LainePoiss®—A Lightweight and Ice-Resistant Wave Buoy

Victor Alari; Jan-Victor Björkqvist; Valdur Kaldvee; Kristjan Mölder; Sander Rikka; Anne Kask-Korb; Kaimo Vahter; Siim Pärt; Nikon Vidjajev; Hannes Tõnisson

doi:10.1175/jtech-d-21-0091.1

LainePoiss®—A Lightweight and Ice-Resistant Wave Buoy

Alari, Victor; Björkqvist, Jan-Victor; Kaldvee, Valdur; Mölder, Kristjan; Rikka, Sander; Kask-Korb, Anne; Vahter, Kaimo; Pärt, Siim; Vidjajev, Nikon; Tõnisson, Hannes 2022-05-03 00:00:00 MAY 2022 ALA R I E T A L. 573 V R a b,a,c d d a VICTOR ALARI, JAN-VICTOR BJÖRKQVIST, VALDUR KALDVEE, KRISTJAN MÖLDER, SANDER RIKKA, e a a a f ANNE KASK-KORB, KAIMO VAHTER, SIIM PÄRT, NIKON VIDJAJEV, AND HANNES TÕNISSON Department of Marine Systems, Tallinn University of Technology, Tallinn, Estonia Norwegian Meteorological Institute, Bergen, Norway Marine Research, Finnish Meteorological Institute, Helsinki, Finland WiseParker OU, Tallinn, Estonia Estonian Maritime Academy, Tallinn University of Technology, Tallinn, Estonia Institute of Ecology, Tallinn University, Tallinn, Estonia (Manuscript received 1 July 2021, in ﬁnal form 4 December 2021) ABSTRACT: Wave buoys are a popular choice for measuring sea surface waves, and there is also an increasing interest for wave information from ice-covered water bodies. Such measurements require cost-effective, easily deployable, and robust devices. We have developed LainePoiss (LP)}an ice-resistant and lightweight wave buoy. It calculates the surface elevation by double integrating the data from the inertial sensors of the microelectromechanical system (MEMS), and transmits wave parameters and spectra in real time over cellular or satellite networks. LP was validated through 1) sensor tests, 2) wave tank experiments, 3) a ﬁeld validation against a Directional Waverider, 4) an intercomparison of several buoys in the ﬁeld, and 5) ﬁeld measurements in the Baltic Sea marginal ice zone. These extensive ﬁeld and laboratory tests conﬁrmed that LP performed well (e.g., the bias of H in the ﬁeld was 0.01 m, with a correlation of 0.99 and a scatter m0 index of 8%; the mean absolute deviation of mean wave direction was 78). LP was also deployed with an unmanned aerial vehicle and we present our experience of such operations. One issue that requires further development is the presence of low-frequency artifacts caused by the dynamic noise of the gyroscope. For now, a correction method is presented to deal with the noise. SIGNIFICANCE STATEMENT: Operational wave buoys are large and therefore expensive and inconvenient to deploy. Many commercially available devices cannot measure short waves and are not tested in ice. Our purpose was to develop an affordable wave buoy that is lightweight, ice resistant, capable of measuring short waves, and also has a lon- ger operating life than existing research buoys. The buoy is easily deployed with a small boat or even an industrial drone, thus reducing operating costs. The buoy is accurate, and captures waves that are too short for operational wave buoys. This is relevant for coastal planning in, e.g., archipelagos and narrow fjords. We measured waves in ice in the Baltic Sea, and are planning to extend these measurements to Antarctica. KEYWORDS: Sea ice; Wind waves; Air-sea interaction; Buoy observations 1. Introduction 1980), Doppler current meters measure the wave-induced orbital motions (Gordon and Lohrmann 2002), and inverted Wind-generated waves with periods of up to 25 s dominate echo sounders measure acoustic travel time between the the spectrum of ocean surface vertical variance (Munk 1950; device and the sea surface (Wadhams 1978). Wave gauges Holthuijsen 2007). These waves are observed visually, but an piercing the sea surface measure the up-and-down movement objective quantiﬁcation of wave heights, lengths, and propa- of water through electrical capacitance or resistance (Donelan gation directions requires measurements with in situ or et al. 1985; Graber et al. 2000). The surface wave spectra is remote sensing technologies. This paper focuses on a newly then calculated from the measured physical quantity by math- developed wave measuring buoy. ematical transformations and wave theory. In situ instruments do not measure wave properties All the measurements techniques in the above (nonexhaus- directly. At the sea surface, wave buoys should follow the tive) list are feasible, but have their own limitations and pecu- three-dimensional movement of water particles while measur- liarities, for example, gaps in data due to salty water over ing the inertial data or the Doppler shift of a GPS signal washing the buoy and blocking the GPS signal (Bjork ¨ qvist (Herbers et al. 2012). Below the sea surface, pressure trans- et al. 2016), spurious data in echo soundings generated by ducers measure wave-induced pressure ﬂuctuations (Cavaleri breaking waves, and diminishing of short waves in pressure recordings (Bishop and Donelan 1987). More generally, the size of the instrument, the basic measurement principle, and Denotes content that is immediately available upon publica- the meteorology–ocean conditions affect the measurement tion as open access. result. Besides inherent limitations, operational and practical considerations, like ease of use and cost of the instrument, Corresponding author: Victor Alari, victor.alari@taltech.ee might be important. DOI: 10.1175/JTECH-D-21-0091.1 Ó 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 574 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 Majority of operational wave measurements are done with for sensor validation, including standstill measurements of surface-following buoys, which may also include sensors for acceleration noise and benchmark tests with monochromatic recording atmospheric and upper-ocean state variables motions. Thereafter, we will describe the accuracy of the (Thomson 2012). These buoys can be tethered to the sea ﬂoor buoy in capturing high-frequency waves in a wave tank. or allowed to drift under the inﬂuence of wind and currents. Section 5 deals with the ﬁeld test results. This includes An advantage of these buoys is their long operational life an extensive validation campaign against a Directional (several years). However, the established operational buoys Waverider and an intercomparison of several LP buoys. We are large and heavy. The National Data Buoy Center of also describe drifting experiments results, where a UAV was NOAA has tailored meteorology–ocean buoys, equipped used as a deployment method. We end section 5 by describing with wave measuring sensors, ranging from 1.8 to 12 m the results of waves-in-ice measurements from the Baltic Sea. in diameter. The widely used Datawell Waverider Mk-III, In section 6, we discuss the limits and merits of the new tech- TRIAXYS Directional Wave Buoy, and Fugro Seawatch nology and conclude our main ﬁndings in section 7. Four Mini II Buoy have diameters of at least 70 cm and weights of appendixes end the paper, with the description of the inertial over 100 kg. These off-the-shelf operational buoys may not be sensor, description of the denoising procedure, calculating an affordable choice for simultaneous deployments, and their validation statistics, and describing our experience of UAV handling requires expertise as well as vessel for deployment. deployments. These issues are somewhat alleviated with buoys as the Data- well DWR-G4, which weighs 17 kg, has a diameter of 40 cm, 2. Materials and methods and has a battery life of 30 days. Recent advances in accurate and low-cost motion sensors a. Technical description of the buoy and GPS technology have led to the development of a low-cost LP is a spherical wave buoy with a diameter of 32 cm, a easy-to-handle wave measurement platform called Spotter height of 22 cm (Fig. 1), and a weight of 3.5 kg. The enclosure (Raghukumar et al. 2019; Lancaster et al. 2021). It is a sea state is made of two tough glass ﬁber halves. Between the halves, detector with unprecedented coverage (Smit et al. 2021; there is a seal that makes the hull waterproof after it has been Houghton et al. 2021) and thanks to its small size, it might turn bolted together. After the buoy is sealed, it can be turned on out to be a practical tool for estimating wind speed from wave and off by holding a magnet to the outside of the hull. spectra (Voermans et al. 2020). First ﬁeld experiments of mea- Rechargeable lithium-ion batteries, with a capacity of suring waves in grease ice with Spotter show promising results 335 W h, can power the buoy for roughly 2 months. in performing these types of observations at a low cost (Kodaira The microcontroller of the buoy is connected to the sen- et al. 2020). The simultaneous deployments of several (tens, sors, the memory, and the communication modems through a hundreds) drifting wave buoys is also beneﬁcial for understand- custom built PCB board (Fig. 2). This controller}using an ing wave–current interaction at coastal and oceanic scales ARM Cortex-M4 core}was chosen because of its low power (Pearman et al. 2014; Veras Guimara ˜es et al. 2018) and wave consumption, ﬂoating point support, and digital signal proc- growth in complex archipelagos (Bjorkqvist et al. 2019)and essing functionality. fjords (Christakos et al. 2021). The inertial sensors of the buoy are a 3D accelerometer, In this paper, we describe and validate a new wave buoy a 3D gyroscope, and a magnetometer. These sensors are called LainePoiss (LP), which uses the microelectromechanical part of the Xsens MTi-3 (see appendix A for more details) system (MEMS) inertial measurement unit to detect surface attitude and heading reference system (AHRS). The inter- motion. LP was originally designed for wave measurements in nal processor of the system synchronizes the sensors, ice, but has over 3 years of research and development matured applies calibration models, and runs the sensor fusion into a valid device; it is already used for real-time wave moni- algorithm (including the extended Kalman ﬁlter), in order toring in the Baltic Sea. When developing the buoy, we have to convert inertial data from buoy body reference frame to kept the following combination of performance characteristics Earth reference frame. Henceforth, raw data will mean in focus: ice resistant, lightweight, operational, small, and the original acceleration data that are transformed to the affordable. These characteristics allow LP to be used for vari- Earth reference frame by the sensor. After assembling the ous research and engineering applications. For example, we buoy, we performed a magnetic calibration that corrected are currently planning to use LP for wave measurements in for the disturbance inﬂictedtothe magnetic ﬁeld of Earth the marginal ice zone, extending measurement times of opera- by ferromagnetic materials. The device location was tional wave buoys in the seasonally ice covered Baltic Sea, logged by a Global Navigation Satellite System (GNSS) ﬁeld measurements of shorter waves in archipelagos and lakes, receiver. and using unmanned aerial vehicles (UAV) as a rapid method We conﬁgured the output frequency of the inertial data to for deployments. LP is also a core infrastructure for validating 50 Hz, and these data are written to an SD card. Depending operational coastal wave models in Estonia. on the conﬁguration set by the user, the raw 50 Hz data and The structure of the paper is as follows. In section 2,we the processed data (wave spectra and bulk parameters) are describe the wave buoy in detail and introduce algorithms for converting the acceleration data into displacement data. In also sent to a cloud server in real time (e.g., every 30 min) section 3, the omnidirectional and directional wave parame- using cellular LTE or only processed data over satellite ters are deﬁned. Section 4 describes different laboratory tests Iridium SBD networks. The buoy can be conﬁgured to use MAY 2022 ALA R I E T A L. 575 FIG. 1. (a) LainePoiss in a moored conﬁguration, (b) transporting with a UAV, and (c) drifted to pancake ice. either one or both of these communication options; the buoy channel because of its signiﬁcantly lower data transmission always prioritizes the cellular network, but can automatically costs. The buoy can therefore also send the raw data through switch to the satellite network if no cellular coverage exists. the cellular network, although this option can be disabled to We chose the cellular network as the primary communication save power. 576 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 amplitudes to 0 below 0.05 Hz. This integration procedure is similar to the one used in Rabault et al. (2020). For the ﬁeld data, a correction to the energy was performed based on the amount of variance that was lost in the denoising. The denois- ing, compensation and integration procedures are docu- mented in detail in appendix B. The 30-min displacement time series were then used to cal- culate wave spectra from 100-s blocks using the Welch method with a 50% overlap (35 segments), resulting in a wave spectrum with a 0.01 Hz resolution. Each segment was tapered with a Hann window. The highest frequency used in the spectrum was 1.28 Hz, which corresponds to a 95 cm deep water wavelength and approximately 3 times the buoy diame- ter. Higher frequencies were starting to be distorted by the size of the buoy when compared to the wave gauge data (see FIG. 2. Scheme of the electronics components of the buoy. section 4c on the wave tank experiment). Note that the data processing procedures in the laboratory b. Data processing experiments differed slightly from the data collected from ﬁeld tests, since the time series were shorter. Please see The buoy sampled the acceleration with a 50 Hz sampling section 4c for details on the exact procedure for laboratory frequency, and (in the ﬁeld tests) these data were saved in data. For the waves-in-ice measurements (section 5d), the ﬁles containing 65 538 measurements (circa 22 min). We have data processing procedure differed also a bit from the other used the raw data which are already transformed into an ﬁeld data}namely, the energy after denoising was not added Earth reference frame by the sensors fusion algorithms. For back because the noise was so dominant. each deployment, these acceleration data were combined into one long time series from which we constructed 30 min dis- 3. Wave parameters placement time series with starting times of :00 and :30 using the following procedure: a. Omnidirectional parameters 1) We constructed 32 min time series from the continuous We used the following deﬁnitions of wave parameters. The acceleration data (:59–:31). spectral moments are deﬁned as 2) The x, y, and z accelerations were low-pass ﬁltered (ﬁlter “biting” between 1.28 and 5.12 Hz) with a ﬁnite impulse m f Ef()df, (1) response (FIR) ﬁlter that had 162 coefﬁcients before being downsampled to a 5.12 Hz resolution using a near- where a lower integration frequency of f = 0.10 Hz and an est neighbor interpolation. Because of the original 50 Hz upper frequency of f = 0.58 Hz was used to match the highest sampling frequency, this resulted in a maximum shift on frequency that was reliably captured by the Waverider. 100 ms of the measurement. Using the spectral moments we deﬁned the signiﬁcant wave 3) The acceleration data were double integrated in Fourier height: space. Before integration, the white noise was removed for frequencies up to 0.10 Hz, and the amplitudes below H 4 m : (2) m 0 0.05 Hz were set to zero (these cutoffs were appropriate for our speciﬁc dataset; see appendix B for details). We The wave periods were deﬁned as removed 30 s from the start and end of the double inte- grated time series to cut out transient data caused by the T , (3) Fourier integration. 0 4) Finally, after accounting for the data lost by FIR ﬁltering T , (4) and Fourier integration, we cut the time series to start 01 exactly at :00 or :30 to a 9216 point long block. These 30 min block coincided exactly with the displacement 0 T , (5) time series of the Waverider at Suomenlinna, which we m used for validation. T argmax Ef() , (6) The denoising of the acceleration data was performed by estimating the mean amplitude of the fast Fourier transform (FFT) of the signal between frequencies 1/100 and 1/30 Hz. f Ef() df The integration was performed in Fourier space, where the T : (7) removing of the low-frequency energy was applied gradually Ef() df below 0.06 Hz using a half-cosine function, setting the MAY 2022 ALA R I E T A L. 577 Here, the peak period T was determined using a parabolic ﬁt. The so-called characteristic period T is of the same type that was originally developed as an alternative to peak fre- quency by Young (1995). Bjo ¨rkqvist et al. (2019) proposed it as a more stable alternative characterization of a repre- sentative wave frequency in archipelago conditions, where the peak period is often ill deﬁned. Note that we use a slight modiﬁcation by integrating a weighted average of the inverse of the frequency (f ) compared to the weighted integration of f by Young (1995) and Bjorkqvist et al. (2019). The narrowness of the spectrum was determined by the k -narrowness parameter (Battjes and van Vledder 1984): ⎧⎪ ⎪ f ⎨ 1 k Ef()cos 2pfT df ⎪ m ⎪ 02 2 ⎪ m FIG. 3. Noise level of a new (LP0) and used (LP1–LP6) AHRS 0 0 in comparison with manufacturers value. The noise height is calcu- ⎫⎪ lated using the ﬁt value to the real sensors. f ⎪ 1 ⎪ 1 Ef sin 2pfT df , (8) () 02 ⎪ f0 The directional spread was deﬁned as where k takes values between 1 (inﬁnitely narrow spectrum) s f 2 2 2m f , (14) () () and 0 (white noise) and has been found to capture the spectral shape better (especially in the archipelago) than width param- where eters depending on high moments (m or m )(Bjorkqvist et al. 2 4 2019). 2 2 m () f a () f 1 b () f : (15) 1 1 1 b. Directional parameters The mean and peak spreads were deﬁned as for the direc- Directional parameters were calculated using the ﬁrst pair tional spread [Eq. (14)] using of Fourier coefﬁcients, a (f) and b (f). These coefﬁcients were 1 1 calculated from the cross-spectra following Longuet-Higgins F 2 m a 1 b , (16) 1 1 (1961): 1 Q () f ye a () f , (9) F 1 2 2 m f a f 1 b f : (17) p p p 1 1 1 C f C f 1 C f () () () yy nn ee Q () f yn 4. Laboratory tests b f , (10) () C f C f 1 C f () () () yy nn ee a. Sensor static noise The manufacturer of the MEMS sensor reports a static where Q(f) and C(f) are the quadrature- and cospectra, with noise density value of 0:12 mg Hz for the acceleration subscripts y, e, and n referring to the vertical, east, and north sensor (mg is milli g it has as value of 9.81/1000). To test if displacements. this represents the actual noise of a single sensor, we con- The mean direction at each frequency was calculated as ducted a standstill measurement, where, at a room tempera- a () f 1 ture of 218C, we let the sensor measure for 3 h. We then u () f arctan 1 1808, (11) b () f calculated the power spectrum of the acceleration noise and transformed it to noise displacement spectra by dividing the with the mean and peak direction being acceleration spectra with (2pf) . We found that the unused sensor has a higher noise density than the manufacturer’s u arctan 1 1808, (12) m value (Fig. 3). We repeated the same procedure for sensors already used in deployments and found that the noise does not increase with the usage of the sensor (LP1 was used the a f 1 p most, 5100 h). Therefore, for the sensor noise, we will use u u f arctan 1 180 , (13) 21 p p b f the value 0:22 mg Hz . From a practical point of view, 1 p this sensor noise level only becomes important when dealing where f is the peak frequency determined without a para- with very low amplitude waves, e.g., waves in ice. For the bolic ﬁt. ﬁeld measurements described in this paper, the static noise 578 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 FIG. 4. Technical drawings of (a) benchstand, (b) wave tank, and (c) recommended mooring setup. of the sensor was subtracted only for the waves-in-ice meas- difference between the prescribed and measured value urements (section 5d). depends on the acceleration}the measured amplitude starts to deviate with decreasing acceleration, being 6% at 0.04 Hz. b. Benchmark test c. Wave tank The benchmark tests were conducted with a custom-made device (Fig. 4a). The amplitude was kept constant at 68 mm We tested the wave buoy’s response to irregular waves in (61 mm), while period was varied between 1 and 25 s by both tethered and free-drift setups. The experiments were adjusting the speed of the device. Since the device did not conducted in a wave tank (Fig. 4b) owned by the Small Craft reproduce a perfect sine wave, all the measured acceleration signals had harmonics at multiples of the dominant signal. TABLE 1. Test bench results. The measured acceleration signal was transferred to fre- Wave period Prescribed amplitude Measured amplitude quency space, the noise was removed and then double inte- (s) (mm) (mm) grated and transferred back to time space. Mean amplitudes of N cycles were calculated. N varied between 8 and 30, 168 69 568 66 depending on the cycle period. 