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A comprehensive simulation study of dissolved Barium and Oxygen isotope ratio in the Arctic Ocean Sha, Yingkai 2017

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A comprehensive simulation study of dissolved Barium and Oxygenisotope ratio in the Arctic OceanbyYingkai ShaB.Sc. Atmospheric Science, Nanjing University of Information Science and Technology, 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Atmospheric Science)The University of British Columbia(Vancouver)March 2017© Yingkai Sha, 2017AbstractThe Arctic Ocean freshwater plays important roles in regional and global climate. Dissolved Bariumand the Oxygen isotope ratio are two tracers that provide key information on the river runoff and thesea-ice melt water as two Arctic Ocean freshwater components. In this research, an offline tracer modelwas developed with dissolved Barium and Oxygen isotope ratio modules and appropriate boundaryconditions were applied to the Arctic Ocean to simulate the spatial and temporal variations of the twotracers. The tracer model was run from 2002 to 2013 after a 24-year spin-up. The simulation resultsshow reasonable tracer climatology and seasonal cycles, agree well with field observations and theArctic freshwater cycle. The tracer model was applied to investigate the atmospheric driven freshwatervariabilities in the upper 130m through linear trend and Empirical Orthogonal Function (EOF) analysis.The linear trend result shows the increase in the transport of Eurasian runoff from the Makarov Basinto the Beaufort Sea and concurrent with the increase in the winter-spring Arctic Oscillation (AO). Thethree EOF modes show the role of the dipole anomaly, the interannual impact of the North AtlanticOscillation (NAO) and the Beaufort Sea anticyclonic anomalous wind, respectively on changing thepathway of the high Barium concentration North American runoff and the impact of the Eurasian runoffalong the continental shelves and in the central Arctic. A case study of the Beaufort Gyre freshwater in2007-2008 revealed the change of Eurasian runoff pathways in three stages with the dipole anomaly andthe transport of Eurasian runoff in the developing stage, the strong anti-cyclonic wind in the BeaufortSea in the mature stage and the weakening of the Beaufort Gyre in the final stage. A linear mixingmodel result confirms the increase of the Eurasian runoff in the Beaufort Gyre in the winter of 2007.iiPrefaceThis thesis contains details of parameterizations, numerical experiments and analysis of the results un-dertaken primarily by the author, Yingkai Sha and supported by the GEOTRACES program funded byClimate Change and Atmospheric Research (CCAR). Susan Allen was the supervisor and was involvedin the concept formation, interpretation of the results and manuscript edits. A manuscript based onChapter 3, and Chapter 4 will be submitted for publication in the future.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Arctic Ocean freshwater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.1 Freshwater components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.2 The indicator: Freshwater Content . . . . . . . . . . . . . . . . . . . . . . . . 42.1.3 Freshwater budget and implications . . . . . . . . . . . . . . . . . . . . . . . 52.2 Dissolved Barium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.1 The geochemical behavior of dissolved Barium . . . . . . . . . . . . . . . . . 62.2.2 External sources and the utility as a tracer . . . . . . . . . . . . . . . . . . . . 72.3 Oxygen isotope ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3.1 Definition and physicochemical properties . . . . . . . . . . . . . . . . . . . . 72.3.2 Role in the hydrological cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 82.4 Modeling of Arctic freshwater and tracers . . . . . . . . . . . . . . . . . . . . . . . . 93 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.1 Model and regional Arctic configuration . . . . . . . . . . . . . . . . . . . . . . . . . 103.2 Tracer parameterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2.1 Riverine tracer input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11iv3.2.2 Sea-ice and precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3 Configuration of numerical experiments . . . . . . . . . . . . . . . . . . . . . . . . . 163.4 Methods and data for analyzing the results . . . . . . . . . . . . . . . . . . . . . . . . 173.4.1 Data applied in model parameterization and evaluations . . . . . . . . . . . . 183.4.2 Methods in the model evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 193.4.3 Physical calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4.4 Statistical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4.5 Indices applied in the research . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4.6 Linear mixing model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.1 Climatology and seasonal cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.1.1 Dissolved Barium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.1.2 Oxygen isotope ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Data model comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.2.1 Dissolved Barium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.2.2 Oxygen isotope ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.3 Linear trends of tracers and Arctic freshwater . . . . . . . . . . . . . . . . . . . . . . 324.4 Tracer anomaly patterns and freshwater variability . . . . . . . . . . . . . . . . . . . . 344.4.1 Mode I: Dipole anomaly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.4.2 Mode II: The interannual effect of NAO . . . . . . . . . . . . . . . . . . . . . 384.4.3 Mode III: The Beaufort Sea high . . . . . . . . . . . . . . . . . . . . . . . . . 414.5 Application: A case study of Beaufort Gyre 2007-2008 . . . . . . . . . . . . . . . . . 444.5.1 Evolution of the FWC anomaly . . . . . . . . . . . . . . . . . . . . . . . . . 454.5.2 Linear mixing model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.1 Model configuration and operations . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.2 Tracer parameterizations, model output and evaluations . . . . . . . . . . . . . . . . . 525.2.1 dissolved Barium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.2.2 Oxygen isotope ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.3 Freshwater, tracers and atmospheric driving factors . . . . . . . . . . . . . . . . . . . 545.4 Insights from the Beaufort Gyre case study . . . . . . . . . . . . . . . . . . . . . . . 555.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.1 Research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.2 Contributions to the existing knowledge . . . . . . . . . . . . . . . . . . . . . . . . . 576.2.1 The Canadian Arctic GEOTRACES Program . . . . . . . . . . . . . . . . . . 576.2.2 Arctic Ocean freshwater studies . . . . . . . . . . . . . . . . . . . . . . . . . 57v6.3 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60A Climatology fields of the physical model . . . . . . . . . . . . . . . . . . . . . . . . . . . 70B Statistical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72B.1 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72B.2 Composite anomaly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73B.3 Linear regression and trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73B.3.1 Least squares method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73B.3.2 Significance test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74B.4 Empirical Orthogonal Function (EOF) . . . . . . . . . . . . . . . . . . . . . . . . . . 74B.4.1 Spatial pattern and principal component . . . . . . . . . . . . . . . . . . . . . 74B.4.2 Explained variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76B.4.3 Rule of thumb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76B.4.4 Spectral analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77C The derivation of wind stress curl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78D Atmospheric tele-connection patterns and CGRF indices . . . . . . . . . . . . . . . . . 79viList of TablesTable 3.1 The riverine Oxygen isotope ratio input of the tracer scheme . . . . . . . . . . . . . 15Table 3.2 Meta data of the field observations . . . . . . . . . . . . . . . . . . . . . . . . . . 18Table 3.3 Tracer end-member settings in Beaufort Sea . . . . . . . . . . . . . . . . . . . . . 23Table 4.1 Total annual riverine dissolved Barium input in this research and the estimate fromGuay and Falkner [1998] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Table 4.2 Mean bias and NRSMD of dissolved Barium comparisons . . . . . . . . . . . . . . 29Table 4.3 Mean bias and NRSMD of Oxygen isotope ratio comparisons . . . . . . . . . . . . 31viiList of FiguresFigure 2.1 Map of the Arctic Ocean with the bathymetry (shaded), continental shelves (blacktext), seas (black, italic), basins (white, bold) and ridges (white, italic). . . . . . . . 4Figure 3.1 MY TRC open boundaries (in black) and internal grid (in dark gray). Grid of AN-HA4 experiments covers all the MY TRC domain (both black and dark gray) andextends to the Atlantic Ocean (light gray). . . . . . . . . . . . . . . . . . . . . . . 10Figure 3.2 The classification of river estuaries in the Arctic Ocean. Rectangular frame on thebottom right is a zoom in CAA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Figure 3.3 Normalized ensemble seasonal cycle of dissolved Barium for the six largest Arcticrivers. The grey solid line is the ensemble result. Black markers indicate all ensem-ble members. Blue bars show the standard deviation. The hatch shows the “dropdown” signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 3.4 The seasonal cycle of dissolved Barium input in all parameterized Arctic rivers. . . 14Figure 3.5 Domain-wide mean dissolved Barium (a) and Oxygen isotope ratio (b) in two spin-up experiments and the formal run. Each of the spin-up experiment was run underAHNA4-EXH005 forcing from 2002 to 2013. . . . . . . . . . . . . . . . . . . . . 17Figure 3.6 The ANHA4 grid based transects in the the Baffin Bay and Hudson Bay (a), FramStrait and Barents Sea openings (b), and the Bering Strait (c). . . . . . . . . . . . 20Figure 3.7 The 2002-2013 mean ANHA4-EXH005 velocities above 130 m and regions thatdefine the TDS intensity (orange) and the Beaufort Gyre intensity (cyan) indices. . 22Figure 4.1 Simulated 2002-2013 climatology state of dissolved Barium above 130 m. (a) isthe annual mean state. (b) is the difference between the mean state in May and (a).(c) is the domain-wide mean dissolved Barium monthly mean timeseries. (d) is theseasonal cycle of (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25viiiFigure 4.2 Simulated dissolved Barium fluxes through different pathways (a) and their seasonalcycles (b). Negative in (a) means out flux and the black line is the net result. (c) and(d) are simulated riverine dissolved Barium input and its seasonal cycle. (d) showsthe time range of 2002-2008, and the 2007-2008 pattern was repeated in the 2009-2013 period. (e) is the riverine dissolved Barium input minus the net in/out flux. (f)is the seasonal cycle of (e). The calculation of (a-d) is based on equation (3.11) andequation (3.12). Rivers input on the southern part of transects (figure 3.5) is smalland not considered. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 4.3 Simulated 2002-2013 climatology state of Oxygen isotope ratio at the surface (1.05m) (a) is the annual mean. (b) is the histogram between the mean surface Oxygenisotope ratio and the sea surface salinity. The shade shows the number of pointsin each hist bin, the black box indicates the sea-ice melt water. (c) is the Oxygenisotope ratio timeseries that has been averaged in the hatched region. (d) is theseasonal cycle of (c). (e) is the domain-wide mean surface Oxygen isotope ratio. (f)is the seasonal cycle of (e). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Figure 4.4 The model output of dissolved Barium comparing with BGEP 2003-2005 (a), CBL32PZ2002 (b), NPEO 2004-2008 and 2013 (c), ARK-XXII/2 2007 (d) and HLY03012003 (e) observations. (f) is the timeseries comparison of BGEP data. (g) is thetimeseries comparison of NPEO data. (h) shows the locations of all samples. Twored circles are the regions that calculate the model mean, minimum and maximumin (f) and (g). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 4.5 Same as figure 4.4 but for Oxygen isotope ratio and without ARK-XXII/2 data. . . 31Figure 4.6 The linear trends of FWC (a), sea surface height and ocean velocities (b), dissolvedBarium (c) and Oxygen isotope ratio (d). All variables except sea surface heightwere averaged from 0 to 130 m depth. Dotted regions have trends that have passeda two-sided t-test. Negative/positive sea surface height in (b) delineates regions ofcyclonic/anti-cyclonic surface geostrophic flow. The velocity trends shown implythat the eastern side of the Beaufort Gyre and the TDS are intensifying. . . . . . . 33Figure 4.7 The October to next year May averaged AO indices and the linear trend from 1950to 2015. The orange line is the NOAA-CPC AO index, the brown solid line is theCGRF AO index. The dark green solid line is the result of linear regression with thetrend of 0.0097. The R-square is 0.098 and the trend passed 0.01 two-sided t-test. . 34Figure 4.8 The FWC EOF mode one spatial pattern (left), PC (top right green solid line) andthe spectral energy of PC (bottom right). The gray line on the top right is the TDSintensity estimated by the mean horizontal speed of surface ocean currents in thehatched region (see section 3.4.5). The red dashed line is the 95% red noise testconfidential interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35ixFigure 4.9 The composite anomalies for mode one PC. Composite anomalies are differencebetween high phase and low phase (section 3.4.4). sea level pressure, 10 m winds(a), wind stress, wind stress curl (b), sea surface height, ocean velocities above 130m (c) and E-P flux (d). Dotted regions have composite anomalies pass the 0.05 levelt-test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36Figure 4.10 The composite anomaly of dissolved Barium (a) and Oxygen isotope ratio (b) inmode one PC and averaged above 130 m. Hatched regions in (a-b) are shallowerthan 30 m. Dotted regions in (a-b) have composite anomaly pass the 0.05 leveltwo-sample t-test. (c) is the sketch of anomalous flow pattern, both in the loweratmosphere (top plane) and the surface ocean (lower plane). On the upper plane, thedipole anomaly with enhanced high pressure over the Beaufort Sea and enhancedlow pressure over the Eurasian Side. Wind barbs show the anomalous winds. Onthe lower plane, circles show the major anomalous currents; 1© and 2© transportsthe Eurasian runoff to the Makarov Basin; 3© is the anomalously strong TDS; 4©indicates the weak CAA - Baffin Bay transport and 5© is the intensified BeaufortGyre. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 4.11 The FWC EOF mode two spatial pattern (left), PC (top right green solid line) andthe spectral energy of PC (bottom right). On the top right plot, the gray dashed lineand gray solid line are the 1-year moving averaged NOAA-CPC NAO and CGRFNAO indices (see section 3.4.5). The red dashed line is the 95% red noise testconfidential interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Figure 4.12 Same as figure 4.9, but for mode two . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 4.13 Same as figure 4.10, but for mode two. (c) is the sketch of anomalous flow pat-tern. In the the lower atmosphere (top plane), the NAO-like anomaly with positivepressure over the North Atlantic and enhanced low pressure over the central Arctic/-Nansen Basin. In the surface ocean (lower plane), circles show the major anoma-lous currents; 1© and 2© are the intensified CAA - Baffin Bay transport with a weakBeaufort Gyre; 3© is the transport of Laptev Sea runoff; 4© is the accumulation ofrunoff water in the Makarov Basin. . . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 4.14 The FWC EOF mode three spatial pattern (left), PC (top right green solid line)and the spectral energy of PC (bottom right). The gray line on the top right plotis the Beaufort Gyre intensity estimated as the maximum sea surface height in theBeaufort Sea (see section 3.4.5). The red dashed line is the 95% red noise testconfidential interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Figure 4.15 Same as figure 4.9, but for mode three . . . . . . . . . . . . . . . . . . . . . . . . 43xFigure 4.16 Same as figure 4.10, but for mode three. (c) is the sketch of anomalous flow pattern.In the the lower atmosphere (top plane), the enhanced low pressure over the NorthAtlantic and Eurasian side of the Arctic intensifies the Beaufort Gyre. In the surfaceocean (lower plane), circles show the major anomalous currents; 1© is the weakCAA - Baffin Bay transport; 2© and 3© are the anticyclonic flow in the Beaufort Seaand the northern side of New Siberian Island; 4© is the transport of East SiberianSea runoff. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Figure 4.17 The Beaufort Gyre freshwater anomaly above 130 m as volume (red, left axis) andthe Beaufort Gyre intensity (black, right axis, see section 3.4.5), the hatched regionis the time span of the case study. . . . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 4.18 2007 June-August mean sea level pressure and 10 m wind anomaly (a). August-October mean sea surface height, ocean velocities (b), FWC (c), E−P (d), dissolvedBarium (e) and Oxygen isotope ratio (f) anomalies. . . . . . . . . . . . . . . . . . 46Figure 4.19 Same as figure 4.18, but for December-February mean, no E−P and δ 18O anomalies. 48Figure 4.20 Same as figure 4.18, but for 2008 and no E−P and δ 18O anomalies. . . . . . . . . 49Figure 4.21 The timeseries of Eurasian (red) and North American (black) runoff fractions inthe Beaufort Gyre (as defined in figure 3.7) from 0-130 m depth. The shade is thevariation range. The time span of the case study is hatched. . . . . . . . . . . . . . 50Figure A.1 CGRF 2002-2013 mean winter (DJF) and summer (JJA) sea level pressure and 10m-wind. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Figure A.2 ANHA4-EXH005 2002-2013 mean sea surface height, ocean velocities (a) andFWC relative to the 34.8 salinity (b) above 130m. The dashed line in (b) is theisoline of 2002-2013 mean March sea-ice larger than 70%; the hatch is the meanSeptember sea-ice larger than 70%. . . . . . . . . . . . . . . . . . . . . . . . . . 71Figure D.1 Spatial patterns of sea level pressure EOF modes (a-c), timeseries in dark red arethe PCs. NOAA-CPC AO and NAO indices were plotted as black dashed lines. . . 79xiGlossaryAGRO Arctic Great River ObservatoryANHA4 Arctic and North Hemisphere Atlantic 1/4 degreeAO Arctic OscillationBGEP Beaufort Gyre Exploration ProjectCAA Canadian Arctic ArchipelagoCGRF Canadian Meteorological Centre Global Deterministic Prediction System ReforecastsEOF Empirical Orthogonal FunctionFWC Freshwater ContentGLORYS Global Ocean Reanalyses and SimulationsLIM2 Louvain-la-Neuve Sea Ice Model version 2NAO North Atlantic OscillationNPEO North Pole Exploration ObservatoryNOAA National Oceanic and Atmospheric AdministrationCPC Climate Prediction CenterNRMSD Normalized Root Mean Square DeviationPARTNERS Pan-Arctic River Transport of Nutrients, Organic Matter, and Suspended SedimentsPC Principal ComponentxiiSCARFS Small Canadian Arctic River FlowsTDS Transpolar Drift StreamNEMO 3.4 Nucleus for European Modelling of the Ocean version 3.4VSMOW Vienna Standard Mean Ocean WaterxiiiAcknowledgmentsHere my sincere thanks to my M.Sc supervisor Dr. Susan Allen for providing me the opportunity topursuit my new research in her GEOTRACES group. She encourages me to practice my own ideas andI feel fully respected as a young researcher. Also, thanks Susan for both your knowledge about NEMOand your critical thinking on scientific problems which make my research moving forward.Thanks to Xianmin Hu and Dr. Paul Myers in University of Alberta for providing me physicaloceanographic simulation results in the Arctic Ocean. Xianmin’s help on the offline model configurationwas important in my research.Thank you Dr. Phil Austin and Dr. Roland Stull for all the help in my courses, TA, and sharingopinions on my scientific questions which promoted my enthusiasm on the atmospheric science.Thank you to Cindy Yu and Melanie Grenier as members in Allen’s GEOTRACES group for thediscussion in the weekly group meeting. Thanks to everyone in the office and everyone in Allen’sresearch groups in the past two years for staying together and sharing our good memories.Finally, thanks to to my parents, friends and roommates for their daily concerns and contacts.