Bloch Equations and Completely Positive Maps

The phenomenological dissipation of the Bloch equations is reexamined in the context of completely positive maps. Such maps occur if the dissipation arises from a reduction of a unitary evolution of a system coupled to a reservoir. In such a case the reduced dynamics for the system alone will always yield completely positive maps of the density operator. We show that, for Markovian Bloch maps, the requirement of complete positivity imposes some Bloch inequalities on the phenomenological damping constants. For non-Markovian Bloch maps some kind of Bloch inequalities involving eigenvalues of the damping basis can be established as well. As an illustration of these general properties we use the depolarizing channel with white and colored stochastic noise.Comment: Talk given at the Conference "Quantum Challenges", Falenty, Poland, September 4-7, 2003. 21 pages, 3 figure

The roles of convection, extratropical mixing, and in-situ freeze-drying in the Tropical Tropopause Layer

Mechanisms for transporting and dehydrating air across the tropical tropopause layer (TTL) are investigated with a conceptual two dimensional (2-D) model. The 2-D TTL model combines the Holton and Gettelman cold trap dehydration mechanism (Holton and Gettelman, 2001) with the two column convection model of Folkins and Martin (2005). We investigate 3 possible transport scenarios through the TTL: 1) slow uniform ascent across the level of zero radiative heating without direct convective mixing, 2) convective mixing of H<sub>2</sub>O vapor at 100% relative humidity with respect to ice (RHi) with no ice retention, and 3) convective mixing of extremely subsaturated air (100% RHi following the moist adiabatic temperature above the level of neutral buoyancy) with sufficient ice retention such that total H<sub>2</sub>O is 100%RHi. The three mechanisms produce similar seasonal cycles for H<sub>2</sub>O that are in good quantitative agreement with the Aura Microwave Limb Sounder (MLS) measurements. We use Aura MLS measurement of CO and Atmospheric Chemistry Experiment-Fourier Transform Spectrometer measurement of HDO to distinguish among the transport mechanisms. Model comparisons with the observations support the view that H<sub>2</sub>O is predominantly controlled by regions having the lowest cold point tropopause temperature but the trace species CO and HDO support the convective mixing of dry air and lofted ice. The model provides some insight into the processes affecting the long term trends observed in stratospheric H<sub>2</sub>O

Long-term changes in the upper stratospheric ozone at Syowa, Antarctica

Analyses of stratospheric ozone data determined from Dobson–Umkehr measurements since 1977 at the Syowa (69.0° S, 39.6° E), Antarctica, station show a significant decrease in ozone at altitudes higher than that of the 4 hPa pressure level during the 1980s and 1990s. Ozone values over Syowa have remained low since 2001. The time series of upper stratospheric ozone from the homogenized NOAA SBUV (Solar Backscatter Ultraviolet Instrument)(/2) 8.6 overpass data (±4°, 24 h) are in qualitative agreement with those from the Syowa station data. Ozone recovery during the austral spring over the Syowa station appears to be slower than predicted by the equivalent effective stratospheric chlorine (EESC) curve. The long-term changes in the station's equivalent latitude (indicative of vortex size/position in winter and spring) are derived from MERRA (Modern Era Retrospective-analysis for Research and Applications) reanalyses at ~ 2 and ~ 50 hPa. These data are used to attribute some of the upper and middle stratospheric ozone changes to the changes in vortex position relative to the station's location. In addition, high correlation of the Southern Hemisphere annular mode (SAM) with polar upper stratospheric ozone during years of maximum solar activity points toward a strong relationship between the strength of the Brewer–Dobson circulation and the polar stratospheric ozone recovery. In the lower stratosphere, ozone recovery attributable to CFCs (chlorofluorocarbons) is still not definitive, whereas the recovery of the upper stratosphere is slower than predicted. Further research indicates that dynamical and other chemical changes in the atmosphere are delaying detection of recovery over this station

The High Arctic in Extreme Winters: Vortex, Temperature, and MLS and ACE-FTS Trace Gas Evolution