10 68 64 The results of the benchmark test for periods 1, 5, 10, 20, 20 68 64 and 25 s are shown in Table 1. The sensor is able to measure 25 68 64 movement in the wind-wave and swell period range. The MAY 2022 ALA R I E T A L. 579 TABLE 2. Wave tank results. H was integrated between 0.30 For the tests, we moored one buoy 2 m from the wave m0 and 1.28 Hz. The peak frequency (f ) corresponds to the wave p gauge and let the other two drift. With the JONSWAP gauge. spectrum, we made 8 tests (Table 2), in which each combi- nation of peak period and signiﬁcant wave height was H (m) m0 repeated twice. For each test, a 3-min-long time series was f (Hz) Wave gauge LP1 LP3 (moored) LP4 analyzed. The time series was converted into a displace- ment power spectra using the Welch method (block length 0.57 0.15 0.16 0.16 0.16 0.63 0.16 0.15 0.17 0.16 30 s, 50% overlap). Neither datasets were decimated; LP 0.53 0.17 0.19 0.20 0.20 data sampled at 50 Hz and wave gauge data sampled at 0.53 0.17 0.19 0.20 0.19 200 Hz were used. 0.77 0.07 0.07 0.07 0.07 Signiﬁcant wave height, integrated between 0.30 and 0.77 0.06 0.08 0.07 0.07 1.28 Hz, shows a satisfactory match between wave gauge and 0.87 0.09 0.11 0.11 0.10 wave buoys (Table 2). The difference in signiﬁcant wave 0.73 0.10 0.10 0.11 0.10 height between the buoys and the wave staff was 21 to 3 cm. The wave spectra (Fig. 5) reveals a similar structure between the wave gauge and buoys up to 1.28 Hz and a slight shift of Competence Centre of the Tallinn University of Technology. frequencies of the drifting buoys due to Doppler shift. The aim was to validate the high-frequency part of the spec- trum and determine the accuracy of LP in conditions which represent wave growth at short fetches. 5. Field tests The 60-m-long, 5-m-wide, and 3-m-deep tank uses 6 pad- dles to generate waves, which are recorded by a capacitance The ﬁeld tests were conducted in the seasonally ice-covered wave height gauge (developed by Akamina Technologies) in Baltic Sea, which is an enclosed basin with a maximum fetch the middle of the tank. The duration of wave generation var- of 700 km. The deployments were made within 5 km from the ied from 210 to 300 s. coast (Fig. 6). FIG. 5. Comparison of drifting and moored LP’s with wave gauge at a wave tank. The wave ﬁeld corresponds to the JONSWAP spectrum. The 1.28 Hz cutoff frequency is marked by a vertical dashed line. 580 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 The spectra from both LP and DWR were integrated between 0.10 and 0.58 Hz (note that the actual low-frequency cutoff of the DWR spectra was 0.025 Hz), and both devices generally agreed on the wave statistics for the ﬁeld experi- ment (Table 4; see appendix C for the deﬁnition of the statisti- cal parameters). The mean signiﬁcant wave height was 0.42 m, which is 0.10 m higher than the 2016–18 measured average (Bjork ¨ qvist et al. 2019). Both LP and DWR measured a simi- lar highest signiﬁcant wave height, with the difference being within the expected sampling variability. The wave periods agreed better the more they were determined by the shorter waves, with T showing the best agreement and T the m02 p worst. The maximum peak period values for LP are probably not realistic but stem from the low-frequency noise dominat- ing the lowest integration frequency when total energy was very low. The dominant wave direction for both instruments was south-southwest. The spreading was, in a mean sense, slightly higher for LP than for DWR. Overall, the signiﬁcant wave height measured by LP and DWR matched well (Figs. 7–9), with a 0.01 m bias and 0.99 correlation coefﬁcient (Table 5). During two occasions in the ﬁrst deployment, LP measured an around 0.2 m higher signiﬁ- FIG. 6. Field test sites where LainePoiss’s were moored (dia- cant wave height than the DWR (Fig. 7b). Both of these cases mond) or deployed as drifters (circle). Existing operational wave took place during around 10 m s easterly winds, but LP and and windmeasurements are shownwitha star andplus signs. DWR matched up well during roughly 13 m s easterly winds in the autumn (Fig. 9b). We have not yet determined a a. Comparison against a Directional Waverider deﬁnitive reason for the discrepancy during the summer cases. We deployed buoys at two locations close to the opera- A tangling of the moorings of the LPs is improbable since tional Directional Waverider DWR-Mk III, which was both LPs measured similar wave heights. moored at a depth of 20 m outside of Suomenlinna in the The wave periods determined from spectral moments Finnish Archipelago (Fig. 6). The measurement area is char- compared well to those from the DWR (Figs. 10b,d,f). The scatterindex was3%–5%, with the biases being no more acterized by tens of islands in varying size and busy recrea- than 0.16 s (Table 5). The scatter index is highest (23%) for tional and commercial vessel trafﬁc, although the commercial the peak period (Table 5). The general poor validation for trafﬁc during the deployments was reduced because of the peak period is explained by the archipelago environ- COVID-19 restrictions to travel. ments, where the peak of the spectrum is often not well With some short gaps, the deployments lasted from June to deﬁned (Bjorkqvist 2020). The wave spectrum was more November 2020 (Table 3). Four different buoys were used, closely unimodal for the strongest southerly winds, and the because the battery life of one device did not last for the peak period therefore matched up well in the case of the entire campaign. The buoys were moored approximately highest signiﬁcant wave heights (Fig. 10j). The characteristic 300 m north of the DWR (Fig. 6), where the water depth was period has been proposed as an alternative to the instances 17 m. The recommended mooring consisted of an anchor, a when the peak period is ill deﬁned. The validation of the surface ﬂoat, LP, ropes connecting the assembly, and weights characteristic period showed that it removed a large part of (Fig. 4c). The mooring endured strong winds from all major 21 the scatter between the two devices while keeping the bias directions. The maximum 10 min averages were 15 m s 21 21 21 at a low 0.03 s value (Fig. 10h, Table 5). (west), 16 m s (north), 14 m s (east), and 21 m s 21 The wave direction measured by LP had a 18–28 bias with (south), with the gusts reaching 27 m s . The buoy was not respect to the DWR (Table 5). While the agreement was dragged from its deployment location, which shows that a good for both the mean and peak directions, the mean 25 kg mooring anchor was sufﬁcient. parameter expectedly has less scatter (Figs. 10c,e). A large Two buoys were deployed in June using a small plastic scatter in directional peak parameters are expected (e.g., motorboat. In August, one of these buoys was removed and Pettersson et al. 2003), especially in the archipelago where the second one was replaced (using the same boat). In the peak values are not even necessarily from the same September, the buoy was replaced again using a motorized wave component. For the same reason, also the peak direc- sailing vessel, and it was ﬁnally retrieved with a pilot boat in tional spreading had a 25% scatter index even though the the beginning of December. bias was only 28 (Table 5). The mean spreading was more robust with a scatter index of only 9% and a correlation of 0.88. Still, LP systematically Then owned by the City of Helsinki, now owned by Finnish Meteorological Institute. measured a slightly higher spreading than the DWR MAY 2022 ALA R I E T A L. 581 TABLE 3. An overview of the ﬁeld experiments where LainePoiss was moored. Deployment 1 Deployment 2 Deployment 3 Deployment 4 Device LP1–LP2 LP3 LP4 LP1–LP4 Location Suomenlinna (S1–S2) Suomenlinna (S1) Suomenlinna (S1) Va ¨ana-J ¨ oesuu ˜ (V1–V4) Depth (m) 17 17 17 19 Period 18 Jun–24 Jul 2020 14 Aug–21 Sep 2020 24 Sep–24 Nov 2020 22 Dec 2020–03 Jan 2021 Mean U (m s ) 6.3 7.3 8.2 4.1 Mean H (m) 0.32 0.39 0.50 0.51 m0 Mean T (s) 4.5 4.4 4.3 5.8 (bias = 38, slope = 1.09; Table 5). A visual comparison validation for this particular parameter. Several width param- (Fig. 10g) reveals that the difference is better explained by a eters are deﬁned using higher moments (Cartwright and Lon- ﬁxed offset than the calculated slope. Le Merle et al. (2021) guet-Higgins 1956) and are therefore sensitive to the high- found an offset of similar magnitude when comparing the frequency part of the spectrum. The validation was therefore (peak) directional spreading between radar and wave buoy partially limited by the 0.58 Hz upper frequency of the DWR. measurements. The laboratory data of Lin et al. (2021) also In the 0.10–0.58 Hz frequency range, LP spectra tend to be showed that wave buoys can underestimate the directional slightly wider than those from the DWR, which might be spread compared to wave gauges with 10%. It is therefore caused by low-frequency artifacts during low sea states. possible that the difference between the spreading mea- The spectral comparison shows a qualitatively good match sured by LP and the DWR might partially be caused by the (Fig. 11) between LP and DWR, except for the low-frequency part where LP has artifacts. During the northerly wind case size difference between the devices. Lin et al. (2021) found (Fig. 11a), the peak of the spectrum was roughly at 0.5 Hz, that the impact of the mooring was small in the laboratory, just below the cutoff frequency of the DWR. Above the but did not exclude that this factor would be more impor- DWR cutoff frequency, LP spectra followed an f tail, which tant in the ﬁeld. All in all, the agreement in the directional is in agreement with theory (Kitaigorodskii 1983; Phillips parameters are good, especially considering the possible 1985). For the easterly and westerly wind events, a clear peak sources of uncertainty. An additional validation of the spectral shape was per- formed by using the spectral narrowness parameter (k ). This parameter was proposed by Battjes and van Vledder (1984) and was found to be suitable for archipelago conditions by Bjorkq ¨ vist et al. (2019). The agreement between DWR and LP was reasonable (Fig. 10i), with a correlation of 0.92 and a bias of 20.02 (Table 5). The scatter index was high (23%), although we are not aware of any other cross-instrumental TABLE 4. LainePoiss and DWR statistics during the deployments (N = 6357). N is smaller than the one used in the validation statistics Table 5 because in June–July 2020 two LP’s were simultaneously measuring. In the validation, both buoys were included against the comparison with DWR; here only LP 1 is used (eastern buoy, Fig. 6). LP/WR Parameter Mean Std Min Max H (m) 0.42/0.42 0.27/0.29 0.04/0.03 1.84/1.90 m0 T (s) 3.05/2.91 0.40/0.43 2.11/1.91 4.87/4.53 m02 T (s) 3.26/3.06 0.46/0.49 2.17/1.93 5.48/4.84 m01 T (s) 3.84/3.44 0.61/0.59 2.44/2.05 6.73/5.86 m10 T (s) 4.40/3.83 1.49/1.12 1.87/1.74 9.53/8.32 T (s) 4.72/3.99 2.10/1.41 1.72/1.72 10.00/8.54 k (–) 0.11/0.13 0.09/0.10 0.00/0.00 0.59/0.68 s ( ) 45/41 12/11 27/23 80/80 s (8) 38/32 15/9 11/9 81/80 Mode Std Min Max FIG. 7. Suomenlinna validation period 1. (a) Solid black line is u (8) 202/198 45/44 5/1 359/359 wind speed and dashed black line is wind direction. (b)–(e) Black u (8) 202/200 52/49 0/0 359/358 lines are DWR and blue lines are LP. 582 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 FIG.8. As in Fig. 7, but for second validation period. FIG.9.As in Fig. 7, but for third validation period. was not deﬁned (Figs. 11b,c), which is a typical situation for retrieval, the instrument was cleaned and dried, and subse- the archipelago-type spectrum with many different fetches for quent tests showed that no permanent harm was done to the ¨ electronics. a ﬁxed wind direction (Bjorkqvist 2020). The highest waves The mean wind speed during the measurement campaign measured during the campaign were due to southerly winds, was 4.1 m s , but gusts at the Pakri weather station reached and both the LP and the DWR spectra showed a good match 21 21 16.5 m s . During moderate wind speeds (over 6 m s ), the even for the longer waves of a 9 s period (Fig. 11d). wind was mainly blowing from north or south. The maximum In summary, the validation conﬁrms the accuracy of LP in signiﬁcant wave height was 1.22 m, and the maximum wave complex wave conditions. The scatter of the peak parameters period was 5.97 s (Fig. 12). With the exception of the north- is explained more by the ill-deﬁned nature of the parameter erly winds, the waves and wind were misaligned. The than any actual differences between the devices. Otherwise, the validation statistics are similar to those determined for other small buoys when validated against established technol- TABLE 5. Validation statistics. N = 7486 for H . For other ogies (Raghukumar et al. 2019; Lancaster et al. 2021). m0 parameters, only cases where the DWR measured H . 0.25 m m0 b. Intercomparison of four moored devices were included (N = 4827). For an intercomparison of several buoys in the same wave Parameter Bias RMSD SI (%) Slope R conditions, we moored four buoys in a square layout with a H (m) 0.01 0.04 8 0.99 0.99 m0 maximum distance of 140 m from each other in places where T (s) 0.06 0.10 3 1.02 0.98 m02 the water depth was 18–19 m (deduced from nautical charts) T (s) 0.08 0.12 3 1.02 0.98 m01 (Fig. 6). The buoys were deployed in December and retrieved T (s) 0.16 0.23 5 1.04 0.96 m10 10 days later in January with a motorboat. The location was T (s) 0.03 0.35 9 1.01 0.91 chosen due to its openness to long waves from the northern T (s) 0.03 0.89 21 0.99 0.66 k (–) 20.02 0.04 23 0.85 0.92 Baltic proper and its gently sloping bottom, which keeps the s (8) 3 5 9 1.09 0.88 spatial wave height gradient small. s (8) 2 8 25 1.03 0.49 The mooring consisted of a 60 m rope from the anchor to the surface ﬂoat and a 20 m rope from the ﬂoat to the wave |Bias| MAD buoy. Unfortunately, LP3 started leaking during the ﬁeld u (8)1 7 campaign, causing the MEMS sensor not to register data. u (8)2 11 We exclude this instrument from further analysis. After MAY 2022 ALA R I E T A L. 583 FIG. 10. Scatterplots of wave parameters during Suomenlinna validation deployment grouped by signiﬁcant wave height. For the deﬁnition of variables see section 3. misalignment was caused by the slanting fetch (Donelan et al. The scatter index between H was 3%–5%, reﬂecting the m0 1985; Pettersson et al. 2010) and local topography. The slant- variability caused by sampling a random process (Donelan ing fetch also increased the directional spreading, since longer and Pierson 1983; Forristall et al. 1996). waves usually came from the west even though the short The outlier was the mean wave direction of LP1. During waves were aligned with the wind. For northerly winds, the the Suomenlinna UAV deployment (described in the next wave and wind directions aligned, leading to a lower spread- section) the release system malfunctioned and the buoy fell to ing compared to other wind directions. rocky ground from approximately 2 m. Although bulk omni- The wave parameters between the different buoys agreed directional parameters and directional spread (which does not well (Fig. 12). The R values (between LP1–LP2, LP1–LP4, depend on true north reference) were reasonable, the yaw and LP2–LP4) for signiﬁcant wave height are over 0.99 and angle probably lost its north referencing capabilities, thus ren- over 0.98 for mean wave period and for directional spreading. dering the directional estimates unreliable. 584 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 FIG. 11. Comparison of wave spectra at Suomenlinna for four different wind directions. Black lines are DWR; blue lines are LP. The thin dotted lines correspond to 30 min spectra, while the thick lines are averaged spectra of seven individual spectra. c. Deployment with an unmanned aerial vehicle as In the Gulf of Riga, we deployed three buoys from ice onto a drifter ice (Fig. 13d). UAV ground stations were approximately 2 km from shore at locations where pack ice was still safe to walk Va ¨ana- ¨ Joesuu ˜ (VJ) was the ﬁrst ever deployment of LP on. The buoys drifted with ice (with occasionally entering with a UAV (Fig. 13a; Table 6). The buoy took about 2 h to open water) up to month. One buoy stopped sending data drift back to the shore. Signiﬁcant wave height was about 1 m, 10 days after the deployment because it was brought directly which also matched the value from a Copernicus CMEMS from another (moored) experiment and the battery level was product (not shown here). already low. Luckily, locals found it on shore and notiﬁed us During the Suomenlinna deployment the buoy was dropped using the contact information on the buoy. The results from near the moored DWR (Fig. 13b). Wind gusts reached the measurements in ice are described in section 5d. 15 m s and the signiﬁcant wave height was around 1 m with The description of the UAV deployment procedures are a wave direction from SSW. The buoy drifted until the next presented in appendix D. day and was picked up from a rocky island with a pilot boat. At Leppneeme (Fig. 13c), the buoy was deployed from the d. Waves in ice measurements shore. Although the wave direction was toward the shore, alongshore currents transported the buoy eastward for about We deployed three drifting buoys in the eastern part of the Gulf of Riga (see section 5c). On 6 March 2021 a strong south- 12 h before it got stuck in pancake ice close to the coast westerly wind event occurred, with the average measured (Fig. 1c). The signiﬁcant wave height was roughly 0.5 m. The UAV ground stations were about 2 km from the wind speed and wind gusts being 15 and 21 m s , respectively deployment sites. During these three experiments, we opera- (Fig. 15a). Sentinel-1 overﬂights in the morning (0400 UTC) tionally estimated the drift of the buoys with Seatrack web and in the evening (1600 UTC) showed that the ice edge (https://stw.smhi.se/) and found that the wind leeway coefﬁ- retreated more than 10 km in about 12 h (Figs. 14a,b). The cient is around 2.5%, which is in the same range as similar Copernicus CMEMS wave ﬁeld forecast predicted a 2 m sig- spherical drifting buoys (Sutherland et al. 2020). niﬁcant wave height near the ice edge close to the wave buoys MAY 2022 ALA R I E T A L. 585 existing waves-in-ice loggers (Kohout et al. 2015; Rabault et al. 2016; Montiel et al. 2018). This is of utmost importance since our knowledge on wave–ice interactions is still limited due to the low number of measurements made in ice (Squire 2020), especially measurements of the directional wave spectrum. Wave heights can be very low in the MIZ, and we have shown that a signiﬁcant wave height of 1 cm is detectable by LP. In the seasonally ice-covered water bodies, a cause for con- cern is the fact that operational devices have to be removed before the arrival of ice to avoid damaging the buoys. None- theless, the harshest wind conditions, and therefore wave con- ditions, can typically distort the wave statistics compiled purely from measurements (Bjorkqvist et al. 2018). Although LP is not designed to replace operational wave buoys, one possible application would be to complement operational measurements by replacing the operational buoy with LP