Parameterization, sensitivity, and uncertainty of 1-D thermodynamic thin-ice thickness retrieval

Retrieval of Thin-Ice Thickness(TIT)using thermodynamic modeling is sensitive to the parameterization of the independent variables(coded in the model)and the uncertainty of the measured input variables.This article examines the deviation of the classical model’s TIT output when using different parameterization schemes and the sensitivity of the output to the ice thickness.Moreover,it estimates the uncertainty of the output in response to the uncertainties of the input variables.The parameterized independent variables include atmospheric longwave emissivity,air density,specific heat of air,latent heat of ice,conductivity of ice,snow depth,and snow conductivity.Measured input parameters include air temperature,ice surface temperature,and wind speed.Among the independent variables,the results show that the highest deviation is caused by adjusting the parameterization of snow conductivity and depth,followed ice conductivity.The sensitivity of the output TIT to ice thickness is highest when using parameterization of ice conductivity,atmospheric emissivity,and snow conductivity and depth.The retrieved TIT obtained using each parameterization scheme is validated using in situ measurements and satellite-retrieved data.From in situ measurements,the uncertainties of the measured air temperature and surface temperature are found to be high.The resulting uncertainties of TIT are evaluated using perturbations of the input data selected based on the probability distribution of the measurement error.The results show that the overall uncertainty of TIT to air temperature,surface temperature,and wind speed uncertainty is around 0.09 m,0.049 m,and−0.005 m,respectively.

Effect of compressive strength on the performance of the NEMO-LIM model in Arctic Sea ice simulation

Satellite records show that the extent and thickness of sea ice in the Arctic Ocean have significantly decreased since the early 1970s.The prediction of sea ice is highly important,but accurate simulation of sea ice variations remains highly challenging.For improving model performance,sensitivity experiments were conducted using the coupled ocean and sea ice model(NEMO-LIM),and the simulation results were compared against satellite observations.Moreover,the contribution ratios of dynamic and thermodynamic processes to sea ice variations were analyzed.The results show that the performance of the model in reconstructing the spatial distribution of Arctic sea ice is highly sensitive to ice strength decay constant(C^(rhg)).By reducing the C^(rhg) constant,the sea ice compressive strength increases,leading to improved simulated sea ice states.The contribution of thermodynamic processes to sea ice melting was reduced due to less deformation and fracture of sea ice with increased compressive strength.Meanwhile,dynamic processes constrained more sea ice to the central Arctic Ocean and contributed to the increases in ice concentration,reducing the simulation bias in the central Arctic Ocean in summer.The root mean square error(RMSE)between modeled and the CryoSat-2/SMOS satellite observed ice thickness was reduced in the compressive strength-enhanced model solution.The ice thickness,especially of multiyear thick ice,was also reduced and matched with the satellite observation better in the freezing season.These provide an essential foundation on exploring the response of the marine ecosystem and biogeochemical cycling to sea ice changes.

Application of the two different salinity parameterization schemes in the sea ice model

In this study, we mainly introduce two salinity parameterization schemes used in Sea Ice Simulator （SIS）, that is, isosaline scheme and salinity profile scheme. Comparing the equation of isosaline scheme with that of salinity profile scheme, we found that there was one different term between the two schemes named the salinity different term. The thermodynamic effect of the salinity difference term on sea ice thickness and sea ice concentration showed that： in the freezing processes from November to next May, the sea ice temperature could rise on the influence of the salinity difference term and restrain sea ice freezing; at the first melting phase from June to August, the upper ice melting rate was faster than the lower ice melting rate. Then sea ice temperature could rise and accelerate the sea ice melting; at the second melting phase from September to October, the upper ice melting rate was slower than the lower ice melting rate, then sea ice temperature could decrease and restrain sea ice melting. However, the effect of the salinity difference term on the sea ice thickness and sea ice concentration was weak. To analyze the impacts of the salinity different term on Arctic sea ice thickness and sea ice concentration, we also designed several experiments by introducing the two salinity parameterizations to the ice-ocean coupled model, Modular Ocean Model （MOM4）, respectively. The simulated results confirmed the previous results of formula derivation.

