Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations

Exact, finite-amplitude, local wave-activity conservation laws are derived for disturbances to steady flows in the context of the two-dimensional anelastic equations. The conservation laws are expressed entirely in terms of Eulerian quantities, and have the property that, in the limit of a small-amplitude, slowly varying, monochromatic wave train, the wave-activity density A and flux F, when averaged over phase, satisfy F = cgA where cg is the group velocity of the waves. For nonparallel steady flows, the only conserved wave activity is a form of disturbance pseudoenergy; when the steady flow is parallel, there is in addition a conservation law for the disturbance pseudomomentum. The above results are obtained not only for isentropic background states (which give the so-called “deep form” of the anelastic equations), but also for arbitrary background potential-temperature profiles θ0(z) so long as the variation in θ0(z) over the depth of the fluid is small compared with θ0 itself. The Hamiltonian structure of the equations is established in both cases, and its symmetry properties discussed. An expression for available potential energy is also derived that, for the case of a stably stratified background state (i.e., dθ0/dz > 0), is locally positive definite; the expression is valid for fully three-dimensional flow. The counterparts to results for the two-dimensional Boussinesq equations are also noted.

Nonlinear stability and the saturation of instabilities to axisymmetric vortices

Nonlinear stability theorems are presented for axisymmetric vortices under the restriction that the disturbance is independent of either the azimuthal or the axial coordinate. These stability theorems are then used, in both cases, to derive rigorous upper bounds on the saturation amplitudes of instabilities. Explicit examples of such bounds are worked out for some canonical profiles. The results establish a minimum order for the dependence of saturation amplitude on supercriticality, and are thereby suggestive as to the nature of the bifurcation at the stability threshold.

On Rossby waves modified by weak sinusoidal shear

The spatial structure of beta-plane Rossby waves in a sinusoidal basic zonal flow U 0cos(γ,y) is determined analytically in the (stable) asymptotic limit of weak shear, U 0γ2 0/β≈1. The propagating neutral normal modes are found to take their greatest amplitude in the region of maximum westerly flow, while their most rapid phase variation is achieved in the region of maximum easterly flow. These results are shown to be consistent with what is obtained by ray-tracing methods in the limit of small meridional disturbance wavelength.

Rossby waves and two-dimensional turbulence in a large-scale zonal jet

The theory of homogeneous barotropic beta-plane turbulence is here extended to include effects arising from spatial inhomogeneity in the form of a zonal shear flow. Attention is restricted to the geophysically important case of zonal flows that are barotropically stable and are of larger scale than the resulting transient eddy field. Because of the presumed scale separation, the disturbance enstrophy is approximately conserved in a fully nonlinear sense, and the (nonlinear) wave-mean-flow interaction may be characterized as a shear-induced spectral transfer of disturbance enstrophy along lines of constant zonal wavenumber k. In this transfer the disturbance energy is generally not conserved. The nonlinear interactions between different disturbance components are turbulent for scales smaller than the inverse of Rhines's cascade-arrest scale κβ[identical with] (β0/2urms)½ and in this regime their leading-order effect may be characterized as a tendency to spread the enstrophy (and energy) along contours of constant total wavenumber κ [identical with] (k2 + l2)½. Insofar as this process of turbulent isotropization involves spectral transfer of disturbance enstrophy across lines of constant zonal wavenumber k, it can be readily distinguished from the shear-induced transfer which proceeds along them. However, an analysis in terms of total wavenumber K alone, which would be justified if the flow were homogeneous, would tend to mask the differences. The foregoing theoretical ideas are tested by performing direct numerical simulation experiments. It is found that the picture of classical beta-plane turbulence is altered, through the effect of the large-scale zonal flow, in the following ways: (i) while the turbulence is still confined to K Kβ, the disturbance field penetrates to the largest scales of motion; (ii) the larger disturbance scales K < Kβ exhibit a tendency to meridional rather than zonal anisotropy, namely towards v2 > u2 rather than vice versa; (iii) the initial spectral transfer rate away from an isotropic intermediate-scale source is significantly enhanced by the shear-induced transfer associated with straining by the zonal flow. This last effect occurs even when the large-scale shear appears weak to the energy-containing eddies, in the sense that dU/dy [double less-than sign] κ for typical eddy length and velocity scales.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

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.

