Comments on some recent measurements of anomalously steep N2O and O3tracer spectra in the stratospheric surf zone

Recent aircraft measurements, primarily in the extratropics, of the horizontal variance of nitrous oxide (N2O) and ozone (O3) in the middle stratosphere indicate that horizontal spectra of the tracer variance scale nearly as k−2, where k is the spatial wavenumber along the aircraft flight track [Strahan and Mahlman, 1994; Bacmeister et al., 1996]. This spectral scaling has been regarded as inconsistent with the accepted picture of stratospheric tracer motion; large-scale quasi-two-dimensional tracer advection typically yields a k−1 scaling (i.e., the classical Batchelor spectrum). In this paper it is argued that the nearly k−2 scaling seen in the measurements is a natural outcome of quasi-two-dimensional filamentation of the polar vortex edge. The accepted picture of stratospheric tracer motion can thus be retained: no additional physical processes are needed to account for deviations from the Batchelor spectrum. Our argument is based on the finite lifetime of tracer filaments and on the “singularity spectrum” associated with a one-dimensional field composed of randomly spaced jumps in concentration.

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids

In addition to the Hamiltonian functional itself, non-canonical Hamiltonian dynamical systems generally possess integral invariants known as ‘Casimir functionals’. In the case of the Euler equations for a perfect fluid, the Casimir functionals correspond to the vortex topology, whose invariance derives from the particle-relabelling symmetry of the underlying Lagrangian equations of motion. In a recent paper, Vallis, Carnevale & Young (1989) have presented algorithms for finding steady states of the Euler equations that represent extrema of energy subject to given vortex topology, and are therefore stable. The purpose of this note is to point out a very general method for modifying any Hamiltonian dynamical system into an algorithm that is analogous to those of Vallis etal. in that it will systematically increase or decrease the energy of the system while preserving all of the Casimir invariants. By incorporating momentum into the extremization procedure, the algorithm is able to find steadily-translating as well as steady stable states. The method is applied to a variety of perfect-fluid systems, including Euler flow as well as compressible and incompressible stratified flow.

On the interpretation of Andrews’ theorem

Andrews (1984) has shown that any flow satisfying Arnol'd's (1965, 1966) sufficient conditions for stability must be zonally-symmetric if the boundary conditions on the flow are zonally-symmetric. This result appears to place very strong restrictions on the kinds of flows that can be proved to be stable by Arnol'd's theorems. In this paper, Andrews’ theorem is re-examined, paying special attention to the case of an unbounded domain. It is shown that, in that case, Andrews’ theorem generally fails to apply, and Arnol'd-stable flows do exist that are not zonally-symmetric. The example of a circular vortex with a monotonic vorticity profile is a case in point. A proof of the finite-amplitude version of the Rayleigh stability theorem for circular vortices is also established; despite its similarity to the Arnol'd theorems it seems not to have been put on record before.

The importance of surface pressure changes in the response of the atmosphere to zonally-symmetric thermal and mechanical forcing

he classical problem of the response of a balanced, axisymmetric vortex to thermal and mechanical forcing is re-examined, paying special attention to the lower boundary condition. The correct condition is DΦ/Dt = 0, where Φ is the geopotential and D/Dt the material derivative, which explicitly accounts for a mass redistribution as part of the mean-flow response. This redistribution is neglected when using the boundary condition Dp/Dt = 0, which has conventionally been applied in this problem. It is shown that applying the incorrect boundary condition, and thereby ignoring the surface pressure change, leads to a zonal wind acceleration δū/δt that is too strong, especially near the surface. The effect is significant for planetary-scale forcing even when applied at tropopause level. A comparison is made between the mean-flow evolution in a baroclinic life-cycle, as simulated in a fully nonlinear, primitive-equation model, and that predicted by using the simulated eddy fluxes in the zonally-symmetric response problem. Use of the correct lower boundary condition is shown to lead to improved agreement.

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

Lower-stratospheric radiative damping and polar-night jet oscillation events

The effect of stratospheric radiative damping time scales on stratospheric variability and on stratosphere–troposphere coupling is investigated in a simplified global circulation model by modifying the vertical profile of radiative damping in the stratosphere while holding it fixed in the troposphere. Perpetual-January conditions are imposed, with sinusoidal topography of zonal wavenumber 1 or 2. The depth and duration of the simulated sudden stratospheric warmings closely track the lower-stratospheric radiative time scales. Simulations with the most realistic profiles of radiative damping exhibit extended time-scale recoveries analogous to polar-night jet oscillation (PJO) events, which are observed to follow sufficiently deep stratospheric warmings. These events are characterized by weak lower-stratospheric winds and enhanced stability near the tropopause, which persist for up to 3 months following the initial warming. They are obtained with both wave-1 and wave-2 topography. Planetary-scale Eliassen–Palm (EP) fluxes entering the vortex are also suppressed, which is in agreement with observed PJO events. Consistent with previous studies, the tropospheric jets shift equatorward in response to the warmings. The duration of the shift is closely correlated with the period of enhanced stability. The magnitude of the shift in these runs, however, is sensitive only to the zonal wavenumber of the topography. Although the shift is sustained primarily by synoptic-scale eddies, the net effect of the topographic form drag and the planetary-scale fluxes is not negligible; they damp the surface wind response but enhance the vertical shear. The tropospheric response may also reduce the generation of planetary waves, further extending the stratospheric dynamical time scales.

