Klaus Hasselmann

Dynamics and Modelling of Ocean Waves

Addresses both fundamental and applied aspects of ocean waves including the use of wave observations made from satellites. More specifically it describes the WAM model, its scientific basis, its actual implementation, and its many applications. This model has been developed by an international group (the Wave Modelling group), and is based on a detailed physical description of air/sea interactions. It is widely used for wave forecasting for meteorological and oceanographic purposes. The three sections of the volume describe the basic statistical theory and the relevant physical processes; the numerical model and its global and regional applications; and satellite observations, their interpretation and use in data assimilation. Written by leading experts, it is a comprehensive guide and reference for researchers and advanced students in physical oceanography, meteorology, fluid dynamics, coastal engineering and physics.

On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory

The energy flux in a finite-depth gravity-wave spectrum resulting from weak non-linear couplings between the spectral components is evaluated by means of a perturbation method. The fifth-order analysis yields a fourth-order effect comparable in magnitude to the generating and dissipating processes in wind-generated seas. The energy flux favours equidistribution of energy and vanishes in the limiting case of a white, isotropic spectrum. The influence on the equilibrium structure of fully developed wave spectra and on other phenomena in random seas is discussed briefly.

On the Existence of a Fully Developed Wind-Sea Spectrum

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 Miless 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...

Transport and storage of CO2 in the ocean ——an inorganic ocean-circulation carbon cycle model

Inorganic carbon in the ocean is modelled as a passive tracer advected by a three-dimensional current field computed from a dynamical global ocean circulation model. The carbon exchange between the ocean and atmosphere is determined directly from the (temperature-dependent) chemical interaction rates in the mixed layer, using a standard CO2 flux relation at the air-sea interface. The carbon cycle is closed by coupling the ocean to a one-layer, horizontally diffusive atmosphere. Biological sources and sinks are not included. In this form the ocean carbon model contains essentially no free tuning parameters. The model may be regarded as a reference for interpreting numerical experiments with extended versions of the model including biological processes in the ocean (Bacastow R and Maier-Reimer E in prep.) and on land (Esser G et al in prep.). Qualitatively, the model reproduces the principal features of the observed CO2 distribution bution in the surface ocean. However, the amplitudes of surface pCO2 are underestimated in upwelling regions by a factor of the order of 1.5 due to the missing biological pump. The model without biota may, nevertheless, be applied to compute the storage capacity of the ocean to first order for anthropogenic CO2 emissions. In the linear regime, the response of the model may be represented by an impulse response function which can be approximated by a superposition of exponentials with different amplitudes and time constants. This provides a simple reference for comparison with box models. The largest-amplitude (∼0.35) exponential has a time constant of 300 years. The effective storage capacity of the oceans is strongly dependent on the time history of the anthropogenic input, as found also in earlier box model studies.

Computations and Parameterizations of the Nonlinear Energy Transfer in a Gravity-Wave Specturm. Part II: Parameterizations of the Nonlinear Energy Transfer for Application in Wave Models

Abstract Four different parameterizations of the nonlinear energy transfer Snl 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 Snl for different values of the peak-enhancement parameter γ. The second parameterization is based on an EOF expansion of a set of Snl 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 ...

On the nonlinear mapping of an ocean wave spectrum into a synthetic aperture radar image spectrum and its inversion

A new, closed nonlinear integral transformation relation is derived describing the mapping of a two-dimensional ocean wave spectrum into a synthetic aperture radar (SAR) image spectrum. The general integral relation is expanded in a power series with respect to orders of nonlinearity and velocity bunching. The individual terms of the series can be readily computed using fast Fourier transforms. The convergence of the series is rapid. The series expansion is also useful in identifying the different contributions to the net imaging process, consisting of the real aperture radar (RAR) cross-section modulation, the nonlinear motion (velocity bunching) effects, and their various interaction products. The lowest term of the expansion with respect to nonlinearity order yields a simple quasi-linear approximate mapping relation consisting of the standard linear SAR modulation expression multiplied by an additional nonlinear Gaussian azimuthal cutoff factor. The cutoff scale is given by the rms azimuthal (velocity bunching) displacement. The same cutoff factor applies to all terms of the power series expansion. The nonlinear mapping relation is inverted using a standard first-guess wave spectrum as regularization term. This is needed to overcome the basic 180° mapping ambiguity and the loss of information beyond the azimuthal cutoff. The inversion is solved numerically using an iteration technique based on the successive application of the explicit solution for the quasi-linear mapping approximation, with interposed corrections invoking the full nonlinear mapping expression. A straightforward application of this technique, however, generally yields unrealistic discontinuities of the best fit wave spectrum in the transition region separating the low azimuthal wave number domain, in which useful SAR information is available and the wave spectrum is modified, from the high azimuthal wave number region beyond the azimuthal cutoff, where the first-guess wave spectrum is retained. This difficulty is overcome by applying a two-step inversion procedure. In the first step the energy level of the wave spectrum is adjusted, and the wave number plane rotated and rescaled, without altering the shape of the spectrum. Using the resulting globally fitted spectrum as the new first-guess input spectrum, the original inversion method is then applied without further constraints in a second step to obtain a final fine-scale optimized spectrum. The forward mapping relation and inversion algorithms are illustrated for three Seasat cases representing different wave conditions corresponding to weakly, moderately, and strongly nonlinear imaging conditions.

