637 research outputs found
The wave model EXACT-NL
No full textThe evolution of a windsea spectrum is strongly controlled by the nonlinear energy transfer Sn1 due to resonant wave---wave interactions. Since the exact computation of this process is very time-consuming, most operational wave models are dependent on some form of parametrization of this source function. However, recent, more efficient methods of computing the exact three-dimensional integral expression for Snl (Hasselmann and Hasselmann, 1981, 1985) have made it feasible to carry out integrations of the wave transport equation with the exact form for Snl, at least for simple cases in which only one integration variable occurs
Reframing the problem of climate change: From zero sum game to win-win solutions
No full textThis book provides an evaluation of the science and policy debates on climate change and offers a reframing of the challenges they pose, as understood by key international experts and players in the field. It also gives an important and original perspective on interpreting climate action and provides compelling evidence of the weakness of arguments that frame climate policy as a win-or-lose situation. At the same time, the book goes beyond providing yet another description of climate change trends and policy processes. Its goal is to make available, in a series of in-depth reflections and insights by key international figures representing science, business, finance and civil society, what is really needed to link knowledge to action. Different contributions convincingly show that it is time – and possible – to reframe the climate debate in a completely new light, perhaps as a system transformative attractor for new green growth, sustainable development, and technological innovation. Reframing the Problem of Climate Change reflects a deep belief that dealing with climate change does not have to be a zero sum game, with winners and losers. The contributors argue that our societies can learn to respond to the challenge it presents and avoid both human suffering and large scale destruction of ecosystems; and that this does not necessarily require economic sacrifice. Therefore, it is vital reading for students, academics and policy makers involved in the debate surrounding climate change. © 2012 Carlo C. Jaeger, Klaus Hasselmann, Gerd Leipold, Diana Mangalagiu and J. David Tàbara
On the existence of a fully developed wind-sea spectrum
No full textWe 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
Implementation of an efficient scheme for calculating nonlinear transfer from wave‐wave interactions
No full textNonlinear transfer from wave-wave interactions is an important term in the action-balance equation governing the evolution of the surface-gravity-wave field. Computation of this term, however, has hitherto been so consuming of computer resources that its full representation has not been feasible in nonparametric two-dimensional computer models of this equation. This paper describes the implementation of a hybrid computational scheme, incorporating a simplification first proposed by Thacker into the EXACT-NL Boltzmann integration scheme of Hasselmann and Hasselmann. This hybrid scheme retains EXACT-NL's symmetry, precision, and two-stage structure, but, by transferring a spectrum-independent preintegration from the second stage to the first, dramatically accelerates the resulting second-stage computation, enabling a relatively efficient and precise determination of nonlinear transfer in two-dimensional wave models. Physically, this preintegration collects together in single hybrid interactions multiple interactions belonging to identical spectral-band quadruplets. Thus all possible interactions are represented, and these interactions are represented in a uniquely efficient manner consistent with the spectral representation. We compute the coefficients in the resulting second-stage hybrid sum by essentially sorting and pre-summing the coefficients generated by a piecewise-constant first-stage EXACT-NL computation, using a variant of EXACT-NL that replaces the gather-scatter operations with a simpler bin-assignment procedure and employs a somewhat simpler set of integration variables. By exploiting the natural scaling of the integrand and partially pre-summing prior to sorting, we are able to further improve the efficiency of this computation for the deep-water case and to refine its integration-grid resolution almost to convergence. In wave-model computations of nonlinear transfer, vectorization on the spatial grid points of the model and selective truncation of the hybrid sum potentially reduce the working computation time for a single model time step to well under one Cray Y-MP single-processor CPU second per hundred grid points, while preserving a remarkably faithful representation of the full transfer
Intertemporal accounting of climate change - Harmonizing economic efficiency and climate stewardship
No full textContinuing a discussion on the intertemporal accounting of climate-change damages initiated by Nordhaus, Heal and Brown in response to the recent demonstration of Hasselmann et al. that standard exponential discounting applied uniformly to all goods and services invariably leads to a `climate catastrophe' in cost-benefit analyses, it is argued that (1) there exists no economically satisfactory alternative to cost-benefit analysis for the determination of optimal climate protection strategies, and (2) it is essential to allow for the different long-term evolution of climate damage costs relative to mitigation costs in determining the optimal cost-benefit solution. A climate catastrophe can be avoided only if it is assumed that climate damage costs increase significantly in the long term relative to mitigation costs. Cost-benefit analysis is regarded here in the generalized sense of optimizing a social welfare function that incorporates all relevant `quality-of-life' factors, including not only consumption and the value of the environment, but also the ethical values of equitable intertemporal and intrasocietal distribution. Thus, economic efficiency and climate stewardship are not regarded as conflicting goals, but as synonyms for a single encompassing economic optimization exercise. The same reasoning applies generally to the problem of sustainable development. To quantify the concept of sustainable development in cost-benefit analyses, the projected time evolution of the future values of natural resources and the environment (judged by the present generation, acting as representative agents of future generations) must be related to the time-evolution of all other relevant quality-of-life factors. Different ethical interpretations of the concept of sustainable development can be readily operationalized by incorporation in a generalized cost-benefit analysis in which the evolution paths of all relevant material and ethical values are explicitly specified
