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.

scholarly journals Impact of spatial aliasing on sea-ice thickness measurements

2015 ◽  
Vol 56 (69) ◽  
pp. 353-362 ◽  
Author(s):  
Cathleen Geiger ◽  
Hans-Reinhard Müller ◽  
Jesse P. Samluk ◽  
E. Rachel Bernstein ◽  
Jacqueline Richter-Menge
Keyword(s):  
Sea Ice ◽  
Spatial Scales ◽  
Thickness Distribution ◽  
Ice Thickness ◽  
Mathematical Functions ◽  
Sea Ice Thickness ◽  
Spatial Aliasing ◽  
Monitoring And Forecasting ◽  
Non Gaussian ◽  
The Impact

AbstractWe explore spatial aliasing of non-Gaussian distributions of sea-ice thickness. Using a heuristic model and >1000 measurements, we show how different instrument footprint sizes and shapes can cluster thickness distributions into artificial modes, thereby distorting frequency distribution, making it difficult to compare and communicate information across spatial scales. This problem has not been dealt with systematically in sea ice until now, largely because it appears to incur no significant change in integrated thickness which often serves as a volume proxy. Concomitantly, demands are increasing for thickness distribution as a resource for modeling, monitoring and forecasting air–sea fluxes and growing human infrastructure needs in a changing polar environment. New demands include the characterization of uncertainties both regionally and seasonally for spaceborne, airborne, in situ and underwater measurements. To serve these growing needs, we quantify the impact of spatial aliasing by computing resolution error (Er) over a range of horizontal scales (x) from 5 to 500 m. Results are summarized through a power law (Er= bxm) with distinct exponents (m) from 0.3 to 0.5 using example mathematical functions including Gaussian, inverse linear and running mean filters. Recommendations and visualizations are provided to encourage discussion, new data acquisitions, analysis methods and metadata formats.

scholarly journals Estimating the sea ice floe size distribution using satellite altimetry: theory, climatology, and model comparison

2019 ◽  
Vol 13 (11) ◽  
pp. 2869-2885 ◽  
Author(s):  
Christopher Horvat ◽  
Lettie A. Roach ◽  
Rachel Tilling ◽  
Cecilia M. 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 sparse – traditionally taken via a painstaking 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 radar altimetric record, covering the period from 2010 to 2018, and incorporating 11 million individual floe samples, we produce the first pan-Arctic 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.

scholarly journals Sea ice floe size: its impact on pan-Arctic and local ice mass, and required model complexity

2021 ◽  
Author(s):  
Adam William Bateson ◽  
Daniel L. Feltham ◽  
David Schröder ◽  
Yanan Wang ◽  
Byongjun Hwang ◽  
...  
Keyword(s):  
Sea Ice ◽  
Size Distribution ◽  
Power Law ◽  
Large Scale ◽  
Prognostic Model ◽  
Thickness Distribution ◽  
Model Complexity ◽  
Distribution Model ◽  
Sea Ice Concentration ◽  
Advantages And Disadvantages

Abstract. Sea ice is composed of discrete units called floes. The size of these floes can determine the nature and magnitude of interactions between the sea ice, ocean, and atmosphere including lateral melt rate, momentum and heat exchange, and surface moisture flux. Large-scale geophysical sea ice models employ a continuum approach and traditionally either assume floes adopt a constant size or do not include an explicit treatment of floe size. Observations show that floes can adopt a range of sizes spanning orders of magnitude, from metres to tens of kilometres. In this study we apply novel observations to analyse two alternative approaches to modelling a floe size distribution (FSD) within the state-of-the-art CICE sea ice model. The first model considered, the WIPoFSD (Waves-in-Ice module and Power law Floe Size Distribution) model, assumes floe size follows a power law with a constant exponent. The second is a prognostic floe size-thickness distribution where the shape of the distribution is an emergent feature of the model and is not assumed a priori. We demonstrate that a parameterisation of in-plane brittle fracture processes should be included in the prognostic model. While neither FSD model results in a significant improvement in the ability of CICE to simulate pan-Arctic metrics in a stand-alone sea ice configuration, larger impacts can be seen over regional scales in sea ice concentration and thickness. We find that the prognostic model particularly enhances sea ice melt in the early melt season, whereas for the WIPoFSD model this melt increase occurs primarily during the late melt season. We then show that these differences between the two FSD models can be explained by considering the effective floe size, a metric used to characterise a given FSD. Finally, we discuss the advantages and disadvantages to these different approaches to modelling the FSD. We note that the WIPoFSD model is less computationally expensive than the prognostic model and produces a better fit to novel FSD observations derived from 2-m resolution MEDEA imagery but is unable to represent potentially important features of annual FSD evolution seen with the prognostic model.