- Yingkai ShaxivChapter 1IntroductionThe hydrological cycle plays a central role in the earth climate system, of which Arctic Ocean is animportant member. The Mediterranean structure of the Arctic Ocean [Aagaard et al., 1985] plus thelarge amount of freshwater input from Arctic rivers, Pacific inflow, precipitation and sea-ice melt, makesArctic the most freshwater-influenced of all oceans [Aagaard et al., 1981, Carmack et al., 2016]. Theincrease of Arctic Ocean freshwater in the past decade [McPhee et al., 2009, Proshutinsky et al., 2009,Rabe et al., 2011] has a strong impact on the stratification state [Aagaard and Carmack, 1989, 1994],Arctic sea-ice cover [Polyakov et al., 2013] and ecological systems [Tremblay and Gagnon, 2009]. Inaddition, the increased Arctic Ocean freshwater export, which participates in the dense water formationin the Greenland, Iceland, Norwegian and Labrador seas, affects the overturning circulation and is thusof global importance [Dickson et al., 1988, Holland et al., 2001, Weaver et al., 1993]. Arctic freshwaterhas different components, including runoff, Pacific inflow, sea-ice melt and precipitation. It is necessaryto track the spatial and temporal variability of different freshwater components to further investigatetheir climatological and environmental impacts.For this objective, several physical and chemical tracers, including salinity, alkalinity (e.g. Yamamoto-Kawai et al. [2005]), dissolved Barium (e.g. [Falkner et al., 1994], Nitrate and Phosphate (e.g. Yamamoto-Kawai et al. [2008]) and Oxygen isotopes (e.g. Ekwurzel et al. [2001], Schlosser et al. [2002]) havebeen measured and analyzed since the 1980s to uncover the distribution and residence time of differentfreshwater components. In the meantime, with the development of ocean general circulation models,simulation studies were widely applied to investigate the variability of Arctic Ocean freshwater (e.g.Holland et al. [2006]). The coupling of these two approaches: freshwater tracer simulation, was imped-ded in the past due to lack of data. Remarkable work from Jahn et al. [2010] shows that, simulatedfreshwater tracers provide unique information on the variability of freshwater components and large-scale atmospheric circulation. Work of Manizza et al. [2009] on the other hand, shows the possibility ofmodeling certain bio-geochemical processes in a numeric system.In this research, with the assistance of field measurements and insights from other tracer modelingresearch, a simulation study of two freshwater tracers: dissolved Barium and Oxygen isotope ratio ispresented. The whole simulation was done by a newly developed tracer parameterization scheme withgiven physical oceanographic states from 2002 to 2013. The model output was analyzed, compared with1field measurements and used to investigate the underlying dynamics of the Arctic Ocean freshwater. Ingeneral, this research answers the following questions:1. How can oceanic distributions of dissolved Barium and Oxygen isotope ratio be simulated in anumeric model?2. What are the distribution and statistical features of the simulated tracers and how does the modeloutput compare with field measurements?3. How does atmospheric variability change the freshwater content in the Arctic?In the coming pages, chapter 2 contains background information about Arctic Ocean freshwater,modeled tracers and pervious research on numeric simulations in this field. Chapter 3 introduces themethodology part, includes model configuration, parameterizations, methods and data applied for theanalysis of the output. In chapter 4, all the results are shown, including the climatology, seasonal cycle,model evaluations, linear trends, anomaly patterns and a case study. Chapter 5 gives the discussion andchapter 6 is the conclusions.2Chapter 2Background2.1 Arctic Ocean freshwater2.1.1 Freshwater componentsThe topography of the Arctic Ocean contains of about half continental shelves and half ridges andbasins. The connections between the Arctic Ocean and other ocean basins through Bering Strait (PacificOcean), Fram Strait, Barents Sea openings and Davis Strait (Atlantic Ocean) are all limited in horizontaland vertical scale (figure 2.1). These two factors make the Arctic Ocean relatively isolated and to behavelike the Mediterranean sea [Aagaard et al., 1985].Even through the Arctic Ocean contains only 1% of the global volume of sea water and 3% of theworld ocean surface, it receives 13% of the world river flow [Dai and Trenberth, 2002, Vo¨ro¨smartyet al., 2000]. The net precipitation over the open ocean, sea-ice melt and salinity deficient Pacificinflow provide additional freshwater. The input of these freshwater sources can be summarized as“freshwater components”. The spatial distribution of freshwater components in the Arctic Ocean is notuniform. In total, the biggest freshwater reservoir is the Beaufort Gyre [Proshutinsky et al., 2002, 2009],the North American side of the Arctic contains more freshwater than the Eurasian side. Accordingto Yamamoto-Kawai et al. [2005], in 1929-2002, the highest sea-ice melt component was located inBarents and Kara Seas, meanwhile the sea-ice melt fraction in Canada Basin is negative, overshadowedby the ice transport. The Canada Basin - Baffin Bay and the Chukchi Sea have high fractions of runoff,precipitation and Pacific inflow (described as “other freshwaters” in Yamamoto-Kawai et al. [2005]).The temporal change of freshwater components has linkages with other processes in the climatesystem on different complexity levels. For example, Pacific origin freshwater input depends on theBering Strait inflow. The net precipitation at the north pole is affected by processes varying fromregional evaporation increase [Bintanja and Selten, 2014] to enhanced polar ward moisture transport[Bengtsson et al., 2011] and anthropogenic greenhouse gases and aerosols [Min et al., 2008]. The riverdischarge is affected by land surface processes since it is a term in the terrestrial water budget in thedrainage basin (e.g. Landerer et al. [2010] for Eurasian runoff). The sea-ice melt freshwater release is3Figure 2.1: Map of the Arctic Ocean with the bathymetry (shaded), continental shelves (blacktext), seas (black, italic), basins (white, bold) and ridges (white, italic).affected by the seasonal freeze-thaw cycle [Parkinson and Cavalieri, 1989], ice-albedo feedback [Curryet al., 1995] and atmospheric oscillation patterns (e.g. Arctic Oscillation (AO), Rigor and Wallace[2004]; diapole anomaly, Wang et al. [2009]; North Atlantic Oscillation (NAO), Deser et al. [2000]).2.1.2 The indicator: Freshwater ContentFreshwater Content (FWC) measures the relative abundance of the freshwater in a certain depth rangebased on a salinity reference. In the Arctic Ocean, following the choice of Aagaard and Carmack [1989],equation (2.1) shows the calculation of FWC from the surface to depth z.FWC =∫ z0(1− S(z)34.8)dz (2.1)4Here 34.8 is the salinity reference using the practical salinity scale [UNESCO et al., 1981]. The choiceis consistent with other previous research (e.g. Aagaard et al. [1985], Jackson et al. [2011], Morisonet al. [2012]). FWC has units of m, which means it is the vertical span of zero salinity water above purereference salinity water. By multiplying with its correspond surface area, FWC can be converted to thevolume of freshwater. Equation (2.1) has been widely used in observational (e.g. Rabe et al. [2011])and modeling (e.g. Jahn et al. [2010]) studies. Its advantage is that, it is constrained by the dynamicsin the system, since the calculation directly relates to the stratification. A limitation of it could be therepresentativeness of the reference salinity [Carmack et al., 2008].In this research, the choice of the depth is z= 130 m which in general captures the freshwater abovethe halocline layer (e.g. in Makarov Basin, the estimation by Steele and Boyd [1998] is 117 m) andshows good response to the atmospheric forcing. For the numeric calculation of FWC, equation (2.1)is discretized onto the model grid (see section 3.1) and the integral was approximated by trapezoidalquadrature.2.1.3 Freshwater budget and implicationsThe estimation of the Arctic freshwater budget, specifically, the balance between freshwater sources andsinks, started in the 1960s [Mosby, 1962]. Then based on FWC as a standardized variable, remarkableworks continued from the 1980s to 2015 [Aagaard and Carmack, 1989, Haine et al., 2015, Serrezeet al., 2006]. To summarize, river runoff is the biggest component of freshwater input. Comparingthe gauge measurements [Lammers et al., 2001] and the 2000-2010 study [Haine et al., 2015], highdischarge Eurasian rivers are the biggest fluvial freshwater input (1813 km3yr−1 Eurasian runoff v.s.4200±420 km3yr−1 total freshwater input). Pacific inflow through Bering Strait is the second largestArctic freshwater source; it has practical salinity lower than 34.8 because it has mixed with Bering Searunoff (i.e. Yukon River, Woodgate and Aagaard [2005]). Net precipitation is the other Arctic freshwatersource and is the input from the atmosphere.Eurasian freshwater mainly flows into the Transpolar Drift Stream (TDS), heading toward FramStrait, and North American freshwater either circles in the Beaufort Gyre and then moves on to the TDSor goes through the Canadian Arctic Archipelago (CAA) - Baffin Bay route from the Beaufort Shelf. Thetracer measurement based estimate of runoff transport time from the East Siberian Sea to Fram Straitthrough the TDS is 2-3 years [Van Der Loeff et al., 1995] and the Eurasian runoff residence time onaverage is 3.5±2 years [Schlosser et al., 2002]. The freshwater export via Fram Strait is slightly higherthan Davis Strait [Haine et al., 2015, Serreze et al., 2006]. The liquid phase export prior to 1989 wasestimated to be lower than the ice phase [Aagaard and Carmack, 1989] but then to be higher in the 21stcentury [Haine et al., 2015, Serreze et al., 2006], which potentially illustrates the Arctic sea-ice declineand the compensation of ice-phase export decrease by liquid-phase export increase [Serreze et al., 2007].The residual of the Arctic Ocean freshwater budget in 2000-2010 was estimated as 1200±730km3yr−1[Haine et al., 2015] which implies an accumulation of surface Arctic freshwater in the past decade[White et al., 2007].Arctic freshwater plays an important role in ocean, atmosphere and ecological systems. The ex-5istence of surface freshwater causes salt stratification in the Arctic Ocean. This stratification forms acold halocline layer in the subsurface which hinders the upward diffusive heat flux and thermally drivenconvection from the Atlantic layer, preserves the Arctic sea-ice [Polyakov et al., 2013] and affects theice-albedo feedback [Aagaard and Carmack, 1989, 1994].Arctic freshwater is also an important factor on marine productivity. Terrestrial origin freshwaterflushes dissolved and particulate materials into the river estuaries, which is then further advected into theArctic Ocean and provides nutrients for phytoplankton growth (e.g. Dittmar and Kattner [2003]; also seeKlunder et al. [2012] for dissolved iron). The Pacific origin freshwater is enriched in phosphate, plays animport role in the biological nitrogen fixation and benefits the productivity in both Arctic and AtlanticOcean [Yamamoto-Kawai et al., 2006]. Also, as previously mentioned, Arctic freshwater causes saltstratification. This stratification blocks nutrient supply from the deep water and is thus a negative factoron marine productivity [Tremblay and Gagnon, 2009].The Arctic Ocean freshwater goes to the North Atlantic Ocean through Fram Strait, Davis Strait andBarents Sea openings, in both liquid-phase and ice-phase [Aagaard and Carmack, 1989, Haine et al.,2015, Serreze et al., 2006]. This freshwater transport affects the stratification of the water column inthe sensitive deep water formation regions of the Greenland, Iceland, Norwegian and Labrador seas,affects the Overturning Circulation [Dickson et al., 1988, Holland et al., 2001, Weaver et al., 1993] andtherefore the global climate [Zickfeld et al., 2007].2.2 Dissolved Barium2.2.1 The geochemical behavior of dissolved BariumDissolved Barium (Bad) is a type of bio-intermediate element which in general behaves like hard-partnutrients [Chan et al., 1977, Falkner et al., 1993]. In many parts of the world oceans, dissolved Bar-ium concentration has a strong correlation with dissolved Silicon and alkalinity [Bacon and Edmond,1972, Chan et al., 1977]. Different from either Silicon which is a bio-limiting element and has almostzero concentration in the surface and alkalinity which reflects the Calcium Carbonate (CaCO3) cycleand is only slightly affected by biological activities, dissolved Barium is depleted in the surface butstill measurable and is enriched along the deep advective flowline [Chan et al., 1977, Falkner et al.,1993]. The main reason for this depletion is the uptake of Barium at the surface as barite (BaSO4). Thenewly formed barite is associated with biological particulate matter on the micro-scale and sinks in theocean. During the sinking process, some of the biological particulate matter decomposes and releasesbarite which results in a Barium maxima in the subsurface, but most of the barite reaches the sedimentsand then can be mobilized back to the ocean by remineralization [Bishop, 1988, Dymond et al., 1992,Falkner et al., 1993, 1994]. Research shows that barite formation could be induced by diatoms’ Bariumaccumulation behavior [Esser and Volpe, 2002]. Acantharia and siliceous radiolaria collect Barium intheir celestite (SrSO4) shells, and the sinking of these shells also contributes to vertical Barium cycling[Bernstein et al., 1992, 1998]. The residence time of Barium was estimated as 1×104 years [Libes,2011].62.2.2 External sources and the utility as a tracerRiver input (e.g. Arctic Ocean, Guay [1997], Guay and Falkner [1998]) and hydrothermal venting (e.g.East Pacific, Von Damm et al. [1985]) are the main external sources of Barium to the world oceans.Hydrothermal Barium is thought to precipitate inorganically as barite around hot spring sources in themid-ocean ridge systems [Von Damm et al., 1985]. For the fluvial input, Barium in the river-borneclays will be desorbed by exchange with other cations in the seawater and thus the dissolved Bariumconcentration increase in the river estuaries. [Edmond et al., 1978, Falkner et al., 1993, Li and Chan,1979].Dissolved Barium was first posed as a tracer of Arctic river and halocline water by Falkner et al.[1994]. Then the on-going field measurements in Beaufort Sea, Chukchi Sea, Laptev Sea and Eurasianmarginal seas found that North American rivers like Yukon and Mackenzie have dissolved Bariumconcentration significantly higher than major Eurasian rivers. Therefore, dissolved Barium is able toseparate North American runoff from Eurasian runoff. [Guay, 1997, Guay and Falkner, 1997, 1998,Taylor et al., 2003]. Since the “background” surface dissolved Barium level in the Arctic Ocean islower than both Eurasian and North American runoff, dissolved Barium also acts as a proxy of Arcticrunoff water in general [Falkner et al., 1994].Dissolved Barium was described previously as a quasi-conservative tracer in the Arctic Ocean sinceits biological modification above the halocline can be roughly averaged out over a long timescale [Tay-lor et al., 2003]. However, with the sea-ice decline in the past decade [Comiso et al., 2008], the increaseof primary production in the Arctic Ocean, especially continental shelves [Arrigo et al., 2008] caus-es concerns regarding the conservative behavior of Barium [Abrahamsen et al., 2009]. According toRoeske et al. [2012], the biological Barium uptake and remineralization may undermine the conserva-tive behavior of Barium, and only if the effect of riverine input is stronger than the biological signal,can the separation between North American and Eurasian runoff can be done unequivocally. In general,dissolved Barium is still a useful tracer of riverine freshwater in the Arctic Ocean but should be usedwith care in high productivity regions.2.3 Oxygen isotope ratio2.3.1 Definition and physicochemical propertiesNaturally Oxygen has three stable isotopes in water (H2O), Oxygen-16 (16O), Oxygen-17 (17O) andOxygen-18 (18O) with abundances of 99.76%, 0.04% and 0.2%. Considering the greater mass differ-ence between Oxygen-16 and Oxygen-18, the term “Oxygen isotope ratio” is usually taken as 18O/16O[Rohling, 2013]. The way to quantitatively estimate the abundance of a minor isotope in water is to com-pare the sample with a standard, and the comparison result is known as “δ”. For the Oxygen isotoperatio, its form in δ is defined in equation (2.2) [Dansgaard, 1964].δ 18O=( 18O16Osam18O16Ostd−1)×1000‰ (2.2)7Here parts per thousand (‰) is the unit, subscript sammeans the sample and std is the standard based onVienna Standard Mean Ocean Water (VSMOW), which is 2005.20±0.43 ppm of 18O/16O. A positiveδ 18O means the enrichment of heavier Oxygen-18 and vice versa.Since all Oxygen isotopes have the same number of protons and electrons, they behave in the sameway in chemical reactions [Rohling, 2013]. However, Oxygen isotopes can be differentiated by theirmass and vibration energy difference. The separation of isotopes between substances with differentisotopic compositions is called “isotopic fractionation” [Rohling, 2013]. In detail, the fractionation canbe divided into the the equilibrium fraction and the kinetic fraction. Equilibrium fractionation happensduring phase changes in which heavier molecules (i.e. H182 O) prefer to stay in the more condensedphase. Kinetic fractionation on the other hand breaks the equilibrium isotopic distribution and is mostlycaused by unidirectional processes (e.g. molecular diffusion, [Craig and Gordon, 1965]).2.3.2 Role in the hydrological cycleIn the global hydrological cycle, isotopic fractionation occurs in evaporation, atmospheric water vaportransport, precipitation and oceanic phase changes such as sea-ice melt. Examining the main responsein each of the process contributes to the understanding of the Oxygen isotope ratio as a freshwater tracerin the Arctic Ocean.During the evaporation, lighter molecules (i.e. H162 O) have lower vibration energy, higher vaporpressure, and are easier to be evaporated into the atmosphere. Meanwhile heavier molecules tend tostay in the liquid phase and thus separation occurs. The equilibrium fractionation during evaporation isthought to decrease with increasing temperature in an exponential relation [Majoube, 1971]. Moleculardiffusion, a kinetic fractionation process, also plays a role in enhancing the separation at the air-seainterface [Craig and Gordon, 1965]. The intensity of molecular diffusion during evaporation was foundto be negatively related with the boundary layer humidity [Craig and Gordon, 1965, Rohling, 2013].Precipitation includes a phase change from atmospheric water vapor to rain droplets. Due to thehigh humidity in the cloud, equilibrium fractionation is the only important fractionation process in thiscase. Since the heavier Oxygen-18 has lower vibration energy, it tends to go into the droplets and leavesthe cloud. Thus, during meridional atmospheric vapor transport, heavier Oxygen-18 is precipitated andlighter Oxygen-16 accumulates. When the air finally reaches high latitudes, the Oxygen-18 depletioncan actually be measured in the precipitated water. Since the precipitation strongly influences the ter-restrial water budget, the Oxygen-18 depletion can also be found in high latitude rivers. Based on fieldmeasurements at the North Pole, the precipitation and runoff (together called “meteoric water”) Oxygenisotope ratio value is about −20‰, significantly lower than mid, low latitude cases (e.g. −8.8−7.1‰for Yellow River and Yangtze River, Zhang et al. [1990]).In the Arctic Ocean, another factor that contributes to the variability of the Oxygen isotope ratiois