List of Commonly Used Variables for Sea-Ice Studies
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Beyond the Classical Stefan Problem
Beyond the classical Stefan problem Francesc Font Martinez PhD thesis Supervised by: Prof. Dr. Tim Myers Submitted in full fulfillment of the requirements for the degree of Doctor of Philosophy in Applied Mathematics in the Facultat de Matem`atiques i Estad´ıstica at the Universitat Polit`ecnica de Catalunya June 2014, Barcelona, Spain ii Acknowledgments First and foremost, I wish to thank my supervisor and friend Tim Myers. This thesis would not have been possible without his inspirational guidance, wisdom and expertise. I appreciate greatly all his time, ideas and funding invested into making my PhD experience fruitful and stimulating. Tim, you have always guided and provided me with excellent support throughout this long journey. I can honestly say that my time as your PhD student has been one of the most enjoyable periods of my life. I also wish to express my gratitude to Sarah Mitchell. Her invaluable contributions and enthusiasm have enriched my research considerably. Her remarkable work ethos and dedication have had a profound effect on my research mentality. She was an excellent host during my PhD research stay in the University of Limerick and I benefited significantly from that experience. Thank you Sarah. My thanks also go to Vinnie, who, in addition to being an excellent football mate and friend, has provided me with insightful comments which have helped in the writing of my thesis. I also thank Brian Wetton for our useful discussions during his stay in the CRM, and for his acceptance to be one of my external referees. Thank you guys. Agraeixo de tot cor el suport i l’amor incondicional dels meus pares, la meva germana i la meva tieta. -
Improved Lumped Parameter Model for Phase Change in Latent Thermal Energy Storage Systems
IX Minsk International Seminar “Heat Pipes, Heat Pumps, Refrigerators, Power Sources”, Minsk, Belarus, 07-10 September, 2015 IMPROVED LUMPED PARAMETER MODEL FOR PHASE CHANGE IN LATENT THERMAL ENERGY STORAGE SYSTEMS Mina Rouhani, Majid Bahrami Laboratory for Alternative Energy Conversion (LAEC), School of Mechatronic Systems Engineering, Simon Fraser University, V3T 0A3 +1 (778) 782-8538/ [email protected] Abstract A modified lumped parameter model has been used to study transient conduction in phase change materials (PCM) in cylindrical coordinates. The two-point Hermite approximation is used to compute the average temperatures and the temperature gradient in each phase. The performance of PCM has been analyzed during the charging processin terms of energy storage and density. The effect of Stefan number on melting front dynamics is comprehensively studied. The results are verified with exact solutions as well as steady-state asymptotes and also show good agreement with existing experimental data. KEYWORDS Stefan problem; Lumped model; phase change material (PCM); Thermal energy storage; Solidification;Hermite approximation INTRODUCTION Thermal energy storage (TES) systems are a sustainable, energy efficient alternative to conventional heating and cooling methods. TES can play a pivotal role in synchronizing energy demand and supply, both on a short and long term basis.TES is divided into sensible, latent, and thermochemical mechanisms. Latent thermal storage using phase change materials(PCM) has a relatively constant melting/solidification temperature,higher energy storage density compared to sensible TES,and less complexity and lower manufacturing cost than the thermochemical TES [1]. Due to the non-linearity of phase change problems, analytical solutions to the analysis of phase change problem are limited by assumptions such as small Stefan number, specific boundary conditions, and simple geometries. -
Verification of a New NOAA/NSIDC Passive Microwave Sea-Ice
