representing a two-dimensional continuum of interactions with respect to a variable reference wavenumber scale and direction) is used to simulate the net effect of the full five-dimensional interaction continuum.

Full access
V. Cardone
,
H. Carlson
,
J. A. Ewing
,
K. Hasselmann
,
S. Lazanoff
,
W. McLeish
, and
D. Ross

Abstract

The surface wave environment in the GATE B/C scale is described from wave measurements made from buoys and aircraft during Phase III (September 1974). Particular emphasis is given to the wave measurements made from the pitch-roll buoy deployed in the B-scale array from the ship Gilliss and a similar buoy deployed in the C-scale array from Quadra. Reduction of the pitch-roll buoy measurements provided estimates of the one-dimensional wave spectrum as well as of the mean direction and spread of wave energy as a function of frequency. The data clearly revealed the importance of external forcing on the wave climate in GATE. Most of the wave energy present in the GATE areas was found to be swell imported from the trade wind circulations of both hemispheres and from an intense extratropical cyclone which crossed the North Atlantic at high latitudes early in Phase III. Locally generated waves were clearly evident in the wave spectra, but their energy level way have been modulated significantly by the low-frequency swell. The GATE wave data set can provide a powerful test of contemporary numerical wave-prediction models. The present study defines the, attributes which are required of such models for meaningful application to the GATE needs.

Full access
T. P. Barnett
,
K. Hasselmann
,
M. Chelliah
,
T. Delworth
,
G. Hegerl
,
P. Jones
,
E. Rasmusson
,
E. Roeckner
,
C. Ropelewski
,
B. Santer
, and
S. Tett

This paper addresses the question of where we now stand with respect to detection and attribution of an anthropogenic climate signal. Our ability to estimate natural climate variability, against which claims of anthropogenic signal detection must be made, is reviewed. The current situation suggests control runs of global climate models may give the best estimates of natural variability on a global basis, estimates that appear to be accurate to within a factor of 2 or 3 at multidecadal timescales used in detection work.

Present uncertainties in both observations and model-simulated anthropogenic signals in near-surface air temperature are estimated. The uncertainty in model simulated signals is, in places, as large as the signal to be detected. Two different, but complementary, approaches to detection and attribution are discussed in the context of these uncertainties.

Applying one of the detection strategies, it is found that the change in near-surface, June through August air temperature field over the last 50 years is generally different at a significance level of 5% from that expected from model-based estimates of natural variability. Greenhouse gases alone cannot explain the observed change. Two of four climate models forced by greenhouse gases and direct sulfate aerosols produce results consistent with the current climate change observations, while the consistency of the other two depends on which model's anthropogenic fingerprints are used. A recent integration with additional anthropogenic forcings (the indirect effects of sulfate aerosols and tropospheric ozone) and more complete tropospheric chemistry produced results whose signal amplitude and pattern were consistent with current observations, provided the model's fingerprint is used and detection carried out over only the last 30 years of annually averaged data. This single integration currently cannot be corroborated and provides no opportunity to estimate the uncertainties inherent in the results, uncertainties that are thought to be large and poorly known. These results illustrate the current large uncertainty in the magnitude and spatial pattern of the direct and indirect sulfate forcing and climate response. They also show detection statements depend on model-specific fingerprints, time period, and seasonal character of the signal, dependencies that have not been well explored.

Most, but not all, results suggest that recent changes in global climate inferred from surface air temperature are likely not due solely to natural causes. At present it is not possible to make a very confident statement about the relative contributions of specific natural and anthropogenic forcings to observed climate change. One of the main reasons is that fully realistic simulations of climate change due to the combined effects of all anthropogenic and natural forcings mechanisms have yet to be computed. A list of recommendations for reducing some of the uncertainties that currently hamper detection and attribution studies is presented.

Full access