Baroclinic stationary waves in aquaplanet models

An aquaplanet model is used to study the nature of the highly persistent low-frequency waves that have been observed in models forced by zonally symmetric boundary conditions. Using the Hayashi spectral analysis of the extratropical waves, the authors find that a quasi-stationary wave 5 belongs to a wave packet obeying a well-defined dispersion relation with eastward group velocity. The components of the dispersion relation with k ≥ 5 baroclinically convert eddy available potential energy into eddy kinetic energy, whereas those with k < 5 are baroclinically neutral. In agreement with Green’s model of baroclinic instability, wave 5 is weakly unstable, and the inverse energy cascade, which had been previously proposed as a main forcing for this type of wave, only acts as a positive feedback on its predominantly baroclinic energetics. The quasi-stationary wave is reinforced by a phase lock to an analogous pattern in the tropical convection, which provides further amplification to the wave. It is also found that the Pedlosky bounds on the phase speed of unstable waves provide guidance in explaining the latitudinal structure of the energy conversion, which is shown to be more enhanced where the zonal westerly surface wind is weaker. The wave’s energy is then trapped in the waveguide created by the upper tropospheric jet stream. In agreement with Green’s theory, as the equator-to-pole SST difference is reduced, the stationary marginally stable component shifts toward higher wavenumbers, while wave 5 becomes neutral and westward propagating. Some properties of the aquaplanet quasi-stationary waves are found to be in interesting agreement with a low frequency wave observed by Salby during December–February in the Southern Hemisphere so that this perspective on low frequency variability, apart from its value in terms of basic geophysical fluid dynamics, might be of specific interest for studying the earth’s atmosphere.

A statistical mechanical approach for the computation of the climatic response to general forcings

The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. In this paper we show for the first time how the Ruelle linear response theory, developed for studying rigorously the impact of perturbations on general observables of non-equilibrium statistical mechanical systems, can be applied with great success to analyze the climatic response to general forcings. The crucial value of the Ruelle theory lies in the fact that it allows to compute the response of the system in terms of expectation values of explicit and computable functions of the phase space averaged over the invariant measure of the unperturbed state. We choose as test bed a classical version of the Lorenz 96 model, which, in spite of its simplicity, has a well-recognized prototypical value as it is a spatially extended one-dimensional model and presents the basic ingredients, such as dissipation, advection and the presence of an external forcing, of the actual atmosphere. We recapitulate the main aspects of the general response theory and propose some new general results. We then analyze the frequency dependence of the response of both local and global observables to perturbations having localized as well as global spatial patterns. We derive analytically several properties of the corresponding susceptibilities, such as asymptotic behavior, validity of Kramers-Kronig relations, and sum rules, whose main ingredient is the causality principle. We show that all the coefficients of the leading asymptotic expansions as well as the integral constraints can be written as linear function of parameters that describe the unperturbed properties of the system, such as its average energy. Some newly obtained empirical closure equations for such parameters allow to define such properties as an explicit function of the unperturbed forcing parameter alone for a general class of chaotic Lorenz 96 models. We then verify the theoretical predictions from the outputs of the simulations up to a high degree of precision. The theory is used to explain differences in the response of local and global observables, to define the intensive properties of the system, which do not depend on the spatial resolution of the Lorenz 96 model, and to generalize the concept of climate sensitivity to all time scales. We also show how to reconstruct the linear Green function, which maps perturbations of general time patterns into changes in the expectation value of the considered observable for finite as well as infinite time. Finally, we propose a simple yet general methodology to study general Climate Change problems on virtually any time scale by resorting to only well selected simulations, and by taking full advantage of ensemble methods. The specific case of globally averaged surface temperature response to a general pattern of change of the CO2 concentration is discussed. We believe that the proposed approach may constitute a mathematically rigorous and practically very effective way to approach the problem of climate sensitivity, climate prediction, and climate change from a radically new perspective.