the sea-ice freeze-thaw cycle. The equilibrium fractionation during sea-ice formation concentratesheavier Oxygen-18 into the ice, and releases it during sea-ice melt. Since high latitude meteoric waterhas low Oxygen isotope ratio values, but sea-ice melt water has Oxygen isotope ratios higher than thesurface ocean, Oxygen isotope ratio has the ability to separate sea-ice melt water from meteoric water8in a δ 18O-Salinity graph. Thus, considering that Oxygen isotope ratio is conservative if the water is notevaporated, it is widely used as a tracer of sea-ice melt water in the Arctic Ocean (e.g. [Ekwurzel et al.,2001, Macdonald et al., 2002, O¨stlund and Hut, 1984, Yamamoto-Kawai et al., 2005, 2008]).2.4 Modeling of Arctic freshwater and tracersModeling of the Arctic Ocean can be traced back to the 1960s [Campbell, 1965]. In the early stages,researchers were mainly focused on the circulation patterns [Galt, 1973] and sea-ice movement [Maykutand Untersteiner, 1971]. The first three-dimensional numerical study of the Arctic Ocean circulationwas done by Semtner Jr [1976] with 110km horizontal resolution and 14 vertical levels. With thedevelopment of community ocean general circulation models, more studies were published in the early2000s, under the topic of Arctic Ocean freshwater, including the freshwater budget (e.g. Miller andRussell [2000], Steele et al. [1996]), the position and size of the Beaufort Gyre (e.g. Proshutinskyet al. [2002]) and the role of atmospheric patterns on freshwater export (e.g. Zhang et al. [2003]).The appearance of climate models, which couple simulation cores of ocean, sea-ice, atmosphere andland, provided a comprehensive numeric environment. Arctic freshwater studies were therefore able toresolve more details, for example, Holland et al. [2006] discussed the freshening of Arctic Ocean inthe 21st century with different freshwater components. Mysak et al. [2005] simulated the Fram Straitsea-ice transport and found correlation with NAO index in an intermediate complexity earth systemmodel.The impact of Arctic Ocean freshwater export in the North Atlantic Ocean is also a field of activeresearch. The numerical study of it started at 1990s. Ha¨kkinen [1993], simulated the effect of sea-iceexport in the Nordic Seas during the Great Salinity Anomaly by using a coupled ice-ocean model. Ina 500-year control experiment, Jungclaus et al. [2005] found the modulation of the overturning circu-lation by Arctic freshwater export. Using an eddy-permitting regional model, Myers [2005] found thefreshwater export from Davis Strait has little impact on the freshening of the Labrador Sea.The numeric study of freshwater relevant tracers in the Arctic is still a newly defined topic. Freshwa-ter tracer simulation has advantages in investigating the deposition of different freshwater components(instead of just the total budget) and their responses to atmospheric forcing. Manizza et al. [2009] sim-ulated the riverine input of dissolved organic carbon and provided insights on parameterizing fluvialtracer export. Jahn et al. [2010] used passive tracers as proxies of river, Pacific Ocean and sea-ice meltfreshwater and investigated the role of atmosphere in the export of different freshwater components.In addition to the integrated studies of Arctic Ocean freshwater mentioned above, many simulationstudies also examined the Arctic precipitation (e.g. Walsh et al. [1998]) or runoff (e.g. Wu et al. [2005])alone, as single terms in the freshwater budget and thus contributed to the understanding of the entiresystem.9Chapter 3Methodology3.1 Model and regional Arctic configurationThe numerical model employed in the study is the tracer model MY TRC. MY TRC is under the numer-ic framework of Nucleus for European Modelling of the Ocean version 3.4 (NEMO 3.4). We parameter-ized the tracer model with dissolved Barium and Oxygen isotope ratio chemistry and used NEMO 3.4[Madec and the NEMO team, 2012] physical schemes. The model was configured on an orthogonalgrid which covers the entire Arctic Ocean with two open boundaries. The open boundary on the NorthAtlantic side is set along the 60◦N parallel, close to the southern edge of Greenland, the other openboundary, which is on the North Pacific side, is set in the Bering Strait, at approximately 64◦N.Figure 3.1: MY TRC open boundaries (in black) and internal grid (in dark gray). Grid of ANHA4experiments covers all the MY TRC domain (both black and dark gray) and extends to theAtlantic Ocean (light gray).Since both dissolved Barium and Oxygen isotope ratio are passive tracers, here MY TRC was op-10erated offline (i.e. the tracer model is run using stored output files from the ocean and sea-ice mod-el) with physical oceanographic and sea-ice output from the Arctic and North Hemisphere Atlantic1/4 degree (ANHA4) experiments [Holdsworth and Myers, 2015]. ANHA4 experiments cover the en-tire domain of the tracer model and extend further southward in the Atlantic Ocean and have lateralboundaries along the 20◦S parallel (figure 3.1).In order to avoid the coordinate transfer between MY TRC fields and ANHA4 forcing variables,the MY TRC grid was chosen to coincide with the ANHA4 grid in the Arctic Ocean, The grid hasabout 11km resolution in the central Arctic and 50 vertical levels with a 1.05 m top layer, decreasing inresolution with increasing depth.3.2 Tracer parameterizationsThe tracer parameterization for dissolved Barium and Oxygen isotope ratio is prognostic. Differentprescribed values were applied for tracers’ sources and sinks near the surface, including river runoff,sea-ice variabilities and precipitation. The budget equation in the tracer model is [Foujols et al., 2000]:∂T∂ t= SMS− v⃗ ·∇T +∇h · (Ah∇hT )+ ∂∂ z(Av∂T∂ z)(3.1)Here T can be dissolved Barium (nM) or Oxygen isotope ratio (‰), v⃗ = (u,v) is the horizontal oceanvelocity. ∇h is the horizontal (x,y) gradient, Ah and Av are the vertical eddy diffusivity parameters. SMSis the net impact of tracer sources and sinks:SMS=(∂T∂ t)R+(∂T∂ t)dil+(∂T∂ t)p+(∂T∂ t)i(3.2)Where the right-hand side terms are the river input, the dilution effect, meteoric impact of Oxygen iso-tope ratio from precipitation and the fractionation during the sea-ice melting/formation, respectively.The river runoff term is explained in the next section and all the other terms are explained in sec-tion 3.2.2.Dissolved Barium in this study is modeled as conservative which means the biological effects arenot included. The small bias raised by this choice will be discussed in section 4.2. Also, the dissolvedBarium contributed by hydrothermal venting is not included as the hydrothermal Barium is mainly inthe particulate phase as barite and precipitates around the hot spring sources [Von Damm et al., 1985]and thus does not impact surface dissolved Barium. Oxygen isotope is modeled as conservative, as nomajor processes changes its value away from the ocean surface.3.2.1 Riverine tracer inputIn order to parameterize the riverine dissolved Barium and Oxygen isotope ratio export, the estuariesof all pan-Arctic rivers were grouped into multiple regions, and a seasonal cycle or a single value wasassigned for each of the regions. In total, the tracer scheme has twenty regions for dissolved Barium(figure 3.2) input and seven regions for Oxygen isotope ratio (table 3.2) input.11During the simulation, the model checks the region of all grid points that have non-zero dischargevalues and calculates the tracer input by applying equation (3.3):(∂T∂ t)R= TR ·R · 1d ·ρ0 (3.3)Here the left of the equation is the fluvial tracer input, which has a unit of c · s−1, c is the unit of eitherdissolved Barium or Oxygen isotope ratio. R is the river discharge which contains non-zero values incoastal regions and over the top 15 m of the water column. In NEMO, runoff is added like rain overa grid cell with units of kg ·m−2 · s−1. d is the vertical scale of the grid. The density of freshwater isρ0 = 1000.0kg ·L−1. TR is the prescribed tracer seasonal cycle or end-member value in given region inc ·L−1 · s−1.Dissolved BariumFigure 3.2: The classification of river estuaries in the Arctic Ocean. Rectangular frame on thebottom right is a zoom in CAAFor the riverine input of dissolved Barium, twenty different regions were used (figure 3.2). Thisdivision is based on the pan-Arctic watersheds defined in Lammers et al. [2001], the data availability ofriverine dissolved Barium records and river discharge in different rivers. As described in section 2.2.1,the amount of Barium in the river depends on the type of river-born clays and sediment loads, so thefine classification in figure 3.2 reflects the diversity of geological environments of Arctic rivers.12The dissolved Barium input in “Greenland” was set as 0.0 nM by assuming that Greenland andIceland river runoff is mainly glacial melt and has little Barium. For other regions, seasonal cycles wereestimated. For each of the regions, except CAA, the biggest river of the region represents the dissolvedBarium input of all other rivers. For regions inside the CAA, the river that has the dissolved Bariumconcentration closest to the average of all rivers in the region was chosen as the representative, sinceCAA rivers have no big differences in size. If a region has a representative river, then the name of theriver is used to name the region (figure 3.2).The Kolyma, Lena, Ob, Yenisey, Mackenzie and Yukon have the most frequent observations andare also the six largest Arctic rivers. Other rivers only have few measurements during the summer. Sohere, the seasonal cycle of these six largest rivers were first calculated, then the similarities among theseseasonal cycles were identified and generalized to other, more poorly, observed rivers. This method iscalled the “ Normalized ensemble seasonal cycle” calculation.Fluvial dissolved Barium and Oxygen isotope ratio records were taken from ARCSS-107, Pan-Arctic River Transport of Nutrients, Organic Matter, and Suspended Sediments (PARTNERS), ArcticGreat River Observatory (AGRO), Small Canadian Arctic River Flows (SCARFS) and River samples inthe GEOTRACES Canadian Arctic Expedition (table 3.2). The data were used for the parameterizationthe riverine tracer input. The discharge of Yukon river was taken from the Piolet Station, United StatesGeological Survey (USGS) [USGS, 2016], the discharge of Mackenzie river was taken from WaterOffice, Environment Canada [EC-Wateroffice, 2016]. Other discharge records were taken from AGRO.The discharge data was used for calculating the flow weighted annual mean tracer input.The discontinuous daily riverine dissolved Barium records were combined into monthly mean time-series. Then for the six largest Arctic rivers, linear interpolation was applied for the month that has nodata, and the seasonal cycle is therefore calculated. After that, the seasonal cycle of the six largest riversare normalized by dividing the flow weighted annual mean dissolved Barium concentration. Finally, thenormalized seasonal cycle was ensemble averaged over the six rivers. For rivers with observations inonly a few months, the normalized seasonal cycle was scaled by the available observations.Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0.250.500.751.001.251.501.75Normalized dissolved Barium (Bad)Normalized ensemblemonmean BadLenaKolymaYeniseyObMackenzieYukon"Drop down" signal Std. dev.Figure 3.3: Normalized ensemble seasonal cycle of dissolved Barium for the six largest Arcticrivers. The grey solid line is the ensemble result. Black markers indicate all ensemble mem-bers. Blue bars show the standard deviation. The hatch shows the “drop down” signal.13Riverine dissolved Barium has strong seasonal variabilities, and this is the reason for using seasonalcycles instead of single end-member values (figure 3.3). The small standard deviations of the ensemblemembers indicate that the normalized seasonal cycles of these six rivers are similar. The biggest similar-ity is hatched and named as the “drop down” signal. The “drop down” signal is a significant decrease ofnormalized riverine Barium concentration from April to May. This “drop down” signal can be explainedby the spring freshet which usually happens in mid-May. During this time, the river discharge increasesstrongly and dilutes the Barium concentration in the river. Previous studies of both Barium and alkalini-ty have seen a similar freshet dilution [Cooper et al., 2008], which supports that the “drop down” signalis not an artificial pattern. Since spring freshet is the dominant hydrological event in Arctic rivers, it iscrucial to have the “drop down” signal in the dissolved Barium seasonal cycle of all Arctic rivers eventhough many of them do not have records in the late spring, early summer. This is also the motivationof “Normalized ensemble seasonal cycle” calculation.JanMaySepDec KolymaYeniseyLenaObMackenzieYukon0100200300400500600700Bad [nM](a) Major Arctic riversJanMaySepDec OlenekTaimyraKhatangaPechoraPyasinaYanaIndigirka020406080100120140160180Bad [nM](b) Small Russian riversJanMaySepDec ClydeCunninghamBackThomsenCresswellCoppermine050100150200250300350400Bad [nM](c) Small North American riversFigure 3.4: The seasonal cycle of dissolved Barium input in all parameterized Arctic rivers.The variability due to the parameterized seasonal cycle is smaller than the difference in annualmean among rivers. North American rivers, like the Mackenzie River, always have dissolved Bariumconcentration higher than the Eurasian rivers (figure 3.4). In other words, dissolved Barium’s ability toseparate the North American runoff from Eurasian runoff is not undermined by the parameterized strongseasonal cycle.Note that, in this section, the term “the six largest Arctic rivers” is used, but the real difference inthe parameterization are “well observed” rivers and “poorly observed” rivers. “Normalized ensembleseasonal cycle” calculation is a way that borrows information from the “well observed” group and usesit for the “poorly observed” group. The reason why we use “the six largest Arctic rivers” is because ofthe fact that big Arctic rivers are also the “well observed” rivers.Oxygen isotope ratioCompared with the large variation of dissolved Barium concentration in Arctic rivers, riverine Oxygenisotopes are more uniform because the diversity of river bed geological structure does not affect thevariability of Oxygen isotopes. As previously mentioned in section 2.3.2, on the scope of the global hy-drological cycle, all Arctic river runoff is generated from high latitude precipitation and called “meteoricwater”.14In the tracer scheme, the riverine Oxygen isotope ratio input has seven different classifications:“Kolyma”, “Lena”, “Ob”, “Yenisey”, “Mackenzie”, “Yukon” and “others” (table 3.1). The riverine inputratios in these seven regions were set to the flow weighted annual mean records. For other rivers, anunified end-member value −20.0‰ was used, consistent with other research [Yamamoto-Kawai et al.,2008].Table 3.1: The riverine Oxygen isotope ratio input of the tracer schemeKolyma Lena Yenisey Ob Yukon Mackenzie Others−22.7‰ −21.6‰ −18.3‰ −15.9‰ −20.7‰ −29.8‰ −20.0‰3.2.2 Sea-ice and precipitationThe dilution effectSea-ice formation/melting, net precipitation (precipitation minus evaporation) and river runoff can beviewed as extra input and output of ocean water and therefore affect the distribution of solute includingmodeled tracers. During the simulation, all the freshwater types dilute the tracer by the ratio of the fluxto the cell depth: (∂T∂ t)dil= (E−P−R) · Ttρr ·d (3.4)In the tracer scheme, ρr = 1025.0km/m3 is the reference density of sea water in NEMO 3.4, R is theamount of river runoff which enters into the Arctic. E−P is the net water loss by net sea-ice formationand net evaporation, both terms have units of kg ·m−2 · s−1. R is the input from ANHA4 runoff forcingand E−P can be calculated by usingE−P=−FS SrS (3.5)which is the reverse of salt flux calculation in Schmitt et al. [1989]. Here FS is the salt flux, which canbe defined as the product of salinity and water flux in the ocean, Sr = 34.7 is the reference salinity ofsea water on the practical salinity scale, and S is the sea-surface salinity. Both FS and S can be takenfrom ANHA4 experiments. Noted that E−P has values in the entire domain.Isotopic fractionationThe amount of Oxygen-18 in sea-ice and precipitation is different due to the fractionation process. Theparameterization of the precipitation input of Oxygen isotope ratio is(∂T∂ t)p=WT ·W · 1− Icd ·ρ0 (3.6)Here (∂T/∂ t)p is the contribution of 5-day average precipitation, WT =−20.0‰ is the Oxygen isotope15ratio end-member value for meteoric water, consistent with other research [Yamamoto-Kawai et al.,2005, 2008] and the riverine end-member settings. W is the net precipitation and Ic is the sea-ice coverin ANHA4 output, so that the precipitation over sea-ice does not impact the Oxygen isotope ratio in theocean. For O18/O16, equilibrium fractionation dominates in the Arctic, so kinetic fractionation is notparameterized.The E−P in equation (3.5) can be used to calculate the isotopic fractionation of Oxygen isotopesduring sea-ice melt or formation periods:(∂T∂ t)i=1d ·ρ0 · [IT ·−(E−P)−W ] (3.7)IT = 1.5‰ is the Oxygen isotope ratio end-member value of sea-ice melt water, this uniform choice isreasonable for the isotopic fractionation in the central Arcitc, Barents Sea and Fram Strait but is likelyan overestimation for the Canada Basin. A detailed discussion is given in section 4.2.2 and section 5.2.2.Note that −(E−P) is the total flux of net sea-ice melt and net precipitation, therefore, −(E−P)−W isthe flux from sea-ice melt water in kg ·m−2 · s−1.3.3 Configuration of numerical experimentsThe tracer model was operated offline from 2002 to 2013 by using the tracer model configuration de-scribed in section 3.1 and tracer parameterizations described in section 3.2. The initial field of dissolvedBarium was created from field measurements through ordinary Kriging interpolation. ARCSS-102,ARK XIV/2A, CBL32PZ, HLY0301, ARK XXII/2, Beaufort Gyre Exploration Project (BGEP) 2003-2005 and North Pole Exploration Observatory (NPEO) 2000-2004 data (table 3.2) were used to estimatethe initial field and the open boundary condition of the dissolved Barium in the tracer model. For theOxygen isotope ratio, the reanalysis data from LeGrande and Schmidt [2006] was chosen and re-mappedto the model grid as the initial field.For the built-in physical schemes in NEMO 3.4, Total Variation Diminishing (TVD) was chosenfor the horizonal advection, Laplacian lateral diffusion was used with a horizontal eddy diffusivity of300.0 m2 · s−1, consistent with the salinity horizontal eddy diffusivity in ANHA4-EXH005 experiment.The model receives runoff with a mixing coefficient of 0.001 m2 · s−1 over the top 15 m of the watercolumn. The edge points of the MY TRC model domain preserved tracer values of the initial field asthe open boundary condition.The oceanic forcing of this simulation is the five-day average output of ANHA4-EXH005. ANHA4-EXH005 is a member of ANAH4 experiment, it runs under the coupled NEMO 3.4 and Louvain-la-Neuve Sea Ice Model version 2 (LIM2) [Vancoppenolle et al., 2012]. The subgrid scale vertical mix-ing was parameterized through a turbulent kinetic energy based second-order turbulent closure scheme[Mellor and Yamada, 1982]. The open boundary condition of ANHA4-EXH005 was driven from GlobalOcean Reanalyses and Simulations (GLORYS) with buffer zones in the Bering Strait, along the 20◦Sparallel in the Southern Atlantic and in the Mediterranean Sea. ANHA4-EXH005 was initialized withGLORYS sea surface height, temperature, salinity and velocities. The Coordinated OceanIce Reference16Experiments (CORE) bulk formulas [Large and Yeager, 2004] were applied to compute fluxes of heat,water, and momentum [Xianmin, 2016].The atmospheric forcing of the ANHA4-EXH005 is Canadian Meteorological Centre Global Deter-ministic Prediction System Reforecasts (CGRF) data. This dataset has a temporal resolution of 6-hourand covers the period of 2002-2013. The CGRF is thought to have comparable quality with reanalysisdata in terms of surface temperature, humidity and winds [Smith et al., 2014]. The high spatial and tem-poral resolution of the CGRF data permits detailed atmospheric structure at high latitudes when used asthe forcing of ANHA4 experiments [Holdsworth and Myers, 2015]. The river discharge forcing of boththe