Scaling Breaks Research Articles

Studying the Impacts of Meteorological Factors on Distribution of Cloud Horizontal Scales Based on Active Satellite

AbstractAs a significant macrophysical property, cloud horizontal scales play a role in cloud radiation, precipitation and vertical cloud overlap. Until now, however, the mechanisms behind the variations in cloud scale distribution have received far less attention. This study utilizes active satellite data from 2007 to 2016 to investigate the spatiotemporal distribution of cloud horizontal scales, and explains the variations through two meteorological factors: wind shear and atmospheric stability. Cloud scales exhibit a distinct power‐law behavior when scale break is not considered, and the power‐law exponent β is a characteristic measure of cloud scale distribution. A smaller power‐law exponent β indicates a higher frequency of large clouds. During boreal summer season, the amount of large clouds is extremely large south of the 40°S but rather small between 10°S and 20°S. As wind shear decreases or atmospheric stability increases, more large clouds occur globally. The underlying mechanisms might be associated with cloud entrainment which can be promoted by wind shear but inhibited by atmospheric stability. However, our analysis of the impacts of these two factors on cloud scale distribution across different regions and heights reveals that both wind shear and atmospheric stability play dual roles on the values of the exponent β. The potential physical mechanisms, including the effects of precipitation, are further discussed. It is observed that precipitation also exerts a dual impact on the values of the exponent β. These findings underscore the significance of considering the impacts of meteorological factors on cloud scale distribution in numerical weather prediction models.

Uncertainty of Line-of-sight Velocity Measurements of Faint Stars from Low- and Medium-resolution Optical Spectra

Massively multiplexed spectrographs will soon gather large statistical samples of stellar spectra. The accurate estimation of uncertainties on derived parameters, such as the line-of-sight velocity v los, especially for spectra with low signal-to-noise ratios (S/Ns), is paramount. We generated an ensemble of simulated optical spectra of stars as if they were observed with low- and medium-resolution fiber-fed instruments on an 8 m class telescope, similar to the Subaru Prime Focus Spectrograph, and determined v los by fitting stellar templates to the simulated spectra. We compared the empirical errors of the derived parameters—calculated from an ensemble of simulations—to the asymptotic errors determined from the Fisher matrix, as well as from Monte Carlo sampling of the posterior probability. We confirm that the uncertainty of v los scales with the inverse square root of the S/N, but also show how this scaling breaks down at low S/N and analyze the error and bias caused by template mismatch. We outline a computationally optimized algorithm to fit multiexposure data and provide a mathematical model of stellar spectrum fitting that maximizes the so called significance, which allows for calculating the error from the Fisher matrix analytically. We also introduce the effective line count, and provide a scaling relation to estimate the errors of v los measurements based on stellar type. Our analysis covers a range of stellar types with parameters that are typical of the Galactic outer disk and halo, together with analogs of stars in M31 and in satellite dwarf spheroidal galaxies around the Milky Way.

Simple scaling of extreme precipitation regime in Senegal

Extreme precipitation exhibits high temporal and spatial variability, and understanding this variability is crucial for designing hydraulic infrastructures and assessing the impacts of natural risks such as floods and droughts. The Simple Scaling (SS) model, which describes the dependence of extreme rainfall statistics on timescales, is used to estimate Intensity Duration Frequency (IDF) curves. This study aims to evaluate the validity of the Simple Scaling (SS) hypothesis for 14 rain gauges in Senegal and explore the existence of breaks in temporal scaling regimes (transition regimes). For the analysis of extreme characteristics, we considered the Annual Maximum Series (AMS) of precipitation in sub-hourly and supra-daily durations ranging from 10 min to 7 days. The empirical validation of the SS models was confirmed for the majority of the scaling intervals. We identified two scaling breaks, indicating the presence of three scaling regimes: short durations (SD), intermediate durations (ID), and long durations (LD). The spatial variation of scaling exponents reveals the existence of different scaling regimes across Senegal. The results are valuable for modeling the spatial distribution of scaling exponents, which can aid in characterizing IDF curves at ungauged locations.

