S. 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 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.

Computations and Parameterizations of the Nonlinear Energy Transfer in a Gravity-Wave Spectrum. Part I: A New Method for Efficient Computations of the Exact Nonlinear Transfer Integral

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.

An improved algorithm for the retrieval of ocean wave spectra from synthetic aperture radar image spectra

An earlier algorithm for retrieving two-dimensional wave spectra from synthetic aperture radar (SAR) image spectra is improved by using a modified cost function and introducing an additional iteration loop in which the first-guess input spectrum is systematically updated. For this purpose a spectral partitioning scheme is applied in which the spectrum is decomposed into a finite number of distinct wave systems. At each iteration step, the individual wave systems of the partitioned nth-guess wave spectrum are adjusted to agree in mean energy, frequency, and direction with the corresponding mean values of the associated wave systems of the SAR-inverted wave spectrum. The algorithm retrieves smooth wave spectra, avoiding the discontinuities which tended to arise in the previous algorithm in the transition region near the azimuthal wavenumber cutoff of the SAR image spectrum. The azimuthal cutoff of the SAR spectrum is also reproduced more accurately. The greatest improvement of the new retrieval algorithm is obtained when the discrepancies between the initial first-guess wave spectrum and the observed SAR spectrum are large. In this case the additional updating loop for the input spectrum enables the retrieved spectrum to adjust such that the simulated SAR spectrum matches more closely the observed SAR spectrum. The overall correlation of a large set of simulated SAR spectra with the measured SAR spectra is found to be significantly higher than with the previous algorithm, indicating that the algorithm not only overcomes isolated shortcomings of the earlier algorithm but also yields retrieved wave spectra which are generally more consistent with the input SAR data. An additional practical advantage of the new algorithm is that it returns spectral partioning parameters which can be used in SAR wave data assimilation schemes.

SENSITIVITY STUDY OF OPTIMAL CO2 EMISSION PATHS USING A SIMPLIFIED STRUCTURAL INTEGRATED ASSESSMENT MODEL (SIAM)

A structurally highly simplified, globally integrated coupled climate-economic costs model SIAM (Structural Integrated Assessment Model) is used to compute optimal paths of global CO2 emissions that minimize the net sum of climate damage and mitigation costs. The model is used to study the sensitivity of the computed optimal emission paths with respect to various critical input assumptions. The climate module is represented by a linearized impulse-response model calibrated against a coupled ocean-atmosphere general circulation climate model and a three-dimensional global carbon-cycle model. The cost terms are represented by strongly simplified expressions designed for maximal transparency with respect to sensitive input assumptions. These include the discount rates for mitigation and damage costs, the inertia of the socio-economic system, and the dependence of climate damages on the change in temperature and the rate of change of temperature. Different assumptions regarding these parameters are believed to be the cause of the marked divergences of existing cost-benefit analyses based on more sophisticated economic models. The long memory of the climate system implies that very long time horizons of several hundred years need to be considered to optimize CO2 emissions on time scales relevant for a policy of sustainable development. Cost-benefit analyses over shorter time scales of a century or two can lead to dangerous underestimates of the long term climatic impact of increasing greenhouse-gas emissions. To avert a major long term global warming, CO2 emissions need to be reduced ultimately to very low levels. However, the draw-down can be realized as a gradual transition process over many decades and even centuries. This should nevertheless not be interpreted as providing a time cushion for inaction: the transition becomes more costly the longer the necessary mitigation policies are delayed. However, the long time horizon provides adequate flexibility for later adjustments. Short term energy conservation alone is insufficient and can be viewed only as a useful measure in support of the necessary long term transition to carbon-free energy technologies. For standard climate damage cost expressions, optimal emission paths limiting long term global warming to acceptable sustainable development levels are recovered only if climate damage costs are not significantly discounted. Discounting of climate damages at normal economic rates yields emission paths that are only weakly reduced relative to business as usual scenarios, resulting in high global warming levels that are incompatible with the generally accepted requirements of sustainable development. The solutions are nevertheless logically consistent with the underlying discounting assumption, namely that the occurrence of global warming damages in the distant future as a result of present human activities is of negligible concern today. It follows that a commitment to long term sustainable development, if it in fact exists, should be expressed by an intertemporal relation for the value of the earths future climate which does not degrade significantly over the time horizon relevant for climate change. Since the future climate is a common assett whose value cannot be determined on the market, the appropriate discount rate for future climate damages should be determined by an assessment of the public willingness to pay today for the mitigation of future climate change. To translate our general conclusions into quantitative cost estimates required by decision makers, the present exploratory study needs to be extended using more detailed disaggregated climate damage and mitigation cost estimates and more realistic socio-economic models, including multi-actor interactions, inherent variability, the role of uncertainty and adaptive control strategies.

