Radiative forcing due to aviation water vapour emissions

Three emissions inventories have been used with a fully Lagrangian trajectory model to calculate the stratospheric accumulation of water vapour emissions from aircraft, and the resulting radiative forcing. The annual and global mean radiative forcing due to present-day aviation water vapour emissions has been found to be 0.9 [0.3 to 1.4] mW m^2. This is around a factor of three smaller than the value given in recent assessments, and the upper bound is much lower than a recently suggested 20 mW m^2 upper bound. This forcing is sensitive to the vertical distribution of emissions, and, to a lesser extent, interannual variability in meteorology. Large differences in the vertical distribution of emissions within the inventories have been identified, which result in the choice of inventory being the largest source of differences in the calculation of the radiative forcing due to the emissions. Analysis of Northern Hemisphere trajectories demonstrates that the assumption of an e-folding time is not always appropriate for stratospheric emissions. A linear model is more representative for emissions that enter the stratosphere far above the tropopause.

Design of delay-tolerant linear dispersion codes

In cooperative communication networks, owing to the nodes' arbitrary geographical locations and individual oscillators, the system is fundamentally asynchronous. This will damage some of the key properties of the space-time codes and can lead to substantial performance degradation. In this paper, we study the design of linear dispersion codes (LDCs) for such asynchronous cooperative communication networks. Firstly, the concept of conventional LDCs is extended to the delay-tolerant version and new design criteria are discussed. Then we propose a new design method to yield delay-tolerant LDCs that reach the optimal Jensen's upper bound on ergodic capacity as well as minimum average pairwise error probability. The proposed design employs stochastic gradient algorithm to approach a local optimum. Moreover, it is improved by using simulated annealing type optimization to increase the likelihood of the global optimum. The proposed method allows for flexible number of nodes, receive antennas, modulated symbols and flexible length of codewords. Simulation results confirm the performance of the newly-proposed delay-tolerant LDCs.

Power allocation strategies for distributed space-time codes in two-way relay networks

We study a two-way relay network (TWRN), where distributed space-time codes are constructed across multiple relay terminals in an amplify-and-forward mode. Each relay transmits a scaled linear combination of its received symbols and their conjugates,with the scaling factor chosen based on automatic gain control. We consider equal power allocation (EPA) across the relays, as well as the optimal power allocation (OPA) strategy given access to instantaneous channel state information (CSI). For EPA, we derive an upper bound on the pairwise-error-probability (PEP), from which we prove that full diversity is achieved in TWRNs. This result is in contrast to one-way relay networks, in which case a maximum diversity order of only unity can be obtained. When instantaneous CSI is available at the relays, we show that the OPA which minimizes the conditional PEP of the worse link can be cast as a generalized linear fractional program, which can be solved efficiently using the Dinkelback-type procedure.We also prove that, if the sum-power of the relay terminals is constrained, then the OPA will activate at most two relays.

Scenario and modelling uncertainty in global mean temperature change derived from emission-driven global climate models

We compare future changes in global mean temperature in response to different future scenarios which, for the first time, arise from emission-driven rather than concentration-driven perturbed parameter ensemble of a global climate model (GCM). These new GCM simulations sample uncertainties in atmospheric feedbacks, land carbon cycle, ocean physics and aerosol sulphur cycle processes. We find broader ranges of projected temperature responses arising when considering emission rather than concentration-driven simulations (with 10–90th percentile ranges of 1.7 K for the aggressive mitigation scenario, up to 3.9 K for the high-end, business as usual scenario). A small minority of simulations resulting from combinations of strong atmospheric feedbacks and carbon cycle responses show temperature increases in excess of 9 K (RCP8.5) and even under aggressive mitigation (RCP2.6) temperatures in excess of 4 K. While the simulations point to much larger temperature ranges for emission-driven experiments, they do not change existing expectations (based on previous concentration-driven experiments) on the timescales over which different sources of uncertainty are important. The new simulations sample a range of future atmospheric concentrations for each emission scenario. Both in the case of SRES A1B and the Representative Concentration Pathways (RCPs), the concentration scenarios used to drive GCM ensembles, lies towards the lower end of our simulated distribution. This design decision (a legacy of previous assessments) is likely to lead concentration-driven experiments to under-sample strong feedback responses in future projections. Our ensemble of emission-driven simulations span the global temperature response of the CMIP5 emission-driven simulations, except at the low end. Combinations of low climate sensitivity and low carbon cycle feedbacks lead to a number of CMIP5 responses to lie below our ensemble range. The ensemble simulates a number of high-end responses which lie above the CMIP5 carbon cycle range. These high-end simulations can be linked to sampling a number of stronger carbon cycle feedbacks and to sampling climate sensitivities above 4.5 K. This latter aspect highlights the priority in identifying real-world climate-sensitivity constraints which, if achieved, would lead to reductions on the upper bound of projected global mean temperature change. The ensembles of simulations presented here provides a framework to explore relationships between present-day observables and future changes, while the large spread of future-projected changes highlights the ongoing need for such work.