Steady-state forms of channel profiles shaped by debris flow and fluvial processes

Abstract. Debris flows regularly traverse bedrock channels that dissect steep landscapes, but our understanding of bedrock erosion by debris flows and their impact on steepland morphology is still rudimentary. Quantitative models of steep bedrock channel networks are based on geomorphic transport laws designed to represent erosion by water-dominated flows. To quantify the impact of debris flow erosion on steep channel network form, it is first necessary to develop methods to estimate spatial variations in bulk debris flow properties (e.g., flow depth, velocity) throughout the channel network that can be integrated into landscape evolution models. Here, we propose and evaluate two methods to estimate spatial variations in bulk debris flow properties along the length of a channel profile. We incorporate both methods into a model designed to simulate the evolution of longitudinal channel profiles that evolve in response to debris flow and fluvial processes. To explore this model framework, we propose a general family of debris flow erosion laws where erosion rate is a function of debris flow depth and channel slope. Model results indicate that erosion by debris flows can explain the occurrence of a scaling break in the slope–area curve at low-drainage areas and that upper-network channel morphology may be useful for inferring catchment-averaged erosion rates in quasi-steady landscapes. Validating specific forms of a debris flow incision law, however, would require more detailed model–data comparisons in specific landscapes where input parameters and channel morphometry can be better constrained. Results improve our ability to interpret topographic signals within steep channel networks and identify observational targets critical for constraining a debris flow incision law.

Optimization and Evaluation of Stochastic Unified Convection Using Single‐Column Model Simulations at Multiple Observation Sites

AbstractWe extend the previously developed stochastic unified convection scheme (UNICON) for shallow convection to deep convection by parameterizing the impact of mesoscale organized flow on updraft properties. The extended stochastic UNICON parameterizes thermodynamic properties of updrafts at the near‐surface as a multivariate Gaussian distribution, where the variances of the distribution are the summation of variances from non‐organized turbulence and mesoscale organized flow. The distribution of updraft radius is parameterized as a power‐law distribution with a scale break which is parameterized as a linear function of the strength of mesoscale organized flow. The proposed parameterization is validated using a series of large‐eddy simulations of deep convection. The free parameters introduced in the formulation of stochastic UNICON are optimized using 10 cases of single‐column model simulations over the ocean. Stochastic UNICON with the optimized parameters significantly reduces the biases of thermodynamic profiles and surface precipitation rates simulated in the original UNICON for tropical convection cases. The simulation of the variation in anomalies of temperature and moisture associated with the Madden‐Julian oscillation is also improved. The overall improvements in simulated thermodynamic profiles are found to be due to the increased heating and drying tendencies by convective processes in stochastic UNICON. An additional simulation of an idealized deep convection case shows that stochastic UNICON produces enhanced cloud variabilities with dependency on updraft radius, indicating its ability to represent the coexistence of shallow and deep convection.

Vortices in a rotating holographic superfluid with Lifshitz scaling

We have extended our previous work [1] on rotating holographic superfluids to include Lifshitz scaling. Presence of this scaling breaks relativistic invariance of the boundary superfluid system and indicates the existence of a Lifshitz fixed point [2]. We have analytically shown that we still get same vortex solutions as discovered earlier in [1]. We have recovered previous results for the case of z = 1, which restores the relativistic invariance in the holographic superfluid system. However, for z $\neq$ 1 this study indicate surprising results regarding dissipation in such a holographic superfluid. We found that higher winding number vortices increase with higher values of imaginary chemical potential for values of z in the open interval (1, 2). This result is remarkable because it asserts that dissipation in the rotating holographic superfluid increases in the presence of Lifshitz scaling.

Topographic and vegetation controls of the spatial distribution of snow depth in agro-forested environments by UAV lidar

Abstract. Accurate knowledge of snow depth distributions in forested regions is crucial for applications in hydrology and ecology. In such a context, understanding and assessing the effect of vegetation and topographic conditions on snow depth variability is required. In this study, the spatial distribution of snow depth in two agro-forested sites and one coniferous site in eastern Canada was analyzed for topographic and vegetation effects on snow accumulation. Spatially distributed snow depths were derived by unmanned aerial vehicle light detection and ranging (UAV lidar) surveys conducted in 2019 and 2020. Distinct patterns of snow accumulation and erosion in open areas (fields) versus adjacent forested areas were observed in lidar-derived snow depth maps at all sites. Omnidirectional semi-variogram analysis of snow depths showed the existence of a scale break distance of less than 10 m in the forested area at all three sites, whereas open areas showed comparatively larger scale break distances (i.e., 11–14 m). The effect of vegetation and topographic variables on the spatial variability in snow depths at each site was investigated with random forest models. Results show that the underlying topography and the wind redistribution of snow along forest edges govern the snow depth variability at agro-forested sites, while forest structure variability dominates snow depth variability in the coniferous environment. These results highlight the importance of including and better representing these processes in physically based models for accurate estimates of snowpack dynamics.