when it is retrieved, thus capturing the open water time before freezing. LP should survive the ice, but if the buoy is lost, the ﬁnancial implications are not as severe (buoy costs roughly EUR 5000) as a loss of an expensive operational buoy, nor do they threaten the continuity of the operational measurements as a whole. Routine measurements also seldom capture waves shorter than 0.5–0.6 Hz, but LP extends the measurement range to 1.28 Hz (roughly 1 m wavelength). These shorter waves have been extensively studied with specialized research setups, e.g., FIG. 12. Intercomparison of three LP’s moored simultaneously using wave staffs or polarimetric cameras. The reason for the about 100 m apart. The dashed black line marks (a) the wind speed persistent scientiﬁc interest for this part of the wave regime is from Pakri weather station and (c) the wind direction. its decisive impact on many sea–atmosphere processes. Waves between 0.58 and 1.28 Hz have been shown to contribute (Fig. 14c). The predicted peak period was 7 s, and the wave 26% of the so-called Stokes drift (Lenain and Pizzo 2020), direction was between SW and W. and they also carry a signiﬁcant part of the wave-induced All three buoys started picking up the wave signal at stress (Janssen 1991; Mueller and Veron 2009). These pro- around noon, and in the evening the signiﬁcant wave height cesses then affect the drift of the object, oil, and other surfac- reached up to 1.2 cm at the buoy that was closest to the ice tants and enhance the upper-layer turbulence and mixing, edge (Fig. 15b). The measured energy was above the sensor thus contributing to the sea–atmosphere ﬂuxes of, e.g., CO . noise threshold for frequencies 0.10–0.14 Hz, and the sur- One possible niche for LP could be regions like archipelagos, face displacement time series showed identiﬁable wave fjords, or small lakes. In these areas, the short waves can carry groups during the time of the maximum signiﬁcant wave a major part of the total wave energy, but establishing elabo- height (Figs. 15c,d). The roll and pitch angles deviated less rate research wave measurement stations might not be feasi- than 18, indicating that the buoys were ﬁrmly lodged in ice ble. From a practical perspective, the measurement of the during the wave event. high-frequency part might require cleaning of the buoy after some time to avoid accumulation of added mass and change of the buoy dimensions due to biofouling (Thomson et al. 6. Discussion 2015; Campos et al. 2021). Research and development of prototype miniature wave Peak wave periods can reach 25 s in the world oceans buoys and loggers has increased in the last decade (e.g., Loehr (Hanaﬁn et al. 2012), but low-frequency noise in wave meas- et al. 2013; Kennedy et al. 2014; Hirakawa et al. 2016; urements are unfortunately a common feature. Ashton and Centurioni et al. 2017; Yurovsky and Dulov 2017; Farber et al. Johanning (2015) found spurious low-frequency energy 2018; Skinner et al. 2018; Zong et al. 2019; Carandell et al. caused by high drift forces brought about by currents and 2020; Cook et al. 2020). Small and affordable emerging wave mooring. Low-frequency artifacts can also be created by a buoys, like Spotter (Raghukumar et al. 2019) and LP, open loss of the GPS signal in buoys that use the Doppler shift to up new possibilities for deploying large numbers of buoys measure the buoy velocity, e.g., the DWR-G4 (Bjork ¨ qvist simultaneously. With the Spotter, this has already been imple- et al. 2016). We found that the MEMS sensor of the LP also mented on oceanic scales through assimilation of wave data in suffers from low-frequency noise. This noise comes from the an operational wave model (Houghton et al. 2021; Smit et al. gyroscope random noise, which affects the pitch, roll, and yaw 2021). The ice resistance allows LP to be deployed in the mar- angles. These angles are then used to calculate the free accel- ginal ice zone in large quantities, thus complementing the eration inside the sensor, and the noise is further ampliﬁed by 586 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 FIG. 13. (a)–(d) Drifting experiments results in four locations. UAV ground stations are marked with asterisks. In (d) only tracks of buoys are displayed, because most of the time no wave motion in ice was present. Also in (d), 3 marks the deployment or retrieval locations. For the dates of the experiments, see Table 6. double integration. Low-frequency noise was also present in this variance back to the higher frequencies in proportion to drifting buoys. the already existing variance (see appendix B). This correc- Yurovsky and Dulov (2020) also identiﬁed low-frequency tion was performed in Fourier space, which means that noise, but did not present any correction method. Earle and already the time series, determined through the inverse trans- Bush (1982) and Lang (1987) proposed a method for denois- form after integration in Fourier space was corrected. ing by subtracting energy present at low frequencies from Although this method is partially ad hoc, it was shown to cor- higher frequency. By comparing several months of LP meas- rect the ﬁnal spectrum for both dominant waves and the spec- urements to coinciding Waverider measurements, we identi- tral tail. Nonetheless, further development, not excluding ﬁed biases in the variance density both for the low and high changing the MEMS sensor, is currently pursued. frequencies, and concluded that these biases are possibly Nontypical deployments, such as aerial deployments by related. When the low-frequency part was denoised, we quan- UAVs, have recently been used as an additional tool in obser- tiﬁed the amount of variance that was lost and reintroduced vational studies (Zappa et al. 2020). UAVs are gaining MAY 2022 ALA R I E T A L. 587 TABLE 6. An overview of drifting experiments where LainePoiss was deployed using a UAV. GoR refers to the Gulf of Riga. Deployment 1 Deployment 2 Deployment 3 Deployment 4 Deployment 5 Deployment 6 Device LP1 LP1 LP5 LP2 LP5 LP6 Location Va ¨ana-J ¨ oesuu ˜ (VJ) Suomenlinna (SO) Leppneeme GoR GoR GoR Type Drifting Drifting Drifting Drifting Drifting Drifting Period 15 Aug 2019 6–7 Dec 2019 27–28 Feb 2021 3–11 Mar 2021 3 Mar–5 Apr 3–30 Mar Mean U (m s ) 8 13 8 In ice In ice In ice Mean H (m) 0.94 0.87 0.41 In ice In ice In ice m0 Mean T (s) 4.2 4.4 2.7 In ice In ice In ice m10 popularity since they can carry lightweight sensors (Fuertes been added to remove the need for opening the buoy and to et al. 2019). These innovative solutions are partially motivated enhance usability. The inertial sensor, electronics, and mea- by environmental concerns, but they also allow to bypass the surement methodology are kept the same. First laboratory cost of a ship. Because of its low weight, LP can be deployed tests of the new design on durability and waterproofness have by an industrial UAV as a drifter. It has already been tested been carried out successfully, but further testing is ongoing to in deployments from shore and from sea ice with the deploy- validate this new design in the ﬁeld. ment range extending to 2 km. These novel deployment tech- niques are still being established, but possible applications can 7. Conclusions include collecting data from surf zones or transporting a buoy A wave buoy [LainePoiss (LP)] was developed. LP weighs onto the MIZ. UAV deployments will continue to be one part 3.5 kg, measures waves up to 1.28 Hz, has a rechargeable bat- of the further development of LP. tery with 2 months of operation, and transmits wave parame- It is possible to extend the operation time of LP by replac- ters and spectra operationally over cellular or satellite ing rechargeable Li-ion batteries with lithium-thionyl chloride networks. From our study, we can conclude the following: primary batteries. These batteries have an energy density that is about 2.5 times higher than that of rechargeable ones. This • Wave parameters measured in the ﬁeld were in good would extend the autonomous operating time to 5 months accordance with those measured by a nearby Directional and make measurements in remote locations more feasible. Waverider: the bias of H was 0.01 m, correlation 0.99, m0 Also, the buoy leaked on two occasions over the course of and scatter index of 8%. The bias of T was 0.14 s, cor- m-10 18 ﬁeld deployments. These incidents have been accounted relation 0.98, and scatter index 4%. The mean absolute for when designing the new hull (Fig. 16). The new hull is deviation of mean wave direction was 78. made of molded plastic and has a sealing O-ring on the top. The high-frequency part of the spectrum (up to 1.28 Hz) External connectors for charging and accessing data have compared well to a wave gauge in the wave tank. The wave FIG. 14. (a) SAR image at 0400 UTC; (b) SAR image at 1600 UTC; (c) CMEMS model wave ﬁeld (signiﬁcant wave height, m; wave directions, arrows) at 1600 UTC. The locations of different LP’s at 1600 UTC are shown with yellow marks. Kihnu weather station is marked with a green ﬁlled triangle. All panels are on 6 Mar 2021. 588 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 Research (Grant PSG22). We thank Lauri Laakso and Roine Tuomo for helping with Suomenlinna ﬁeld experiments. We appreciate discussions with Kimmo Kahma. We thank Rivo ¨ ¨ Uiboupin, Juri Elken, Aarne Mannik, and Sigrid Aas for keep- ing the administrative matters under control. We thank Tarmo Kouts for helping us with the ﬁrst versions of real-time display of data on a website. The ﬁrst author thanks (little) Aran Alari for inspiring the wave buoy name LP. We thank the following institutions and enterprises for their successful participation in the applications of LainePoiss: the Maritime Administration of Estonia, the Estonian Environment Agency, AS Saarte Liinid, OU Lainemudel, TalTech Small Craft Competence Centre, and the City of Helsinki. We thank the anonymous reviewers for their constructive critique and comments}they helped us improve our article. Valdur Kaldvee and Kristjan Mol ¨ der are the founders, and the sole owners and employees of WiseParker OU, who produce the LainePoiss wave buoy presented in this manuscript. The development of LainePoiss has been made in cooperation with Tallinn University of Technology Data availability statement. The data used in this manu- script will be made openly available upon the publication of the ﬁnal paper. The LainePoiss MATLAB processing scripts are publicly available at https://github.com/bjorkqvi/LPP/ releases/tag/v1.0.0. FIG. 15. Waves in ice measurements. (a) Wind speed and direc- APPENDIX A tion at Kihnu weather station (for location, see Fig. 14;direction marked with dots); (b) signiﬁcant wave height from three buoys in The MTi-3 Sensor ice; (c) spectra of three buoys with thin dotted lines corresponding to 30 min single spectra and thick lines corresponding to averaged This appendix provides the details of the Xsens MTi-3 spectra; dashed black line shows the sensor noise ﬂoor; (d) surface sensor to the degree the information is publicly available. displacement for buoy 6 in ice. The sensor measures all 6 degrees of freedom (using a 3D accelerometer and 3D gyroscope) and provides the ori- spectrum of LP was validated up to a Waverider cutoff fre- entation (using a magnetometer). The technical speciﬁca- quency of 0.58 Hz in the ﬁeld, and the spectral tail of LP tions of the sensor (as provided by the manufacturer) can had an expected power-law behavior up to 1.28 Hz. be found in Tables A1 and A2. The integrated microcon- • LP can measure waves in ice with a signiﬁcant wave height troller unit (MCU) synchronizes the various sensors, which as low as 1 cm. This was conﬁrmed in an over a month-long is required for the onboard conversion of the acceleration experiment where several LP’s were deployed in ice in the signals from device to Earth-referenced frame. The role of Baltic Sea. the MCU is described by the manufacturer (Xsens 2019)as • Because of its low weight, LP can be deployed as a drifter follows: to a distance of at least 2 km using an unmanned aerial The MCU applies calibration models (unique to each sensor vehicle (UAV). and including orientation, gain and bias offsets, plus more Noise in the gyroscopic sensor resulted in low-frequency arti- advanced relationships such as nonlinear temperature effects facts, but the displacement time series can be corrected (see and other higher order terms) and runs the Xsens optimized appendix B). However, with the current validation and testing strapdown algorithm, which performs highrate dead-reckoning we can only conﬁrm the buoy’s capability to measure waves calculations at 800 Hz, allowing accurate capture of high fre- quency motions and coning and sculling compensation. The downto0.1 Hz}this was a suitable rangefor the datawehad Xsens sensor fusion engine combines all sensor inputs and opti- available for the validation, although it precludes most of the mally estimates the orientation, position and velocity at an out- oceanic applications. We will continue testing the wave buoy put data rate of up to 100 Hz. The MTi 1-s is easily configurable and expand our measurement areas outside of the Baltic Sea to for the outputs and depending on the application’sneeds can be capture longer waves. Depending on the MEMS sensor noise set to use one of the filter profiles available within the Xsens levels in these conditions, we can decide whether to replace the sensor fusion engine. wave buoy’s sensor for one with several times less noise. The exact details of the built-in fusion algorithm}which Acknowledgments. This work was supported by the Personal transforms the signal from the sensor references to the Earth Research Funding of the Estonian Ministry of Education and referenced frame}are not made public by the manufacturer. MAY 2022 ALA R I E T A L. 589 FIG. 16. New version of the buoy, with the charging and data acquisition connectors brought outside the buoy to reduce buoy openings. However, the process includes an extended Kalman ﬁlter Of the available ﬁlter proﬁles, we used the proﬁle (Xsens 2015). The process and the different options for ﬁlter- “North referenced” (see Table 16 of Xsens 2019). We cali- ing are described by the manufacturer (Xsens 2019): brated the magnetometer for hard iron distortion after assembling the whole device. This was done following the Xsens sensor fusion algorithm optimally estimates the orien- manufacturers speciﬁcation using their Magnetic Field tation with respect to an Earth fixed frame utilizing the 3D Mapper application. The process consisted of starting the inertial sensor data (orientation and velocity increments) and application and rotating the buoy over a large number of 3D magnetometer. The user can set the sensor fusion algo- orientations. After that, the tool calculated new calibration rithm with different filter profiles in order to get the best per- parameters and those were saved to the sensor memory. formance based on the application scenario (see Table 16). This had to bedone onlyonceafter assemblingthe device. These filter profiles contain predefined filter parameter set- The calibration of the internal temperature sensor used tings suitable for different user application scenarios. In addi- for thermal compensation was already done by the manu- tion, all filter profiles can be used with the Active Heading facturer. The manufacturer states that the sensor has been Stabilization (AHS) setting, which significantly reduces head- ing drift during magnetic disturbances. The Inrun Compass calibrated to operate between 2408 and 858C. Calibration (ICC) setting can be used to compensate for mag- To bring out the difference between the Earth referenced netic distortions that are caused by every object the MTi is acceleration data and data in the body reference frame of attached to. the buoy, consider once more the benchmark tests from TABLE A1. Speciﬁcations for the gyroscope and accelerometer of TABLE A2. Speciﬁcations and performance statistics for the MTi-3 as given by the manufacturer (Xsens 2019). magnetometer and orientation of MTi-3 as given by the manufacturer (Xsens 2019). Gyroscope Accelerometer Value Standard full range 62000 s 16g 8 Standard full range 8 G In-run bias stability 10 h 0.03 mg Bandwidth (23 dB) 255 Hz 324 Nonlinearity 0.2% √ √ 21 21 Noise density 0:0078 s Hz 0:12 mg Hz Total RMS noise 0.5 mG Sensitivity variation 0.05% 0.05% Resolution 0.25 mG Nonlinearity 0.1%FS 0.5%FS Roll/pitch static RMS 0.58 g sensitivity (calibrated) 0.0018 (s g) } Roll/pitch dynamic RMS 0.88 Max output frequency 800 Hz 800 Hz Yaw dynamic RMS 28 590 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 D« Ef() 2 E () f , (B3) f f and Ef and E (f) are the power spectra of the unprocessed () and denoised signals. D« quantiﬁes how much variance den- sity of the signal has been lost. Especially, if D« = 0 then no further correction is necessary. In practice, this denoising and compensation is performed during the integration, which results in a clean displacement signal from which the power spectrum can be calculated in a normal fashion without having to deal with the above compensation after the fact. Low-frequency acceleration data are ﬁrst denoised using the following procedure: the average squared Fourier amplitude is calculated for the frequencies 1/100 to 1/30 Hz: a Af() , (B4) FIG. A1. Raw 50 Hz Z-oriented acceleration data in Earth refer- 1=100# f # 1=30 ence frame and body reference frame. where Af() F at() is the Fourier transform of the accel- eration signal and Af is its modulus. section 4b. This time the sensor was placed so that the pitch () angle was approximately 458. We repeated the experiment This mean value (the noise) is then removed from the for 5 s motion period (Fig. A1). The acceleration in the Fourier transform by body reference frame is a fraction of the acceleration in the !" Earth reference frame, with a cosine dependence of roll Af() 2 a 1 2 R () f A () f max 0,Af() , (B5) and pitch angles (Bender et al. 2010). We calculated the Af() Earth referenced acceleration by dividing the body refer- enced acceleration with the cosines of roll and pitch angles where R(f) is a response function: and found that it very well matches the values obtained with ⎧⎪ 0, 0 , f , f MTi-3 onboard processing (Fig. A1). The match of course is ⎪ 1 not one-to-one, since the MTi-3 fusion is much more elaborate ⎪ 1 f 2 f R () f 1 2 cos p f # f # f : (B6) and uses the accelerations from all three axes along with pitch f 1 2 ⎪ 2 f 2 f ⎪ 2 1 and roll. For our benchmark test the implication of using ⎪ 1 f , f # f Earth referenced data is straightforward. When the Earth ref- 2 N erenced accelerations are used, calculated amplitude is off by Here f = 0.08 Hz and f = 0.10 Hz. In other words, the 1 1 1 mm from the prescribed amplitude, while in the case of Fourier transform for f . 