Measurements of Air-Ice Drag Coefficient over the Ice- Covered Sea of Okhotsk

Transcription

1 Journal of Oceanography, Vol. 65, pp. 487 to 498, 2009 Measurements of Air-Ice Drag Coefficient over the Ice- Covered Sea of Okhotsk AYUMI FUJISAKI 1 *, HAJIME YAMAGUCHI 1, TAKENOBU TOYOTA 2, AKIO FUTATSUDERA 1 and MASARU MIYANAGA 1 1 Applied Fluids Engineering Laboratory, Department of Environmental and Ocean Engineering, School of Engineering, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo , Japan 2 Institute of Low Temperature Science, Hokkaido University, Kita-ku, Sapporo , Japan (Received 17 April 2008; in revised form 7 October 2008; accepted 13 March 2009) The air-ice drag coefficient under neutral stratification C DN was measured with the eddy correlation method in the southern Sea of Okhotsk. The disturbance of the wind field caused by the ship s structure was evaluated by computational fluid dynamics (CFD), and two types of correction methods were applied to estimate the error span of C DN : one is based on the results of CFD, and the other is based on the parameterization of C DN over open water suggested by Taylor and Yelland (2001). The C DN 10 3 values finally obtained ranged from 1.9 to 5.4 with a mean value of 2.7 by the CFD correction and from 1.5 to 5.0 with a mean value of 3.1 by the other method. This is somewhat larger than the value of 2.5 suggested by Shirasawa (1981), and in the same range as over rough ice and over very rough ice, values which were complied by Guest and Davidson (1991) for first year ice. Most of the ice conditions were characterized by broken floes with a diameter less than 100 m and raised rims, which made the surface rougher than flat, level ice. The relation between C DN and ice concentration was not clear, mainly because the contribution of the form drag caused at the freeboard was undetectable due to the great variation of ice surface condition. The roughness length z M was also evaluated using the model developed for snow covered ice in a previous study. Keywords: Sea ice, Sea of Okhotsk, air-ice drag coefficient, eddy correlation method. 1. Introduction The air-ice drag coefficient is a dominant factor for correctly predicting the wind stress in numerical models. In the Sea of Okhotsk, the practical value for the drag coefficient over sea ice is very ambiguous as there have been very few direct observations. Toyota et al. (2004) showed from in-situ observations that ice samples obtained in the southern Sea of Okhotsk are composed of several layers, 5 to 10 cm thick on average, and the ice structure comprised granular ice rather than columnar ice. They suggested that the frazil ice formation and piling-up processes are much more important than a congelation process. Thus, floes in the Sea of Okhotsk are subject to dynamic deformation and bumpy surfaces are expected; and the air-ice drag coefficient is expected to be large. * Corresponding author. fujisaki@1.k.u-tokyo.ac.jp Copyright The Oceanographic Society of Japan/TERRAPUB/Springer However, very few direct observations of the air-ice drag coefficient in the Sea of Okhotsk has been made hitherto, because of the economic and technical barriers to observation in the ice-covered seas. Two previous studies can be cited: the measurements taken by Shirasawa (1981), and the others by Shirasawa and Aota (1991). Shirasawa (1981) obtained a drag coefficient of over hummocked ice near Saruru, Hokkaido Coast. In the latter study, Shirasawa and Aota (1991) reviewed the drag coefficients and the roughness lengths obtained in the coastal region off Hokkaido, including in their analysis the results of data obtained at the marine tower 600 m offshore. They obtained drag coefficients of , , and over compacted pack ice. However, their measurements were confined to the very coastal region near Hokkaido. On the other hand, more measurements have been accumulated in the polar region. Most of them were performed in experiment projects, such as the Arctic Ice Dynamics Joint Experiment: AIDJEX (Banke et al., 1980), the Marginal Ice Zone Experiment: MIZEX 487