Moliverse: Contextually embedding the microcosm into the universe

We present Moliverse, an integration of the molecular visualization framework VIAMD into the astronomical visualization software OpenSpace, allowing us to bridge the two extreme ends of the scale spectrum to show, for example, the gas composition in a planet’s atmosphere or molecular structures in comet trails and can empower the creation of educational exhibitions. For that purpose we do not use a linear scale traversal but break the scale continuity and show molecular simulations as focus in the context of celestial bodies. We demonstrate the application of our concept in two storytelling scenarios and envision the application both for science presentations to lay audiences and for dedicated exploration, potentially also in a molecule-only environment.

Entropy scaling of viscosity for molecular models of molten salts.

Entropy scaling relates dynamic and thermodynamic properties by reducing the viscosity to a function of only the residual entropy. Molecular simulations are used to investigate the entropy scaling of the viscosity of three models of sodium chloride and five monovalent salts. Even though the correlation between the potential energy and the virial is weak, entropy scaling applies at liquid densities for all models and salts investigated. At lower densities, entropy scaling breaks down due to the formation of ion pairs and chains. Entropy scaling can be used to develop more extendable correlations for the dynamic properties of molten salts.

Generic generation of noise-driven chaos in stochastic time delay systems: Bridging the gap with high-end simulations

Nonlinear time delay systems produce inherently delay-induced periodic oscillations, which are, however, too idealistic compared to observations. We exhibit a unified stochastic framework to systematically rectify such oscillations into oscillatory patterns with enriched temporal variabilities through generic, nonlinear responses to stochastic perturbations. Two paradigms of noise-driven chaos in high dimension are identified, fundamentally different from chaos triggered by parameter-space noise. Noteworthy is a low-dimensional stretch-and-fold mechanism, leading to stochastic strange attractors exhibiting horseshoe-like structures mirroring turbulent transport of passive tracers. The other is high-dimensional , with noise acting along the critical eigendirection and transmitted to "deeper" stable modes through nonlinearity, leading to stochastic attractors exhibiting swarm-like behaviors with power-law and scale break properties. The theory is applied to cloud delay models to parameterize missing physics such as intermittent rain and Lagrangian turbulent effects. The stochastically rectified model reproduces with fidelity complex temporal variabilities of open-cell oscillations exhibited by high-end cloud simulations.

A Decentralized Approach for Modeling Organized Convection Based on Thermal Populations on Microgrids

AbstractIn this study, a spectral model for convective transport is coupled to a thermal population model on a two‐dimensional horizontal “microgrid,” covering the typical gridbox size of general circulation models. The goal is to explore new ways of representing impacts of spatial organization in cumulus cloud fields. The thermals are considered the smallest building block of convection, with thermal life cycle and movement represented through binomial functions. Thermals interact through two simple rules, reflecting pulsating growth and environmental deformation. Long‐lived thermal clusters thus form on the microgrid, exhibiting scale growth and spacing that represent simple forms of spatial organization and memory. Size distributions of cluster number are diagnosed from the microgrid through an online clustering algorithm, and provided as input to a spectral multiplume eddy‐diffusivity mass flux scheme. This yields a decentralized transport system, in that the thermal clusters acting as independent but interacting nodes that carry information about spatial structure. The main objectives of this study are (a) to seek proof of concept of this approach, and (b) to gain insight into impacts of spatial organization on convective transport. Single‐column model experiments demonstrate satisfactory skill in reproducing two observed cases of continental shallow convection. Metrics expressing self‐organization and spatial organization match well with large‐eddy simulation results. We find that in this coupled system, spatial organization impacts convective transport primarily through the scale break in the size distribution of cluster number. The rooting of saturated plumes in the subcloud mixed layer plays a key role in this process.

