Extreme Value Estimation of Beaufort Sea Ice Dynamics Driven by Global Wind Effects
Extreme Value Estimation of Beaufort Sea Ice Dynamics Driven by Global Wind Effects
Sinsabvarodom, Chana; Næss, Arvid; Leira, Bernt J.; Chai, Wei
2022-08-01 00:00:00
The purpose of the present study is to investigate the extreme values of the ice drift speed, which are also considered in the light of the magnitude of the simultaneous wind speed. The relationship between wind speed and ice drift speed is studied. The long-term ice drift data is collected by using local subsurface measurements based on acoustic Doppler current profilers (ADCP) in the Beaufort Sea during the period of 2006−2017. Upward-looking sonars (ULS) are deployed in order to observe the ice thickness as well as to identify events that correspond to open water condi- tions. The relationship between the ice drift speed and the wind speed is also investigated. It is found that the magnitude of the average ice drift speed is approximately 2.5% of the wind speed during the winter season. Estimation of the extreme values of the ice drift speed is studied by application of the average conditional exceedance rate (ACER) method. It is found that the extreme ice drift speed during the ice melt season (i.e. the summer season) is approximately 20%−30% higher than that during the ice growth season (i.e. the winter season). The extreme ice drift speed can be effectively estimated based on the 2.5% wind speed. Moreover, the extreme ice drift speed can be obtained based on the extreme values of 2.5% of the wind speed based on multiplying with an amplification factor which varies in the range from 1.7 to 2.0 during the growth season, corresponding to increasing return periods of 10, 25, 50 and 100 years. Key words: ice drift, extreme wind speed, extreme ice-drift speed Citation: Sinsabvarodom, C., Næss, A., Leira, B. J., Chai, W., 2022. Extreme value estimation of Beaufort Sea ice dynamics driven by global wind effects. China Ocean Eng., 36(4): 532–541, doi: https://doi.org/10.1007/s13344-022-0046-3 1 Introduction motion of the oceanic boundary layer (OBL) beneath the ice. Driftting of sea ice takes places as a result of forces The motion of the drifting ice also depends on its inertia, the caused by the surrounding environmental processes related rheology and the re-distribution of its thickness variation to wind, current, Coriolis force, tilting of the ocean surface (Leppäranta et al., 2012). as well as internal contact stresses. The main effects, which In general, several measurement techniques have been dominate the ice drift behavior are those due to wind, current applied in order to observe the ice drift, such as local moni- and internal contact stresses, respectively (Campbell, 1965; toring (e.g., ADCP), GPS tracking, satellite imaging etc. Steele et al., 1997). Global wind plays an important role in Each method provides a different precision level corre- the ice drift, especially for the time scale of days or weeks. sponding to the sensor characteristics and the payload of the Wind blowing across the surface of the sea ice creates drag apparatus. GPS tracking can be used to observe the drift forces which lead to drifting of the sea ice. The magnitude motion of sea ice, such as ice floes and icebergs. It provides of the drag force depends on the wind speed as well as on the drift speed and trajectory data of the relevant objects the characteristics of the surface roughness of the ice itself, (Negrel et al., 2018; Yulmetov et al., 2016). At a particular or the snow cover when present (Leppäranta, 2011). location, local monitoring is an alternative to observation of Momentum from the wind is transferred to the sea ice and the sea ice drift in a specific area. Typically, underwater further down to the water body. Furthermore, both mooring buoys are employed in order to record the ice geostrophic ocean currents and tidal currents influence the thickness, drift speed, temperature, water pressure, etc. Gen- Foundation item: Open Access funding provided by NTNU Norwegian University of Science and Technology (incl St. Olavs Hospital - Trondheim University Hospital). *Corresponding author. E-mail: chana.sinsabvarodom@ntnu.no Chana Sinsabvarodom et al. China Ocean Eng., 2022, Vol. 36, No. 4, P. 532–541 533 erally, the upward looking acoustic Doppler current profile speed of sea ice becomes a key parameter also for design of (ADCP) instrument is installed at the top of mooring buoys mooring lines design in these regions (Sinsabvarodom et al., in order to observe the ice motion (Teigen et al., 2018; Visbeck 2020b). Typically, the mooring system design is based on the limit state approach. Both the short-term and long-term and Fischer, 1995). Satellites are commonly used to investi- gate the climate at larger scales. The information from satel- operation conditions