Southern annular mode dynamics in observations and models, Part I: The influence of climatological zonal wind biases in a comprehensive GCM

A common bias among global climate models (GCMs) is that they exhibit tropospheric southern annular mode (SAM) variability that is much too persistent in the Southern Hemisphere (SH) summertime. This is of concern for the ability to accurately predict future SH circulation changes, so it is important that it be understood and alleviated. In this two-part study, specifically targeted experiments with the Canadian Middle Atmosphere Model (CMAM) are used to improve understanding of the enhanced summertime SAM persistence. Given the ubiquity of this bias among comprehensive GCMs, it is likely that the results will be relevant for other climate models. Here, in Part I, the influence of climatological circulation biases on SAM variability is assessed, with a particular focus on two common biases that could enhance summertime SAM persistence: the too-late breakdown of the Antarctic stratospheric vortex and the equatorward bias in the SH tropospheric midlatitude jet. Four simulations are used to investigate the role of each of these biases in CMAM. Nudging and bias correcting procedures are used to systematically remove zonal-mean stratospheric variability and/or remove climatological zonal wind biases. The SAM time-scale bias is not alleviated by improving either the timing of the stratospheric vortex breakdown or the climatological jet structure. Even in the absence of stratospheric variability and with an improved climatological circulation, the model time scales are biased long. This points toward a bias in internal tropospheric dynamics that is not caused by the tropospheric jet structure bias. The underlying cause of this is examined in more detail in Part II of this study.

The effect of non-uniform radiative damping on the zonal-mean dynamics of the extratropical middle atmosphere

The effect of spatial and temporal variations in the radiative damping rate on the response to an imposed forcing or diabatic heating is examined in a zonal-mean model of the middle atmosphere. Attention is restricted to the extratropics, where a linear approach is viable. It is found that regions with weak radiative damping rates are more sensitive in terms of temperature to the remote influence of the diabatic circulation. The delay in the response in such regions can mean that ‘downward’ control is not achieved on seasonal time-scales. A seasonal variation in the radiative damping rate modulates the evolution of the response and leaves a transient-like signature in the annual mean temperature field. Several idealized examples are considered, motivated by topical questions. It is found that wave drag outside the polar vortex can significantly affect the temperatures in its interior, so that high-latitude, high-altitude gravity-wave drag is not the only mechanism for warming the southern hemisphere polar vortex. Diabatic mass transport through the 100 hPa surface is found to lag the seasonal evolution of the wave drag that drives the transport, and thus cannot be considered to be in the downward control regime. On the other hand, the seasonal variation of the radiative damping rate is found to make only a weak contribution to the annual mean temperature increase that has been observed above the ozone hole. Copyright © 2002 Royal Meteorological Society.

Satellite observations and modeling of transport in the upper troposphere through the lower mesosphere during the 2006 major stratospheric sudden warming

An unusually strong and prolonged stratospheric sudden warming (SSW) in January 2006 was the first major SSW for which globally distributed long-lived trace gas data are available covering the upper troposphere through the lower mesosphere. We use Aura Microwave Limb Sounder (MLS), Atmospheric Chemistry Experiment-Fourier Transform Spectrometer (ACE-FTS) data, the SLIMCAT Chemistry Transport Model (CTM), and assimilated meteorological analyses to provide a comprehensive picture of transport during this event. The upper tropospheric ridge that triggered the SSW was associated with an elevated tropopause and layering in trace gas profiles in conjunction with stratospheric and tropospheric intrusions. Anomalous poleward transport (with corresponding quasi-isentropic troposphere-to-stratosphere exchange at the lowest levels studied) in the region over the ridge extended well into the lower stratosphere. In the middle and upper stratosphere, the breakdown of the polar vortex transport barrier was seen in a signature of rapid, widespread mixing in trace gases, including CO, H2O, CH4 and N2O. The vortex broke down slightly later and more slowly in the lower than in the middle stratosphere. In the middle and lower stratosphere, small remnants with trace gas values characteristic of the pre-SSW vortex lingered through the weak and slow recovery of the vortex. The upper stratospheric vortex quickly reformed, and, as enhanced diabatic descent set in, CO descended into this strong vortex, echoing the fall vortex development. Trace gas evolution in the SLIMCAT CTM agrees well with that in the satellite trace gas data from the upper troposphere through the middle stratosphere. In the upper stratosphere and lower mesosphere, the SLIMCAT simulation does not capture the strong descent of mesospheric CO and H2O values into the reformed vortex; this poor CTM performance in the upper stratosphere and lower mesosphere results primarily from biases in the diabatic descent in assimilated analyses.

[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.

