Technical note: A new day- and night-time Meteosat Second Generation Cirrus Detection Algorithm MeCiDA

A new cirrus detection algorithm for the Spinning Enhanced Visible and Infra-Red Imager (SEVIRI) aboard the geostationary Meteosat Second Generation (MSG), MeCiDA, is presented. The algorithm uses the seven infrared channels of SEVIRI and thus provides a consistent scheme for cirrus detection at day and night. MeCiDA combines morphological and multi-spectral threshold tests and detects optically thick and thin ice clouds. The thresholds were determined by a comprehensive theoretical study using radiative transfer simulations for various atmospheric situations as well as by manually evaluating actual satellite observations. The cirrus detection has been optimized for mid- and high latitudes but it could be adapted to other regions as well. The retrieved cirrus masks have been validated by comparison with the Moderate Resolution Imaging Spectroradiometer (MODIS) Cirrus Reflection Flag. To study possible seasonal variations in the performance of the algorithm, one scene per month of the year 2004 was randomly selected and compared with the MODIS flag. 81% of the pixels were classified identically by both algorithms. In a comparison of monthly mean values for Europe and the North-Atlantic MeCiDA detected 29.3% cirrus coverage, while the MODIS SWIR cirrus coverage was 38.1%. A lower detection efficiency is to be expected for MeCiDA, as the spatial resolution of MODIS is considerably better and as we used only the thermal infrared channels in contrast to the MODIS algorithm which uses infrared and visible radiances. The advantage of MeCiDA compared to retrievals for polar orbiting instruments or previous geostationary satellites is that it permits the derivation of quantitative data every 15 min, 24 h a day. This high temporal resolution allows the study of diurnal variations and life cycle aspects. MeCiDA is fast enough for near real-time applications

The asymptotic limits of zero modes of massless Dirac operators

Asymptotic behaviors of zero modes of the massless Dirac operator $H=\alpha\cdot D + Q(x)$ are discussed, where $\alpha= (\alpha_1, \alpha_2, \alpha_3)$ is the triple of $4 \times 4$ Dirac matrices, $D=\frac{1}{i} \nabla_x$, and $Q(x)=\big(q_{jk} (x) \big)$ is a $4\times 4$ Hermitian matrix-valued function with $| q_{jk}(x) | \le C ^{-\rho}$, $\rho >1$. We shall show that for every zero mode $f$, the asymptotic limit of $|x|^2f(x)$ as $|x| \to +\infty$ exists. The limit is expressed in terms of an integral of $Q(x)f(x)$.Comment: 9 page

On the observation of unusual high concentration of small chain-like aggregate ice crystals and large ice water contents near the top of a deep convective cloud during the CIRCLE-2 experiment

During the CIRCLE-2 experiment carried out over Western Europe in May 2007, combined in situ and remote sensing observations allowed to describe microphysical and optical properties near-top of an overshooting convective cloud (11 080 m/−58 °C). The airborne measurements were performed with the DLR Falcon aircraft specially equipped with a unique set of instruments for the extensive in situ cloud measurements of microphysical and optical properties (Polar Nephelometer, FSSP-300, Cloud Particle Imager and PMS 2-D-C) and nadir looking remote sensing observations (DLR WALES Lidar). Quasi-simultaneous space observations from MSG/SEVIRI, CALIPSO/CALIOP-WFC-IIR and CloudSat/CPR combined with airborne RASTA radar reflectivity from the French Falcon aircraft flying above the DLR Falcon depict very well convective cells which overshoot by up to 600 m the tropopause level. Unusual high values of the concentration of small ice particles, extinction, ice water content (up to 70 cm−3, 30 km−1 and 0.5 g m−3, respectively) are experienced. The mean effective diameter and the maximum particle size are 43 μm and about 300 μm, respectively. This very dense cloud causes a strong attenuation of the WALES and CALIOP lidar returns. The SEVIRI retrieved parameters confirm the occurrence of small ice crystals at the top of the convective cell. Smooth and featureless phase functions with asymmetry factors of 0.776 indicate fairly uniform optical properties. Due to small ice crystals the power-law relationship between ice water content (IWC) and radar reflectivity appears to be very different from those usually found in cirrus and anvil clouds. For a given equivalent reflectivity factor, IWCs are significantly larger for the overshooting cell than for the cirrus. Assuming the same prevalent microphysical properties over the depth of the overshooting cell, RASTA reflectivity profiles scaled into ice water content show that retrieved IWC up to 1 g m−3 may be observed near the cloud top. Extrapolating the relationship for stronger convective clouds with similar ice particles, IWC up to 5 g m−3 could be experienced with reflectivity factors no larger than about 20 dBZ. This means that for similar situations, indication of rather weak radar echo does not necessarily warn the occurrence of high ice water content carried by small ice crystals. All along the cloud penetration the shape of the ice crystals is dominated by chain-like aggregates of frozen droplets. Our results confirm previous observations that the chains of ice crystals are found in a continental deep convective systems which are known generally to generate intense electric fields causing efficient ice particle aggregation processes. Vigorous updrafts could lift supercooled droplets which are frozen extremely rapidly by homogeneous nucleation near the −37 °C level, producing therefore high concentrations of very small ice particles at upper altitudes. They are sufficient to deplete the water vapour and suppress further nucleation as confirmed by humidity measurements. These observations address scientific issues related to the microphysical properties and structure of deep convective clouds and confirm that particles smaller than 50 μm may control the radiative properties in convective-related clouds. These unusual observations may also provide some possible insights regarding engineering issues related to the failure of jet engines commonly used on commercial aircraft during flights through areas of high ice water content. However, large uncertainties of the measured and derived parameters limit our observations

