UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Seasonality in the response of sea ice and upwelling to wind forcing in the southern Beaufort Sea Wang, Qiang 2007

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
24-ubc_2008_spring_wang_qiang.pdf [ 4.88MB ]
Metadata
JSON: 24-1.0053231.json
JSON-LD: 24-1.0053231-ld.json
RDF/XML (Pretty): 24-1.0053231-rdf.xml
RDF/JSON: 24-1.0053231-rdf.json
Turtle: 24-1.0053231-turtle.txt
N-Triples: 24-1.0053231-rdf-ntriples.txt
Original Record: 24-1.0053231-source.json
Full Text
24-1.0053231-fulltext.txt
Citation
24-1.0053231.ris

Full Text

Seasonality in the Response of Sea Ice and Upwelling to Wind Forcing in the southern Beaufort Sea by Qiang Wang B.S., Ocean University of China, 2000 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Sciences in The Faculty of Graduate Studies (Oceanography) The University of British Columbia December, 2007 © Qiang Wang 2007 Abstract The seasonal pattern of ice motion in response to wind forcing and potential consequences to upwelling on the Mackenzie Shelf are considered using satellite-derived ice motion data from the National Snow and Ice Data Center and the NCEP 10 m wind data. The frequency of strong upwelling-favorable alongshore ice motion is high in early winter (November and December) compared to middle and late winter (January to May). For periods when the alongshore component of the wind is upwelling-favorable, the ratio of ice drift divided by wind speed on the Mackenzie Shelf is 0.024 in November and 0.008 in March; we conjecture that this ratio decreases as winter progresses because the internal ice stress becomes stronger as both ice thickness and ice concentration increase. This constitutes a possible 10-fold decrease in the seasonal transmission of wind stress to the underlying water from November to March. This ratio in May (0.015) is higher than that in March. We suggest that it is because the internal ice stress becomes weaker as ice concentration decreases on the Mackenzie Shelf in May. Hence, under the same wind forcing, the potential for winter upwelling on Mackenzie Shelf may be enhanced if climate warming results in reduced ice thickness and/or ice concentration. Numerical model results show that the stress on the shelf could be reduced because of the internal ice stress from the pack ice over the deep ocean when the ice moves like a rigid body. We found that the model results are not realistic when the ice strength is 5,000 Nm -2 . When the ice strength is 27,500 Nm -2 , the model results are more realistic. ii Acknowledgements I would like to give my sincere thanks to my late supervisor, Prof R. Grant Ingram. Without his directions and encouragements, this work would not be possible. Prof. R. Grant Ingram unexpectedly passed away while working in his office on June 13, 2007. He was the prime mover of this study and I will sorely miss him. I am grateful to Prof William Hsieh for taking over the supervisor's task after the passing of Prof Ingram. It is also with gratitude that I acknowledge Dr. Eddy Carmack for his guidance. Also, thanks go to Prof. Susan Allen, Prof. Richard Pawlowicz, and Dr. William Williams for their helpful discussion. I would like to thank Jennifer Jackson, Andrew Hamilton, and all the other students and post-docs in physical oceanography. All of them have helped me in some way during these years, either with technical advice or assistance after my supervisor passed away. I would like to thank Dr. Paul Budgell who sent me his ice model. I also would like to express my gratitude to Profs. Douw Steyn and Neil Balmforth in the department for their excellent teaching. I would like to thank Dr. James Overland and Dr. Peter Wadhams for permitting me to use their figures in this thesis. iii Contents Abstract^  ii Acknowledgements^  iii List of Tables vi List of Figures^ vii 1. Introduction 1 1.1 Background^ 1 1.1.1 Ice dynamics  ^ 1 1.1.2 The response of sea ice motion to the wind ^2 1.1.3 Drag coefficient between the ice and atmosphere .3 1.1.4 Ice edge upwelling/downwelling^ 4 1.1.5 Ice rheology^  .5 1.2. Study area 9 1.3 Objectives  ^ 13 1.4 Methods and structure of the thesis ^ 14 2. Observational data and results  15 2.1 Data^  15 2.2 Seasonal response of sea ice to wind forcing^  . 16 2.2.1 Seasonal variation of sea ice concentration and ice thickness^ 16 2.2.2 Seasonal response of sea ice to wind forcing on the Mackenzie Shelf^ 18 2.2.3 Monthly mean sea ice motion^ .24 2.2.4 Seasonal response of sea ice to wind forcing in the southern Beaufort Sea....27 iv 2.3 The effect of sea ice concentration of ice motion^ 34 3. Numerical model and model results.. 47 3.1 Sea ice model ^47 3.2 Ocean modeling and ice-ocean coupling^ .51 3.3 Model configuration^ .51 3.4 Model results 54 3.4.1. Case 1^ ..54 3.4.2 Sensitivity to ice strength^ 59 3.4.3. Sensitivities to ice thickness 63 3.5 Summary ^ ..67 4. Discussion^ . 68 4.1 The effect of atmospheric boundary layer structure^ 68 4.2 The wind stress and ice stress on the water^ 72 4.3 The upwelling index^ 73 4.4 Arctic Oscillation 75 5. Summary and Conclusions^ 77 References ^82 Appendix A^ 89 v List of Tables Table 1.1 Air-ice drag coefficient^ 4 Table 3.1 Parameter and constants used in the model run^ 52 Table 3.2 Wind stress, initial ice thickness, and ice strength for 5 cases^ .53 vi List of Figures 1.1 Various sea ice rheologies shown in one dimension ^6 1.2 A yield curve showing allowable stress states for viscous plastic rheologies ^ . 7 1.3 A map of the Canada Basin and the Beaufort Sea^  8 1.4 A map of the Mackenzie Shelf and the surrounding area 10 1.5 Time series of (a) along shore wind stress, (b) along shore ice velocity squared. (c) equivalent depth^ 12 2.1 Monthly average sea ice concentration data from the SSMR and SSM/I passive microwave radiometer from 1985 to 2002^ 17 2.2 Yearly average sea ice concentrations in the red region in the top right figure for May 14 to May 21 from 1993 to 2007^  18 2.3 (a) Histogram of the time fraction when the daily alongshore component of wind stress is greater than 0 134, 0.086, 0.036, 0 for each month of the calendar year from November to May between 1985 and 2002 at site 1. (b) Histogram of the time fraction when the daily alongshore component of ice velocity is greater than 10.2, 6.2, 2.6, 0 cm s -1 for each month of the calendar year from November to May between 1985 and 2002 at site 1  19 2.4 The ratio u, /um versus wind direction (a) in November (b) in January (c) in March (d) in May from 1985 to 2002 at site 1^ 20 2.5 The mean ice motion in the southern Beaufort Sea from 1985 to 2002^ ..22 2.6 The ratio U, Iu lo versus ice direction in February, March, and April from 1985 to 2002 at site 1^ 23 2.7 Monthly mean sea ice motion from 1985 to 2002^ 25 vii 2.8 The contours of MUSR in November from 1985 to 2002^ 29 2.9 The contours of MUSR in December from 1985 to 2002 29 2.10 The contours of MUSR in January from 1985 to 2002^ ..30 2.11 The contours of MUSR in February from 1985 to 2002 30 2.12 The contours of MUSR in March from 1985 to 2002^ 31 2.13 The contours of MUSR in April from 1985 to 2002 ..31 2.14 The contours of MUSR in May from 1985 to 2002^ 32 2.15 The contours of the ratio of MUSR in November divided by MUSR in March from 1985 to 2002^ 32 2.16 The ratio u 1 /um versus ice direction in February, March, and April from 1985 to 2002 at site 2^ ... 33 2.17 (a) The ice concentration in the southern Beaufort Sea on December 19, 1995. (b) The ice motion vectors in the southern Beaufort Sea on the same day^ 33 2.18 The time series of (a) the ice motion vector at site 1, (b) the alongshore component of wind stress at site 1, (c) the average sea ice concentration and the minimum sea ice concentration in the area 1, and (d) the wind vector at site 1 from February 29 to March 7, 2000^ ..35 2.19 Sea ice concentration in the southern Beaufort Sea on Feb 29 to March 7, 2000...36 2.20 Wind fields over the southern Beaufort Sea on Feb 29 to March 7, 2000^ 37 2.21 Ice motion vectors in the southern Beaufort Sea on Feb 29 to March 7, 2000^38 2.22 The time series of (a) the ice motion vector at site 1, (b) the alongshore component of wind stress at site 1, (c) the average sea ice concentration and the minimum sea viii ice concentration in area 1, and (d) the wind vector at site 1 from February 25 to March 4, 2003^  .40 2.23 Sea ice concentration in the southern Beaufort Sea on Feb 25 to March 4, 2003...41 2.24 Wind fields over the southern Beaufort Sea on Feb 25 to March 4, 2003^ 42 2.25 Ice motion vectors in the southern Beaufort Sea on Feb 25 to March 4, 2003.... 43 2.26 The probability density functions of average sea ice concentration in area 1 when the ice direction is in the range of 142-270°T and (a) the alongshore ice speed was above 9.3 cm s -1 and (b) the ice speed was below 9.3 cm s -1 from January 1 to May 30 between 1989 and 2002. The probability density functions of minimum sea ice concentration data in the same area when the ice direction is in the range of 142- 270°T and (c) the alongshore ice speed was above 9.3 cm s -1 and (d) below 9.3 cm s -1 during the same period  45 3.1 (a) The model bathymetry in the offshore direction, and (b) the initial density profile. ^ 53 3.2. Alongshore components (top) and cross-components (bottom) of the ice velocity at day 1, 3, and 6 plotted as a function of the offshore distance^ .54 3.3 Momentum balance for ice in (a) alongshore direction and (b) cross-shore directionat day 6. (c) shows the momentum balance for ice at 100 km offshore at day 6 .55 3.4 Time-offshore distance contour plot of the alongshore component of stress on the ocean^ 57 3.5 Cross-sections of (a) the cross-shore and (b) alongshore components of the water velocities at day 6^ 57 ix 3.6 The cross-shore sections of salinity at (a) day 1, (b) day 2, (c) day 3, and (d) day 6....  59 3.7. Alongshore ice speed, cross-shore ice speed, and ice speed at day 6 for (a) case 2 and (b) case 3^ 60 3.8. Momentum balance for ice in (a) alongshore direction and (b) cross-shore direction at day 6 for case 2. Figure (c) shows the momentum balance for ice at 150 km offshore at day 6^ 61 3.9. Momentum balance for ice in (a) cross-shore direction and (b) cross-shore direction at day 6 for case 3. Figure (c) shows the momentum balance for ice at 150 km offshore at day 6^ 62 3.10 Alongshore ice speed, cross-shore ice speed, and ice speed at day 6 for (a) case 4, (b) case 5^ 63 3.11 Ice thickness at day 6 for (a) case 4; (b) case 5^ 64 3.12 Momentum balance for ice in (a) cross-shore direction and (b) cross-shore direction at day 6 for case 4. Figure (c) shows the momentum balance for ice at 200 km offshore at day 6 64 3.13 Momentum balance for ice in cross-shore direction at day 6 for case 5. (c) momentum balance for ice at 200 km offshore at day 6^ 66 4.1 Typical winter air temperature profiles taken near Wrangel Island by the Maud expedition^ .68 4.2 Mean air temperature profiles for February 1987 from six locations located around the periphery of the Arctic Ocean: (1) Krenkel (81°N, 58°E) (2) Chelyuskin (78°N, x 104°E), (3) Kotelny (76 ° N, 138° E), (4) Barrow (71 ° N, 86 °W), (5) Mould Bay (76 ° N, 119°W) and (6) Eureka (80 ° N, 86 ° W)^ 69 4.3 Second-order closure model results showing dependence of the geostrophic drag coefficient u. I G on z. = u. l fZ, and CD^ .70 4.4 The alongshore stress on the ocean at site 1 in 1987^ 74 4.5 Ice drift patterns for a) years with low AO - index (anticyclonic conditions) and b) high AO + index (cyclonic conditions) Time taken in years for year ice to reach Fram Strait is shown for c) low AO - index conditions and d) high AO + index conditions 76 xi 1. Introduction One of the most important physical and biogeochemical processes in the coastal ocean is shelf-break upwelling, which draws water from the deeper, offshore layers of the sea onto the shelf and to the surface. The process provides a major flux of nutrients to the surface layer. Recently, upwelling under ice-covered conditions has begun to be studied (Carmack and Chapman, 2003, Williams et al., 2006). However, the role of ice on upwelling in the southern Beaufort Sea is still not clear. In order to understand the upwelling under the sea ice, we need to understand the response of sea ice motion to wind forcing. 1.1 Background 1.1.1 Ice dynamics The force balance of sea ice is as follows: Mass xacceleration of element = wind stress + water stress + Coriolis force + internal ice stress + force due to sea surface tilt (Wadhams, 2000). The internal ice stress depends on the ice thickness, floe size and ice concentration (cf. Hibler, 1979), and plays an important part in the momentum balance (Steele et al, 1997). Internal ice stress is believed to be important only for densely packed ice floe fields, where ice concentrations exceed 0.8 (Beckmann and Birnbaum, 2001). When the ice is thin, the internal ice stress is likewise small. When the ice diverges, the internal ice stress is near-zero. 1 1.1.2 The response of sea ice motion to the wind Nansen (1902) was the first to report that the pack ice generally moves at about 2% of the surface wind speed and 30° to the right of the wind velocity vector. In the northeastern Bering Sea, the ice speed is about 2%-3% of the 10-m wind speed (Overland et al., 1984, Pease and Salo, 1987). The ratio of ice speed divided by 10 m wind speed is related to water depth. When the water depth is about 80m, the ratio is about 0.03 (Overland et al., 1984). The ratio of ice speed divided by wind speed is also related to wind speed. Overland et al. (1984) used a model to show there is a 20% increase in the ratio of ice speed to wind speed as the wind speed increases from 10 to 25 m/s. Thorndike and Colony (1982) have used a linear regression model to find the relationship between the ice drift and geostrophic winds in the Arctic Ocean using 1979 and 1980 data from an array of surface drifting buoys. The relationship between ice velocity u, the geostrophic wind G, and the mean ocean current c was examined in the form u=A G+CH-E where A is a complex constant and vectors u, G, c , and c are thought of as complex valued. The complex coefficient A involves a scaling factor IA l and a turning angle 0 A =I Ale -1° . They used the model to show that on average, the ice moves 8° to the right of the geostrophic wind direction and at 0.008 of its speed. In winter and spring, the scaling factor is approximately 0.007 and the turning angle is 5°. In summer, the scaling factor increases to about 0.011 and the turning angle is 18°. Serreze et al. (1989) obtained similar results using a longer data record. Thorndike and Colony (1982) also pointed out 2 that the ratio of the ice speed divided by geostrophic wind when the geostrophic wind direction is the same as mean ice motion direction is higher than that when the geostrophic wind direction is against the mean ice motion direction. Thorndike and Colony (1982) found that the effect of the coastline is felt within 400 km of the coast. Within 400 km from coasts, internal ice stresses are important in winter when the ice converges. Kimura and Wakatsuchi (2000) studied the relationship between sea-ice motion derived from the Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave Imager (SSM/I) imagery and the geostrophic wind in the Northern Hemisphere for seven winters (1991/92-1997/1998) using the same method as Thorndike and Colony (1982). The sea ice motion is highly correlated with the geostrophic wind except for some coastal regions. The scaling factor 12611 is about 0.02 in the seasonal ice zone (e.g. Bering Sea) but is less than 0.008 in the Arctic. Kimura (2004) also applied the same method to study sea ice motion in response to the wind in the Southern Ocean. 