Averaging, slaving and balance dynamics in a simple atmospheric model

We report numerical results from a study of balance dynamics using a simple model of atmospheric motion that is designed to help address the question of why balance dynamics is so stable. The non-autonomous Hamiltonian model has a chaotic slow degree of freedom (representing vortical modes) coupled to one or two linear fast oscillators (representing inertia-gravity waves). The system is said to be balanced when the fast and slow degrees of freedom are separated. We find adiabatic invariants that drift slowly in time. This drift is consistent with a random-walk behaviour at a speed which qualitatively scales, even for modest time scale separations, as the upper bound given by Neishtadt’s and Nekhoroshev’s theorems. Moreover, a similar type of scaling is observed for solutions obtained using a singular perturbation (‘slaving’) technique in resonant cases where Nekhoroshev’s theorem does not apply. We present evidence that the smaller Lyapunov exponents of the system scale exponentially as well. The results suggest that the observed stability of nearly-slow motion is a consequence of the approximate adiabatic invariance of the fast motion.

Nonlinear symmetric stability of planetary atmospheres

The energy–Casimir method is applied to the problem of symmetric stability in the context of a compressible, hydrostatic planetary atmosphere with a general equation of state. Formal stability criteria for symmetric disturbances to a zonally symmetric baroclinic flow are obtained. In the special case of a perfect gas the results of Stevens (1983) are recovered. Finite-amplitude stability conditions are also obtained that provide an upper bound on a certain positive-definite measure of disturbance amplitude.

Nonlinear saturation of baroclinic instability: part I: the two-layer model

A rigorous bound is derived which limits the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow within the context of the two-layer model. The bound is valid for conservative (unforced) flow, as well as for forced-dissipative flow that when the dissipation is proportional to the potential vorticity. The method used to derive the bound relies on the existence of a nonlinear Liapunov (normed) stability theorem for subcritical flows, which is a finite-amplitude generalization of the Charney-Stern theorem. For the special case of the Philips model of baroclinic instability, and in the limit of infinitesimal initial nonzonal disturbance amplitude, an improved form of the bound is possible which states that the potential enstrophy of the nonzonal flow cannot exceed ϵβ2, where ϵ = (U − Ucrit)/Ucrit is the (relative) supereriticality. This upper bound turns out to be extremely similar to the maximum predicted by the weakly nonlinear theory. For unforced flow with ϵ < 1, the bound demonstrates that the nonzonal flow cannot contain all of the potential enstrophy in the system; hence in this range of initial supercriticality the total flow must remain, in a certain sense, “close” to a zonal state.

Time development of small disturbances to plane Couette Flow

The question of linear sheared-disturbance evolution in constant-shear parallel flow is here reexamined with regard to the temporary-amplification phenomenon noted first by Orr in 1907. The results apply directly to Rossby waves on a beta-plane, and are also relevant to the Eady model of baroclinic instability. It is shown that an isotropic initial distribution of standing waves maintains a constant energy level throughout the shearing process, the amplification of some waves being precisely balanced by the decay of the others. An expression is obtained for the energy of a distribution of disturbances whose wavevectors lie within a given angular wedge and an upper bound derived. It is concluded that the case for ubiquitous amplification made in recent studies may have been somewhat overstated: while carefully-chosen individual Fourier components can amplify considerably before they decay. a general distribution will tend to exhibit little or no amplification.

Seasonal to interannual Arctic sea-ice predictability in current GCMs

We establish the first inter-model comparison of seasonal to interannual predictability of present-day Arctic climate by performing coordinated sets of idealized ensemble predictions with four state-of-the-art global climate models. For Arctic sea-ice extent and volume, there is potential predictive skill for lead times of up to three years, and potential prediction errors have similar growth rates and magnitudes across the models. Spatial patterns of potential prediction errors differ substantially between the models, but some features are robust. Sea-ice concentration errors are largest in the marginal ice zone, and in winter they are almost zero away from the ice edge. Sea-ice thickness errors are amplified along the coasts of the Arctic Ocean, an effect that is dominated by sea-ice advection. These results give an upper bound on the ability of current global climate models to predict important aspects of Arctic climate.

