scholarly journals On reconciling disparate studies of the sea-ice floe size distribution

Elem Sci Anth ◽  
2018 ◽  
Vol 6 ◽  
Author(s):  
Harry L. Stern ◽  
Axel J. Schweiger ◽  
Jinlun Zhang ◽  
Michael Steele
Keyword(s):  
Sea Ice ◽  
Size Distribution ◽  
Power Law ◽  
Goodness Of Fit ◽  
Accurate Method ◽  
Spatial And Temporal Variability ◽  
Size Distributions ◽  
Power Law Model ◽  
Power Law Distribution ◽  
Goodness Of Fit Test

The size distribution of sea-ice floes is an important descriptor of the sea-ice cover. Most studies report that floe sizes follow a power-law distribution over some size range, but the power-law exponents often differ substantially. Other studies report two power-law regimes over different size ranges, or more complicated behavior. We review the construction of power-law floe size distributions and compare the results of previous studies. Differences between studies may be due to spatial and temporal variability of the floe size distribution, sampling variability, inadequacy of the power-law model, or flaws in the mathematical analysis. For a power-law model, the most accurate method for determining the exponent from data is Maximum Likelihood Estimation; least-squares methods based on log-log plots of the data yield biased estimates. After calculating the power-law exponent from data, a goodness-of-fit test should be applied to determine whether or not the power-law model actually describes the distribution of the data. These analysis principles have been described in the literature but have not generally been applied to floe size distributions. Numerical ice-ocean models are beginning to simulate the floe size distribution, which should give further insight into the interpretation of observational studies.

POWER-LAW DISTRIBUTION OF RIVER BASIN SIZES

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 521-528 ◽  
Author(s):  
HIDEKI TAKAYASU
Keyword(s):  
Size Distribution ◽  
River Basin ◽  
Power Law ◽  
Point Of View ◽  
The Self ◽  
General Point ◽  
Size Distributions ◽  
Power Law Distribution ◽  
River Models ◽  
River Pattern

River models are reviewed with emphasis on the power-law nature of basin size distributions. From a general point of view, the whole river pattern on a surface can be regarded as a kind of tiling by random self-affine branches. Applying the idea of stable distributions, we show that the self-affinity and tiling condition naturally derive the power-law basin size distribution.

A comparison of two alternative approaches to modelling the sea ice floe size distribution.

2020 ◽  
Author(s):  
Adam Bateson ◽  
Daniel Feltham ◽  
David Schröder ◽  
Lucia Hosekova ◽  
Jeff Ridley ◽  
...  
Keyword(s):  
Sea Ice ◽  
Size Distribution ◽  
Power Law ◽  
Spatial Scales ◽  
Thickness Distribution ◽  
Power Law Distribution ◽  
Momentum Exchange ◽  
Alternative Approaches ◽  
The Impact ◽  
Large Response

<p>Sea ice exists as individual units of ice called floes. These floes can vary by orders of magnitude in diameter over small spatial scales. They are better described by a floe size distribution (FSD) rather than by a single diameter. Observations of the FSD are frequently fitted to a power law with a negative exponent. Floe size can influence several sea ice processes including the lateral melt rate, momentum exchange between the sea ice, ocean and atmosphere, and sea ice rheology. There have been several recent efforts to develop a model of the floe size distribution to include within sea ice models to improve the representation of floe size beyond a fixed single value. Some of these involve significant approximations about the shape and variability of the distribution whereas others adopt a more prognostic approach that does not restrict the shape of the distribution.</p><p>In this study we compare the impacts of two alternative approaches to modelling the FSD within the CICE sea ice model. The first assumes floes follow a power law distribution with a constant exponent. Parameterisations of processes thought to influence the floe size distribution are expressed in terms of a variable FSD tracer. The second uses a prognostic floe size-thickness distribution. The sea ice area in individual floe size categories evolves independently such that the shape of distribution is an emergent behaviour rather than imposed. Here we compare the impact of the two modelling approaches on the thermodynamic evolution of the sea ice. We show that both predict an increase in lateral melt with a compensating reduction in basal melt. We find that the magnitude of this change is highly dependent on the form of the distribution for the smallest floes. We also explore the impact of both FSD models on the momentum exchange of the sea ice and find a large response in the spatial distribution of sea ice volume. Finally, we will discuss whether the results from the prognostic FSD model support the assumptions required to construct the power law derived FSD model.</p>

scholarly journals Estimating The Sea Ice Floe Size Distribution Using Satellite Altimetry: Theory, Climatology, and Model Comparison

2019 ◽  
Author(s):  
Christopher Horvat ◽  
Lettie Roach ◽  
Rachel Tilling ◽  
Cecilia Bitz ◽  
Baylor Fox-Kemper ◽  
...  
Keyword(s):  
Sea Ice ◽  
Size Distribution ◽  
Power Law ◽  
Model Comparison ◽  
Climate Model ◽  
Thickness Distribution ◽  
Wave Model ◽  
Polar Regions ◽  
Scaling Exponent ◽  
Ocean Surface Waves

Abstract. In sea-ice-covered areas, the sea ice floe size distribution (FSD) plays an important role in many processes affecting the coupled sea-ice-ocean-atmosphere system. Observations of the FSD are spare – traditionally taken via a pain-staking analysis of ice surface photography – and the seasonal and inter-annual evolution of floe size regionally and globally is largely unknown. Frequently, measured FSDs are assessed using a single number, the scaling exponent of the closest power law fit to the observed floe size data, although in the absence of adequate datasets there have been limited tests of this power-law hypothesis. Here we derive and explain a mathematical technique for deriving statistics of the sea ice FSD from polar-orbiting altimeters, satellites with sub-daily return times to polar regions with high along-track resolutions. Applied to the CryoSat-2 radio altimetric record, covering the period from 2010–2018, and incorporating 11 million individual floe samples, we produce the first climatology and seasonal cycle of sea ice floe size statistics. We then perform the first pan-Arctic test of the power law hypothesis, finding limited support in the range of floe sizes typically analyzed in photographic observational studies. We compare the seasonal variability in observed floe size to fully coupled climate model simulations including a prognostic floe size and thickness distribution and coupled wave model, finding good agreement in regions where modeled ocean surface waves cause sea ice fracture.

Power Law Distributions and the Size Distribution of Strikes

2017 ◽  
Vol 48 (3) ◽  
pp. 561-587 ◽  
Author(s):  
Michele Campolieti
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Model Fit ◽  
Power Law Distribution ◽  
Policy Perspective ◽  
Methodological Research ◽  
Canadian Data ◽  
Alternative Measures ◽  
Power Law Distributions ◽  
Research And Policy

Using Canadian data from 1976 to 2014, I study the size distribution of strikes with three alternative measures of strike size: the number of workers on strike, strike duration in calendar days, and the number of person calendar days lost to a strike. I use a maximum likelihood framework that provides a way to estimate distributions, evaluate model fit, and also test against alternative distributions. I consider a few theories that can create power law distributions in strike size, such as the joint costs model that posits strike size is inversely proportional to dispute costs. I find that the power law distribution fits the data for the number of lost person calendar days relatively well and is also more appropriate than the lognormal distribution. I also discuss the implications of my findings from a methodological, research, and policy perspective.

Country Dependence on Company Size Distributions and a Numerical Model Based on Competition and Cooperation

Fractals ◽  
1998 ◽  
Vol 06 (01) ◽  
pp. 67-79 ◽  
Author(s):  
Hideki Takayasu ◽  
Kenji Okuyama
Keyword(s):  
Numerical Model ◽  
Power Law ◽  
Growth Rates ◽  
Company Size ◽  
Size Distributions ◽  
Competitive Growth ◽  
Small Companies ◽  
Power Law Distribution ◽  
Protection Effect ◽  
Competition And Cooperation

By analyzing international company data we find that company size distributions are not universal but clearly depend on country. In each country, the size distributions for different categories of business are quite similar. In order to understand the country dependence we introduce a numerical model of company size which is based on two effects: stochastic competitive growth by capital exchange, and deterministic protection of small companies by equi-partition of taxed wealth. A power law distribution is realized when the protection effect is negligible. The model is also consistent with the empirical laws for company's growth rates.

scholarly journals Modeling the seasonal evolution of the Arctic sea ice floe size distribution

Elem Sci Anth ◽  
2016 ◽  
Vol 4 ◽  
Author(s):  
Jinlun Zhang ◽  
Harry Stern ◽  
Byongjun Hwang ◽  
Axel Schweiger ◽  
Michael Steele ◽  
...  
Keyword(s):  
Sea Ice ◽  
Size Distribution ◽  
Power Law ◽  
Annual Cycle ◽  
Arctic Sea Ice ◽  
The Arctic ◽  
Ice Thickness ◽  
First Year ◽  
Seasonal Evolution ◽  
Marginal Ice Zone