1.1.3 Drag coefficient between the ice and atmosphere The wind stress on the surface can be considered as T r 2 r=cDPauio where u, c, is the wind speed at 10 m above the surface, and c, is the drag coefficient between air and surface (water or ice), pa is the density of the air. Normally, 10 3 C„ is — 1.5 over the ocean (Fairall et al. 1996). The drag coefficient over the sea ice varies with the roughness of the surface and ice types (cf. Overland, 1985, Wadhams, 2000). The value of 10 3 CD is 1.3-1.5 for smooth ice but is much greater for 3 nonflat surfaces (Overland, 1985). When the wind speeds are greater than 5 m/s and air temperatures are below freezing, the 10 3 cD is 2.5-3.0 for nearly continuous pack ice, such as first-year ice in seasonal ice zones and central Arctic basin (Overland, 1985). The drag coefficient is also related to the difference between surface ice temperature and surface air temperature (Brown, 1990). The drag coefficient between ice and air is relatively high at the ice edge because the ice edge may consist of rafted and broken-up ice alternating with water (cf. Overland, 1985, Wadhams, 2000). Table 1.1 provides some typical values used in models. The value of 2.8x10 -3 is used by ice-ocean modelers to forecast ice drift along the Canadian east coast. Table 1.1. Air-ice drag coefficient Reference Location Ca, x moo Yao and Tang (2003) North Water 3.0 Tang and Yao (1992) Newfoundland Shelf 2.8 Tang and Gui (1996) Labrador Shelf 2.3 McPhee^(1978) Beaufort Sea 2.7 1.1.4 Ice edge upwelling/downwelling According to equation (1.1), under the same 10 m wind speed, the wind stress on the ice could be higher than the wind stress on the water if the drag coefficient between the ice and atmosphere is higher than the drag coefficient between the water and atmosphere. When the ice is freely drifting, the wind stress on the ice is mainly balanced by water stress on the ice. When the ice is freely drifting, the coupling between ice and water could enhance the stress on the ocean. 4 Using a two dimensional ice-ocean coupled model, Rued and O'Brien (1983) studied response of the ice and ocean to wind forcing. The ocean is covered by sea ice on one side and is ice-free on the other side. The ratio of drag coefficient ((air/ice)/(air/ocean)) is set to 2. The wind is along the ice edge and the ice is to the left side of the wind direction. If the ice could not move, there is upwelling near the ice edge. However, there is downwelling near the ice edge if the ice could move along with the wind because the drag coefficient between the ice and the atmosphere is higher than that the drag coefficient between the water and the atmosphere. Ikeda (1985) studied processes at an ice-covered shelf applicable to the Labrador coast. He used a two-dimensional (vertical seaward) ice-ocean coupled model to study the ice movement driven by alongshore winds with land to the right of the wind. The shelf is covered by sea ice while the deep ocean is ice free. With an air-ice drag coefficient that is twice the air-water drag coefficient, the model produced upwelling at the ice edge by inducing stronger Ekman transport underneath the ice than in the open ocean. At the coast the same wind induces downwelling, giving rise to a nearly closed cross-shelf circulation. He found that the ice/water movement is sensitive to the ice strength and the cross-shore component of the wind. Winsor pointed out that there is ice edge upwelling in a coastal polynya region if the ice is freely drifting because the drag coefficient between the ice and atmosphere is higher than that between water and atmosphere (from Wadhams, 2000). 1.1.5 Ice rheology In order to find the response of ice and ocean to the upwelling favorable wind, we need to calculate the internal ice stress. A nonlinear viscous-plastic rheology proposed by 5 0- ----- Ideal Plastic ^ Viscous Plastic Collision-induced Reology Hibler (1979) has become the standard sea ice dynamics model. A viscous-plastic (VP) rheology is based on quasi-linear dependence between stress and strain rate. Figure 1.1 shows the relation of internal ice stress tensor (Note that in Hibler (1979), the internal ice stress tensor is called internal ice stress) to the strain rates in one dimension. The internal ice stress is proportional to strain rate for small rates, but then reaches a steady level at high rates (Hibler, 1979, see Figure 1.1). 0- S. Free Drift^E 0-  Linear Viscosity Figure 1.1. Various sea ice rheologies shown in one dimension (from Wadhams, 2000), with a being the stess and e the strain rate. Positive strain rate represents convergence. There are other ice rheologies. The stress is proportional to strain rate in the linear viscous rheology. The material yields when the stress reaches a certain level in an ideal plastic rheology (Coon, 1980, see Figure 1.1). In some rheologies based on the mechanics of floe collisions, the stress rises more rapidly than linearly with the rate of convergence (From Wadhams, 2000, see Figure 1.1). The stress tensor a is given by ( a xx^. In a rotation of coordinates with rotation angle 0, the stress tensor transforms to 6 'cos9 sine \ ( crxx cryx 'cos^-sine' - sine cos^o-^sine cosJ\, xY^YY j\. When crx'y and 6 .4 are equal to zero, cr xx and ay'y are called the principal stresses. Figure 1.2 is a elliptical yield curve showing allowable stress states for viscous and plastic rheologies. In Figure 1.2, 0- 1 and 0-2 are the principal components of the two dimensional stress tensor and define the two axes of the yield curve. For the plastic flow, the stress states would lie on the solid curve. For the viscous-plastic ice rheology, the stress states would lie on or in the plastic curve. Figure removed for copyright reason. The original source is Figure 4.6 in Wadhams (2000). Figure 1.2. A yield curve showing allowable stress states for viscous plastic rheologies. (from Wadhams, 2000). Because of large viscosities in regions of nearly rigid ice, the ice model equations based on the VP rheology are typically solved with implicit methods (Hibler, 1979; Zhang and Hibler, 1997). The VP rheology has been used by Yao et al. (2000a, 2000b) to forecast the ice movement and ice concentration for the Labrador Sea and the surrounding continental shelves. Hunke and Dukowicz (1997) modified the viscous-plastic rheology by incorporating an elastic closure, which leads to a fully explicit form. They proposed that the Elastic- Viscous-Plastic (EVP) rheology could respond to wind forcing more quickly and thus is ^o- ' = 0_ xxr^ yx \ xy^0- YY 7 144°W^132 W physically more realistic when atmospheric forcing has a short (hourly or daily) timescale. The EVP rheology could essentially reproduce the VP ice behavior of Hibler (1979) but is computationally more efficient (Hunke and Dukowicz 1997). Employing linearization of viscosities about ice velocities at every elastic time step, as recommended by Hunke (2001), produces the desirable property of maintaining the internal ice stress state on or in the plastic yield curve. There is a parameter which is called "ice strength" in the VP and EVP ice rheology. The higher the ice strength, the stronger is the interaction within the sea ice. The ice strength used in the ice model ranges 5,000Nm -2 to 27,500 Nm -2 (Hibler 1979, Hunke, 2001). Figure 1.3. A map of the Canada Basin and the Beaufort Sea showing the location of Mackenzie Canyon, at the southern edge of the Beaufort Sea, and Barrow Canyon at the eastern edge of the Chuckchi Sea, and Banks Island. 8 1.2. Study area The Mackenzie Shelf is a rectangular platform bordered by Amundsen Gulf to the east and Mackenzie Canyon to the west (Figure 1.3 and 1.4). The length of the Mackenzie Shelf is about 530 km and the width is about 120 km (based on the distance between the coast and the 200m isobath). The Alaskan Beaufort Shelf is between Mackenzie Canyon to the east and Barrow Canyon to the west (Figure 1.3 and 1.4). The width of the Alaskan Beaufort Shelf is about 80 km and the length is about 600 km. The Mackenzie Shelf and the Alaskan Beaufort Shelf are covered with sea-ice from mid-October to June. The ice boundary in summer is highly variable from year to year (Carmack and Chapman, 2003) and varies on shorter time-scales in response to wind events. The landfast ice thickens through winter to about 2 m in April and then melts and/or breaks up by early July (c.f. Dunton et al., 2006). The landfast ice extends seaward to about the 20m isobath (Macdonald and Carmack, 2002). The width of landfast ice on the Mackenzie Shelf is about 60km, while on the Alaskan Beaufort Shelf the width is about 20 km. The outer shelf and slope of both shelves are under the influence of the clockwise movement of sea ice within the Beaufort Gyre. However, there is a narrow slope current towards east along the continental slope deeper than 50m. This slope current is called the Beaufort Undercurrent (Aagaard, 1984; Pickart, 2004). Evidence of upwelling is frequently observed at the offshore edge of the shelf in the southern Beaufort Sea (Carmack and Kulikov, 1998). Upwelling can be strongly influenced by topography, as evidenced in Mackenzie Canyon which crosses the shelf in the southern Beaufort Sea (see Figure 1.3 and Figure 1.4). During conditions favorable to 9 upwelling, upward vertical displacements within the canyon reach 400 m or more (Carmack and Kulikov, 1998). Carmack and Kulikov (1998) found that the upwelling in the Mackenzie Canyon is correlated with northeasterly winds and that relaxation of the upwelled isopycnals after an upwelling event creates an internal Kelvin wave that propagates along the slope to the northeast. These events occur in spite of the nearly continuous sea ice cover that is present from mid-October to May (Williams et al, 2006). Figure 1.4. A map of the Mackenzie Shelf and the surrounding area showing the location of the ice velocity measurements (black square boxes, site 1, and site 2) which are used to study the relationship between ice and wind. The black stars are the four locations of the four NCEP grid points which are nearest to the mooring location. Site 1 and site 2 are two ice motion vector grid points. The distances from site 2 to the Alaskan Beaufort Shelf and to the Mackenzie Shelf are both about 200 km. Site 1 is located on the shelf break. The upper boundary of the Chukchi Summer Water (CSW), originating from the Pacific Ocean lies at a depth of 80 to 100 m, approximately the depth of the shelf break (Shimada et al., 2001). Carmack and Chapman (2003) pointed out that replacement of 10 existing shelf water with CSW by upwelling can potentially enhance ice melt, and provide nutrients for production because the CSW is warmer and nutrient enriched compared to ambient shelf waters. Carmack and Chapman (2003) used a ROMS model (regional ocean model systems) to study upwelling and the shelf/basin exchange (SBE) on the Mackenzie Shelf during the summer. Assuming a fixed ice cover, they found that SBE is small under upwelling favorable wind as long as the ice edge of the offshore ice extends onto the shelf. But an abrupt onset of shelf-break upwelling transpires when the ice edge retreats beyond the shelf break. Williams et al. (2006) studied upwelling forced by wind stress and ice motion within the Mackenzie Canyon. They surprisingly found that smaller alongshore wind stress under ice-covered conditions could cause a similar upwelling magnitude as that caused by larger alongshore wind stress under ice-free conditions. Figure 1.5 (from Williams et al. 2006) shows time series of (a) along shore wind stress, (b) alongshore ice velocity squared. (c) equivalent depth (different color means different mooring locations). The equivalent depth of a particular measured salinity is the depth at which the average offshore CTD profile has that salinity. They assumed a drag coefficient of 1.5 x10 -3 when they calculated wind stress on the surface. From 21 September to 23 October 1995, there was strong upwelling during ice-free conditions. From 16 December 1995 to 25 January 1996, there was similar magnitude of upwelling (in terms of maximum equivalent depth) but it occurred under ice-covered conditions and the alongshore components of wind stress were in general smaller than those from 21 September to 23 October 1995. It seems that the presence of ice appears to amplify the wind-stress. 11 0.2 0.1 (a) -0. 1 Ny 0.1 0.05cr 0 06 -0.05 -0.1 (.) 400 Q. 300 >Tti^200 w 100 b) (c) J^O^J^A^J^O^J^A^J ^ J^A ^J 1994 1995 1996 Figure. 1.5. Time series of (a) along shore wind stress, (b) along shore ice velocity squared. (c) equivalent depth (different color means different mooring locations) (from Williams et al. 2006). Williams et al. (2006) suggested three possible reasons: the first being that the enhanced drag between the wind/ice and ice/water could lead to increased surface stress on the ocean in comparison to that on an ice-free ocean. The second reason is that the internal ice stress, in response to the ice motion on the larger scale of the Beaufort Gyre, is propelling the ice. Williams et al (2006) also pointed out the third reason that could enhance upwelling under ice-covered conditions. Williams et al. (2006) pointed out that under downwelling- favorable wind-stress, the downwelling-favorable ice motion may be blocked so that the presence of ice appears to reduce the wind-stress. The internal ice stress is weaker when the wind is upwelling-favorable than that when the wind is downwelling-favorable. Due 12 to the asymmetry in the internal ice stress, ice motion on the Mackenzie Shelf is preferentially upwelling-favorable. The net effect should lead to greater upwelling over the Mackenzie Shelf than would be calculated from wind-stress alone. 