Statistical analysis and intercomparison of WAM model data with global ERS-1 SAR wave mode spectral retrievals over 3 years

Ocean wave spectra were retrieved from a set of ERS-I synthetic aperture radar (SAR) wave mode (SWM) spectra between January 1993 and December 1995. An assessment is given of the SWM data quality and the retrieval performance as well as the operational feasibility of the retrieval algorithm. Sensitivity studies are performed to demonstrate the weak residual dependence of the retrieval on the first-guess input spectrum. The mean spectral parameters of the SWM retrievals are compared with spectral parameters from collocated wave model (WAM) spectra. The time series of SWM-retrieved and WAM-derived monthly mean significant wave heights Hs in various ocean basins show good overall agreement but with a small systematic underestimation of Hs by the WAM. A decomposition of the wave spectra into wind sea and swell reveals an average 10% overprediction of the wind sea by the WAM while swell is underpredicted by 20–30%. The positive wind-sea bias exhibits no clear wave height dependence, while the negative swell bias decreases with swell wave height. This could be due to a too strong damping in the WAM at low frequencies. Detailed regional investigations point to the existence of smaller-scale phenomena, which may not be adequately reproduced by the WAM at the present resolution of the wind forcing. Finally, an intercomparison is made of the observed and modeled azimuthal cutoff length scales, and global distributions are investigated. Ratios of the observed azimuthal cutoff wavenumber to the mean azimuthal wavenumber component indicate that about 75% of the swell can be directly resolved by the SAR, while about 70% of the wind sea lies at least partially beyond the cutoff.

An optimal interpolation scheme for the assimilation of spectral wave data

An optimal interpolation scheme for assimilating two-dimensional wave spectra is presented which is based on a decomposition of the spectrum into principal wave systems. Each wave system is represented by three characteristic parameters: significant wave height, mean propagation direction, and mean frequency. The spectrum is thereby reduced to a manageable number of parameters. From the correction of the wind-sea system a correction of the local wind is derived. A 2-month test of the system using wave spectra retrieved from ERS 1 synthetic aperture radar wave mode data in the Atlantic yielded consistent corrections of winds and waves. However, the corrected wind data alone, although valuable in identifying wind errors in critical high wind speed regions, are too sparsely distributed in space and time to be used in isolation and need to be combined with other data in an atmospheric data assimilation scheme. This emphasizes the need for the development of combined wind and wave data assimilation schemes for the optimal use of satellite wind and wave data.

Validation and assimilation of Seasat altimeter wave heights using the WAM wave model

The mutual consistency of the Seasat global data sets of scatterometer winds and altimeter wave heights is investigated for the complete Seasat period using the third-generation wave model WAM. The wave model was driven by surface (1000 hPa) wind and surface stress fields constructed by the Goddard Laboratory for Atmospheres (GLA) by assimilation of the scatterometer winds in an atmospheric model. For the 10-day period September 7–17 the intercomparison was extended to two further scatterometer wind fields: a 1000-hPa assimilated wind field from the European Centre for Medium-Range Weather Forecasts and a subjectively analyzed 19.5-m-height surface wind field from the Jet Propulsion Laboratory. On the global average, the modeled and observed wave heights agree reasonably well. Regional differences, however, can be large and sometimes exceed 40%. The errors are attributed mainly to deficiencies in the forcing wind fields. Low wind speeds are found to be overestimated and high wind speeds underestimated by the Seasat scatterometer algorithm. The friction velocities of the GLA model are found to be significantly underestimated in the high-wind belt of the southern hemisphere. The analysis demonstrates the diagnostic advantages of applying a wave model for the quality assessment of satellite wind and wave data. A preliminary wave data assimilation scheme is presented in which the wave field is updated without changing the forcing wind field. A considerable improvement of the computed wave field is achieved, particularly in regions in which the wave energy is dominated by swell. However, a more general assimilation scheme including modifications of the wind field is needed to upgrade wind sea forecasts.

Gene therapy for HIV infection: what does it need to make it work?

The efficacy of antiviral drug therapy for HIV infection is limited by toxicity and viral resistance. Thus, alternative therapies need to be explored. Several gene therapeutic strategies for HIV infection have been developed, but in clinical testing therapeutically effective levels of the transgene product were not achieved. This review focuses on the determinants of therapeutic efficacy and discusses the potential and also the limits of current gene therapy approaches for HIV infection. Copyright

Computations of the Response of a Wave Spectrum to a Sudden Change in Wind Direction

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 ...