RESEARCH/REVIEW ARTICLE Verification of a new NOAA/NSIDC passive microwave sea-ice concentration climate record Walter N. Meier,1 Ge Peng,2,3 Donna J. Scott4 & Matt H. Savoie4 1 Cryospheric Sciences Lab, Code 615, National Aeronautics and Space Administration Goddard Space Flight Center, Greenbelt, MD 20771, USA 2 Cooperative Institute for Climate and Satellites, North Carolina State University, Raleigh, NC, USA 3 Remote Sensing and Applications Division, National Oceanic and Atmospheric Administration National Climatic Data Center, 151 Patton Avenue, Asheville, NC 28801, USA 4 National Snow and Ice Data Center, University of Colorado, UCB 449, Boulder CO 80309, USA Keywords Abstract Sea ice; Arctic and Antarctic oceans; climate data record; evaluation; passive A new satellite-based passive microwave sea-ice concentration product microwave remote sensing. developed for the National Oceanic and Atmospheric Administration (NOAA) Climate Data Record (CDR) programme is evaluated via comparison with Correspondence other passive microwave-derived estimates. The new product leverages two Walter N. Meier, Cryospheric Sciences well-established concentration algorithms, known as the NASA Team and Lab, Code 615, National Aeronautics and Bootstrap, both developed at and produced by the National Aeronautics and Space Administration Goddard Space Space Administration (NASA) Goddard Space Flight Center (GSFC). The sea- Flight Center, Greenbelt, MD 20771, USA. ice estimates compare well with similar GSFC products while also fulfilling all E-mail: [email protected] NOAA CDR initial operation capability (IOC) requirements, including (1) self- describing file format, (2) ISO 19115-2 compliant collection-level metadata, (3) Climate and Forecast (CF) compliant file-level metadata, (4) grid-cell level metadata (data quality fields), (5) fully automated and reproducible processing and (6) open online access to full documentation with version control, including source code and an algorithm theoretical basic document. -
Numerical Solution to Two-Phase Stefan Problems by the Heat Balance Integral Method J. Caldwell & C.K. Chiu Department of Ma
Transactions on Engineering Sciences vol 5, © 1994 WIT Press, www.witpress.com, ISSN 1743-3533 Numerical solution to two-phase Stefan problems by the heat balance integral method J. Caldwell & C.K. Chiu Department of Mathematics, City Polytechnic of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong ABSTRACT Caldwell and Chiu [1, 2] have used a simple front-fixed method, namely, the Heat Balance Integral Method (HBIM), to solve one-phase solidification problems. In this paper the method is extended to two-phase Stefan prob- lems which arise when the effect of sub-cooling is taken into consideration. Numerical results for the two-phase cylindrical problem are obtained for a range of sub-divisions (n), sub-cooling parameters (0), Stefan number (a) and ratio of conductivities (/<i/%2). The effects of variation of parameters on the solidification process are also studied. INTRODUCTION Melting and solidification problems occur in numerous important areas of science, engineering and industry. For example, freezing and thawing of foods, production of ice, ice formation on pipe surface, solidification of steel and chemical reaction all involve either a melting or solidification process. Mathematically, melting/solidification problems are special cases of mov- ing boundary problems. Problems in which the solution of a differential equation has to satisfy certain conditions on the boundary of a prescribed domain are referred to as boundary-value problems. In the cases of melt- ing/solidification problems, however, the boundary of the domain is not known in advance, so the solution of melting/solidification problems re- quires solving the diffusion or heat-conduction equation in an unknown re- gion which has also to be determined as part of the solution. -
Sea Ice Concentration Products Over Polar Regions with Chinese FY3C/MWRI Data