The first three Canadian Arctic Atmospheric Chemistry Experiment (ACE) Validation Campaigns at Eureka (80° N, 86° W) were during two extremes of Arctic winter variability: Stratospheric sudden warmings (SSWs) in 2004 and 2006 were among the strongest, most prolonged on record; 2005 was a record cold winter. New satellite measurements from ACE-Fourier Transform Spectrometer (ACE-FTS), Sounding of the Atmosphere using Broadband Emission Radiometry, and Aura Microwave Limb Sounder (MLS), with meteorological analyses and Eureka lidar and radiosonde temperatures, are used to detail the meteorology in these winters, to demonstrate its influence on transport and chemistry, and to provide a context for interpretation of campaign observations. During the 2004 and 2006 SSWs, the vortex broke down throughout the stratosphere, reformed quickly in the upper stratosphere, and remained weak in the middle and lower stratosphere. The stratopause reformed at very high altitude, above where it could be accurately represented in the meteorological analyses. The 2004 and 2006 Eureka campaigns were during the recovery from the SSWs, with the redeveloping vortex over Eureka. 2005 was the coldest winter on record in the lower stratosphere, but with an early final warming in mid-March. The vortex was over Eureka at the start of the 2005 campaign, but moved away as it broke up. Disparate temperature profile structure and vortex evolution resulted in much lower (higher) temperatures in the upper (lower) stratosphere in 2004 and 2006 than in 2005. Satellite temperatures agree well with Eureka radiosondes, and with lidar data up to 50–60 km. Consistent with a strong, cold upper stratospheric vortex and enhanced radiative cooling after the SSWs, MLS and ACE-FTS trace gas measurements show strongly enhanced descent in the upper stratospheric vortex during the 2004 and 2006 Eureka campaigns compared to that in 2005

Quantum Markov Channels for Qubits

We examine stochastic maps in the context of quantum optics. Making use of the master equation, the damping basis, and the Bloch picture we calculate a non-unital, completely positive, trace-preserving map with unequal damping eigenvalues. This results in what we call the squeezed vacuum channel. A geometrical picture of the effect of stochastic noise on the set of pure state qubit density operators is provided. Finally, we study the capacity of the squeezed vacuum channel to transmit quantum information and to distribute EPR states.Comment: 18 pages, 4 figure

Validation of the Aura Microwave Limb Sounder HNOmeasurements

We assess the quality of the version 2.2 (v2.2) HNO3 measurements from the Microwave Limb Sounder (MLS) on the Earth Observing System Aura satellite. The MLS HNO3 product has been greatly improved over that in the previous version (v1.5), with smoother profiles, much more realistic behavior at the lowest retrieval levels, and correction of a high bias caused by an error in one of the spectroscopy files used in v1.5 processing. The v2.2 HNO3 data are scientifically useful over the range 215 to 3.2 hPa, with single-profile precision of ∼0.7 ppbv throughout. Vertical resolution is 3–4 km in the upper troposphere and lower stratosphere, degrading to ∼5 km in the middle and upper stratosphere. The impact of various sources of systematic uncertainty has been quantified through a comprehensive set of retrieval simulations. In aggregate, systematic uncertainties are estimated to induce in the v2.2 HNO3 measurements biases that vary with altitude between ±0.5 and ±2 ppbv and multiplicative errors of ±5–15% throughout the stratosphere, rising to ∼±30% at 215 hPa. Consistent with this uncertainty analysis, comparisons with correlative data sets show that relative to HNO3 measurements from ground-based, balloon-borne, and satellite instruments operating in both the infrared and microwave regions of the spectrum, MLS v2.2 HNO3 mixing ratios are uniformly low by 10–30% throughout most of the stratosphere. Comparisons with in situ measurements made from the DC-8 and WB-57 aircraft in the upper troposphere and lowermost stratosphere indicate that the MLS HNO3 values are low in this region as well, but are useful for scientific studies (with appropriate averaging)