0.10 Hz is not touched. The using acceleration data in body reference frame the calculated 0.1 Hz cutoff was appropriate for our datasets in the Baltic amplitude is 14 mm lower compared to the prescribed ampli- Sea. For oceanic conditions this cutoff needs to be set to a tude (for the test case of 5 s period motion). lower value, but validating these lower frequencies would require additional ﬁeld measurements that include longer APPENDIX B waves. Following, e.g., Rabault et al. (2020), the acceleration val- Renormalization in Integration ues are then integrated in Fourier space: The limitations of the sensor create low-frequency noise, but we have concluded that this noise is actually a mis- X () f 2A () f R () f ·() 2pf , (B7) 0 0 f placed signal from other frequencies. If the low-frequency noise is removed, it should be added back to the frequen- ˆ ˆ Xf() 2Af()R () f ·() 2pf , (B8) cies, so that the power spectrum fulﬁlls the following: where f = 0.05 Hz and f = 0.06 Hz in the response func- 1 2 D«E () f Ef() E () f 1 (B1) 0 tion R (f). E () f That is, Xf and X (f) are now the uncorrected and () denoised Fourier transform of the displacement signal. We quantify how much of the squared amplitudes of the signal ⎡⎢⎢ ⎤⎥⎥ ⎢ D« ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ E () f ⎢ 1 1 ⎥ , (B2) were lost by the low-frequency correction: 0 ⎢⎢ ⎥⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ E () f ⎥ ⎢ 0 ⎥ ⎢⎢ ⎥⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ DX Xf() 2 || X () f : (B9) where f f MAY 2022 ALA R I E T A L. 591 This lost signal information will be added back in a way where x are observations and r are the reference values i i that will compensate the power spectrum as outlined in (typically from the Waverider). Eq. (B2): The variance and standard deviation are 2 Var x Cov x , x , (C5) $ () i () i i DX Xf() X () f 1 1 (B10) || X () f Std x Var x : (C6) () i () i $ For cross comparison of datasets, we deﬁned the follow- $ 2 Xf() 2 || X () f $ 0 ing parameters: f f X () f 1 1 (B11) Bias x 2 r : (C7) || X () f i i The root-mean-square deviation, mean absolute deviation and scatter index (in percent) are deﬁned: $ 2 Xf() $ ( X f 1 1 2 1 (B12) () 0 RMSD x 2 r , (C8) () i i || X f () N || x 2 r # i i $ i $ ˆ $ Xf MAD , (C9) () % f X () f : (B13) Xf () $ $ 2 $ () x 2 x 2() r 2 r f i i i i SI 100 : (C10) The displacement time series is then given by the inverse Fourier transform: The slope is deﬁned as a least squares ﬁt x = Kr xt() F Xf() : (B14) x r i i This time series is now corrected for the low-frequency K , (C11) artifacts, which has been redistributed to the other frequen- cies. The power spectrum or any other statistics can now be calculated from this displacement time series without fur- and the Pearson correlation coefﬁcient is ther corrections. Cov x , r () i i R : (C12) APPENDIX C Std x Std r () () i i Statistical Parameters With N is the number of data points we used the follow- APPENDIX D ing statistical parameters: Experiences from UAV Deployments Mean x x : (C1) i i N In this appendix, we document our experiences from six events where an industrial UAV was used to deploy LP as For angular quantities, u, the mean is deﬁned as a ﬂoating device. Our deployments were made in Estonia and Finland during 2019–21. The guidelines and regulations sin() u governing the use of UAV’s change and differ from country u arctan (C2) to country, especially outside of the European Union. cos() u Make sure to get correct information and follow any local and the difference laws and ordinances when considering deploying LP with a &' UAV. Also note that the steps below do not guarantee a || u 2 u min|| u 2 u , 3608 2|| u 2 u : (C3) 1 2 1 2 1 2 safe or successful deployment. The UAV should be regularly maintained to be sure of The covariance is the condition of the equipment; motors, blades, batteries, and the remote controller have to be working properly. Firmware and software should alsobe uptodate. Noti- Cov x , r x 2 x r 2 r : (C4) ()() () i i i i i i N 2 1 ﬁcations through, e.g., the remote controller or pilot 592 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 application should be taken seriously, and they need to be REFERENCES resolved before ﬂight. Before deploying the actual device, Ashton, I., and L. Johanning, 2015: On errors in low frequency we recommend practicing with, e.g., sandbags that have the wave measurements from wave buoys. Ocean Eng., 95,11– same weight as LP. 22, https://doi.org/10.1016/j.oceaneng.2014.11.033. A successful UAV deployment starts with a comprehen- Battjes, J. A., and G. P. van Vledder, 1984: Veriﬁcation of Kimu- sive preparation and plan for the ﬂight and requires at least ra’s theory for wave group statistics. Proc. 19th Int. Conf. on two persons. The ﬁrst person ﬂies the drone while the sec- Coastal Engineering, New York, NY, ASCE, 642–648, https:// ond person assists at lift-off and landing. We used a DJI doi.org/10.1061/9780872624382.044. Matrice 600 Pro industrial drone with a release mechanism Bender, L. C., N. L. Guinasso, J. N. Walpert, and S. D. Howden, (Fig. 1b). A 5-m-long ﬁshing thread (we used Dyneema 2010: A comparison of methods for determining signiﬁcant wave heights}Applied to a 3-m discus buoy during Hurricane 0.3 mm with a breaking strength of 25 kg) was found suit- Katrina. J. Atmos. Oceanic Technol., 27, 1012–1028, https://doi. able for connecting the UAV and the wave buoy. A longer org/10.1175/2010JTECHO724.1. thread could make releasing the LP more convenient as the Bishop, C. T., and M. A. Donelan, 1987: Measuring waves with UAV can be higher, thus having a stronger signal strength. pressure transducers. Coastal Eng., 11, 309–328, https://doi. Nonetheless, a shorter thread minimizes the motion of the org/10.1016/0378-3839(87)90031-7. buoy during ﬂight. The lift-off is the riskiest part: the second Bjo ¨rkqvist, J.-V., 2020: Waves in archipelagos. Ph.D. thesis, person has to hold the thread downwind and low to the University of Helsinki, 58 pp. ground to minimize the risk of the thread being caught by }},H.Pettersson, L. Laakso,K. K. Kahma, H.Jokinen, and the UAV motors. This has to be done while keeping a dis- P. Kosloff, 2016: Removing low-frequency artefacts from tance of at least a few meters from the UAV. For the safety Datawell DWR-G4 wave buoy measurements. Geosci. Ins- trum. Methods Data Syst., 5,17–25, https://doi.org/10.5194/gi- of the assisting person, the pilot should guide the UAV 5-17-2016. upward for the ﬁrst couple of meters as quickly as possible. }}, I. Lukas, V. Alari, G. P. van Vledder, S. Hulst, H. Pettersson, The rest of the lift-off can happen at a slower pace until A. Behrens, and A. Ma ¨nnik, 2018: Comparing a 41-year model thewavebuoy is up in theair. Weused a ﬂight height of hindcast with decades of wave measurements from the Baltic 20–30 m when transporting the wave buoy to the drop- Sea. Ocean Eng., 152,57–71, https://doi.org/10.1016/j.oceaneng. off location. 2018.01.048. With fully charged batteries at lift-off, we deployed the }}, H. Pettersson, and K. K. Kahma, 2019: The wave spectrum buoy at a distance of up to 2 km. We started guiding the in archipelagos. Ocean Sci., 15, 1469–1487, https://doi.org/10. UAV back toward the ground station before the battery 5194/os-15-1469-2019. dropped below 50%. In our deployments we ﬂew upwind Campos, R. M., H. Islam, T. R. Ferreira, and C. Guedes Soares, with the heavy weight, thus returning to the ground station 2021: Impact of heavy biofouling on a nearshore heave-pitch- roll wave buoy performance. Appl. Ocean Res., 107, 102500, downwind. We found that the battery charge at landing was https://doi.org/10.1016/j.apor.2020.102500. still at about 20%. Carandell, M., D. M. Toma, J. P. Pinto, M. Gasulla, and Below is a step-by-step checklist that we have used in J. del Rıo, 2020: Impact on the wave parameters estima- our deployments: tion of a kinetic energy harvester embedded into a drifter. • Global Oceans 2020: Singapore–U.S. Gulf Coast, Biloxi, The pilot does a UAV precheck a day before ﬂight as well MS, IEEE, https://doi.org/10.1109/IEEECONF38699.2020. as on the ﬁeld. If applicable, follow the messages from the pilot application. Cartwright, D. E., and M. S. Longuet-Higgins, 1956: The statistical The second person, crouching at least 2 m from the UAV, distribution of the maxima of a random function. Proc. Roy. holds the thread under tension between the UAV and the Soc. London, 237A,212–232, https://doi.org/10.1098/rspa. person’s hand, ready to give slack as the UAV is ascending. 1956.0173. The pilot loudly notiﬁes the other persons before activating Cavaleri, L., 1980: Wave measurement using pressure transducer. motors and makes sure everybody is ready for lift-off. Oceanol. Acta, 3, 339–346. The pilot ascends the ﬁrst 2 m as quickly as possible, and Centurioni, L., L. Braasch, E. Di Lauro, P. Contestabile, F. De Leo, the second person gives slack to the thread as the UAV R. Casotti, L. Franco, and D. Vicinanza, 2017: A new strategic takes off. wave measurement station off Naples port main breakwa- • ter. Coastal Eng. Proc., 1, 36, https://doi.org/10.9753/icce. A second person must hold the thread under tension v35.waves.36. between the UAV and their hand until the LP is up in the Christakos, K., J.-V. Bjorkqvist, L. Tuomi, B. R. Furevik, and Ø. air. Breivik, 2021: Modelling wave growth in narrow fetch geom- Thread should be downwind, even though the UAV might etries: The white-capping and wind input formulations. Ocean deviate also downwind where the second person is holding Modell., 157, 101730, https://doi.org/10.1016/j.ocemod.2020. the thread. Cook, A., A. Babanin, D. Sgarioto, P. Graham, J. Mathew, A. Recommendations for the pilot: Skvortsov, R. Manasseh, and D. Tothova, 2020: A UAV Flight height between 20 and 30 m. ‘mobile buoy’ for measuring surface waves. 22nd Australasian Do not ﬂy farther than 50% of the battery capacity; ideally Fluid Mechanics Conf., Brisbane, Australia, University of ﬂy upwind with payload and return with tailwind. Queensland, https://doi.org/10.14264/8e7141e. MAY 2022 ALA R I E T A L. 593 Donelan, M. A., and W. J. Pierson, 1983: The sampling vari- Kitaigorodskii, S. A., 1983: On the theory of the equilibrium ability of estimates of spectra of wind-generated gravity range in the spectrum of wind-generated gravity waves. waves. J. Geophys. Res., 88, 4381–4392, https://doi.org/10. J. Phys. Oceanogr., 13, 816–827, https://doi.org/10.1175/ 1029/JC088iC07p04381. 1520-0485(1983)0130816:OTTOTE2.0.CO;2. }},J.Hamilton,and W. H. Hui, 1985:Directional spectra of Kodaira, T., T. Waseda, T. Nose, K. Sato, J. Inoue, J. Voermans, wind-generated waves. Philos. Trans. Roy. Soc. London, and A. Babanin, 2020: Observation of on-ice wind waves 315A,509–562, https://doi.org/10.1098/rsta.1985.0054. under grease ice in the western Arctic Ocean. Polar Sci., 27, Earle, M., and K. Bush, 1982: Strapped-down accelerometer 100567, https://doi.org/10.1016/j.polar.2020.100567. effects on NDBO wave measurements. OCEANS 82, Kohout, A. L., B. Penrose, S. Penrose, and M. J. Williams, 2015: Washington, DC, IEEE, 838–848, https://doi.org/10.1109/ A device for measuring wave-induced motion of ice ﬂoes in OCEANS.1982.1151908. the Antarctic marginal ice zone. Ann. Glaciol., 56, 415–424, Farber, S., H. Allaka, I. Klein, and M. Groper, 2018: Estimating https://doi.org/10.3189/2015AoG69A600. sea state using a low cost buoy. 2018 IEEE Int. Conf. on the Lancaster, O., R. Cossu, S. Boulay, S. Hunter, and T. E. Baldock, Science of Electrical Engineering in Israel, Eilat, Israel, IEEE, 2021: Comparative wave measurements at a wave energy site https://doi.org/10.1109/ICSEE.2018.8646100. with a recently developed low-cost wave buoy (Spotter), Forristall, G. Z., J. C. Heideman, I. M. Leggett, B. Roskam, ADCP, and pressure loggers. J. Atmos. Oceanic Technol., 38, and L. Vanderschuren, 1996: Effect of sampling variability 1019–1033, https://doi.org/10.1175/JTECH-D-20-0168.1. on hindcast and measured wave heights. J. Waterw. Port Lang, N., 1987: The empirical determination of a noise function Coastal Ocean Eng., 122, 216–225, https://doi.org/10.1061/ for NDBC buoys with strapped-down accelerometers. (ASCE)0733-950X(1996)122:5(216). OCEANS’87, Halifax, NS, Canada, IEEE, 225–228, https:// Fuertes, F. C., L. Wilhelm, and F. Porte- ´ Agel, 2019: Multirotor doi.org/10.1109/OCEANS.1987.1160904. UAV-based platform for the measurement of atmospheric Le Merle, E., D. Hauser, C. Peureux, L. Aouf, P. Schippers, turbulence: Validation and signature detection of tip vortices C. Dufour, and A. Dalphinet, 2021: Directional and fre- of wind turbine blades. J. Atmos. Oceanic Technol., 36, quency spread of surface ocean waves from SWIM measure- 941–955, https://doi.org/10.1175/JTECH-D-17-0220.1. ments. J. Geophys. Res. Oceans, 126, e2021JC017220, https:// Gordon, L., and A. Lohrmann, 2002: Near-shore Doppler current doi.org/10.1029/2021JC017220. meter wave spectra. Proc. Int. Symp. on Ocean Wave Mea- Lenain, L., and N. Pizzo, 2020: The contribution of high-frequency surement and Analysis, San Francisco, CA, American Society wind-generated surface waves to the Stokes drift. J. Phys. of Civil Engineers, 33–43, https://doi.org/10.1061/40604(273)4. Oceanogr., 50, 3455–3465, https://doi.org/10.1175/JPO-D-20- Graber, H. C., E. A. Terray, M. A. Donelan, W. M. Drennan, 0116.1. J. C. Van Leer, D. B. Peters, and J. C. V. Leer, 2000: Lin, Z., T. A. A. Adcock, and M. L. McAllister, 2021: Estimating ASIS}A new air–sea interaction spar buoy: Design and per- ocean wave directional spreading using wave following buoys: formance at sea. J. Atmos. Oceanic Technol., 17, 708–720, A comparison of experimental buoy and gauge data. https://doi.org/10.1175/1520-0426(2000)0170708:AANASI2. J. Ocean Eng. Mar. Energy, 8,83–97, https://doi.org/10.1007/ 0.CO;2. s40722-021-00218-7. Hanaﬁn, J. A., and Coauthors, 2012: Phenomenal sea states and Loehr, H., and Coauthors, 2013: Development of a low cost wave swell from a North Atlantic storm in February 2011: A com- buoy by utilising smartphone technology. 21st Australasian prehensive analysis. Bull. Amer. Meteor. Soc., 93,1825–1832, Coastal and Ocean Engineering Conf.–14th Australasian Port https://doi.org/10.1175/BAMS-D-11-00128.1. and Harbour Conf., Barton, Australia, Engineers Australia. Herbers, T. H. C., P. F. Jessen, T. T. Janssen, D. B. Colbert, and Longuet-Higgins, M. S., 1961: Observations of the directional J. H. MacMahan, 2012: Observing ocean surface waves with spectrum of sea waves using the motions of a ﬂoating buoy. GPS-tracked buoys. J. Atmos. Oceanic Technol., 29, 944–959, Ocean Wave Spectra, Prentice-Hall, 111–136. https://doi.org/10.1175/JTECH-D-11-00128.1. Montiel, F., V. Squire, M. Doble, J. Thomson, and P. Wadhams, Hirakawa, Y., T. Takayama, T. Hirayama, and H. Susaki, 2016: 2018: Attenuation and directional spreading of ocean waves Development of mini-buoy for short term measurement of during a storm event in the autumn Beaufort Sea marginal ocean wave. OCEANS 2016 MTS/IEEE Monterey,Monterey, ice zone. J. Geophys. Res. Oceans, 123, 5912–5932, https://doi. CA, IEEE, https://doi.org/10.1109/OCEANS.2016.7761337. org/10.1029/2018JC013763. Holthuijsen, L., 2007: Waves in Oceanic and Coastal Waters. Mueller, J. A., and F. Veron, 2009: Nonlinear formulation of the Cambridge University Press, 387 pp. bulk surface stress over breaking waves: Feedback mecha- Houghton, I., P. Smit, D. Clark, C. Dunning, A. Fisher, N. Nidzieko, nisms from air-ﬂow separation. Bound.-Layer Meteor., 130, P. Chamberlain, and T. Janssen, 2021: Performance statistics of 117–134, https://doi.org/10.1007/s10546-008-9334-6. a real-time Paciﬁc Ocean weather sensor network. J. Atmos. Munk, W. H., 1950: Origin and generation of waves. Proc. First Oceanic Technol., 38, 1047–1058, https://doi.org/10.1175/JTECH- Conf. Coastal Engineering, Long Beach, CA, ASCE, 1–4, D-20-0187.1. https://doi.org/10.9753/icce.v1.1. Janssen, P. A., 1991: Quasi-linear theory of wind-wave genera- Pearman, D.,T.Herbers, T. Janssen, H. vanEttinger,S.McIntyre, tion applied to wave forecasting. J. Phys. Oceanogr., 21, and P. Jessen, 2014: Drifter observations of the effects of 1631–1642, https://doi.org/10.1175/1520-0485(1991)021,1631: shoals and tidal-currents on wave evolution in San Francisco QLTOWW.2.0.CO;2. Bight. Cont. Shelf Res., 91,109–119, https://doi.org/10.1016/j. Kennedy, D., M. Walsh, and B. O’Flynn, 2014: Development of a csr.2014.08.011. miniature, low-cost wave measurement solution. 2014 Pettersson, H., H. C. Graber, D. Hauser, C. Quentin, Oceans}St. John’s, St. John’s, NL, Canada, IEEE, https:// K. K. Kahma, W. M. Drennan, and M. A. Donelan, 2003: doi.org/10.1109/OCEANS.2014.7003217. Directional wave measurements from three wave sensors 594 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 during the FETCH experiment. J. Geophys. Res., 108, }}, and Coauthors, 2015: Biofouling effects on the response of a wave measurement buoy in deep water. J. Atmos. Oceanic 8061, https://doi.org/10.1029/2001JC001164. Technol., 32, 1281–1286, https://doi.org/10.1175/JTECH-D-15- }}, K. K. Kahma, and L. Tuomi, 2010: Wave directions in a nar- 0029.1. row bay. J. Phys. Oceanogr., 40, 155–169, https://doi.org/10. Veras Guimarae ˜ s, P., and Coauthors, 2018: A surface kinematics 1175/2009JPO4220.1. buoy (SKIB) for wave–current interaction studies. Ocean Phillips, O. M., 1985: Spectral and statistical properties of the Sci., 14, 1449–1460, https://doi.org/10.5194/os-14-1449-2018. equilibrium range in wind-generated gravity waves. Voermans, J., P. Smit, T. Janssen, and A. Babanin, 2020: Estimat- J. Fluid Mech., 156, 505–531, https://doi.org/10.1017/ ing wind speed and direction using wave spectra. J. Geophys. S0022112085002221. Res. Oceans, 125, e2019JC015717, https://doi.org/10.1029/ Rabault, J., G. Sutherland, B. Ward, K. H. Christensen, 2019JC015717. T. Halsne, and A. Jensen, 2016: Measurements of waves in Wadhams, P., 1978: Wave decay in the marginal ice zone mea- landfast ice using inertial motion units. IEEE Trans. Geo- sured from a submarine. Deep-Sea Res., 25,23–40, https://doi. sci. Remote Sens., 54, 6399–6408, https://doi.org/10.1109/ org/10.1016/S0146-6291(21)00004-7. TGRS.2016.2584182. Xsens, 2015: Data sheet MTi 1-series: 3D AHRS/VRU/IMU mod- }}, }}, O. Gundersen, A. Jensen, A. Marchenko, and ule. Xsens Doc. MT0512P, Revision B, 35 pp., http://www. Ø. Breivik, 2020: An open source, versatile, affordable waves sensores-de-medida.es/uploads/xsens_mti-1-series_datasheet.pdf. in ice instrument for scientiﬁc measurements in the polar }}, 2019: MTi 1-series datasheet: IMU, VRU, AHRS and regions. Cold Reg. Sci. Technol., 170, 102955, https://doi.org/ GNSS/INS module. Xsens Doc. MT0512P, Revision 10.1016/j.coldregions.2019.102955. 2019.A, 40 pp., https://www.xsens.com/hubfs/Downloads/ Raghukumar, K., G. Chang, F. Spada, C. Jones, T. Janssen, and Manuals/MTi-1-series-datasheet.pdf. A. Gans, 2019: Performance characteristics of “Spotter,” a Young, I. R., 1995: The determination of conﬁdence limits associ- newly developed real-time wave measurement buoy. ated with estimates of the spectral peak frequency. Ocean J. Atmos. Oceanic Technol., 36, 1127–1141, https://doi.org/10. Eng., 22,669–686, https://doi.org/10.1016/0029-8018(95)00002-3. 1175/JTECH-D-18-0151.1. Yurovsky, Y. Y., and V. Dulov, 2017: Compact low-cost Arduino- Skinner, E., M. Rooney, and M. Hinders, 2018: Low-cost wave based buoy for sea surface wave measurements. 2017 Pro- characterization modules for oil spill response. J. Ocean Eng. gress in Electromagnetics Research Symp.}Fall, Singapore, Sci., 3,96–108, https://doi.org/10.1016/j.joes.2018.05.003. IEEE, 2315–2322, https://doi.org/10.1109/PIERS-FALL.2017. Smit, P. B., I. A. Houghton, K. Jordanova, T. Portwood, E. Shapiro, D. Clark, M. Sosa, and T. T. Janssen, 2021: }},and }}, 2020: MEMS-based wave buoy: Towards short Assimilation of signiﬁcant wave height from distributed wind-wave sensing. Ocean Eng., 217, 108043, https://doi.org/ ocean wave sensors. Ocean Modell., 159, 101738, https://doi. 10.1016/j.oceaneng.2020.108043. org/10.1016/j.ocemod.2020.101738. Zappa, C. J., S. M. Brown, N. J. M. Laxague, T. Dhakal, Squire, V. A., 2020: Ocean wave interactions with sea ice: A reap- R. A. Harris, A. M. Farber, and A. Subramaniam, 2020: praisal. Annu. Rev. Fluid Mech., 52,37–60, https://doi.org/10. Using ship-deployed high-endurance unmanned aerial vehicles 1146/annurev-ﬂuid-010719-060301. for the study of ocean surface and atmospheric boundary layer Sutherland, G., and Coauthors, 2020: Evaluating the leeway coef- processes. Front.Mar.Sci., 6, 777, https://doi.org/10.3389/fmars. ﬁcient of ocean drifters using operational marine environ- 2019.00777. mental prediction systems. J. Atmos. Oceanic Technol., 37, Zong, Y., H.-Y. Cheng, H. Chien, and B. Koppe, 2019: Miniature 1943–1954, https://doi.org/10.1175/JTECH-D-20-0013.1. wave buoy}Laboratory and ﬁeld tests for development of a Thomson, J., 2012: Wave breaking dissipation observed with robust low-cost measuring technique. Coastal Structures 2019, “swift” drifters. J. Atmos. Oceanic Technol., 29, 1866–1882, Hannover, Germany, Bundesanstalt fur Wasserbau, 453–462, https://doi.org/10.1175/JTECH-D-12-00018.1. https://doi.org/10.18451/978-3-939230-64-9_046. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Atmospheric and Oceanic Technology American Meteorological Society http://www.deepdyve.com/lp/american-meteorological-society/lainepoiss-a-lightweight-and-ice-resistant-wave-buoy-opp2bc2Qw5