1.3 Objectives Can upwelling driven by wind be enhanced under ice-covered condition? The ice extent in the Arctic Ocean has reduced by about 20% over the last two and half decades, primarily in the western Arctic (Overland and Wang, 2005). Will upwelling be enhanced under the same wind in the future? I want to use a combination of observational results and numerical modeling results to solve this problem. The objectives of this research are thus as follows: (1) To determine if upwelling is enhanced under conditions of reduced ice concentration (e.g. fractional coverage) and decreased ice thickness. (2) To understand which factors influence the ice motion on the Mackenzie Shelf (3) To understand climatological monthly upwelling patterns on the Mackenzie Shelf (4) To develop a practical upwelling index for ice-covered conditions. This work will also help to understand the occurrence of ecological "hot spots" in the area and the impact of reduced sea ice to be generated by warmer temperatures in the western Canadian Arctic. Based on observational results and numerical model results, we can give a better estimate of the ice strength parameter used in the sea ice model. My work is an extension of Dr. Carmack's and Dr. Williams' work. 13 1.4 Methods and structure of the thesis I will use observational data to demonstrate that the ice motion is strongly retarded in March, compared to earlier in the winter. A numerical model is used to demonstrate that the internal ice stress from the pack ice over the deep ocean could reduce the momentum transfer to the water on the shelf when the ice converges. The rest of the thesis is organized as follows: In Chapter 2, there is a description of the observational data. This chapter shows the response of sea ice motion to the wind forcing in the southern Beaufort Sea, and explains why there is less frequent upwelling in August. This chapter also shows the importance of sea ice concentration. In Chapter 3, a numerical model is used to demonstrate other possible reasons besides the landfast ice that can reduce the stress on the ocean under upwelling-favorable winds. The model sensitivities to ice strength and ice thickness are also studied. The result shows which ice strength parameter is more realistic. In section 4.1, the effect of the atmospheric bottom boundary layer on the wind stress acting on the surface is discussed. In section 4.2, we show how much stress is reduced in March. In section 4.3, the relationship between ice motion in the southern Beaufort Sea and the Arctic Oscillation index is discussed. An upwelling index under ice-covered condition is given in section 4.4. In Chapter 5, some conclusions and directions for future work are presented. 14 2. Observational data and results In this chapter, I use observational data to study the response of ice motion to wind forcing in the southern Beaufort Sea. In section 2.1, a description of the observed data is presented. In section 2.2, the results of the seasonality of sea ice response to the wind forcing at a location which is located on the Mackenzie Shelf break are shown. In section 2.2, the monthly mean ice motion is also shown. The spatial pattern of the response of sea ice motion to the wind forcing in each month from November to May is also presented in section 2.2. In section 2.3, we show the importance of sea ice concentration on the ice motion on the Mackenzie Shelf. 2.1 Data The daily NCEP 10m wind data and daily NCEP surface momentum flux data are used in this thesis. The spatially averaged wind from 4 NCEP grid points surrounding site 1 (see Figure 1.4) was used. NCEP wind is currently judged to be the best available estimate of marine wind velocity over the Mackenzie Shelf (Williams et al., 2006). The average direction of the Mackenzie Shelf break is 52°T (Williams et al. 2006). In the NCEP/NCAR reanalysis model, the sea ice does not move and is assumed to be of 100% concentration (i.e., any area over 55% ice concentration was made 100%; areas under 55% were made 0%). The surface drag was evaluated assuming a "land" surface. As the reanalysis model uses a boundary layer model to calculate momentum flux between the sea ice and atmosphere, the momentum flux data is likely to be more accurate than the wind stress calculated based on equation 1.1, and thus the NCEP surface momentum flux data were used. 15 Sea ice concentration data from the SSMR and SSM/I passive microwave radiometer were obtained from the National Snow and Ice Data Center (see Cavalieri et al., 1996, for description). The accuracy of the ice concentration is about ± 5% in winter. The accuracy of ice concentration is relatively low when the ice is thin (below 20 cm). The ice motion data set used here was developed by Fowler (2003) and is available on a 25-km grid from the National Snow and Ice Data Center (NSIDC). The ice motion is derived from the NOAA Advanced Very High Resolution Radiometer (AVHRR), the Nimbus 7 Scanning Multichannel Microwave Radiometer (SMMR), the DMSP Special Sensor Microwave/Imager (SSM/I), and the International Arctic Buoy Programme (IABP) buoy data sets. The accuracy of ice motion degrades during summer due to melt effects (Serreze and Barry, 2005). Therefore, only the ice motion data from November 1 to May 31 is used in this study. 2.2 Seasonal response of sea ice to wind forcing 2.2.1. Seasonal variation of sea ice concentration and ice thickness Figure 2.1 shows the average monthly sea ice concentration from 1985 to 2002. The sea ice concentration increases from September to March. From March to May, the mean ice concentration decreases on the Mackenzie Shelf The average sea ice concentration on the Mackenzie Shelf is above 0.95 in March. In November, the average sea ice concentration near the coast on the Mackenzie Shelf and Alaskan Beaufort Shelf is approximately 0.85. The reduction of sea ice concentration in April and in May is caused by westward ice motion on the Mackenzie Shelf The annual variability of sea ice concentration is high. For example, Figure 2.2 shows the yearly average sea ice 16 (d) Apr (e) May ^ (f) Jun o4 , (b) Feb 140 0W^1Ve* (c) Mar "e4 760o, 140 °W°^1205 \14 ot, ,>s oiv ot, 760 a 1 000 0 975 0 350 0 925 0.900 0.875 0.850 0 825 0800 — 000 (I) Dec e Iv ? 6,9 oAi / 180 140°W concentration in the red region in the top right figure from May 14 to May 21 from 1993 to 2007 (from Canadian Ice Service). (a) Jan .>s •>2 750 ati, 140'w X120°W 6,9 V 69°N 180 0C:̂ _ 140 °W J12O'N^140°W (g) Jul^ (h) Aug^ (i) Sep ,>.$ 84,^ ?..4 04/^,),5- 04,, .,:e 0A" .,̂  o ..,,a oAi 6gN^ 89 71/ / es on/ 760 o ''..7 -*---- ____ _ _.—- --":,,,^16'^---—..-,A;cso No 0 IV . .ti, ,-..____7 0 oc, 4 , 140°W^Azo- " 140°W^140°W^12e44 0 925 0 900 .>,s 04/ 89 ot 760 °pp 1405w 1z0"0 0.975 0 950 (j) Oct (k) Nov Ai^ 7;9 ov^ \\Ts a 7,5 ov i \^ \..,e ov^,,e ovis, \ 69 cA. i I 8. 9 °Iv I '.\50 o4......i  -,......,_^-- ----^lea °C._^...--"No.1 140°w^120u* pi, "----------- 140w^120 " 44 0 875 0 050 0 925 5- 0 500 Figure 2.1 Monthly average sea ice concentration data from the SSMR and SSM/I passive microwave radiometer from 1985 to 2002. 17 by the Canadian Ise Service - Envirsnrnent Canada par le Service ,anadien des places - Environnement Canada 70 ■ ru Data / assure donnee a Old Ice / stelae glace First Sear Ice c glare de premiere annee Y.Ing 1,2 !leans alai, New ice c nouwelle glace —average / maAnne 199a-2007 Sea-ice draft is the thickness of the part of the ice that is submerged under the sea. Melling et al. (2005) has shown that the ice draft increases from October to March on the Mackenzie Shelf The ice draft remains the same from March to June (Melling et al., 2005). The average ice draft is less than 1.0 m in November but is about 2 m from March to June (Melling et al., 2005). 2.2.2. Seasonal response of sea ice to wind forcing on the Mackenzie Shelf 100 - 90 • Historical Total Accumulated Ice Coverage by Type for 0514-0521 Total accumule de la couverture des places hlstorlque par type 0514-0521 CIS WA Beaufort Sea: Mackenzie CIS WA Mer de Beaufort : Mad enz le  80 Canadl Figure 2.2 Yearly average sea ice concentrations in the red region in the top right figure for May 14 to May 21 from 1993 to 2007 (from Canadian Ice Service). We study the response of sea ice to wind forcing on the Mackenzie Shelf at site 1, which is located near the Mackenzie Shelf break (see Figure 1.4). Site 1 is one of the ice motion vector grid points. Figure 2.3 (a) shows a histogram of the time fraction when the daily alongshore component of wind stress is greater than 0.134, 0.086, 0.036 and 0 Pa for each month of 18 -- >0.0 Pa — >0.036 Pa^>0.086 Pa >0.134 Pa .... ..... • .......... . 4.0^ 80 .. afor .... ".^ ...... . ,fte ......^ . ............ .......... •-•"-**# -7,- 60 aTi Ci; 40 E- LI: 20 >0.0 cm/s — >2.6 cm/s ---- >6.2 cm/s ^ >10.2 cm/s (b) 60 - l' ^ "i 40 cur LL 20 .... ......... the calendar year from November to May between 1985 and 2002 at site 1 (see Figure 1.4) (the remainder of the wind stress values are downwelling). Figure 2.3 (b) shows a histogram of the time fraction when the daily alongshore ice speed is greater than 10.2, 6.2, 2.6 and 0 cm s -1 for each month of the calendar year from November to May between 1985 and 2002 at site 1 (Upwelling-favorable ice speed is positive). The 87.5th, 75th, 50th and 0th percentile values of the upwelling-favorable alongshore component of the wind stress are 0.134, 0.086, 0.036 and 0 Pa, respectively. The 87.5th, 75th, 50th, 0th percentile values of the upwelling-favorable alongshore ice speed are 10.2, 6.2, 2.6 and 0 cm s-1 , respectively. 0 ^ Nov Dec^Jan^Feb^Mar^Apr^May Figure 2.3 (a) Histogram of the time fraction when the daily alongshore component of wind stress is greater than 0.134 Pa (thin solid line), 0.086 Pa (thin dashed line), 0.036 Pa (thick solid line), 0 Pa (thick dashed line) for each month of the calendar year from November to May between 1985 and 2002 at site 1 (the remainder of the wind stress values are downwelling). (b) Histogram of the time fraction when the daily alongshore component of ice velocity is greater than 10.2 cm ^ (thin solid line), 6.2 cm s -I (thin dashed line), 2.6 cm^(thick solid line), 0 cm s i (thick dashed line) for each month of the calendar year from November to May between 1985 and 2002 at site 1 (upwelling-favorable ice speed is positive). 19 Figure 2.4. The ratio U, /Ulo versus wind direction (a) in November (b) in January (c) in March (d) in May from 1985 to 2002 at site 1. The red dashed lines are the median of SR versus wind direction; the blue circles represent SR equal to 0.02; while the bold black lines represents the average trend of the coastline of the Mackenzie Shelf. The arrows point to the north. Normally, the Mackenzie Shelf is covered by ice from mid-October to May with more pronounced ice motion in November and December. This implies greater potential for upwelling in November and December compared to other months. The percentages of alongshore ice speed greater than 10.2 cm s -1 and 6.2 cm s -1 decrease from December to March and then increase from March to May. Although the frequencies of alongshore 20 components of wind stress greater than 0.086 Pa and 0.134 Pa in November and March are similar, the percentages of alongshore ice speed greater than 6.2 cm s -1 , and 10.2 cm s -1 in November are higher than those in March. This implies that the internal ice stress is higher in March than that in November on the Mackenzie Shelf The ratio u, ulo is the speed ratio (hereinafter SR), with U, the ice speed and U to the wind speed. Figure 2.4 shows the SR versus wind direction in November, January, March, and May from 1985 to 2002 at site 1. The median SR when the alongshore components of winds are upwelling-favorable are 0.024, 0.021, 0.017, 0.012, 0.008, 0.011, and 0.015 in November, December, January, February, March, April, and May, respectively. A high SR means that the ice moves relatively fast under the same wind. In November, the median SR is relatively large. This implies that the internal ice stress is not strong when the wind is upwelling-favorable in November. The internal ice stress is not strong because the ice concentration is around 0.85 and ice thickness is below lm near the coast on the Alaskan Beaufort Shelf and the Mackenzie Shelf in November. When the alongshore component of winds are upwelling-favorable, the median SR is lowest in March. The average ice concentration is above 0.95 and the ice thickness is around 2m in March on the Mackenzie Shelf. It would appear that the internal ice stress substantially retards the sea ice motion in March. The median SR in May is higher than in March. One possible reason is that the monthly average ice concentration on the Mackenzie Shelf is relatively small (about 0.8) in May (Figure 2.1). Although the sea ice concentration is relatively small in May compared to that in December and January, the SR in May is smaller than that in December and January. The percentage of alongshore ice speed greater than 10.2 cm s -1 is smaller in May than that in January although there are more 21 upwelling-favorable winds in May than that in January. One possible reason is that the ice is thick in May. The average wind-driven ice circulation pattern from 1988 to 1994 in the Beaufort Sea and Beaufort Gyre is an anti-cyclone circulation (Emery et al., 1997). Figure 2.5 shows the mean sea ice motion in the southern Beaufort Sea from 1985 to 2002 using yearly averaged ice motion data from NSIDC (Fowler, 2003). The ice moves southwestward near Banks Island and then moves westward on the Mackenzie Shelf. From Figure 2.3, we can see that the SR when the wind blew to the east is smaller than that when the wind blew to the west in November. Williams et al. (2006) points out that the eastward motion tends to be blocked by Banks Island and the Canadian Archipelago and is against the climatological drift of ice in the Beaufort region. Figure 2.5 The mean ice motion in the southern Beaufort Sea from 1985 to 2002. Figure 2.6 shows the ratio u, /u i , versus ice direction in February, March, and April from 1985 to 2002 at site 1. In February, March, and April, the internal ice stress is high because the sea ice concentration is high and ice is thick on the Mackenzie Shelf The SR 22 is low when the ice moves toward the south. When the ice moves along —275°T, the SR is the highest. The occurrence of landfast ice on the Mackenzie Shelf, combined with the stamukhi, or rubble ice field formed by an ice convergence at the outer boundary of the landfast ice, complicates the interpretation of ice motion. Figure 2.6 The ratio U, /Ulo versus ice direction in February, March, and April from 1985 to 2002 at site 1. The red dashed line in figure is the median of SR versus ice direction while the blue circle denotes SR equal to 0.02. The arrow points to the north. The landfast ice extends approximately to the 20 m isobath on the Mackenzie Shelf at the end of the winter (Carmack and Macdonald, 2002). The trend of the 20 m isobath at same latitude as site 1 is about 277°T. As 275 °T and 277 °T are about the same, it would appear that the stamukhi zone on the Mackenzie Shelf exhibits a strong influence on the ice motion when the ice moves toward the landfast ice and sea ice concentration is high and ice is thick on the Mackenzie Shelf. Thorndike and Colony (1982) found that the effect of the coastline is felt within 400 km of the coast. Within 400 km from coasts, 23 internal ice stresses are important in winter when the ice converges. The distance from site 1 to the Mackenzie Shelf coast and Alaskan Beaufort Shelf coast are about 120 km and 260 km, respectively. There is a 55 degree difference between the two coastlines near Mackenzie Canyon (Williams et al. 2006). The alongshore ice motion on the Mackenzie Shelf could also be retarded by the landfast ice on the Alaskan Beaufort shelf when the ice concentration is high and ice is thick. When the ice moves northward, the SR is small because the mean sea ice motion near Banks Island is southward. 