Climate responses to anthropogenic emissions of short-lived climate pollutants

Policies to control air quality focus on mitigating emissions of aerosols and their precursors, and other short-lived climate pollutants (SLCPs). On a local scale, these policies will have beneficial impacts on health and crop yields, by reducing particulate matter (PM) and surface ozone concentrations; however, the climate impacts of reducing emissions of SLCPs are less straightforward to predict. In this paper we consider a set of idealised, extreme mitigation strategies, in which the total anthropogenic emissions of individual SLCP emissions species are removed. This provides an upper bound on the potential climate impacts of such air quality strategies. We focus on evaluating the climate responses to changes in anthropogenic emissions of aerosol precursor species: black carbon (BC), organic carbon (OC) and sulphur dioxide (SO2). We perform climate integrations with four fully coupled atmosphere-ocean global climate models (AOGCMs), and examine the effects on global and regional climate of removing the total land-based anthropogenic emissions of each of the three aerosol precursor species. We find that the SO2 emissions reductions lead to the strongest response, with all three models showing an increase in surface temperature focussed in the northern hemisphere high latitudes, and a corresponding increase in global mean precipitation and run-off. Changes in precipitation and run-off patterns are driven mostly by a northward shift in the ITCZ, consistent with the hemispherically asymmetric warming pattern driven by the emissions changes. The BC and OC emissions reductions give a much weaker forcing signal, and there is some disagreement between models in the sign of the climate responses to these perturbations. These differences between models are due largely to natural variability in sea-ice extent, circulation patterns and cloud changes. This large natural variability component to the signal when the ocean circulation and sea-ice are free-running means that the BC and OC mitigation measures do not necessarily lead to a discernible climate response.

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Clear-sky biases in satellite infrared estimates of upper tropospheric humidity and its trends

We use microwave retrievals of upper tropospheric humidity (UTH) to estimate the impact of clear-sky-only sampling by infrared instruments on the distribution, variability and trends in UTH. Our method isolates the impact of the clear-sky-only sampling, without convolving errors from other sources. On daily time scales IR-sampled UTH contains large data gaps in convectively active areas, with only about 20-30 % of the tropics (30 S­ 30 N) being sampled. This results in a dry bias of about -9 %RH in the area-weighted tropical daily UTH time series. On monthly scales, maximum clear-sky bias (CSB) is up to -30 %RH over convectively active areas. The magnitude of CSB shows significant correlations with UTH itself (-0.5) and also with the variability in UTH (-0.6). We also show that IR-sampled UTH time series have higher interannual variability and smaller trends compared to microwave sampling. We argue that a significant part of the smaller trend results from the contrasting influence of diurnal drift in the satellite measurements on the wet and dry regions of the tropics.

Observed changes in top-of-the-atmosphere radiation and upper-ocean heating consistent within uncertainty

Global climate change results from a small yet persistent imbalance between the amount of sunlight absorbed by Earth and the thermal radiation emitted back to space. An apparent inconsistency has been diagnosed between interannual variations in the net radiation imbalance inferred from satellite measurements and upper-ocean heating rate from in situ measurements, and this inconsistency has been interpreted as ‘missing energy’ in the system. Here we present a revised analysis of net radiation at the top of the atmosphere from satellite data, and we estimate ocean heat content, based on three independent sources. We find that the difference between the heat balance at the top of the atmosphere and upper-ocean heat content change is not statistically significant when accounting for observational uncertainties in ocean measurements, given transitions in instrumentation and sampling. Furthermore, variability in Earth’s energy imbalance relating to El Niño-Southern Oscillation is found to be consistent within observational uncertainties among the satellite measurements, a reanalysis model simulation and one of the ocean heat content records. We combine satellite data with ocean measurements to depths of 1,800 m, and show that between January 2001 and December 2010, Earth has been steadily accumulating energy at a rate of 0.50±0.43 Wm−2 (uncertainties at the 90% confidence level). We conclude that energy storage is continuing to increase in the sub-surface ocean.

The upper end of climate model temperature projections is inconsistent with past warming

Climate models predict a large range of possible future temperatures for a particular scenario of future emissions of greenhouse gases and other anthropogenic forcings of climate. Given that further warming in coming decades could threaten increasing risks of climatic disruption, it is important to determine whether model projections are consistent with temperature changes already observed. This can be achieved by quantifying the extent to which increases in well mixed greenhouse gases and changes in other anthropogenic and natural forcings have already altered temperature patterns around the globe. Here, for the first time, we combine multiple climate models into a single synthesized estimate of future warming rates consistent with past temperature changes. We show that the observed evolution of near-surface temperatures appears to indicate lower ranges (5–95%) for warming (0.35–0.82 K and 0.45–0.93 K by the 2020s (2020–9) relative to 1986–2005 under the RCP4.5 and 8.5 scenarios respectively) than the equivalent ranges projected by the CMIP5 climate models (0.48–1.00 K and 0.51–1.16 K respectively). Our results indicate that for each RCP the upper end of the range of CMIP5 climate model projections is inconsistent with past warming.

An improved sum-product estimate for general finite fields

An improved sum-product estimate for subsets of a finite field whose order is not prime is provided. It is shown, under certain conditions, that max{∣∣∣A+A∣∣∣,∣∣∣A⋅A∣∣∣}≫∣∣A∣∣12/11(log2∣∣A∣∣)5/11. This new estimate matches, up to a logarithmic factor, the current best known bound obtained over prime fields by Rudnev