2 (Anderson, 1987), the Surface Heat Budget of the Arctic Ocean Project: SHEBA (Andreas et al., 2005a, b). Overland (1985) summarized all the wind stress measurements available at that time. In a somewhat later study, Guest and Davidson (1991) summarized the measurement results of four field programs conducted in the marginal ice zone, which has ice conditions similar to that of the Sea of Okhotsk. They listed the air-ice drag coefficients under neutral stratification C DN over different types of sea ice. We refer to the C DN 10 3 values over the firstyear ice which they compiled: 1.5 over very smooth ice, 2.0 over smooth ice, 3.1 over rough ice, and 4.2 over very rough ice. Thus, the C DN value varies greatly with surface conditions and it is important to know the range the C DN values take in the Sea of Okhotsk. In such a situation, measurements of the turbulent fluxes with the eddy correlation method were performed during the cruises of the Patrol Vessel Soya in Februaries from 2002 to 2005, as the first series of measurements in the offshore region. In this paper the measured C DN values obtained during those observation series are tabulated and compared with the values obtained in the previous measurement campaigns in the coastal region off Hokkaido, and with those over first-year ice in the Arctic Ocean. Since it is inevitable that the mean wind speed and the turbulence quantities are affected by the disturbance caused by the ship s structure, we investigated the influence of the presence of the hull by computational fluid dynamics (CFD). Based on the CFD result, we apply a correction method for the mean wind speed, and apply two types of correction methods to the C DN values. The roughness length z M is also compared with previous studies and evaluated using the model developed by Andreas et al. (2005a), which relates the z M values and the friction velocity u*. 2. Measurement 2.1 Eddy correlation method The results presented here are based on the eddy correlation method. The momentum flux in the surface boundary layer is described by Eq. (1): 2 τ = ρ uw = ρu, () 1 where τ is air stress and ρ is the air density. u w denotes the correlation of the horizontal and vertical wind velocity fluctuations u and w from the mean values. The air-ice drag coefficient C D at a certain reference height is: C u U D =, ( ) where u* is the friction velocity and U is the mean wind velocity at a reference height, which is 10 m in this study. Hereafter, most of the quantities, including the drag coefficients, mean wind speed, and air temperature, will be the values at 10 m, if not specified otherwise. When we discuss the ice-surface roughness, it is convenient to define the air-ice drag coefficient under neutral stratification C DN as: C DN = 12 CD + κ / Ψ 12 / M ref DN 2 z = z exp κc, () 3 ( ) ( 4) where z ref is a reference height, 10 m here. z M is the momentum roughness length. κ is the Von Kármán constant, which is assumed to be 0.4 here. Ψ is a function of the stability factor ζ = z ref /L. L is the Obukhov length. L 3 Tu gκ w T = ( 5 ) Ψ( ζ)= αζ ( stable 0 < ζ < 1) ( 6) ( ) ( ) 14 / + αζ αζ Ψ( ζ )= + 12 / ln ln / π 2tan [( 1 αζ ) ] + unstable 2 < ζ < ( ) ( ) Here, g is gravitational acceleration, which is assumed to be 9.8 m/s 2. α is 4.7 for the stable condition and 16 for the unstable condition. The eddy correlation method is based on the measurement of the covariance between u and w. We used a sonic anemometer to measure the high-frequency components of the wind velocity and air temperature. The measured quantities were divided into the mean components, u v w T, and the fluctuating components, u v w T from the mean components, respectively. The covariances of u w and w T, u = U and T = T yield C DN and z M by Eqs. (2) (7). While the eddy correlation method is a direct method for measuring the turbulent flux in the surface boundary layer, it is sensitive to disturbance by the ship s structure. Therefore, we performed a CFD evaluation prior to our measurements, which provided an estimation of the error span of the drag coefficients, and the correction method for the mean wind velocity U. The details are given in Subsection A. Fujisaki et al.