2.2.3. Monthly mean sea ice motion Figure 2.7 shows monthly mean sea ice motion in the southern Beaufort Sea from 1985 to 2002. The monthly mean sea ice motion direction near the coast is nearly parallel to the coast and upwelling-favorable from October to June. The mean sea ice motion is westward on the Mackenzie Shelf from October to June. The mean westward sea ice speed at site 1 is about 4 cm s -1 in November and in December. The mean westward ice speed decreases from November to March. In March, the mean westward ice speed at site 1 is about 1 cm s -1 . The mean westward ice speed increases from March to May. In May, the mean westward ice speed is about 3 cm s -1 . The anti-cyclonic sea ice motion (centered at 79°N, 140°W in May) retreats south into the Beaufort Sea in June (centered at 75°N, 140°W). In July and in September, the mean anti-cyclonic ice motion is weak. In August, the mean ice motion in the Beaufort Sea is not anti-cyclonic. Serreze et al (1989) pointed out that the ice motion in the Canada Basin can become net cyclonic for periods lasting at least 30 days in late summer to early autumn. This is the reason why the mean ice motion is not anti-cyclonic in the Canada 24 Basin in August. From November to June, upwelling-favorable winds occur more frequently than downwelling-favorable winds on the Mackenzie Shelf. Because the mean ice motion is westward in May and June in the southern Beaufort Sea, the sea ice concentration is lower on the Mackenzie Shelf than that on the Alaskan Beaufort Shelf. In summer, upwelling-favorable winds occur less frequently than those in winter on the Mackenzie Shelf, hence there is more upwelling on the Mackenzie Shelf in October, November, and December than in August. (a) Jan^ (b) Feb Figure 2.7. Monthly mean sea ice motion from 1985 to 2002. 25 (i) Sep (k) Nov (j) Oct (e) May ^ (f) Jun Figure 2.7. Monthly mean sea ice motion from 1985 to 2002. 26 2.2.4. Seasonal response of sea ice to wind forcing in the southern Beaufort Sea Now we consider the spatial distribution of the median ratio of ice speed divided by wind speed when the Ci10 • ri,„ >0 , where Ci io is the daily 10 m wind vector at one location and 0 1„ is the mean ice motion from 1985 to 2002 at the same location. When (1- 10 • (7- Ice > ° the angle between the wind direction and mean ice motion direction is less than 90°. Therefore, wind direction is not against the mean ice motion when Ow • U1Ce > ° • When 010 • (I- we > 0 , most winds are upwelling-favorable near the coast because mean ice motion near the coast is nearly parallel to the coast and upwelling-favorable. Therefore, we call the ratio an upwelling-favorable speed ratio, USR. We calculate the median USR (MUSR) in each month from November to May. Figure 2.8-2.14 show the contours of MUSR in November, December, January, February, March, April, and May, respectively. The MUSR is about 0.02 in the Canada Basin in November. The internal ice stress is not strong in November in central Arctic. Note, the ratio has been scaled by a factor of 100 in Figures 2.8 to 2.15. Because both ice thickness and ice concentration are high near Banks Island (c.f. Serreze and Barry, 2005), the MUSR is lowest near Banks Island from November to May. From November to March, the MUSR reduces because both ice concentration and ice thickness increase in the southern Beaufort Sea. From March to May, the MUSR increases because the mean ice concentration decreases from March to May. Note that the reduction of mean ice concentration on the Mackenzie Shelf is because the mean ice motion is westward on the Mackenzie Shelf. From December to May, the MUSR in the eastern part of Alaskan Beaufort Shelf coast is smaller than that near Barrow Canyon. The internal ice stress is relatively small near 27 Barrow Canyon because the ice concentration is relatively low and ice is less thick near the Barrow Canyon from November to May. The seasonal variation of MUSR is relatively small in the central Canada Basin than that near the coast. Figure 2.15 shows the contours of the ratio of MUSR in November divided by MUSR in March. The ratio is about 2 in the central Canada Basin, but about 4 on the Mackenzie Shelf and on the Alaskan Beaufort Shelf, since the internal ice stress is stronger near the landfast ice than in the central Canada Basin. Figure 2.16 shows the ratio u 1 iulo versus ice direction in February, March, and April from 1985 to 2002 at site 2. From this figure, we can see that the ice motion at site 2 is strongly retarded when the ice moves toward the landfast ice. The distances from site 2 to the landfast ice on the Alaskan Beaufort Shelf coast and the Mackenzie Shelf coast are both about 170 km. Therefore, when the sea ice moves toward the landfast ice, the landfast ice could strongly retard sea ice motion located 170 km away when the ice is thick and the ice concentration is high. 28 Figure 2.8. The contours of MUSR in November from 1985 to 2002. MUSR means the median ratio of ice speed divided by 10 m wind speed when the angle between daily wind direction and mean ice motion direction is less than 90°. The ratio has been multiplied by a factor of 100 in this and subsequent figures. Figure 2.9. The contours of MUSR in December from 1985 to 2002. 29 Figure 2.10. The contours of MUSR in January from 1985 to 2002. Figure 2.11. The contours of MUSR in February from 1985 to 2002. 30 Figure 2.12. The contours of MUSR in March from 1985 to 2002. Figure 2.13. The contours of MUSR in April from 1985 to 2002. 31 May Figure 2.14. The contours of MUSR in May from 1985 to 2002. Figure 2.15. The contours of the ratio of MUSR in November divided by MUSR in March from 1985 to 2002. 32 (a) 1 9-Dec-1 995 74 °N 73°N 72 °N 77°N i 70°N, 69°N I = 740314, 1350W 0,0) 130°W 1250W 124 (b)^1 9-Dec-1 995 140°1/4/ 135 0w 130 °W 125°W 12eW 1 000 0 975 - 0 950 1 0.925 0,900 0.875 0.850 0 825 4 800 Figure 2.16 The ratio U, /U10 versus ice direction in February, March, and April from 1985 to 2002 at site 2. The meaning of the red dashed line and solid blue line is the same as in figure 2.6. The arrow points to the north. Figure 2.17. (a) The ice concentration in the southern Beaufort Sea on December 19, 1995. The star in the figure is the position of site 1. (b) The ice motion vectors in the southern Beaufort Sea on the same day. The scale placed in the Amundsen Gulf denotes an ice velocity of 20 cm s-1. 33 2.3 The effect of sea ice concentration of ice motion Although in general the ice motion is strongly retarded in mid-winter (February, March, April), sometimes the ice can move fast in mid-winter. For example, the ice speed was higher than 30 cm s -1 on the Mackenzie Shelf on March 28, 2003. Why is there strong ice motion in mid-winter when the ice thickness is about 2m and average ice concentration is high? The following analysis shows that sea ice concentration has a strong effect on the sea ice motion. One major cause for sea ice motion attenuation at site 1 is the internal ice stress from the landfast ice. Area 1 is the boxed area in Figure 2.17 (a). If part of the ice concentration in area 1 is low, the internal ice stress from the landfast ice is low. Figure 2.17 (a) shows the ice concentration in the southern Beaufort Sea on December 19, 1995. Figure 2.17 (b) shows the ice motion vectors in the southern Beaufort Sea on the same day. The internal ice stress from the landfast ice on the Alaskan Beaufort Shelf is small because the ice concentration on the Alaskan Beaufort Shelf near the Mackenzie Canyon was below 0.8. The ice speed in Mackenzie Canyon was above 20 cm s -1 implying that the internal ice stress from the landfast ice was small on that day. However, the average sea ice concentration in area 1 was high because the ice concentration in most areas on the Mackenzie Shelf was above 0.95 on that day. Therefore, we also consider the minimum sea ice concentration in area 1. With 66 ice concentration grid points in area 1, the minimum ice concentration in area 1 means the smallest ice concentration among the 66 values. We use minimum ice concentration because the internal ice stress from landfast ice on the Alaskan Beaufort Shelf and/or the Mackenzie Shelf is low if the minimum sea ice concentration in area 1 is low. 34 7') 10 f!. 0 a -(a) 0.2 0.1 ah 0 (c) , (d) , 29 ^ 1 ^ 2 ^ 3 ^ 4 ^ 5 ^ 6 ^ 7 Feb ^ Mar 2000 Figure 2.18 The time series of (a) the ice motion vector at site 1, (b) the alongshore component of wind stress at site 1, (c) the average sea ice concentration (blue line) and the minimum sea ice concentration (red line) in the area 1 [which is surrounded by the box in Figure 2.17(a)], and (d) the wind vector at site 1 from February 29 to March 7, 2000. 0 0.8 0.6 s. 4 3 2 a. %I -2 -4 35 Tze125'w140°W 135 °W 130°W 140°W 135°W 1 30°W 730°W 1 250w 120 " 06-Mar-2000 73°N 77 N 70QN 69)v I4ew 135 0w 1300w 125 0w 120 29-Feb-2000 74 °N 7954 73°N 71°N 70°N, 69 t„ 140°W 135 0W _ A0.4,1 130aW 125 ° W 02-Mar-2000 74'N 73°N 72°N 71°N 70'N , 63'N / 140c1/4, 135°W 04-Mar-2000 74°N 73°N , , 72°N 71°N 1 70°N 69 / NOw 135°W 130 °W 1Z5 °*1 73°N,„ 72°N ! 71°N 70°N „. °N lzew 12° " 01-Mar-2000 74°N 73°N 7°A4 77°N 1 63°N I4eW 1350W 130aW 125°W 12e" 0 900 03-Mar-2000 74°N ^ 73N 72"N 77 N 70°14 1 1 89°N I 05-Mar-2000 74 °N 0 500 07-Mar-2000 74 °N 73°N 73°N I 77°N I TO°N 69 a,, 140°W 135°W <0 000 1 000 0.975 0.950 0.925 0.875 0 850 0.625 <0.600 1 000 0.975 0.950 0 925 0.875 0.650 0 825 Figure 2.19. Sea ice concentration in the southern Beaufort Sea on Feb 29 to March 7, 2000. The stars show the location of site 1. 36 02-Mar-2000 744 QW 132 °W^120°W 04-Mar-2000 0.5 144 °14,^1320w^12ew 06-Mar-2000 03-Mar-2000 744 °4, 132ow vew 05-Mar-2000 29-Feb-2000 ^ 01 -Mar-2000 07-Mar-2000 Figure 2.20. Wind fields over the southern Beaufort Sea on Feb 29 to March 7, 2000. The points show the location of site 1. 37 03-Mar-2000 05-Mar-2000 144°W 132 °W 12()" 29-Feb-2000 ^ 01-Mar-2000 02-Mar-2000 04-Mar-2000 06-Mar-2000 ^ 07-Mar-2000 Figure. 2.21. Ice motion vectors in the southern Beaufort Sea on Feb 29 to March 7, 2000. The points show the location of site 1. 38 We next contrast 2 periods (the first from Feb. 29 to Mar. 7, 2000 and the second from Feb. 25 to Mar. 4, 2003 to demonstrate that the ice concentration exhibits a strong influence on the ice motion when the ice concentration is high and the ice is thick. Figure 2.18 shows the time series from Feb. 29 to Mar. 7, 2000 for (a) the ice motion velocity at site 1, (b) the alongshore component of wind stress at site 1, (c) the average ice concentration in area 1 (blue line) and the minimum sea ice concentration in area 1 (red line), and (d) the wind velocity at site 1. Figure 2.19 shows the sea ice concentration in the southern Beaufort Sea from Feb. 29 to Mar. 7, 2000. Figure 2.20 shows the wind fields over the southern Beaufort Sea from Feb. 29 to Mar. 7, 2000. Figure 2.21 shows the ice motion vectors in the southern Beaufort Sea from Feb. 29 to Mar. 7, 2000. During this period, the alongshore wind stress is above 0.05 Pa (Figure 2.18b). Figure 2.20 shows that the wind storm were relatively large from Mar. 1 to Mar. 4. Because the wind storms were relatively large, the internal ice stresses caused by wind convergence were not strong during this period. However, the ice speeds on the Mackenzie Shelf were less than 10 cm s -1 during this period (Figure 2.18c). Figure 2.19 shows that sea ice concentration in the southern Beaufort Sea was high (above 0.95) during this period. In late February and March, the ice is normally about 2 meters. The internal ice stress was strong because ice was thick and ice concentration was high during this period (Figure 2.22b). Next contrast with the situation during Feb. 25 to Mar. 4, 2003. In figure 2.22, from Feb.25 to Mar. 4, 2003, the ice speeds at site 1 were relatively high (above 10 cm s -1 ). On Feb. 28, the ice speed at site 1 was higher than 30 cm s -I . The alongshore wind stresses were higher than 0.05 Pa from February 27 to March 4. 39 0.2 0.1 (b) 25 Feb 2003 26 27 28 1 Mar 2 3 4 S' to a o aco ti -to 0 0 0.8 t; 0.6 .r.4 4 2 m 0 0 v -2 1 -4 Figure 2.22. The time series of (a) the ice motion vector at site 1, (b) the alongshore component of wind stress at site 1, (c) the average sea ice concentration (blue line) and the minimum sea ice concentration (red line) in area 1, and (d) the wind vector at site 1 from February 25 to March 4, 2003. 40 25-Feb-2003 74°N 7,, 73°N, 72°N, 71°N 1 7o°N1 63°N1 1400,4( 135°‘N 130°W 125 0w 120 74 °N 73°N1 720Ni. 710N) ff 70°N 69°N 740°W 135°W 160 °W 1Z5°W 120 26-Feb-2003 74°Nr 73°N 1fri 72 °N k. 77°N 70 0N '33 N, 12°N4 140°W 135 °W 130°W 125 °w 0.900 28-Feb-2003 1 000 0.975 0.950 0 925 0 875 0.850 0.825 <0.800 27-Feb-2003 02-Mar-2003 74°N 73°N 1 72 0N 7 7 °N 70 °N A 69 ON 41fte. 140°w 1350w _ z2_ 0,44 1 30°W 1 25°W ° 03-Mar-2003 74°N —ft__ 73°N 72° 71°N 70°At 69°N 01 -Mar-2003 74°N 730N1 11, 72°N New 135ow 130 0W 125°W 120 1 000 0 975 0.950 0.925 0.900 0 875 0.850 0 825 <0 800 140°w 135 0w 04-Mar-2003 74 t)/y 73°N 72°N j. 71 0N TON ti^69°N 140°W 135°W130°W izs'w 12e* _ ^o 1 30°w 125'w 120 71°N 70° , 6-9 0N/ Figure 2.23 Sea ice concentration in the southern Beaufort Sea on Feb 25 to March 4, 2003. The stars show the location of site 1. 41 27-Feb-2003 01-Mar-2003 6:9 0 744 °4' new azew 03-Mar-2003 28-Feb-2003 144°14' new 120°44 02-Mar-2003 04-Mar-2003 25-Feb-2003 ^ 26-Feb-2003 Figure 2.24 Wind fields over the southern Beaufort Sea on Feb 25 to March 4, 2003. The points show the location of site 1. 42 25-Feb-2003 27-Feb-2003 144 'w 1 32°w 12e14 01-Mar-2003 26-Feb-2003 28-Feb-2003 02-Mar-2003 / 4401,v 132-„W %L'° ' 03-Mar-2003 ^ 04-Mar-2003 Figure. 2.25 Ice motion vectors in the southern Beaufort Sea on Feb 25 to March 4, 2003. The points show the location of site 1. 