Implementing REDD through community-based forest management: lessons from Tanzania

REDD (reduced emissions from deforestation and degradation) aims to slow carbon releases caused by forest disturbance by making payments conditional on forest quality over time. Like earlier policies to slow deforestation, REDD must change the behaviour of forest degrading actors. Broadly, it can be implemented with payments to forest users in exchange for improved forest management, thus creating incentives; through payments for enforcement, thus creating disincentives; or through addressing external drivers such as urban charcoal demand. In Tanzania, community-based forest management (CBFM), a form of participatory forest management, was chosen by the Tanzania Forest Conservation Group, a local NGO, as a model for implementing REDD pilot programmes. Payments are made to villages that have the rights to forest carbon. In exchange, the villages must demonstrably reduce deforestation at the village level. In this paper, using this pilot programme as a case study, combined with a review of the literature, we provide insights for REDD implementation in sub-Saharan Africa. We pay particular attention to leakage, monitoring and enforcement. We suggest that implementing REDD through CBFM-type structures can create appropriate incentives and behaviour change when the recipients of the REDD funds are also the key drivers of forest change. When external forces drive forest change, however, REDD through CBFM-type structures becomes an enforcement programme with local communities rather than government agencies being responsible for the enforcement. That structure imposes costs on local communities, whose local authority limits the ability to address leakage outside the particular REDD village.

Large inert carbon pool in the terrestrial biosphere at the Last Glacial Maximum

During each of the late Pleistocene glacial–interglacial transitions, atmospheric carbon dioxide concentrations rose by almost 100 ppm. The sources of this carbon are unclear, and efforts to identify them are hampered by uncertainties in the magnitude of carbon reservoirs and fluxes under glacial conditions. Here we use oxygen isotope measurements from air trapped in ice cores and ocean carbon-cycle modelling to estimate terrestrial and oceanic gross primary productivity during the Last Glacial Maximum. We find that the rate of gross terrestrial primary production during the Last Glacial Maximum was about 40±10 Pg C yr−1, half that of the pre-industrial Holocene. Despite the low levels of photosynthesis, we estimate that the late glacial terrestrial biosphere contained only 330 Pg less carbon than pre-industrial levels. We infer that the area covered by carbon-rich but unproductive biomes such as tundra and cold steppes was significantly larger during the Last Glacial Maximum, consistent with palaeoecological data. Our data also indicate the presence of an inert carbon pool of 2,300 Pg C, about 700 Pg larger than the inert carbon locked in permafrost today. We suggest that the disappearance of this carbon pool at the end of the Last Glacial Maximum may have contributed to the deglacial rise in atmospheric carbon dioxide concentrations.

[Global climate] global aerosols [in state of the climate in 2008]

The global mean temperature in 2008 was slightly cooler than that in 2007; however, it still ranks within the 10 warmest years on record. Annual mean temperatures were generally well above average in South America, northern and southern Africa, Iceland, Europe, Russia, South Asia, and Australia. In contrast, an exceptional cold outbreak occurred during January across Eurasia and over southern European Russia and southern western Siberia. There has been a general increase in land-surface temperatures and in permafrost temperatures during the last several decades throughout the Arctic region, including increases of 1° to 2°C in the last 30 to 35 years in Russia. Record setting warm summer (JJA) air temperatures were observed throughout Greenland. The year 2008 was also characterized by heavy precipitation in a number of regions of northern South America, Africa, and South Asia. In contrast, a prolonged and intense drought occurred during most of 2008 in northern Argentina, Paraguay, Uruguay, and southern Brazil, causing severe impacts to agriculture and affecting many communities. The year began with a strong La Niña episode that ended in June. Eastward surface current anomalies in the tropical Pacific Ocean in early 2008 played a major role in adjusting the basin from strong La Niña conditions to ENSO-neutral conditions by July–August, followed by a return to La Niña conditions late in December. The La Niña conditions resulted in far-reaching anomalies such as a cooling in the central tropical Pacific, Arctic Ocean, and the regions extending from the Gulf of Alaska to the west coast of North America; changes in the sea surface salinity and heat content anomalies in the tropics; and total column water vapor, cloud cover, tropospheric temperature, and precipitation patterns typical of a La Niña. Anomalously salty ocean surface salinity values in climatologically drier locations and anomalously fresh values in rainier locations observed in recent years generally persisted in 2008, suggesting an increase in the hydrological cycle. The 2008 Atlantic hurricane season was the 14th busiest on record and the only season ever recorded with major hurricanes each month from July through November. Conversely, activity in the northwest Pacific was considerably below normal during 2008. While activity in the north Indian Ocean was only slightly above average, the season was punctuated by Cyclone Nargis, which killed over 145,000 people; in addition, it was the seventh-strongest cyclone ever in the basin and the most devastating to hit Asia since 1991. Greenhouse gas concentrations continued to rise, increasing by more than expected based on with CO2 the 1979 to 2007 trend. In the oceans, the global mean uptake for 2007 is estimated to be 1.67 Pg-C, about CO2 0.07 Pg-C lower than the long-term average, making it the third-largest anomaly determined with this method since 1983, with the largest uptake of carbon over the past decade coming from the eastern Indian Ocean. Global phytoplankton chlorophyll concentrations were slightly elevated in 2008 relative to 2007, but regional changes were substantial (ranging to about 50%) and followed long-term patterns of net decreases in chlorophyll with increasing sea surface temperature. Ozone-depleting gas concentrations continued to fall globally to about 4% below the peak levels of the 2000–02 period. Total column ozone concentrations remain well below pre-1980, levels and the 2008 ozone hole was unusually large (sixth worst on record) and persistent, with low ozone values extending into the late December period. In fact the polar vortex in 2008 persisted longer than for any previous year since 1979. Northern Hemisphere snow cover extent for the year was well below average due in large part to the record-low ice extent in March and despite the record-maximum coverage in January and the shortest snow cover duration on record (which started in 1966) in the North American Arctic. Limited preliminary data imply that in 2008 glaciers continued to lose mass, and full data for 2007 show it was the 17th consecutive year of loss. The northern region of Greenland and adjacent areas of Arctic Canada experienced a particularly intense melt season, even though there was an abnormally cold winter across Greenland's southern half. One of the most dramatic signals of the general warming trend was the continued significant reduction in the extent of the summer sea-ice cover and, importantly, the decrease in the amount of relatively older, thicker ice. The extent of the 2008 summer sea-ice cover was the second-lowest value of the satellite record (which started in 1979) and 36% below the 1979–2000 average. Significant losses in the mass of ice sheets and the area of ice shelves continued, with several fjords on the northern coast of Ellesmere Island being ice free for the first time in 3,000–5,500 years. In Antarctica, the positive phase of the SAM led to record-high total sea ice extent for much of early 2008 through enhanced equatorward Ekman transport. With colder continental temperatures at this time, the 2007–08 austral summer snowmelt season was dramatically weakened, making it the second shortest melt season since 1978 (when the record began). There was strong warming and increased precipitation along the Antarctic Peninsula and west Antarctica in 2008, and also pockets of warming along coastal east Antarctica, in concert with continued declines in sea-ice concentration in the Amundsen/Bellingshausen Seas. One significant event indicative of this warming was the disintegration and retreat of the Wilkins Ice Shelf in the southwest peninsula area of Antarctica.