3 5 FEB 10 FEB 15 FEB FEB 10 FEB 15 FEB FEB 10 FEB 15 FEB FEB 15 FEB 20 FEB 2005 Fig. 1. Sites of turbulence measurements during Lines denote the ice edges, where the ice concentration is around 10%. 2.2 Instruments and platform The observations were performed every February during the cruises of the ice-breaker Patrol Vessel Soya. They consist of various measurements, including ice-core extraction, air observation, sea-surface temperature and salinity observation, and so on. The turbulence measurements with a sonic anemometer were done during four seasons from 2002 to The measurement sites are shown in Fig. 1. The ship stopped its navigation during the measurements with a sonic anemometer. The platform was installed on the balcony outside the bridge (Fig. 2), z = 10.5 m where the disturbance by the ship structure could be relatively well suppressed, which was found by CFD as described in Subsection 2.4. The sonic anemometer (KAIJO DA-600-3) and the inclinometer (KAIJO CM- 100R) were extended out from the balustrade of the balcony by 1.5 m in order to decrease the hull s influence on the turbulence quantities. One run is measured for seconds, and 1 3 runs were obtained at one measurement site. Data with more than one run were combined to calculate the covariance and the mean wind velocity. Therefore, the shortest interval of the averaging of turbulent fluxes and wind velocity is 500 seconds, which is similar to the 600 seconds of Shirasawa and Aota (1991), but notably short compared with values listed by Guest and Davidson (1991). The shorter averaging interval might result in a stronger random scatter of the results. Typical ice types were observed visually. We decided among ice cake (φ = 2 20 m), small floe (φ = m), medium floe (φ = m), large floe (φ = 500 m 2 km), nilas, grease ice, and open water. Here, φ denotes a floe diameter. Ice concentrations were also observed visually. They were checked against the advanced-report diagrams of sea ice provided by the Ice Information Center (the First Regional Coast Guard Headquarters, Japan). Typical ice concentrations A were divided into 6 levels: A = 0%, A = 20% (0 30%), A = 40% (30 50%), A = 60% (50 70%), A = 80% (70 90%), and A = 100% (90 100%). 2.3 Data processing The three-dimensional wind velocities and air temperature were recorded with a sonic anemometer at 100 Hz, and the inclinations due to the ship s pitching and rolling were corrected. Next we determined the main stream of the wind direction from the streamlines distorted by the ship s structure. The XYZ axes were rotated to X Y Z so that the mean velocities of the Y and Z axes were zero and the X axis had the main stream direction of wind velocity. After the main stream directions of the wind field were calculated, we calculated the average values and fluctuations of wind velocities and air tem- Measurements of Air-Ice Drag Coefficient over the Ice-Covered Sea of Okhotsk 489

4 Fig. 2. Platform for the measurement of turbulent fluxes, installed on the terrace outside the bridge at z = 10.5 m above the sea level. The sonic anemometer and the inclinometer are extended out from the terrace by 1.5 m (the left bridge in 2002, and the right bridge in ). Fig. 3. Full-scale shape of the Soya used to generate the computational grid. perature u, v, w, T from the mean values. We found a 5/3 slope at Hz in the spectra of the fluctuations, which is an inertial sub-range, and the spectra higher than 20 Hz seemed to be influenced by aliasing. Therefore, the time series were low-pass filtered at 20 [Hz] to remove the aliasing, and the linear trends were also removed. Finally, we calculated the covariances u w and w T, and the drag coefficients under neutral stratification by Eqs. (2) (7). Some instrument trouble meant we could not directly measure T in Therefore, we substituted the sensible heat flux derived by the bulk method (Andreas and Makshtas, 1985) to calculate the Obukhov length L. 2.4 Evaluation of the hull s influence It was inevitable that the measurement at the platform installed on the ship would be affected by the disturbance of the wind field caused by the presence of the Fig. 4. Distribution of the intensity of the disturbance k d 1/2 / U inf near the ship s structure. k d is the component of the total turbulent kinetic energy distorted by the presence of the hull, and U inf is the undisturbed mean wind speed. The section is at a solid line in Fig. 3. The platform was located at the point shown with a circle. hull. Consequently, such disturbance intensifies the turbulence fluxes near the ship and the corresponding drag coefficient can be over-estimated. Therefore, we performed CFD prior to our measurements to evaluate the influence of the ship s structure on the turbulent kinetic energy and the mean wind speed, using a commercial CFD code Fluent (ANSYS), which is general purpose software for thermal fluid analysis. The turbulence model was the k-ε model, which solves the transport equations for the turbulent kinetic energy k = (u 2 + v 2 + w 2 )/2 and the turbulent dissipation rate ε. Figure 3 shows a full-scale shape of the Soya, which was used to generate the com- 490 A. Fujisaki et al.