Time-dependent greenhouse warming computations with a coupled ocean-atmosphere model

Climate changes during the next 100 years caused by anthropogenic emissions of greenhouse gases have been simulated for the Intergovernmental Panel on Climate Change Scenarios A (“business as usual”) and D (“accelerated policies”) using a coupled ocean-atmosphere general circulation model. In the global average, the near-surface temperature rises by 2.6 K in Scenario A and by 0.6 K in Scenario D. The global patterns of climate change for both IPCC scenarios and for a third step-function 2 x CO2 experiment were found to be very similar. The warming delay over the oceans is larger than found in simulations with atmospheric general circulation models coupled to mixed-layer models, leading to a more pronounced land-sea contrast and a weaker warming (and in some regions even an initial cooling) in the Southern Ocean. During the first forty years, the global warming and sea level rise due to the thermal expansion of the ocean are significantly slower than estimated previously from box-diffusion-upwelling models, but the major part of this delay can be attributed to the previous warming history prior to the start of present coupled ocean-atmosphere model integration (cold start).

A Parametric Wave Prediction Model

Abstract Measurements of fetch-limited wave spectra from various sources indicate an approximate invariance of the normalized spectral shape with fetch. It has been suggested from investigations of the spectral energy balance that this can be explained by the shape-stabilizing influence of nonlinear resonant wave-wave interactions, which are also responsible for the migration of the spectral peak to lower frequencies. Analyses of a series of further data sets obtained under non-uniform, non-stationary wind conditions show that the invariance of the spectral shape is not restricted to uniform-wind, fetch-limited situations, but applies generally for a growing wind sea. The observed shape invariance is exploited in a wave prediction model by projecting the full transport equation for the two-dimensional spectral continuum onto two variables characterizing the energy and frequency scales of the spectrum. Inspection of the resultant equations reveals further simplifications, enabling the system to be reduced ...

Global warming feedbacks on terrestrial carbon uptake under the Intergovernmental Panel on Climate Change (IPCC) Emission Scenarios

A coupled physical-biogeochemical climate model that includes a dynamic global vegetation model and a representation of a coupled atmosphere-ocean general circulation model is driven by the nonintervention emission scenarios recently developed by the Intergovernmental Panel on Climate Change (IPCC). Atmospheric CO2, carbon sinks, radiative forcing by greenhouse gases (GHGs) and aerosols, changes in the fields of surface-air temperature, precipitation, cloud cover, ocean thermal expansion, and vegetation structure are projected. Up to 2100, atmospheric CO2 increases to 540 ppm for the lowest and to 960 ppm for the highest emission scenario analyzed. Sensitivity analyses suggest an uncertainty in these projections of � 10 to +30% for a given emission scenario. Radiative forcing is estimated to increase between 3 and 8 W m -2 between now and 2100. Simulated warmer conditions in North America and Eurasia affect ecosystem structure: boreal trees expand poleward in high latitudes and are partly replaced by temperate trees and grasses at lower latitudes. The consequences for terrestrial carbon storage depend on the assumed sensitivity of climate to radiative forcing, the sensitivity of soil respiration to temperature, and the rate of increase in radiative forcing by both CO2 and other GHGs. In the most extreme cases, the terrestrial biosphere becomes a source of carbon during the second half of the century. High GHG emissions and high contributions of non-CO2 agents to radiative forcing favor a transient terrestrial carbon source by enhancing warming and the associated release of soil carbon.

Mean Circulation of the Hamburg LSG OGCM and Its Sensitivity to the Thermohaline Surface Forcing

Abstract The sensitivity of the global ocean circulation to changes in surface heat flux forcing is studied using the Hamburg Large Scale Geostrophic (LSG) ocean circulation model. The simulated mean ocean circulation for appropriately chosen surface forcing fields reproduces the principal water mass properties, residence times, and large-scale transport properties of the observed ocean circulation quite realistically within the constraints of the model resolution. However, rather minor changes in the formulation of the high-latitude air–sea heat flux can produce dramatic changes in the structure of the ocean circulation. These strongly affect the deep-ocean overturning rates and residence times, the oceanic heat transport, and the rate of oceanic uptake of CO2. The sensitivity is largely controlled by the mechanism of deep-water formation in high latitudes. The experiments support similar findings by other authors on the sensitivity of the ocean circulation to changes in the fresh-water flux and are cons...