ANHA4-EXH005 and this simulation is a re-mapped monthly river discharge from Dai et al. [2009]and the Greenland glacier melt from Bamber et al. [2012]. The former is reanalysis data from gaugerecords and Community Land Model version 3 (CLM3), the latter is based on field observations.55.557.559.561.5Bad [nM](a) Domain-wide mean dissolved Barium (dep<130m)2.72.62.52.42.32.2δ18O [1E-3]Spin-up 01 Spin-up 02 Formal run(b) Domain-wide mean Oxygen isotope ratio (dep<130m)Figure 3.5: Domain-wide mean dissolved Barium (a) and Oxygen isotope ratio (b) in two spin-upexperiments and the formal run. Each of the spin-up experiment was run under AHNA4-EXH005 forcing from 2002 to 2013.Before the 2002-2013 simulation, the tracer model was spun-up for 24 years. The first 12-year usedthe ANHA4-EXH005 forcing from 2002-2013. The second 12-year used the same forcing again. A24-year spin-up is longer than many other regional modeling studies. Such a long spin-up was neededto provide stable seasonal cycles and balance the riverine tracer input with the tracer flux going out ofthe Arctic Ocean (figure 3.5). The model simulation results above 130 m after spin-up were thoughtto be independent from the dissolved Barium measurements which were used as the initial field andthen also used in the model evaluation. In the intermediate and deep layers, the tracer values were stilltrending due to the lack of vertical tracer dynamics. Both dissolved Barium and Oxygen isotope ratiofields were saved as monthly averages.3.4 Methods and data for analyzing the resultsThe domain-wide average was calculated in the entire MY TRC domain (section 3.1) to examine thetime evolution of the tracer simulation result. The vertical mean from surface to 130 m is calculat-ed for examining the tracer anomalies and dissolved Barium climatology which is consistent with the17depth range of FWC calculation and represents the distribution of tracers above the halocline layer (sec-tion 2.1.2). The climatology of Oxygen isotope ratio was calculated on the first model layer (i.e. 1.05m) since it is directly modified by meteoric and sea-ice melt water and shows the highest variability.3.4.1 Data applied in model parameterization and evaluationsTable 3.2: Meta data of the field observationsProject/Data Cruise Platform Time SourceARCSS-107 Various Various 1993-1996 1PARTNERS - - 2004-2007 2AGRO I/II - - 2009-2015 2SCARFS - - 2014 3GEOTRACES -Canadian ArcticExpedition- - 2014-2015 4ARCSS-102HX171 R/V Alpha Helix 19935ARCRAD-93 USCGC Polar Star 1993ARK IX/4 R/V Polarstern 1993Larsen-93 CCGS Henry Larsen 1993HX174 R/V Alpha Helix 1993ARCSS-105 ARK XIV/2A R/V Polarstern 1998 6CBL32PZ CBL32PZ USCGC Polar Star 2002 7HLY0301 HLY0301 R/V Healy 2003 8GEOTRACES ARK XXII/2 R/V Polarstern 2007 9NPEO Various Various 2000-2013 10BGEP Various Various 2003-2005 111. Falkner [2009c], https://data.eol.ucar.edu/dataset/106.ARCSS1072. AGRO [2016], http://www.arcticgreatrivers.org/data.html3. Alkire [2015], https://arcticdata.io/catalog/#view/doi:10.18739/A2CP8H4. Kristina A. Brown (kbrown@whoi.edu)5. Falkner [2009a], https://data.eol.ucar.edu/dataset/106.ARCSS1026. Falkner [2009b], https://data.eol.ucar.edu/dataset/106.ARCSS1057. Woodgate [2015], https://cchdo.ucsd.edu/cruise/32PZ200208198. Falkner [2014], https://cchdo.ucsd.edu/cruise/32H1200307219. Roeske et al. [2012], http://www.bodc.ac.uk/geotraces/data/inventories/arkxxii 2/10. NPEO [2015], http://psc.apl.washington.edu/northpole/Data.html11. Proshutinsky and Krishfield [2016], http://www.whoi.edu/website/beaufortgyre/expeditionsBoth field observations (table 3.2) and forcing variables were used in analyzing the model output.CGRF sea level pressure and horizontal 10 m-wind were used in the composite anomaly calculations.Sea level pressure was also used to calculate AO and NAO indices. ANHA4 salinity was used tocalculate the FWC; sea surface height and horizontal velocities were used to investigate surface oceancirculation. ANHA4 wind stress was applied for diagnosing the intensity of Ekman divergence andconvergence. E−Pwhich was calculated in the tracer scheme was also used for analyzing the variabilityof FWC and Oxygen isotope ratio.183.4.2 Methods in the model evaluationNormalized Root Mean Square Deviation (NRMSD) and mean bias were used in the model evaluationand their definitions are:NRMSD=RSMDmax(x)−min(x) , RSMD=√E[(x̂− x)2]Mean bias= E(x)−E(x̂)(3.8)Here, x is the field measurement, x̂ is the model output, x is the average of x and E means expectation.Observations and model output are considered as two groups in the comparison. Each sample of theproject/cruise is compared with the model output on its closest model grid. The date of samples arematched with the corresponding month in the model output. When the NRMSD and mean bias arecalculated over different depths, observations were vertically interpolated to the model depth. If at acertain depth, the total number of samples is smaller than 10, then the NRMSD will not be calculatedsince the maximum minus minimum may not have an enough range for the normalization.CBL32PZ, HLY0301, ARK XXII/2 (contains dissolved Barium only), BGEP 2003-2005, NPEO2004-2008, 2010 (contains Oxygen isotope ratio only) and 2013 data were used in the model evaluation(table 3.2). BGEP and NPEO have observations in the Canada Basin and the central Arctic in multipleyears (BGEP has data from 2003 to 2005; NPEO has data from 2004 to 2008 and 2010, 2013; 2010 datacontains only Oxygen isotope ratio records). The data in all available years will be used for the NRMSDand mean bias calculation. Observations and all the model result in a certain area (the central Arctic forNPEO and the Beaufort Sea for BGEP) above 130 m will be averaged and compared as timeseries.3.4.3 Physical calculationsBecause the NEMO grid is not a simple rectilinear grid, the ANHA4-EXH005 wind stress curl wascalculated by re-mapping the wind stress onto a Mercator grid and applying the finite difference calcu-lation:curlz (⃗τ) =∆τφ∆x− ∆τλ∆y+τλRtanφ (3.9)where τ is the wind stress, R is the radius of the earth, φ is latitude, λ is longitude, ∆x and ∆y are thesizes of grid.∆x= Rcosφ∆λ ∆y= R∆φ (3.10)for all the ∆ terms, first order forward and backward difference were applied for edge points and secondorder central difference was used for all the interior points. The derivation is in appendix C.The dissolved Barium fluxes, through the Bering Strait, Fram Strait, the Barents Sea and Baffin Bayare calculated to estimate the total budget of dissolved Barium in the Arctic. The tracer flux is given by:19F (Bad) =i1, j1∑i=i0j= j0Ti, jAi, j (v⃗i, j · n⃗) (3.11)where F is the tracer flux with the unit of mol · s−1. T is the tracer concentration. (i0, j0) and (i1, j1) arethe starting and ending indices of latitudes and longitudes of the transects in ANHA4 grid. A is the areaof the transect grid cells and calculated as “depth grid size”דhorizontal grid size”.Figure 3.6: The ANHA4 grid based transects in the the Baffin Bay and Hudson Bay (a), FramStrait and Barents Sea openings (b), and the Bering Strait (c).The Fram Strait transect was set from the East Greenland coast to the Svalbard; the Barents Seatransect was set from the Svalbard to the Norwegian coast. The Bering Strait transect was built close tothe 64◦N parallel. The Baffin Bay transect has two parts, one cross the Davis Strait and the other onecovers the entrance from the Hudson Bay to the North Atlantic (figure 3.6).The total input of dissolved Barium is also estimated. The calculation is based on the ANHA4-EXH005 river discharge forcing (section 3.3) and the riverine dissolved Barium parameterization (sec-tion 3.2):Fr (Bad) =1ρ0R ·AhTr×10−6 (3.12)Here Fr is the dissolved Barium input from rivers, the unit is mol · s−1. Ah is the horizontal area of thesurface grid cell. Note that, Fr is two dimensional, and it will be summed by the estuary of a certainriver or the regional classification (figure 3.2).203.4.4 Statistical methodsThe anomaly of variables was calculated relative to the 2002-2013 monthly mean results. The compositeanomaly was calculated as the difference of the average of a timeseries in its high and low phases.Higher than the standard deviation (σ ) or lower than the negative standard deviation (−σ ) are definedas high and low phases. The significance test for the composite anomaly is the two-sample t-test.Linear regression with a two-sided t-test was applied for estimating the trend. The Empirical OrthogonalFunction (EOF) decomposition [Lorenz, 1956] was applied to the monthly detrended FWC anomaliesto investigate the dominate modes of variations. The first three modes were analyzed with compositeanomaly of CGRF and ANHA4 variables. The sampling error of the EOF is estimated by the “ruleof thumb” [North et al., 1982] with the effective degree of freedom calculated as Bretherton et al.[1999] suggested. The EOF does not contain the information of climatology, seasonal cycle and lineartrends. Each EOF mode is shown as a spatial patterns (with the FWC scale) and a normalized PrincipalComponent (PC) (without the FWC scale, and here after simplified as “PC”). Spectral analysis by theFast Fourier Transform (FFT) based “periodogram” technique was used for analyzing the PC of eachmode. In this research, the high spectral powers of the PCs are found in the low frequency bands, andthe red noise test requires higher spectral power to pass. Hence, only the red noise confidential intervalswill be shown. Pearson correlation was applied for investigating the atmospheric driving factors and theresponse of modeled tracers. Full details are in appendix B.3.4.5 Indices applied in the researchThe TDS intensity index is calculated as the mean horizontal speed above 130 m in an area from thecentral Arctic to the Fram Strait. The Beaufort Gyre intensity index is estimated as the sea surface heightmaximum in the Beaufort Gyre (figure 3.7).By applying an EOF decomposition to the CGRF sea level pressure in 20◦N-90◦N, the first threemodes can be identified as AO, dipole anomaly and NAO (see appendix D). Among which the dipoleanomaly is a newly detected atmospheric teleconnection pattern [Wu et al., 2006]. The positive phase ofthe dipole anomaly has positive sea level pressure anomaly in the Canada Basin and CAA and negativesea level pressure anomaly on the Eurasian side of the Arctic with strong meridional wind in the TDSregion [Watanabe et al., 2006, Wu et al., 2006]. In this research, the impact of dipole anomaly onthe surface ocean is quantified by the TDS intensity index. For the rest of modes, the PC of the firstmode was applied as the AO index and the PC of the third mode was used as the NAO index. The AOand NAO indices from National Oceanic and Atmospheric Administration (NOAA)-Climate PredictionCenter (CPC) [CPC-NOAA, 2016] were also used as they have longer time span. The CGRF andNOAA-CPC indices are both normalized and significantly correlated (AO indices: R= 0.86, p< 0.01;NAO indices: R= 0.37, p< 0.01). More details can be found in appendix D.3.4.6 Linear mixing modelThe term “Linear mixing model” means the reverse calculation of the mixing of different end-members.It works well for estimating different freshwater components in the Arctic. The linear mixing model21Figure 3.7: The 2002-2013 mean ANHA4-EXH005 velocities above 130 m and regions that definethe TDS intensity (orange) and the Beaufort Gyre intensity (cyan) indices.is used to calculate the fraction of North American and Eurasian runoff in the Beaufort Gyre. In thisresearch, we focused on real ocean tracers, not passive tracers to identify single rivers. Similar toobservations, the origin of the freshwater can be estimated through a linear mixing model. Tracersavailable for the linear mixing model include salinity, dissolved Barium and Oxygen isotope ratio.fNASNABaNAδ 18ONA1.0+ fEUSEUBaEUδ 18OEU1.0+ fiSiBaiδ 18Oi1.0+ foSoBaoδ 18Oo1.0=SBadδ 18O1.0 (3.13)Here the subscript “NA”, “EU”, “i” and “o” means North American runoff, Eurasian runoff, Sea-icemelt water and Ocean water. f is the fraction of each component, the sum of all the fractions shouldbe 1.0, and except fi, other fractions cannot be negative. The top-three elements in all matrixes inequation (3.13) are the chosen end-member values.22Table 3.3: Tracer end-member settings in Beaufort SeaTracer North American runoff Eurasian runoff Sea-ice melt OceanSalinity 0.0 0.0 0-0.4 32.0-34.8Bad [nM] 371.08* 101.67* 0.0* 59.2δ 18O [‰] -19.76* -19.61* 1.5* 0.0Symbol “*” means the end-member value is prescribed in the tracer scheme.The linear mixing model is used in the Beaufort Gyre to analyze the fraction of Eurasian and NorthAmerican runoff. Given the location, the dissolved Barium and Oxygen isotope ratio end-membersof North American runoff are the flow weighted annual mean estimates for the Mackenzie river. Thetracer end-members of Eurasian runoff are the mean input of Kolyma and Lena as these two rivers arethe big Eurasian rivers that are close to the Beaufort Sea and thus their runoff dominates any Eurasianrunoff that is transported into the Beaufort Gyre (e.g. in the simulation study of [Jahn et al., 2010],it takes about six years for East Siberian Sea runoff to reach the western side of CAA). These valueswere calculated during the parameterization stage and prescribed in the tracer scheme (section 3.2). Thesea-ice melt Oxygen isotope ratio end-member value 1.5‰ is consistent with that used in the tracermodel. The dissolved Barium end-member value in the ocean is the grid weighted average of the initialfield above 130 m. This is close to the observation based end-member set in Taylor et al. [2003] whichis 57.0 nM. We assume the ocean end-member value of Oxygen isotope ratio is 0.0‰ as defined byVienna Standard Mean Ocean Water (VSMOW) (table 3.3).Note that, sea-ice melt and ocean salinity end-members have ranges, the former is because of thediverse choice by different research, and the latter is because the three tracers in this research cannotseparate the Pacific Ocean water from Atlantic Ocean water, so the “ocean” component is considered tohave variations and can represent both the Atlantic and Pacific water mass.23Chapter 4Results4.1 Climatology and seasonal cyclesThe Arctic ocean dissolved Barium and Oxygen isotope ratio were simulated for the period of 2002-2013 using forcing from the atmosphere, ocean and Arctic rivers. This section will consider the tempo-rally averaged results of the two tracers and their seasonal cycle. Together, the climatology and seasonalcycles can explain most of the tracer distribution and provide spatial and temporal insights into the twotracers.4.1.1 Dissolved BariumThe climatological state of dissolved Barium concentration above 130 m (figure 4.1, a) varies from40 nM to 90 nM; in river estuaries, the value can be higher than 100 nM. The North American side ofthe Arctic, including the Canada Basin, part of the Chukchi Sea and the Alpha - Mendeleyev Ridge, hashigh dissolved Barium concentration which reflects the contribution of high Barium concentration riverslike the Mackenzie River. The dissolved Barium concentration is relatively low in the Barents Sea, theKara Sea and the Nansen Basin, because The West Spitsbergen Current and Norwegian Currents bringlow dissolved Barium water into the Arctic. Similarly, West Greenland Current transports the lowdissolved Barium concentration water across the Davis Strait and the dissolved Barium value in BaffinBay is therefore low. Dissolved Barium concentration is higher in the Beaufort Sea than in the LincolnSea and the northern part of the CAA due to the larger input of Barium from the Mackenzie Riverthan from the lower Barium concentration and lower flux from the CAA rivers. The dissolved Bariumconcentration is high in the coastal parts of the East Siberian and Laptev Seas; this is a combined effectof shallow water and river input. Indeed, the volume of the shallow (< 30 m) coastal regions is smalland easily flushed by the discharge from the Lena and other high Barium concentration Eurasian rivers.The shallow topography also makes the East Siberian Sea and Laptev Sea water easily modified andtherefore these regions have high variabilitiesThe timeseries of dissolved Barium (figure 4.1, c) has been averaged horizontally over the wholemodel domain and vertically from the surface to 130 m depth. The dissolved Barium value fluctuates24Figure 4.1: Simulated 2002-2013 climatology state of dissolved Barium above 130 m. (a) is theannual mean state. (b) is the difference between the mean state in May and (a). (c) is thedomain-wide mean dissolved Barium monthly mean timeseries. (d) is the seasonal cycle of(c).by 1 nM about the climatological state of 59 nM. The peak of the seasonal cycle of the domain-widemean dissolved Barium appears in May, and the trough happens in September (d). This peak-to-troughpattern is the effect of both the riverine tracer input and the sea-ice freeze-thaw cycle. In the late springand early summer, the spring freshet significantly increases the river discharge and brings more Bariuminto the domain. Then during the July-September period, the dilution effect due to the sea-ice meltplus the decrease of both riverine Barium input (section 3.1) and river discharge make the domain-widedissolved Barium reach its minimum. After that, from November to April of the next year, riverineBarium input is relatively low and stable, but the increase of sea-ice formation, increases the salinityand also the dissolved Barium concentration.The positive difference between May and the annual mean dissolved Barium in Arctic river estuariesclearly shows the contribution of riverine dissolved Barium during the spring freshet period (figure 4.1,b) and is consistent with the seasonal cycle result in (figure 4.1, d). The small negative differenceoffshore during May is due to the sea-ice freeze-thaw cycle. In May, the Arctic is in the early part of the25thaw.Figure 4.2: Simulated dissolved Barium fluxes through different pathways (a) and their seasonalcycles (b). Negative in (a) means out flux and the black line is the net result. (c) and (d) aresimulated riverine dissolved Barium input and its seasonal cycle. (d) shows the time rangeof 2002-2008, and the 2007-2008 pattern was repeated in the 2009-2013 period. (e) is theriverine dissolved Barium input minus the net in/out flux. (f) is the seasonal cycle of (e).The calculation of (a-d) is based on equation (3.11) and equation (3.12). Rivers input on thesouthern part of transects (figure 3.5) is small and not considered.The timeseries of dissolved Barium fluxes through the transects in Bering Strait, Fram Strait, BaffinBay and Barents Sea (figure 4.2, a) was calculated and summed from surface to bottom. Fram Strait andBaffin Bay dissolved Barium fluxes are negative which reflect the dissolved Barium out flux driven bythe TDS and the Labrador Sea Current, respectively. Meanwhile Bering Strait and Barents Sea dissolvedBarium fluxes are positive due to net inflows. The net flux is negative, and reveals that, more dissolvedBarium goes out of the Arctic Ocean than comes in. The total in-out and net dissolved Barium fluxesdo not have a strong seasonality (figure 4.2, b).The riverine dissolved Barium input (figure 4.2, c) and seasonal cycle (d) were calculated andsummed over regions (figure 3.2). From November to April, the dissolved Barium delivered from therivers is low and stable, then it quickly reaches a peak in June after the spring freshet and graduallydecreases from July to October. The high dissolved Barium input in the Beaufort Sea shows the impactof the high dissolved Barium end-member value in the Mackenzie River. The high input in the LaptevSea reflects the role of high discharge Eurasian rivers like the Lena. Also note that, the peak of riverineBarium input is in June, but the peak of domain-wide averaged dissolved Barium is May. This shift is26because the sea-ice melt water dilutes the surface dissolved Barium in June and makes the model valuelower.Considering the Barium budget of the Arctic as a whole, the total amount of riverine dissolvedBarium input is roughly balanced by the net dissolved Barium out flux during the simulation (figure 4.2,e-f). The balance explains the stable dissolved Barium results (figure 4.1) and shows that the model hasreached equilibrium state after its 24-year spin-up. The contrast between the strong seasonality in theriver input and the weak seasonality