5 α U Fig. 5. Relationship between the wind angle α [ ] and U/U inf estimated by the CFD of Futatsudera et al. (2002). putational grid. Two cases were evaluated, where the wind blows from the bow and from the beam were evaluated. The numbers of the cell are about for the wind from the bow case and about for the wind from the beam case. Only the results that are relevant to this present paper are described here. See Futatsudera et al. (2002) for the details. Influence on the turbulent fluxes Figure 4 shows the turbulent intensity k d 1/2 /U inf. k d denotes the component of the total turbulent kinetic energy which is distorted by the presence of the hull. U inf denotes the non-disturbed mean wind speed. It was found that the disturbance k d 1/2 /U inf could be suppressed to less than 2% for the two cases, if the platform was extended out from the balcony by more than 4m. However, in practice, we could extend the platform which was fixed to steal frames only by 1.5 m due to the difficult of installation. At this region, the disturbance k d 1/2 /U inf becomes larger, up to (=6 12%). Based on this information on the disturbance, we can estimate how much the measured turbulent kinetic energy k o is disturbed by the presence of the hull, and the corresponding error range of the measured friction velocity u o *. This point is discussed in detail in Section 3, CFD correction. Influence on the mean wind velocity The method for correcting the mean wind velocity was also evaluated. The ratio of the disturbed and nondisturbed mean wind velocity U/U inf around the platform ranged from , and depended on the wind angle α. Figure 5 shows the relation between the wind angle α and the U/U inf. We corrected the measured mean wind speed using this relation. Figure 6 shows a comparison between the mean wind speeds measured by the sonic anemometer which were corrected with the ratio U/U inf and the vane anemometer (YOUNG MODEL05103) in 2002, when the two anemometers were installed on the same side. The vane anemometer was installed at the upper bridge at z = 13.7 m. Note that the wind speeds were corrected to the values at 10 m height according to the Monin-Obukhov similarity law. They agree well, with a correlation coefficient of We confirmed the mean Fig. 6. Comparison of wind speeds [m/s] measured by vane anemometer and sonic anemometer in The correlation coefficient is Note that wind speeds measured by vane anemometer were corrected to the values at 10.5 m height by the Monin-Obukhov similarity law, and the wind speeds measured by the sonic anemometer were corrected with the ratio U/U inf in Fig. 5. wind velocities were reasonably corrected by the U/U inf - α relation. 3. Results The overall conditions during the measurements are listed in Table 1. We excluded the small turbulent fluxes which were of the same order as the accuracy of the sonic anemometer ( u w < , w T < ). Data with stability factor ζ > 1 and ζ < 2 were also excluded because of the applicable range of Eqs. (6) and (7). One sample, with a C DN that was unrealistically large compared with ice condition ( in 2002), was also excluded. Finally, 46 runs over ice-covered sea and 8 runs over open water were obtained as valid data. As a whole, the raw drag coefficients seemed to be over-estimated for the reason described in Subsection 2.4. Therefore, we corrected them with two methods, as described below. Measurements of Air-Ice Drag Coefficient over the Ice-Covered Sea of Okhotsk 491

6 Table 1. Overall conditions during the turbulence measurements. CFD correction As shown in Subsection 2.4, the observed turbulence intensity S o = k o 1/2 /U inf around the ship s structure could be over-estimated by 6 12%. The turbulence measured at the platform S o included both the true turbulence over the ice-covered sea surface, S t = k t 1/2 /U inf, and the disturbance caused by the ship s structure S d = k d 1/2 /U inf. Here we estimate the true turbulence S t from the measured turbulence S o and the disturbance S d, which was evaluated by CFD. Assuming the correlation between the true turbulence over the ice-covered sea surface S t and the disturbance caused by the ship s structure S d is negligible, the relation between S o, S t, and S d can be described as follows: S = S + S. () 8 o t d The CFD result shows that the turbulence intensity around the ship structure did not change much for the mean wind speed U. Therefore, the following relation can be approximated: k k k = +. ( 9) o t d Assuming the turbulence kinetic energy k is proportional to the Reynolds stress u w = u* 2, the ratio of the true friction velocity u t * to the