A coupled ice-ocean model for the Bohai SeaⅡ.Case study

The coupled ice- ocean model for the Bohai Sea is used for simulating the freezing, melting, and variation of ice cover and the heat bal- ance at the sea- ice, air- ice, and air- sea interfaces of the Bohai Sea during the entire winter in 1998￣1999 and 2000￣2001. The cou- pled model is forced by real time numerical weather prediction fields. The results show that the thermodynamic effects of atmosphere and ocean are very important for the evolvement of ice in the Bohai Sea, especially in the period of ice freezing and melting. Ocean heat flux plays a key role in the thermodynamic coupling. The simulation also presents the different thermodynamic features in the ice covered region and the marginal ice zone. Ice thickness, heat budget at the interface, and surface sea temperature, etc. between the two representative points are discussed.

Experimental Study on the Resistance of a Transport Ship Navigating in Level Ice

This study investigates the resistance of a transport ship navigating in level ice by conducting a series of model tests in an ice tank at Tianjin University. The laboratory-scale model ship was mounted on a rigid carriage using a one-directional load cell and then towed through an ice sheet at different speeds. We observed the ice-breaking process at different parts of the ship and motion of the ice floes and measured the resistances under different speeds to determine the relationship between the ice-breaking process and ice resistance. The bending failure at the shoulder area was found to cause maximum resistance. Furthermore, we introduced the analytical method of Lindqvist （1989） for estimating ice resistance and then compared these calculated results with those from our model tests. The results indicate that the calculated total resistances are higher than those we determined in the model tests.

A coupled ice-ocean model for the Bohai Sea Ⅰ. Study on model and parameter

According to the earlier international studies on the coupled iceocean model and the hydrology, meteorology, and icefeatures in the Bohai Sea, a coupled iceocean model is developed based on the National Marine EnvironmentForecast Centers (NMEFC) numerical forecasting ice model of the Bohai Sea and the Princeton ocean model (POM).In the coupled model, the transfer of momentum and heat between ocean and ice is two-way, and the change of icethickness and concentration depends on heat budget not only at the surface and bottom of ice, but also at the surfaceof open water between ices. The dynamic and thermodynamic coupling process is expatiated emphatically. Somethermodynamic parameters are discussed as well.

Modeling of Arctic Sea Ice Variability During 1948–2009: Validation of Two Versions of the Los Alamos Sea Ice Model(CICE)

The Los Alamos sea ice model(CICE) is used to simulate the Arctic sea ice variability from 1948 to 2009. Two versions of CICE are validated through comparison with Hadley Centre Global Sea Ice and Sea Surface Temperature(Had ISST) observations. Version 5.0 of CICE with elastic-viscous-plastic(EVP) dynamics simulates a September Arctic sea ice concentration(SASIC) trend of –0.619 × 1012 m2 per decade from 1969 to 2009, which is very close to the observed trend(-0.585 × 1012 m2 per decade). Version 4.0 of CICE with EVP dynamics underestimates the SASIC trend(-0.470 × 1012 m2 per decade). Version 5.0 has a higher correlation(0.742) with observation than version 4.0(0.653). Both versions of CICE simulate the seasonal cycle of the Arctic sea ice, but version 5.0 outperforms version 4.0 in both phase and amplitude. The timing of the minimum and maximum sea ice coverage occurs a little earlier(phase advancing) in both versions. Simulations also show that the September Arctic sea ice volume(SASIV) has a faster decreasing trend than SASIC.