Controlling market power of vertically integrated firms in electricity networks: demand response of aggregator agents

This article reports the results of an experiment that examined how demand aggregators can discipline vertically-integrated firms - generator and distributor-retailer holdings-, which have a high share in wholesale electricity market with uniform price double auction (UPDA). We initially develop a treatment where holding members redistribute the profit based on the imposition of supra-competitive prices, in equal proportions (50%-50%). Subsequently, we introduce a vertical disintegration (unbundling) treatment with holding-s information sharing, where profits are distributed according to market outcomes. Finally, a third treatment is performed to introduce two active demand aggregators, with flexible interruptible loads in real time. We found that the introduction of responsive demand aggregators neutralizes the power market and increases market efficiency, even beyond what is achieved through vertical disintegration.

High-latitude influence of the quasi-biennial oscillation

The interannual variability of the stratospheric winter polar vortex is correlated with the phase of the quasi-biennial oscillation (QBO) of tropical stratospheric winds. This dynamical coupling between high and low latitudes, often referred to as the Holton–Tan effect, has been the subject of numerous observational and modelling studies, yet important questions regarding its mechanism remain unanswered. In particular it remains unclear which vertical levels of the QBO exert the strongest influence on the winter polar vortex, and how QBO–vortex coupling interacts with the effects of other sources of atmospheric interannual variability such as the 11-year solar cycle or the El Nino Southern Oscillation. As stratosphere-resolving general circulation models begin to resolve the QBO and represent its teleconnections with other parts of the climate system, it seems timely to summarize what is currently known about the QBO’s high-latitude influence. In this review article, we offer a synthesis of the modelling and observational analyses of QBO–vortex coupling that have appeared in the literature, and update the observational record.

SPARC Data Initiative: Comparison of water vapor climatologies from international satellite limb sounders

Within the SPARC Data Initiative, the first comprehensive assessment of the quality of 13 water vapor products from 11 limb-viewing satellite instruments (LIMS, SAGE II, UARS-MLS, HALOE, POAM III, SMR, SAGE III, MIPAS, SCIAMACHY, ACE-FTS, and Aura-MLS) obtained within the time period 1978-2010 has been performed. Each instrument's water vapor profile measurements were compiled into monthly zonal mean time series on a common latitude-pressure grid. These time series serve as basis for the "climatological" validation approach used within the project. The evaluations include comparisons of monthly or annual zonal mean cross sections and seasonal cycles in the tropical and extratropical upper troposphere and lower stratosphere averaged over one or more years, comparisons of interannual variability, and a study of the time evolution of physical features in water vapor such as the tropical tape recorder and polar vortex dehydration. Our knowledge of the atmospheric mean state in water vapor is best in the lower and middle stratosphere of the tropics and midlatitudes, with a relative uncertainty of. 2-6% (as quantified by the standard deviation of the instruments' multiannual means). The uncertainty increases toward the polar regions (+/- 10-15%), the mesosphere (+/- 15%), and the upper troposphere/lower stratosphere below 100 hPa (+/- 30-50%), where sampling issues add uncertainty due to large gradients and high natural variability in water vapor. The minimum found in multiannual (1998-2008) mean water vapor in the tropical lower stratosphere is 3.5 ppmv (+/- 14%), with slightly larger uncertainties for monthly mean values. The frequently used HALOE water vapor data set shows consistently lower values than most other data sets throughout the atmosphere, with increasing deviations from the multi-instrument mean below 100 hPa in both the tropics and extratropics. The knowledge gained from these comparisons and regarding the quality of the individual data sets in different regions of the atmosphere will help to improve model-measurement comparisons (e.g., for diagnostics such as the tropical tape recorder or seasonal cycles), data merging activities, and studies of climate variability.

The potential impact of changes in lower stratospheric water vapour on stratospheric temperatures over the past 30 years

This study investigates the potential contribution of observed changes in lower stratospheric water vapour to stratospheric temperature variations over the past three decades using a comprehensive global climate model (GCM). Three case studies are considered. In the first, the net increase in stratospheric water vapour (SWV) from 1980–2010 (derived from the Boulder frost-point hygrometer record using the gross assumption that this is globally representative) is estimated to have cooled the lower stratosphere by up to ∼0.2 K decade−1 in the global and annual mean; this is ∼40% of the observed cooling trend over this period. In the Arctic winter stratosphere there is a dynamical response to the increase in SWV, with enhanced polar cooling of 0.6 K decade−1 at 50 hPa and warming of 0.5 K decade−1 at 1 hPa. In the second case study, the observed decrease in tropical lower stratospheric water vapour after the year 2000 (imposed in the GCM as a simplified representation of the observed changes derived from satellite data) is estimated to have caused a relative increase in tropical lower stratospheric temperatures by ∼0.3 K at 50 hPa. In the third case study, the wintertime dehydration in the Antarctic stratospheric polar vortex (again using a simplified representation of the changes seen in a satellite dataset) is estimated to cause a relative warming of the Southern Hemisphere polar stratosphere by up to 1 K at 100 hPa from July–October. This is accompanied by a weakening of the westerly winds on the poleward flank of the stratospheric jet by up to 1.5 m s−1 in the GCM. The results show that, if the measurements are representative of global variations, SWV should be considered as important a driver of transient and long-term variations in lower stratospheric temperature over the past 30 years as increases in long-lived greenhouse gases and stratospheric ozone depletion.