Spin - or, actually: Spin and Quantum Statistics

The history of the discovery of electron spin and the Pauli principle and the mathematics of spin and quantum statistics are reviewed. Pauli's theory of the spinning electron and some of its many applications in mathematics and physics are considered in more detail. The role of the fact that the tree-level gyromagnetic factor of the electron has the value g = 2 in an analysis of stability (and instability) of matter in arbitrary external magnetic fields is highlighted. Radiative corrections and precision measurements of g are reviewed. The general connection between spin and statistics, the CPT theorem and the theory of braid statistics are described.Comment: 50 pages, no figures, seminar on "spin

Stability of Relativistic Matter With Magnetic Fields

Stability of matter with Coulomb forces has been proved for non-relativistic dynamics, including arbitrarily large magnetic fields, and for relativistic dynamics without magnetic fields. In both cases stability requires that the fine structure constant alpha be not too large. It was unclear what would happen for both relativistic dynamics and magnetic fields, or even how to formulate the problem clearly. We show that the use of the Dirac operator allows both effects, provided the filled negative energy `sea' is defined properly. The use of the free Dirac operator to define the negative levels leads to catastrophe for any alpha, but the use of the Dirac operator with magnetic field leads to stability.Comment: This is an announcement of the work in cond-mat/9610195 (LaTeX

Ground-based imaging remote sensing of ice clouds : uncertainties caused by sensor, method and atmosphere

In this study a method is introduced for the retrieval of optical thickness and effective particle size of ice clouds over a wide range of optical thickness from ground-based transmitted radiance measurements. Low optical thickness of cirrus clouds and their complex microphysics present a challenge for cloud remote sensing. In transmittance, the relationship between optical depth and radiance is ambiguous. To resolve this ambiguity the retrieval utilizes the spectral slope of radiance between 485 and 560 nm in addition to the commonly employed combination of a visible and a short-wave infrared wavelength. An extensive test of retrieval sensitivity was conducted using synthetic test spectra in which all parameters introducing uncertainty into the retrieval were varied systematically: ice crystal habit and aerosol properties, instrument noise, calibration uncertainty and the interpolation in the lookup table required by the retrieval process. The most important source of errors identified are uncertainties due to habit assumption: Averaged over all test spectra, systematic biases in the effective radius retrieval of several micrometre can arise. The statistical uncertainties of any individual retrieval can easily exceed 10 µm. Optical thickness biases are mostly below 1, while statistical uncertainties are in the range of 1 to 2.5. For demonstration and comparison to satellite data the retrieval is applied to observations by the Munich hyperspectral imager specMACS (spectrometer of the Munich Aerosol and Cloud Scanner) at the Schneefernerhaus observatory (2650 m a.s.l.) during the ACRIDICON-Zugspitze campaign in September and October 2012. Results are compared to MODIS and SEVIRI satellite-based cirrus retrievals (ACRIDICON – Aerosol, Cloud, Precipitation, and Radiation Interactions and Dynamics of Convective Cloud Systems; MODIS – Moderate Resolution Imaging Spectroradiometer; SEVIRI – Spinning Enhanced Visible and Infrared Imager). Considering the identified uncertainties for our ground-based approach and for the satellite retrievals, the comparison shows good agreement within the range of natural variability of the cloud situation in the direct surrounding