Ecophysiological and bioclimatic foundations for a global plant functional classification

Question: What plant properties might define plant functional types (PFTs) for the analysis of global vegetation responses to climate change, and what aspects of the physical environment might be expected to predict the distributions of PFTs? Methods: We review principles to explain the distribution of key plant traits as a function of bioclimatic variables. We focus on those whole-plant and leaf traits that are commonly used to define biomes and PFTs in global maps and models. Results: Raunkiær's plant life forms (underlying most later classifications) describe different adaptive strategies for surviving low temperature or drought, while satisfying requirements for reproduction and growth. Simple conceptual models and published observations are used to quantify the adaptive significance of leaf size for temperature regulation, leaf consistency for maintaining transpiration under drought, and phenology for the optimization of annual carbon balance. A new compilation of experimental data supports the functional definition of tropical, warm-temperate, temperate and boreal phanerophytes based on mechanisms for withstanding low temperature extremes. Chilling requirements are less well quantified, but are a necessary adjunct to cold tolerance. Functional traits generally confer both advantages and restrictions; the existence of trade-offs contributes to the diversity of plants along bioclimatic gradients. Conclusions: Quantitative analysis of plant trait distributions against bioclimatic variables is becoming possible; this opens up new opportunities for PFT classification. A PFT classification based on bioclimatic responses will need to be enhanced by information on traits related to competition, successional dynamics and disturbance.

Assessment and management of anxiety disorders in children and adolescents

Anxiety disorders in childhood and adolescence are extremely common and are often associated with lifelong psychiatric disturbance. Consistent with DSM-5 and the extant literature, this review concerns the assessment and treatment of specific phobias, separation anxiety disorder, generalised anxiety disorder, social anxiety disorder, panic disorder and agoraphobia. Evidence-based psychological treatments (cognitive behaviour therapy; CBT) for these disorders have been developed and investigated, and in recent years promising low-intensity versions of CBT interventions have been proposed that offer a means to increase access to evidence-based treatments. There is some evidence of effectiveness of pharmacological treatments for anxiety disorders in children and young people, however, routine prescription is not recommended due to concerns about potential harm.

Investigating hydrological regimes and processes in a set of catchments with temporary waters in Mediterranean Europe

Seven catchments of diverse size in Mediterranean Europe were investigated in order to understand the main aspects of their hydrological functioning. The methods included the analysis of daily and monthly precipitation, monthly potential evapotranspiration rates, flow duration curves, rainfall runoff relationships and catchment internal data for the smaller and more instrumented catchments. The results showed that the catchments were less dry than initially considered. Only one of them was really semi-arid throughout the year. All the remaining catchments showed wet seasons when precipitation exceeded potential evapotrans-piration, allowing aquifer recharge, wet runoff generation mechanisms and relevant baseflow contribution. Nevertheless, local infiltration excess (Hortonian) overland flow was inferred during summer storms in some catchments and urban overland flow in some others. The roles of karstic groundwater, human disturbance and low winter temperatures were identified as having an important impact on the hydrological regime in some of the catchments.