scholarly journals Impact of sea ice floe size distribution on seasonal fragmentation and melt of Arctic sea ice

2020 ◽  
Vol 14 (2) ◽  
pp. 403-428 ◽  
Author(s):  
Adam W. Bateson ◽  
Daniel L. Feltham ◽  
David Schröder ◽  
Lucia Hosekova ◽  
Jeff K. Ridley ◽  
...  
Keyword(s):  
Sea Ice ◽  
Size Distribution ◽  
Power Law ◽  
Climate Models ◽  
Ice Cover ◽  
Arctic Sea Ice ◽  
Arctic Sea ◽  
Marginal Ice Zone ◽  
Break Up ◽  
The Impact

Abstract. Recent years have seen a rapid reduction in the summer Arctic sea ice extent. To both understand this trend and project the future evolution of the summer Arctic sea ice, a better understanding of the physical processes that drive the seasonal loss of sea ice is required. The marginal ice zone, here defined as regions with between 15 % and 80 % sea ice cover, is the region separating pack ice from the open ocean. Accurate modelling of this region is important to understand the dominant mechanisms involved in seasonal sea ice loss. Evolution of the marginal ice zone is determined by complex interactions between the atmosphere, sea ice, ocean, and ocean surface waves. Therefore, this region presents a significant modelling challenge. Sea ice floes span a range of sizes but sea ice models within climate models assume they adopt a constant size. Floe size influences the lateral melt rate of sea ice and momentum transfer between atmosphere, sea ice, and ocean, all important processes within the marginal ice zone. In this study, the floe size distribution is represented as a power law defined by an upper floe size cut-off, lower floe size cut-off, and power-law exponent. This distribution is also defined by a new tracer that varies in response to lateral melting, wave-induced break-up, freezing conditions, and advection. This distribution is implemented within a sea ice model coupled to a prognostic ocean mixed-layer model. We present results to show that the use of a power-law floe size distribution has a spatially and temporally dependent impact on the sea ice, in particular increasing the role of the marginal ice zone in seasonal sea ice loss. This feature is important in correcting existing biases within sea ice models. In addition, we show a much stronger model sensitivity to floe size distribution parameters than other parameters used to calculate lateral melt, justifying the focus on floe size distribution in model development. We also find that the attenuation rate of waves propagating under the sea ice cover modulates the impact of wave break-up on the floe size distribution. It is finally concluded that the model approach presented here is a flexible tool for assessing the importance of a floe size distribution in the evolution of sea ice and is a useful stepping stone for future development of floe size modelling.

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.

scholarly journals New insight from CryoSat-2 sea ice thickness for sea ice modelling

2018 ◽  
Author(s):  
David Schröder ◽  
Danny L. Feltham ◽  
Michel Tsamados ◽  
Andy Ridout ◽  
Rachel Tilling
Keyword(s):  
Sea Ice ◽  
Thickness Distribution ◽  
Arctic Sea Ice ◽  
Ice Thickness ◽  
Atmospheric Conditions ◽  
Sea Ice Concentration ◽  
Sea Ice Thickness ◽  
Ice Growth ◽  
Melt Pond ◽  
The Impact