Convective updrafts near sea-breeze fronts

Abstract. Sea-breeze fronts (SBFs) are frequently found to trigger deep convection. The convective updrafts near the SBF are critical in this triggering process. Here, the size and strength of the updrafts near an idealized SBF are investigated with large-eddy simulations. A central focus of this study is to compare the updrafts near the SBF, which are substantially affected by the SBF, to the updrafts ahead of the SBF, which develop in a typical convective boundary layer. It is found that the updrafts near the SBF are larger than but have similar strength to the updrafts ahead of the SBF. The larger updrafts near the SBF are produced through the merger between the postfrontal streaky structures and the updrafts originating near the SBF. Lagrangian budget analysis of vertical momentum reveals that the dynamics experienced by the parcels constituting the updrafts near the SBF is almost the same as that ahead of the SBF, so that the strength of the updrafts near the SBF is similar to that ahead of the SBF. It is also found that when the environmental wind is not included, the size and strength of the updrafts near the SBF scale with the boundary-layer height and the convective velocity scale, respectively, like those in the typical convective boundary layer; however, when the environmental wind is included, the aforementioned scaling breaks down. The present results should also apply to other boundary-layer convergence lines similar to the SBF.

Studying Interstellar Turbulence Driving Scales Using the Bispectrum

We demonstrate the utility of the bispectrum, the Fourier three-point correlation function, for studying driving scales of magnetohydrodynamic (MHD) turbulence in the interstellar medium. We calculate the bispectrum by implementing a parallelized Monte Carlo direct measurement method, which we have made publicly available. In previous works, the bispectrum has been used to identify nonlinear scaling correlations and break degeneracies in lower-order statistics like the power spectrum. We find that the bicoherence, a related statistic which measures phase coupling of Fourier modes, identifies turbulence-driving scales using density and column density fields. In particular, it shows that the driving scale is phase-coupled to scales present in the turbulent cascade. We also find that the presence of an ordered magnetic field at large scales enhances phase coupling as compared to a pure hydrodynamic case. We therefore suggest the bispectrum and bicoherence as tools for searching for non-locality for wave interactions in MHD turbulence.

Source Properties of Hydraulic‐Fracturing‐Induced Earthquakes in the Kiskatinaw Area, British Columbia, Canada

AbstractThis work presents a high resolution source property study of hydraulic fracturing induced earthquakes in the Montney Formation, a low‐permeability tight shale reservoir in the Kiskatinaw area, northeast British Columbia, Canada. We estimate source parameters, including focal mechanism solutions (FMSs), seismic moment, spectral corner frequency, and static stress drop values of earthquakes recorded between July 2017 and July 2020. Waveform‐similarity‐based event classification of 8,283 earthquakes yields 52 event families (clusters) and 1,014 isolated events (individuals). We calculate a total of 64 FMSs of events ML > 2.5 with high‐quality waveforms. Of the 64 solutions, 54 come from events within families, and are used to infer an additional 3,500 focal mechanisms of smaller‐magnitude events with similar waveforms. The other 10 are isolated events. The dominant faulting style inferred from FMSs highlights multiple cascading, shallow, strike‐slip events and generally isolated, larger‐magnitude reverse‐style events in close proximity to the Fort St. John Graben system. Inferred nodal planes of strike‐slip events are at low‐angles to regional SHmax, suggesting optimally oriented, left‐lateral faults. Reverse faulting nodal planes are roughly perpendicular to SHmax and have an orientation consistent with the reactivation of pre‐existing normal basement faults. Source spectral analysis using three approaches, including spectral‐ratio fitting, suggests a constant stress drop of 1–10 MPa and self‐similarity for induced events. Constant stress drop scaling breaks down at magnitudes smaller than ∼ML 2.0, likely due to observational bandwidth limitations.

Relations in the Size Variation of Plant Organs: a Case Study of Staghorn Sumac Leaves and Longleaf Pine Cone Scales

Plants automatically control the size variations in organs to achieve efficient exploitation of resources. However, it is unclear whether the scaling relationships of plant organs share a similar character for different individuals under varied micro-conditions (e.g., light and soil water). We conducted a case study of the lengths of staghorn sumac leaves and longleaf pine cone scales to test the relationships. Our results indicated that although there were size variations, there existed power laws of frequency in the lengths of staghorn sumac leaves and longleaf pine cone scales. The exponents differed but were positively correlated with the minimum length of leaves or cone scales. Taylor’s Law existed in the lengths of cone scales and some tree leaves, and scale break was observed. This study provides new information on scaling relationships and self-organization in the patterns of tree parts arrangement. Taylor’s Law may be used to detect minor changes in the growth regime.