measured friction velocity u o * can be estimated by the following equation: ut kt ko k u = k = k o o Number of runs Open water Mean wind velocity [m/s] (through observation period) Mean air temperature [degree] (through observation period) o d. ( 10) We modified the measured friction velocities u o * by multiplying the factor obtained by Eq. (10). The sensible heat fluxes w T o were also modified in the same way assuming they are proportional to the u o * values. In this correction method, the factor obtained from Eq. (10) can be near zero when the true turbulence intensity over the ice-covered sea surface S t is relatively small compared with the disturbance caused by the ship s structure S d. Such a large modification could include a significant modification error. Therefore, we excluded data with measured turbulence intensity S o less than 25%, about the twice of the upper limit of S d. The range 6 12% and the median value 9% of S d were used to calculate the correction using Eq. (10). Correction based on the parameterization of Taylar and Yelland (2001) The second correction method, hereafter referred to the T&Y correction, used the relation between the drag coefficients over open water measured in this study and those derived by the function of Taylor and Yelland (2001), that is, Eq. (11). The relations over open water were used to modify the drag coefficients over an icecovered region: CDN = ( U U ) ( over open water). ( 11) The ratios between the two drag coefficients over open water had an average of 0.71 and a standard deviation of 0.11, yielding a factor of (0.71 ± 0.11). The measured C DN values over ice covered areas were modified with this factor. The modified C DN values, mean wind speed, and the other quantities are listed in Tables 2 and 3. In terms of the CFD correction, the error ranges are asymmetric to the center values and only the larger error widths are shown. One sample obtained at 11 am on 13th February, 2004, was excluded in the later consideration because the C DN values corrected by the two methods inconsistently differ by about a double factor (7.2 ± by the CFD correction, 4.2 ± by the T&Y correction). 3.1 Comparison of C DN with the other measurement results Table 4 shows the C DN values at ice concentration A > 70%. A similar list, without the results under the stable stratification ζ > 0, is shown in Table 5, which was prepared because the amount of correction to the neutral value is significantly large under stable stratification by Eq. (6) and there might be erroneous estimations of the neutral values. The corrected C DN 10 3 values at ice concentration A > 70% were distributed in with the median value of 2.6 and the mean value of 3.2 by the CFD correction, and in with the median value of 3.2 and the mean value of 3.1 by the T&Y correction. They are somewhat larger than the value 2.5 suggested by Shirasawa (1981), who performed the measurements with the eddy correlation method at the coastal region of Hokkaido. They are also in the same range as over rough ice and over very rough ice, which are listed for first year ice 492 A. Fujisaki et al.

7 Table 2. Drag coefficients under neutral stratification C DN 10 3, and the roughness length z M, the sensible heat flux H s, and the other quantities obtained over ice-covered region. Only first decimal place is shown for the C DN 10 3 values, while full digits of the C DN values were used in the calculation of the z M values. Date Ice type A [%] C DN 10 3 k U ζ u* [m/s] z M [m] U [m] H s [W/m 2 ] T [ C] Averaging period [s] CFD T&Y CFD T&Y 2/11/02 11 am C ± ± /11/02 3 pm N ± /12/02 10 am C ± ± rums 2/12/02 10 am C ± ± /12/02 3 pm S ± ± /13/02 9 am N ± ± /13/02 3 pm M ± ± /13/02 4 pm M ± ± /15/02 8 am C ± ± runs 2/7/03 2 pm M ± /9/03 9 am S ± ± runs 2/10/03 2 pm S ± ± /12/03 11 am M ± ± /12/03 1 pm S ± ± /13/03 11 am L ± /13/03 1 pm C ± ± /7/04 3 pm S ± ± runs 2/8/04 12 am S ± ± runs 2/9/04 8 am C ± ± runs 2/9/04 10 am S ± ± runs 2/11/04 2 am C ± ± runs 2/12/04 11 am S ± ± runs 2/13/04 11 am C ± ± runs 2/13/05 1 pm N ± ± runs 2/14/05 12 am S ± ± runs 2/14/05 3 pm S ± ± runs 2/15/05 12 am S ± ± runs 2/16/05 12 am C ± ± Ice types are denoted by N: Nilas, C: Ice cake (φ = 2 20 m), S: Small floe (φ = m), M: Medium floe (φ = m), L: Large floe (φ = km). Measurements of Air-Ice Drag Coefficient over the Ice-Covered Sea of Okhotsk 493