remote sensing Article Sea Ice Concentration Products over Polar Regions with Chinese FY3C/MWRI Data Lijian Shi 1,2,*, Sen Liu 1,2,3, Yingni Shi 4, Xue Ao 1,2, Bin Zou 1,2 and Qimao Wang 1,2 1 National Satellite Ocean Application Service, Beijing 100081, China; [email protected] (S.L.); [email protected] (X.A.); [email protected] (B.Z.); [email protected] (Q.W.) 2 Key Laboratory of Space Ocean Remote Sensing and Application, MNR, Beijing 100081, China 3 Zhuhai Orbita Aerospace Science & Technology Co., Ltd., Zhuhai 519080, China 4 Independent Researcher, Mailbox No. 5111, Beijing 100094, China; [email protected] * Correspondence: [email protected]; Tel.: +86-010-8248-1859 Abstract: Polar sea ice affects atmospheric and ocean circulation and plays an important role in global climate change. Long time series sea ice concentrations (SIC) are an important parameter for climate research. This study presents an SIC retrieval algorithm based on brightness temperature (Tb) data from the FY3C Microwave Radiation Imager (MWRI) over the polar region. With the Tb data of Special Sensor Microwave Imager/Sounder (SSMIS) as a reference, monthly calibration models were established based on time–space matching and linear regression. After calibration, the correlation between the Tb of F17/SSMIS and FY3C/MWRI at different channels was improved. Then, SIC products over the Arctic and Antarctic in 2016–2019 were retrieved with the NASA team (NT) method. Atmospheric effects were reduced using two weather filters and a sea ice mask. A minimum ice concentration array used in the procedure reduced the land-to-ocean spillover effect. -
Lecture 1 (Pdf)
GFD 2006 Lecture 1: Introduction to Ice Grae Worster; notes by Rachel Zammett and Devin Conroy March 15, 2007 1 Introduction Our aim in this course is to understand some of the processes associated with ice in the natural environment. Figure 1 shows the location of some of Earth's ice during the north- ern winter. These ice deposits may be categorized as sea ice, ice sheets and shelves, and permafrost. Figure 1: Satellite image showing the ice cover in the northern hemisphere during northern winter, showing sea ice lying in the Arctic basin, the permanent ice sheet over Greenland and permafrost in the exposed land surface. 2 Ice sheets Firstly, figure 1 shows the ice sheet that covers approximately 80% of Greenland. This is about 105 years old and reaches depths of 2{3 kilometers. On large scales, ice can be treated as a highly viscous, non-Newtonian fluid that can flow because it is a polycrystalline solid and contains a percentage of unfrozen water (figure 2). Looking on a scale of about 100µm, 1 Figure 2: Image of the intersection of four ice grains. Between these grains lie the veins containing liquid water and dissolved impurities. The scale bar on this picture is 100 µm. we can see the ice grain junctions and the veins which lie between them. The liquid water contained in the veins between the ice crystals lubricates the flow, allowing the ice to flow more easily. This water can also transport dissolved impurities, which will therefore move relative to the ice crystals; this is important when analyzing ice cores, for example. -
A Continuum Model for Meltwater Flow Through Compacting Snow
The Cryosphere, 11, 2799–2813, 2017 https://doi.org/10.5194/tc-11-2799-2017 © Author(s) 2017. This work is distributed under the Creative Commons Attribution 4.0 License. A continuum model for meltwater flow through compacting snow Colin R. Meyer1 and Ian J. Hewitt2 1John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA 2Mathematical Institute, Woodstock Road, Oxford, OX2 6GG, UK Correspondence to: Colin R. Meyer ([email protected]) Received: 2 July 2017 – Discussion started: 19 July 2017 Revised: 13 October 2017 – Accepted: 23 October 2017 – Published: 11 December 2017 Abstract. Meltwater is produced on the surface of glaciers health of glaciers and ice sheets under atmospheric warming and ice sheets when the seasonal energy forcing warms the (Harper et al., 2012; Enderlin et al., 2014; Forster et al., 2014; snow to its melting temperature. This meltwater percolates Koenig et al., 2014; Machguth et al., 2016). The balance be- into the snow and subsequently runs off laterally in streams, tween runoff, refreezing, and storage is controlled by the me- is stored as liquid water, or refreezes, thus warming the sub- chanics and thermodynamics of the porous snow. These pro- surface through the release of latent heat. We present a con- cesses also underlie the rate of compaction of firn into ice and tinuum model for the percolation process that includes heat therefore control the average temperature and accumulation conduction, meltwater percolation and refreezing, as well as rate that provide surface boundary conditions to numerical mechanical compaction. The model is forced by surface mass ice-sheet models (which typically do not include the com- and energy balances, and the percolation process is described pacting firn layer explicitly). -