Ionospheric ion and electron heating at the poleward boundary of a poleward expanding substorm-disturbed region

We present observations of a poleward propagating substorm-disturbed region which was observed by the European Incoherent SCATter (EISCAT) radar and the Svalbard International Monitor for Auroral Geomagnetic Effects (IMAGE) magnetometers in the postmidnight sector. The expansion of the disturbance was launched by a substorm intensification which started similar to 25 min after the initial onset, and similar to 10 min before the disturbance arrived over Svalbard. In association with the magnetic disturbance, a poleward expanding enduring enhancement in the F region electron temperature was observed, indicative of soft electron precipitation, with a narrow band of enhanced ion temperature straddling its poleward edge, indicative of fast ion flows and ion-neutral collisional heating. This electron temperature boundary was coincident with the poleward propagating electrojet current system detected by the high-latitude IMAGE magnetometer stations and is taken to be a proxy for the observation of a substorm auroral bulge. The electron temperature boundary is inferred to have a width comparable or less than one radar range gate (similar to 60 km transverse to the magnetic field), while the region of high ion temperature was found to be approximately three gates wide, extending approximately two gates (similar to 120 km) poleward of the electron temperature boundary, and approximately one gate (similar to 60 km) equatorward. The two-beam radar line-of-sight velocity data are found to be consistent with the existence of a layer of high-speed flow in the boundary, peaking at values similar to1.5-3 km s(-1), roughly consistent with the ion temperature data. The flow is directed either east or west along the boundary depending on the direction of the flow in the poleward region. We infer that the flow is deflected along and around the boundary of the substorm-disturbed region due to the high conductivity of the latter. Variations in the flow poleward of the boundary produced no discernible magnetic effects on the ground, confirming the low conductivity of the preboundary ionosphere.

Dayside ionospheric convection changes in response to long-period interplanetary Magnetic field oscillations: Determination of the ionospheric phase velocity

Ground magnetic field perturbations recorded by the CANOPUS magnetometer network in the 7 to 13 MLT sector are used to examine how reconfigurations of the dayside polar ionospheric flow take place in response to north-south changes of the IMF. During the 6-hour interval in question IMF Bz oscillates between ±7 nT with about a 1-hour period. Corresponding variations in the ground magnetic disturbance are observed which we infer are due to changes in ionospheric flow. Cross correlation of the data obtained from two ground stations at 73.5° magnetic latitude, but separated by ∼2 hours in MLT, shows that changes in the flow are initiated in the prenoon sector (∼10 MLT) and then spread outward toward dawn and dusk with a phase speed of ∼5 km s−1 over the longitude range ∼8 to 12 MLT, slowing to ∼2 km s−1 outside this range. Cross correlating the data from these ground stations with IMP 8 IMF Bz records produces a MLT variation in the ground response delay relative to the IMF which is compatible with these deduced phase speeds. We interpret these observations in terms of the ionospheric response to the onset, expansion and decay of magnetic reconnection at the dayside magnetopause.

The excitation of plasma convection in the high-latitude ionosphere

Recent observations of ionospheric flows by ground-based radars, in particular by the European Incoherent Scatter (EISCAT) facility using the “Polar” experiment, together with previous analyses of the response of geomagnetic disturbance to variations of the interplanetary magnetic field (IMF), suggest that convection in the high-latitude ionosphere should be considered to be the sum of two intrinsically time-dependent patterns, one driven by solar wind-magnetosphere coupling at the dayside magnetopause, the other by the release of energy in the geomagnetic tail (mainly by dayside and nightside reconnection, respectively). The flows driven by dayside coupling are largest on the dayside, where they usually dominate, are associated with an expanding polar cap area, and are excited and decay on ∼10-min time scales following southward and northward turnings of the IMF, respectively. The latter finding indicates that the production of new open flux at the dayside magnetopause excites magnetospheric and ionospheric flow only for a short interval, ∼10 min, such that the flow driven by this source subsequently decays on this time scale unless maintained by the production of more open flux tubes. Correspondingly, the flows excited by the release of energy in the tail, mainly during substorms, are largest on the nightside, are associated with a contracting polar cap boundary, and are excited on ∼1-hour time scales following a southward turn of the IMF. In general, the total ionospheric flow will be the sum of the flows produced by these two sources, such that due to their different response times to changes in the IMF, considerable variations in the flow pattern can occur for a given direction and strength of the IMF. Consequently, the ionospheric electric field cannot generally be regarded as arising from a simple mapping of the solar wind electric field along open flux tubes.