Loading next page...

References (88)

D. E. Cartwright (1956)
212
, 237A
H. Loehr (2013)
Development of a low cost wave buoy by utilising smartphone technology
M. Earle, K. Bush (1982)
Strapped-down accelerometer effects on NDBO wave measurements
G. Z. Forristall (1996)
216
, 122
E. Le Merle (2021)
e2021JC017220
, 126
M. A. Donelan, W. J. Pierson (1983)
The sampling variability of estimates of spectra of wind-generated gravity waves
, 88
L. Centurioni (2017)
36
, 1
L. Cavaleri (1980)
Wave measurement using pressure transducer
, 3
C. J. Zappa (2020)
777
, 6
E. Skinner (2018)
96
, 3
K. Raghukumar (2019)
1127
, 36
J. Thomson (2012)
1866
, 29
L. Lenain (2020)
3455
, 50
M. S. Longuet-Higgins (1961)
111
H. Pettersson (2010)
155
, 40
G. Sutherland (2020)
1943
, 37
M. Earle (1982)
838
Y. Y. Yurovsky (2020)
108043
, 217
R. M. Campos, H. Islam, T. R. Ferreira, C. Guedes Soares (2021)
Impact of heavy biofouling on a nearshore heave-pitch-roll wave buoy performance
, 107
C. T. Bishop (1987)
309
, 11
S. Farber (2018)
Estimating sea state using a low cost buoy
H. Pettersson (2003)
8061
, 108
J. Rabault (2016)
6399
, 54
J. Voermans (2020)
e2019JC015717
, 125
M. A. Donelan, J. Hamilton, W. H. Hui (1985)
Directional spectra of wind-generated waves
, 315A
J.-V. Björkqvist (2016)
17
, 5
N. Lang (1987)
225
M. A. Donelan (1983)
4381
, 88
V. A. Squire (2020)
37
, 52
J. Thomson (2015)
1281
, 32
J.-V. Björkqvist (2018)
57
, 152
L. Gordon (2002)
33
A. L. Kohout (2015)
415
, 56
I. R. Young (1995)
669
, 22
A. Cook (2020)
A UAV ‘mobile buoy’ for measuring surface waves
T. H. C. Herbers (2012)
944
, 29
O. Lancaster (2021)
1019
, 38
I. Houghton (2021)
1047
, 38
T. Kodaira (2020)
100567
, 27
J.-V. Björkqvist, H. Pettersson, L. Laakso, K. K. Kahma, H. Jokinen, P. Kosloff (2016)
Removing low-frequency artefacts from Datawell DWR-G4 wave buoy measurements
, 5
Data sheet MTi 1-series: 3D AHRS/VRU/IMU module
H. C. Graber, E. A. Terray, M. A. Donelan, W. M. Drennan, J. C. Van Leer, D. B. Peters, J. C. V. Leer (2000)
ASIS—A new air–sea interaction spar buoy: Design and performance at sea
, 17
L. C. Bender (2010)
1012
, 27
D. Kennedy (2014)
Development of a miniature, low-cost wave measurement solution
J.-V. Björkqvist, I. Lukas, V. Alari, G. P. van Vledder, S. Hulst, H. Pettersson, A. Behrens, A. Männik (2018)
Comparing a 41-year model hindcast with decades of wave measurements from the Baltic Sea
, 152
J. A. Mueller (2009)
117
, 130
J.-V. Björkqvist (2020)
58
L. Cavaleri (1980)
339
, 3
D. E. Cartwright, M. S. Longuet-Higgins (1956)
The statistical distribution of the maxima of a random function
, 237A
F. C. Fuertes (2019)
941
, 36
Y. Hirakawa (2016)
Development of mini-buoy for short term measurement of ocean wave
J. A. Battjes (1984)
642
L. Gordon, A. Lohrmann (2002)
Near-shore Doppler current meter wave spectra
L. Holthuijsen (2007)
387
C. T. Bishop, M. A. Donelan (1987)
Measuring waves with pressure transducers
, 11
M. A. Donelan (1985)
509
, 315A
J. A. Hanafin (2012)
1825
, 93
S. A. Kitaigorodskii (1983)
816
, 13
J. Rabault (2020)
102955
, 170
J.-V. Björkqvist, H. Pettersson, K. K. Kahma (2019)
The wave spectrum in archipelagos
, 15
O. M. Phillips (1985)
505
, 156
D. Pearman (2014)
109
, 91
P. B. Smit (2021)
101738
, 159
K. Christakos, J.-V. Björkqvist, L. Tuomi, B. R. Furevik, Ø. Breivik (2021)
Modelling wave growth in narrow fetch geometries: The white-capping and wind input formulations
, 157
Y. Y. Yurovsky (2017)
2315
J.-V. Björkqvist (2020)
Waves in archipelagos
K. Christakos (2021)
101730
, 157
F. Montiel (2018)
5912
, 123
M. Carandell (2020)
Impact on the wave parameters estimation of a kinetic energy harvester embedded into a drifter
P. Wadhams (1978)
23
, 25
F. C. Fuertes, L. Wilhelm, F. Porté-Agel (2019)
Multirotor UAV-based platform for the measurement of atmospheric turbulence: Validation and signature detection of tip vortices of wind turbine blades
, 36
I. Ashton (2015)
11
, 95
J.-V. Björkqvist (2019)
1469
, 15
P. Veras Guimarães (2018)
1449
, 14
I. Ashton, L. Johanning (2015)
On errors in low frequency wave measurements from wave buoys
, 95
J. A. Battjes, G. P. van Vledder (1984)
Verification of Kimura’s theory for wave group statistics
P. A. Janssen (1991)
1631
, 21
Z. Lin (2021)
83
, 8
Y. Zong (2019)
453
L. C. Bender, N. L. Guinasso, J. N. Walpert, S. D. Howden (2010)
A comparison of methods for determining significant wave heights—Applied to a 3-m discus buoy during Hurricane Katrina
, 27
H. C. Graber (2000)
708
, 17
T. H. C. Herbers, P. F. Jessen, T. T. Janssen, D. B. Colbert, J. H. MacMahan (2012)
Observing ocean surface waves with GPS-tracked buoys
, 29
R. M. Campos (2021)
102500
, 107
L. Centurioni, L. Braasch, E. Di Lauro, P. Contestabile, F. De Leo, R. Casotti, L. Franco, D. Vicinanza (2017)
A new strategic wave measurement station off Naples port main breakwater
, 1
G. Z. Forristall, J. C. Heideman, I. M. Leggett, B. Roskam, L. Vanderschuren (1996)
Effect of sampling variability on hindcast and measured wave heights
, 122
MTi 1-series datasheet: IMU, VRU, AHRS and GNSS/INS module
W. H. Munk (1950)
1
J. A. Hanafin (2012)
Phenomenal sea states and swell from a North Atlantic storm in February 2011: A comprehensive analysis
, 93

Publisher: American Meteorological Society
Copyright: Copyright © American Meteorological Society
ISSN: 1520-0426
eISSN: 1520-0426
DOI: 10.1175/jtech-d-21-0091.1
Publisher site: See Article on Publisher Site

