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A sign pattern is an array with entries in $\{+,-,0\}$. A real matrix $Q$ is row orthogonal if $QQ^T = I$. The Strong Inner Product Property (SIPP), introduced in [B.A. Curtis and B.L. Shader, Sign patterns of orthogonal matrices and the strong inner product property, Linear Algebra Appl. 592: 228-259, 2020], is an important tool when determining whether a sign pattern allows row orthogonality because it guarantees there is a nearby matrix with the same property, allowing zero entries to be perturbed to nonzero entries, while preserving the sign of every nonzero entry. This paper uses the SIPP to initiate the study of conditions under which random sign patterns allow row orthogonality with high probability. Building on prior work, $5\times n$ nowhere zero sign patterns that minimally allow orthogonality are determined. Conditions on zero entries in a sign pattern are established that guarantee any row orthogonal matrix with such a sign pattern has the SIPP.

 

Abstract. Observations collected during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) provide a detailed description of the impact of thermodynamic and kinematic forcings on atmospheric boundary layer (ABL) stability in the central Arctic. This study reveals that the Arctic ABL is stable and near-neutral with similar frequencies, and strong stability is the most persistent of all stability regimes. MOSAiC radiosonde observations, in conjunction with observations from additional measurement platforms, including a 10 m meteorological tower, ceilometer, microwave radiometer, and radiation station, provide insight into the relationships between atmospheric stability and various atmospheric thermodynamic and kinematic forcings of ABL turbulence and how these relationships differ by season. We found that stronger stability largely occurs in low-wind (i.e., wind speeds are slow), low-radiation (i.e., surface radiative fluxes are minimal) environments; a very shallow mixed ABL forms in low-wind, high-radiation environments; weak stability occurs in high-wind, moderate-radiation environments; and a near-neutral ABL forms in high-wind, high-radiation environments. Surface pressure (a proxy for synoptic staging) partially explains the observed wind speeds for different stability regimes. Cloud frequency and atmospheric moisture contribute to the observed surface radiation budget. Unique to summer, stronger stability may also form when moist air is advected from over the warmer open ocean to over the colder sea ice surface, which decouples the colder near-surface atmosphere from the advected layer, and is identifiable through observations of fog and atmospheric moisture.

 

As part of the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC), the HELiX uncrewed aircraft system (UAS) was deployed over the sea ice in the central Arctic Ocean during summer 2020. Albedo measurements were obtained with stabilized pyranometers, and melt pond fraction was calculated from orthomosaic imagery from a surface-imaging multispectral camera. This study analyzed HELiX flight data to provide insights on the temporal and spatial evolution of albedo and melt pond fraction of the MOSAiC floe during the melt season as it drifted south through Fram Strait. The surface albedo distributions showed peak values changing from high albedo (0.55–0.6) to lower values (0.3) as the season advanced. Inspired by methods developed for satellite data, an algorithm was established to retrieve melt pond fraction from the orthomosaic images. We demonstrate that the near-surface observations of melt pond fraction were highly dependent on sample area, offering insight into the influence of subgrid scale features and spatial heterogeneity in satellite observations. Vertical observations conducted with the HELiX were used to quantify the influence of melt pond scales on observed surface albedo as a function of sensor footprint. These scaling results were used to link surface-based measurements collected during MOSAiC to broader-scale satellite data to investigate the influence of surface features on observed albedo. Albedo values blend underlying features within the sensor footprint, as determined by the melt pond size and concentration. This study framed the downscaling (upscaling) problem related to the airborne (surface) observations of surface albedo across a variety of spatial scales. 

The Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) was a yearlong expedition supported by the icebreakerR/V Polarstern, following the Transpolar Drift from October 2019 to October 2020. The campaign documented an annual cycle of physical, biological, and chemical processes impacting the atmosphere-ice-ocean system. Of central importance were measurements of the thermodynamic and dynamic evolution of the sea ice. A multi-agency international team led by the University of Colorado/CIRES and NOAA-PSL observed meteorology and surface-atmosphere energy exchanges, including radiation; turbulent momentum flux; turbulent latent and sensible heat flux; and snow conductive flux. There were four stations on the ice, a 10 m micrometeorological tower paired with a 23/30 m mast and radiation station and three autonomous Atmospheric Surface Flux Stations. Collectively, the four stations acquired ~928 days of data. This manuscript documents the acquisition and post-processing of those measurements and provides a guide for researchers to access and use the data products.

 

We present the results of a series of laboratory low-speed impacts (< 4 m s⁻¹) of centimeter-sized spherical projectiles into simulated dry and icy regolith samples. The target material was comprised of JSC-1 (Johnson Space Center) lunar simulant grains in the size range 100–250μm, mixed with similar-sized water ice grains. Impacts were performed under vacuum, either at room temperature for JSC-1 samples or at cryogenic temperatures (<150 K) for icy mixtures. We measured the ejecta masses from a collection plate and impact crater dimensions from post-impact crater photographs. We find that both the ejecta masses and crater diameters followed trends predicted by established scaling laws, albeit with different fitting parameters, and we were able to fit a strength regimeπscaling to our measured crater diameters. The water ice in our target material took two forms: grains mixed with the regolith grains and frost from air condensation coating regolith grains. In both cases, the presence of water ice in the sample led to lower ejected masses and smaller crater sizes. In addition, our measured crater sizes were several orders of magnitude larger than expected for impacts into solid rock or water ice. Using our measured scaling parameters, we applied our findings to a planetary context for the study of secondary craters on icy moons, as well as eroding collisions occurring in Saturn’s rings. We found that the deviation of our measurements from solid targets and from commonly used scaling parameters allowed us to reconcile our measurements with the models in both cases.