must then be considered to achieve a lites consists of various types of data such as ice concentra- proper design. (API, 1996; DNVGL, 2015). The probability tion, ice thickness, ice drift speed, etc., in the form of aerial of overloading the mooring systems can be estimated based images. The data generally cover quite large areas, while on on the prediction of extreme values corresponding to a spec- the other hand this type of data is not characterized by a ified return period to cover all loading uncertainties. very high precision level. In the present study, the ice data that are collected by In the central Arctic, the ice drift velocity can be ADCP instruments installed at local mooring stations as part of the Beaufort Gyre exploration project are analyzed. This observed by using satellite measurements (Spreen et al., 2011). It was found that wind is the major influencing factor project was carried out by the Woods Hole Oceanographic in relation to ice drift, which is approximately one to two Institute (https://www.whoi.edu/). Upwards looking sonars (ULS) are also deployed in order to identify open water percent of the mean wind speed above the ice surface during the winters (October−May) from 1992/1993 to 2008/2009. events at the different stations. The magnitudes and co-vari- In the range of low wind speeds, a nonlinear relationship is ation of the global wind speed and the ice drift speed are found between the ice drift speed and the wind speed, but investigated. Subsequently, long-term time series of the ice the relationship becomes approximately linear within the drift speed and the reduction magnitude of wind speed are applied in order to perform an extreme value analysis based range of high wind speeds (Thorndike and Colony, 1982). In the Subarctic regions, the wind-induced drift due to the on the average conditional exceedance rate (ACER, 2013) atmospheric circulation causes exchange of sea ice between method corresponding to the various exceedance probabilities (which correspond to different return periods). the Kara Sea and the Central Arctic Ocean (Vinje and Kvambekk, 1991). The ice concentration (i.e. the fraction of 2 Mooring buoy locations in the Beaufort Sea areal coverage provided by the ice) is another key parameter Estimation of the ice drift speed is performed by using that influences the ice drift speed. In general, the three char- the time series data from underwater mooring buoys acteristic values represented by ice concentration, ice thick- installed in the Beaufort Gyre region. The data is publicly ness and ice drift speed are of key importance in any study available online at http://www.whoi.edu. Bottom-tethered related to ice drift. moorings were installed on the seabed at the four locations The drift of the sea ice is one of the main parameters illustrated in Fig. 1. Information about the relevant measure- associated with the magnitude of the ice loading on ships ment site locations and the recording intervals for each station and offshore structures, and this applies not the least when is listed in Table 1. including dynamic effects (ISO, 2010). The mechanical properties of sea ice inherently depend on the sea ice forma- tion in different areas, which causes uncertainties associated with ice load levels (Sinsabvarodom et al., 2020a). For vertical fixed offshore structures, different ranges of ice drift speeds cause vibration of the strusture, i.e. the so-called ice- induced vibration (IIV). It is an importance issue regarding the safety of structures in ice-covered regions, such as off- shore drilling platforms, lighthouses, and bridge piers. The intensive resonant response due to IIV may produce a sub- stantial structural acceleration which can also exceed acceptable levels for people working on the structures (Huang and Liu, 2008; Matlock et al., 1971). Different ice Fig. 1. Sites for collection of data in the Beaufort Gyre region in the drift speeds can also cause different ice-structure interaction Beaufort Sea, the red dots on the map represent the relevant locations (htt processses, for example, intermittent ice crushing , frequency ps://earth.google.com/web/). locking and continuous brittle crushing (ISO, 2010; Määtänen et al., 2012). As illustrated in Fig. 2 and Fig. 3, the mooring buoy at For ships and offshore structures operating in drifting each station is equipped with four instruments: bottom pres- ice, increasing drift speed tends to increase the global ice sure recorder (BPR), a McLane moored profiler (MMP), an load acting on the surface of the structure. The global ice upward looking sonar (ULS) and an acoustic Doppler current load on a station-keeping ship in drifting ice can be estimated profiler (ADCP) (Krishfield and Proshutinsky, 2006; Krish- by using the ice resistance method. Therefore, the drift field et al., 2003). Different types of physical properties 534 Chana Sinsabvarodom et al. China Ocean Eng., 2022, Vol. 36, No. 4, P. 532–541 Table 1 Location and data recording intervals for the different measurement stations Available data (year) Water Station Latitude Longitude 2006− 2007− 2008− 2009− 2010− 2011− 2012− 2013− 2014− 2015− 2016− depth (m) 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 A 750.0270'N 14959.9659'W 3825 − − − − O O − O O O O B 7759.8615'N 14957.6695'W 3821 − − − − O O O O O O − C 7659.063'N 13957.222'W 3722 − − − − − − − − − − − D 740.0007'N 1400.0606'W 3521 O O O O O O O O O O O the ice drift velocity by utilization of the average conditional exceedance rate (ACER) method. 