Abstract

MAY 2022 ALA R I E T A L. 573 V R a b,a,c d d a VICTOR ALARI, JAN-VICTOR BJÖRKQVIST, VALDUR KALDVEE, KRISTJAN MÖLDER, SANDER RIKKA, e a a a f ANNE KASK-KORB, KAIMO VAHTER, SIIM PÄRT, NIKON VIDJAJEV, AND HANNES TÕNISSON Department of Marine Systems, Tallinn University of Technology, Tallinn, Estonia Norwegian Meteorological Institute, Bergen, Norway Marine Research, Finnish Meteorological Institute, Helsinki, Finland WiseParker OU, Tallinn, Estonia Estonian Maritime Academy, Tallinn University of Technology, Tallinn, Estonia Institute of Ecology, Tallinn University, Tallinn, Estonia (Manuscript received 1 July 2021, in ﬁnal form 4 December 2021) ABSTRACT: Wave buoys are a popular choice for measuring sea surface waves, and there is also an increasing interest for wave information from ice-covered water bodies. Such measurements require cost-effective, easily deployable, and robust devices. We have developed LainePoiss (LP)}an ice-resistant and lightweight wave buoy. It calculates the surface elevation by double integrating the data from the inertial sensors of the microelectromechanical system (MEMS), and transmits wave parameters and spectra in real time over cellular or satellite networks. LP was validated through 1) sensor tests, 2) wave tank experiments, 3) a ﬁeld validation against a Directional Waverider, 4) an intercomparison of several buoys in the ﬁeld, and 5) ﬁeld measurements in the Baltic Sea marginal ice zone. These extensive ﬁeld and laboratory tests conﬁrmed that LP performed well (e.g., the bias of H in the ﬁeld was 0.01 m, with a correlation of 0.99 and a scatter m0 index of 8%; the mean absolute deviation of mean wave direction was 78). LP was also deployed with an unmanned aerial vehicle and we present our experience of such operations. One issue that requires further development is the presence of low-frequency artifacts caused by the dynamic noise of the gyroscope. For now, a correction method is presented to deal with the noise. SIGNIFICANCE STATEMENT: Operational wave buoys are large and therefore expensive and inconvenient to deploy. Many commercially available devices cannot measure short waves and are not tested in ice. Our purpose was to develop an affordable wave buoy that is lightweight, ice resistant, capable of measuring short waves, and also has a lon- ger operating life than existing research buoys. The buoy is easily deployed with a small boat or even an industrial drone, thus reducing operating costs. The buoy is accurate, and captures waves that are too short for operational wave buoys. This is relevant for coastal planning in, e.g., archipelagos and narrow fjords. We measured waves in ice in the Baltic Sea, and are planning to extend these measurements to Antarctica. KEYWORDS: Sea ice; Wind waves; Air-sea interaction; Buoy observations 1. Introduction 1980), Doppler current meters measure the wave-induced orbital motions (Gordon and Lohrmann 2002), and inverted Wind-generated waves with periods of up to 25 s dominate echo sounders measure acoustic travel time between the the spectrum of ocean surface vertical variance (Munk 1950; device and the sea surface (Wadhams 1978). Wave gauges Holthuijsen 2007). These waves are observed visually, but an piercing the sea surface measure the up-and-down movement objective quantiﬁcation of wave heights, lengths, and propa- of water through electrical capacitance or resistance (Donelan gation directions requires measurements with in situ or et al. 1985; Graber et al. 2000). The surface wave spectra is remote sensing technologies. This paper focuses on a newly then calculated from the measured physical quantity by math- developed wave measuring buoy. ematical transformations and wave theory. In situ instruments do not measure wave properties All the measurements techniques in the above (nonexhaus- directly. At the sea surface, wave buoys should follow the tive) list are feasible, but have their own limitations and pecu- three-dimensional movement of water particles while measur- liarities, for example, gaps in data due to salty water over ing the inertial data or the Doppler shift of a GPS signal washing the buoy and blocking the GPS signal (Bjork ¨ qvist (Herbers et al. 2012). Below the sea surface, pressure trans- et al. 2016), spurious data in echo soundings generated by ducers measure wave-induced pressure ﬂuctuations (Cavaleri breaking waves, and diminishing of short waves in pressure recordings (Bishop and Donelan 1987). More generally, the size of the instrument, the basic measurement principle, and Denotes content that is immediately available upon publica- the meteorology–ocean conditions affect the measurement tion as open access. result. Besides inherent limitations, operational and practical considerations, like ease of use and cost of the instrument, Corresponding author: Victor Alari, victor.alari@taltech.ee might be important. DOI: 10.1175/JTECH-D-21-0091.1 Ó 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 574 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 Majority of operational wave measurements are done with for sensor validation, including standstill measurements of surface-following buoys, which may also include sensors for acceleration noise and benchmark tests with monochromatic recording atmospheric and upper-ocean state variables motions. Thereafter, we will describe the accuracy of the (Thomson 2012). These buoys can be tethered to the sea ﬂoor buoy in capturing high-frequency waves in a wave tank. or allowed to drift under the inﬂuence of wind and currents. Section 5 deals with the ﬁeld test results. This includes An advantage of these buoys is their long operational life an extensive validation campaign against a Directional (several years). However, the established operational buoys Waverider and an intercomparison of several LP buoys. We are large and heavy. The National Data Buoy Center of also describe drifting experiments results, where a UAV was NOAA has tailored meteorology–ocean buoys, equipped used as a deployment method. We end section 5 by describing with wave measuring sensors, ranging from 1.8 to 12 m the results of waves-in-ice measurements from the Baltic Sea. in diameter. The widely used Datawell Waverider Mk-III, In section 6, we discuss the limits and merits of the new tech- TRIAXYS Directional Wave Buoy, and Fugro Seawatch nology and conclude our main ﬁndings in section 7. Four Mini II Buoy have diameters of at least 70 cm and weights of appendixes end the paper, with the description of the inertial over 100 kg. These off-the-shelf operational buoys may not be sensor, description of the denoising procedure, calculating an affordable choice for simultaneous deployments, and their validation statistics, and describing our experience of UAV handling requires expertise as well as vessel for deployment. deployments. These issues are somewhat alleviated with buoys as the Data- well DWR-G4, which weighs 17 kg, has a diameter of 40 cm, 2. Materials and methods and has a battery life of 30 days. Recent advances in accurate and low-cost motion sensors a. Technical description of the buoy and GPS technology have led to the development of a low-cost LP is a spherical wave buoy with a diameter of 32 cm, a easy-to-handle wave measurement platform called Spotter height of 22 cm (Fig. 1), and a weight of 3.5 kg. The enclosure (Raghukumar et al. 2019; Lancaster et al. 2021). It is a sea state is made of two tough glass ﬁber halves. Between the halves, detector with unprecedented coverage (Smit et al. 2021; there is a seal that makes the hull waterproof after it has been Houghton et al. 2021) and thanks to its small size, it might turn bolted together. After the buoy is sealed, it can be turned on out to be a practical tool for estimating wind speed from wave and off by holding a magnet to the outside of the hull. spectra (Voermans et al. 2020). First ﬁeld experiments of mea- Rechargeable lithium-ion batteries, with a capacity of suring waves in grease ice with Spotter show promising results 335 W h, can power the buoy for roughly 2 months. in performing these types of observations at a low cost (Kodaira The microcontroller of the buoy is connected to the sen- et al. 2020). The simultaneous deployments of several (tens, sors, the memory, and the communication modems through a hundreds) drifting wave buoys is also beneﬁcial for understand- custom built PCB board (Fig. 2). This controller}using an ing wave–current interaction at coastal and oceanic scales ARM Cortex-M4 core}was chosen because of its low power (Pearman et al. 2014; Veras Guimara ˜es et al. 2018) and wave consumption, ﬂoating point support, and digital signal proc- growth in complex archipelagos (Bjorkqvist et al. 2019)and essing functionality. fjords (Christakos et al. 2021). The inertial sensors of the buoy are a 3D accelerometer, In this paper, we describe and validate a new wave buoy a 3D gyroscope, and a magnetometer. These sensors are called LainePoiss (LP), which uses the microelectromechanical part of the Xsens MTi-3 (see appendix A for more details) system (MEMS) inertial measurement unit to detect surface attitude and heading reference system (AHRS). The inter- motion. LP was originally designed for wave measurements in nal processor of the system synchronizes the sensors, ice, but has over 3 years of research and development matured applies calibration models, and runs the sensor fusion into a valid device; it is already used for real-time wave moni- algorithm (including the extended Kalman ﬁlter), in order toring in the Baltic Sea. When developing the buoy, we have to convert inertial data from buoy body reference frame to kept the following combination of performance characteristics Earth reference frame. Henceforth, raw data will mean in focus: ice resistant, lightweight, operational, small, and the original acceleration data that are transformed to the affordable. These characteristics allow LP to be used for vari- Earth reference frame by the sensor. After assembling the ous research and engineering applications. For example, we buoy, we performed a magnetic calibration that corrected are currently planning to use LP for wave measurements in for the disturbance inﬂictedtothe magnetic ﬁeld of Earth the marginal ice zone, extending measurement times of opera- by ferromagnetic materials. The device location was tional wave buoys in the seasonally ice covered Baltic Sea, logged by a Global Navigation Satellite System (GNSS) ﬁeld measurements of shorter waves in archipelagos and lakes, receiver. and using unmanned aerial vehicles (UAV) as a rapid method We conﬁgured the output frequency of the inertial data to for deployments. LP is also a core infrastructure for validating 50 Hz, and these data are written to an SD card. Depending operational coastal wave models in Estonia. on the conﬁguration set by the user, the raw 50 Hz data and The structure of the paper is as follows. In section 2,we the processed data (wave spectra and bulk parameters) are describe the wave buoy in detail and introduce algorithms for converting the acceleration data into displacement data. In also sent to a cloud server in real time (e.g., every 30 min) section 3, the omnidirectional and directional wave parame- using cellular LTE or only processed data over satellite ters are deﬁned. Section 4 describes different laboratory tests Iridium SBD networks. The buoy can be conﬁgured to use MAY 2022 ALA R I E T A L. 575 FIG. 1. (a) LainePoiss in a moored conﬁguration, (b) transporting with a UAV, and (c) drifted to pancake ice. either one or both of these communication options; the buoy channel because of its signiﬁcantly lower data transmission always prioritizes the cellular network, but can automatically costs. The buoy can therefore also send the raw data through switch to the satellite network if no cellular coverage exists. the cellular network, although this option can be disabled to We chose the cellular network as the primary communication save power. 576 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 amplitudes to 0 below 0.05 Hz. This integration procedure is similar to the one used in Rabault et al. (2020). For the ﬁeld data, a correction to the energy was performed based on the amount of variance that was lost in the denoising. The denois- ing, compensation and integration procedures are docu- mented in detail in appendix B. The 30-min displacement time series were then used to cal- culate wave spectra from 100-s blocks using the Welch method with a 50% overlap (35 segments), resulting in a wave spectrum with a 0.01 Hz resolution. Each segment was tapered with a Hann window. The highest frequency used in the spectrum was 1.28 Hz, which corresponds to a 95 cm deep water wavelength and approximately 3 times the buoy diame- ter. Higher frequencies were starting to be distorted by the size of the buoy when compared to the wave gauge data (see FIG. 2. Scheme of the electronics components of the buoy. section 4c on the wave tank experiment). Note that the data processing procedures in the laboratory b. Data processing experiments differed slightly from the data collected from ﬁeld tests, since the time series were shorter. Please see The buoy sampled the acceleration with a 50 Hz sampling section 4c for details on the exact procedure for laboratory frequency, and (in the ﬁeld tests) these data were saved in data. For the waves-in-ice measurements (section 5d), the ﬁles containing 65 538 measurements (circa 22 min). We have data processing procedure differed also a bit from the other used the raw data which are already transformed into an ﬁeld data}namely, the energy after denoising was not added Earth reference frame by the sensors fusion algorithms. For back because the noise was so dominant. each deployment, these acceleration data were combined into one long time series from which we constructed 30 min dis- 3. Wave parameters placement time series with starting times of :00 and :30 using the following procedure: a. Omnidirectional parameters 1) We constructed 32 min time series from the continuous We used the following deﬁnitions of wave parameters. The acceleration data (:59–:31). spectral moments are deﬁned as 2) The x, y, and z accelerations were low-pass ﬁltered (ﬁlter “biting” between 1.28 and 5.12 Hz) with a ﬁnite impulse m f Ef()df, (1) response (FIR) ﬁlter that had 162 coefﬁcients before being downsampled to a 5.12 Hz resolution using a near- where a lower integration frequency of f = 0.10 Hz and an est neighbor interpolation. Because of the original 50 Hz upper frequency of f = 0.58 Hz was used to match the highest sampling frequency, this resulted in a maximum shift on frequency that was reliably captured by the Waverider. 100 ms of the measurement. Using the spectral moments we deﬁned the signiﬁcant wave 3) The acceleration data were double integrated in Fourier height: space. Before integration, the white noise was removed for frequencies up to 0.10 Hz, and the amplitudes below H 4 m : (2) m 0 0.05 Hz were set to zero (these cutoffs were appropriate for our speciﬁc dataset; see appendix B for details). We The wave periods were deﬁned as removed 30 s from the start and end of the double inte- grated time series to cut out transient data caused by the T , (3) Fourier integration. 0 4) Finally, after accounting for the data lost by FIR ﬁltering T , (4) and Fourier integration, we cut the time series to start 01 exactly at :00 or :30 to a 9216 point long block. These 30 min block coincided exactly with the displacement 0 T , (5) time series of the Waverider at Suomenlinna, which we m used for validation. T argmax Ef() , (6) The denoising of the acceleration data was performed by estimating the mean amplitude of the fast Fourier transform (FFT) of the signal between frequencies 1/100 and 1/30 Hz. f Ef() df The integration was performed in Fourier space, where the T : (7) removing of the low-frequency energy was applied gradually Ef() df below 0.06 Hz using a half-cosine function, setting the MAY 2022 ALA R I E T A L. 577 Here, the peak period T was determined using a parabolic ﬁt. The so-called characteristic period T is of the same type that was originally developed as an alternative to peak fre- quency by Young (1995). Bjo ¨rkqvist et al. (2019) proposed it as a more stable alternative characterization of a repre- sentative wave frequency in archipelago conditions, where the peak period is often ill deﬁned. Note that we use a slight modiﬁcation by integrating a weighted average of the inverse of the frequency (f ) compared to the weighted integration of f by Young (1995) and Bjorkqvist et al. (2019). The narrowness of the spectrum was determined by the k -narrowness parameter (Battjes and van Vledder 1984): ⎧⎪ ⎪ f ⎨ 1 k Ef()cos 2pfT df ⎪ m ⎪ 02 2 ⎪ m FIG. 3. Noise level of a new (LP0) and used (LP1–LP6) AHRS 0 0 in comparison with manufacturers value. The noise height is calcu- ⎫⎪ lated using the ﬁt value to the real sensors. f ⎪ 1 ⎪ 1 Ef sin 2pfT df , (8) () 02 ⎪ f0 The directional spread was deﬁned as where k takes values between 1 (inﬁnitely narrow spectrum) s f 2 2 2m f , (14) () () and 0 (white noise) and has been found to capture the spectral shape better (especially in the archipelago) than width param- where eters depending on high moments (m or m )(Bjorkqvist et al. 2 4 2019). 2 2 m () f a () f 1 b () f : (15) 1 1 1 b. Directional parameters The mean and peak spreads were deﬁned as for the direc- Directional parameters were calculated using the ﬁrst pair tional spread [Eq. (14)] using of Fourier coefﬁcients, a (f) and b (f). These coefﬁcients were 1 1 calculated from the cross-spectra following Longuet-Higgins F 2 m a 1 b , (16) 1 1 (1961): 1 Q () f ye a () f , (9) F 1 2 2 m f a f 1 b f : (17) p p p 1 1 1 C f C f 1 C f () () () yy nn ee Q () f yn 4. Laboratory tests b f , (10) () C f C f 1 C f () () () yy nn ee a. Sensor static noise The manufacturer of the MEMS sensor reports a static where Q(f) and C(f) are the quadrature- and cospectra, with noise density value of 0:12 mg Hz for the acceleration subscripts y, e, and n referring to the vertical, east, and north sensor (mg is milli g it has as value of 9.81/1000). To test if displacements. this represents the actual noise of a single sensor, we con- The mean direction at each frequency was calculated as ducted a standstill measurement, where, at a room tempera- a () f 1 ture of 218C, we let the sensor measure for 3 h. We then u () f arctan 1 1808, (11) b () f calculated the power spectrum of the acceleration noise and transformed it to noise displacement spectra by dividing the with the mean and peak direction being acceleration spectra with (2pf) . We found that the unused sensor has a higher noise density than the manufacturer’s u arctan 1 1808, (12) m value (Fig. 3). We repeated the same procedure for sensors already used in deployments and found that the noise does not increase with the usage of the sensor (LP1 was used the a f 1 p most, 5100 h). Therefore, for the sensor noise, we will use u u f arctan 1 180 , (13) 21 p p b f the value 0:22 mg Hz . From a practical point of view, 1 p this sensor noise level only becomes important when dealing where f is the peak frequency determined without a para- with very low amplitude waves, e.g., waves in ice. For the bolic ﬁt. ﬁeld measurements described in this paper, the static noise 578 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 FIG. 4. Technical drawings of (a) benchstand, (b) wave tank, and (c) recommended mooring setup. of the sensor was subtracted only for the waves-in-ice meas- difference between the prescribed and measured value urements (section 5d). depends on the acceleration}the measured amplitude starts to deviate with decreasing acceleration, being 6% at 0.04 Hz. b. Benchmark test c. Wave tank The benchmark tests were conducted with a custom-made device (Fig. 4a). The amplitude was kept constant at 68 mm We tested the wave buoy’s response to irregular waves in (61 mm), while period was varied between 1 and 25 s by both tethered and free-drift setups. The experiments were adjusting the speed of the device. Since the device did not conducted in a wave tank (Fig. 4b) owned by the Small Craft reproduce a perfect sine wave, all the measured acceleration signals had harmonics at multiples of the dominant signal. TABLE 1. Test bench results. The measured acceleration signal was transferred to fre- Wave period Prescribed amplitude Measured amplitude quency space, the noise was removed and then double inte- (s) (mm) (mm) grated and transferred back to time space. Mean amplitudes of N cycles were calculated. N varied between 8 and 30, 168 69 568 66 depending on the cycle period. 10 68 64 The results of the benchmark test for periods 1, 5, 10, 20, 20 68 64 and 25 s are shown in Table 1. The sensor is able to measure 25 68 64 movement in the wind-wave and swell period range. The MAY 2022 ALA R I E T A L. 579 TABLE 2. Wave tank results. H was integrated between 0.30 For the tests, we moored one buoy 2 m from the wave m0 and 1.28 Hz. The peak frequency (f ) corresponds to the wave p gauge and let the other two drift. With the JONSWAP gauge. spectrum, we made 8 tests (Table 2), in which each combi- nation of peak period and signiﬁcant wave height was H (m) m0 repeated twice. For each test, a 3-min-long time series was f (Hz) Wave gauge LP1 LP3 (moored) LP4 analyzed. The time series was converted into a displace- ment power spectra using the Welch method (block length 0.57 0.15 0.16 0.16 0.16 0.63 0.16 0.15 0.17 0.16 30 s, 50% overlap). Neither datasets were decimated; LP 0.53 0.17 0.19 0.20 0.20 data sampled at 50 Hz and wave gauge data sampled at 0.53 0.17 0.19 0.20 0.19 200 Hz were used. 0.77 0.07 0.07 0.07 0.07 Signiﬁcant wave height, integrated between 0.30 and 0.77 0.06 0.08 0.07 0.07 1.28 Hz, shows a satisfactory match between wave gauge and 0.87 0.09 0.11 0.11 0.10 wave buoys (Table 2). The difference in signiﬁcant wave 0.73 0.10 0.10 0.11 0.10 height between the buoys and the wave staff was 21 to 3 cm. The wave spectra (Fig. 5) reveals a similar structure between the wave gauge and buoys up to 1.28 Hz and a slight shift of Competence Centre of the Tallinn University of Technology. frequencies of the drifting buoys due to Doppler shift. The aim was to validate the high-frequency part of the spec- trum and determine the accuracy of LP in conditions which represent wave growth at short fetches. 5. Field tests The 60-m-long, 5-m-wide, and 3-m-deep tank uses 6 pad- dles to generate waves, which are recorded by a capacitance The ﬁeld tests were conducted in the seasonally ice-covered wave height gauge (developed by Akamina Technologies) in Baltic Sea, which is an enclosed basin with a maximum fetch the middle of the tank. The duration of wave generation var- of 700 km. The deployments were made within 5 km from the ied from 210 to 300 s. coast (Fig. 6). FIG. 5. Comparison of drifting and moored LP’s with wave gauge at a wave tank. The wave ﬁeld corresponds to the JONSWAP spectrum. The 1.28 Hz cutoff frequency is marked by a vertical dashed line. 580 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 The spectra from both LP and DWR were integrated between 0.10 and 0.58 Hz (note that the actual low-frequency cutoff of the DWR spectra was 0.025 Hz), and both devices generally agreed on the wave statistics for the ﬁeld experi- ment (Table 4; see appendix C for the deﬁnition of the statisti- cal parameters). The mean signiﬁcant wave height was 0.42 m, which is 0.10 m higher than the 2016–18 measured average (Bjork ¨ qvist et al. 2019). Both LP and DWR measured a simi- lar highest signiﬁcant wave height, with the difference being within the expected sampling variability. The wave periods agreed better the more they were determined by the shorter waves, with T showing the best agreement and T the m02 p worst. The maximum peak period values for LP are probably not realistic but stem from the low-frequency noise dominat- ing the lowest integration frequency when total energy was very low. The dominant wave direction for both instruments was south-southwest. The spreading was, in a mean sense, slightly higher for LP than for DWR. Overall, the signiﬁcant wave height measured by LP and DWR matched well (Figs. 7–9), with a 0.01 m bias and 0.99 correlation coefﬁcient (Table 5). During two occasions in the ﬁrst deployment, LP measured an around 0.2 m higher signiﬁ- FIG. 6. Field test sites where LainePoiss’s were moored (dia- cant wave height than the DWR (Fig. 7b). Both of these cases mond) or deployed as drifters (circle). Existing operational wave took place during around 10 m s easterly winds, but LP and and windmeasurements are shownwitha star andplus signs. DWR matched up well during roughly 13 m s easterly winds in the autumn (Fig. 9b). We have not yet determined a a. Comparison against a Directional Waverider deﬁnitive reason for the discrepancy during the summer cases. We deployed buoys at two locations close to the opera- A tangling of the moorings of the LPs is improbable since tional Directional Waverider DWR-Mk III, which was both LPs measured similar wave heights. moored at a depth of 20 m outside of Suomenlinna in the The wave periods determined from spectral moments Finnish Archipelago (Fig. 6). The measurement area is char- compared well to those from the DWR (Figs. 10b,d,f). The scatterindex was3%–5%, with the biases being no more acterized by tens of islands in varying size and busy recrea- than 0.16 s (Table 5). The scatter index is highest (23%) for tional and commercial vessel trafﬁc, although the commercial the peak period (Table 5). The general poor validation for trafﬁc during the deployments was reduced because of the peak period is explained by the archipelago environ- COVID-19 restrictions to travel. ments, where the peak of the spectrum is often not well With some short gaps, the deployments lasted from June to deﬁned (Bjorkqvist 2020). The wave spectrum was more November 2020 (Table 3). Four different buoys were used, closely unimodal for the strongest southerly winds, and the because the battery life of one device did not last for the peak period therefore matched up well in the case of the entire campaign. The buoys were moored approximately highest signiﬁcant wave heights (Fig. 10j). The characteristic 300 m north of the DWR (Fig. 6), where the water depth was period has been proposed as an alternative to the instances 17 m. The recommended mooring consisted of an anchor, a when the peak period is ill deﬁned. The validation of the surface ﬂoat, LP, ropes connecting the assembly, and weights characteristic period showed that it removed a large part of (Fig. 4c). The mooring endured strong winds from all major 21 the scatter between the two devices while keeping the bias directions. The maximum 10 min averages were 15 m s 21 21 21 at a low 0.03 s value (Fig. 10h, Table 5). (west), 