Abstract. Estimates of Arctic sea ice thickness are available from the CryoSat-2 (CS2) radar altimetry mission during ice growth seasons since 2010. We derive the sub-grid scale ice thickness distribution (ITD) with respect to 5 ice thickness categories used in a sea ice component (CICE) of climate simulations. This allows us to initialize the ITD in stand-alone simulations with CICE and to verify the simulated cycle of ice thickness. We find that a default CICE simulation strongly underestimates ice thickness, despite reproducing the inter-annual variability of summer sea ice extent. We can identify the underestimation of winter ice growth as being responsible and show that increasing the ice conductive flux for lower temperatures (bubbly brine scheme) and accounting for the loss of drifting snow results in the simulated sea ice growth being more realistic. Sensitivity studies provide insight into the impact of initial and atmospheric conditions and, thus, on the role of positive and negative feedback processes. During summer, atmospheric conditions are responsible for 50 % of September sea ice thickness variability through the positive sea ice and melt pond albedo feedback. However, atmospheric winter conditions have little impact on winter ice growth due to the dominating negative conductive feedback process: the thinner the ice and snow in autumn, the stronger the ice growth in winter. We conclude that the fate of Arctic summer sea ice is largely controlled by atmospheric conditions during the melting season rather than by winter temperature. Our optimal model configuration does not only improve the simulated sea ice thickness, but also summer sea ice concentration, melt pond fraction, and length of the melt season. It is the first time CS2 sea ice thickness data have been applied successfully to improve sea ice model physics.

scholarly journals Phase Synchronization Stability of Non-Homogeneous Low-Voltage Distribution Networks with Large-Scale Distributed Generations

Energies ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1257 ◽  
Author(s):  
Shi Chen ◽  
Hong Zhou ◽  
Jingang Lai ◽  
Yiwei Zhou ◽  
Chang Yu
Keyword(s):  
Power Law ◽  
Coupling Strength ◽  
Large Scale ◽  
Phase Synchronization ◽  
Distribution Networks ◽  
Critical Coupling ◽  
Power Law Distribution ◽  
Distributed Generations ◽  
Strength Formula ◽  
The Impact

The ideal distributed network composed of distributed generations (DGs) has unweighted and undirected interactions which omit the impact of the power grid structure and actual demand. Apparently, the coupling relationship between DGs, which is determined by line impedance, node voltage, and droop coefficient, is generally non-homogeneous. Motivated by this, this paper investigates the phase synchronization of an islanded network with large-scale DGs in a non-homogeneous condition. Furthermore, we explicitly deduce the critical coupling strength formula for different weighting cases via the synchronization condition. On this basis, three cases of Gaussian distribution, power-law distribution, and frequency-weighted distribution are analyzed. A synthetical analysis is also presented, which helps to identify the order parameter. Finally, this paper employs the numerical simulation methods to test the effectiveness of the critical coupling strength formula and the superiority over the power-law distribution.

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.

scholarly journals A prognostic model of the sea ice floe size and thickness distribution

2015 ◽  
Vol 9 (3) ◽  
pp. 2955-2997 ◽  
Author(s):  
C. Horvat ◽  
E. Tziperman
Keyword(s):  
Sea Ice ◽  
Size Distribution ◽  
Prognostic Model ◽  
Climate Models ◽  
Thickness Distribution ◽  
Lateral Side ◽  
Test Cases ◽  
Multiple Processes ◽  
Oceanic Forcing ◽  
Ice Pack

Abstract. Sea ice exhibits considerable seasonal and longer-term variations in extent, concentration, thickness and age, and is characterized by a complex and continuously changing distribution of floe sizes and thicknesses. Models of sea ice used in current climate models keep track of its concentration and of the distribution of ice thicknesses, but do not account for the floe size distribution and its potential effects on air–sea exchange and sea-ice evolution. Accurately capturing sea-ice variability in climate models may require a better understanding and representation of the distribution of floe sizes and thicknesses. We develop and demonstrate a model for the evolution of the joint sea-ice floe size and thickness distribution that depends on atmospheric and oceanic forcing fields. The model accounts for effects due to multiple processes that are active in the marginal and seasonal ice zones: freezing and melting along the lateral side and base of floes, mechanical interactions due to floe collisions (ridging and rafting) and sea-ice fracture due to swell propagation into the ice pack. The model is then examined and demonstrated in a series of idealized test cases.

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