in the net Barium fluxes results in the seasonal cycle of dissolvedBarium in the Arctic ocean. The weak seasonality that is seen in the net Barium export is primarily dueto changes in water flux through the Straits, not in Barium concentration changes.Table 4.1: Total annual riverine dissolved Barium input in this research and the estimate fromGuay and Falkner [1998]Mackenzie Ob Yenisey Lena PechoraThis research1.5×108mol 4.3×107mol 7.6×107mol 6.1×107mol 1.6×107molGuay and Falkner [1998]1.6×108mol 6.8×107mol 7.8×107mol 4.0×107mol 1.3×107molPrevious observation based estimate of Barium input from Arctic rivers are available Guay andFalkner [1998] for comparison (table 4.1). The model simulation results are similar with larger outputfrom the Lena River and smaller output from the Ob River. Overall the model results are 4% lowermainly due to a 7% lower value for the Mackenzie River.4.1.2 Oxygen isotope ratioThe surface climatology of Oxygen isotope ratio (figure 4.3, a) varies from −5‰ to 0.5‰. In the riverestuaries, especially along the coast of the East Siberian and the Laptev Seas, Oxygen isotope ratioslower than −10‰ are simulated which reflects the effect of the Eurasian river runoff. The Oxygenisotope ratio in the Greenland Sea, the Barents Sea and the Kara Sea is the highest in the Arctic oceanwhich shows the contribution of high salinity, high Oxygen isotope ratio water from the North Atlantic.In the Makarov Basin, the Amundsen Basin and Fram Strait, the Oxygen isotope ratio value is about−3.0‰, lower than the North American side of the Arctic; these low values occur because these regionsare in the pathway of the TDS which brings Eurasian runoff into Fram Strait. In Bering Strait and theChukchi Sea, the high Oxygen isotope ratio reflects the existence of the Pacific inflow.On an Oxygen isotope ratio versus sea surface salinity plot (figure 4.3, b), most of the results arelocated in two regions. One can be characterized as a practical salinity range of 34 to 35 and δ 18Orange of 0.5‰ to −0.5‰. The other one is centered at a salinity of 30 and δ 18O of −3.0‰. These tworegions represent the Greenland Sea, Barents Sea and Kara Sea water and the Alpha-Mendeleyev Ridgeand Makarov Basin Arctic water, respectively (figure 4.3, a). Results with high δ 18O and low salinityare related to the sea-ice melt water. The low salinity low δ 18O “tails” are ocean water that has mixedwith meteoric water which has very low δ 18O end-members.27Figure 4.3: Simulated 2002-2013 climatology state of Oxygen isotope ratio at the surface (1.05m) (a) is the annual mean. (b) is the histogram between the mean surface Oxygen isotoperatio and the sea surface salinity. The shade shows the number of points in each hist bin, theblack box indicates the sea-ice melt water. (c) is the Oxygen isotope ratio timeseries that hasbeen averaged in the hatched region. (d) is the seasonal cycle of (c). (e) is the domain-widemean surface Oxygen isotope ratio. (f) is the seasonal cycle of (e).The timeseries of Oxygen isotope ratio was averaged horizontally over the region which has 2002-2013 September mean Sea-ice cover larger than 70% (figure 4.3, c). Since September is the sea-iceminimum, sea-ice cover in this month represents the semi-permanent sea-ice covered region. Underthe permanent sea-ice, the averaged Oxygen isotope ratio fluctuates by 0.2‰ on a climatological valueof −2.0‰. The seasonal cycle shows that Oxygen isotope ratio is relatively low and stable during thesea-ice formation period from November to March, and rapidly increases during the summer reaching28its maximum in August. Since sea-ice melt in the tracer model has a higher Oxygen isotope ratio end-member value than meteoric water and Arctic ocean water, the seasonal cycle reflects the impact ofsea-ice formation and melt.The domain-wide mean Oxygen isotope ratio has a larger uncertainty in its seasonality (red shadesin figure 4.3, e-f), and the mean state of the domain-wide result is about −2.7‰, lower than the valueunder permanent ice. The domain-wide average shows the combined effect of sea-ice variability andmeteoric water, especially river runoff. Specifically, during April to June, the spring freshet increasesthe meteoric water input from Arctic rivers which lowers the Oxygen isotope ratio, but the rising temper-ature means more sea-ice to melt which increases the Oxygen isotope ratio. During November-March,the decreased river discharge which increases the Oxygen isotope ratio, opposes the sea-ice formationwhich decreases the Oxygen-18 by fractionation. Therefore, throughout the year, river input and sea-icemelt-formation always counter-act. So when they were both summed up in the (e) timeseries, moresmall scale perturbations can be found.4.2 Data model comparisons4.2.1 Dissolved BariumTable 4.2: Mean bias and NRSMD of dissolved Barium comparisonsDepth BGEP CBL32PZ NPEO ARK-XXII/2 HLY0301Mean bias [nM]0-20 m 2.92 5.82 4.25 5.01 1.9320-60 m 4.00 4.42 9.38 5.05 1.9360-130 m -2.48 -5.10 9.34 3.66 4.342-4 km -6.73 -5.77 - -4.87 -44.01NRMSD [%]0-20 m 8.71 25.12 6.51 14.55 34.9420-60 m 14.79 28.55 25.11 25.29 32.8760-130 m 12.26 20.78 29.49 24.72 26.962-4 km 47.95 - - - -Dissolved Barium samples from BGEP (the Beaufort Sea), CBL32PZ (the Chukchi Sea), NPEO(the central Arctic), ARK-XXII/2 (the Nansen Basin and Laptev Sea coast) and HLY0301 (The NareStrait and Baffin Bay) are compared with the model output and in general show a good agreement ontheir minimum and maximum ranges (figure 4.4, a-e and h). Both the data and the model output in theBeaufort Sea have the highest mean profiles with strong variations. The BGEP and the CBL32PZ com-parisons have the highest overestimation (positive mean bias) in 20-60 m and show an underestimationat 60-130 m and 2-4 km (table 4.2). The NPEO and ARK-XXII/2 comparisons have an overestimationof 4−9 nM above 130 m and the ARK-XXII/2 comparison show an underestimation of 4.87 nM at 2-4km. NPEO observations were only taken down to 400 m, so there is no information in the deep ocean.29Figure 4.4: The model output of dissolved Barium comparing with BGEP 2003-2005 (a),CBL32PZ 2002 (b), NPEO 2004-2008 and 2013 (c), ARK-XXII/2 2007 (d) and HLY03012003 (e) observations. (f) is the timeseries comparison of BGEP data. (g) is the timeseriescomparison of NPEO data. (h) shows the locations of all samples. Two red circles are theregions that calculate the model mean, minimum and maximum in (f) and (g).The HLY0301 comparison has an overestimation on the surface ocean and the mean bias above 60 m isthe lowest. In the deep ocean, a strong underestimation can be seen (figure 4.4, e) with the mean bias of44 nM (table 4.2).Both the data and model output in the Beaufort Sea have low temporal variation from 2003 to2005. The comparison of the two is in general good with a slight overestimation of 4 nM in 2003 mean(figure 4.4, f). The timeseries comparison of NPEO data in the central Arctic is good in 2004 and2005 but overestimation can be seen in 2006-2008 and 2013 with the highest bias of 16 nM in 2013(figure 4.4, g).4.2.2 Oxygen isotope ratioOxygen isotope ratio results were compared with BGEP (the Beaufort Sea), CBL32PZ (the ChukchiSea), NPEO (the central Arctic) and HLY0301 (the Nare Strait and Baffin Bay) and in general show30Figure 4.5: Same as figure 4.4 but for Oxygen isotope ratio and without ARK-XXII/2 data.Table 4.3: Mean bias and NRSMD of Oxygen isotope ratio comparisonsDepth BGEP CBL32PZ NPEO HLY0301Mean bias [‰]0-20 m 1.11 0.51 0.88 0.4120-60 m 1.12 0.09 0.47 0.2960-130 m 0.35 0.14 -0.25 0.082-4 km -0.043 -0.079 - 0.06NRMSD [%]0-20 m 27.57 28.69 15.01 25.5820-60 m 11.88 19.22 20.30 21.8560-130 m 6.14 16.69 28.64 8.642-4 km 3.62 - - -good agreement (figure 4.5, a-d and g). In the depth range of 0-60 m, an overestimation can be seenin the BGEP comparison with the mean bias of −1.1‰ (table 4.3). The overestimation decreases withincreasing depth and shows little impact below 60 m. The comparison in the Chukchi Sea has relativelylow model bias; the minimum and maximum of the model output and CBL32PZ data are well matched.31The NPEO data in the central Arctic varies from −4.5‰ to 0.5‰. This high variation is well capturedby the model output. The comparison in Baffin Bay with HLY0301 samples shows an overestimationsimilar to the comparison in the Beaufort Sea but with lower bias. In the deep ocean. The model doesbetter in the 2-4 km deep ocean than at the surface.The overestimation of about −1.0‰ at the surface of the Beaufort Sea was found in 2003-2005 inthe timeseries comparison (figure 4.5, e), consistent with the overestimation above 60 m in (a). Thetimeseries comparison of NPEO data in the central Arctic is good, with the model output well capturesthe observed low values in 2005-2006 and high values in 2006-2007 (figure 4.5, f). By comparing withfigure 4.4, f, the model simulates Oxygen isotope ratio better in the central Arctic.4.3 Linear trends of tracers and Arctic freshwaterThe FWC shows a trend over the modeled 12 years. A linear trend was fit to the data (figure 4.6); allother variability is captured in the EOF analysis performed next. The FWC linear trend (figure 4.6,a) is positive in the Beaufort Sea, the East Greenland Sea and the CAA but negative in the MakarovBasin and part of the East Siberian Sea. This contrast between the North American side and Eurasianside of the Arctic is consistent with observed rate of change from 2005 to 2008 [Morison et al., 2012].The sea surface height (figure 4.6, b) decreases with the FWC. In the Makarov Basin, the negative seasurface height trend and cyclonic surface velocity trend show that Makarov Basin is continuously losingits surface water. In the Canada Basin, East Greenland Sea and CAA, the velocity trend indicates thatthe eastern side of the Beaufort Gyre and the TDS are intensifying, and simultaneously we can see thatthe CAA - Baffin Bay transport is weakening as the trend velocity (figure 4.6, a) is out of the CAAand Baffin Bay, against the mean velocity (figure A.2). Dissolved Barium is decreasing in the MakarovBasin (figure 4.6, c), consistent with the decreases of FWC and the sea surface height.Since dissolved Barium is a tracer of river runoff, decreasing Barium means that the accumulationof Eurasian runoff in Makarov Basin seen in the mean state (figure 4.1, figure A.2) is decreasing. Onthe North American side of the Arctic, the dissolved Barium is increasing in the eastern Beaufort Sea,Lincoln and East Greenland Seas showing the increased accumulation of runoff water compared to themean state (figure 4.1, figure A.2). This runoff accumulation is consistent with the intensified BeaufortGyre and TDS as well as with the FWC increases (figure 4.6). In the CAA, the decreasing Barium butincreasing FWC and sea surface imply an accumulation of low dissolved Barium concentration runoffwhich would come from local CAA river runoff rather than Beaufort Sea originated runoff. Also notethat, the positive dissolved Barium trends on the North American side of the Arctic have a larger spatialfootprint than the positive trends of FWC. This difference could be related with the shift of Eurasianrunoff pathways to the Beaufort Sea due to the cyclonic circulation [Morison et al., 2012] and hencebrings more dissolved Barium than usual.The linear trend of Oxygen isotope ratio is positive in the Makarov Basin, the Laptev Sea, CAA andnegative in the East Siberian Sea and Greenland Sea. These patterns are consistent in the opposite signwith dissolved Barium trends and show the decrease and increase of river runoff compared to the mean.In addition to the linear trends of ANHA4 forcing variables and simulated tracers, a steady increase32Figure 4.6: The linear trends of FWC (a), sea surface height and ocean velocities (b), dissolvedBarium (c) and Oxygen isotope ratio (d). All variables except sea surface height were aver-aged from 0 to 130 m depth. Dotted regions have trends that have passed a two-sided t-test.Negative/positive sea surface height in (b) delineates regions of cyclonic/anti-cyclonic sur-face geostrophic flow. The velocity trends shown imply that the eastern side of the BeaufortGyre and the TDS are intensifying.of October to next year May AO (winter-spring AO) was found (figure 4.7). From 1950 to 2015, thewinter-spring averaged NOAA-CPC AO index shows a steady increase with the slope of 0.009 per year.The CGRF winter-spring averaged AO index from 2002 to 2013 was calculated from CGRF sea levelpressure forcing used in the physical model and it agrees with the NOAA-CPC index (see appendix D).As the AO increases, cyclonic wind stress increases in the East Siberian Sea and Laptev Sea; thiscauses Ekman divergence which diverges and thus thins the sea-ice. This thinning plays a role on alonger time scale due to the “memory” of sea-ice [Rigor et al., 2002]. Therefore, the linear increaseof AO during the simulation period is thought to be the driving factor for the simulated linear trends331950 1960 1970 1980 1990 2000 20101.51.00.50.00.51.01.5AO indexR-square = 0.098t-test p = 0.010Slope = 0.0097Trend of Oct-May mean AO indexNOAA-CPCCGRF SLP foringTrendModel time rangeFigure 4.7: The October to next year May averaged AO indices and the linear trend from 1950 to2015. The orange line is the NOAA-CPC AO index, the brown solid line is the CGRF AOindex. The dark green solid line is the result of linear regression with the trend of 0.0097.The R-square is 0.098 and the trend passed 0.01 two-sided t-test.by producing the Ekman divergence and anomalous cyclonic ocean flow in the Makarov Basin, and theaccumulation of surface water in the Beaufort Sea and anticyclonic anomalous wind in the CAA - BaffinBay region.4.4 Tracer anomaly patterns and freshwater variability4.4.1 Mode I: Dipole anomalyThe EOF mode one of FWC (figure 4.8) accounts for 30.7% of the total variance. The spatial patternhas negative FWC anomalies on the northern side of New Siberian Island and in the coastal Laptev Sea,and positive anomalies located in the Beaufort Sea, CAA, the North American side of the central Arcticand extending southward into the East Greenland Sea. The PC of mode one steadily increased from2002 to 2008 and then decreased, and reaches its negative phase in 2011 winter. The temporal variationof mode one is correlated with the TDS intensity (r= 0.805, p< 0.02), the latter is calculated as themean 0-130 m ocean velocity in the hatched region in figure 4.8 (also see section 3.4.5). The spectralpower of the PC has a peak at the 1/12 cycle per year frequency band which indicates that mode onemay have decadal variabilities. According to the “rule of thumb”, mode one is well separated from itsneighbouring modes ([North et al., 1982], section 3.4.4).In order to determine the atmospheric driving factor of the FWC mode one, the composite anomalyof CGRF and ANHA4 forcing variables was calculated (figure 4.9). The composite anomaly of sealevel pressure shows a dipole structure with positive sea level pressure above the Canada Basin, CAAand South Greenland Sea and with negative sea level pressure above the Eurasian side of the Arctic andits marginal seas. The boundary between the two opposite signed anomalies is along a line through the342002 2004 2006 2008 2010 2012 201421012Norm. PCTDS IntensityNorm. PC0.2 0.4 0.6 0.8 1.0Freq. [cycle per year]02468Spectral power1e1Red noise 95% confidential intervalSpectral power of PC2.12.42.73.03.3TDS intensity1e 2120°WTDS positionMode I  [30.7%]R = 0.805p < 0.02-1.4-0.60.21.01.8FWC [m]Figure 4.8: The FWC EOF mode one spatial pattern (left), PC (top right green solid line) and thespectral energy of PC (bottom right). The gray line on the top right is the TDS intensityestimated by the mean horizontal speed of surface ocean currents in the hatched region (seesection 3.4.5). The red dashed line is the 95% red noise test confidential interval.Chukchi Sea - central Arctic - Fram Strait. This anomalous pattern has been previously named as theatmospheric dipole anomaly and is independent from other atmospheric teleconnections including AOand NAO [Watanabe et al., 2006, Wu et al., 2006] (see appendix D). During the positive phase of modeone, the dipole pattern in the sea level pressure causes strong meridional wind in the central Arctic,anticyclonic wind with negative wind stress curl in the Canada Basin and cyclonic wind with positivewind stress curl in the Eurasian Basins. Due to the generated surface Ekman flux, the sea surface heightdrops on the Eurasian side, and rises on the North American side of the Arctic. This sea surface heightanomaly pattern creates strong pressure gradients in the central Arctic and intensifies the TDS, whichexplains the high positive correlation between mode one PC and TDS intensity (figure 4.8). Therefore,considering the dipole structure of sea level pressure anomalies, the meridionality of the wind stress inthe central Arctic and the fact that 2007-2008 is the peak of the mode one PC and also a well studiedpositive dipole anomaly stage [Wang et al., 2009], we suggest the atmospheric dipole anomaly as thedriving factor of the mode one.During the positive phase of the dipole anomaly, the Eurasian oriented freshwater is transportedfurther northeast, freshening the central Arctic. The anomalous anticyclonic flow in the East SiberianSea causes the river runoff to accumulate. The strong TDS brings more freshwater southward to FramStrait and stretches the positive FWC anomaly pattern. The anomalous anticyclonic flow, as well asthe positive sea surface height in the CAA, blocks and slows down the CAA - Baffin Bay transport,but causes the local CAA runoff to accumulate due to Ekman convergence. Therefore the effect of lessBeaufort Sea runoff is compensated by the accumulation of CAA local runoff and no big FWC anomalycan be seen in the CAA.35Figure 4.9: The composite anomalies for mode one PC. Composite anomalies are difference be-tween high phase and low phase (section 3.4.4). sea level pressure, 10 m winds (a), windstress, wind stress curl (b), sea surface height, ocean velocities above 130 m (c) and E-P flux(d). Dotted regions have composite anomalies pass the 0.05 level t-test.The E−P composite anomaly is negative which indicates strong sea-ice melt on the northern sideof the Chukchi Sea and over most of the Eurasian side of the Arctic (figure 4.9, d). This anomaloussea-ice melt is consistent with previous studies, which found that the dipole anomaly enhances oceanicheat flux through Bering Strait and increases the summer sea-ice melt [Wang et al., 2009, Wu et al.,2006].In mode one, a strong positive anomaly for dissolved Barium shows in the central Arctic, and neg-ative anomalies in the Makarov Basin and CAA (figure 4.10, a). As dissolved Barium is a tracer ofrunoff water, the negative pattern in the Makarov Basin indicates a reduction in the transport of the EastSiberian Sea and Laptev Sea runoff as a response of the eastward anomalous flow along the Russiancoast and the anomalous flow from the Laptev Sea to the Makarov Basin (figure 4.10, c). The negative36Figure 4.10: The composite anomaly of dissolved Barium (a) and Oxygen isotope ratio (b) in modeone PC and averaged above 130 m. Hatched regions in (a-b) are shallower than 30 m. Dottedregions in (a-b) have composite anomaly pass the 0.05 level two-sample t-test. (c) is thesketch of anomalous flow pattern, both in the lower atmosphere (top plane) and the surfaceocean (lower plane). On the upper plane, the dipole anomaly with enhanced high pressureover the Beaufort Sea and enhanced low pressure over the Eurasian Side. Wind barbs showthe anomalous winds. On the lower plane, circles show the major anomalous currents; 1©and 2© transports the Eurasian runoff to the Makarov Basin; 3© is the anomalously strongTDS; 4© indicates the weak CAA - Baffin Bay transport and 5© is the intensified BeaufortGyre.37dissolved Barium anomaly in the CAA and the positive anomaly in the northern Canada Basin indicatesthat, due to the anomalous anticyclonic flow in the Beaufort Sea and the anomalous flow from CAAchannels to the Beaufort Shelf, Beaufort Sea runoff is trapped by the Beaufort Gyre instead of exitingthrough the CAA - Baffin Bay route. The positive dissolved Barium anomaly in the central Arctic fromthe Chukchi Sea to the Fram Strait shows the accumulation of runoff water in the strong transport bythe anomalously strong TDS.The composite anomaly for Oxygen isotope ratio shows a positive