3.1 Calculation of horizontal ice drift speed and direction The speed and direction of the ice drift are ideally corre- sponding to a Brownian motion. The external forces that influence the ice drift are generated by the surrounding environment. The ADCP instrument employs a series of acoustic transducers that emit and receive pings through the above sea ice cover at many different angles simultaneously. This allows to determine the speed and direction of the object. The primary records from the ADCP measurements are adjusted for speed of sound and depth variations relative Fig. 2. Illustration of monitoring instruments with corresponding mooring to the vertical center. It is converted to Earth-referenced system (Source: https://www2.whoi.edu/site/beaufortgyre/data/mooring- velocities and corrected for magnetic declination (https:// data/mooring-data-description/). www2.whoi.edu/site/beaufortgyre/data/mooring-data/ mooring-data-description/). In the present research, the vector components of the ice drift velocity during each hour, t, referred to a three-dimensional earth coordinate system in terms of north−south, east−west, and up−down with origin just above the respective observation point. The magnitude of the ice drift speed in the horizontal direction, v (t) is expressed by Eq. (1): 2 2 v (t) = v (t) + v (t) ; (1) Fig. 3. Subsurface mooring buoy redeployment [Photo by Peter Lourie, h N E October 4, 2016] (Source: https://archives.whoi.edu/beaufortgyre/www. where v (t) and v (t) are the horizontal velocity vectors in N E whoi.edu/page.do@pid=155296.html). the directions of the latitude (N) and the longitude (E), respectively. The direction of the ice drift is specified in were recorded by theses instruments. The BPR is employed terms of rotation angle, θ, corresponding to a polar coordinate in order to measure the pressure at the sea bed. The MMP is system with origin at the observation station. The rotational an autonomous instrument, which is deployed in order to angle, θ can obtain values in the range from 0° to 360°. It is profile the temperature and the salinity of the surrounding calculated based on the components of the velocity vector, i. water at each station. The Acoustic Doppler Current Profiler e. v (t) and v (t), as given in Eq. (2): N E (ADCP) is a sonar device, which transmits the acoustic ( ) (sound) signals at a fixed frequency with 600 kHz that are θ = arctan : (2) reflected by the sea ice. The returned echo signal is then E transformed into ice velocity. The upward-looking sonar 3.2 Extreme value prediction (ULS) is used in order to observe the draft of the sea ice The objective of the extreme value analysis is to provide cover ( Sinsabvarodom et al., 2019). a prediction of the largest ice drift speed corresponding to 3 Theoretical background specified probability of exceedance levels (or equivalently In this section, characterization of ice drift behavior and return periods). The ice drift data observed at each station is corresponding analysis methods are presented. The magni- then considered to represent an underlying stochastic pro- cess. The relevant time interval, for which the ice drift speed, tude and direction of the ice drift are calculated from its velocity components, which were monitored by means of V, is considered, and taken to be [0, T]. the ADCP equipment. The velocity vectors in the horizontal In the present study, prediction of the extreme value of plane are employed in order to predict the extreme values of the ice drift speed is performed by means of the average Chana Sinsabvarodom et al. China Ocean Eng., 2022, Vol. 36, No. 4, P. 532–541 535 conditional exceedance rate (ACER) method, which is a The optimal values of b and c parameters are now k k numerical approach in order to estimate the extreme values found by means of the Levenberg-Marquardt method. The by constructing the corresponding ACER functions (Næss final ACER function can be estimated from the fitted curve and Gaidai, 2009) of different order, k. It can be applied to in order to optimize the confidence interval of the predicted analyze time series realizations of a stochastic process for value. The selection of threshold values for