Greenland Ice Sheet Contribution to Future Global Sea Level Rise based on CMIP5 Models

Sea level rise （SLR） is one of the major socioeconomic risks associated with global warming. Mass losses from the Greenland ice sheet （GrIS） will be partially responsible for future SLR, although there are large uncertainties in modeled climate and ice sheet behavior. We used the ice sheet model SICOPOLIS （Simulation COde for POLythermal Ice Sheets） driven by climate projections from 20 models in the fifth phase of the Coupled Model Intercomparison Project （CMIP5） to estimate the GrlS contribution to global SLR. Based on the outputs of the 20 models, it is estimated that the GrIS will contribute 0-16 （0-27） cm to global SLR by 2100 under the Representative Concentration Pathways （RCP） 4.5 （RCP 8.5） scenarios. The projected SLR increases further to 7-22 （7-33） cm with 2~basal sliding included. In response to the results of the multimodel ensemble mean, the ice sheet model projects a global SLR of 3 cm and 7 cm （10 cm and 13 cm with 2~basal sliding） under the RCP 4.5 and RCP 8.5 scenarios, respectively. In addition, our results suggest that the uncertainty in future sea level projection caused by the large spread in climate projections could be reduced with model-evaluation and the selective use of model outputs.

Ice Resistance Assessment for a Large Size Vessel Running in a Narrow Ice Channel Behind an Icebreaker

Large size vessels sailing in continuous level ice and broken ice of high concentration are mostly assisted by icebreakers.This is done in order to provide for fast transportation through the North Sea Route and safe operation in extreme ice conditions.Currently,new large size gas and oil carriers and container ships are being designed and built with beams much greater than the beams of existing icebreakers.At the same time,no mathematical description exists for the breaking mechanism of ice channel edges,when such vessels move under icebreaker escort.This paper suggests a simple method for assessment of the ice resistance in the case of a large ship running in an icebreaker channel;the method is based on modification of well-known semi-empirical methods for calculation of the ice resistance to ships in level and broken ice.The main feature of the proposed calculation scheme consists in that different methods are applied to estimate the ice resistance in broken ice and due to breaking of level ice edges.The combination of these methods gives a deliverable ice resistance of a large size vessel moving under icebreaker assistance in a newly made ice channel.In general,proposed method allows to define the speed of a carrier moving in an ice channel behind a modern linear icebreaker and could be applied at the ship design stage and during development of the marine transportation system.The paper also discusses the ways for further refinement of the assessment procedure suggested.

Comprehensive two-dimensional river ice model based on boundary-fitted coordinate transformation method

River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.

The Shielding Effect of Multi-Pile Structures on Ice Force

The shielding effect of the front pile-row on the ice force acting on the back pile-row is studied by ice force model tests. In the tests, the front pile-row is designed to model jacket legs and the back pile-row to model the water resisting pipe-phalanx within the jacket. The shielding factor for ice force corresponding to different conditions are given in this paper. The research indicates that there are many factors, including the longitudinal and lateral spacing between the front and back pile-row, ice attacking angle and the ratio of pile diameter to ice thickness, that influence the shielding effect on ice force.

An Experimental Study of Several Special Issues Regarding the Ice Force on Conical Structures

The effect of the cone spacing of a conieal structure on the ice force is studied by model experiments. The ice force reduction coefficient presented in this paper expresses the relationship between the ice force and the arrangement of cones. The experiments prove that the mode of the ice failure before the boundary of upward-downward bending cone (UDBC) is crushing. A conclusion can also be drawn from the experiments that the ice force on the boundary of UDBC is by far less than that on a vertical pile with the same diameter. Moreover, the ice force frequencies on upright and inve-rted cones are obtained under the field condition of the platform JZ20-2, respectively. The results show that the alterna-tion of the ice force on UDBC can hardly induce resonance of platform JZ20-2.