8 Table 3. Similar to Table 2 but over open water. o ζ u* [m/s] z M [m] U [m/s] H s [m/s] T [ C] Averaging period [s] Date C DN 10 3 k U CFD T&Y CFD T&Y 2/9/02 10 am 2.0 ± ± /9/02 4 pm 1.4 ± ± /13/02 8 am 1.0 ± ± /13/02 12 am 1.5 ± ± /15/02 11 am 1.5 ± ± runs 2/13/05 10 am 1.0 ± ± S by Guest and Davidson (1991). Hereafter, their study will be referred as G&D. Large floe Only one valid sample was obtained over a large floe (Fig. 7). The surface condition was characterized by snow cover of about 10 cm. The ice surface condition in Fig. 7 seems somewhat rougher than completely level ice without snow cover due to remnants of the piling up processes, the surface seems somewhat hummocky. Almost no freeboard was found because the floes were compacted. The C DN 10 3 value was 1.5 ± 0.1 by the T&Y correction, while the CFD correction was not applicable to this sample due to the relatively small k o 1/2 /U value. This value is within the range of with the mean value of 1.5 over very smooth first year ice listed by G&D, and somewhat smaller than the drag coefficient of , which was obtained over a large but visually rough floe in the Gulf of St. Lawrence at the measurement site with the wind profile method by Seifert and Langleben (1972). Medium floe Two valid samples were obtained over medium floes. One sample was obtained at the site shown in Fig. 8. The C DN 10 3 value was 2.4 ± 0.4 by the T&Y correction. The CFD correction was not applicable. The typical diameters of floes were m, infilled with young ice. The raised rims of the floes made the surface of the ice field rougher. This sample was obtained during the stable stratification. The C DN 10 3 value is comparable with , the mean value of 3.1 over rough ice compiled by G&D. The other sample was obtained at the site shown in Fig. 9. Hummocked ice can be observed in the distance, and there are fractional open water regions. The corresponding freeboard likely contributed to the form drag in no small measure. The C DN 10 3 values were 4.0 ± 1.0 by the CFD correction and 3.7 ± 0.6 by the T&Y correction. These values are comparable with , the mean value of 4.2 over very rough ice compiled by G&D. Small floe, ice cake A relatively large number of samples was obtained over small floes and ice cakes, that is, the ice fields was more frequently occupied by broken floes than those characterized by level ice. This is consistent with the findings of Toyota et al. (2004), who suggested that the piling up of relatively small floes is a dominant factor in ice thickness growth rather than the congelation process in the Sea of Okhotsk. At ice concentration A > 70%, we obtained seven samples over small ice and six samples over ice cake. The C DN 10 3 values over small floes were with the mean value of 2.6 ± 1.0 by the CFD correction, with the mean value of 3.0 ± 0.5 by the T&Y correction. In some cases, nilas or young ice infilled the narrow spaces (Fig. 10). The C DN 10 3 values over ice cakes 494 A. Fujisaki et al.

9 Table 4. C DN 10 3 values at ice concentration A > 70%. Digits in parentheses denotes the numbers of data. CFD min max T&Y min max Nilas 0.9 ± 0.3 (1) 0.9 ± 0.1 (1) Ice cake 3.8 ± 0.9 (6) ± 0.6 (6) Small 2.6 ± 1.0 (7) ± 0.5 (7) Medium 4.0 ± 1.0 (1) 3.1 ± 0.5 (2) Large 1.5 ± 0.2 (1) Table 5. Similar to Table 4 except data under stable stratification. CFD min max T&Y min max Ice cake 3.6 ± 1.0 (5) ± 0.6 (5) Small 2.3 ± 0.9 (4) ± 0.4 (4) Medium 4.0 ± 1.0 (1) 3.7 ± 0.6 (1) Large 1.5 ± 0.2 (1) were with the mean value of 3.8 ± 0.9 by the CFD correction, with the mean value of 3.6 ± 0.6 by the T&Y correction. In most regions where ice cakes were typical, there were partial stretches of open water, and ice fields were not completely compacted. The C DN 10 3 values over these two types were comparable with , the mean value of 4.2 over very rough ice compiled by G&D for the two corrections. The same can be said of the results without stable stratification. Thus, we compared the results with the previous measurements over similar ice types. At most of the measurement sites, small floes and ice cakes were typical and the C DN values measured there were similar to those over rough or very rough ice compiled by G&D. While Shirasawa (1981) recommended the drag coefficient of to estimate the wind stress in the Sea of Okhotsk, our result suggests much larger values may possibly be appropriate. 3.2 Relation with ice concentration Figure 11 shows the plot of the C DN values against the categorized ice concentrations, except nilas. The relation between them is ambiguous. In a less compacted ice region, the freeboard of the ice lateral side can contribute significantly to the form drag significantly, and so larger C DN values than that for a compacted ice region should be expected. However, such a tendency was not clearly found. Although the second-order regression lines are convex upward, the data are too scattered to conclude that they reflect the freeboard effects. In this observation series, various ice conditions were observed, including compacted floes covered with snow, floes with raised rims, hummocks as tall as 1 m, and so on. Such a variety of surface conditions would be a reason for the ambiguous relation between the measured C DN values and ice concentration. 