prediction of the both stationary and non-stationary data sets. The principle extreme value is not a very critical issue, however, they and development of extreme value estimation by means of should still be chosen with some care. Finally, with the ACER functions are described in more detail by Næss and assistance of the efficient extrapolation scheme, which is Gaidai (2009) and Næss et al. (2013). These functions are based on the assumption of regularity of the ACER functions applied as a basis for developing the function given in with respect to the deep tail regions, the extreme distribution Eq. (3): of ice drift speed can be obtained. ( ) [ ( )] In the present study, the analysis procedure starts by P η exp (N k+ 1)εˆ η ; (3) obtaining time series of the ice drift velocity and the ice where εˆ (η) is the empirical ACER function of order, k as thickness from the ADCP and the ULS measurements. After given in Eq. (4). Although increasing accuracy is obtained that, classification of the ice cover is applied in order to dis- for increasing order k of the ACER function, the number of tinguish between the presence of ice versus open water. Cal- data points for calculation of εˆ (η) is reduced according to culation of both ice drift speed and direction are required in the corresponding numerical scheme. Generally, the ACER order to interpret the collected time-series. The seasonal functions of level η are highly regular in the tail region, dependence of ice drift behavior for the growth season versus assumed to apply for levels beyond a suitably chosen tail the melting season is investigated. The influence and rela- marker η . tionship between the wind speed and the ice drift speed are ( ) [ ( ) ] ε η q exp a η b ; η≥η ; (4) k k k k studied. Subsequently, anextreme value analysis is performed based on the different steps that are illustrated in Fig. 4. where a , b , c and q are parameter constants, that are k k k k dependent upon the order, k. The valid range for the values 4 Results of the ACER coefficients are a > 0, b ≤η and c > 0. k k k When the values of a , b , c and q are obtained, the k k k k 4.1 Joint variation of wind speed and ice drift speed extrapolation scheme described by Eq. (4) can be applied to Long-term ice drift data are collected from the ADCP provide reasonably accurate estimation of deep tail extreme measurements which are recorded once in an hour. Data values needed for obtaining long return period design values. records at Stations A, B and D are available. Unfortunately, The optimal values of the parameters are obtained by mini- for Station C, no data is obtained. The ice data record starts mizing the mean square error as expressed in Eq. (5). on 1st October of each year corresponding to the specified ∑ start of the winter season according to the Canadian regula- [ ( )] ( ) ( ) F a ;b ;c ;q = ρ ln εˆ η lnq+ a η b ; (5) k k k k k j i i tions. The ADCP measurements provide the velocity com- i=1 ponents in three orthogonal directions as referred to the where ρ is a weight factor to enhance the influence from the global Cartesian coordinate system. The calculation of hori- most reliable data points. η, i = 1; ; M are levels of the zontal ice drift speed is carried out by means of Eq. (1). ACER function, for which data points are available. The Long-term data of ice drift time series are considered as a ( ) + + data fitting here is based on ρ = lnCI (n ) lnCI (n ) basis for the extreme value analysis. Due to different time i i intervals for the records from the ULS and the ADCP mea- where CI and CI are the bounds of the 95% confidence surements, data points of ice thickness at the same time interval (CI). By fixing the values of b and c parameters, k k instants as those available for the ice drift speed are selected. obtaining optimal values of a and lnq parameters reduces k k This also allows identification of open water conditions, to a standard weighted linear regression problem in terms of [ ( )] which correspond to the ice thickness from the ULS mea- ρ,y = ln εˆ η and x = (η b) . Specifically, the optimal i k j i i j surement being equal to zero. values of a and lnq are expressed by Eqs. (6) and (7). k k The wind is generally assumed to play an important role in relation to the magnitude and direction of the ice drift in ρ (x x¯) (y y¯) i i the oceans (Leppäranta, 2011). The exposed area of the ice i=1 a (b ;c ) = ; (6) k k M surface is subjected to aerodynamic drag forces caused by ρ (x x¯) the wind-induced airflow. The present study considers the i=1 joint variation of the ice drift speed and the seasonal wind [ ] speed. The wind speed data were obtained from the Ventusky ln q (b ;c ) = y¯ + a (b ;c ) x¯; (7) k k k k k k web application, which has been developed by the company / / M M M M ∑ ∑ ∑ ∑ InMeteo. This web application is a platform for weather pre- where x¯ = ρ x ρ and y¯ = ρ y ρ . i i i i i i diction and visualization of metorological data at a global i=1 i=1 i=1 i=1 536 Chana Sinsabvarodom et al. China Ocean Eng., 2022, Vol. 36, No. 4, P. 532–541 Fig. 4. Flowchart of the steps related to the extreme value analysis. scale (https://www.ventusky.com/). A numerical model for during the winter season is about 2.5% of the wind speed. weather prediction has been developed by the Canadian Examples of scatter plots between the ice drift speed and 2.5% Meteorological Centre, CMC. Usually, the calculations are of the wind speed during the growth season and the melt performed every 3 hours with a grid resolution of roughly season are shown in Fig. 5. The ice drift speed exhibits a 25 km. The data is updated every 12 hours and the web higher correlation with 2.5% of the wind speed during the application has been available since 2016. The wind speed growth season from October to June than for the summer at 10 m above the water surface at the ADCP measurement season from June to August. The development of the ice stations is employed in order to study the joint variation of thickness during the growth season and the melt season can the wind and ice drift speeds. The data points for the ice be clearly observed from the ULS measurements. The sea drift speed that coincide in time with the more sparse data ice starts to form in October and reaches the highest thickness points for the wind speed are selected as a basis for the anal- around June. Subsequently, the ice thickness starts to ysis. Data records obtained from ADCP measurement in the decrease and mainly disappears around the end of August. year 2016−2017 were available only for Stations A and D, The time series of the ice drift speed, ice thickness and 2.5% and the distance between these two stations is 316.8 km. of the wind speed from the field measurements are shown in From the recorded time series, it is found that there are Fig. 6. seasonal differences in relation to the joint variation of the Furthurmore, formation of the ice can also be obsered wind speed and the ice drift speed during the growth season form satellite images. However, such observations have versus the melt season. The thickness of the sea ice will some limitation during cloudy weather, when the sky is have a physical effect on the dynamics of the ice drift process blocked. Some satellite images obtained during 2016–2017 owing to the inertia forces and rheological properties are shown in Fig. 7. The most serious ice conditions are (Leppäranta et al., 2012). Typically, the ice drift speed is seen to take place in June, while the ice tends to disappear approximately 2%−3% of the surface wind speed in the in August. Arctic Ocean (Kawaguchi et al., 2019; Leppäranta et al., 4.2 Extreme value analysis 2012). In the Beaufort Gyre, it is presently found that the magnitude of the ice drift speed for both Stations A and D Extreme value analysis of ice drift speed at each station Fig. 5. Relationship between ice drift speed and 2.5% of the wind speed at Station A during the growth season and the melt seasion during 2016−2017. Chana Sinsabvarodom et al. China Ocean Eng., 2022, Vol. 36, No. 4, P. 532–541 537 employed for the analysis because the wind speed data does not clearly differentiate with respect to seasonal variations of the sea ice. This can also be seen from the magnitude of the wind speed in the time series illustrated in Fig. 6. How- ever, It still seems that the wind speeds are higher in November to March than from April to October. From the ACER function plots b ≤η , the effect of dependence between data points can be quantified. The effect of this dependence gradually diminishes when the levels of the ice drift speed and the wind speed increase. In the uppermost tail, the effect of this dependence vanishes completely. Coalescence of the functions in the tail region allows application of the lower order ACER functions for extrapolation proposes. While the higher orders of the ACER functions provide a closer fit to the extreme value distribution inherent in the data, the number of data points which are available for estimation purposes are reduced according to the numerical estimation scheme. Hence, the Fig. 6. Time series of ice drift speed and 2.5% of the wind speed together lower order ACER functions may give more robust extrapo- with the ice thickness variation during 2016−2017 for Station A (a) and lation results. Station D (b). For the present analysis, the values of k are selected for the purpose of extreme value prediction corresponding to is performed in order to estimate the characteristic largest the number of collected data points in the long-term series. drift speed corresponding to given return periods. Generally, The bounds of the confidence interval estimated from the high drift speed is associated with an ice failure mechanism