Eigenvalues for radially symmetric non-variational fully nonlinear operators

In this paper we present an elementary theory about the existence of eigenvalues for fully nonlinear radially symmetric 1-homogeneous operators. A general theory for first eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear operators exists in the framework of viscosity solutions. Here we want to show that for the radially symmetric operators (and one dimensional) a much simpler theory can be established, and that the complete set of eigenvalues and eigenfuctions characterized by the number of zeroes can be obtained

How can aerosols affect the Asian summer monsoon? Assessment during three consecutive pre-monsoon seasons from CALIPSO satellite data

The impact of aerosols above and around the Tibetan Plateau on the Asian Summer Monsoon during pre-monsoon seasons March-April-May 2007, 2008, and 2009 is investigated by means of remote sensing and radiative transfer modelling. Four source regions are found to be responsible for the high aerosol loading around the Tibetan Plateau: the Taklamakan Desert, the Ganges Plains, the Indus Plains, and the Arabian Sea. CALIPSO lidar satellite data, providing vertically resolved images of aerosols, shows aerosol concentrations to be highest in the lower 5 km of the atmosphere with only little amounts reaching the Tibetan Plateau altitude. Using a radiative transfer model we find that aerosol plumes reduce shortwave radiation throughout the Monsoon region in the seasonal average by between 20 and 30 W/m<sup>2</sup>. Peak shortwave heating in the lower troposphere reaches 0.2 K/day. In higher layers this shortwave heating is partly balanced by longwave cooling. Although high-albedo surfaces, such as deserts or the Tibetan Plateau, increase the shortwave heating by around 10%, the overall effect is strongest close to the aerosol sources. A strong elevated heating which could influence large-scale monsoonal circulations as suggested by previous studies is not found

Geographically versus dynamically defined boundary layer cloud regimes and their use to evaluate general circulation model cloud parameterizations

Regimes of tropical low-level clouds are commonly identified according to large-scale subsidence and lower tropospheric stability (LTS). This definition alone is insufficient for the distinction between regimes and limits the comparison of low-level clouds from CloudSat radar observations and the ECHAM5 GCM run with the COSP radar simulator. Comparisons of CloudSat radar cloud altitude-reflectivity histograms for stratocumulus and shallow cumulus regimes, as defined above, show nearly identical reflectivity profiles, because the distinction between the two regimes is dependent upon atmospheric stability below 700 hPa and observations above 1.5 km. Regional subsets, near California and Hawaii, for example, have large differences in reflectivity profiles than the dynamically defined domain; indicating different reflectivity profiles exist under a given large-scale environment. Regional subsets are better for the evaluation of low-level clouds in CloudSat and ECHAM5 as there is less contamination between 2.5 km and 7.5 km from precipitating hydrometeors which obscured cloud reflectivities. Key Points: Identification of low clouds by large-scale dynamics insufficient for radar Stratocumulus and shallow cumulus regimes have nearly identical reflectivities Geographical regions are better for evaluating low-level clouds with a radar. © 2013. American Geophysical Union. All Rights Reserved

Determination of radiation couplings in climate change simulations: analysis with two different linearization methods

Zeitreihen von Monatsmittelwerten des Windes in der Mesosphäre/unteren Thermosphäre über Collm werden auf mögliche Korrelationen mit der Nordatlantischen Oszillation (NAO) und der Südlichen Oszillation (SO) hin untersucht. Während eine positive Korrelation bis in die 1990er Jahre existiert, schwächt sich diese in der Folge ab und kehrt sich teilweise um. Da NAO und SO gekoppelt sind, erfolgen diese Änderungen etwa zur selben Zeit. Die Änderung der Kopplung steht wahrscheinlich in Verbindung mit einer generellen Änderung der Dynamik der mittleren Atmosphäre

Variation of cloud horizontal sizes and cloud fraction over Europe 1985–2018 in high-resolution satellite data

Aerosol-cloud interactions are a major uncertainty in estimating the anthropogenic climate change. Adjustments of cloud properties to an aerosol perturbation concern among others the cloud fraction, and have been emphasised as particularly complex. Cloud adjustments can generate important responses on the distribution of cloud horizontal sizes. We derive the cloud-size distribution as observational constraint for the cloud-fraction response from high-resolution Landsat satellite data. The goal is to carry out long-term trends in cloud sizes and cloud fraction over Europe during 1985–2018 to investigate the impact of major aerosol reductions during that time. Landsat data with a high spatial resolution of 30m was preprocessed via the web-based platform Google Earth Engine to evade the obstacle of high computational effort and time to handle the comprehensive data archive. The observed multidecadal trends indicate a widespread increase in cloud fraction during 1985–2018. This corresponds to a decrease in the number of small clouds of several 10–100m cloud length, whereas larger clouds (1 km and more), which contribute more to the cloud fraction, became more numerous. We confirm this by showing a largescale decrease of the power-law exponent describing the relative abundance of small and large clouds in the cloud-size distribution. Even though we can interpret the observed changes in cloud properties as significant trends, we do not explicitly identify a clear aerosol signal. Untangling the pure aerosol effect from other confounding factors (e.g., the local meteorology) is therefore left as an outlook for subsequent studies.Aerosol-Wolken-Wechselwirkungen stellen eine große Unsicherheit in der Quantifizierung des anthropogenen Klimawandels dar. Die sekundären Anpassungen von Wolken an eine Veränderung atmosphärischer Aerosolkonzentrationen betreffen beispielsweise denWolken-Bedeckungsgrad und sind besonders komplex. Wolkenanpassungen können sich in der Veränderung der Wolkengrößen-Verteilung widerspiegeln. Wir präsentieren eine Methode, um mittels Beobachtungen der Wolkengrößen- Verteilung zeitliche Veränderungen in Aerosol-Wolken-Wechselwirkungen nachzuweisen. Wolkengrößen-Verteilung und Wolkenbedeckungsgrad wurden mittels hochauflösender Satellitendaten der Landsat-Serie berechnet. Das Ziel ist es, langjährige Trends im Wolkenbedeckungsgrad über Europa im Zeitraum 1985–2018 herzuleiten und ggf. den Einfluss stark rückläufiger Aerosolkonzentrationen während dieser Zeit zu identifizieren. Landsat-Daten haben eine räumliche Auflösung von bis zu 30 Metern. Um die damit verbundenen großen Datenmengen prozessieren zu können, nutzen wir dieWeb-basierte Plattform Google Earth Engine. Unsere langjährigen Trends zeigen eine großskaligen Zunahme im Wolkenbedeckungsgrad zwischen 1985 und 2018. Dies ist zurückzuführen auf einen relativen Rückgang in der Anzahl kleinerer Wolken (einige 10 bis 100 Meter Länge), während größere Wolken (mehrere Kilometer),welche mehr zum Bedeckungsgrad beitragen, häufiger wurden. Dies zeigt sich im negativen Trend des Power-Law-Exponenten der Wolkengrößen- Verteilung, welcher die relative Anzahl kleiner und großer Wolken beschreibt. Auch wenn sich diese Beobachtungen als signifikante Trends herausstellen, identifizieren wir darin kein klares Aerosol-Signal. Die Isolierung des puren Aerosoleffekts von anderen beeinflussenden Faktoren, wie der lokalen Meteorologie, bietet einen Ansatzpunkt für aufbauende Studien