Eigenfunctions at the threshold energies of magnetic Dirac operators

Discussed are $\pm m$ modes and $\pm m$ resonances of Dirac operators with vector potentials $H_{\!A}= \alpha \cdot (D - A(x)) + m \beta$. Asymptotic limits of $\pm m$ modes at infinity are derived when $|A(x)| \le C^{-\rho}$, $\rho > 1$, provided that $H_A$ has $\pm m$ modes. In wider classes of vector potentials, sparseness of the vector potentials which give rise to the $\pm m$ modes of $H_A$ are established. It is proved that no $H_A$ has $\pm m$ resonances if $|A(x)|\le C^{-\rho}$, $\rho >3/2$.Comment: 25 pages, New results are adde

Influence of temperature and humidity on contrail formation regions in the general circulation model EMAC: a spring case study

While carbon dioxide emissions from aviation often dominate climate change discussions, non-CO2 effects such as contrails and contrail cirrus must also be considered. Despite varying estimates of their radiative forcing, avoiding contrails is a reasonable strategy for reducing aviation’s climate effects. This study examines temperature and humidity, key atmospheric parameters for contrail formation, across different ECHAM/MESSy (European Centre Hamburg General Circulation Model/Modular Earth Submodel System) Atmospheric Chemistry (EMAC) model setups. EMAC, a general circulation model, is evaluated with various vertical resolutions and two nudging methods across seven specified dynamics setups. A higher vertical resolution aims to capture steep water vapour gradients near the tropopause, crucial for accurate contrail prediction. Comparisons with reanalysis data (March–April 2014) indicate a systematic cold bias (approximately 3–5 K in mid-latitudes), particularly in setups without mean temperature nudging. In the upper troposphere and lower stratosphere, all simulations exhibit a wet bias, while lower altitudes display a dry bias, both affecting contrail formation estimates. Point-by-point comparisons along aircraft trajectories confirm similar biases. Sensitivity experiments with varying thresholds of relative humidity over ice illustrate trade-offs between achieving high hit rates and minimising false alarms in contrail detection. A single-day case study integrating aircraft and satellite observations demonstrates that EMAC’s predicted contrail coverage aligns well with the observed formation. These results suggest that, despite existing temperature and humidity biases, EMAC generally captures regions favourable for contrail formation across diverse atmospheric conditions. Addressing model biases by refining temperature and humidity representation could significantly improve contrail prediction accuracy, strengthening contrail-avoidance strategies and supporting climate-optimised flight routing to mitigate aviation's overall climate effect.</p

Air traffic and contrail changes over Europe during COVID-19: a model study

The strong reduction of air traffic during the COVID-19 pandemic provides a unique test case for the relationship between air traffic density, contrails, and their radiative forcing of climate change. Here, air traffic and contrail cirrus changes are quantified for a European domain for March to August 2020 and compared to the same period in 2019. Traffic data show a 72 % reduction in flight distance compared with 2019. This paper investigates the induced contrail changes in a model study. The contrail model results depend on various methodological details as discussed in parameter studies. In the reference case, the reduced traffic caused a reduction in contrail length. The reduction is slightly stronger than expected from the traffic change because the weather conditions in 2020 were less favorable for contrail formation than in 2019. Contrail coverage over Europe with an optical depth larger than 0.1 decreased from 4.6 % in 2019 to 1.4 % in 2020; the total cirrus cover amount changed by 28 % to 25 %. The reduced contrail coverage caused 70 % less longwave and 73 % less shortwave radiative forcing but, because of various nonlinearities, only 54 % less net forcing in this case. The methods include recently developed models for performance parameters and soot emissions. The overall propulsion efficiency of the aircraft is about 20 % smaller than estimated in earlier studies, resulting in 3 % fewer contrails. Considerable sensitivity to soot emissions is found, highlighting fuel and engine importance. The contrail model includes a new approximate method to account for water vapor exchange between contrails and background air and for radiative forcing changes due to contrail–contrail overlap. The water vapor exchange reduces available ice supersaturation in the atmosphere, which is critical for contrail formation. Contrail–contrail overlap changes the computed radiative forcing considerably. Comparisons to satellite observations are described and discussed in a parallel publication