data, i.e. CI ,CI correspond to the 95% confidence inter- (when interacting with a structure) referred to as continuous val. The 100-year return period levels are estimated in the brittle crushing. This applies in particular for the case of present analysis. The extreme values corresponding to these dynamic ice action on vertical fixed offshore structures (ISO, horizontal lines are estimated by specifying a target 2010). For station-keeping of ships in ice, higher drift exceedance probability (or equivalently: a return period) speeds imply higher global ice loading which is reflected by which is set equal to the probability level of the ACER the so-called ice resistance approach (Sinsabvarodom et al., function as given by Eq. (4). The ACER functions can be 2021). The extreme value of the ice drift speed (corresponding extrapolated to determine the corresponding extreme value to a given design return period) implies the largest value of of the ice drift speed (for the 100-year return period) as the ice loading on ships and/or offshore structures during illustrated by the red horizontal lines in Fig. 9. the same period. The results of the extreme values for the ice drift speed Extreme value analysis by means of the ACER method ( ) and 2.5% of the wind speed for each station corresponding is based on the empirical ACER functions, εˆ η , which are to a range of different return periods ranging from 10 to 100 plotted versus the amplitude of ice drift speed for different yeas are listed in Table 2. orders, k. Examples of ACER functions for the ice drift speed for Station D corresponding to various values of k in 5 Discussion the growth and melt seasons are illustrated in Fig. 8a. For the wind, the ACER functions of the time series of 2.5% of 5.1 Relationship between the global wind speed and ice the wind speed from 2016−2017 are determined for various drift speed k as illustrated in Fig. 8b. The yearly wind data are In the Beaufort Sea, the sea ice tends to drift at approxi- Fig. 7. Satellite images from observation area in the Beaufort Sea (source: https://zoom.earth). 538 Chana Sinsabvarodom et al. China Ocean Eng., 2022, Vol. 36, No. 4, P. 532–541 Fig. 8. Examples of ACER functions of ice drift speed and 2.5% of the wind speed. Fig. 9. Extreme value prediction by the ACER method. mately 2.5% of the global wind speed (as referred to a trends to provide strong correlation with the fraction of height of 10 m above the sea surface). The 2.5%-value is wind speed in the growth season as illustrated in Fig. 5a. similar to the rule of thumb which was suggested by Then the degree of correlation physically tends to diminish Leppäranta (2011). Moreover, it is found that the sea ice when sea ice starts to melt. The sea ice tends to drift faster Chana Sinsabvarodom et al. China Ocean Eng., 2022, Vol. 36, No. 4, P. 532–541 539 Table 2 Results of the extreme value prediction by ACER method Extreme ice drift speed (m/s) Extreme wind speed (m/s) Return period (year) Station A Station B Station D Station A Station D Growth season Melt season Growth season Melt season Growth season Melt season 2.5% wind speed 2.5% wind speed 10 1.08 1.34 0.99 1.39 1.03 1.39 0.52 0.52 25 1.14 1.38 1.03 1.44 1.06 1.44 0.57 0.56 50 1.17 1.42 1.06 1.48 1.07 1.48 0.60 0.59 100 1.21 1.45 1.09 1.52 1.09 1.52 0.62 0.61 in the summer or melt season. The slope of linear fitting approximately 12%. Concerning the extreme values for the between the ice drift speed and 2.5% wind speed is flatter ice drift speed during the melt season, Station D exhibits due to the faster drift speed. This can be observed in Fig. 5b. higher extreme values than Stations B and A, respectively. The differences in extreme values between the three stations The drift speed is higher in the summer season owing to are approximately 5%. melting of the sea ice. This leads to ice free intervals on the The extreme values are next normalized with the water surface as shown on the satellite images in Fig. 7. The observed maximum values during the recording period in internal stress between the ice floes is then reduced. order to study the relative increase corresponding to increas- 5.2 Extreme value of ice drift speed ing return periods. The percentwise increase of the ice drift The extreme values of the ice drift speed during the winter speed (relative to the maximum observed value) is seen to season and the melt season are estimated by means of the be approximately 10%, 15%, 20%, and 25% for return periods ACER method. A comparison between the extreme values of 10-, 25-, 50- and 100-year, respectively, as illustrated by of the ice drift speed corresponding respectively to 10-, 25-, Fig. 11. 