16 m s (north), 14 m s (east), and 21 m s 21 The wave direction measured by LP had a 18–28 bias with (south), with the gusts reaching 27 m s . The buoy was not respect to the DWR (Table 5). While the agreement was dragged from its deployment location, which shows that a good for both the mean and peak directions, the mean 25 kg mooring anchor was sufﬁcient. parameter expectedly has less scatter (Figs. 10c,e). A large Two buoys were deployed in June using a small plastic scatter in directional peak parameters are expected (e.g., motorboat. In August, one of these buoys was removed and Pettersson et al. 2003), especially in the archipelago where the second one was replaced (using the same boat). In the peak values are not even necessarily from the same September, the buoy was replaced again using a motorized wave component. For the same reason, also the peak direc- sailing vessel, and it was ﬁnally retrieved with a pilot boat in tional spreading had a 25% scatter index even though the the beginning of December. bias was only 28 (Table 5). The mean spreading was more robust with a scatter index of only 9% and a correlation of 0.88. Still, LP systematically Then owned by the City of Helsinki, now owned by Finnish Meteorological Institute. measured a slightly higher spreading than the DWR MAY 2022 ALA R I E T A L. 581 TABLE 3. An overview of the ﬁeld experiments where LainePoiss was moored. Deployment 1 Deployment 2 Deployment 3 Deployment 4 Device LP1–LP2 LP3 LP4 LP1–LP4 Location Suomenlinna (S1–S2) Suomenlinna (S1) Suomenlinna (S1) Va ¨ana-J ¨ oesuu ˜ (V1–V4) Depth (m) 17 17 17 19 Period 18 Jun–24 Jul 2020 14 Aug–21 Sep 2020 24 Sep–24 Nov 2020 22 Dec 2020–03 Jan 2021 Mean U (m s ) 6.3 7.3 8.2 4.1 Mean H (m) 0.32 0.39 0.50 0.51 m0 Mean T (s) 4.5 4.4 4.3 5.8 (bias = 38, slope = 1.09; Table 5). A visual comparison validation for this particular parameter. Several width param- (Fig. 10g) reveals that the difference is better explained by a eters are deﬁned using higher moments (Cartwright and Lon- ﬁxed offset than the calculated slope. Le Merle et al. (2021) guet-Higgins 1956) and are therefore sensitive to the high- found an offset of similar magnitude when comparing the frequency part of the spectrum. The validation was therefore (peak) directional spreading between radar and wave buoy partially limited by the 0.58 Hz upper frequency of the DWR. measurements. The laboratory data of Lin et al. (2021) also In the 0.10–0.58 Hz frequency range, LP spectra tend to be showed that wave buoys can underestimate the directional slightly wider than those from the DWR, which might be spread compared to wave gauges with 10%. It is therefore caused by low-frequency artifacts during low sea states. possible that the difference between the spreading mea- The spectral comparison shows a qualitatively good match sured by LP and the DWR might partially be caused by the (Fig. 11) between LP and DWR, except for the low-frequency part where LP has artifacts. During the northerly wind case size difference between the devices. Lin et al. (2021) found (Fig. 11a), the peak of the spectrum was roughly at 0.5 Hz, that the impact of the mooring was small in the laboratory, just below the cutoff frequency of the DWR. Above the but did not exclude that this factor would be more impor- DWR cutoff frequency, LP spectra followed an f tail, which tant in the ﬁeld. All in all, the agreement in the directional is in agreement with theory (Kitaigorodskii 1983; Phillips parameters are good, especially considering the possible 1985). For the easterly and westerly wind events, a clear peak sources of uncertainty. An additional validation of the spectral shape was per- formed by using the spectral narrowness parameter (k ). This parameter was proposed by Battjes and van Vledder (1984) and was found to be suitable for archipelago conditions by Bjorkq ¨ vist et al. (2019). The agreement between DWR and LP was reasonable (Fig. 10i), with a correlation of 0.92 and a bias of 20.02 (Table 5). The scatter index was high (23%), although we are not aware of any other cross-instrumental TABLE 4. LainePoiss and DWR statistics during the deployments (N = 6357). N is smaller than the one used in the validation statistics Table 5 because in June–July 2020 two LP’s were simultaneously measuring. In the validation, both buoys were included against the comparison with DWR; here only LP 1 is used (eastern buoy, Fig. 6). LP/WR Parameter Mean Std Min Max H (m) 0.42/0.42 0.27/0.29 0.04/0.03 1.84/1.90 m0 T (s) 3.05/2.91 0.40/0.43 2.11/1.91 4.87/4.53 m02 T (s) 3.26/3.06 0.46/0.49 2.17/1.93 5.48/4.84 m01 T (s) 3.84/3.44 0.61/0.59 2.44/2.05 6.73/5.86 m10 T (s) 4.40/3.83 1.49/1.12 1.87/1.74 9.53/8.32 T (s) 4.72/3.99 2.10/1.41 1.72/1.72 10.00/8.54 k (–) 0.11/0.13 0.09/0.10 0.00/0.00 0.59/0.68 s ( ) 45/41 12/11 27/23 80/80 s (8) 38/32 15/9 11/9 81/80 Mode Std Min Max FIG. 7. Suomenlinna validation period 1. (a) Solid black line is u (8) 202/198 45/44 5/1 359/359 wind speed and dashed black line is wind direction. (b)–(e) Black u (8) 202/200 52/49 0/0 359/358 lines are DWR and blue lines are LP. 582 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 FIG.8. As in Fig. 7, but for second validation period. FIG.9.As in Fig. 7, but for third validation period. was not deﬁned (Figs. 11b,c), which is a typical situation for retrieval, the instrument was cleaned and dried, and subse- the archipelago-type spectrum with many different fetches for quent tests showed that no permanent harm was done to the ¨ electronics. a ﬁxed wind direction (Bjorkqvist 2020). The highest waves The mean wind speed during the measurement campaign measured during the campaign were due to southerly winds, was 4.1 m s , but gusts at the Pakri weather station reached and both the LP and the DWR spectra showed a good match 21 21 16.5 m s . During moderate wind speeds (over 6 m s ), the even for the longer waves of a 9 s period (Fig. 11d). wind was mainly blowing from north or south. The maximum In summary, the validation conﬁrms the accuracy of LP in signiﬁcant wave height was 1.22 m, and the maximum wave complex wave conditions. The scatter of the peak parameters period was 5.97 s (Fig. 12). With the exception of the north- is explained more by the ill-deﬁned nature of the parameter erly winds, the waves and wind were misaligned. The than any actual differences between the devices. Otherwise, the validation statistics are similar to those determined for other small buoys when validated against established technol- TABLE 5. Validation statistics. N = 7486 for H . For other ogies (Raghukumar et al. 2019; Lancaster et al. 2021). m0 parameters, only cases where the DWR measured H . 0.25 m m0 b. Intercomparison of four moored devices were included (N = 4827). For an intercomparison of several buoys in the same wave Parameter Bias RMSD SI (%) Slope R conditions, we moored four buoys in a square layout with a H (m) 0.01 0.04 8 0.99 0.99 m0 maximum distance of 140 m from each other in places where T (s) 0.06 0.10 3 1.02 0.98 m02 the water depth was 18–19 m (deduced from nautical charts) T (s) 0.08 0.12 3 1.02 0.98 m01 (Fig. 6). The buoys were deployed in December and retrieved T (s) 0.16 0.23 5 1.04 0.96 m10 10 days later in January with a motorboat. The location was T (s) 0.03 0.35 9 1.01 0.91 chosen due to its openness to long waves from the northern T (s) 0.03 0.89 21 0.99 0.66 k (–) 20.02 0.04 23 0.85 0.92 Baltic proper and its gently sloping bottom, which keeps the s (8) 3 5 9 1.09 0.88 spatial wave height gradient small. s (8) 2 8 25 1.03 0.49 The mooring consisted of a 60 m rope from the anchor to the surface ﬂoat and a 20 m rope from the ﬂoat to the wave |Bias| MAD buoy. Unfortunately, LP3 started leaking during the ﬁeld u (8)1 7 campaign, causing the MEMS sensor not to register data. u (8)2 11 We exclude this instrument from further analysis. After MAY 2022 ALA R I E T A L. 583 FIG. 10. Scatterplots of wave parameters during Suomenlinna validation deployment grouped by signiﬁcant wave height. For the deﬁnition of variables see section 3. misalignment was caused by the slanting fetch (Donelan et al. The scatter index between H was 3%–5%, reﬂecting the m0 1985; Pettersson et al. 2010) and local topography. The slant- variability caused by sampling a random process (Donelan ing fetch also increased the directional spreading, since longer and Pierson 1983; Forristall et al. 1996). waves usually came from the west even though the short The outlier was the mean wave direction of LP1. During waves were aligned with the wind. For northerly winds, the the Suomenlinna UAV deployment (described in the next wave and wind directions aligned, leading to a lower spread- section) the release system malfunctioned and the buoy fell to ing compared to other wind directions. rocky ground from approximately 2 m. Although bulk omni- The wave parameters between the different buoys agreed directional parameters and directional spread (which does not well (Fig. 12). The R values (between LP1–LP2, LP1–LP4, depend on true north reference) were reasonable, the yaw and LP2–LP4) for signiﬁcant wave height are over 0.99 and angle probably lost its north referencing capabilities, thus ren- over 0.98 for mean wave period and for directional spreading. dering the directional estimates unreliable. 584 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 FIG. 11. Comparison of wave spectra at Suomenlinna for four different wind directions. Black lines are DWR; blue lines are LP. The thin dotted lines correspond to 30 min spectra, while the thick lines are averaged spectra of seven individual spectra. c. Deployment with an unmanned aerial vehicle as In the Gulf of Riga, we deployed three buoys from ice onto a drifter ice (Fig. 13d). UAV ground stations were approximately 2 km from shore at locations where pack ice was still safe to walk Va ¨ana- ¨ Joesuu ˜ (VJ) was the ﬁrst ever deployment of LP on. The buoys drifted with ice (with occasionally entering with a UAV (Fig. 13a; Table 6). The buoy took about 2 h to open water) up to month. One buoy stopped sending data drift back to the shore. Signiﬁcant wave height was about 1 m, 10 days after the deployment because it was brought directly which also matched the value from a Copernicus CMEMS from another (moored) experiment and the battery level was product (not shown here). already low. Luckily, locals found it on shore and notiﬁed us During the Suomenlinna deployment the buoy was dropped using the contact information on the buoy. The results from near the moored DWR (Fig. 13b). Wind gusts reached the measurements in ice are described in section 5d. 15 m s and the signiﬁcant wave height was around 1 m with The description of the UAV deployment procedures are a wave direction from SSW. The buoy drifted until the next presented in appendix D. day and was picked up from a rocky island with a pilot boat. At Leppneeme (Fig. 13c), the buoy was deployed from the d. Waves in ice measurements shore. Although the wave direction was toward the shore, alongshore currents transported the buoy eastward for about We deployed three drifting buoys in the eastern part of the Gulf of Riga (see section 5c). On 6 March 2021 a strong south- 12 h before it got stuck in pancake ice close to the coast westerly wind event occurred, with the average measured (Fig. 1c). The signiﬁcant wave height was roughly 0.5 m. The UAV ground stations were about 2 km from the wind speed and wind gusts being 15 and 21 m s , respectively deployment sites. During these three experiments, we opera- (Fig. 15a). Sentinel-1 overﬂights in the morning (0400 UTC) tionally estimated the drift of the buoys with Seatrack web and in the evening (1600 UTC) showed that the ice edge (https://stw.smhi.se/) and found that the wind leeway coefﬁ- retreated more than 10 km in about 12 h (Figs. 14a,b). The cient is around 2.5%, which is in the same range as similar Copernicus CMEMS wave ﬁeld forecast predicted a 2 m sig- spherical drifting buoys (Sutherland et al. 2020). niﬁcant wave height near the ice edge close to the wave buoys MAY 2022 ALA R I E T A L. 585 existing waves-in-ice loggers (Kohout et al. 2015; Rabault et al. 2016; Montiel et al. 2018). This is of utmost importance since our knowledge on wave–ice interactions is still limited due to the low number of measurements made in ice (Squire 2020), especially measurements of the directional wave spectrum. Wave heights can be very low in the MIZ, and we have shown that a signiﬁcant wave height of 1 cm is detectable by LP. In the seasonally ice-covered water bodies, a cause for con- cern is the fact that operational devices have to be removed before the arrival of ice to avoid damaging the buoys. None- theless, the harshest wind conditions, and therefore wave con- ditions, can typically distort the wave statistics compiled purely from measurements (Bjorkqvist et al. 2018). Although LP is not designed to replace operational wave buoys, one possible application would be to complement operational measurements by replacing the operational buoy with LP when it is retrieved, thus capturing the open water time before freezing. LP should survive the ice, but if the buoy is lost, the ﬁnancial implications are not as severe (buoy costs roughly EUR 5000) as a loss of an expensive operational buoy, nor do they threaten the continuity of the operational measurements as a whole. Routine measurements also seldom capture waves shorter than 0.5–0.6 Hz, but LP extends the measurement range to 1.28 Hz (roughly 1 m wavelength). These shorter waves have been extensively studied with specialized research setups, e.g., FIG. 12. Intercomparison of three LP’s moored simultaneously using wave staffs or polarimetric cameras. The reason for the about 100 m apart. The dashed black line marks (a) the wind speed persistent scientiﬁc interest for this part of the wave regime is from Pakri weather station and (c) the wind direction. its decisive impact on many sea–atmosphere processes. Waves between 0.58 and 1.28 Hz have been shown to contribute (Fig. 14c). The predicted peak period was 7 s, and the wave 26% of the so-called Stokes drift (Lenain and Pizzo 2020), direction was between SW and W. and they also carry a signiﬁcant part of the wave-induced All three buoys started picking up the wave signal at stress (Janssen 1991; Mueller and Veron 2009). These pro- around noon, and in the evening the signiﬁcant wave height cesses then affect the drift of the object, oil, and other surfac- reached up to 1.2 cm at the buoy that was closest to the ice tants and enhance the upper-layer turbulence and mixing, edge (Fig. 15b). The measured energy was above the sensor thus contributing to the sea–atmosphere ﬂuxes of, e.g., CO . noise threshold for frequencies 0.10–0.14 Hz, and the sur- One possible niche for LP could be regions like archipelagos, face displacement time series showed identiﬁable wave fjords, or small lakes. In these areas, the short waves can carry groups during the time of the maximum signiﬁcant wave a major part of the total wave energy, but establishing elabo- height (Figs. 15c,d). The roll and pitch angles deviated less rate research wave measurement stations might not be feasi- than 18, indicating that the buoys were ﬁrmly lodged in ice ble. From a practical perspective, the measurement of the during the wave event. high-frequency part might require cleaning of the buoy after some time to avoid accumulation of added mass and change of the buoy dimensions due to biofouling (Thomson et al. 6. Discussion 2015; Campos et al. 2021). Research and development of prototype miniature wave Peak wave periods can reach 25 s in the world oceans buoys and loggers has increased in the last decade (e.g., Loehr (Hanaﬁn et al. 2012), but low-frequency noise in wave meas- et al. 2013; Kennedy et al. 2014; Hirakawa et al. 2016; urements are unfortunately a common feature. Ashton and Centurioni et al. 2017; Yurovsky and Dulov 2017; Farber et al. Johanning (2015) found spurious low-frequency energy 2018; Skinner et al. 2018; Zong et al. 2019; Carandell et al. caused by high drift forces brought about by currents and 2020; Cook et al. 2020). Small and affordable emerging wave mooring. Low-frequency artifacts can also be created by a buoys, like Spotter (Raghukumar et al. 2019) and LP, open loss of the GPS signal in buoys that use the Doppler shift to up new possibilities for deploying large numbers of buoys measure the buoy velocity, e.g., the DWR-G4 (Bjork ¨ qvist simultaneously. With the Spotter, this has already been imple- et al. 2016). We found that the MEMS sensor of the LP also mented on oceanic scales through assimilation of wave data in suffers from low-frequency noise. This noise comes from the an operational wave model (Houghton et al. 2021; Smit et al. gyroscope random noise, which affects the pitch, roll, and yaw 2021). The ice resistance allows LP to be deployed in the mar- angles. These angles are then used to calculate the free accel- ginal ice zone in large quantities, thus complementing the eration inside the sensor, and the noise is further ampliﬁed by 586 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 FIG. 13. (a)–(d) Drifting experiments results in four locations. UAV ground stations are marked with asterisks. In (d) only tracks of buoys are displayed, because most of the time no wave motion in ice was present. Also in (d), 3 marks the deployment or retrieval locations. For the dates of the experiments, see Table 6. double integration. Low-frequency noise was also present in this variance back to the higher frequencies in proportion to drifting buoys. the already existing variance (see appendix B). This correc- Yurovsky and Dulov (2020) also identiﬁed low-frequency tion was performed in Fourier space, which means that noise, but did not present any correction method. Earle and already the time series, determined through the inverse trans- Bush (1982) and Lang (1987) proposed a method for denois- form after integration in Fourier space was corrected. ing by subtracting energy present at low frequencies from Although this method is partially ad hoc, it was shown to cor- higher frequency. By comparing several months of LP meas- rect the ﬁnal spectrum for both dominant waves and the spec- urements to coinciding Waverider measurements, we identi- tral tail. Nonetheless, further development, not excluding ﬁed biases in the variance density both for the low and high changing the MEMS sensor, is currently pursued. frequencies, and concluded that these biases are possibly Nontypical deployments, such as aerial deployments by related. When the low-frequency part was denoised, we quan- UAVs, have recently been used as an additional tool in obser- tiﬁed the amount of variance that was lost and reintroduced vational studies (Zappa et al. 2020). UAVs are gaining MAY 2022 ALA R I E T A L. 587 TABLE 6. An overview of drifting experiments where LainePoiss was deployed using a UAV. GoR refers to the Gulf of Riga. Deployment 1 Deployment 2 Deployment 3 Deployment 4 Deployment 5 Deployment 6 Device LP1 LP1 LP5 LP2 LP5 LP6 Location Va ¨ana-J ¨ oesuu ˜ (VJ) Suomenlinna (SO) Leppneeme GoR GoR GoR Type Drifting Drifting Drifting Drifting Drifting Drifting Period 15 Aug 2019 6–7 Dec 2019 27–28 Feb 2021 3–11 Mar 2021 3 Mar–5 Apr 3–30 Mar Mean U (m s ) 8 13 8 In ice In ice In ice Mean H (m) 0.94 0.87 0.41 In ice In ice In ice m0 Mean T (s) 4.2 4.4 2.7 In ice In ice In ice m10 popularity since they can carry lightweight sensors (Fuertes been added to remove the need for opening the buoy and to et al. 2019). These innovative solutions are partially motivated enhance usability. The inertial sensor, electronics, and mea- by environmental concerns, but they also allow to bypass the surement methodology are kept the same. First laboratory cost of a ship. Because of its low weight, LP can be deployed tests of the new design on durability and waterproofness have by an industrial UAV as a drifter. It has already been tested been carried out successfully, but further testing is ongoing to in deployments from shore and from sea ice with the deploy- validate this new design in the ﬁeld. ment range extending to 2 km. These novel deployment tech- niques are still being established, but possible applications can 7. Conclusions include collecting data from surf zones or transporting a buoy A wave buoy [LainePoiss (LP)] was developed. LP weighs onto the MIZ. UAV deployments will continue to be one part 3.5 kg, measures waves up to 1.28 Hz, has a rechargeable bat- of the further development of LP. tery with 2 months of operation, and transmits wave parame- It is possible to extend the operation time of LP by replac- ters and spectra operationally over cellular or satellite ing rechargeable Li-ion batteries with lithium-thionyl chloride networks. From our study, we can conclude the following: primary batteries. These batteries have an energy density that is about 2.5 times higher than that of rechargeable ones. This • Wave parameters measured in the ﬁeld were in good would extend the autonomous operating time to 5 months accordance with those measured by a nearby Directional and make measurements in remote locations more feasible. Waverider: the bias of H was 0.01 m, correlation 0.99, m0 Also, the buoy leaked on two occasions over the course of and scatter index of 8%. The bias of T was 0.14 s, cor- m-10 18 ﬁeld deployments. These incidents have been accounted relation 0.98, and scatter index 4%. The mean absolute for when designing the new hull (Fig. 16). The new hull is deviation of mean wave direction was 78. made of molded plastic and has a sealing O-ring on the top. The high-frequency part of the spectrum (up to 1.28 Hz) External connectors for charging and accessing data have compared well to a wave gauge in the wave tank. The wave FIG. 14. (a) SAR image at 0400 UTC; (b) SAR image at 1600 UTC; (c) CMEMS model wave ﬁeld (signiﬁcant wave height, m; wave directions, arrows) at 1600 UTC. The locations of different LP’s at 1600 UTC are shown with yellow marks. Kihnu weather station is marked with a green ﬁlled triangle. All panels are on 6 Mar 2021. 588 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 Research (Grant PSG22). We thank Lauri Laakso and Roine Tuomo for helping with Suomenlinna ﬁeld experiments. We appreciate discussions with Kimmo Kahma. We thank Rivo ¨ ¨ Uiboupin, Juri Elken, Aarne Mannik, and Sigrid Aas for keep- ing the administrative matters under control. We thank Tarmo Kouts for helping us with the ﬁrst versions of real-time display of data on a website. The ﬁrst author thanks (little) Aran Alari for inspiring the wave buoy name LP. We thank the following institutions and enterprises for their successful participation in the applications of LainePoiss: the Maritime Administration of Estonia, the Estonian Environment Agency, AS Saarte Liinid, OU Lainemudel, TalTech Small Craft Competence Centre, and the City of Helsinki. We thank the anonymous reviewers for their constructive critique and comments}they helped us improve our article. Valdur Kaldvee and Kristjan Mol ¨ der are the founders, and the sole owners and employees of WiseParker OU, who produce the LainePoiss wave buoy presented in this manuscript. The development of LainePoiss has been made in cooperation with Tallinn University of Technology Data availability statement. The data used in this manu- script will be made openly available upon the publication of the ﬁnal paper. The LainePoiss MATLAB processing scripts are publicly available at https://github.com/bjorkqvi/LPP/ releases/tag/v1.0.0. FIG. 15. Waves in ice measurements. (a) Wind speed and direc- APPENDIX A tion at Kihnu weather station (for location, see Fig. 14;direction marked with dots); (b) signiﬁcant wave height from three buoys in The MTi-3 Sensor ice; (c) spectra of three buoys with thin dotted lines corresponding to 30 min single spectra and thick lines corresponding to averaged This appendix provides the details of the Xsens MTi-3 spectra; dashed black line shows the sensor noise ﬂoor; (d) surface sensor to the degree the information is publicly available. displacement for buoy 6 in ice. The sensor measures all 6 degrees of freedom (using a 3D accelerometer and 3D gyroscope) and provides the ori- spectrum of LP was validated up to a Waverider cutoff fre- entation (using a magnetometer). The technical speciﬁca- quency of 0.58 Hz in the ﬁeld, and the spectral tail of LP tions of the sensor (as provided by the manufacturer) can had an expected power-law behavior up to 1.28 Hz. be found in Tables A1 and A2. The integrated microcon- • LP can measure waves in ice with a signiﬁcant wave height troller unit (MCU) synchronizes the various sensors, which as low as 1 cm. This was conﬁrmed in an over a month-long is required for the onboard conversion of the acceleration experiment where several LP’s were deployed in ice in the signals from device to Earth-referenced frame. The role of Baltic Sea. the MCU is described by the manufacturer (Xsens 2019)as • Because of its low weight, LP can be deployed as a drifter follows: to a distance of at least 2 km using an unmanned aerial The MCU applies calibration models (unique to each sensor vehicle (UAV). and including orientation, gain and bias offsets, plus more Noise in the gyroscopic sensor resulted in low-frequency arti- advanced relationships such as nonlinear temperature effects facts, but the displacement time series can be corrected (see and other higher order terms) and runs the Xsens optimized appendix B). However, with the current validation and testing strapdown algorithm, which performs highrate dead-reckoning we can only conﬁrm the buoy’s capability to measure waves calculations at 800 Hz, allowing accurate capture of high fre- quency motions and coning and sculling compensation. The downto0.1 Hz}this was a suitable rangefor the datawehad Xsens sensor fusion engine combines all sensor inputs and opti- available for the validation, although it precludes most of the mally estimates the orientation, position and velocity at an out- oceanic applications. We will continue testing the wave buoy put data rate of up to 100 Hz. The MTi 1-s is easily configurable and expand our measurement areas outside of the Baltic Sea to for the outputs and depending on the application’sneeds can be capture longer waves. Depending on the MEMS sensor noise set to use one of the filter profiles available within the Xsens levels in these conditions, we can decide whether to replace the sensor fusion engine. wave buoy’s sensor for one with several times less noise. The exact details of the built-in fusion algorithm}which Acknowledgments. This work was supported by the Personal transforms the signal from the sensor references to the Earth Research Funding of the Estonian Ministry of Education and referenced frame}are not made public by the manufacturer. MAY 2022 ALA R I E T A L. 589 FIG. 16. New