Probing the timescale dependency of local and global variations in surface air temperature from climate simulations and reconstructions of the last millennia.

Earth's climate can be understood as a dynamical system that changes due to external forcing and internal couplings. Essential climate variables, such as surface air temperature, describe this dynamics. Our current interglacial, the Holocene (11700 yr ago to today), has been characterized by small variations in global mean temperature prior to anthropogenic warming. However, the mechanisms and spatiotemporal patterns of fluctuations around this mean, called temperature variability, are poorly understood despite their socioeconomic relevance for climate change mitigation and adaptation. Here we examine discrepancies between temperature variability from model simulations and paleoclimate reconstructions by categorizing the scaling behavior of local and global surface air temperature on the timescale of years to centuries. To this end, we contrast power spectral densities (PSD) and their power-law scaling using simulated and observation-based temperature series of the last 6000 yr. We further introduce the spectral gain to disentangle the externally forced and internally generated variability as a function of timescale. It is based on our estimate of the joint PSD of radiative forcing, which exhibits a scale break around the period of 7 yr. We find that local temperature series from paleoclimate reconstructions show a different scaling behavior than simulated ones, with a tendency towards stronger persistence (i.e., correlation between successive values within a time series) on periods of 10 to 200 yr. Conversely, the PSD and spectral gain of global mean temperature are consistent across data sets. Our results point to the limitation of climate models to fully represent local temperature statistics over decades to centuries. By highlighting the key characteristics of temperature variability, we pave a way to better constrain possible changes in temperature variability with global warming and assess future climate risks.

Bulk viscosity from Urca processes: npeμ matter in the neutrino-trapped regime

In this work, we extend our previous study of the bulk viscosity of hot and dense $npe$ matter induced by the Urca processes in the neutrino trapped regime to $npe\ensuremath{\mu}$ matter by adding the muonic Urca processes as well as the purely leptonic electroweak processes involving electron-muon transition. The nuclear matter is modeled in a relativistic density functional approach with two different parametrizations which predict neutrino dominated matter (DDME2 model) and antineutrino dominated matter (NL3 model) at temperatures for which neutrinos/antineutrinos are trapped. In the case of neutrino-dominated matter, the main equilibration mechanism is lepton capture, whereas in the case of antineutrino-dominated matter this is due to neutron decay. We find that the equilibration rates of Urca processes are higher than that of the pure leptonic processes, which implies that the Urca-process-driven bulk viscosity can be computed with the leptonic reactions assumed to be frozen. We find that the bulk viscosity decreases with temperature as $\ensuremath{\zeta}\ensuremath{\sim}{T}^{\ensuremath{-}2}$ at moderate temperatures. At high temperatures this scaling breaks down by sharp drops of the bulk viscosity close to the temperature where the proton fraction is density-independent and the matter becomes scale-invariant. This occurs also when the matter undergoes a transition from the antineutrino-dominated regime to the neutrino-dominated regime where the bulk viscosity attains a local maximum. We also estimate the bulk viscous dissipation timescales and find that these are in the $\mathrm{range}\ensuremath{\gtrsim}1\text{ }\text{ }\mathrm{s}$ for temperatures above the neutrino trapping temperature. These timescales would be relevant only for long-lived objects formed in binary neutron star mergers and hot proto-neutron stars formed in core-collapse supernovas.