Computation of the nonlinear energy transfer in a narrow gravity wave spectrum with a method derived by Dungey and Hui
No full textIn this report the method of Dungey and Hui is summarized and extended to include the effect of skewness of the directional distribution. Additional information is given about the derivation and computation of the single integrations mentioned above. The method of Dungey and Hui is applied to a number of theoretical spectra. The results of these computations are compared with the results of exact computations by Sell and Hasselmann (1972) and Hasselmann and Hasselmann (1981). Finally, some comments are made about computational aspects of the method of Dungey and Hui.Hydraulic EngineeringCivil Engineering and Geoscience
Stochastic climate models - 2. Application to sea-surface temperature anomalies and thermocline variability
No full textThe concept of stochastic climate models developed in Part I of this series (Hasselmann, 1976) is applied to the investigation of the low frequency variability of the upper ocean. It is shown that large-scale, long-time sea surface temperature (SST) anomalies may be explained naturally as the response of the oceanic surface layers to short-time-scale atmospheric forcing. The white-noise spectrum of the atmospheric input produces a red response spectrum, with most of the variance concentrated in very long periods. Without stabilizing negative feedback, the oceanic response would be nonstationary, the total SST variance growing indefinitely with time. With negative feedback, the response is asymptotically stationary. These effects are illustrated through numerical experiments with a very simple ocean-atmosphere model. The model reproduces the principal features and orders of magnitude of the observed SST anomalies in mid-latitudes. Independent support of the stochastic forcing model is provided by direct comparisons of observed sensible and latent heat flux spectra with SST anomaly spectra, and also by the structure of the cross correlation functions of atmospheric surface pressure and SST anomaly patterns. The numerical model is further used to simulate anomalies in the near-surface thermocline through Ekman pumping driven by the curl of the wind stress. The results suggest that short-time-scale atmospheric forcing should be regarded as a possible candidate for the origin of large-scale, low-period variability in the seasonal thermoclin
Modelling the impacts of a national carbon tax in a country with inhomogeneous regional development: an actor-based system-dynamic approach
No full textDifferent countries of the world are affected differently by the adverse impacts of anthropogenic climate change. For a large country consisting of several regions with different geographical conditions, the direct geographical impacts of climate change may differ significantly. Given the inhomogeneous regional economic development typical for many large countries already for the present climate, this suggests that regional economic disparities may increase even further as global warming develops. It is thus important that the impacts of climate mitigation policies are assessed not only on global and national levels, but also on the regional level. The key tool for assessing the efficiency of climate mitigation policies and their impacts are Integrated Assessment models (IAMs), i.e. dynamic models of the coupled climate?socioeconomic system. The family of IAMs described in the present paper represent extensions and modifications of a set of actor-based system-dynamics models reported earlier in Hasselmann K. (2013), Detecting and responding to climate change, Tellus B 65, 20088, http://dx.doi.org/10.3402/tellusb.v65i0.20088 (open access). The models focus on the strategies of key decision-making aggregate economic actors (often pursuing conflicting goals) that jointly govern the dynamic evolution of the socio-economic system. We start from a global IAM in which both fossil-fuel-based capital and renewable-energy-based capital determine the production function. We compare a business-as-usual scenario (no mitigation policy) with various mitigation scenarios with different global carbon tax rates. The revenues from the carbon tax in the mitigation scenarios are recirculated into the economy in the form of investments in renewable-energy-based capital. We explore both the case of constant productivity of renewable-energy-based capital and the case with endogenous improvement of renewable-energy productivity through learning-by-doing effects. The model simulations demonstrate that efficient mitigation policies are feasible with readily affordable costs. From this we develop a regionalized IAM along the same methodological lines. We consider a large country composed of two regions characterized by different climates and levels of economic development. This is coupled to large residual "country" representing the "rest of the world". It is assumed that a harmonized carbon tax is imposed in both regions of the country and also in the rest of the world. We explore to which extent the transfer of money from carbon tax revenues between the two regions undertaken by a national government can moderate regional disparities in economic development and climate change impacts. The research leading to these results has received funding from the European Community's Seventh Framework Programme under Grant Agreement No. 308601 (COMPLEX)
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