43 Figure 2.23 shows the sea ice concentration from Feb. 25 to Mar. 4, 2003. Figure 2.24 shows that the winds were upwelling-favorable from Feb. 26 to Mar. 4, 2003. Figure 2.25 shows the ice motion fields in the southern Beaufort Sea from Feb. 25 to Mar. 4, 2003. The sea ice concentration on the Mackenzie Canyon and Mackenzie Shelf decreased from Feb. 25 to Feb. 28, 2003 (Figure 2.23). The ice concentration near the Mackenzie Shelf coast decreased because ice moved away from the landfast ice on the Mackenzie Shelf (Figure 2.25). The internal ice stress is nearly zero when ice diverges. Because the internal ice stress from the landfast ice on the Mackenzie Shelf from Feb. 25 to Feb. 28, 2003 was weak, the ice could move fast during this period. On March 4, 2003, the wind direction was toward the landfast ice on the Alaskan Beaufort Shelf (Figure 2.22d). The ice on the Mackenzie Shelf could move fast because sea ice concentration on the Mackenzie Shelf was less than 0.8 on March 4, 2003 (Figure 2.23). From the above two cases, we see that the response of ice motion to wind forcing has strong relationship with sea ice concentration. The sea ice concentration is related to the wind forcing. The reduction of sea ice concentration on the Mackenzie Shelf from Feb. 25 to Mar. 1 is because the wind pushed the ice away from the landfast ice on the Mackenzie Shelf. The ice could move fast towards the coast on Mar. 4 as the ice concentration was low on the Mackenzie Shelf. The alongshore ice motion has a strong relationship with sea ice concentration on the Mackenzie Shelf because the internal ice stress is high when the ice concentration is high and the ice is thick. The ice motion within 142°T (°T represents degree from true north) and 270°T is considered here. Under such conditions, the ice motion is upwelling- 44 I II0 0^0.2^0.4^0.6^0.8 Ice concentration 0.2^0.4^0.6^0.8 Ice concentration (c) Ui> 9.3 cm/s Minimum ice concentration Average ice concentration favorable and the ice moves toward the landfast ice on the Mackenzie Shelf and/or on the Alaskan Beaufort Shelf. Figure 2.26 (a) and (b) show the probability density functions of daily average ice concentration of area 1 when the ice motion direction is in the range of 142-270°T and the alongshore component of ice speed is above 9.3 cm s -1 and below 9.3 cm s -1 from January 1 to May 30 between 1989 and 2002, respectively. The standard deviation of the alongshore ice speed is 4.67 cm s -1 from January 1 to May 31 between 1985 and 2000 at site 1. The value of 9.3 cm s -1 is twice the standard deviation. The median daily average sea ice concentrations in area 1 when the alongshore ice speed is above 9.3 cm s -1 and below 9.3 cm s -1 are 0.90 and 0.95, respectively. Figure 2.26. The probability density functions of average sea ice concentration in area 1 when the ice direction is in the range of 142-270°T and (a) the alongshore ice speed was above 9.3 cm s -1 and (b) the ice speed was below 9.3 cm s' from January 1 to May 30 between 1989 and 2002. The probability density functions of minimum sea ice concentration data in the same area when the ice direction is in the range of 142-270°T and (c) the alongshore ice speed was above 9.3 cm s -1 and (d) below 9.3 cm s -1 during the same period. Ui in the figure means the alongshore component of the ice velocity. 45 Figure 2.26 (c) and (d) show the probability density functions of minimum ice concentration of area 1 when the ice direction is in the range of 142-270°T and the alongshore ice speed is above 9.3 cm s -1 and below 9.3 cm s -1 , respectively. The minimum ice concentration is considered here because the internal ice stress from the landfast ice on the Alaskan Beaufort Shelf and/or the Mackenzie Shelf is low if the minimum sea ice concentration in area 1 is low. Note that high alongshore ice speed tends to be associated with low minimum ice concentration in area 1, e.g. 64% of the high velocity cases has minimum ice concentration smaller than 0.8 versus only 32% of the low velocity cases. From the two cases (Feb. 29 to Mar. 7, 2000 and Feb. 25 to Mar. 4, 2003) and Figure 2.26, we see that sea ice concentration in area 1 has a strong impact on the ice motion on the Mackenzie Shelf. In general, the ice motion is retarded in mid winter and spring (January to May) because the ice thickness is above 1.5 m in the southern Beaufort Sea. The ice could move fast during January to May when the minimum sea ice concentration in area 1 is not high. The strong ice motion from Feb. 25 to Mar. 4, 2003 shows that the ice motion on a certain day is not only related to the wind on that day, but is also related to the winds on the previous days. 46 3 Numerical model and model results In this chapter, I use a numerical model to show that the alongshore ice stress on the shelf water could be smaller than that on the deep water under the same surface wind if the ice converges. The model sensitivity to the ice strength parameter and ice thickness is studied. The model results are found to be realistic when the ice strength parameter is taken to be 27,500 Nm-2 rather than 5,000 Nm2 . 3.1 Sea ice model In dynamic-thermodynamic ice models (e.g., Hibler, 1979), the internal ice force F is expressed as the divergence of the isotropic two-dimensional internal stress tensor a, i.e. F = V • 0- , which depends on the stress-strain relationship. In keeping with common usage we refer to P' as the internal ice stress. The ice model employed here uses the Dr. Paul Budgell's ice model in ROMS (regional ocean model system) version 3.0. Under wind forcing, four external forcing mechanisms (Coriolis force, wind stress fa, ice-water stress i-s,„ and gravity due to the tilt of the ocean surface H0 ) and the internal ice stress F , drive the ice motion. The governing equations for ice motion are as follows: u,^ Ha om( a — fv,)= c z- +^+ — mg at ax av,^ Ha0m(— + fu,)= craly + crat wty + F y — mg Here x, y are the alongshore and seaward coordinates, while u,, v, are the respective ice velocities, fa„ -taw are the wind stress on the ice and ocean, respectively. The suffixes x and y on r r„„ , F denote the x and y components of each term, f is the Coriolis ay (3.1) (3.2) 47 parameter, m = p,h, where h is the equivalent ice thickness (c multiplied by the mean ice thickness, c is the ice concentration), and p, is the ice density. The ice-water stress zw i on the ice is given by a quadratic stress law: PW C1W[(U 1 ^)2 + (vi 17,4, ) 2v /2 (u, iiw )^(3.3) Twi,y^PwCiw[Oit 1702 ± (vi^il/ 2 (v^(3.4) Here /7,,,,Tw represent the average alongshore and cross-shore components of water velocity above 10 m depth, respectively, while C,w is the drag coefficient between the sea ice and water, and pw is water density. The parameter c, w, is taken as 0.0075 as given in Budgell's model. The viscous-plastic rheology proposed by Hibler (1979) is given by a constitutive law that relates ay and the rates of strain E ij through an internal ice pressure P and nonlinear bulk and shear viscosities, c - and?? , such that the principal components of stress lie on an elliptical yield curve. The constitutive law is given by cry =^+ (C. q)i.kkgi; – —P2 gy ^ (3.5) where au^1 ,au av, .^av .^au av , 512=-2 l—ay + —a ) , 622 =^ekk = ell ± e22 = aX ay au =i ifi=j andOifi ^ j. Alternatively, (3.5) can be rewritten in the form — 1 cso +77–c  o-,81+-4c- 456=eu•277^477c- (3.7) (3.6) 48 The viscosities are defined in terms of the strain rates, P 24 24e 2 A = [(g.121 + ^ )( 1 e -2 ) 4e -242 2Z. I1L'22^e-2 / 2 and become infinite in the limit of zero strain rate. Here, e= 2 is the ratio of the major and minor axis lengths of the elliptical yield curve. Using this constitutive law, the force components due to internal ice stress (calculated from F, =^ax ., are a „^,au^ av P, a^ au av„ JFx^+ CJ— + LC —71 J — --I +- 1. 77l— +—) ax ay 2 ay ay ax a „^,av r^,au P, a^au av„ F^+ LC —71 J—^+—[77(— + —).1Y ay aX 2 ax^ax In the ice model, the ice pressure is given by: P = P *hexp(—C * (1— c))^(3.8) where C* is a constant parameter and set to 20 to produce a rapid decrease in viscosity for ice concentration less than 85% (Hakkinen, 1990), and P* is called the ice strength. Hunke and Dukowicz (1997) presented an alternative regularization, accomplished by introducing an elastic contribution to the strain rate in such a way that the elastic-viscous- plastic (EVP) and viscous-plastic (VP) models are identical at steady state, ^1 ea,^1 j ^0", + 71^crkk8, + 8, =E at^277^477c 44- (3.9) where E is the elastic parameter. E is defined in terms of a damping timescale T for elastic waves, as E _ T 49 ao-, e 2^1— e 2^P^P — ±^ C r 8^=^6at^2T u^4T kk u 4T u 2TO, m(a2 /3 2 )u n+, = ^ (au" + fiv")+ a Ate r^n+1 +r,ax. + fi ^ + T y aX\ tacr l;i' where T is a tunable parameter (Hunke, 2001). Then the stress equation (3.9) becomes (3.10) All of the coefficients on the left-hand side are constant except for P , which changes only on the longer time step At. The method to calculate o-u is shown in Appendix A. Given the updated stress tensor^, the momentum equations (3.1) and (3.2) are marched forward as follows: n+1^n n+1 U — U^(ICU—m^ u n+1 )+ mfv n+1 Ate^axi^at ,x^w ax n+1^n V^— V^u'-' n,., 2 j n+1 ar--4m —^ +i-c„,,, +ci(17,,„ —v n+1 )— mfu n+1 — mg Ate^axi ay (3.11) (3.12) where c' =^, Ate is the EVP subcycling time step, and r-i„, represents the average water velocity above 10 m depth. Equations (3.11) and (3.12) can be solved for the velocity components as follows: (a 2 + 13 2 )1) n+1 =^(avn — flun)+ a Ate ( 2,1̂ + T aX a 0_ in; F 1 +fi ^ ax; + TX where a = m I Ate +c', = mfAt „ Tx = ,x^w mg aX Ty ^axo c17,‘„ mg^ To make the ice model stable, the following requirement needs to be satisfied: 50 T> P(1  e 2 ) 2 At:, 32mAx 2 e 2 A (Hunke, 2001)^(3.13) In the model, A min =10 -11 s -1 . This means we limited the viscosity c above with max = 5.0 x 10 1° P kg/s because P_ 2A 3.2 Ocean modeling and ice-ocean coupling The ocean model component is based on the ROMS version 3.0. ROMS is a baroclinic general ocean model, the development of which is described in a series of papers (Song and Haidvogel, 1994; Haidvogel and Beckmann, 1999). ROMS uses a topography- following coordinate system in the vertical that permits enhanced resolution near the surface and bottom (Song and Haidvogel, 1994). The stress on the ocean is given by: = (1—^+ c z,w . (3.14) where Fm„, , f,„, are the wind stress and ice stress on the ocean, respectively, and c is the sea ice concentration. The wind stress on the water is assumed to be b,z a, , where b, denotes the ratio of the air-ice drag coefficient to air-water drag coefficient. In the model, b = 1.0 . (The model is not sensitive to this value in the five cases that I have run because there is no open water.) The ice-water stress on the water z, w is —fw i 3.3 Model configuration A two-dimensional model is devised to study upwelling under the ice. The grids consist of four grids in the x direction (alongshore) and 325 grids in the y direction 51 (cross-shore) with the land at the south boundary. The alongshore boundary conditions are periodic for all variables. Anf-plane approximation is used, with f =1.4 x 10 -4 s -1 . Table 3.1 Parameter and constants used in the model run Parameter Symbol Value The ratio of air-ice drag coefficient divided by air-water drag coefficient k 1 Ice-water drag coefficient Cw 0.0075 Bottom drag coefficient 7 5x10-4 ms -1 Ice pressure parameter C* 20 Ice density p 910 kg M -3 Reference water density 13, 1025 kg M -3 Coriolis parameter f 1.4x10-4 m s' Subcycling time step for ice model Ate 0.0025 s damping timescale T 37.5 s Time step for internal mode 150 s Time step for external mode 5 s Horizontal grid spacing is 1 km between the coast and 200 km offshore. From 200 km to 640 km, the spacing increases from 1 km to 6 km. Figure 3.1 shows the model bathymetry and initial density profile. The 30 vertical grid points are used with more grid points concentrated near the surface and bottom to resolve the boundary layers. Standard dynamical assumptions are made: no flow or density flux through solid boundaries, linearized bottom stress with a coefficient of 5x10 -4 m s-I , and a Mellor—Yamada level- 2.5 turbulence closure scheme (Mellor and Yamada, 1982). The offshore boundary 52 50 50 100 100i 150ft 150 200 200 250 250 0 ^ (a)^ (b) 300 ^300^0 50^100^150^200 1020^1022 1024 1026 1028 1030 Offshore Distance (km) Density (kg m condition used is the zero gradient boundary condition. The model uses a no-slip boundary condition at the coastal boundary. The model parameters are shown Table 3.1. Note the Subcycling time step for the ice model ( At e ) is small here in order to satisfy the requirement (3.13). Table 3.2 shows the wind stress, initial ice thickness and ice strength used for 5 cases which will be discussed. Figure 3.1. (a) The model bathymetry in the offshore direction, and (b) the initial density profile. Table 3.2. Wind stress, initial ice thickness, and ice strength for 5 cases. Alongshore component wind stress (Pa) Cross-shore component wind stress (Pa) Initial ice thickness (m) Ice strength (Nm-2) Case 1 -0.08 a -0.08b 1.5 9,000 Case 2 0 -0.08 2.0 27,500 Case 3 0 -0.08 2.0 5,000 Case 4 0 -0.08 0.5 27,500 Case 5 0 -0.08 1.5 27,500 a. The upwelling-favorable winds are negative in alongshore direction. b. In cross-shore direction, the wind stress is negative when the wind is toward the coast. 53 0-0.028 o -0.03 3.4 Model results 3.4.1. Case 1 The alongshore component of wind stress is upwelling-favorable and is 0.08 Pa. The cross-shore component of wind stress is towards the coast and is 0.08 Pa. P * is 9000 Nm -2 . This value is smaller than 27,500 Nm -2 , which is commonly used in the ice model (cf. Hunk, 2001). The value of 9000 Nm -2 was used by Ikeda (1985). With the small value of ice strength used, the interaction within the sea ice will decrease. The initial ice thickness is 1.5 m and ice concentration is 1. Because the ice concentration is 1 and the ice converges in this case, the selection of b does not influence the model results since the wind stress on the water is O. 0 -0.05 -oa) c,9-. -0.1 a) O ci -0.15 rn 0 Zc -0.2  ^day 1 - day 3 - - - day 6 ■ I X 50 100 150 200 250 300 350 400 1 , —day 1 — day 3 _ - day 6 50^100^150^200^250 ^ 300 ^ 350 ^ 400 Offshore Distance (km) Figure 3.2. Alongshore components (top) and cross-components (bottom) of the ice velocity at day 1 (solid line), day3 (dashed line), and day 6 (dash-dot line) plotted as a function of the offshore distance. 54 50 100 150 200 250 300 Offshore Distance (km) 50 100 150 200 250 300 Offshore Distance (km) ,0 5 0. 0.05 § 0 5 ta, -0.05 0 4 (a) a 0.05 § 0 ^ ; -0.05 -(p) 2 Figure 3.2 shows the alongshore and cross-shore components of the ice velocity at day 1, day 3, and day 6. The dynamical balance for the ice is examined using each term plotted in Figure 3.3. From 50 km offshore, the internal ice stresses make the ice a nearly rigid body (Figure 3.2). (c)^ y^day 6 y-100 km Coriolis^Water Internal x Tilt Wind Figure 3.3. Momentum balance for ice in (a) alongshore direction and (b) cross-shore direction at day 6. The red line represents water stress on the ice; the blue line is the wind stress on the ice; the green line is the Coriolis force on the ice; the black line is the force cause by sea surface tilt; while the magenta line denotes the internal ice stress. Figure (c) shows the momentum balance for ice at 100 km offshore at day 6. The alongshore component of the ice velocity from 50 km offshore to 400 km offshore is about 13, 17, 20 cm s-1 at day 1, 3, and 6, respectively (Figure 3.2). The alongshore 55 components of the Coriolis force are negative because the ice moves on-shore under onshore winds (Figure 3.3c). The internal ice stresses prevent the ice motion on the shelf in the alongshore direction. The internal ice stress decreases significantly while the water stress on the ice increases with the offshore distance (Figure 3.3a). Because the ice moves onshore, there is strong internal ice stress from the coast. The cross-shore and alongshore components of ice velocities increase offshore (Figure 3.2). In the cross-shore direction, the Coriolis force, sea surface tilt, internal ice stress, water stress on the ice, and wind stress are all important in the momentum balance (Figure 3.3b). Under such wind conditions, the cross-shore components of water stress and Coriolis force are seaward on the shelf. The internal ice stress and gravity forces due to ocean surface tilt prevent the ice on the shelf from moving offshore. The sea surface tilts and internal ice stress decrease offshore from near the shelf break (Figure 3.3b). The water stresses on the ice increase with the offshore distance. Figure 3.4 shows the time series of the stress on the ocean from lkm to 200 km offshore. Under such wind conditions, the alongshore stress from the ice on the water is below -0.05 Pa within 100 km offshore from day 1 to day 6 although the alongshore wind stress on the ice is -0.08 pa on the shelf from day 1 to day 6. Near the shelf break (120 km), the alongshore stress on the ocean increases with the offshore distance. The model shows that the alongshore stress on the water could be reduced significantly compared to that under ice-free conditions due to the presence of sea ice under such wind conditions. 