version of the buoy, with the charging and data acquisition connectors brought outside the buoy to reduce buoy openings. However, the process includes an extended Kalman ﬁlter Of the available ﬁlter proﬁles, we used the proﬁle (Xsens 2015). The process and the different options for ﬁlter- “North referenced” (see Table 16 of Xsens 2019). We cali- ing are described by the manufacturer (Xsens 2019): brated the magnetometer for hard iron distortion after assembling the whole device. This was done following the Xsens sensor fusion algorithm optimally estimates the orien- manufacturers speciﬁcation using their Magnetic Field tation with respect to an Earth fixed frame utilizing the 3D Mapper application. The process consisted of starting the inertial sensor data (orientation and velocity increments) and application and rotating the buoy over a large number of 3D magnetometer. The user can set the sensor fusion algo- orientations. After that, the tool calculated new calibration rithm with different filter profiles in order to get the best per- parameters and those were saved to the sensor memory. formance based on the application scenario (see Table 16). This had to bedone onlyonceafter assemblingthe device. These filter profiles contain predefined filter parameter set- The calibration of the internal temperature sensor used tings suitable for different user application scenarios. In addi- for thermal compensation was already done by the manu- tion, all filter profiles can be used with the Active Heading facturer. The manufacturer states that the sensor has been Stabilization (AHS) setting, which significantly reduces head- ing drift during magnetic disturbances. The Inrun Compass calibrated to operate between 2408 and 858C. Calibration (ICC) setting can be used to compensate for mag- To bring out the difference between the Earth referenced netic distortions that are caused by every object the MTi is acceleration data and data in the body reference frame of attached to. the buoy, consider once more the benchmark tests from TABLE A1. Speciﬁcations for the gyroscope and accelerometer of TABLE A2. Speciﬁcations and performance statistics for the MTi-3 as given by the manufacturer (Xsens 2019). magnetometer and orientation of MTi-3 as given by the manufacturer (Xsens 2019). Gyroscope Accelerometer Value Standard full range 62000 s 16g 8 Standard full range 8 G In-run bias stability 10 h 0.03 mg Bandwidth (23 dB) 255 Hz 324 Nonlinearity 0.2% √ √ 21 21 Noise density 0:0078 s Hz 0:12 mg Hz Total RMS noise 0.5 mG Sensitivity variation 0.05% 0.05% Resolution 0.25 mG Nonlinearity 0.1%FS 0.5%FS Roll/pitch static RMS 0.58 g sensitivity (calibrated) 0.0018 (s g) } Roll/pitch dynamic RMS 0.88 Max output frequency 800 Hz 800 Hz Yaw dynamic RMS 28 590 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 D« Ef() 2 E () f , (B3) f f and Ef and E (f) are the power spectra of the unprocessed () and denoised signals. D« quantiﬁes how much variance den- sity of the signal has been lost. Especially, if D« = 0 then no further correction is necessary. In practice, this denoising and compensation is performed during the integration, which results in a clean displacement signal from which the power spectrum can be calculated in a normal fashion without having to deal with the above compensation after the fact. Low-frequency acceleration data are ﬁrst denoised using the following procedure: the average squared Fourier amplitude is calculated for the frequencies 1/100 to 1/30 Hz: a Af() , (B4) FIG. A1. Raw 50 Hz Z-oriented acceleration data in Earth refer- 1=100# f # 1=30 ence frame and body reference frame. where Af() F at() is the Fourier transform of the accel- eration signal and Af is its modulus. section 4b. This time the sensor was placed so that the pitch () angle was approximately 458. We repeated the experiment This mean value (the noise) is then removed from the for 5 s motion period (Fig. A1). The acceleration in the Fourier transform by body reference frame is a fraction of the acceleration in the !" Earth reference frame, with a cosine dependence of roll Af() 2 a 1 2 R () f A () f max 0,Af() , (B5) and pitch angles (Bender et al. 2010). We calculated the Af() Earth referenced acceleration by dividing the body refer- enced acceleration with the cosines of roll and pitch angles where R(f) is a response function: and found that it very well matches the values obtained with ⎧⎪ 0, 0 , f , f MTi-3 onboard processing (Fig. A1). The match of course is ⎪ 1 not one-to-one, since the MTi-3 fusion is much more elaborate ⎪ 1 f 2 f R () f 1 2 cos p f # f # f : (B6) and uses the accelerations from all three axes along with pitch f 1 2 ⎪ 2 f 2 f ⎪ 2 1 and roll. For our benchmark test the implication of using ⎪ 1 f , f # f Earth referenced data is straightforward. When the Earth ref- 2 N erenced accelerations are used, calculated amplitude is off by Here f = 0.08 Hz and f = 0.10 Hz. In other words, the 1 1 1 mm from the prescribed amplitude, while in the case of Fourier transform for f . 0.10 Hz is not touched. The using acceleration data in body reference frame the calculated 0.1 Hz cutoff was appropriate for our datasets in the Baltic amplitude is 14 mm lower compared to the prescribed ampli- Sea. For oceanic conditions this cutoff needs to be set to a tude (for the test case of 5 s period motion). lower value, but validating these lower frequencies would require additional ﬁeld measurements that include longer APPENDIX B waves. Following, e.g., Rabault et al. (2020), the acceleration val- Renormalization in Integration ues are then integrated in Fourier space: The limitations of the sensor create low-frequency noise, but we have concluded that this noise is actually a mis- X () f 2A () f R () f ·() 2pf , (B7) 0 0 f placed signal from other frequencies. If the low-frequency noise is removed, it should be added back to the frequen- ˆ ˆ Xf() 2Af()R () f ·() 2pf , (B8) cies, so that the power spectrum fulﬁlls the following: where f = 0.05 Hz and f = 0.06 Hz in the response func- 1 2 D«E () f Ef() E () f 1 (B1) 0 tion R (f). E () f That is, Xf and X (f) are now the uncorrected and () denoised Fourier transform of the displacement signal. We quantify how much of the squared amplitudes of the signal ⎡⎢⎢ ⎤⎥⎥ ⎢ D« ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ E () f ⎢ 1 1 ⎥ , (B2) were lost by the low-frequency correction: 0 ⎢⎢ ⎥⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ E () f ⎥ ⎢ 0 ⎥ ⎢⎢ ⎥⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ DX Xf() 2 || X () f : (B9) where f f MAY 2022 ALA R I E T A L. 591 This lost signal information will be added back in a way where x are observations and r are the reference values i i that will compensate the power spectrum as outlined in (typically from the Waverider). Eq. (B2): The variance and standard deviation are 2 Var x Cov x , x , (C5) $ () i () i i DX Xf() X () f 1 1 (B10) || X () f Std x Var x : (C6) () i () i $ For cross comparison of datasets, we deﬁned the follow- $ 2 Xf() 2 || X () f $ 0 ing parameters: f f X () f 1 1 (B11) Bias x 2 r : (C7) || X () f i i The root-mean-square deviation, mean absolute deviation and scatter index (in percent) are deﬁned: $ 2 Xf() $ ( X f 1 1 2 1 (B12) () 0 RMSD x 2 r , (C8) () i i || X f () N || x 2 r # i i $ i $ ˆ $ Xf MAD , (C9) () % f X () f : (B13) Xf () $ $ 2 $ () x 2 x 2() r 2 r f i i i i SI 100 : (C10) The displacement time series is then given by the inverse Fourier transform: The slope is deﬁned as a least squares ﬁt x = Kr xt() F Xf() : (B14) x r i i This time series is now corrected for the low-frequency K , (C11) artifacts, which has been redistributed to the other frequen- cies. The power spectrum or any other statistics can now be calculated from this displacement time series without fur- and the Pearson correlation coefﬁcient is ther corrections. Cov x , r () i i R : (C12) APPENDIX C Std x Std r () () i i Statistical Parameters With N is the number of data points we used the follow- APPENDIX D ing statistical parameters: Experiences from UAV Deployments Mean x x : (C1) i i N In this appendix, we document our experiences from six events where an industrial UAV was used to deploy LP as For angular quantities, u, the mean is deﬁned as a ﬂoating device. Our deployments were made in Estonia and Finland during 2019–21. The guidelines and regulations sin() u governing the use of UAV’s change and differ from country u arctan (C2) to country, especially outside of the European Union. cos() u Make sure to get correct information and follow any local and the difference laws and ordinances when considering deploying LP with a &' UAV. Also note that the steps below do not guarantee a || u 2 u min|| u 2 u , 3608 2|| u 2 u : (C3) 1 2 1 2 1 2 safe or successful deployment. The UAV should be regularly maintained to be sure of The covariance is the condition of the equipment; motors, blades, batteries, and the remote controller have to be working properly. Firmware and software should alsobe uptodate. Noti- Cov x , r x 2 x r 2 r : (C4) ()() () i i i i i i N 2 1 ﬁcations through, e.g., the remote controller or pilot 592 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 application should be taken seriously, and they need to be REFERENCES resolved before ﬂight. Before deploying the actual device, Ashton, I., and L. Johanning, 2015: On errors in low frequency we recommend practicing with, e.g., sandbags that have the wave measurements from wave buoys. Ocean Eng., 95,11– same weight as LP. 22, https://doi.org/10.1016/j.oceaneng.2014.11.033. A successful UAV deployment starts with a comprehen- Battjes, J. A., and G. P. van Vledder, 1984: Veriﬁcation of Kimu- sive preparation and plan for the ﬂight and requires at least ra’s theory for wave group statistics. Proc. 19th Int. Conf. on two persons. The ﬁrst person ﬂies the drone while the sec- Coastal Engineering, New York, NY, ASCE, 642–648, https:// ond person assists at lift-off and landing. We used a DJI doi.org/10.1061/9780872624382.044. Matrice 600 Pro industrial drone with a release mechanism Bender, L. C., N. L. Guinasso, J. N. Walpert, and S. D. Howden, (Fig. 1b). A 5-m-long ﬁshing thread (we used Dyneema 2010: A comparison of methods for determining signiﬁcant wave heights}Applied to a 3-m discus buoy during Hurricane 0.3 mm with a breaking strength of 25 kg) was found suit- Katrina. J. Atmos. Oceanic Technol., 27, 1012–1028, https://doi. able for connecting the UAV and the wave buoy. A longer org/10.1175/2010JTECHO724.1. thread could make releasing the LP more convenient as the Bishop, C. T., and M. A. Donelan, 1987: Measuring waves with UAV can be higher, thus having a stronger signal strength. pressure transducers. Coastal Eng., 11, 309–328, https://doi. Nonetheless, a shorter thread minimizes the motion of the org/10.1016/0378-3839(87)90031-7. buoy during ﬂight. The lift-off is the riskiest part: the second Bjo ¨rkqvist, J.-V., 2020: Waves in archipelagos. Ph.D. thesis, person has to hold the thread downwind and low to the University of Helsinki, 58 pp. ground to minimize the risk of the thread being caught by }},H.Pettersson, L. Laakso,K. K. Kahma, H.Jokinen, and the UAV motors. This has to be done while keeping a dis- P. Kosloff, 2016: Removing low-frequency artefacts from tance of at least a few meters from the UAV. For the safety Datawell DWR-G4 wave buoy measurements. Geosci. Ins- trum. Methods Data Syst., 5,17–25, https://doi.org/10.5194/gi- of the assisting person, the pilot should guide the UAV 5-17-2016. upward for the ﬁrst couple of meters as quickly as possible. }}, I. Lukas, V. Alari, G. P. van Vledder, S. Hulst, H. Pettersson, The rest of the lift-off can happen at a slower pace until A. Behrens, and A. Ma ¨nnik, 2018: Comparing a 41-year model thewavebuoy is up in theair. Weused a ﬂight height of hindcast with decades of wave measurements from the Baltic 20–30 m when transporting the wave buoy to the drop- Sea. Ocean Eng., 152,57–71, https://doi.org/10.1016/j.oceaneng. off location. 2018.01.048. With fully charged batteries at lift-off, we deployed the }}, H. Pettersson, and K. K. Kahma, 2019: The wave spectrum buoy at a distance of up to 2 km. We started guiding the in archipelagos. Ocean Sci., 15, 1469–1487, https://doi.org/10. UAV back toward the ground station before the battery 5194/os-15-1469-2019. dropped below 50%. In our deployments we ﬂew upwind Campos, R. M., H. Islam, T. R. Ferreira, and C. Guedes Soares, with the heavy weight, thus returning to the ground station 2021: Impact of heavy biofouling on a nearshore heave-pitch- roll wave buoy performance. Appl. Ocean Res., 107, 102500, downwind. We found that the battery charge at landing was https://doi.org/10.1016/j.apor.2020.102500. still at about 20%. Carandell, M., D. M. Toma, J. P. Pinto, M. Gasulla, and Below is a step-by-step checklist that we have used in J. del Rıo, 2020: Impact on the wave parameters estima- our deployments: tion of a kinetic energy harvester embedded into a drifter. • Global Oceans 2020: Singapore–U.S. Gulf Coast, Biloxi, The pilot does a UAV precheck a day before ﬂight as well MS, IEEE, https://doi.org/10.1109/IEEECONF38699.2020. as on the ﬁeld. If applicable, follow the messages from the pilot application. Cartwright, D. E., and M. S. Longuet-Higgins, 1956: The statistical The second person, crouching at least 2 m from the UAV, distribution of the maxima of a random function. Proc. Roy. holds the thread under tension between the UAV and the Soc. London, 237A,212–232, https://doi.org/10.1098/rspa. person’s hand, ready to give slack as the UAV is ascending. 1956.0173. The pilot loudly notiﬁes the other persons before activating Cavaleri, L., 1980: Wave measurement using pressure transducer. motors and makes sure everybody is ready for lift-off. Oceanol. Acta, 3, 339–346. The pilot ascends the ﬁrst 2 m as quickly as possible, and Centurioni, L., L. Braasch, E. Di Lauro, P. Contestabile, F. De Leo, the second person gives slack to the thread as the UAV R. Casotti, L. Franco, and D. Vicinanza, 2017: A new strategic takes off. wave measurement station off Naples port main breakwa- • ter. Coastal Eng. Proc., 1, 36, https://doi.org/10.9753/icce. A second person must hold the thread under tension v35.waves.36. between the UAV and their hand until the LP is up in the Christakos, K., J.-V. Bjorkqvist, L. Tuomi, B. R. Furevik, and Ø. air. Breivik, 2021: Modelling wave growth in narrow fetch geom- Thread should be downwind, even though the UAV might etries: The white-capping and wind input formulations. Ocean deviate also downwind where the second person is holding Modell., 157, 101730, https://doi.org/10.1016/j.ocemod.2020. the thread. Cook, A., A. Babanin, D. Sgarioto, P. Graham, J. Mathew, A. Recommendations for the pilot: Skvortsov, R. Manasseh, and D. Tothova, 2020: A UAV Flight height between 20 and 30 m. ‘mobile buoy’ for measuring surface waves. 22nd Australasian Do not ﬂy farther than 50% of the battery capacity; ideally Fluid Mechanics Conf., Brisbane, Australia, University of ﬂy upwind with payload and return with tailwind. Queensland, https://doi.org/10.14264/8e7141e. MAY 2022 ALA R I E T A L. 593 Donelan, M. A., and W. J. Pierson, 1983: The sampling vari- Kitaigorodskii, S. A., 1983: On the theory of the equilibrium ability of estimates of spectra of wind-generated gravity range in the spectrum of wind-generated gravity waves. waves. J. Geophys. Res., 88, 4381–4392, https://doi.org/10. J. Phys. Oceanogr., 13, 816–827, https://doi.org/10.1175/ 1029/JC088iC07p04381. 1520-0485(1983)0130816:OTTOTE2.0.CO;2. }},J.Hamilton,and W. H. Hui, 1985:Directional spectra of Kodaira, T., T. Waseda, T. Nose, K. Sato, J. Inoue, J. Voermans, wind-generated waves. Philos. Trans. Roy. Soc. London, and A. Babanin, 2020: Observation of on-ice wind waves 315A,509–562, https://doi.org/10.1098/rsta.1985.0054. under grease ice in the western Arctic Ocean. Polar Sci., 27, Earle, M., and K. Bush, 1982: Strapped-down accelerometer 100567, https://doi.org/10.1016/j.polar.2020.100567. effects on NDBO wave measurements. OCEANS 82, Kohout, A. L., B. Penrose, S. Penrose, and M. J. Williams, 2015: Washington, DC, IEEE, 838–848, https://doi.org/10.1109/ A device for measuring wave-induced motion of ice ﬂoes in OCEANS.1982.1151908. the Antarctic marginal ice zone. Ann. Glaciol., 56, 415–424, Farber, S., H. Allaka, I. Klein, and M. Groper, 2018: Estimating https://doi.org/10.3189/2015AoG69A600. sea state using a low cost buoy. 2018 IEEE Int. Conf. on the Lancaster, O., R. Cossu, S. Boulay, S. Hunter, and T. E. Baldock, Science of Electrical Engineering in Israel, Eilat, Israel, IEEE, 2021: Comparative wave measurements at a wave energy site https://doi.org/10.1109/ICSEE.2018.8646100. with a recently developed low-cost wave buoy (Spotter), Forristall, G. Z., J. C. Heideman, I. M. Leggett, B. Roskam, ADCP, and pressure loggers. J. Atmos. Oceanic Technol., 38, and L. Vanderschuren, 1996: Effect of sampling variability 1019–1033, https://doi.org/10.1175/JTECH-D-20-0168.1. on hindcast and measured wave heights. J. Waterw. Port Lang, N., 1987: The empirical determination of a noise function Coastal Ocean Eng., 122, 216–225, https://doi.org/10.1061/ for NDBC buoys with strapped-down accelerometers. (ASCE)0733-950X(1996)122:5(216). OCEANS’87, Halifax, NS, Canada, IEEE, 225–228, https:// Fuertes, F. C., L. Wilhelm, and F. Porte- ´ Agel, 2019: Multirotor doi.org/10.1109/OCEANS.1987.1160904. UAV-based platform for the measurement of atmospheric Le Merle, E., D. Hauser, C. Peureux, L. Aouf, P. Schippers, turbulence: Validation and signature detection of tip vortices C. Dufour, and A. Dalphinet, 2021: Directional and fre- of wind turbine blades. J. Atmos. Oceanic Technol., 36, quency spread of surface ocean waves from SWIM measure- 941–955, https://doi.org/10.1175/JTECH-D-17-0220.1. ments. J. Geophys. Res. Oceans, 126, e2021JC017220, https:// Gordon, L., and A. Lohrmann, 2002: Near-shore Doppler current doi.org/10.1029/2021JC017220. meter wave spectra. Proc. Int. Symp. on Ocean Wave Mea- Lenain, L., and N. Pizzo, 2020: The contribution of high-frequency surement and Analysis, San Francisco, CA, American Society wind-generated surface waves to the Stokes drift. J. Phys. of Civil Engineers, 33–43, https://doi.org/10.1061/40604(273)4. Oceanogr., 50, 3455–3465, https://doi.org/10.1175/JPO-D-20- Graber, H. C., E. A. Terray, M. A. Donelan, W. M. Drennan, 0116.1. J. C. Van Leer, D. B. Peters, and J. C. V. Leer, 2000: Lin, Z., T. A. A. Adcock, and M. L. McAllister, 2021: Estimating ASIS}A new air–sea interaction spar buoy: Design and per- ocean wave directional spreading using wave following buoys: formance at sea. J. Atmos. Oceanic Technol., 17, 708–720, A comparison of experimental buoy and gauge data. https://doi.org/10.1175/1520-0426(2000)0170708:AANASI2. J. Ocean Eng. Mar. Energy, 8,83–97, https://doi.org/10.1007/ 0.CO;2. s40722-021-00218-7. Hanaﬁn, J. A., and Coauthors, 2012: Phenomenal sea states and Loehr, H., and Coauthors, 2013: Development of a low cost wave swell from a North Atlantic storm in February 2011: A com- buoy by utilising smartphone technology. 21st Australasian prehensive analysis. Bull. Amer. Meteor. Soc., 93,1825–1832, Coastal and Ocean Engineering Conf.–14th Australasian Port https://doi.org/10.1175/BAMS-D-11-00128.1. and Harbour Conf., Barton, Australia, Engineers Australia. Herbers, T. H. C., P. F. Jessen, T. T. Janssen, D. B. Colbert, and Longuet-Higgins, M. S., 1961: Observations of the directional J. H. MacMahan, 2012: Observing ocean surface waves with spectrum of sea waves using the motions of a ﬂoating buoy. GPS-tracked buoys. J. Atmos. Oceanic Technol., 29, 944–959, Ocean Wave Spectra, Prentice-Hall, 111–136. https://doi.org/10.1175/JTECH-D-11-00128.1. Montiel, F., V. Squire, M. Doble, J. Thomson, and P. Wadhams, Hirakawa, Y., T. Takayama, T. Hirayama, and H. Susaki, 2016: 2018: Attenuation and directional spreading of ocean waves Development of mini-buoy for short term measurement of during a storm event in the autumn Beaufort Sea marginal ocean wave. OCEANS 2016 MTS/IEEE Monterey,Monterey, ice zone. J. Geophys. Res. Oceans, 123, 5912–5932, https://doi. CA, IEEE, https://doi.org/10.1109/OCEANS.2016.7761337. org/10.1029/2018JC013763. Holthuijsen, L., 2007: Waves in Oceanic and Coastal Waters. Mueller, J. A., and F. Veron, 2009: Nonlinear formulation of the Cambridge University Press, 387 pp. bulk surface stress over breaking waves: Feedback mecha- Houghton, I., P. Smit, D. Clark, C. Dunning, A. Fisher, N. Nidzieko, nisms from air-ﬂow separation. Bound.-Layer Meteor., 130, P. Chamberlain, and T. Janssen, 2021: Performance statistics of 117–134, https://doi.org/10.1007/s10546-008-9334-6. a real-time Paciﬁc Ocean weather sensor network. J. Atmos. Munk, W. H., 1950: Origin and generation of waves. Proc. First Oceanic Technol., 38, 1047–1058, https://doi.org/10.1175/JTECH- Conf. Coastal Engineering, Long Beach, CA, ASCE, 1–4, D-20-0187.1. https://doi.org/10.9753/icce.v1.1. Janssen, P. A., 1991: Quasi-linear theory of wind-wave genera- Pearman, D.,T.Herbers, T. Janssen, H. vanEttinger,S.McIntyre, tion applied to wave forecasting. J. Phys. Oceanogr., 21, and P. Jessen, 2014: Drifter observations of the effects of 1631–1642, https://doi.org/10.1175/1520-0485(1991)021,1631: shoals and tidal-currents on wave evolution in San Francisco QLTOWW.2.0.CO;2. Bight. Cont. Shelf Res., 91,109–119, https://doi.org/10.1016/j. Kennedy, D., M. Walsh, and B. O’Flynn, 2014: Development of a csr.2014.08.011. miniature, low-cost wave measurement solution. 2014 Pettersson, H., H. C. Graber, D. Hauser, C. Quentin, Oceans}St. John’s, St. John’s, NL, Canada, IEEE, https:// K. K. Kahma, W. M. Drennan, and M. A. Donelan, 2003: doi.org/10.1109/OCEANS.2014.7003217. Directional wave measurements from three wave sensors 594 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 39 during the FETCH experiment. J. Geophys. Res., 108, }}, and Coauthors, 2015: Biofouling effects on the response of a wave measurement buoy in deep water. J. Atmos. Oceanic 8061, https://doi.org/10.1029/2001JC001164. Technol., 32, 1281–1286, https://doi.org/10.1175/JTECH-D-15- }}, K. K. Kahma, and L. Tuomi, 2010: Wave directions in a nar- 0029.1. row bay. J. Phys. Oceanogr., 40, 155–169, https://doi.org/10. Veras Guimarae ˜ s, P., and Coauthors, 2018: A surface kinematics 1175/2009JPO4220.1. buoy (SKIB) for wave–current interaction studies. Ocean Phillips, O. M., 1985: Spectral and statistical properties of the Sci., 14, 1449–1460, https://doi.org/10.5194/os-14-1449-2018. equilibrium range in wind-generated gravity waves. Voermans, J., P. Smit, T. Janssen, and A. Babanin, 2020: Estimat- J. Fluid Mech., 156, 505–531, https://doi.org/10.1017/ ing wind speed and direction using wave spectra. J. Geophys. S0022112085002221. Res. Oceans, 125, e2019JC015717, https://doi.org/10.1029/ Rabault, J., G. Sutherland, B. Ward, K. H. Christensen, 2019JC015717. T. Halsne, and A. Jensen, 2016: Measurements of waves in Wadhams, P., 1978: Wave decay in the marginal ice zone mea- landfast ice using inertial motion units. IEEE Trans. Geo- sured from a submarine. Deep-Sea Res., 25,23–40, https://doi. sci. Remote Sens., 54, 6399–6408, https://doi.org/10.1109/ org/10.1016/S0146-6291(21)00004-7. TGRS.2016.2584182. Xsens, 2015: Data sheet MTi 1-series: 3D AHRS/VRU/IMU mod- }}, }}, O. Gundersen, A. Jensen, A. Marchenko, and ule. Xsens Doc. MT0512P, Revision B, 35 pp., http://www. Ø. Breivik, 2020: An open source, versatile, affordable waves sensores-de-medida.es/uploads/xsens_mti-1-series_datasheet.pdf. in ice instrument for scientiﬁc measurements in the polar }}, 2019: MTi 1-series datasheet: IMU, VRU, AHRS and regions. Cold Reg. Sci. Technol., 170, 102955, https://doi.org/ GNSS/INS module. Xsens Doc. MT0512P, Revision 10.1016/j.coldregions.2019.102955. 2019.A, 40 pp., https://www.xsens.com/hubfs/Downloads/ Raghukumar, K., G. Chang, F. Spada, C. Jones, T. Janssen, and Manuals/MTi-1-series-datasheet.pdf. A. Gans, 2019: Performance characteristics of “Spotter,” a Young, I. R., 1995: The determination of conﬁdence limits associ- newly developed real-time wave measurement buoy. ated with estimates of the spectral peak frequency. Ocean J. Atmos. Oceanic Technol., 36, 1127–1141, https://doi.org/10. Eng., 22,669–686, https://doi.org/10.1016/0029-8018(95)00002-3. 1175/JTECH-D-18-0151.1. Yurovsky, Y. Y., and V. Dulov, 2017: Compact low-cost Arduino- Skinner, E., M. Rooney, and M. Hinders, 2018: Low-cost wave based buoy for sea surface wave measurements. 2017 Pro- characterization modules for oil spill response. J. Ocean Eng. gress in Electromagnetics Research Symp.}Fall, Singapore, Sci., 3,96–108, https://doi.org/10.1016/j.joes.2018.05.003. IEEE, 2315–2322, https://doi.org/10.1109/PIERS-FALL.2017. Smit, P. B., I. A. Houghton, K. Jordanova, T. Portwood, E. Shapiro, D. Clark, M. Sosa, and T. T. Janssen, 2021: }},and }}, 2020: MEMS-based wave buoy: Towards short Assimilation of signiﬁcant wave height from distributed wind-wave sensing. Ocean Eng., 217, 108043, https://doi.org/ ocean wave sensors. Ocean Modell., 159, 101738, https://doi. 10.1016/j.oceaneng.2020.108043. org/10.1016/j.ocemod.2020.101738. Zappa, C. J., S. M. Brown, N. J. M. Laxague, T. Dhakal, Squire, V. A., 2020: Ocean wave interactions with sea ice: A reap- R. A. Harris, A. M. Farber, and A. Subramaniam, 2020: praisal. Annu. Rev. Fluid Mech., 52,37–60, https://doi.org/10. Using ship-deployed high-endurance unmanned aerial vehicles 1146/annurev-ﬂuid-010719-060301. for the study of ocean surface and atmospheric boundary layer Sutherland, G., and Coauthors, 2020: Evaluating the leeway coef- processes. Front.Mar.Sci., 6, 777, https://doi.org/10.3389/fmars. ﬁcient of ocean drifters using operational marine environ- 2019.00777. mental prediction systems. J. Atmos. Oceanic Technol., 37, Zong, Y., H.-Y. Cheng, H. Chien, and B. Koppe, 2019: Miniature 1943–1954, https://doi.org/10.1175/JTECH-D-20-0013.1. wave buoy}Laboratory and ﬁeld tests for development of a Thomson, J., 2012: Wave breaking dissipation observed with robust low-cost measuring technique. Coastal Structures 2019, “swift” drifters. J. Atmos. Oceanic Technol., 29, 1866–1882, Hannover, Germany, Bundesanstalt fur Wasserbau, 453–462, https://doi.org/10.1175/JTECH-D-12-00018.1. https://doi.org/10.18451/978-3-939230-64-9_046.

Journal

Journal of Atmospheric and Oceanic Technology – American Meteorological Society

Published: May 3, 2022

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

LainePoiss®—A Lightweight and Ice-Resistant Wave Buoy

LainePoiss®—A Lightweight and Ice-Resistant Wave Buoy

Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

LainePoiss®—A Lightweight and Ice-Resistant Wave Buoy

LainePoiss®—A Lightweight and Ice-Resistant Wave Buoy

References (88)

Abstract

Journal

Recommended Articles

There are no references for this article.

Our policy towards the use of cookies