anomaly in the Laptev Sea,consistent with the negative dissolved Barium anomaly and shows the transport of runoff from theEurasian marginal seas to the Makarov Basin and the central Arctic. The negative Oxygen isotope ratioanomaly in the coastal East Siberian Sea, concentrated in shallow water, indicates the accumulationof East Siberian Sea runoff. In the Makarov Basin and further north, a negative Oxygen isotope ratioanomaly of less than −0.2‰ can be seen. This anomaly shows the appearance of Eurasian runoff in thecentral Arctic.Compared to the positive dissolved Barium composite anomaly in the central Arctic, the footprintof negative Oxygen isotope ratio anomaly is only about half the area, which indicates that, North Amer-ican river and Eurasian river inputs have about the same total amount input of Barium (see table 4.1).However for Oxygen isotope ratio, which has end-member values of about −20‰ for all Arctic rivers,the Eurasian rivers, which have higher discharge, have a larger impact. This difference also explains thecontrast between the positive FWC anomaly and the negative dissolved Barium composite anomaly inthe East Greenland Sea. The Oxygen isotope ratio anomaly in the East Greenland Sea is negative, whichimplies the accumulation of meteoric water (figure 4.10, b). However, the negative dissolved Bariumanomaly in the same region implies this meteoric water is not typical, high Barium concentration NorthAmerican runoff but is more likely to be Eurasian runoff or low dissolved Barium concentration CAArunoff.4.4.2 Mode II: The interannual effect of NAOThe FWC EOF mode two (figure 4.11) accounts for 14.0% of the total variance. The spatial patternshows negative FWC anomalies in the East Siberian Sea, on the northern side of the Canada Basin andnear New Siberian Island, and positive FWC anomalies in the Chukchi Sea and over part of the MakarovBasin. The PC of mode two underwent a steady increase from 2002 to 2004, switched from the negativeto positive phase, then stabilized in the positive phase from 2004 to 2008. In 2008-2010, it went backto its negative phase and then had a steady increase from 2010 to 2013. The temporal variation of themode two PC has a good positive correlation with the 1-year moving average NOAA-CPC NAO index(r= 0.378, p< 0.1) and with the 1-year moving average NAO index calculated from the CGRF sealevel pressure forcing (r= 0.495, p< 0.05, appendix D). The spectral power of the PC has peaks at the1/12 and 1/8 cycle per year frequency bands. Mode two is well separated from its neighbouring modesby the “rule of thumb” ([North et al., 1982], section 3.4.4).The composite anomaly of sea level pressure has a negative anomaly over the Baffin Bay and theGreenland and Nordic Seas. The negative anomaly is surrounded by two positive anomalies, one located382002 2004 2006 2008 2010 2012 201421012Norm. PCNOAA-CPC NAOCGRF NAONorm. PC0.2 0.4 0.6 0.8 1.0Freq. [cycle per year]0.01.53.04.5Spectral power1e1Red noise 95% confidential intervalSpectral power of PC1.00.50.00.51.0NAO index120°WMode II  [14.0%]RNOAA = 0.378; p < 0.1RCGRF = 0.495; p < 0.05-1.05-0.450.150.751.35FWC [m]Figure 4.11: The FWC EOF mode two spatial pattern (left), PC (top right green solid line) and thespectral energy of PC (bottom right). On the top right plot, the gray dashed line and graysolid line are the 1-year moving averaged NOAA-CPC NAO and CGRF NAO indices (seesection 3.4.5). The red dashed line is the 95% red noise test confidential interval.over the North Atlantic Ocean and the other one located over the North Pacific Ocean. The compositeanomaly of mode two sea level pressure is similar to the NAO pattern [Hurrell, 1995].The composite anomaly of near surface wind stress curl shows a positive anomaly in the East Green-land Sea, Nansen Basin and Canada Basin during the positive phase of mode two, consistent with thenegative sea level pressure. Anticyclonic wind and negative wind stress curl occurs on the Pacific sideof the Arctic including the Chukchi Sea and the East Siberian Sea. As a result, due to the surface Ek-man flow, the sea surface height is depressed in both the Canada Basin and Nansen Basin, and rises inthe Chukchi Sea and the Eurasia marginal seas as shown in the sea surface height composite anomaly(figure 4.12).Due to the spatial distribution of sea level pressure composite anomaly and the significant positivecorrelation between mode two PC and NAO indices, NAO is thought to be the atmospheric driver ofmode two. During the positive phase of the NAO, the cyclonic anomalous wind on the North Americanside of the Arctic spins-down the Beaufort Gyre and intensifies the CAA - Baffin Bay transport. Mean-while the anticyclonic anomalous winds on the Pacific side of the Arctic increase the surface FWC in theMakarov Basin. Also, the anomalous flow pattern along the Eurasian coast brings more East SiberianSea runoff to the eastern side of the Laptev Sea and then transports it further north, so the pathway ofEurasian marginal sea runoff is also changed. Different from mode one, mode two does not have a largeE−P composite anomaly, only a small sea-ice melt signal can be seen near the Eurasian coast.A positive dissolved Barium anomaly can be seen in the Chukchi Sea, the Makarov Basin, BaffinBay and the southern part of CAA. Strong negative anomalies are located in the East Greenland Sea,the northern side of the Beaufort Sea and the northwestern side of CAA. The contrast between the39Figure 4.12: Same as figure 4.9, but for mode twonegative dissolved Barium composite anomaly in the Beaufort Sea and the positive anomaly in CAA,especially in Lancaster Sound and Barrow Strait, indicates that the weakening of the Beaufort Gyreduring the mode two positive phase encourages more North American runoff to go the CAA - BaffinBay route which is a reverse of the mode one positive phase (figure 4.10). The positive dissolved Bariumcomposite anomaly in Makarov Basin reveals the transport and accumulation of Eurasian runoff water(figure 4.13).The composite anomaly of Oxygen isotope ratio mainly shows the change of meteoric water, es-pecially Eurasian runoff, since mode two does not have significant impact on the sea-ice variability. Astrong positive anomaly in the East Siberian Sea, and a negative anomaly in the coastal Laptev Sea canbe seen. Both are consistent with the dissolved Barium composite anomalies and show the transport ofEurasian marginal seas runoff. Meanwhile, from the Laptev Sea to Fram Strait, the negative Oxygenisotope ratio anomaly which is characterized by the−0.2‰ isoline, shows the accumulation of Eurasianrunoff in the Makarov Basin and the change of its pathway to the Fram Strait (figure 4.12).40Figure 4.13: Same as figure 4.10, but for mode two. (c) is the sketch of anomalous flow pattern.In the the lower atmosphere (top plane), the NAO-like anomaly with positive pressure overthe North Atlantic and enhanced low pressure over the central Arctic/Nansen Basin. In thesurface ocean (lower plane), circles show the major anomalous currents; 1© and 2© are theintensified CAA - Baffin Bay transport with a weak Beaufort Gyre; 3© is the transport ofLaptev Sea runoff; 4© is the accumulation of runoff water in the Makarov Basin.4.4.3 Mode III: The Beaufort Sea highThe FWC EOF mode three (figure 4.14) accounts for 7.8% of the total variance. The spatial patternshows negative FWC anomalies in the Beaufort Sea and along the East Siberian Sea coast, and positiveFWC anomalies in the Canada Basin and the Makarov Basin. Comparing to modes one and two, the412002 2004 2006 2008 2010 2012 201421012Norm. PCBG IntensityNorm. PC0.2 0.4 0.6 0.8 1.0Freq. [cycle per year]0.00.81.62.43.24.0Spectral power1e1Red noise 95% confidential intervalSpectral power of PC4.03.53.02.52.0TDS intensity1e 1120°WBG positionMode III  [7.8%]R = 0.52p < 0.01-0.7-0.30.10.50.9Figure 4.14: The FWC EOF mode three spatial pattern (left), PC (top right green solid line) andthe spectral energy of PC (bottom right). The gray line on the top right plot is the Beau-fort Gyre intensity estimated as the maximum sea surface height in the Beaufort Sea (seesection 3.4.5). The red dashed line is the 95% red noise test confidential interval.magnitude of the mode three spatial pattern is relatively low, and about half of mode one’s. The differ-ence reflects the relative importance of these three modes. The PC of mode three has more short timefluctuations than the previous modes. In general it can be characterized by the peak from winter 2007 tospring-summer 2008 and troughs in winter 2004, fall-winter 2009 and spring 2013. The temporal varia-tion of mode three has a good positive correlation with the Beaufort Gyre intensity (r= 0.52, p< 0.01)which was estimated as the maximum sea surface height in the hatched region in figure 4.14 (also seesection 3.4.5). The spectral power of the mode three PC has a peak at 1/4 cycle per year frequency bandand has relatively higher spectral power in 1/2 cycle per year frequency bands than other the two modes.Mode three is well separated from its neighbouring modes by the “rule of thumb” ([North et al., 1982],section 3.4.4).The composite anomaly of sea level pressure has a large negative anomaly that covers almost the en-tire Arctic Ocean. Low anomaly centers locate at the Eurasian coast and the southern part of Greenland.In the Beaufort Sea, the negative sea level pressure composite anomaly is relatively weak. An anticy-clonic wind stress pattern can be seen in the Arctic, consistent with the sea level pressure anomalies.This anticyclonic wind pattern creates positive sea surface height in the Canada Basin and the MakarovBasin due to Ekman convergence, strongly intensifies the Beaufort Gyre, accumulates freshwater andtherefore is considered as the atmospheric driving factor for the FWC mode three. The E−P compositeanomaly shows a sea-ice melt signal in the Fram Strait and the Barents Sea, and a sea-ice formation sig-nal in the Beaufort Sea and along the East Siberian Sea coast. The latter is consistent with the negativeFWC anomaly pattern (figure 4.15).A strong positive dissolved Barium anomaly occurs in the Beaufort Sea, North American side of42Figure 4.15: Same as figure 4.9, but for mode threethe Arctic, the Lincoln Sea and along the East Greenland coast. Negative dissolved Barium compositeanomalies occur in the CAA and the Baffin Bay. On the Eurasian side of the Arctic, the dissolvedBarium composite anomaly is scattered with positive anomalies on the northern side of New SiberianIsland and negative anomalies in the Laptev Sea and over part of the Mendeleev Ridge. The positiveanomaly in the Beaufort Sea and the negative anomaly in the CAA shows the role of an extra strong andextended Beaufort Gyre, which stores extra runoff. This response is the same as mode one (figure 4.10)and the reverse of mode two (figure 4.13). On the Eurasian side, the positive dissolved Barium anomalyon the northern side of New Siberian Island shows the impact of the anticyclonic flow and the westwardanomalous flow along the East Siberian Sea coast, produced by the Ekman convergence. The compositeanomaly of Oxygen isotope ratio has a positive anomaly on the Eurasia coast, showing the role of sea-ice melt (figure 4.15). Meanwhile its negative anomaly on the northern side of the New Siberian Islandand the Kara Sea coast are consistent with the positive dissolved Barium anomaly in figure (figure 4.16,a) and reflect the accumulation of Eurasian runoff.43Figure 4.16: Same as figure 4.10, but for mode three. (c) is the sketch of anomalous flow pattern.In the the lower atmosphere (top plane), the enhanced low pressure over the North Atlanticand Eurasian side of the Arctic intensifies the Beaufort Gyre. In the surface ocean (lowerplane), circles show the major anomalous currents; 1© is the weak CAA - Baffin Bay trans-port; 2© and 3© are the anticyclonic flow in the Beaufort Sea and the northern side of NewSiberian Island; 4© is the transport of East Siberian Sea runoff.4.5 Application: A case study of Beaufort Gyre 2007-2008The Beaufort Gyre is the biggest freshwater reservoir in the Arctic Ocean [Proshutinsky et al., 2009]and plays an important role in regulating the Arctic climate [Proshutinsky et al., 2002]. According tomany studies, freshwater has accumulated in the past few decades in the Beaufort Gyre, and especially44in the 2007-2008 period. Hydrographical observations show that in March-April 2008, the BeaufortGyre FWC rapidly increased, compared with the 1970s and 1980s winter season climatology in thePolar Hydrographic Climatology (PHC) dataset [McPhee et al., 2009]. The FWC in Beaufort Sea andthe southern Canada Basin in 2006-2008 was higher than in 1992-1999 [Rabe et al., 2011]. The ArcticOcean Model Intercomparison Project (AOMIP) models applying the wind forcing of 2007, all showa similar accumulation of 14m-22m of FWC in the Beaufort Gyre [Proshutinsky et al., 2011]. Finally,at the end of 2008, the Arctic Ocean, predominately, the Canada Basin had gained four times morefreshwater water compared to the “Great Salinity Anomaly” period [Morison et al., 2012]. Differenttheories have been posed to explain the rapid change of freshwater, including the “Flywheel” theory[Proshutinsky et al., 2002], impacts of atmospheric factors like NAO [Condron et al., 2009] and AO[Morison et al., 2012, Zhang et al., 2003], changes in the Pacific Summer Water (PSW) [Jackson et al.,2011] and the sea-ice decline [McPhee et al., 1998].2002 2004 2006 2008 2010 2012 201442024Beaufort Gyre freshwater anomalydepth = 0 - 130m1e2 [volume, km3]Beaufort G. freshwater anomalyBeaufort G. intensity0.000.090.180.270.36Beaufort Gyre intensity [m]2007/07 - 2008/06Figure 4.17: The Beaufort Gyre freshwater anomaly above 130 m as volume (red, left axis) andthe Beaufort Gyre intensity (black, right axis, see section 3.4.5), the hatched region is thetime span of the case study.The increase of the Beaufort Gyre FWC in 2007-2008 is simulated by the ANHA4-EXH005 exper-iment (figure 4.17). From summer 2007 to 2008, a significant increase can be seen in both the BeaufortGyre intensity and its anomaly of freshwater volume above 130 m. The following section will diagnosethe increase of Beaufort Gyre FWC by CGRF and ANHA4-EXH005 forcing and the tracer simulation.This case study will provide an example of how the EOF based “idealized” FWC anomaly patterns insection 4.4 can be projected onto a given case, and how the simulated dissolved Barium and Oxygenisotope ratio can be used in the analysis of freshwater components.4.5.1 Evolution of the FWC anomalyThe evolution of the Beaufort Gyre FWC increase can be divided into three stages: a developing stage(summer 2007), a mature stage (winter 2007- spring 2008) and a vanishing stage (2008 summer), In thedeveloping stage, a dipole-like anomaly pattern is seen with a positive sea level pressure anomaly on45Figure 4.18: 2007 June-August mean sea level pressure and 10 m wind anomaly (a). August-October mean sea surface height, ocean velocities (b), FWC (c), E−P (d), dissolved Barium(e) and Oxygen isotope ratio (f) anomalies.46the North American side of the Arctic, which extends southward to the Greenland Sea and with anegative sea level pressure anomaly on the Eurasian side of the Arctic. Similar to FWC EOF mode one(section 4.4.1), the meridionality of the sea level pressure anomaly creates a strong meridional wind inthe central Arctic, and results in surface Ekman transport from Eurasian side to the North Americanside of the Arctic. This process is consistent with the positive sea surface height anomaly in the centralArctic, and the negative anomaly in the Makarov Basin (figure 4.18). Comparing to the mode one dipoleanomaly pattern, 2007 summer has a stronger North American side positive sea level pressure anomaly,but in general, the 2007 anomaly pattern provides the same cyclonic flow in the Makarov Basin and theEurasian runoff accumulation in the central Arctic. The dipole anomaly has an impact on the Arcticsummer sea-ice melt (section 4.4.1) and therefore negative E −P and positive Oxygen isotope ratioanomalies can be seen on the Eurasian side of the Arctic, this sea-ice melt signal also contributes to theincrease of FWC.Thus in the developing stage (2007 summer), the dipole anomaly driven accumulation of Eurasianrunoff water in the central Arctic is the most important process. The strong summer sea-ice melt alsocontributes to the FWC anomaly.In the mature stage (winter 2007 - spring 2008, figure 4.19), the Beaufort Gyre intensity reaches itspeak and so does the Beaufort Gyre FWC. A strong negative anomaly in sea surface pressure occurs overthe southern part of Greenland and on the Eurasian side of the Arctic, while in the Canada Basin, the sealevel pressure is slightly positive. This sea level pressure anomaly pattern is similar to the atmosphericdriving force in FWC mode three (section 4.4.3). An important feature of this pattern is the stronganticyclonic surface wind anomaly in the Canada Basin (figure 4.18 and compare figure 4.15). Underthe impact of this anomalous anticyclonic wind, the Ekman convergence raises the sea surface height,strongly intensifies the Beaufort Gyre and makes it extend further into the central Arctic. Since in thiscase the sea level pressure anomaly in Canada Basin is more positive than for the mode three case, sothe intensification of the Beaufort Gyre is stronger (figure 4.19).During the developing stage (2007 summer), Eurasian runoff water accumulated in the central Arcticdue to the dipole-like anomalies. Therefore, in the mature stage, when the Beaufort Gyre is intensifiedand extends into the central Arctic, its anticyclonic surface circulation and Ekman convergence movesthe accumulated Eurasian runoff to the Canada Basin. Indeed a “tail” can be found on the North Amer-ican side of the positive FWC anomaly, which indicates the effect of Eurasian runoff transport. Thepositive dissolved Barium anomaly in the Canada basin grows stronger (figure 4.19).During the mature stage (winter 2007 - spring 2008), the anticyclonic anomalous wind in the CanadaBasin intensifies the Beaufort Gyre, makes it extend into the central Arctic where it entrains the pre-exiting pool of Eurasian runoff. Therefore, both the FWC and Beaufort Gyre sea surface height reachtheir maximums.The increase of the Beaufort Gyre FWC from 2007 to 2008 has two major contributors: the existenceof accumulated Eurasian runoff in the central Arctic and a strong Beaufort Gyre. Thus, when either ofthese two factors are undermined, the situation will become less suitable for the increase of BeaufortGyre FWC, and it starts to vanish (summer 2008). The magnitude of sea level pressure anomaly during47Figure 4.19: Same as figure 4.18, but for December-February mean, no E−P and δ 18O anomalies.the vanishing stage is lower than the developing and mature stages (figure 4.20), which means that thesea level pressure in the vanishing stage approaches climatology. In the Canada Basin, a negative sealevel pressure anomaly with cyclonic anomalous wind occurred, which indicates that, in the vanishingstage, the atmospheric forcing does not support the growth of the Beaufort Gyre. As a response, thepositive sea surface height anomaly in the Canada Basin becomes weaker. During the vanishing stage,a negative sea surface height anomaly can already be seen in the eastern side of the Beaufort Gyre. Thepositive FWC anomaly which was in the central Arctic during the mature stage has been transportedfurther south toward Fram Strait. The “tail” from the FWC positive anomaly center to the Beaufort Seacan still be seen, but in time, this bulk of Eurasian runoff leaves the control of the Beaufort Gyre. Anegative dissolved Barium anomaly can be seen on the eastern side of the Beaufort Gyre, indicating thelack of river runoff.During the vanishing stage (summer 2008), the atmospheric state is not suitable for the intensifica-48Figure 4.20: Same as figure 4.18, but for 2008 and no E−P and δ 18O anomalies.tion of the Beaufort Gyre, so the Beaufort Gyre spins-down and on longer able to hold a large amount offreshwater. The accumulated Eurasian runoff in the central Arctic is gradually transported further southaway from the control of the surface circulation of the Beaufort Gyre.The case study in this section considers both the Ekman transport and the Eurasian runoff, unlikeprevious studies that considered one or the other [Morison et