Validation of ACE and OSIRIS Ozone and NO2 Measurements Using Ground Based Instruments at 80° N

The Optical Spectrograph and Infra-Red Imager System (OSIRIS) and the Atmospheric Chemistry Experiment (ACE) have been taking measurements from space since 2001 and 2003, respectively. This paper presents intercomparisons between ozone and NO2 measured by the ACE and OSIRIS satellite instruments and by ground-based instruments at the Polar Environment Atmospheric Research Laboratory (PEARL), which is located at Eureka, Canada (80◦ N, 86◦ W) and is operated by the Canadian Network for the Detection of Atmospheric Change (CANDAC). The ground-based instruments included in this study are four zenith-sky differential optical absorption spectroscopy (DOAS) instruments, one Bruker Fourier transform infrared spectrometer (FTIR) and four Brewer spectrophotometers. Ozone total columns measured by the DOAS instruments were retrieved using new Network for the Detection of Atmospheric Composition Change (NDACC) guidelines and agree to within 3.2 %. The DOAS ozone columns agree with the Brewer spectrophotometers with mean relative differences that are smaller than 1.5 %. This suggests that for these instruments the new NDACC data guidelines were successful in producing a homogenous and accurate ozone dataset at 80◦ N. Satellite 14–52km ozone and 17–40km NO2 partial columns within 500km of PEARL were calculated for ACE-FTS Version 2.2 (v2.2) plus updates, ACE-FTS v3.0, ACE-MAESTRO (Measurements of Aerosol Extinction in the Stratosphere and Troposphere Retrieved by Occultation) v1.2 and OSIRIS SaskMART v5.0x ozone and Optimal Estimation v3.0 NO2 data products. The new ACE-FTS v3.0 and the validated ACE-FTS v2.2 partial columns are nearly identical, with mean relative differences of 0.0±0.2% and −0.2±0.1% for v2.2 minus v3.0 ozone and NO2, respectively. Ozone columns were constructed from 14–52km satellite and 0–14km ozonesonde partial columns and compared with the ground-based total column measurements. The satellite-plus-sonde measurements agree with the ground-based ozone total columns with mean relative differences of 0.1–7.3 %. For NO2, partial columns from 17km upward were scaled to noon using a photo-chemical model. Mean relative differences between OSIRIS, ACE-FTS and ground-based NO2 measurements do not exceed 20 %. ACE-MAESTRO measures more NO2 than the other instruments, with mean relative differences of 25–52 %. Seasonal variation in the differences between NO2 partial columns is observed, suggesting that there are systematic errors in the measurements and/or the photochemical model corrections. For ozone spring-time measurements, additional coincidence criteria based on stratospheric temperature and the location of the polar vortex were found to improve agreement between some of the instruments. For ACE-FTS v2.2 minus Bruker FTIR, the 2007–2009 spring-time mean relative difference improved from−5.0±0.4%to−3.1±0.8% with the dynamical selection criteria. This was the largest improvement, likely because both instruments measure direct sunlight and therefore have well-characterized lines-of-sight compared with scattered sunlight measurements. For NO2, the addition of a±1◦ latitude coincidence criterion improved spring-time intercomparison results, likely due to the sharp latitudinal gradient of NO2 during polar sunrise. The differences between satellite and ground-based measurements do not show any obvious trends over the missions, indicating that both the ACE and OSIRIS instruments continue to perform well

Technical Note: A trace gas climatology derived from the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) data set