Abstract To better simulate the seasonal evolution of sea ice in the Arctic, with particular attention to the marginal ice zone, a sea ice model of the distribution of ice thickness, floe size, and enthalpy was implemented into the Pan-arctic Ice–Ocean Modeling and Assimilation System (PIOMAS). Theories on floe size distribution (FSD) and ice thickness distribution (ITD) were coupled in order to explicitly simulate multicategory FSD and ITD distributions simultaneously. The expanded PIOMAS was then used to estimate the seasonal evolution of the Arctic FSD in 2014 when FSD observations are available for model calibration and validation. Results indicate that the simulated FSD, commonly described equivalently as cumulative floe number distribution (CFND), generally follows a power law across space and time and agrees with the CFND observations derived from TerraSAR-X satellite images. The simulated power-law exponents also correlate with those derived using MODIS images, with a low mean bias of –2%. In the marginal ice zone, the modeled CFND shows a large number of small floes in winter because of stronger winds acting on thin, weak first-year ice in the ice edge region. In mid-spring and summer, the CFND resembles an upper truncated power law, with the largest floes mostly broken into smaller ones; however, the number of small floes is lower than in winter because floes of small sizes or first-year ice are easily melted away. In the ice pack interior there are fewer floes in late fall and winter than in summer because many of the floes are “welded” together into larger floes in freezing conditions, leading to a relatively flat CFND with low power-law exponents. The simulated mean floe size averaged over all ice-covered areas shows a clear annual cycle, large in winter and smaller in summer. However, there is no obvious annual cycle of mean floe size averaged over the marginal ice zone. The incorporation of FSD into PIOMAS results in reduced ice thickness, mainly in the marginal ice zone, which improves the simulation of ice extent and yields an earlier ice retreat.

scholarly journals Size distribution of particles in Saturn’s rings from aggregation and fragmentation

2015 ◽  
Vol 112 (31) ◽  
pp. 9536-9541 ◽  
Author(s):  
Nikolai Brilliantov ◽  
P. L. Krapivsky ◽  
Anna Bodrova ◽  
Frank Spahn ◽  
Hisao Hayakawa ◽  
...  
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Momentum Conservation ◽  
Power Law Distribution ◽  
Water Ice ◽  
Flat Disk ◽  
Cutoff Radius ◽  
Saturn’S Rings ◽  
Saturn's Rings ◽  
Interparticle Collisions

Saturn’s rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, ∼r−q with q≈3, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent q to be constrained to the interval 2.75≤q≤3.5. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of microstructures seen in Saturn’s rings.

The Size Distribution of Particles Released by Garments During Helmke Drum Tests

2001 ◽  
Vol 44 (4) ◽  
pp. 24-27 ◽  
Author(s):  
David Ensor ◽  
Jenni Elion ◽  
Jan Eudy
Keyword(s):  
Particle Size ◽  
Size Distribution ◽  
Power Law ◽  
High Performance ◽  
Fine Particles ◽  
Particle Diameter ◽  
Test Method ◽  
Power Law Distribution ◽  
Controlled Environments ◽  
Size Distribution Of Particles

The Helmke Drum test method to measure particles shed from garments was developed twenty years ago. It consists of a tumbling drum containing the garment under test. A probe connected to an optical particle counter is used to transport the sample from the drum. Dilution air is drawn into the drum from the surrounding cleanroom. The optical particle counters at the time of development were limited in resolution to 0.5 μm diameter. This particle size requirement is still in the current version of IEST-RP-CC003.2, Garment Systems Considerations for Cleanrooms and Other Controlled Environments. A question was raised in the current IEST Contamination Control Working Group 003, "Garment System Considerations for Cleanrooms and Other Controlled Environments," as to whether the method could be extended to smaller particle diameters. The method would benefit by including measurements of smaller particle diameters for two reasons: the higher particle counts expected for sub-0.5 μm particles might improve the statistics of the method; and there is a growing need to consider contamination by ultra-fine particles during the manufacture of high performance products. We hypothesized that the size distribution of particles released by garments follows a power law similar to that for cleanroom classes. The form of the power law distribution is N(d) = Ad(-B), where N(d) is the cumulative concentration greater to or equal to d, d is the particle diameter, and A and B are statistically determined coefficients. The size distributions from a number of Helmke Drum tests were analyzed and were found to be highly correlated to the power law equation. However, the slopes appeared to vary depending on the type of garment tested. These results support including guidance with respect to particle size in the Helmke Drum test section in the upcoming revision of IEST-RP-CC003.2.

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