Towards a semi-empirical model of the sea ice thickness based on hyperspectral remote sensing in the Bohai Sea

Sea ice thickness is one of the most important input parameters for the prevention and mitigation of sea ice disasters and the prediction of local sea environments and climates. Estimating the sea ice thickness is currently the most important issue in the study of sea ice remote sensing. With the Bohai Sea as the study area, a semiempirical model of the sea ice thickness（SEMSIT） that can be used to estimate the thickness of first-year ice based on existing water depth estimation models and hyperspectral remote sensing data according to an optical radiative transfer process in sea ice is proposed. In the model, the absorption and scattering properties of sea ice in different bands（spectral dimension information） are utilized. An integrated attenuation coefficient at the pixel level is estimated using the height of the reflectance peak at 1 088 nm. In addition, the surface reflectance of sea ice at the pixel level is estimated using the 1 550–1 750 nm band reflectance. The model is used to estimate the sea ice thickness with Hyperion images. The first validation results suggest that the proposed model and parameterization scheme can effectively reduce the estimation error associated with the sea ice thickness that is caused by temporal and spatial heterogeneities in the integrated attenuation coefficient and sea ice surface. A practical semi-empirical model and parameterization scheme that may be feasible for the sea ice thickness estimation using hyperspectral remote sensing data are potentially provided.

An Arctic Sea Ice Simulation Using an Ocean-Ice Coupled Model

This paper evaluates the simulation of Arctic sea ice states using an ocean-ice coupled model that employs LASG/IAP(the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics/the Institute of Atmospheric Physics) Climate Ocean Model(LICOM) and the sea-ice model from the Bergen Climate Model(BCM).It is shown that the coupled model can reasonably reproduce the major characteristics of the mean state,annual cycle,and interannual variability of the Arctic sea ice concentration.The coupled model also shows biases that were generally presented in other models,such as the underestimation of summer sea ice concentration and thickness as well as the unsatisfactory sea ice velocity.Sensitivity experiments indicate that the insufficient performance of the ocean model at high latitudes may be the main reason for the biases in the coupled model.The smoother and the fake "island",which had to be used due to the model's grid in the North Pole region,likely caused the ocean model's weak performance.Sea ice model thermodynamics are also responsible for the sea ice simulation biases.Therefore,both the thermodynamic module of the sea ice component and the model grid of the ocean component need to be further improved.

Variation of Sea Ice Temperature from CHINARE 2003 and Its Application on Sea Ice Model Evaluation

Variation of vertical profiles of sea ice temperature and adjacent atmosphere and ocean temperatures were measured by ice drifting buoys deployed in the northeast Chukchi Sea as part of the 2003 Chinese Arctic Research Expedition.The buoy observations (September 2003 to February 2005) show that the cooling of the ice began in late September,propagated down through the ice,reaching the bottom of the ice in December,and continued throughout the winter.In winter 2003/04,some obvious warmings were observed in the upper portion of the ice in response to major warmings in the overlying atmosphere associated with the periodicity of storms in the northeast Chukchi Sea.It is found that the melt season at the buoy site in 2004 was about 15% longer than normal.The buoy observed vertical ice temperature profiles were used as a diagnostic for sea ice model evaluation.The results show that the simulated ice temperature profiles have large discrepancies as compared with the observations.

A coupled multi-category sea ice model and POM for Baffin Bay and the Labrador Sea

An overview of the seasonal variation of sea-ice cover in Baffin Bay and the Labrador Sea is given. A coupled ice-ocean model, CECOM, has been developed to study the seasonal variation and associated ice-ocean processes. The sea-ice component of the model is a multi-category ice model in which mean concentration and thickness are expressed in terms of a thickness distribution function. Ten categories of ice thickness are specified in the model. Sea ice is coupled dynamically and thermodynamically to the Princeton Ocean Model. Selected results from the model including the seasonal variation of sea ice in Baffin Bay, the North Water polynya and ice growth and melt over the Labrador Shelf are presented.