The Atmospheric Chemistry Experiment-Fourier Transform Spectrometer (ACE-FTS) aboard the Canadian satellite SCISAT (launched in August 2003) was designed to investigate the composition of the upper troposphere, stratosphere, and mesosphere. ACE-FTS utilizes solar occultation to measure temperature and pressure as well as vertical profiles of over thirty chemical species including O<sub>3</sub>, H<sub>2</sub>O, CH<sub>4</sub>, N<sub>2</sub>O, CO, NO, NO<sub>2</sub>, N<sub>2</sub>O<sub>5</sub>, HNO<sub>3</sub>, HCl, ClONO<sub>2</sub>, CCl<sub>3</sub>F, CCl<sub>2</sub>F<sub>2</sub>, and HF. Global coverage for each species is obtained approximately over a three month period and measurements are made with a vertical resolution of typically 3–4 km. A quality-controlled climatology has been created for each of these 14 baseline species, where individual profiles are averaged over the period of February 2004 to February 2009. Measurements used are from the ACE-FTS version 2.2 data set including updates for O<sub>3</sub> and N<sub>2</sub>O<sub>5</sub>. The climatological fields are provided on a monthly and three-monthly basis (DJF, MAM, JJA, SON) at 5 degree latitude and equivalent latitude spacing and on 28 pressure surfaces (26 of which are defined by the Stratospheric Processes And their Role in Climate (SPARC) Chemistry-Climate Model Validation Activity). The ACE-FTS climatological data set is available through the ACE website

The Evolution of the Stratopause During the 2006 Major Warming: Satellite Data and Assimilated Meteorological Analyses

Microwave Limb Sounder and Sounding of the Atmosphere with Broadband Emission Radiometry data show the polar stratopause, usually higher than and separated from that at midlatitudes, dropping from <55-60 to near 30 km, and cooling dramatically in January 2006 during a major stratospheric sudden warming (SSW). After a nearly isothermal period, a cool stratopause reforms near 75 km in early February, then drops to <55 km and warms. The stratopause is separated in longitude as well as latitude, with lowest temperatures in the transition regions between higher and lower stratopauses. Operational assimilated meteorological analyses, which are not constrained by data at stratopause altitude, do not capture a secondary temperature maximum that overlies the stratopause or the very high stratopause that reforms after the SSW; they underestimate the stratopause altitude variation during the SSW. High-quality daily satellite temperature measurements are invaluable in improving our understanding of stratopause evolution and its representation in models and assimilation systems

Jet characterization in the upper troposphere/lower stratosphere (UTLS): applications to climatology and transport studies

A method of classifying the upper tropospheric/lower stratospheric (UTLS) jets has been developed that allows satellite and aircraft trace gas data and meteorological fields to be efficiently mapped in a jet coordinate view. A detailed characterization of multiple tropopauses accompanies the jet characterization. Jet climatologies show the well-known high altitude subtropical and lower altitude polar jets in the upper troposphere, as well as a pattern of concentric polar and subtropical jets in the Southern Hemisphere, and shifts of the primary jet to high latitudes associated with blocking ridges in Northern Hemisphere winter. The jet-coordinate view segregates air masses differently than the commonly-used equivalent latitude (EqL) coordinate throughout the lowermost stratosphere and in the upper troposphere. Mapping O3 data from the Aura Microwave Limb Sounder (MLS) satellite and the Winter Storms aircraft datasets in jet coordinates thus emphasizes different aspects of the circulation compared to an EqL-coordinate framework: the jet coordinate reorders the data geometrically, thus highlighting the strong PV, tropopause height and trace gas gradients across the subtropical jet, whereas EqL is a dynamical coordinate that may blur these spatial relationships but provides information on irreversible transport. The jet coordinate view identifies the concentration of stratospheric ozone well below the tropopause in the region poleward of and below the jet core, as well as other transport features associated with the upper tropospheric jets. Using the jet information in EqL coordinates allows us to study trace gas distributions in regions of weak versus strong jets, and demonstrates weaker transport barriers in regions with less jet influence. MLS and Atmospheric Chemistry Experiment-Fourier Transform Spectrometer trace gas fields for spring 2008 in jet coordinates show very strong, closely correlated, PV, tropopause height and trace gas gradients across the jet, and evidence of intrusions of stratospheric air below the tropopause below and poleward of the subtropical jet; these features are consistent between instruments and among multiple trace gases. Our characterization of the jets is facilitating studies that will improve our understanding of upper tropospheric trace gas evolution