Identifying and quantifying nonconservative energy production/destruction terms in hydrostatic Boussinesq primitive equation models

This paper seeks to illustrate the point that physical inconsistencies between thermodynamics and dynamics usually introduce nonconservative production/destruction terms in the local total energy balance equation in numerical ocean general circulation models (OGCMs). Such terms potentially give rise to undesirable forces and/or diabatic terms in the momentum and thermodynamic equations, respectively, which could explain some of the observed errors in simulated ocean currents and water masses. In this paper, a theoretical framework is developed to provide a practical method to determine such nonconservative terms, which is illustrated in the context of a relatively simple form of the hydrostatic Boussinesq primitive equation used in early versions of OGCMs, for which at least four main potential sources of energy nonconservation are identified; they arise from: (1) the “hanging” kinetic energy dissipation term; (2) assuming potential or conservative temperature to be a conservative quantity; (3) the interaction of the Boussinesq approximation with the parameterizations of turbulent mixing of temperature and salinity; (4) some adiabatic compressibility effects due to the Boussinesq approximation. In practice, OGCMs also possess spurious numerical energy sources and sinks, but they are not explicitly addressed here. Apart from (1), the identified nonconservative energy sources/sinks are not sign definite, allowing for possible widespread cancellation when integrated globally. Locally, however, these terms may be of the same order of magnitude as actual energy conversion terms thought to occur in the oceans. Although the actual impact of these nonconservative energy terms on the overall accuracy and physical realism of the oceans is difficult to ascertain, an important issue is whether they could impact on transient simulations, and on the transition toward different circulation regimes associated with a significant reorganization of the different energy reservoirs. Some possible solutions for improvement are examined. It is thus found that the term (2) can be substantially reduced by at least one order of magnitude by using conservative temperature instead of potential temperature. Using the anelastic approximation, however, which was initially thought as a possible way to greatly improve the accuracy of the energy budget, would only marginally reduce the term (4) with no impact on the terms (1), (2) and (3).

Signal detection for orthogonal space-time block coding over time-selective fading channels: the H(i) systems

One major assumption in all orthogonal space-time block coding (O-STBC) schemes is that the channel remains static over the length of the code word. However, time-selective fading channels do exist, and in such case conventional O-STBC detectors can suffer from a large error floor in the high signal-to-noise ratio (SNR) cases. As a sequel to the authors' previous papers on this subject, this paper aims to eliminate the error floor of the H(i)-coded O-STBC system (i = 3 and 4) by employing the techniques of: 1) zero forcing (ZF) and 2) parallel interference cancellation (PIC). It is. shown that for an H(i)-coded system the PIC is a much better choice than the ZF in terms of both performance and computational complexity. Compared with the, conventional H(i) detector, the PIC detector incurs a moderately higher computational complexity, but this can well be justified by the enormous improvement.

Performance comparison of the optimal and the zero-forcing beamforming algorithms under practical conditions

The optimal and the zero-forcing beamformers are two commonly used algorithms in the subspace-based blind beamforming technology. The optimal beamformer is regarded as the algorithm with the best output SINR. The zero-forcing algorithm emphasizes the co-channel interference cancellation. This paper compares the performance of these two algorithms under some practical conditions: the effect of the finite data length and the existence of the angle estimation error. The investigation reveals that the zero-forcing algorithm can be more robust in the practical environment than the optimal algorithm.

Influence of dynamics on the changes in tropical cloud radiative forcing during the 1998 El Niño

Satellite measurements of the radiation budget and data from the U.S. National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis are used to investigate the links between anomalous cloud radiative forcing over the tropical west Pacific warm pool and the tropical dynamics and sea surface temperature (SST) distribution during 1998. The ratio, N, of the shortwave cloud forcing (SWCF) to longwave cloud forcing (LWCF) (N = −SWCF/LWCF) is used to infer information on cloud altitude. A higher than average N during 1998 appears to be related to two separate phenomena. First, dynamic regime-dependent changes explain high values of N (associated with low cloud altitude) for small magnitudes of SWCF and LWCF (low cloud fraction), which reflect the unusual occurrence of mean subsiding motion over the tropical west Pacific during 1998, associated with the anomalous SST distribution. Second, Tropics-wide long-term changes in the spatial-mean cloud forcing, independent of dynamic regime, explain the higher values of N during both 1998 and in 1994/95. The changes in dynamic regime and their anomalous structure in 1998 are well simulated by version HadAM3 of the Hadley Centre climate model, forced by the observed SSTs. However, the LWCF and SWCF are poorly simulated, as are the interannual changes in N. It is argued that improved representation of LWCF and SWCF and their dependence on dynamical forcing are required before the cloud feedbacks simulated by climate models can be trusted.

