Quasi-generalized variables

The numerical solution of a system of differential and algebraic equations is difficult, due to the appearance of numerical instabilities. A method is presented here which permits numerical solutions of such a system to be obtained which satisfy the algebraic constraint equations exactly without reducing the order of the differential equations. The method is demonstrated using examples from mechanics

Doppler Rayleigh/Mie/Raman lidar for wind and temperature measurements in the middle atmosphere up to 80 km

A direct detection Doppler lidar for measuring wind speed in the middle atmosphere up to 80 km with 2 h resolution was implemented in the ALOMAR Rayleigh/Mie/Raman lidar (69° N, 16° E). The random error of the line of sight wind is about 0.6 m/s and 10 m/s at 49 km and 80 km, respectively. We use a Doppler Rayleigh Iodine Spectrometer (DoRIS) at the iodine line 1109 (~532.260 nm). DoRIS uses two branches of intensity cascaded channels to cover the dynamic range from 10 to 100 km altitude. The wind detection system was designed to extend the existing multi-wavelength observations of aerosol and temperature performed at wavelengths of 355 nm, 532 nm and 1064 nm. The lidar uses two lasers with a mean power of 14 W at 532 nm each and two 1.8 m diameter tiltable telescopes. Below about 49 km altitude the accuracy and time resolution is limited by the maximum count rate of the detectors used and not by the number of photons available. We report about the first simultaneous Rayleigh temperature and wind measurements by lidar in the strato- and mesosphere on 17 and 23 January 2009

Temporal variability of tidal and gravity waves during a record long 10-day continuous lidar sounding

Gravity waves (GWs) as well as solar tides are a key driving mechanism for the circulation in the Earth's atmosphere. The propagation of gravity waves is strongly affected by tidal waves as they modulate the mean background wind field and vice versa, which is not yet fully understood and not adequately implemented in many circulation models. The daylight-capable Rayleigh–Mie–Raman (RMR) lidar at Kühlungsborn (54° N, 12° E) typically provides temperature data to investigate both wave phenomena during one full day or several consecutive days in the middle atmosphere between 30 and 75 km altitude. Outstanding weather conditions in May 2016 allowed for an unprecedented 10-day continuous lidar measurement, which shows a large variability of gravity waves and tides on timescales of days. Using a one-dimensional spectral filtering technique, gravity and tidal waves are separated according to their specific periods or vertical wavelengths, and their temporal evolution is studied. During the measurement period a strong 24 h wave occurs only between 40 and 60 km and vanishes after a few days. The disappearance is related to an enhancement of gravity waves with periods of 4–8 h. Wind data provided by ECMWF are used to analyze the meteorological situation at our site. The local wind structure changes during the observation period, which leads to different propagation conditions for gravity waves in the last days of the measurement period and therefore a strong GW activity. The analysis indicates a further change in wave–wave interaction resulting in a minimum of the 24 h tide. The observed variability of tides and gravity waves on timescales of a few days clearly demonstrates the importance of continuous measurements with high temporal and spatial resolution to detect interaction phenomena, which can help to improve parametrization schemes of GWs in general circulation models

Solar and lunar tides in noctilucent clouds as determined by ground-based lidar

Noctilucent clouds (NLCs) occur during summer from midlatitudes to high latitudes. They consist of nanometer-sized ice particles in an altitude range from 80 to 90 km and are sensitive to ambient temperature and water vapor content, which makes them a suitable tracer for variability on all timescales. The data set acquired by the ALOMAR Rayleigh-Mie-Raman (RMR) lidar covers 21 years and is investigated regarding tidal signatures in NLCs. For the first time solar and lunar tidal parameters in NLCs were determined simultaneously from the same data. Several NLC parameters are subject to persistent mean variations throughout the solar day as well as the lunar day. Variations with lunar time are generally smaller compared to variations with solar time. NLC occurrence frequency shows the most robust imprint of the lunar semidiurnal tide. Its amplitude is about 50 % of the solar semidiurnal tide, which is surprisingly large. Phase progressions of NLC occurrence frequency indicate upward propagating solar tides. Below 84 km altitude the corresponding vertical wavelengths are between 20 and 30 km. For the lunar semidiurnal tide phase progressions vary symmetrically with respect to the maximum of the NLC layer. © Author(s) 2018

On the evaluation of the phase relation between temperature and wind tides based on ground-based measurements and reanalysis data in the middle atmosphere

The variability in the middle atmosphere is driven by a variety of waves covering different spatial and temporal scales. We diagnose the variability in the thermal tides due to changes in the background wind by an adaptive spectral filter, which takes the intermittency of tides into account. We apply this diagnostic to temperature observations from daylight-capable lidar at midlatitudes (54° N, 12° E) as well as to reanalysis data of horizontal winds from Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2). These reanalysis data provide additional wind information in the altitude range between 30 and 70 km at the location of the lidar as well as on a global scale. Using the global data gives information on the tidal modes seen at one location. A comparison of the temperature and wind information affirms whether there is a fixed phase relation of the tidal waves in the temperature and the wind data. We found that in general the local tidal signatures are dominated by migrating tidal modes, and the signature is weaker in temperatures than in winds. While the meridional wind tide leads the zonal wind tide by 90°, the phase relation between the temperature and the wind tide is more complex. At certain altitudes the temperature tide follows the zonal wind tide. This knowledge helps in improving the interpretation of the seasonal variation in tides from different observables, especially when only data from single locations are used. The findings provide additional information about the phase stability of tidal waves, and the results clearly show the importance of a measurement acquisition on a routine basis with high temporal and spatial resolution. © 2019 Author(s)