3.3 Roughness length The roughness length z M is determined by the C DN values by Eq. (4). Therefore, comparison of the z M values corresponds to the C DN values. Because some previous studies focused on the z M values more than C DN values, the z M values obtained in this study are compared with those listed in the previous studies. The roughness lengths, z M, estimated by the CFD correction were distributed within m with the mean value of m, and z M over nilas had values 2 or 3 orders smaller. A somewhat smaller range m with the mean value of m was obtained if the T&Y correction was applied. Shirasawa and Aota (1991) showed that the roughness lengths over hummocked ice were mainly distributed within the range of m with some values beyond 10 2 m at the coastal region of Hokkaido (figure 5 in their paper). Considering the fluctuation of the z M values, our range of z M is reasonable. On the other hand, there was an attempt to relate the z M values with the friction velocity u* over sea ice, by Andreas et al. (2005a). They formulated a model that parameterized three regimes on the ice surface: the aerodynamically smooth regime, the drag caused by meterscale roughness, and the high-wind saltation of snow cover. They confirmed that their model agreed well with the multi-year ice at the Ice Station Weddell (ISW) and during the Surface Heat Budget of the Arctic Ocean project (SHEBA). The detailed formulations are described in their paper. Here we apply their model to the results obtained in this study and compare the distribution of the Measurements of Air-Ice Drag Coefficient over the Ice-Covered Sea of Okhotsk 495

10 Fig. 7. Large floe (φ ⱋ km) at around 10 am on February 13th, A = 100%. The CDN 103 value is 1.5 ± 0.2 by the T&Y correction. The CFD correction was not applicable. Fig. 9. Medium floe (φ ⱋ km) at around 11 am on February 12th, A = 100%. The C DN 10 3 values are 4.0 ± 1.0 by the CFD correction and 3.7 ± 0.6 by the T&Y correction. Fig. 8. Medium floe ( φ ⱋ km) at around 2 pm on February 7th, A = 100%. The C DN 10 3 value is 2.4 ± 0.4 by the T&Y correction. The CFD correction was not applicable. The size of the basket is 1.5 m (width) 1.5 m (width) 1.0 m (height). Fig. 10. Small floe (φ ⱋ m) at around 12:00 on February 14th, A = 100%. The CDN 103 values are 2.3 ± 1.3 by the CFD correction and 3.4 ± 0.5 by the T&Y correction. z M values with those obtained at the ISW and during the SHEBA campaign. Figure 12 shows the plot of zm against u*. Three lines in Fig. 12 are derived from the model of Andreas et al. (2005a). They fit the zm values over multiyear ice obtained at the ISW and during SHEBA, and for the zm values obtained in this study. The former two measurements over multi-year ice were performed over snowcovered, highly compacted, and relatively smooth surfaces. Therefore, the corresponding zm values are likely 496 A. Fujisaki et al. small and it is conceivable that our z M values were larger than those obtained at the ISW and during SHEBA. It is interesting that the trend of the zm-u* relation obtained in this study showed reasonable agreement with the model of Andreas et al. (2005a), which was developed for highly compacted snow-covered ice regions, not for a marginal ice zone like the south part of the Sea of Okhotsk. Although the ice fields in the Sea of Okhotsk are often covered with snow, the ice fields are not always compacted, and especially in the southern part, ice con-

11 Fig. 11. Drag coefficients under neutral stratification C DN 10 3 sorted by ice concentration. Data over nilas is not included. centration less than 100% is frequent, as shown in Table 2. Therefore, in such conditions, high wind could cause not only saltation of the snow cover but also piling up of the petty floes or other deformation processes. The agreement of the z M values obtained in this study with the model of Andreas et al. (2005a) suggests that a similar parameterization to theirs might be possible for sea ice in the Sea of Okhotsk in future. 