50- and 100-year return periods at each station is shown in The wind during the winter season has a strong influence Fig. 10. The extreme value of the ice drift speed during the on the ice drift. The magnitude of the ice drift speed is winter season for Station A is higher than that for Stations D approximately 2.5% of the wind speed in the Beaufort Sea and B, respectively. The extreme values for the different during this season. In this section, the relationship between stations (corresponding to the same return periods) vary by the extreme values of the ice drift speed and 2.5% of the Fig. 10. Comparison of extreme ice drift speeds corresponding to different return periods calculated by the ACER method for the growth season versus the melt season. Fig. 11. Normalization of extreme value ice drift speeds with maximum observed values during the recording period for the growth and melt seasons at each station. 540 Chana Sinsabvarodom et al. China Ocean Eng., 2022, Vol. 36, No. 4, P. 532–541 wind speed is investigated. It is found that a rough estimate measurements were collected and published by the Beaufort of the extreme ice drift speed can be obtained based on 2.5% Gyre Exploration Program based at the Woods Hole of the wind speed. The extreme values of the ice drift speed Oceanographic Institution (http://www.whoi.edu/beaufort- are typically higher than 2.5% of the wind speed by approx- gyre) in collaboration with researchers from Fisheries and imately a factor of 1.7−2.0 as illustrated by Fig. 12. This is Oceans Canada at the Institute of Ocean Sciences. The wind of significant advantage since the wind data are generally data was available from Ventusky web application, which available via the common weather forecast. Accordingly, has been developed by InMeteo company (https://www. the 2.5% value of the extreme wind speed can be employed ventusky.com) and Satellites immage above obsevation area to predict the extreme ice drift speed by multiplication with in the Beaufort Sea from Zoom Earth Website (https:// an amplification factor of around 1.7−2.0. zoom.earth ). Right and permissions Open Access This article is licensed under a Creative Com- mons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Fig. 12. Comparison of the extreme ice drift speed with the 2.5% wind Commons licence and your intended use is not permitted by speed for each station corresponding to four different return periods. statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons. 6 Conclusions org/licenses/by/4.0/. The upward looking sonar (ULS) is beneficial in order to classify data associated with ice cover thickness and for References joint recording of data together with the acoustic Doppler ACER, 2013. The ACER User Resources. https://folk.ntnu.no/arvidn/ current profiler (ADCP). These combined records allow ACER/. quite accurate estimation of the existing sea ice on the water API, 1996. Recommended Practice for Design and Analysis of Station- surface. The ACER method is applied to estimate the keeping Systems for Floating Structures, American Petroleum Insti- extreme values of the ice drift speed in the Beaufort Sea. tute. Campbell, W.J., 1965. The wind-driven circulation of ice and water in According to the present study, the following conclusions a polar ocean, Journal of Geophysical Research, 70(14), can be drawn. 3279–3301. (1) The ice drift speed is approximately 2.5% of the DNVGL, 2015. Position Mooring, DNVGL-OS-E301, DNV GL, Oslo. global wind speed (as referred to a height of 10 m above the Huang, G. and Liu, P., 2008. A dynamic model for ice-induced vibration water surface) during the winter season in the Beaufort Sea. of structures, Journal of Offshore Mechanics and Arctic Engineer- (2) The ice drift speed has a stronger correlation with the ing, 131(1), 011501. 2.5% wind speed during the growth season versus the melt ISO, 2010. ISO 19906:2010-Petroleum and natural gas industries–Arctic season. offshore structures. (3) The extreme values of the ice drift speed in the melt Kawaguchi, Y., Itoh, M., Fukamachi, Y., Moriya, E., Onodera, J., season corresponding to different return periods have higher Kikuchi, T. and Harada, N., 2019. Year-round observations of sea- ice drift and near-inertial internal waves in the Northwind Abyssal values than those for the growth season, and the speeds are Plain, Arctic Ocean, Polar Science, 21, 212–223. typically being increased by around 20%−30%. Krishfield, R. and Proshutinsky, A., 2006. BGOS ULS Data Processing (4) The observed extreme values of the ice drift speed Procedure, Woods Hole Oceanographic Institution. are higher than the 2.5% wind speed during the winter season Krishfield, R., Toole, J. and Proshutinsky, A., 2003. BGFE 2003–2004 by a factor of approximately 1.7−2.0. MMP EMCTD and ACM Data Processing Procedures. Leppäranta, M., 2011. The Drift of Sea Ice, second ed., Springer, Acknowledgments Berlin, Heidelberg. 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Extreme Value Estimation of Beaufort Sea Ice Dynamics Driven by Global Wind Effects