A study on remote sensing models of sea ice thickness by microwave radiometry

Extrapolating from the propagation theories of electromagnetic waves in a layered medium, a three-layer medium model is deduced in this paper by using microwave radiometric remote sensing technology which is suitable to first-year sea ice condition of the northern part of China seas. Comparison with in situ data indicates that for microwave wavelength of 10 cm, the coherent model gives a quite good fit result for the thickness of sea ice less than 20 cm, and the incoherent model also works well for thickness within 20 to 40 cm. Based on three theoretical models, the inversion soft ware from microwave remote sensing data for calculating the thickness of sea ice can be set up. The relative complex dielectrical constants of different types of sea ice in the Liaodong Gulf calculated by using these theoretical models and measurement data are given in this paper. The extent of their values is (0. 5-4. 0)-j(0. 07~0. 19).

Melt Pond Scheme Parameter Estimation Using an Adjoint Model

Melt ponds significantly affect Arctic sea ice thermodynamic processes.The melt pond parameterization scheme in the Los Alamos sea ice model(CICE6.0) can predict the volume,area fraction(the ratio between melt pond area to sea ice area in a model grid),and depth of melt ponds.However,this scheme has some uncertain parameters that affect melt pond simulations.These parameters could be determined through a conventional parameter estimation method,which requires a large number of sensitivity simulations.The adjoint model can calculate the parameter sensitivity efficiently.In the present research,an adjoint model was developed for the CESM(Community Earth System Model) melt pond scheme.A melt pond parameter estimation algorithm was then developed based on the CICE6.0 sea ice model,melt pond adjoint model,and L-BFGS(Limited-memory Broyden-Fletcher-Goldfard-Shanno) minimization algorithm.The parameter estimation algorithm was verified under idealized conditions.By using MODIS(Moderate Resolution Imaging Spectroradiometer)melt pond fraction observation as a constraint and the developed parameter estimation algorithm,the melt pond aspect ratio parameter in CESM scheme,which is defined as the ratio between pond depth and pond area fraction,was estimated every eight days during summertime for two different regions in the Arctic.One region was covered by multi-year ice(MYI) and the other by first-year ice(FYI).The estimated parameter was then used in simulations and the results show that:(1) the estimated parameter varies over time and is quite different for MYI and FYI;(2) the estimated parameter improved the simulation of the melt pond fraction.

Scallop ice shape characteristics of swept wing based on large-scale icing wind tunnel experiment

Scallop ice is a special phenomenon that occurs during swept wing aircraft passing through icing clouds.It poses a great challenge for the icing safety assessment that the complex scallop ice shape feature and its mechanism are still unclear.In this work,a large-scale icing wind tunnel experiment of swept wing designed by NACA0012 airfoil is conducted in the Icing Wind Tunnel of China Aerodynamics Research and Development Center.The detailed three-dimensional ice shapes under 0°,15°,30°and 45°swept angles are obtained by laser scanning technology.The experimental results show that with the swept angle increasing from 0°to 45°,the 2D double ice horn structures show certain spanwise variation,and finally transform into complete scallop ice with ice thickness greatly enhanced in the stagnation line region.The empirical mode decomposition of the spanwise ice curve captures the high-frequency fluctuation on the scallop ice caused by the small-scale roughness element,while the trend with low frequency is not obvious.Based on the experimental data,a new complete scallop ice geometric model,named 5Points-5Lines-2Arcs(5P-5L-2A)model,is proposed,which can provide important basis for the quantitative description of complex scallop ice shape.

Numerical Simulation on Freezing Process of Saturated Granular Soil

The relation between ice pressure and load as a criterion of segregated ice initiation is introduced into the rigid ice model to simulate frost heave in saturated and granular soil. The calculated results show that unfrozen water content, thermal conductivity and hydraulic conductivity change greatly in frozen fringe. In numerical simulations, the influence of load, hydraulic conductivity and property of soil containing water on the process of soil freezing are analyzed, and the simulation curves such as cumulative heave, the change of depth of frozen and the distributions of water content are similar to the observations reported elsewhere.