Finite size spectrum of the staggered six-vertex model with Uq($$ \mathfrak{sl} $$(2))-invariant boundary conditions

The finite size spectrum of the critical ℤ2-staggered spin-1/2 XXZ model with quantum group invariant boundary conditions is studied. For a particular (self-dual) choice of the staggering the spectrum of conformal weights of this model has been recently been shown to have a continuous component, similar as in the model with periodic boundary conditions whose continuum limit has been found to be described in terms of the non-compact SU(2, ℝ)/U(1) Euclidean black hole conformal field theory (CFT). Here we show that the same is true for a range of the staggering parameter. In addition we find that levels from the discrete part of the spectrum of this CFT emerge as the anisotropy is varied. The finite size amplitudes of both the continuous and the discrete levels are related to the corresponding eigenvalues of a quasi-momentum operator which commutes with the Hamiltonian and the transfer matrix of the model.

Measurement report: Three years of size-resolved eddy-covariance particle number flux measurements in an urban environment

Size-resolved particle number fluxes in the size range of 10 nm < particle diameter (Dp) < 200 nm were measured over a 3-year period (April 2017–March 2020) using the eddy-covariance technique at an urban site in Berlin, Germany. The observations indicated the site as a net source of particles with a median total particle number flux of FTNC=0.86 × 108 m−2 s−1. The turbulent surface–atmosphere exchange of particles was clearly dominated by ultrafine particles (Dp < 100 nm) with a share of 96 % of total particle number flux (FUFP=0.83 × 108 m−2 s−1). Annual estimates of median FTNC and FUFP slightly decreased by −9.6 % (−8.9 % for FUFP) from the first to the second observation year and a further −5.9 % (−6.1 % for FUFP) from the second to the third year. The annual variation might be due to different reasons such as the variation of flux footprints in the individual years, a slight reduction of traffic intensity in the third year, or a progressive transition of the vehicle fleet towards a higher share of low-emission standards or electric drive. Size-resolved measurements illustrated events of bidirectional fluxes, i.e. simultaneous emission and deposition fluxes within the size spectrum, which occurred more often in spring, late summer, and autumn than in winter. Multi-year observations of size-resolved particle fluxes proved to be important for a deeper understanding of particle exchange processes with the urban surface and the pronounced influence of traffic at this urban site.

Microphysical Characteristics and Environmental Isotope Effects of the Micro-Droplet Groups under the Action of Acoustic Waves

Acoustics can cause particles/droplets to agglomerate in the air medium, thereby accelerating gravity sedimentation. To assess the microphysical characteristics and environmental isotope effects of micro-droplet groups under the action of acoustic waves, an air chamber experimental platform was established, and 100 groups of controlled experiments were conducted. The characteristic particle size, size spectrum, isotope values, corresponding linear relationships with hydrogen and oxygen, and d values were analyzed. The isotope exchange equation between the micro-droplet groups and environmental water vapor inside the air chamber was investigated. The results showed that the peak size values of the micro-droplet groups increased under the action of acoustic waves. The characteristic particle size (D90) showed a “trigger effect” with the acoustic operation with a positive deviation in the size spectrum and isotope exchange between the micro-droplet groups and environmental water vapor. The relative variations in theoretical values for different sedimentation conditions were consistent with those of the experimental results. Environment isotopes could be used to trace the acoustic agglomeration process of micro-droplets in the future.

Horizontal geometry of trade-wind cumuli – aircraft observations from shortwave infrared imager versus radar profiler

This study elaborates how aircraft-based horizontal geometries of trade-wind cumulus clouds differ whether a one-dimensional (1D) profiler or a two-dimensional (2D) imager is used. While nadir profiling devices are limited to 1D realisation of the cloud transect size with limited representativeness of horizontal cloud extension, 2D imagers enhance our perspectives by mapping the horizontal cloud field. Both require high-resolution to detect the lower end of the cloud size spectrum. In this regard, the payload aboard the High Altitude and Long Range Research Aircraft (HALO) achieves a comparison and also a synergy of both measurement systems. Using the NARVAL-II campaign, we combine HALO observations from a 35.2 GHz cloud and precipitation radar (1D) and from the hyperspectral 2D imager specMACS, having a 30 times higher along-track resolution and compare their cloud masks. We examine cloud size distributions in terms of sensitivity to sample size, resolution and the considered field of view (2D or 1D). This specifies impacts on horizontal cloud sizes derived from the across-track perspective of the high-resolution imager in comparison to the radar curtain. We assess whether and how the trade-wind field amplifies uncertainties in cloud geometry observations along 1D transects through directional cloud elongation. Our findings reveal that each additional dimension, no matter of the device, causes a significant increase of observed clouds. The across-track field yields the highest increase in the cloud sample. The radar encounters difficulties to characterize the trade-wind cumuli size distribution. More than 60 % of clouds are subgrid scale for the radar. While the radar cannot resolve clouds shorter than 200 m and has a lower sensitivity, the amount of small invisible clouds leads to deviations in the size distribution. Double power law characteristics in the imager based cloud size distribution do not occur in radar observations. Along-track measurements do not necessarily cover the predominant cloud extent and inferred geometries lack of representativeness. Trade-wind cumuli show horizontal patterns similar to ellipses with a mean aspect ratio of 3 : 2. Instead of circular estimations based on the 1D transect, elliptic fits maintain the cloud area size distribution. Increasing wind speed tends to stretch clouds more and tilts them into the wind field, which makes transect measurements more representative along this axis.

Global nutrient cycling by commercially-targeted marine fish

Throughout the course of their lives fish ingest food containing essential elements, including nitrogen (N), phosphorus (P) and iron (Fe). Some of these elements are retained in the fish body to build new biomass, which acts as a stored reservoir of nutrients, while the rest is excreted or egested, providing a recycling flux to water. Fishing activity has modified the fish biomass distribution worldwide and consequently may have altered fish-mediated nutrient cycling, but this possibility remains largely unassessed, mainly due to the difficulty of estimating global fish biomass and metabolic rates. Here we quantify the role of commercially-targeted marine fish between 10 g and 100 kg () in the cycling of N, P and Fe in the global ocean, and its change due to fishing activity, by using a global size-spectrum model of marine fish populations calibrated to observations of fish catches. Our results show that the amount of nutrients stored in the global pristine , biomass was generally small compared to the ambient surface nutrient concentrations but significant in the nutrient-poor regions of the world: the North Atlantic for P, the oligotrophic gyres for N and the High Nutrient Low Chlorophyll (HNLC) regions for Fe. Similarly, the rate of nutrient removed from the ocean through fishing is globally small compared to the inputs, but can be important locally especially for Fe in the equatorial Pacific and along the western margin of South America and Africa. This model allowed us to compute the spatial distribution of the cycling of elements by the biomass at pristine and global peak catch state, which is relatively small compared to the estimated primary production demand for nutrients and estimated export production of nutrients. Pristine cycling (excretion + egestion) accounted for less than 2.7 % of the primary productivity demand for N, P and Fe globally. Relative to the export of nutrients, modeled global pristine egestion represents on average 2.3 %, 3.0 % and 1.1–22 % for N, P and Fe (low-high estimates), respectively, with a higher fraction in the low-export oligotrophic tropical gyres. Our study highlights the role of the fraction of the icthyosphere (i.e. does not include non-commercial species such as mesopelagic fish) on nutrient storage and cycling, and the potential role of fishing activities on this cycling, which could be of importance in regions of low nutrient concentration, high fish biomass and/or high productivity demand, and especially at the more local scale for Fe.