al., 2012, Proshutinsky et al., 2009]. Previ-ous research stressed the role of the AO [Morison et al., 2012] but in this study we have seen the role ofthe dipole anomaly on the transport of Eurasian runoff. The variability of Beaufort Gyre FWC is the netresult of different atmospheric processes. For this case, the dipole anomaly and anticyclonic anomalouswind in the Canada Basin both play important roles.494.5.2 Linear mixing modelAs discussed above, the increase of Beaufort Gyre FWC in 2007-2008 is due to the increased transportof Eurasian runoff. Based on observations in 2007 and 2008, Alkire et al. [2010] found that Eurasianrunoff and Pacific inflow both have a significant contribution to the meteoric water pool in the southernpart of Canada Basin in the cold halocline. Also, Brown et al. [2014] found a predominance of Eurasianriver source on the particulate organic Carbon in the Canada Basin. So it is no surprise to see Eurasianrunoff in the Beaufort Gyre.Considering that one of the simulated tracers in this research, dissolved Barium is able to separateNorth American runoff from Eurasian runoff [Guay and Falkner, 1997, 1998], a linear mixing model isapplied to estimate the amount and temporal variations of Eurasian and North American runoff fractions.The theory and end-member choices of the linear mixing model was described in section 3.4.6.2002 2004 2006 2008 2010 2012 201402468Fraction [%] Eurasian runoffNorth American runoffEurasian runoff min/maxNorth American runoff min/max2007/07 - 2008/06depth = 0 - 130mFigure 4.21: The timeseries of Eurasian (red) and North American (black) runoff fractions in theBeaufort Gyre (as defined in figure 3.7) from 0-130 m depth. The shade is the variationrange. The time span of the case study is hatched.According to the linear mixing model results, the North American runoff fraction varies 1% to3% and reaches its peak in early summer, consistent with the seasonal cycle of riverine water input(figure 4.21). The Eurasian runoff fraction varies from 6% to 9%. It is higher than the North Americanrunoff fraction, reflecting the high discharge of Eurasian rivers. The temporal variability of the Eurasianrunoff fraction in Beaufort Sea is opposite the North American runoff and has a minimum each year inthe late spring, early summer. The reason for the time lag can be explained by the time for transport ofrunoff water from the Eurasian marginal seas to the Beaufort Sea.The range of possible values for the runoff fractions is about 1%. The lower bounds for both runofffractions come from the lower salinity end-member; the range of sea-ice melt salinity end-member doesnot have a significant impact on the linear mixing model results. During the 2007-2008 period, espe-50cially during the mature stage of the 2007-2008 event, the Eurasian runoff fraction reaches its maximumwhich shows the increase of Eurasian runoff in the Beaufort Gyre, consistent with the conclusion forthe case evolution study above. Also the fact that Beaufort Sea has a positive Eurasian runoff fractionsupports the findings of Alkire et al. [2010].51Chapter 5Discussion5.1 Model configuration and operationsIn this research, the tracer simulation was done offline using oceanographic variables from the ANHA4-EXH005 experiment. The choice to run offline is possible because dissolved Barium and Oxygen iso-tope ratio have no effect on the physical state of the ocean, or in other words, they are passive tracersand no tracer - physical ocean interaction needs to be modeled. Technically, since the ANHA4 exper-iments were run by another research team, the choice of offline simulation significantly reduced therequired computational resources. The offline simulation means the tracers behave as a direct responseto the ANHA4 forcing. Since the ANHA4 experiments have CGRF atmospheric forcing, the simulatedtracer values were also indirectly affected by the CGRF atmosphere. Therefore, the overall simulationframework of this research is: CGRF atmosphere drives ANHA4 ocean, which drives the tracers. BothMY TRC and ANHA4 need to be forced with river discharge. In this research, the choice of river dis-charge is consistent between the ANAH4 experiments and the tracer model. Thus there are no conflictsbetween the ANHA4 riverine freshwater input and MY TRC tracer input.5.2 Tracer parameterizations, model output and evaluations5.2.1 dissolved BariumThe dissolved Barium scheme in this research defined twenty different estuaries since riverine dissolvedBarium input only depends on the river borne clay types in the drainage basin which is a very localizedfeature. A coarse river estuary classification in a fine model grid may result in unrealistic tracer patterns.The classified regions also makes the model able to consider the spatial distribution of estuaries as anarea source instead of point source. This is important for simulating rivers with big estuaries, using anarea source makes sure that the estuarine tracer gradient will be consistent with the estuarine salinitygradient.For the reconstructions of the seasonality of riverine dissolved Barium input, the biggest assumptionis the “Normalized ensemble seasonal cycle” calculation which characterized the similarity of the sea-52sonal cycle normalized by the mean dissolved Barium concentration and provided reasonable estimatesfor dissolved Barium values in poorly observed Arctic rivers. A significant feature of the “Normalizedensemble seasonal cycle” calculation is the “drop down” signal which shows the effect of the springfreshet. This signal can also be seen in the observations of Cooper et al. [2008] for dissolved Bariumand alkalinity. Thus, the appearance of this “drop down” signal during the late spring early summer,may also have the potential to be generalized in quantifying the river input of other hard-part nutrients.Dissolved Barium in this research is modeled as conservative with external sources of river inputand inflow from the open boundaries. Since the biological Barium cycling is not parameterized, thetracer model is not able to simulate the depletion of dissolved Barium at the surface due to the bariteformation and the enrichment in the halocline and deep ocean due to the sinking and the remineralization(section 2.2). This creates bias in the model (section 4.2.1).The lack of a Barium depletion signal was found in all comparisons with data above 60 m. TheBeaufort Sea (BGEP), Chukchi Sea (CBL32PZ), the Nansen Basin and the Kara Sea (ARK-XXII/2)samples show an overestimate of about 4−6 nM; in the central Arctic (NPEO), the mode has an largeoverestimation of 10 nM. The large dissolved Barium overestimate at the 20-60 m depth in the Beau-fort Sea and the Chukchi Sea is consistent with intensive biological activities at the the sub-surfaceChlorophyll-a maximum Arrigo et al. [2011]. One can calculate the ratio between the Barium depletionand the conservative Barium model output to estimate the relative importance of the biological Bari-um uptake. The ratio calculated through the Nansen Basin and the Kara Sea (ARK-XXII/2) samplesabove 60 m is about 15%, in general consistent with the estimate in Roeske et al. [2012]. For the highoverestimate in the central Arctic (10 nM mean bias) above 130 m, we should consider that: (1) theNPEO data was observed in April-May, which is not the peak of biological productivity in the Arcticocean. (2) The sample locations are consistently covered by sea-ice and in the region that has the lowestbiological productivity in the Arctic Arrigo et al. [2008]. (3) In the timeseries comparison (figure 4.4,b.2), the overestimate did not show up in 2004 and 2005, but biological modification should be hap-pening every year. (4) The model does well for simulating Oxygen isotope ratio in the central Arctic(figure 4.5), which means the combined effect of sea-ice variability and runoff were properly modeledby the ANHA4 forcing. By considering all the factors, I think this overestimation is neither the effectof localized biological Barium uptake nor too much river runoff, but an advected biological signal, inother words, Eurasian runoff that has passed a productive region. The NPEO’s sample location is underthe TDS, which is the major pathway of Eurasian runoff water. If the un-parameterized biological pro-cesses make the model overestimate the dissolved Barium on the Eurasian continental shelf, then thisbias could be transported to the central Arctic. Due to lack of data, this assumption cannot be directlytested, but previous research indicates that the coastal Kara Sea and the Laptev Sea have strong sea-icedecline in the past decade [Parkinson and Cavalieri, 2008], which benefits the biological productivity[Arrigo et al., 2008], and evidence of Eurasian runoff was found in the halocline of the central Arctic[Alkire et al., 2010] and therefore able to affect the surface dissolved Barium concentration.The underestimate due to the un-parameterized, biological induced dissolved Barium sinking wasfound in the Beaufort Sea and the Chukchi Sea in the 60-130 m depth. In the deep ocean (2-4 km)53all comparisons except the HLY0301 Baffin Bay samples show an underestimate of about 5 nM, ingeneral balancing their overestimation at the surface and showing the role of remineralization. Thestrong underestimate in Baffin Bay (44 nM mean bias) can be explained by the long residence time ofdeep Baffin Bay water. The lack of ventilation in the deep Baffin Bay accumulates the remineralizedBarium and the observed Barium concentration records can be higher than 100 nM.5.2.2 Oxygen isotope ratioThe parameterization of the riverine Oxygen isotope ratio input uses seven different regions, since com-paring with dissolved Barium, the Oxygen isotopes ratio in the Arctic rivers is more uniform. The sixdefined regions, by the names of their biggest rivers are Kolyma, Lena, Yenisey, Ob, Mckenzie andYukon. Unique annual mean Oxygen isotope ratio values were applied for each region since observa-tions show river-to-river differences, especially the Ob/Yenisey and Lena [Cooper et al., 2008].The parameterization of fractionation during the sea-ice freeze-thaw cycle is end-member valuebased. The sea-ice melt water Oxygen isotope ratio is prescribed as 1.5‰ which is a good estimate forthe central Arctic, close to the end-member choice in O¨stlund and Hut [1984] and Ekwurzel et al. [2001]and leads to good model-observation comparisons in the Amundsen Basin and over the LomonosovRidge. In the Canada Basin, 1.5‰ is probably too high when compared with previous research [Mac-donald et al., 2002, Yamamoto-Kawai et al., 2008], and this potentially causes the overestimate ofOxygen isotope ratio in the Canada basin. We did not fix this bias since no comprehensive studies aboutthe distribution of Oxygen-18 in the Arctic sea-ice can be found and hence there is no objective way todefine the boundary between different sea-ice melt Oxygen isotope ratio end-member values.5.3 Freshwater, tracers and atmospheric driving factorsThe FWC was chosen as the object of the linear trend and EOF decomposition analysis, since thevariability of FWC contains the change of all freshwater components and therefore can be explained bythe two tracers. In addition, FWC variability reflects the change of near surface atmospheric circulations;directly impacts the stratification of the ocean, is a good represention of the Arctic atmosphere-oceansystem and can be more readily compared to previous studies.The linear trends and first three EOF modes for the FWC were extracted, different atmosphericfactors were applied to explain the dynamics of FWC and the tracer patterns. The AO is the mostimportant as the increase of winter-spring AO drives the linear trends of both FWC and tracers. TheDipole anomaly is the second most important factor, as it drives EOF mode one. The interannual signalof NAO is thought to play a role in EOF mode two and the localized anticyclonic anomalous wind inCanada Basin affects mode three. This sequence in general agrees with the EOF calculation of NorthHemisphere sea level pressure by other research (e.g. [Thompson and Wallace, 1998], Wu et al. [2006]).The linear trend was removed before the EOF calculations since the Arctic Ocean in 2002-2013 is ina rapidly changing stage with the accelerated hydrological cycle [Carmack et al., 2016]. Removinglinear trends a priori also makes all the EOF modes comparable. Indeed, if it is not removed, the linearmode will explain about 60% of the total variance and makes it difficult to separate other modes in the54remaining 40% of total variance. By the rule of thumb [North et al., 1982], in this research, all the threeEOF modes were well separated.5.4 Insights from the Beaufort Gyre case studyThe Beaufort Gyre FWC study shows how the statistically based EOF modes and the tracer simulationscan be used in a specific case. The rapid increase of the Beaufort Gyre FWC is a well studied topicand different explanations have been used to explain its change in the past decade. Our research showsthat from 2007 to 2008 summer, the peak of the Beaufort Gyre FWC is a combined effect of the at-mospheric dipole anomaly and an extraordinary strong Beaufort Gyre. The result of the linear mixingmodel indicates an increase of Eurasian runoff fraction, consistent with Morison et al. [2012]. Howeverdifferent from Morison et al. [2012], here the transport of Eurasian runoff is not due to the increase ofthe AO but due to the dipole anomaly. Two insights come from this case study: (1) The Eurasian runoffpathways can be modulated by different atmospheric factors, not just the AO. (2) Monitoring the changeof Eurasian runoff contributes to the understanding of the disposition of Arctic FWC, and tracers likedissolved Barium and Oxygen isotope ratio can be the key to this effort.5.5 SummaryAn offline simulation with parameterized dissolved Barium and Oxygen isotope ratio was applied tothe Arctic Ocean. The two simulated tracers show reasonable climatology and seasonal cycles, agreewell with field observations and can be used as a tool for freshwater tracking. The tracer scheme isan example of parameterizing passive tracers by the balance between sources and sinks. The tracermodel was applied to investigate the FWC variabilities and the atmospheric factors that drive them.The linear trend and EOF analysis of the physical variables and tracers show the role of the AO, thedipole anomaly, the NAO and the Beaufort Sea anticyclonic anomalous wind. In the case study ofthe Beaufort Gyre FWC in 2007-2008, the change of the Eurasian runoff pathways by dipole anomalyand the accumulation of Eurasian runoff in the Beaufort Gyre by a strong anticyclonic wind pattern wasfound. The case study explains the increase of FWC in the Beaufort Gyre from 2007 to 2008 and revealsthe power of tracer simulation in the research of Arctic freshwater.55Chapter 6Conclusions6.1 Research questions1. How can dissolved Barium and Oxygen isotope ratio be simulated in a numeric model?Dissolved Barium and Oxygen isotope ratio were modeled as conservative with parameterizedsources and sinks. The river input is the most important dissolved Barium source and was parameterizedin twenty different regions with seasonal cycles. The estuarine tracer input locations are consistent withthe estuarine freshwater input. The riverine input of Oxygen isotope ratio was modeled in a similar wayas dissolved Barium but has fewer regions and uses annual mean input. The fractionation of the sea-icefreeze-thaw cycle was modeled for the Oxygen isotope ratio with an uniform end-member and the netsea-ice melt from the physical model. The inflow of the tracer into the Arctic was determined by theopen boundary condition.2. What is the distribution and statistical features of the simulated tracers and how does the modeloutput compare with field measurements?In the climatology, modeled dissolved Barium is high in the estuaries and on the North Americanside of the Arctic. The domain-wide mean dissolved Barium timeseries has an average of 59 nM andshows the seasonality of river input. The dissolved Barium fluxes through the Arctic Ocean and the fluxof riverine input are well balanced. The total riverine Barium inputs of the simulation in the Mackenzie,Lena, Kolyma, Ob, Yenisey and Pechora Rivers are consistent with the estimates in Guay and Falkner[1998]. The model evaluation of dissolved Barium is in general good with overestimation above 60 mand underestimation along the halocline and at 2-4 km depth. The dissolved Barium model bias canbe explained by the un-parameterized biological Barium cycling, including the barite formation at thesurface, the sinking in the intermediate depth and the remineralization in the deep ocean.The spatial variability of the modeled climatology of Oxygen isotope ratio is consistent with thedistribution of sea surface salinity and is able to separate sea-ice melt water from meteoric water in aδ 18O-Salinity graph. The domain-wide averaged Oxygen isotope ratio timeseries and seasonal cycleshow the mixed effect of meteoric water input and sea-ice melt and formation. In the semi-permanent56sea-ice covered region, the signal of parameterized sea-ice fractionation is stronger and helps confirmthat it is properly modeled. The model evaluation of Oxygen isotope ratio is good with overestimationin the Beaufort Sea due to the choice of the sea-ice melt end-member.3. How does atmospheric variability change the freshwater content in the Arctic ?The simulated tracer anomalies can explain the FWC variability well by linking to their geochemicalbehaviors. When a positive dissolved Barium anomaly co-occurs with positive sea surface height andFWC anomalies, it indicates the increase of FWC is due to runoff. The two common regions thatdissolved Barium anomalies can be found are the Beaufort Sea - CAA, which indicates the the shift ofthe pathway of high Barium concentration North American runoff and the Makarov Basin which showsthe lose or gain of the East Siberian and Laptev Seas runoff.The Oxygen isotope ratio anomalies have the information of net sea-ice melt and meteoric watercombined. Since the Eurasian rivers together have higher discharge than the North American runoff,the Oxygen isotope ratio anomalies along the Eurasian coast and in the central Arctic usually meansthe change of Eurasian runoff. The positive Oxygen isotope ratio can also be linked to the increase ofsea-ice melt, especially in the Laptev and Kara Seas which was reported to have significant summersea-ice cover retreat [Parkinson and Cavalieri, 2008].The linear mixing model is another way of using dissolved Barium and Oxygen isotope ratio toexplain the FWC change. This approach was practiced in the case study in 2007-2008 to estimate theEurasian and North American runoff fractions in the Beaufort Sea. The estimated temporal evolution ofthe runoff fractions, consistent well with the theory and the observational evidence, confirmed that, sim-ulated dissolved Barium and Oxygen isotope ratio can be used to investigate freshwater end-membersin the same manner that observations are used.6.2 Contributions to the existing knowledge6.2.1 The Canadian Arctic GEOTRACES ProgramThis research is the first numeric model simulation of dissolved Barium in the Arctic Ocean and animportant part of the Canadian Arctic GEOTRACES Program. The comprehensive, four-dimensionaltracer model with implemented geochemical processes, provides a good reference for climatology stateof the tracers. The comparison between the model output with GEOTRACES field observations, im-proves the understanding of the conservative behavior of dissolved Barium and its usability as a tracerof Arctic river runoff; the Oxygen isotope ratio comparison result highlights the end-member differencebetween the Beaufort Sea side and the Eurasian side sea-ice melt water. All this information will beuseful for further tracer model development.6.2.2 Arctic Ocean freshwater studiesOn the scope of Arctic Ocean freshwater science, in previous research, the dipole anomaly was thoughtto have an impact on the Arctic summer sea-ice cover [Wang et al., 2009]. In this research, the conclu-57sion from Wang et al. [2009] is confirmed with the simulated Oxygen isotope ratio composite anomalyresult. However, we found the dipole anomaly also has a significant impact on the redistribution of otherfreshwater components, including Eurasian and North American runoff.From summer 2007 