Characterizing the effects of dry antecedent soil moisture conditions, channel transmission losses, and variable precipitation on peak flow scaling

Peak discharge to drainage area relationships are widely applied engineering solutions for design flood estimation in ungauged basins. In this study we investigated the effects of antecedent moisture conditions (AMC), rainfall duration, and channel transmission losses on discharge-drainage area power law scaling relationships. The spatial organization of peak discharges were evaluated through coupled surface-subsurface physics based numerical modeling. We take advantage past research and the detailed flexibility of HydroGeoSphere, the numerical modeling platform, to systematically vary AMC and rainfall depths evolving the current understanding of the effects on discharge-drainage area relationships. Channel network dynamics in the Beaver Creek watershed dominated the location of a scale break, or the location where the log-log linear relationship between peak discharge and drainage area is best described by two or more slopes. Single peaked hydrographs and high-quality power law scaling relationships resulted from wet AMC conditions or high precipitation depths. As we reduced the AMC, under low rainfall depths, the hillslope response diverged from the channel response, providing an unorganized system response no longer fitting the power law scaling relationship. Additionally, when initializing the system under losing stream conditions, where the stream channel is assumed unsaturated, a single peaked response ensued whereby the channel and hillslope responded in unison. This study adds to our current understanding of the physical basis of the variability of the scaling structure of peak discharges that is observed in single rainfall-runoff events by investigating the spatial organization of peak discharges under exceedingly dry antecedent soil moisture conditions.

Evolution of the magnetic and charge orders in La0.15Pr0.45Ca0.40MnO3: Assessing the role of particle size and magnetic field

The evolution of the ferromagnetic (FM)/antiferromagnetic (AFM) orders and charge order (CO) as a function of the particle size and applied magnetic field (H) has been studied in detail in the canonical phase-separated system La1−x−yPryCaxMnO3 with larger Pr content (La0.15Pr0.45Ca0.40MnO3). At lower particle size (~ 45 nm) a low TC FM phase dominates with no direct evidence of the AFM and CO phases in the magnetization (M) data. As the particle size increases, the AFM and CO grow with a concomitant decrease in the FM fraction, as shown by a decrease in the magnetization and explicit transitions. All three electronic orders become distinctly visible at particle size ~ 139 nm, with TCO ~ 213 K, TN ~ 173 K, and TC ~ 58 K. At larger sizes, e.g., ~ 370 nm, FM appears as the robust phase while the AFM and CO are quenched. However, the presence of the AFM/CO clusters in this sample is signed by the hysteresis in the FCC and FCW magnetization in the FM regime. The paramagnetic (PM) region susceptibility as a function of temperature exhibits scaling of the type χ=C(T-TCON)γ, where TCON is the temperature at which the FM response becomes visible. The exponent remains γ ≈ 1.17 for samples with less dominant CO. At the ~ 139 nm, the CO is the most robust, and the exponent takes a value γ ≈ 1.31. The effect of the magnetic field in the case of the ~ 139 nm samples shows that the AFM melts at HAFM ~ 40 kOe, while the CO melts at HCO ~ 50 kOe. The scaling of the paramagnetic regime susceptibility (H/M) at different H shows that γ remains confined to the range 1.30–1.34 up to 20 kOe, and then decreases slightly to ≈1.24 at 30 kOe. At the AFM melting magnetic field ~ 40 kOe, it drops to ≈1.13, and at further higher fields, the above scaling breaks down. Thus TCON remains a good substitute for the canonical TC in the scaling law χ=C(T-TCON)γ in strongly phase-separated manganite. Our results show that a phase-separated system with FM dominance deviates from the Curie-Weiss law valid for canonical ferromagnets. However, the presence of explicit CO makes the H/M – T scaling akin to a 3D Heisenberg ferromagnet.

Smartrock Transport From Seconds to Seasons: Shear Stress Controls on Gravel Diffusion Inferred From Hop and Rest Scaling

AbstractOur ability to test probabilistic models linking clast movements to bedload diffusion is most limited by basic field data, because measuring transport statistics during natural floods is difficult. We embedded accelerometers and gyroscopes into artificial cobbles, and measured transport during 28 daily snowmelt floods in Halfmoon Creek, Colorado, USA. The tracers captured ≈6 orders of temporal magnitude of rest durations in one data set for the first time. Motions and rests suggest a scaling transition around ≈12.5 min from subdiffusion to superdiffusion with increasing shear stress and timescale. We interpret that diurnal hydrograph cyclicity may cause another diffusion scaling break at ≈12 h. Shear stress controls and scaling uncertainties may explain differences in diffusion exponents found in several field data sets, suggesting that gravel superdiffusion scaling may be relatively universal over minutes to seasons. Methodologically, “smartrocks” can quantify field transport probabilities previously only possible in laboratory experiments.