56 5.5 j' -0.02 -0.03 20^40^60^80^100^120^140 160 180 200 0 ° 6 -0.08 rrlii -0.09 -0.1 4.5 4 3.5 1-- 2.5 -0.04 -0.05 -0.06 -0.07 2 1.5 C:(11:025 ^ ---.. --11=---,..---_,_^c 0.025 20 -^ --..,k,___ ---.-: ..._ ^ -E-^-.-.. 40 - (a) a 60 - n - 0.005 alongshore components of stress on the ocean Figure 3.4. Time-offshore distance contour plot of the alongshore component of stress on the ocean. 20^40^60^80^100^120^140^160^180 ^ 200 -0.1 20E 40 60 (b) 40^60^80^100^120 Offshore Distance (km) 140^160^180^200 Figure 3.5. Cross-sections of (a) the cross-shore and (b) alongshore components of the water velocities at day 6. 57 The response of the water to upwelling favorable winds under ice-covered conditions resembles the classic upwelling circulation under ice-free conditions (Austin and Lentz, 2002). Figure 3.5 shows cross-sections of cross-shore and alongshore components of water velocities at day 6. The surface water moves offshore and the water moves on- shore in the bottom boundary layer. In the alongshore direction, the surface water from 50km to 120 km moves faster than that in the deep ocean. The water stress on the ice is related to the speed difference between the surface water (above 10m) and the ice (see equations 3.3 and 3.4). As the ice speed is nearly the same near the shelf break the ice stresses on the water increase as the distance from coast increases. Figure 3.6 shows the cross-shore sections of salinity at day 1, day 3, and day 6. After one day, the wind stress accelerates a surface alongshore flow, which in turn accelerates an offshore flow due to the Coriolis force, resulting in the formation of a surface Ekman layer. The offshore Ekman transport in the surface boundary layer generates a cross-shelf pressure gradient that drives an onshore return flow. A bottom mixed layer has formed where the pycnocline intersects the bottom, while the isopycnals have begun to move onshore. After two days, divergence in the wind-driven offshore transport near the coast forces upwelling that causes the pycnocline to intersect the surface, forming an upwelling front approximately 25 km offshore. After six days, the upwelling front has moved further offshore (35 km). From 140 km offshore to 160 km offshore, the stress on the ocean increases (Figure 3.4). The increase of stress in this region causes upwelling near 150 km offshore, causing the isohalines to slightly tilt upward toward the coast near 150 km offshore at day 6. 58 180 \ ■ 20^40^60^80^100 120 140 160 150 20^40^60^80^100 120 140 160 180 50 E 4.c-o_a) 1 oo 150 20^40^60^80^100 120 140 Offshore Distance (km) 50 100 150 160^180^20^40^60^80^100 120 140 160^180 Offshore Distance (km) 0 Figure 3.6. The cross-shore sections of salinity at (a) day 1, (b) day 2, (c) day 3, and (d) day 6. Salinity contours are 25.0 to 34.6 by 0.4. 3.4.2 Sensitivity to ice strength In the model, the ice strength is an important factor. In the work by Hibler (1979), P* = 5000 Nm -2 , while in work by Hibler and Walsh (1982) the value was increased by a factor of 5.5 to P* = 27,500 Nm -2 , which was tuned to give the best buoy/model ice velocity correlations when daily wind data were used. Most papers used the latter number, while in some papers (e.g. Tang and Gui, 1996), the previous number was used. Tremblay and Hakakian (2006) estimated sea ice strength P t using satellite-derived ice motion data. The results show lower and upper bounds on the ice strength of 30,000 and 40,000 Nm -2 , and 35,000 and 45,000 Nm -2 for the winters of 1992/93 and 1996/97, respectively. Here we study the sensitivities to the ice strength using the numerical model. 59 12 10 8 Do 6 (a) Ice strength: 27500 — Alongshore speed - -- Cross-shore speed - - speed — Alongshore speed - -- Cross-shore speed - _ . speed 0^ 0 100^200^300^400^ 100^200^300 Offshore Distance (km) Offshore Distance (km) 12 10 8 6 4 2 (b) Ice strength: 5000 400 In case 2, with P* = 27,500 Nm -2, the initial ice thickness is 2m and the initial ice concentration is 1. The wind blows toward the coast. The alongshore and cross-shore component wind stress are 0, and -0.08 Pa. In case 3, conditions are same as those conditions in case 2 except P* = 5000 Nm-2 . The ice thickness is 2 meters here because in mid-winter (February to April), the average ice thickness is about 2 meters on the Mackenzie Shelf. Figure 3.7 (a) and (b) show the alongshore ice speed, cross-shore ice speed and ice speed at day 6 for case (2) and case (3), respectively. Because the wind blows toward the coast, the ice moves toward the coast. Because of the Coriolis force, the ice motion is upwelling favorable. Figure 3.8 and 3.9 show the momentum balance for ice in (a) the alongshore direction and (b) the cross-shore direction at day 6 for case 2 and case 3, respectively. Figure 3.7. Alongshore ice speed, cross-shore ice speed, and ice speed at day 6 for (a) case 2 and (b) case 3. Note the alongshore component of ice velocity is negative. The cross-shore component of ice velocity is toward the coast, which is also negative. 60 ag 0.05 0 U^0 gIn S, -0.05 0a- In E0 0=N -0,05crs 2 50 100 150 200 250 300 Offshore Distance (km) 50 100 150 200 250 300 Offshore Distance (km) (b)(a) Figure 3.8. Momentum balance for ice in (a) alongshore direction and (b) cross-shore direction at day 6 for case 2. Figure (c) shows the momentum balance for ice at 150 km offshore at day 6. The force caused by the sea surface tilt is not shown here because it is very small in this case. Each color has the same meaning as pointed out in figure 3.3. Comparing the results of case (2) and (3), we can see that the internal ice stress in the cross-shore direction at 150 km offshore is strong for case 2 at day 6, but weak for case 3 (compare Figure 3.8b versus Figure 3.9b). The ice speed at 150 km offshore is below 5 cm s -1 for case 2 at day 6, but above 11 cm s -1 for case 3 (Figure 3.7 a,b). The angle between ice direction and coast direction are both about 45° for both cases 2 and case 3. The distances from site 2 to the Alaskan Beaufort Shelf coast and the Mackenzie Shelf coast are both about 200 km. The distance from site 2 to landfast ice on the Alaskan Beaufort Shelf is about 170 km. From observational results, the ratio of ice speed divided 61 c-0.05 0 Zt. by the 10m wind speed at site 2 is below 0.01 when the ice motion is upwelling favorable and the angle between ice direction and the Alaskan Beaufort Shelf coast direction is about 45°. If the ice is freely drifting, the ratio should be about 0.02. The ice motion at site 2 is strongly retarded in mid-winter when the ice motion is upwelling favorable and the angle between ice direction and the Alaskan Beaufort Shelf coast direction is about 45°. Therefore, P* = 5000 NM -2 is too small based on the model results. P* = 27,500 Nm -2 gives realistic results. 2 .a 0.05 §u^000 =,T, -0.05v■a(a) (b) 50 100 150 200 250 300^50 100 150 200 250 300 Offshore Distance (km) ^ Offshore Distance (km) (c) ^ Y ^ day 6 Water ^y-150 km Coriolis Internal • x Wind Figure 3.9. Momentum balance for ice in (a) cross-shore direction and (b) cross-shore direction at day 6 for case 3. Figure (c) shows the momentum balance for ice at 150 km offshore at day 6. The force caused by the sea surface tilt is not shown here because it is very small in this case. Each color has the same meaning as pointed out in figure 3.3. 62 12 (b) Initial ice thickness: 1.5m 10 —Alongshore speed - --Cross-shore speed - - speed 100^200^300 ^ 400 Offshore Distance (km) 3.4.3. Sensitivities to ice thickness In this section, we study the model sensitivities to ice thickness when the sea ice compressive strength parameter P * is 27,500 Nm -2 . In case 4, the initial ice thickness is 0.5 m and the initial ice concentration is 1. The wind blows toward the coast. The alongshore and cross-shore component wind stress are 0, and -0.08 Pa. In case 5, conditions are same as those conditions in case 4 except that the initial ice thickness is 1.5m. 12  (a) Initial ice thickness: 0.5m / 10 - I i i / I i 2 — Alongshore speed - -- Cross-shore speed - - speed 0 100^200^300^400 Offshore Distance (km) Figure 3.10. Alongshore ice speed, cross-shore ice speed, and ice speed at day 6 for (a) case 4, (b) case 5. Note the alongshore component of ice velocity is negative. The cross-shore component of ice velocity is toward the coast, which is also negative. Figure 3.10 (a), (b) shows the alongshore ice speed, cross-shore ice speed and ice speed at day 6 when the initial ice thickness is 0.5 m and 1.5 m, respectively. The ice moves towards the coast under the wind forcing. Due to the Coriolis force, the ice also moves along the shelf. The land is to the left of alongshore ice motion. The ice speed is above 10 cm s -1 from 160 km offshore in case 4 at day 6, but below 7 cm s -1 in case 5 63 (c) Y• Water day 6 y-200 km Coriolis j Internal x Wind (b)6', -0.05c0a 50 100 150 200 250 300 () Offshore Distance (km) 50 100 150 200 250 300 Offshore Distance (km) ...." d9ca 0.05 u°a, . 0 1„1,' -0.05 0 0 (Figure 3.10). The ice speed is sensitive to the ice thickness when the ice moves towards the landfast ice and the ice concentration is high. ^2 ^2 ^ i 1.5^ 1.5 to vsas ^42 ▪  1^(a) 1 ^0.5 ^0.5 0^50^100^150^200 0 Offshore Distance (km) 50^100^150^200 Offshore Distance (km) Figure 3.11. Ice thickness at day 6 for (a) case 4; (b) case 5. Figure 3.12. Momentum balance for ice in (a) cross-shore direction and (b) cross-shore direction at day 6 for case 4. Figure (c) shows the momentum balance for ice at 200 km offshore at day 6. The force on the ice caused by sea surface tilt is not shown in (c) because it is very small. Each color has the same meaning as pointed out in figure 3.3. 64 Figure 3.11 (a) and (b) show the ice thickness at day 6 in case 4 and case 5, respectively. The ice thickness increases near the coast because the ice converges near the coast. Figure 3.12 (a) and (b) show the dynamical balance in the alongshore direction and cross-shore direction at day 6 for case 4, while Figure 3.12 (c) shows the momentum balance at 200 km offshore at day 6. Figure 3.13 (a) and (b) show the dynamical balance in the alongshore direction and cross-shore direction at day 6 for case 5. From Figures 3.12 (b) and 3.13 (b), we can see that the Coriolis force and the force caused by sea surface tilt are small for both case 4 and 5 in the cross-shore direction. In case 4, the Coriolis force is small because the ice thickness is small, while in case 5, the Coriolis force is small because the alongshore ice speed is small. The major forces in the cross-shore direction are the water stress on the ice, wind stress on the ice, and internal ice stress (Figure 3.12b, 3.13b). The internal ice stress in the cross-shore direction decreases from 0 km to 150 km offshore, and then more slowly to 200km offshore. In case 4, the internal ice stress is below 0.013 Pa at 180 km offshore, while in case 2, it is about 0.05 Pa at 300 km offshore. The observational results show that the internal ice stress is not strong when the ice motion is upwelling-favorable in November as the ratio of ice speed to wind speed is about 0.02-0.03. When the ice is freely drifting, the ratio of ice speed to wind speed is about 0.02-0.03. In November, the ice thickness on the Mackenzie Shelf is below 1 m. The ice can move fast in November even when the sea ice concentration is high (the minimum sea ice concentration in area 1 is above 0.90, not shown here). When the initial ice thickness is 0.5 m and the ice strength is 27,500 Nm -2, the numerical model results show that the internal ice stress at 200 km offshore is weak, agreeing with the 65 observational results. When the initial ice thickness is 1.5 m and the ice strength is 27,500 Nm-2 , the model results show that internal ice stress is strong and ice motion is strongly retarded. In January, the ice thickness is about 1.5 m and the ice motion is retarded. Therefore, when the ice strength is 27,500 Nm -2 , the model results agree with the observed seasonal response of ice motion to the wind forcing.  tin 5.9 0.05 • 0 84) 1.1; -0.05 0.050. 0E• 0 0 -0.05 0 (a) (b) 50 100 150 200 250 300 () ^ 50 100 150 200 250 300 Offshore Distance (km) ^ Offshore Distance (km) (c) y ^ day 6 Internal ^y-200 km Water Coriolis • X Wind Figure 3.13. Momentum balance for ice in cross-shore direction at day 6 for case 5. Figure (c) shows the momentum balance for ice at 200 km offshore at day 6. The force on the ice caused by sea surface tilt is not shown in (c) because it is very small. Each color has the same meaning as pointed out in figure 3.3. 66 3.5 Summary In this chapter, ROMS (version 3.0) was used to study the upwelling under the ice- covered conditions. From case 1, we found that there is another mechanism that could reduce the stress on the shelf ocean. In case 1, when the ice converges, the ice moves at the same speed over the shelf and the deep ocean as the internal ice stress tends to reduce the difference in ice speed. Because the surface water moves relatively faster on the shelf than that in the deep ocean, the ice stress on the shelf water is smaller than that on the deep ocean water, as the ice stress on water is related to the difference between water speed and ice speed. In case 2 and case 3, the initial ice thickness is 2 m, which is about the average ice thickness from February to April. When the ice strength is 5,000 Nm -2, the internal ice stress is weak at 150 km offshore even when the wind blows towards the coast. It is not realistic because the ice motion is strongly retarded from February to April. When the ice strength is 27,500 Nm -2 , the model results show the ice motion is strongly retarded when the wind blows towards the coast. Therefore, 27,500 Nm -2 is a more realistic parameter for ice strength. When ice strength is 27,500 Nm -2 , the model results (case 4 and case 5) agree with the observed seasonal response of ice motion to the wind forcing. Therefore, 27,500 Nm -2 is a good ice strength parameter for ice model. 67 January 1924 500 — E x 1000 500 23 4. Discussion 4.1 The effect of atmospheric boundary layer structure During the winter season, air temperature inversions (i.e., temperature increases with height) occur above a shallow (30-80 m) mixed layer over the ice-covered ocean in nearly all profiles in the Arctic (from Serreze and Barry, 2005). An inversion represents strong vertical stability. Typical vertical temperature structures for winter are provided in Figure 4.1 and Figure 4.2. MAUD SOUNDINGS (KITES) — 35 ° —30 ° —25° —20° —15° Temperature (°C) Figure 4.1. Typical winter air temperature profiles taken near Wrangel Island by the Maud expedition (Sverdrup, 1933). Numbers are the date, and the heavy profile is a composite. These profiles were obtained from kites, which provided high resolution in the lower temperature. A low level inversion below a warm temperature maximum layer is the typical structure (From Overland, 1991). 