Long-term effect of volcanic forcing on ocean heat content

Explosive volcanic eruptions cause episodic negative radiative forcing of the climate system. Using coupled atmosphere-ocean general circulation models (AOGCMs) subjected to historical forcing since the late nineteenth century, previous authors have shown that each large volcanic eruption is associated with a sudden drop in ocean heat content and sea-level from which the subsequent recovery is slow. Here we show that this effect may be an artefact of experimental design, caused by the AOGCMs not having been spun up to a steady state with volcanic forcing before the historical integrations begin. Because volcanic forcing has a long-term negative average, a cooling tendency is thus imposed on the ocean in the historical simulation. We recommend that an extra experiment be carried out in parallel to the historical simulation, with constant time-mean historical volcanic forcing, in order to correct for this effect and avoid misinterpretation of ocean heat content changes

Changes to Indian Ocean subantarctic mode water in a coupled climate model as CO2 forcing increases

Subantarctic mode water (SAMW) has been shown to be a good indicator of anthropogenic climate change in coupled climate models. SAMW in a coupled climate model and the response of modeled SAMW to increasing CO2 are examined in detail. How SAMW adjusts from climatological values toward a new equilibrium in the coupled model, with different climatological temperature and salinity properties, is shown. The combined formation rate of SAMW and Antarctic intermediate water is calculated as approximately 18 Sv (Sv ≡ 106 m3 s−1) in the Indian sector of the Southern Ocean, slightly lower than climatological values would suggest. When forced with increasing CO2, SAMW is produced at a similar rate but at lower densities. This result suggests that the rate of heat uptake in this part of the ocean will be unchanged by anthropogenic forcing. The important signal in the response of SAMW is the shift to colder and fresher values on isopycnals that is believed to be related to changes in thermodynamic surface forcing. It is shown that, given uniform forcing, SAMW is expected to enhance the signal relative to other water masses. Independent increases in surface heating or freshwater forcing can produce changes similar to those observed, but the two different types of forcing are distinguishable using separate forcing experiments, hodographs, and passive anomaly tracers. The changes in SAMW forced by increasing CO2 are dominated by surface heating, but changes to freshwater fluxes are also important.

Uncertainty in the relationship between climate forcing and hydrological response in UK catchments

This paper assesses the relationship between amount of climate forcing – as indexed by global mean temperature change – and hydrological response in a sample of UK catchments. It constructs climate scenarios representing different changes in global mean temperature from an ensemble of 21 climate models assessed in the IPCC AR4. The results show a considerable range in impact between the 21 climate models, with – for example - change in summer runoff at a 2oC increase in global mean temperature varying between -40% and +20%. There is evidence of clustering in the results, particularly in projected changes in summer runoff and indicators of low flows, implying that the ensemble mean is not an appropriate generalised indicator of impact, and that the standard deviation of responses does not adequately characterise uncertainty. The uncertainty in hydrological impact is therefore best characterised by considering the shape of the distribution of responses across multiple climate scenarios. For some climate model patterns, and some catchments, there is also evidence that linear climate change forcings produce non-linear hydrological impacts. For most variables and catchments, the effects of climate change are apparent above the effects of natural multi-decadal variability with an increase in global mean temperature above 1oC, but there are differences between catchments. Based on the scenarios represented in the ensemble, the effect of climate change in northern upland catchments will be seen soonest in indicators of high flows, but in southern catchments effects will be apparent soonest in measures of summer and low flows. The uncertainty in response between different climate model patterns is considerably greater than the range due to uncertainty in hydrological model parameterisation.

Remote forcing of the Antarctic Circumpolar Current by diapycnal mixing

We show that diapycnal mixing can drive a significant Antarctic Circumpolar Current (ACC) volume transport, even when the mixing is located remotely in northern-hemisphere ocean basins. In the case of remote forcing, the globally-averaged diapycnal mixing coefficient is the important parameter. This result is anticipated from theoretical arguments and demonstrated in a global ocean circulation model. The impact of enhanced diapycnal mixing on the ACC during glacial periods is discussed.