4. Summary In this study we performed measurements of C DN with the eddy correlation method in the southern part of the Sea of Okhotsk. The disturbance of the wind field near the platform caused by the ship s structure was preliminarily evaluated by CFD, and two correction methods, the CFD correction and the T&Y correction, were introduced. The C DN 10 3 values finally obtained ranged from 1.9 to 5.4, with a mean value of 2.7 by the CFD correction, and from 1.5 to 5.0 with a mean value of 3.1 by the other correction. These are somewhat larger than the value Fig. 12. Scatter plot of roughness length z M against frictional velocity u*. Lines derived from the model of Andreas et al. (2005a) are also shown. Line M1 is fitted to the data obtained during the Surface HEat Budget of the Arctic Ocean dataset, and line M2 is fitted to the data at the Ice Station Weddell, respectively. Line M3 is fitted to this study. suggested by Shirasawa (1981), and lie in the same range as over rough ice and over very rough ice, complied by Guest and Davidson (1991) for first year ice. While Shirasawa (1981) suggests a drag coefficient of to estimate wind stress in the Sea of Okhotsk, a much larger value might be proper, based on our results. Most of the measurements in ice-covered regions were performed over small floe or ice cake, which indicates that floes deformed or crushed into small pieces were typical. The mean C DN 10 3 values over small floe (φ = m) were 2.6 ± 1.0 by the CFD correction and 3.0 ± 0.5 by the T&Y correction, while those over ice cake (φ = 2 20 m) were 3.8 ± 0.9 by the CFD correction and 3.6 ± 0.6 by the T&Y correction. Our result is consistent with the expectation that the smaller floes have experienced more deformation process and make the surface rougher, resulting in the larger C DN values. Although the form drag at the freeboard in a median Measurements of Air-Ice Drag Coefficient over the Ice-Covered Sea of Okhotsk 497

12 ice concentration could contribute significantly to the total drag, the relation between the C DN values and ice concentration was not clarified in the present study, mainly due to the great variation of the ice-surface roughness. The roughness z M was also evaluated using the model of Andreas et al. (2005a). The z M values obtained in this study were 1 2 orders larger than those found at the ISW and during the SHEBA project, because the two previous measurements were performed over multiyear ice with a surface smoothed by snow cover. In addition, they were performed in a highly compacted region, which does not provide a freeboard at the ice lateral side. While our measurements were taken only in the southern part of the Sea of Okhotsk, most of the floes were conveyed from the northern part by the East Sakhalin Current. Therefore, the knowledge obtained in this study could be extended to the whole region on some level. The C DN values over an ice covered region obtained in this study showed great variation, by a factor of 3 for the various surface conditions. In future, it would be desirable for numerical models to parameterize C DN as the function of ice concentration, mean wind speed, floe size, and other variables which can be related with C DN. At this stage, it is necessary to accumulate many more measurements with synchronous and qualitative observations of ice concentration. Some of the authors are engaged in the investigation of the sensitivity study of the air-ice drag coefficient, using the high resolution ice-ocean model for the Sea of Okhotsk. The results of this study will be a good supplement to such sensitivity studies. Acknowledgements The authors sincerely wish to thank the crew of the P/V Soya of the Japan Coast Guard, the scientific members of the Institute of Low Temperature Science, and all colleagues for their kind cooperation throughout the cruises. We are also grateful to the anonymous reviewers, who provided us insightful comments and suggestions. This work was supported by Grant-in-Aid for the Japan Society for the Promotion of Science Fellows ( ). References Anderson, R. J. (1987): Wind stress measurements over rough ice during the 1984 Marginal Ice Zone Experiment. J. Geophys. Res., 92(C7), , 7C0072. Andreas, E. L. (1995): Air-ice drag coefficients in the western Weddell Sea 2. A model based on form drag and drifting snow. J. Geophys. Res., 100(C3), , doi: / 94JC Andreas, E. L. and K. J. Claffey (1995): Air-ice drag coefficients in the western Weddell Sea 1. Values deduced from profile measurements. J. Geophys. Res., 100(C3), , doi: /94jc Andreas, E. L. and A. P. Makshtas (1985): Energy exchange over Antarctic sea ice in the spring. J. Geophys. Res., 90(C4), Andreas, E. L., R. E. Jordan and A. P. Makshtas (2005a): Parameterizing turbulent exchange over sea ice: the Ice Station Weddell results. 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