68 1 0  1 Krcnkcl Chelyuskin 3 Kotelny 4 Borrow 5 Mould Bay 6 Eureka _ ao 4 - 2 -I 1 / I^ -60^--50^10^-30^-20 Figure 4.2 Mean air temperature profiles for February 1987 from six locations located around the periphery of the Arctic Ocean: (1) Krenkel (81°N, 58°E) (2) Chelyuskin (78'N, 104°E), (3) Kotelny (76 ° N, 138° E), (4) Barrow (71 ° N, 86 °W), (5) Mould Bay (76 ° N, 119°W) and (6) Eureka (80 °N, 86 ° W) (from Overland et al., 1997). Williams et al. (2006) used the 10-m wind to calculate the wind stress on the surface. Under the same 10-m wind, the wind stress on the surface (ice or water) is sensitive to the magnitude of drag coefficient between the surface and the atmosphere (see equation 1.1). Because the drag coefficient between ice and air could be two times as the drag coefficient between water and air, the coupling among air/ice/water could enhance the stress on the water if the ice is freely drifting (Williams et al. 2006). However, Overland (1985) shows that under the same geostrophic winds, the wind stress on the surface is not sensitive to the magnitude of drag coefficient (CD ) between the surface and atmosphere if the height of lowest inversion base is low. 69 50 0.0200-- 40 0.0300 0.0350 0.0375 1 2.0^2.5^3.0^3.5^4.0^4.5 101 C0 30 N 20 I0 0 0.0250 Overland (1985) used a turbulent closure boundary layer model to study the relation of wind stress to the geostrophic wind. In the following, we discuss his results. First, we define the geostrophic drag coefficient (Cg ): Cg = u* I G ^ (4.1) where u * is the friction velocity, G is geostrophic wind speed and u* r I pa l" According to (4.1), r = pa C,G 2 . If Cg is high, the stress on the surface is high under the same geostrophic winds. Figure 4.3 shows the relation of Cg to the drag coefficient and the regional average height of the lowest inversion base (Z,). This figure is from Overland (1985). Figure 4.3 Second-order closure model results showing dependence of the geostrophic drag coefficient u* I G on Z* = u* / fZ, and CD , where Z, is the regional average height of the lowest 2  inversion base, CD = U 2 , G being the geostrophic wind speed and G =12.5 ms 1 , and u * is theu10 friction velocity (after Overland, 1985). The blue point in this figure shows that Cg is less than 0.025 when CD = 2.7 x10 -3 and Z* = 40. The red point in this figure shows that Cg is higher than 0.025 when Co =1.5 x 10 -3 and Z* = 20 . 70 His model results show that Cg has strong relationship with Z,. Under the same CD, Cg decreases as Z. increases if Z. >10 (Figure 4.3), where Z. is u. I fZ, , and f is Coriolis parameter (Overland, 1985). The winter Arctic is characterized by Z. of 20-40 (Overland, 1985) because of the height of lowest inversion base is low (<100m). Z. is high when z, is low. We assume that CD is 2.7x10 -3 and Z. is 40 in November on the Mackenzie Shelf From Figure 4.3, we see that the Cg is less than 0.025 when CD is 2.7x10 -3 and z. is 40 (blue point in Figure 4.3). We call this value Cgi. Note that 2.7x10 -3 is the typical values of drag coefficient between ice and atmosphere in winter. In view of the fact that Z, is larger in summer than in winter (Serreze and Barry, 2005), we might conjecture that under global warming, Z, will also increase. In the future, we assume that in November, Z. is 20 if we assume that Z, increases under the scenario of global warming. We also assume that the Mackenzie Shelf is not covered by sea ice in November in the future. We assume that CD is 1.5x10 -3 , which is the typical value of drag coefficient between water and atmosphere. From Figure 4.3, we see that Cg is higher than 0.025 when CD is 1.5 x10 -3 and z. is 20 (red point in Figure 4.3). We call this value Cg2. As Cgi is less than Cg2, the wind stress on the surface when CD =1.5 x10 -3 and Z. = 20 is higher than that when CD = 2.7 x10 -3 and z. = 40 . The wind stress on the surface has strong relationship with the height of lowest inversion base. In the future, it is possible that the wind stress on the surface under the same geostrophic winds will increase although the drag coefficient between the surface and atmosphere decreases provided that Z, increases under the scenario of global warming. 71 Williams et al (2006) thought that the coupling of air/ice/water will increase the stress on the ocean because the drag coefficient between the ice and atmosphere is higher than the drag coefficient between water and atmosphere. In the future, it is possible that under the same 10-m winds, the stress on the ocean will decrease if the Mackenzie Shelf is not covered by sea ice. However, based on the Overland (1985) model results, under the same geostrophic winds, the stress has strong relationship with the height of lowest temperature inversion base. Under the scenario of global warming, it is likely that the Z, will increase. Under the same geostrophic winds, it is possible that the stress on the ocean will be higher than the stress on the ice if Z, increase. 4.2 The wind stress and ice stress on the water In the Beaufort Sea, the ratio of the ice speed to the 10-m wind speed (viz. speed ratio, i.e., SR) is about 0.02 in summer when the ice is freely drifting (McPhee, 1980). This means that the SR is 0.02 in the deep ocean when the ice is freely drifting. When the water depth is about 80 m, the SR is about 0.03 when the ice is freely drifting (Overland et al., 1984). In the Bering Sea where the ice is regarded as freely drifting, the SR is about 0.02-0.03 (Overland et al. 1984). The water depth at site 1 is about 80 m. In November, the median SR at site 1 when the alongshore components of wind stress is upwelling-favorable is 0.024 (Figure 2.4). It seems that the internal ice stress is not strong in November. The wind stress on the ice is mainly balanced by water stress on the ice. Therefore, the stress on the ocean is about same as the stress on the ice. Note the offshore Ekman transport is proportional to alongshore component of wind stress. It is hard to say whether the upwelling will be enhanced or not in the future in October and November. 72 The ice stress on the water is related to many factors: water velocity, under ice roughness, ice concentration, stratification, hydraulic effects and form drag in the boundary layer (McPhee, 1990). In order to simplify the problem, the stress on the water can be calculated using the following formula: iw = Pw C iw I ° I (Wg ° )e I8  (4.2) Where B is the turning angle and is 25° (Wadhams, 2000), Wsgr is the water velocity below the surface boundary layer, 0, is the ice velocity, C, is the drag coefficient between ice and water, and pw is the water density. In March, the median SR at site 1 when the alongshore component of wind stress is upwelling-favorable is 0.008. Under the same surface wind, the ice motion is strongly retarded compared to the ice motion in November. If the water speed below the surface boundary layer is zero, the stress on the ocean is nearly proportional to 0,2 based on equation (4.2). In general, under the same geostrophic wind, the wind stress transferred to the ocean is reduced by a factor of 10 in March because (0.024/0.008) 2 is 9. The upwelling is reduced because of the presence of ice in March. In the future, the upwelling in March will be enhanced under the same geostrophic wind if the ice thickness decreases. 4.3 The upwelling index Since the sea ice motion is not only related to the wind field, but also related to the sea ice concentration, it is better to set an upwelling index based on ice motion data. Kinematic ice/ocean stress fn, =I ci.0 I fit° , where ii.0 is friction velocity at the interface) was calculated as a function of the ice velocity relative to underlying geostrophic ocean current (McPhee et al., 2003). 73 1987 0.25 - 0.2 - 0.15 - -0.1- 0 -0.15 - -0.2 - -0.25 150^200 Day of Year 50 100 250 300 350 — = log^A iB , use^fro Kr (4.3) where v is the ice velocity relative to the surface geostrophic flow, K is von Karman's constant (0.4), f is the Coriolis parameter, z0 is the hydraulic roughness of the ice undersurface, A and B are constants, with values 2.12 and 1.91, respectively. On the short time scales associated with individual storm events, ice drift velocity usually far exceeds the geostrophic ocean current, so we assume V to be the actual ice velocity. Figure 4.4. The alongshore stress on the ocean at site 1 in 1987 based on equation (4.3) and (4.4). Upwelling-favorable stress is positive. The alongshore stress ralong on the ocean is the combination of the ice stress on the ocean and wind stress on the ocean. r along =^,w-along (1 — a)r as-along ^ (4.4) Here^ long is the alongshore ice stress on the water, raw-along is the alongshore wind stress on the ocean, r as-along is the alongshore wind stress on the surface (ice or ocean) 74 which is based on the NCEP daily surface momentum flux data, and a is the daily sea ice concentration. Figure 4.4 shows the alongshore stress on the ocean at site 1 in 1987 based on equation (4.3) and (4.4). Although it is not accurate because we assume the geostrophic flow is zero, it is a good approximation of stress on the ocean. Carmack et al. (2004) calculated the daily phytoplankton productivity for 1987. The upwelling-index could be helpful for studying the daily change of phytoplankton or particulate organic carbon. 4.4 Arctic Oscillation The ice motion in the southern Beaufort Sea is related to the Arctic Oscillation (AO). Figure 4.5 (a) and (b) show the ice drift patterns for years with low AO index and years with high AO index, respectively. Figure 4.5 (c) and (d) show the time taken in years for sea ice to reach Fram Strait for low AO index and high AO index, respectively (from Stein and Macdonald, 2004). During high AO conditions, the Beaufort Gyre shrinks back into the Beaufort Sea (Rigor et al., 2002). During low AO conditions, the mean westward ice motion is faster in the southern Beaufort Sea. During high AO conditions, the mean westward ice motion is slower in the southern Beaufort Sea (Figure 4.5). The mean multi-year ice thickness is smaller under low AO because it takes shorter time for sea ice in the Beaufort Sea to reach Fram Strait (Holloway and Sou 2002). The reduction of multiyear sea ice thickness means that the ice could move faster under the same surface winds. 75 Figure removed for copyright reason. The original source is the Figure 1.2.9 in the book "The organic carbon cycle in the Arctic Ocean" (2004). Figure 4.5 Ice drift patterns for a ) years with low AO - index (anticyclonic conditions) and b) high AO + index (cyclonic conditions) Time taken in years for year ice to reach Fram Strait is shown for c) low AO - index conditions and d) high AO + index conditions (from Stein and Macdonald, 2004). From about 1970 through early 1990s, there was a general upward tendency in AO index (c.f. Carmack et al, 2006). However, the AO index has decreased recently (Overland and Wang, 2005). Shimada et al. (2006) have pointed out that the mean westward ice motion increases after 1998 and this trend is not related with AO. If the AO increases in the future, the ice motion in the southern Beaufort Sea in winter will perhaps be slower. Because the frequency of upwelling-favorable winds will possibly decrease, the upwelling events will possible decrease in the future. 76 5. Summary and Conclusions In this thesis, the effect of ice on upwelling was studied using observational data and numerical model. The satellite-derived ice motion data and ice concentration data are from the National Snow and Ice Data Center. NCEP/NCAR reanalysis 10m wind data is used here. An ice-ocean coupled model was also used to study the effect of ice on upwelling. In Chapter 2, seasonal patterns of sea ice motion and the ice motion response to the wind forcing on the Mackenzie Shelf have been studied. The frequency of strong upwelling-favorable alongshore ice motion is high in early winter (November and December) compared to middle and late winter (January to May). For periods when the alongshore component of the wind is upwelling-favorable, the ratio of ice drift divided by wind speed at site 1, which is located at the shelf break of the Mackenzie Shelf, is 0.024 in November and 0.008 in March; we conjecture that this ratio decreases as winter progresses because the internal ice stress becomes stronger as both ice thickness and ice concentration increase. In May, this ratio is 0.015, higher than in March. We conjecture that this ratio increases because the sea ice concentration on the Mackenzie Shelf decreases in May. When the ice is freely drifting, the ice speed is about 2%-3% of the wind speed. In November, the internal ice stress is not strong because the ratio of the ice speed to wind speed is 0.024. In mid-winter, the median ratio is less than 0.01 when the ice moves towards the landfast ice. Therefore, when the sea ice moves towards the landfast ice and the ice is thick and the ice concentration is high, the landfast ice on the Mackenzie Shelf could strongly retard the sea ice motion on the Mackenzie Shelf. For 77 example, the ice motion from Feb. 29 to Mar. 7, 2000 was strongly retarded because sea ice concentration was high during this period. Chapter 2 also shows the spatial pattern of the ratio of the ice speed to wind speed in the Beaufort Sea. The results show that the seasonal variability of the response of sea ice motion to wind forcing is stronger on the Mackenzie Shelf and on the Alaskan Beaufort Shelf than in the central Canada Basin. The upwelling in August on the Mackenzie Shelf is less frequent because there are less upwelling-favorable winds in August. Most of the minimum ice concentration values on the Mackenzie Shelf were less than 0.8 when the alongshore ice motion were higher than 9.3 cm s -1 and the ice direction were within 142-270°T on the Mackenzie Shelf from Jan. 1 to May 31 from 1989 to 2002. When the alongshore ice motion values were lower than 9.3 cm s -1 , most of minimum sea ice concentration values on the Mackenzie Shelf were higher than 0.8 during the same period. Therefore, the ice concentration has strong effect on the alongshore ice motion when the ice direction is within 142-270°T and the ice is thick. Although in general the ice motion is strongly retarded in mid-winter (February to April), the ice could move fast sometime in February, March and April. The ice moved fast from Feb. 26 to Mar. 4, 2003. It is because the wind first pushed ice away from the coast, thus reducing sea ice concentration on the Mackenzie Shelf. Then the wind blew the ice to move along the coast, causing strong alongshore ice motion on the Mackenzie Shelf because the ice concentration is low. A numerical model was used to study the effect of ice on upwelling in Chapter 3. The numerical model showed another mechanism that could reduce the stress on the ocean besides the landfast ice. When the ice converges, the ice speed over the shelf (except near 78 the coast) and deep ocean is about same