On microphysical processes of noctilucent clouds (NLC): Observations and modeling of mean and width of the particle size-distribution

Noctilucent clouds (NLC) in the polar summer mesopause region have been observed in Norway (69° N, 16° E) between 1998 and 2009 by 3-color lidar technique. Assuming a mono-modal Gaussian size distribution we deduce mean and width of the particle sizes throughout the clouds. We observe a quasi linear relationship between distribution width and mean of the particle size at the top of the clouds and a deviation from this behavior for particle sizes larger than 40 nm, most often in the lower part of the layer. The vertically integrated particle properties show that 65% of the data follows the linear relationship with a slope of 0.42±0.02 for mean particle sizes up to 40 nm. For the vertically resolved particle properties (Δz = Combining double low line 0.15 km) the slope is comparable and about 0.39±0.03. For particles larger than 40 nm the distribution width becomes nearly independent of particle size and even decreases in the lower part of the layer. We compare our observations to microphysical modeling of noctilucent clouds and find that the distribution width depends on turbulence, the time that turbulence can act (cloud age), and the sampling volume/time (atmospheric variability). The model results nicely reproduce the measurements and show that the observed slope can be explained by eddy diffusion profiles as observed from rocket measurements. © 2010 Author(s)

Quantification of waves in lidar observations of noctilucent clouds at scales from seconds to minutes

We present small-scale structures and waves observed in noctilucent clouds (NLC) by lidar at an unprecedented temporal resolution of 30 s or less. The measurements were taken with the Rayleigh/Mie/Raman lidar at the ALOMAR observatory in northern Norway (69 N) in the years 2008-2011. We find multiple layer NLC in 7.9% of the time for a brightness threshold of δ β 12 × 10-10 m-1 sr-1. In comparison to 10 min averaged data, the 30 s dataset shows considerably more structure. For limited periods, quasi-monochromatic waves in NLC altitude variations are common, in accord with ground-based NLC imagery. For the combined dataset, on the other hand, we do not find preferred periods but rather significant periods at all timescales observed (1 min to 1 h). Typical wave amplitudes in the layer vertical displacements are 0.2 km with maximum amplitudes up to 2.3 km. Average spectral slopes of temporal altitude and brightness variations are-2.01 ± 0.25 for centroid altitude,-1.41 ± 0.24 for peak brightness and-1.73 ± 0.25 for integrated brightness. Evaluating a new single-pulse detection system, we observe altitude variations of 70 s period and spectral slopes down to a scale of 10 s. We evaluate the suitability of NLC parameters as tracers for gravity waves

Polar middle atmosphere temperature climatology from Rayleigh lidar measurements at ALOMAR (69° N)

Rayleigh lidar temperature profiles have been derived in the polar middle atmosphere from 834 measurements with the ALOMAR Rayleigh/Mie/Raman lidar (69.3° N, 16.0° E) in the years 1997–2005. Since our instrument is able to operate under full daylight conditions, the unique data set presented here extends over the entire year and covers the altitude region 30 km–85 km in winter and 30 km–65 km in summer. Comparisons of our lidar data set to reference atmospheres and ECMWF analyses show agreement within a few Kelvin in summer but in winter higher temperatures below 55 km and lower temperatures above by as much as 25 K, due likely to superior resolution of stratospheric warming and associated mesospheric cooling events. We also present a temperature climatology for the entire lower and middle atmosphere at 69° N obtained from a combination of lidar measurements, falling sphere measurements and ECMWF analyses. Day to day temperature variability in the lidar data is found to be largest in winter and smallest in summer

Offshoring, tasks, and the skill-wage pattern

The paper investigates the relationship between offshoring, wages, and the ease with which individuals' tasks can be offshored. Our analysis relates to recent theoretical contributions arguing that there is only a loose relationship between the suitability of a task for offshoring and the associated skill level. Accordingly, wage effects of offshoring can be very heterogeneous within skill groups. We test this hypothesis by combining micro-level information on wages and demographic and workplace characteristics as well as occupational infor- mation relating to the degree of offshorability with industry-level data on offshoring. Our main results suggest that in partial equilibrium, wage effects of offshoring are fairly modest but far from homogeneous and depend significantly on the extent to which the respective task requires personal interaction or can be described as non-routine. When allowing for cross-industry movement of workers, i.e., looking at a situation closer to general equilibrium, the magnitude of the wage effects of offshoring becomes substantial. Low- and medium-skilled workers experience significant wage cuts due to offshoring which, however, again strongly depend on the degree of personal interaction and non-routine content