The Step-Like Evolution of Arctic Open Water Michael A
www.nature.com/scientificreports OPEN The step-like evolution of Arctic open water Michael A. Goldstein 1,2, Amanda H. Lynch 3,4, Andras Zsom5, Todd Arbetter3, Andres Chang3 & Florence Fetterer6 Received: 18 December 2017 September open water fraction in the Arctic is analyzed using the satellite era record of ice Accepted: 31 October 2018 concentration (1979–2017). Evidence is presented that three breakpoints (shifts in the mean) occurred Published: xx xx xxxx in the Pacifc sector, with higher amounts of open water starting in 1989, 2002, and 2007. Breakpoints in the Atlantic sector record of open water are evident in 1971 in longer records, and around 2000 and 2011. Multiple breakpoints are also evident in the Canadian and Russian halves. Statistical models that use detected breakpoints of the Pacifc and Atlantic sectors, as well as models with breakpoints in the Canadian and Russian halves and the Arctic as a whole, outperform linear trend models in ftting the data. From a physical standpoint, the results support the thesis that Arctic sea ice may have critical points beyond which a return to the previous state is less likely. From an analysis standpoint, the fndings imply that de-meaning the data using the breakpoint means is less likely to cause spurious signals than employing a linear detrend. In the most recent decade, summer minimum sea ice extent has retreated to levels not seen since the beginning of the satellite record1. Te confuence of opportunity and risk at the retreating ice edge2 raises critical questions as to how well we observe and simulate Arctic ice area and extent. -
Characterization of Moisture Sources for Austral Seas and Relationship with Sea Ice Concentration
atmosphere Article Characterization of Moisture Sources for Austral Seas and Relationship with Sea Ice Concentration Michelle Simões Reboita 1, Raquel Nieto 2 , Rosmeri P. da Rocha 3, Anita Drumond 4, Marta Vázquez 2,5 and Luis Gimeno 2,* 1 Instituto de Recursos Naturais, Universidade Federal de Itajubá, Itajubá 37500-903, Minas Gerais, Brazil; [email protected] 2 Environmental Physics Laboratory (EPhysLab), CIM-UVigo, Universidade de Vigo, 32004 Ourense, Spain; [email protected] (R.N.); [email protected] (M.V.) 3 Departamento de Ciências Atmosféricas, Universidade de São Paulo, São Paulo 05508-090, Brazil; [email protected] 4 Instituto de Ciências Ambientais, Químicas e Farmacêuticas, Universidade Federal de São Paulo, Diadema 09913-030, Brazil; [email protected] 5 Instituto Dom Luiz, Universidade de Lisboa, 1749-016 Lisboa, Portugal * Correspondence: [email protected] Received: 7 August 2019; Accepted: 12 October 2019; Published: 17 October 2019 Abstract: In this study, the moisture sources acting over each sea (Weddell, King Haakon VII, East Antarctic, Amundsen-Bellingshausen, and Ross-Amundsen) of the Southern Ocean during 1980–2015 are identified with the FLEXPART Lagrangian model and by using two approaches: backward and forward analyses. Backward analysis provides the moisture sources (positive values of Evaporation minus Precipitation, E P > 0), while forward analysis identifies the moisture sinks (E P < 0). − − The most important moisture sources for the austral seas come from midlatitude storm tracks, reaching a maximum between austral winter and spring. The maximum in moisture sinks, in general, occurs in austral end-summer/autumn. There is a negative correlation (higher with 2-months lagged) between moisture sink and sea ice concentration (SIC), indicating that an increase in the moisture sink can be associated with the decrease in the SIC. -
A Spurious Jump in the Satellite Record: Has Antarctic Sea Ice Expansion Been Overestimated?