to winter 2008, we found that the dipole anomaly, combined with a strongBeaufort Gyre, played an important role in transporting Eurasian runoff into the Beaufort Sea; thisresult provides new insight on the freshwater storage in the Beaufort Gyre after Morison et al. [2012]identified the role of the AO. On the methodology level, this research brings EOF and spectral analysisinto the Arctic Ocean freshwater science, extending data interpretation.6.3 Future researchMany improvements could be made to provide better tracer simulation results. In the model evaluation,the un-parameterized biological Barium cycling is thought to generate systematic errors in the modelresults. This problem can be solved by adding the surface barite formation, the sinking of barite withorganic particles and the remineralization in the sediments to the tracer scheme. The observation ofother biological tracers can help divide the model domain into different categories by the importanceof biological induced Barium cycling. The difference between the “modeled as conservative” and “bi-ologically modified” dissolved Barium also provides on estimate of surface Barium depletion. For theOxygen isotope ratio, more field observations at the edge of Beaufort Sea in summer can help adjustingthe parameterization of sea-ice melt fractionation. By incorporating more field observations in the smalland poorly observed Arctic rivers in the future, especially in the Eurasian side of the Arctic, the modelwould have a better estimate of the riverine tracer input. The configuration of the open boundaries inthe Bering Strait, the Fram Strait, the Davis Strait and the Barents Sea openings depend on the the fieldobservations. If more observations are available in these Arctic Ocean inflow and outflow channels, themodel will have a better estimate of the open boundary conditions.For using simulated freshwater tracers to investigate the variability of the Arctic freshwater, sensitiveexperiments may provide new insights about how the atmospheric circulations can change the surfaceArctic FWC and how the effect of circulation can be tested by the freshwater tracer field observations.Interesting sensitivity experiments include the atmospheric forcing of AO, dipole anomaly and NAOsince all these anomaly patterns have different impacts on the Arctic Ocean freshwater. Longer simula-tions can be prepared to investigate the long-term variabilities of the Arctic freshwater and tracers in thepast. In this research, the linear mixing model applied for the simulated tracers cannot separate Pacificwater from North Atlantic water and therefore uncertainties remain; in future studies, this problem couldbe solved by adding tracers for Pacific inflow (e.g. nitrate and phosphate).Based on the trend of a positive temperature in polar regions, it is believed that the Arctic Oceanwill become ice-free in the middle-21st century with a rapid increase of its surface freshwater [Hu andMyers, 2014, Wang and Overland, 2009]. Climate models in the IPCC-AR5 suggest intensified AOand NAO with anthropogenic forcing [IPCC, 2013]. These two teleconnection patterns may play animportant role in redistributing surface freshwater in the future. Based on the result in 4.3 and 4.4, AOleads to an increased transport of surface freshwater from the Eurasian side of the Arctic to the Beaufort58Sea, meanwhile the asymmetric NAO leads to an accumulation of freshwater in the Makarov Basin.The interplay of these two patterns will preserve and increase the FWC or salinity gradient betweenthe North American side and the Eurasian side of the Arctic. The response of different freshwatercomponents depends highly on the interactions and down-stream effects which require more on-goingresearch. The tracer model in this research provides an opportunity for projection of the future state. Byapplying different climate change scenarios, the possible change of the Arctic Ocean freshwater and itstracers in the future can be identified.59BibliographyK. Aagaard and E. C. Carmack. The role of sea ice and other fresh water in the Arctic circulation. J.Geophys. Res.: Oceans (1978–2012), 94(C10):14485–14498, 1989. → pages 1, 4, 5, 6K. Aagaard and E. C. 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ANHA4 simulation table. Accessed 2016/11/08.http://knossos.eas.ualberta.ca/xianmin/anha/anhatable.html, 2016. → pages 17M. Yamamoto-Kawai, N. Tanaka, and S. Pivovarov. Freshwater and brine behaviors in the ArcticOcean deduced from historical data of δ 18O and alkalinity (1929–2002 ad). J. Geophys. Res.:Oceans (1978–2012), 110(C10), 2005. → pages 1, 3, 9, 16M. Yamamoto-Kawai, E. Carmack, and F. McLaughlin. Nitrogen balance and Arctic throughflow.Nature, 443(7107):43–43, 2006. → pages 6M. Yamamoto-Kawai, F. A. McLaughlin, E. C. Carmack, S. Nishino, and K. Shimada. Freshwaterbudget of the Canada Basin, Arctic Ocean, from salinity, δ 18O, and nutrients. J. Geophys. Res.:Oceans (1978–2012), 113(C1), 2008. → pages 1, 9, 15, 16, 54J. Zhang, R. Letolle, J. M. Martin, C. Jusserand, and J. M. Mouchel. Stable Oxygen isotopedistribution in the Huanghe (Yellow River) and the Changjiang (Yangtze River) estuarine systems.Cont. Shelf Res., 10(4):369–384, 1990. → pages 868X. Zhang, M. Ikeda, and J. E. Walsh. Arctic sea ice and freshwater changes driven by the atmosphericleading mode in a coupled sea ice-ocean model. J. Climate, 16(13):2159–2177, 2003. → pages 9, 45K. Zickfeld, A. Levermann, M. G. Morgan, T. Kuhlbrodt, S. Rahmstorf, and D. W. Keith. Expertjudgements on the response of the Atlantic meridional overturning circulation to climate change.Climatic Change, 82(3-4):235–265, 2007. → pages 669Appendix AClimatology fields of the physical modelFigure A.1: CGRF 2002-2013 mean winter (DJF) and summer (JJA) sea level pressure and 10m-wind.The winter mean of CGRF sea level pressure over the north hemisphere correctly shows the locationof the Icelandic Low and the Aleutian Low with cyclonic 10m-wind (figure A.1, a). In the central Arctica strong Beaufort high can be characterized by the 1020hPa isoline as the northward extension of theSiberian High. The summer mean CGRF sea level pressure has lower pressure gradients in the northhemisphere with a weak Icelandic Low (figure A.1, b). The Aleutian Low disappears and the centralArctic is covered by a weak anticyclonic wind pattern.The 12-year mean ANHA4-EXH005 sea surface height is in general less than zero in the Arctic(figure A.2, a). The sea surface height on the North American side of the Arctic is higher than onthe Eurasian side of the Arctic. Sea surface height maxima can be found in the Bering Strait and theBeaufort Sea meanwhile the East and South Greenland Seas have sea surface height minima. The 0-130m averaged ANHA4 ocean velocities follow the sea surface height isolines and show the TDS and70Figure A.2: ANHA4-EXH005 2002-2013 mean sea surface height, ocean velocities (a) and FWCrelative to the 34.8 salinity (b) above 130m. The dashed line in (b) is the isoline of 2002-2013 mean March sea-ice larger than 70%; the hatch is the mean September sea-ice largerthan 70%.the Beaufort Gyre. Other major currents including the Labrador Sea current in the Baffin Bay, the WestSpitsbergen Current near the Svalbard and the Bering Strait inflow are also reproduced.The climatology of ANHA4-EXH005 FWC shows similar distributions as the sea surface height,with high FWC on the North American side and low FWC on the Eurasian side of the Arctic (figure A.2,b). The high FWC along the Eurasian marginal coast indicates the contribution of the Eurasian riversand the zero FWC in the Barents Sea and the Greenland Sea means that the salinity above 130m is equalor higher than the 34.8 reference. By comparing the regions with mean sea-ice cover larger than 70% inMarch and September, significant ice loss can be seen in the Eurasian continental shelves, the ChukchiSea and part of the Beaufort Shelf. Since September is the sea-ice minima, the sea-ice cover in thismonth also represents the semi-permanent sea-ice covered region.71Appendix BStatistical methodsThis appendix contains information about the statistical methods which were used in the research. Othercalculations (average, weighted average, anomaly, normalization etc.) are assumed known and notdocumented.B.1 CorrelationIn this research, all correlations between two variables, X and Y , were calculated as the traditional“Pearson product-moment correlation”:R=E[(X −X )(Y −Y )T ]√E(X 2)−E (X )2√E (Y 2)−E (Y )2 (B.1)Here E means expectation and overline means average. t-statistics can be applied to test the significanceof R with the null case that X and Y have zero correlation.T = R√N1−R2 (B.2)Here N is the degree of freedom. A traditional estimate of N is n−2. However for the time series withstrong autocorrelations, n−2 is over optimistic, so in this research, N is estimated based on the effectivesample size (n∗) [Hsieh, 2009]:n∗ = n[L∑l=−L(ρ lxxρ lyy+ρxylρ lyx)]−1(B.3)Here ρ lxx and ρ lyy are l-lagged autocorrelations of X and Y . ρ lxy and ρ lyx are cross-correlations. L is themaximum lag which usually can be no larger than n/3, in this research, L = n/4. The critical value ofT is obtained from the Student’s t-distribution with n∗− 2 degrees of freedom and 1−α significance.The null case can be rejected if |T | is larger than the critical value:tα/2,N ≤ |T | (B.4)72B.2 Composite anomalyComposite anomaly means the difference of the average of a variable in the high and low phases of atimeseries (t). In this research, composite anomaly was applied to examine the correspond change ofCGRF, ANHA4 variables and modeled tracers in three EOF mode PCs. The criteria for the high andlow phase is the standard deviation of the timeseries (σ ).X = Xi−X j, i ∈ {t, t > σt}j ∈ {t, t <−σt}(B.5)The two-sample t-test examines if the mean of the two phases are equal. The null case of the t-test isthe two phases are the same (high phase and low phase have no statistical difference), the t-statistics isgiven as:T =Xi−X j√S21/N1+S22/N2(B.6)Here N is the degrees of freedom and assumed to be the sample size (n). The critical value of T isobtained by Student’s t-distribution with n−2 degree of freedom and 1−α significance. The null casecan be rejected if |T | is larger than the critical value:tα/2,n−2 ≤ |T | (B.7)B.3 Linear regression and trendsIn this research, linear regression was used to investigate the trend of ANHA4 variables, modeled tracersand AO indices. In all the cases, the regression was done by least squares method.B.3.1 Least squares methodAssuming independent variable x and dependent variable y with sample size n, the linear regressionmodel is given as follows:y= kx+b+ ε (B.8)Least squares method calculates trend k and offset b to make the square sum of the error [equation (B.9)]reach the global minimum.R2 =n∑i=1(yi− kxi−b)2 (B.9)Since R2 is a function of k and b, its extremum is where the partial derivative equals zero:73∂R2∂k= 0∂R2∂b= 0⇒nk+bn∑i=1xi =n∑i=1yikn∑i=1xi+bn∑i=1x2i =n∑i=1xiyi(B.10)k and b can therefore be solved as equation (B.11) shows.b=y(n∑i=1x2i)− x(n∑i=1xiyi)n∑i=1x2i −nx2k =(n∑i=1xiyi)−nxyn∑i=1x2i −nx2(B.11)B.3.2 Significance testStudent’s t test can be used to examine the regression parameters and Fisher’s F test can be used fortesting the general fitness of the regression. In this research, the objectiveness of the linear regression iscalculating the trend, hence only t-test for the trend was applied.The null case of the t-test is: the true slope of x, k0 is zero (no linear relation), and the t-statistics is:T = (k− k0)√√√√√√√√(n−2)n∑i=1(xi− x)2n∑i=1(yi− y)2(B.12)Here k is the slope calculated by least square method. The critical value of T is obtained by the Student’st-distribution with n−2 degrees of freedom and 1−α significance. The null case can be rejected if |T |is larger than the critical value:tα/2,n−2 ≤ |T | (B.13)B.4 Empirical Orthogonal Function (EOF)EOF is a data analysis method that extracts important patterns from the input. In this research, EOF isused for investigating the variability of FWC and to calculate AO and NAO indices (see appendix D).B.4.1 Spatial pattern and principal componentThis section briefly summarizes the idea of EOF and procedures for calculating the spatial pattern andPrincipal Component (PC) of EOF modes. The math derivation here is abbreviated and detailed discus-sion can be seen in Lorenz [1956] and other text books.Assuming anomaly data X is distributed over m different grids and n different times. It can bewritten as vectors:74X t =x1tx2t...xmt , t = 1,2, . . .n (B.14)If we define m different grids as m dimensions, Xt can then be expressed by m different orthogonal basevectors (V k):X t =m∑k=1αk(t)V k (B.15)However, the relative importance of these base vectors is not the same, since the projections of X t ontoV k, the weighting parameters αk(t) are not the same. Hence, some base vectors may explain the majorityof X t , but some contribute little. In an extreme example, if α ′k(t) = 0, then V′k can be totally ignored.The goal of EOF analysis is to choose base vectors which explain the highest variation of X t , reduce thedimensionality of the system and identify important patterns.In case of the first mode, equation (B.15) can be written with an error term:X t = α1(t)V 1+ εt (B.16)The first base vector satisfies the condition that the expectation of the variance of error reaches its globalminimum:E1 =1nn∑t=1εTt εt = εTt εt (B.17)By using the method of Lagrange multipliers with constant λ , equation (B.17) changes into:F(V1) = E1(V 1)+λ1(V T1V 1−1)∂F∂V 1=−2E (X tX Tt )V 1+2λ1V 1 = 0 (B.18)Since X is anomaly field, E(X tX Tt)is known as the covariance matrix (Σ). The solution of equa-tion (B.18) is an eigenvalue problem:ΣV 1 = λ1V 1 (B.19)It can be proven that E1 reaches a global minimum with the highest eigenvalue λ1. Then, the mode onespatial pattern is the eigenvector (V 1), the PC at time t is X Tt V 1 and the eigenvalue (λ1) indicates therelative importance of the mode one.When it calculates the EOF mode two, the contribution of mode one will be removed from equa-tion (B.15), so on for the other modes.75Due to the property of eigenvalues, the spatial pattern and PC can change signs and multiply withconstants. In this research, α(t) is normalized and V contains the magnitude, that is, it is multiplied bythe standard deviation of X .B.4.2 Explained varianceThe total variance of the original data X is the trace of its covariance matrix Σ. As a real-symmetricmatrix, the trace of Σ equals to the sum of its eigenvalues:TrΣ =m∑k=1λk (B.20)The explained variance of ith mode is the ratio of its eigenvalue to the sum of all eigenvalues:λi(m∑k=1λk)−1(B.21)The accumulated contribution of the first I modes is the sum of their explained variance:I∑k=1λk(m∑k=1λk)−1(B.22)B.4.3 Rule of thumbThe rule of thumb [North et al., 1982] can be used to investigate the sampling error of EOF modes:δλk = λk√2N(B.23)According to the rule, two neighboring modes are considered to be well separated if their difference islarger than the sampling error:λk−λk+1 > δλk (B.24)The N in equation (B.23) is the sample number (n) in [North et al., 1982], but other research suggeststhat, it is better to have N as the effective degrees of freedom (N∗). In this research, N∗ is calculated asBretherton et al. [1999] suggested:N∗ =(n∑k=1λk)2/n∑k=1λ 2k (B.25)Bretherton et al. [1999] also proved that, if eigenvalues drop down geometrically, then the accumulatedcontribution of first N∗ modes should be roughly 86% (may have small uncertainty since N∗ can bea non-integer). Also note that, Rule of thumb examines the “separation” of neighboring modes, if twomodes do not pass the test, then they are not well separated, but they can still have physical explanations.76B.4.4 Spectral analysisPower spectrum also known as Power Spectral Density (PSD) is power values of a signal as a functionof frequency. In this research, power spectrum was calculated for the PCs of EOF modes to examinethe frequency band of their major variabilities. A Fast Fourier Transform (FFT) based “periodogram”technique was applied for the estimation of power spectrum.Suppose signal t is sampled at n different times, with a uniform spacing of ∆t, then the powerspectrum of t can be roughly represented by its periodogram, which is the square of the magnitude ofthe signal’s FFT:G( f ) =δ tn∣∣∣∣∣n−1∑k=0xke−i2πkδ t f∣∣∣∣∣2, f <12∆t(B.26)Here G is the periodogram, frequency f should be lower than the Nyquist frequency 1/2∆t. Differentfrom typical signal processing problems, here ∆t is one month, and the unit of frequency is “cycles permonth”.Since the spectral powers of random processes are not strictly zero, a test should be made for in-vestigating the significance of the periodogram. The null case of the test is the time series t is a noisesignal. The type of noise includes “white noise” and “red noise”. White noise follows zero mean normaldistribution and red noise is the first order Auto-Regressive (AR) process. The statistics of the two noisetypes obey the χ2 distribution with N∗ degrees of freedom.χ2w = N∗G( fk)G( f ), N∗ = 2n (B.27)χ2r = N∗G( fk)G( f )L, L=1−ρ211+ρ21 −2ρ1 cos(2 fkπ)(B.28)Here L is the standard red noise spectrum [Gilman et al., 1963]. G( f ) is the mean of spectral power inthe interval [ f1, fm], fk means k’s frequency, ρ1 is the 1st-lagged autocovariance of t. In this research,since PCs are standardized timeseries, ρ1 is also the lag-one autocorrelation. When testing the entirespectrum, χ2-statistics have n different values. If for frequency fk, χ2-statistics is larger than χ2(α,N∗),the null case will be rejected, G( fk) has 1−α significance.Periodogram has spectral leakage due to numeric operations. Smoothing or using window functions(e.g. Bartlett’s method, Welch’s Method) can partially reduce the leakage [Stoica and Moses, 1997],but since the power spectrum in this research is only calculated for qualitative analysis (e.g. whichfrequency band has the highest spectral power), no adjustment has been made.77Appendix CThe derivation of wind stress curlIn a spherical coordinate system with radius (R r̂), zenith angle (ϕ ) and azimuthal angle (θ ), the radialcomponent of the curl of a vector F⃗ is:curlz(F⃗)= ∇× F⃗ · r̂ = 1Rsinϕ[∂∂ϕ(Fθ sinϕ)− ∂Fϕ∂θ](C.1)The zenith and azimuthal angles can be converted into latitude (φ) and longitude (λ ):φ =π2−ϕ , λ = θ (C.2)Then the curl equation can be rewritten as:curlz(F⃗)=1Rcosφ(Fλ sinφ−∂Fλ∂φcosφ+∂Fφ∂λ)(C.3)The curl can be discretized with grid spacing (∆x,∆y), and equation (C.3) can be rewritten as follows:curlz(F⃗)=∆Fφ∆x− ∆Fλ∆y+FλRtanφ (C.4)78Appendix DAtmospheric tele-connection patterns andCGRF indicesFigure D.1: Spatial patterns of sea level pressure EOF modes (a-c), timeseries in dark red are thePCs. NOAA-CPC AO and NAO indices were plotted as black dashed lines.79An EOF decomposition was applied to the CGRF sea level pressure from 20◦N to 90◦N (figure D.1).Mode one accounts for 37.9% of the total variance and its spatial distribution shows an annular distri-bution with negative sea level pressure anomaly in the Arctic and positive sea level pressure anomaly inthe mid-latitudes, consistent with the definition of AO [Thompson and Wallace, 1998]. The PC of modeone has a significant positive correlation (R = 0.86, p < 0.01) with the NOAA-CPC AO index, whichwas calculated based on the NCEP-NCAR 1000hPa geo-potential height anomalies from 1948 to thepresent.Mode two accounts for 11.46% of the total variance and its spatial pattern shows negative sea levelpressure anomaly above the Eurasian side of the Arctic and positive anomaly above the North Americanside of the Arctic with strong meridionality above the TDS region. This spatial distribution is consistentwith the description of the dipole anomaly [Wang et al., 2009, Watanabe et al., 2006, Wu et al., 2006]and is independent from the other atmospheric teleconnections.Mode three accounts for 9.35% of the total variance with positive sea level pressure anomalies inboth the North Atlantic and the Pacific side of the Arctic and with a negative sea level pressure anomalycentered in the Greenland Sea, consistent with the definition of NAO near the surface [Hurrell, 1995].The PC of the mode three has a significant correlation with the NOAA-CPC NAO index (R = 0.37,p< 0.01), the latter was estimated from the standardized 500hPa Geo-potential height from 1948 to thepresent.80

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