because of the internal ice stress. Because the surface water moves relatively faster on the shelf than that in the deep ocean, the ice stress on the shelf water is smaller than that on the deep ocean water, as the ice stress on water is related to the difference between water speed and ice speed. In November and December, this mechanism will probably reduce the stress on the shelf when the internal ice stress from landfast ice is not strong. When the initial ice thickness is 2m, the wind blows towards landfast ice, and the ice strength is 5,000 Nm -2 , the model results show that the internal ice stress at 150 km offshore is weak. The internal ice stress at 150 offshore is strong when the ice strength is 27,500 Nm -2 under the same conditions. Because the observational data shows that the ice motion at about 200 km offshore is strongly retarded by landfast ice in mid-winter when the ice moves toward the landfast ice, the numerical model results suggest that 27,500 Nm -2 is a more realistic value for ice strength rather than 5,000 Nm -2 . When the ice thickness is 0.5m, the internal ice stress at 200 km offshore is weak when the ice strength is 27,500 Nm -2 . It agrees with observational results that in November, the effect of landfast ice on ice motion is weak when ice thickness is below 0.8 m. Therefore, 27,500 Nm -2 is a more realistic value for ice strength rather than 5,000 Nm -2 In Chapter 4, the effect of atmospheric boundary layer on the surface stress is discussed. In Arctic winter, the height of lowest temperature inversion base is less than 100m (Overland 1985; Serreze and Barry, 2005). Overland (1985) pointed out under the same geostrophic winds, the stress has strong relationship with Z,, the height of lowest temperature inversion base. Under the scenario of global warming, it is likely that Z, will increase. Under the same geostrophic winds, it is possible that the stress on the ocean 79 (future global warming scenario) will be higher than the wind stress on the ice (current conditions) if Z, increases (despite the drag coefficient between atmosphere and ocean being lower than that between atmosphere and ice). Future work could include studying the seasonal variability of the atmospheric boundary layer over the Mackenzie Shelf. This work could be done within the Surface Heat Budget of the Arctic Ocean Project (SHEBA). The ice stress on water can be regarded as proportional to the ice speed squared although the stress on the water is related to many other factors, e.g. geostrophic currents, drag coefficient between water and ice etc. For periods when the alongshore component of the wind is upwelling-favorable, the ratio of the ice drift to the wind speed on the Mackenzie Shelf is 0.024, in November and 0.008 in March. This constitutes a possible 10-fold decrease in the seasonal transmission of wind stress to the underlying water from November to March. Hence, under the same wind forcing, the potential for winter upwelling on Mackenzie Shelf may be enhanced if climate warming results in reduced ice thickness and/or ice concentration. A major unknown remains — the effective coupling of wind to water as the ice concentrations and relative roughness decrease. In Chapter 4, an upwelling index under ice-covered condition is given although it is an approximation since we do not know the water velocities. It may be useful for study the daily change of phytoplankton or particulate organic carbon. In the future, the Arctic Oscillation index will probably increase, possibly causing the frequency of upwelling- favorable wind events to reduce on the Mackenzie Shelf Williams et al. (2006) thought that the presence of ice could enhance upwelling based on initial observed results. Now the observed results show that in general the presence of 80 ice reduces upwelling in March. However, it is not clear regarding the role of ice on upwelling when the ice concentration near the landfast ice on the Mackenzie Shelf is below 0.5. In summer, satellite data is not accurate (from Serreze and Barry, 2005). Future work could use ice motion data measured by ADCP to study the role of ice on upwelling in late spring and early summer. 81 References Aagaard, K., 1984, The Beaufort Undercurrent, in The Alaskan Beaufort Sea, ecosystems and environments, edited by P. W. Barnes, D. M. Schell, and E. Reimnitz, Academic, Orlando, FL, 47-71. Albright, M., 1980, Geostrophic wind calculations for AIDJEX, in Sea Ice Processes and Models, edited by R.S. Pritchard, University of Washington Press, Seattle, 402-409. Austin, J.A., Lentz, S. J., 2002, The inner shelf response to wind-driven upwelling and downwelling, Journal of Physical Oceanography, 32, 2171-2193. Beckmann, A., G. Birnbaum, 2001, Coupled sea ice ocean models, Encyclopedia of Ocean Sciences, Academic Press, San Deigo. Brown, R.A., 1990, Meteorology, in Polar Oceanography, edited by W. Smith. pp. 287- 334. Academic, San Diego. Calif. Budgell, W.P., 2005, Numerical simulation of ice-ocean variability in the Barents Sea region: Towards dynamical downscaling, Ocean Dynamics, doi 10.1007/s10236-005- 0008-3. Bakun, A., 1973, Coastal upwelling indices, west coast of North America, 1946-71. U.S. Dept. of Commerce, NOAA Tech. Rep., NMFS SSRF-671, 103p. Carmack E., D. C. Chapman, 2003, Wind-driven shelf/basin exchange on an Arctic shelf: The joint roles of ice cover extent and shelf-break bathymetry, Geophys. Res. Lett., 30, 1778, doi:10.1029/2003GL017526, 2003. Carmack, E. and Macdonald, R.W., 2002, Oceanography of the Canadian Shelf of the Beaufort Sea: A Setting for Marine Life, Arctic, 55, Supp. 29-45. 82 Carmack, E., Macdonald, R.W., Jasper, S., 2004, Phytoplankton productivity on the Canadian Shelf on the Beaufort Sea, Marine Ecology Progress Series, 227, 27-50. Carmack, E. C., and E. A. Kulikov, 1998, Wind-forced upwelling and internal Kelvin wave generation in Mackenzie Canyon, Beaufort Sea, I Geophys. Res., 103, 18447- 18458, 10.1029/98JC00113. Carmack, E., D.G. Barber, J.R. Christensen, R.W. Macdonald, B. Rudels and E. Sakshaug, 2006, Climate variability and physical forcing of the food webs and the carbon budget on panarctic shelves. Progress in Oceanography. 71: 145-181. Cavalieri, D., C. Parkinson, P. Gloersen, and H. J. Zwally. 1996, updated 2006. Sea ice concentrations from Nimbus-7 SMMR and DMSP SSM/I passive microwave data, Boulder, Colorado USA: National Snow and Ice Data Center. Digital media. Coon, M.D., 1980. A review of AIDJEX modeling. In Sea Ice Processes and Models (ed. R.S. Pritchard), Univ. Washington Press, Seattle, 12-27. Dunton, K.H., Weingartner,T., Carmack,E.C., 2006, The nearshore western Beaufort Sea ecosystem: Circulation and importance of terrestrial carbon in arctic coastal food webs Progress In Oceanography, 71, 362-378 Emery, W. J., C. W. Fowler, J. A. Maslanik, 1997, Satellite-derived maps of Arctic and Antarctic sea ice motion: 1988 to 1994, Geophys. Res. Lett., 24, 897-900, 10.1029/97GL00755. Fairall, C. W., Bradley, E. F., Rogers, D. P., Edson, J. B., Young, G. S., 1996, Bulk parameterization of air-sea fluxes for Tropical Ocean-Global Atmosphere Coupled- Ocean Atmosphere Response Experiment, J. Geophys. Res., 101, 3747-3764 83 Fowler, C. 2003. Polar Pathfinder Daily 25 km EASE-Grid Sea Ice Motion Vectors. Boulder, CO, USA: National Snow and Ice Data Center. Digital media. Haidvogel, D.B., and A. Beckmann, 1999, Numerical ocean circulation modeling. Imperial College Press., London. Hakkine, S., 1990, Models and their applications in Polar Oceanography, in Polar Oceanography, edited by W. Smith., 287-334. Academic, San Diego. Calif. Hasse, L. and Wagner, V., 1971, On the relationship between geostrophic and surface wind, Monthly Weather Review, 99, 255-260. Hibler, W. D. III., 1979. A dynamic thermodynamic sea ice model. J. of Phys. Oceanogr. , 9, 815-846. Hibler, W. D. III., and Walsh, J.E., 1982, On Modeling Seasonal and Interannual Fluctuations of Arctic Sea Ice, I Phys. Oceanogr. , 12, 1514-1523 Holloway, G. and T. Sou., 2002, Has Arctic Sea ice rapidly thinned? Journal of Climate, 15: 1691-1701. Hunke, E.C.. 2001, Viscous-Plastic Sea Ice Dynamics with the EVP Model: Linearization Issues, Journal of Computational Physics, 170, 18-38. Hunke, E.C. and J. K. Dukowicz., 1997, An Elastic-Viscous-Plastic Model for Sea Ice Dynamics, J. Phys. Oceanogr., 27, 1849-1867. Hunke, E.C. and Lipscomb, W.H., 2004, CICE: the Los Alamos sea ice model documentation and software user's manual. Ikeda, M., 1985, A coupled ice-ocean model of a wind-driven coastal flow, J. Geophys. Res., 90, 9119-9128. 84 Kellner, G., Wamser, G., Brown, R.A., 1987, An observation of the planetary boundary layer in the marginal ice zone, Journal of Geophys. Res., 92, 6955-6965. Kimura, N., Wakatsuchi, M., 2000, Relationship between sea-ice motion and geostrophic wind in the Northern Hemisphere, Geophys. Res. Lett., 27, 3735-3738 Kimrua, N., 2004, Sea Ice Motion in Response to Surface Wind and Ocean Current in the Southern Ocean, Journal of the Meteorological Society of Japan, 82, 1223-1231. Marsden, S.F., 1987, A comparison between geostrophic and directly measured surface winds over the Northeast Pacific Ocean, Atmosphere-Ocean, 25, 387-401. McPhee, M.G., 1978, A simulation of inertial oscillations in drifting pack ice, Dyn. Atmos. Oceans., 2, 107-122. McPhee, M.G., 1980, An analysis of pack ice drift in summer, Sea ice processes and models, University of Washington Press, Seattle, Edited by Pritchard, R.S., 62-75. McPhee M., 1990, Small scale processes, in Polar Oceanography, edited by W. Smith. 287-334. Academic, San Diego. Calif. McPhee M. G., Kikuchi, T., Morison, J. H., Stanton, T.P., 2003, Ocean-to-ice heat flux at the North Pole environmental observatory, Geophys. Res. Lett., 30, 2274, doi:10.1029/2003GL018580. Melling H., D. A. Riedel, Z. Gedalof, 2005, Trends in the draft and extent of seasonal pack ice, Canadian Beaufort Sea, Geophys. Res. Lett., 32, L24501, doi:10.1029/2005GL024483. Mellor, GL and T. Yamada, 1982, Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys., 20, 851-875. 85 Nansen, F., 1902, The Norwegian Polar Expedition, 1893-1896, Scientific Results. Oslo: Jacob Dybwad, 6 vols. Overland, J.E., 1985, Atmospheric boundary layer structure and drag coefficients over sea ice, I of Geophys. Res., 90, 9029-9050. Overland, J.E., Mofjeld, H.O., and Pease, C.H., 1984, Wind-driven ice drift in a shallow sea. J. Geophys. Res., 89, 6525-6531. Overland, J. E., P. S. Guest, 1991, The Arctic snow and air temperature budget over sea ice during winter, I Geophys. Res., 96, 4651-4662, 10.1029/90JCO2264. Overland, JE, Adams, JM, Bond, NA, 1997, Regional variation of winter temperatures in the Arctic, J Climate 10, 821-837 Overland, J. E., Wang, M., 2005, The Arctic climate paradox: The recent decrease of the Arctic Oscillation, Geophys. Res. Lett., 32, L06701, doi:10.1029/2004GL021752. Pickart, R. S., 2004, Shelfbreak circulation in the Alaskan Beaufort Sea: Mean structure and variability, I Geophys. Res., 109, C04024, doi:10.1029/2003JC001912 Roed, L.P. and O'Brien, 1983, A coupled ice-ocean model of upwelling in the marginal ice zone, I Geophys. Res., 88, 2863-2872. Rigor, I. G., J. M. Wallace, and R. L. Colony, 2002, Response of sea-ice to the Arctic Oscillation, I Clim., 15, 2648-2663 Serreze, M. C., R. G. Barry, 2005, The Arctic climate system, Cambridge University Press, 385pp. 86 Serreze, M. C., Barry, R. G., McLaren, A. S., 1989, Seasonal variations in sea ice motion and effects on sea ice concentration in the Canada Basin, Journal of Geophysical Research, 94, 10955-10970. Shimada, K., E. C. Carmack, K. Hatakeyama, and T. Takizawa, 2001, Varieties of shallow temperature maximum waters in the Western Canadian Basin of the Arctic Ocean, Geophys. Res. Lett., 28, 3441-3444. Shimada K., T. Kamoshida, M. Itoh, S. Nishino, E. Carmack, F. A. McLaughlin, S. Zimmermann, A. Proshutinsky, 2006, Pacific Ocean inflow: Influence on catastrophic reduction of sea ice cover in the Arctic Ocean, Geophys. Res. Lett., 33, L08605, doi:10.1029/2005GL025624. Song, Y.H., and Haidvogel, D.B., 1994: A semi-implicit ocean circulation model using a generalized topography-following coordinate system, J. Comput. Phys., 115, 228-244. Steele, M., J. Zhang, D. Rothrock, H. Stern, The force balance of sea ice in a numerical model of the Arctic Ocean, J. Geophys. Res., 102, 21061-21080, 10.1029/97JC01454, 1997 Stein, R., and MacDonald, RW, 2004, The Organic Carbon Cycle in the Arctic Ocean, Springer-Verlag, New York, 267 pp. Sverdrup, H.U., 1933, The Norwegian North Polar Expedition with the "Maud", Vol. II, Meteorology, 331 pp., Geophysical Institute, Bergen, Norway. Tang, C.L. and Q. Gui, 1996, A dynamical model for wind-driven ice motion: Application to ice drift on the Labrador Shelf, Journal of Geophysical Research, 101, 28343-28364. 87 Tang, C.L. and T. Yao, 1992, A simulation of sea-ice motion and distribution off Newfoundland during LIMEX, March 1987 ,  Atmosphere-Ocean., 30., 270-296. Thorndike and Colony, 1982, Sea ice motion response to geostrophic winds. J. Geophys. Res. 87, 5845-5852. Tremblay, L.B, and Hakakian, 2006, Estimating the Sea Ice Compressive Strength from Satellite-Derived Sea Ice Drift and NCEP Reanalysis Data, J. Phys. Oceanogr., 36, 2165-2172 Wadhams, 2000, Ice in the ocean, Gordon and Breach Science Publishers, 351pp. Walter, B.A., J.E. Overland, and R.O. Gilmer, 1984, Air-ice drag coefficients for first year sea ice derived from aircraft measurements, J. Geophys. Res., 89, 3550-3560. Williams, W., Carmack, E., K. Shimada, H. Melling, K. Aagaard, R.W. Macdonald, G. Ingram, 2006, Joints effects of wind and ice motion in forcing upwelling in Mackenzie Canyon, Arctic Ocean, Continental Shelf research, 26, 2352-2366. Yao, T., C. L. Tang T. Carrieres and D. H. Tran, 2000a, Verification of a Coupled Ice Ocean Forecasting System for the Newfoundland Shelf, Atmosphere-Ocean., 38, 557 - 575. Yao, T., C. L. Tang, I. K. Peterson, 2000b, Modeling the seasonal variation of sea ice in the Labrador Sea with a coupled multicategory ice model and the Princeton ocean model, J. Geophys. Res., 105, 1153-1166, 10.1029/1999JC900264. Yao, T. and C. L. Tang, 2003, The formation and maintenance of the North Water polynya, Atmosphere-Ocean., 41,187-201. Zhang, J., Hibler, W.D. III, 1997, On an efficient numerical method for modeling sea ice dynamics, J. Geophys. Res., 102, 8691-8702, 10.1029/96JCO3744. 88 Appendix A. Equation (3.10) is discretized in time as follows: If n indicates the previous time step, then n+1^n^2^ 2 ^CrY — cry  -V e^n+1 ^ ,^ n+1^P   • n= e At^2T^Y + kk4T^4T ° - 2TAn (a) For convenience, the stress tensor a - is set in terms of 61 = 611 + 622^(b) , = al I — 622 (c), This method has been used in the CICE model (Hunke and Lipscomb, 2004). Based on equation (a), (b), and (c), we can get: ao-, 6, P^P ii+ 6 22 )at 2T 2T 2TA 50-2 e 2 a2 at ± 2T^2TA (eii E22 ) ao-12 e 2 Ci l2 P=^ at^2T 2TA Solving equations (d), (e) and (f), gives: At P a = (cr i2 + 2T A 12 ) 1(1+ Ate e 2 / 2T), Ate ?  e,, + 622 oT+I^+ 2T ^A^ + At e / 2T), a;'+' = [cr;7+1 —A2Tte —AP(Z.11 –Z - 22 )]/(1 Ate e 2 I2T). 89

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.24.1-0053231/manifest

Comment

Related Items