Supplement of The Cryosphere, 8, 1289–1296, 2014 http://www.the-cryosphere.net/8/1289/2014/ doi:10.5194/tc-8-1289-2014-supplement © Author(s) 2014. CC Attribution 3.0 License. Supplement of A spurious jump in the satellite record: has Antarctic sea ice expansion been overestimated? I. Eisenman et al. Correspondence to: I. Eisenman ([email protected]) I. Eisenman et al.: Antarctic sea ice record S-1 Supplemental Discussion and Figures derestimating sea ice concentrations (Comiso et al., 1997). Both algorithms have empirically adjusted parameters that differ between the two hemispheres, and the parameters in S1 Detailed description of data and methods the Bootstrap algorithm also vary on a daily basis. Various steps go into processing the ice concentration data Here we discuss the ice concentration fields analyzed in this to intercalibrate across the transition from one sensor to an- study and the resulting time series of ice extent and ice area other and to fill in missing or identifiably erroneous pixels. that we calculate. Although a number of brief data gaps exist, the instruments have provided data for at least 20 days of every month (10 S1.1 Ice concentration days for SMMR) from November 1978 to present with the exception of December 1987 and January 1988, when the The ice concentration data sets considered in this study are SSM/I instrument was turned off between 3 December 1987 derived from passive microwave measurements from instru- and 13 January 1988 due to overheating issues. ments flown on a series of satellites. The Scanning Multi- The effective resolution (sensor footprint) of the mi- channel Microwave Radiometer (SMMR) was flown on the crowave measurements vary as a function of frequency, with NASA Nimbus 7 satellite and provided data between 26 Oc- the resolution of the most coarse frequency used by the Boot- tober 1978 and 20 August 1987, with the Bootstrap sea ice strap and NASA Team algorithms being approximately 40 concentration using the data between 1 November 1978 and km 70 km. -
Towards Improved Sea Ice Initialization and Forecasting with the IFS
844 Towards Improved Sea Ice Initialization and Forecasting with the IFS B. Balan Sarojini, S. Tietsche, M. Mayer, M. A. Balmaseda, and H. Zuo Research Department March 2019 Series: ECMWF Technical Memoranda A full list of ECMWF Publications can be found on our web site under: http://www.ecmwf.int/en/research/publications Contact: [email protected] c Copyright 2019 European Centre for Medium-Range Weather Forecasts Shinfield Park, Reading, RG2 9AX, England Literary and scientific copyrights belong to ECMWF and are reserved in all countries. This publication is not to be reprinted or translated in whole or in part without the written permission of the Director- General. Appropriate non-commercial use will normally be granted under the condition that reference is made to ECMWF. The information within this publication is given in good faith and considered to be true, but ECMWF accepts no liability for error, omission and for loss or damage arising from its use. Level-3 OSISAF sea ice cover and CS2-SMOS sea ice thickness constraints Contents 1 Introduction 3 2 Sea Ice Assimilation and Initialization4 2.1 Models and Methodology..................................5 2.2 Current operational Level-4 SIC issues and Level-3 SIC..................5 2.3 Observations and Ocean-Sea-Ice Assimilation experiments................7 2.4 Impact of improved observations on the sea ice state....................9 2.4.1 Level-3 sea ice cover assimilation versus Level-4 sea ice cover assimilation...9 2.4.2 Sea ice thickness constraint against Level-4 sea ice cover assimilation...... 11 3 Sea Ice Forecasting 11 3.1 Sea-ice related SEAS5 biases............................... -
Assessment of Contemporary Satellite Sea Ice Thickness Products
The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-197 Manuscript under review for journal The Cryosphere Discussion started: 24 September 2018 c Author(s) 2018. CC BY 4.0 License. Assessment of Contemporary Satellite Sea Ice Thickness Products for Arctic Sea Ice Heidi Sallila1, Joshua McCurry2,3, Sinéad Louise Farrell2,3 and Eero Rinne1 1Finnish Meteorological Institute, Helsinki, Finland 5 2Cooperative Institute for Climate and Satellites, University of Maryland, College Park, MD, USA 3NOAA Laboratory for Satellite Altimetry, College Park, MD, USA Correspondence to: Heidi Sallila ([email protected]) Abstract. Advances in remote sensing of sea ice over the past two decades have resulted in a wide variety of satellite- derived sea ice thickness data products becoming publicly available. Selecting the most appropriate product is challenging 10 given objectives range from incorporating satellite-derived thickness information in operational activities, including sea ice forecasting, routing of maritime traffic, and search and rescue, to climate change analysis, longer-term modeling, prediction, and future planning. Depending on the use case, selecting the most suitable satellite data product can depend on the region of interest, data latency, and whether the data are provided routinely, for example via a climate or maritime service provider. Here we examine a suite of current sea ice thickness data products, collating key details of primary interest to end users. We 15 assess sea ice thickness observations derived from sensors onboard the CryoSat-2 (CS2), Advanced Very-High-Resolution Radiometer (AVHRR) and Soil Moisture and Ocean Salinity (SMOS) satellites. We evaluate the satellite-only observations with independent ice draft and thickness measurements obtained from the Beaufort Gyre Exploration Project (BGEP) upward looking sonars (ULS) and Operation IceBridge, respectively.