Observations of Surface Currents and Tidal Variability Off of Northeastern Taiwan from Shore-Based High Frequency Radar

remote sensing

Article Observations of Surface Currents and Tidal Variability Off of Northeastern Taiwan from Shore-Based High Frequency Radar

Yu-Ru Chen 1 , Jeffrey D. Paduan 2 , Michael S. Cook 2, Laurence Zsu-Hsin Chuang 1 and Yu-Jen Chung 3,*

1 Institute of Ocean Technology and Marine Affairs, National Cheng Kung University, Tainan 701, Taiwan; [email protected] (Y.-R.C.); [email protected] (L.Z.-H.C.) 2 Department of Oceanography, Naval Postgraduate School—NPS, Monterey, CA 93943, USA; [email protected] (J.D.P.); [email protected] (M.S.C.) 3 Department of Marine Science, Naval Academy, Kaohsiung 813, Taiwan * Correspondence: [email protected]

Abstract: A network of high-frequency radars (HFRs) has been deployed around Taiwan. The wide-area data coverage is dedicated to revealing near real-time sea-surface current information. This paper investigates three primary objectives: (1) describing the seasonal current synoptic variability; (2) determining the influence of wind forcing; (3) describing the tidal current field pattern and variability. Sea surface currents derived from HFR data include both geostrophic components and wind-driven components. This study explored vector complex correlations between the HFR time series and wind, which was sufficient to identify high-frequency components, including an Ekman balance among the surface currents and wind. Regarding the characteristics of mesoscale events and the tidal field, a year-long high-resolution surface dataset was utilized to observe the current–eddy– tide interactions over four seasons. The harmonic analysis results derived from surface currents off Citation: Chen, Y.-R.; Paduan, J.D.; Cook, M.S.; Chuang, L.Z.-H.; Chung, of northeastern Taiwan during 2013 are presented. The results agree well with the tidal parameters Y.-J. Observations of Surface Currents estimated from tide-gauge station observations. The analysis shows that this region features a strong, and Tidal Variability Off of mixed, mainly semidiurnal tide. Continued monitoring by a variety of sensors (e.g., satellite and Northeastern Taiwan from HFR) would improve the understanding of the circulation in the region. Shore-Based High Frequency Radar. Remote Sens. 2021, 13, 3438. https:// Keywords: high-frequency radar (HFR); surface currents; tidal variability; harmonic analysis doi.org/10.3390/rs13173438

Academic Editors: Miroslav Gaˇci´c, Milena Menna and Yukiharu Hisaki 1. Introduction Taiwan is situated between the Asian continent and the Paciﬁc Ocean. It is a large Received: 6 June 2021 island with a total coastline length of approximately 1200 km. In terms of atmospheric Accepted: 24 August 2021 Published: 30 August 2021 forcing, synoptic scale systems occur frequently in the spring, typhoons are common in summer, and frontal systems with strong winds and heavy rainfall are common in winter

Publisher’s Note: MDPI stays neutral due to Taiwan’s subtropical climate. These variable monsoon systems drive sea-surface with regard to jurisdictional claims in currents in the waters around the island. The interactions within the Western Boundary published maps and institutional affil- Current system between the warm Kuroshio Current and the rugged seafloor topography iations. create a complex ocean current system around Taiwan [1,2]. The Kuroshio Current moves rapidly off of northeastern Taiwan and is commonly associated with seasonal cyclones worthy of long-term observations. To routinely monitor the currents and sea state around Taiwan, a current measurement network consisting of 19 SeaSonde® high-frequency radar (HFR) systems was established in 2008. Copyright: © 2021 by the authors. Remote measurement and monitoring of the sea state using HFRs has become an Licensee MDPI, Basel, Switzerland. This article is an open access article indispensable field in marine science and technology. Such systems have the capability distributed under the terms and to measure near real-time surface currents with good temporal resolution with operating conditions of the Creative Commons frequencies ranging between 3 and 50 MHz. Regarding the general rule for electromagnetic Attribution (CC BY) license (https:// radiation (EM) in the high-frequency band, the EM signal coupled with the sea surface creativecommons.org/licenses/by/ can propagate via groundwaves over the horizon (OTH) [3]. In this study, two of the HFR 4.0/). network stations located off northeastern Taiwan were used as research instruments (the

Remote Sens. 2021, 13, 3438. https://doi.org/10.3390/rs13173438 https://www.mdpi.com/journal/remotesensing Remote Sens. 2021, 13, x FOR PEER REVIEW 2 of 19

Remote Sens. 2021, 13, 3438 HFR network stations located off northeastern Taiwan were used as research instruments2 of19 (the two green squares shown in Figure 1). HFRs have the capability to measure near real- time complete currents with good temporal and spatial resolutions. Figure 1 shows the areatwo of green maximum squares coverage shown inin Figure2013. Areas1). HFRs with have data the coverage capability of to75% measure or more near are real-time shown incomplete yellow, while currents areas with with good lower temporal data coverage and spatial are shown resolutions. in blue. The Figure data1 shows coverage the was area calculatedof maximum from coveragethe totals indata 2013. (TUV) Areas files, with which data are coverage generated of 75% by combining or more are the shown radial in datayellow, from while the two areas stations with lowerinto the data total coverage velocities are shownaccording in blue.to CODAR’s The data strict coverage quality was controlcalculated (QA) frommechanism. the totals This data study (TUV) exploits files, whichthe hourly are generated TUV files byfrom combining 2013 (8410 the in radial total).data Each from circle the in two Figure stations 1 represents into the totalthe position velocities of a according current vector. to CODAR’s The data strict coverage quality overcontrol the course (QA) mechanism.of the year, counted This study based exploits on the number the hourly of observations, TUV files from is displayed 2013 (8410 as in a percentage.total). Each circleThese in radar Figure coverage1 represents areas the incl positionude the of islands a current of Yonaguni vector. The and data Iriomote, coverage whichover theare courseJapanese of theislands year, in counted the middle based and on on the the number eastern of observations,edge of the coverage is displayed area, as respectively.a percentage. The These red triangles radar coverage in Figure areas 1 repres includeent tide the islands(i.e., sea of level Yonaguni elevation) and stations Iriomote, onwhich the shoreline. are Japanese The data islands from in these the middle HFRs andand tide on the stations eastern are edge used of in the the coverage subsequent area, analysis.respectively. In addition The red to routinely triangles ininvestigatin Figure1 representg mesoscale tide oceanic (i.e., sea processes, level elevation) the HFRs stations also provideon the the shoreline. opportunity The data to resolve from thesethe tidal HFRs constituents and tide stations around areTaiwan. used HFRs in the have subsequent been usedanalysis. to map In tidal addition constituents to routinely and investigatinghighlight the mesoscaleeffects of tidal oceanic and processes, wind drivers the HFRson diur- also nalprovide movements the opportunity [4]. While tothese resolve direct the observat tidal constituentsions of tidal-period around Taiwan. current HFRs fluctuations have been existused for to some map tidalregions, constituents most tidal and studies highlight ha theve effectsbeen based of tidal on and cro windss-validation drivers on of diurnaltide- gaugemovements data and [4 ].models While these[5]. This direct study observations utilizes both of tidal-periodHFR and sea current level fluctuationsobservations existto describefor some the regions, tidal characteristics most tidal studies off northeastern have been based Taiwan. on cross-validation of tide-gauge data and models [5]. This study utilizes both HFR and sea level observations to describe the tidal characteristics off northeastern Taiwan.

90 00 -8 LD 25˚ 25°N N 80 WS 70 -800 40′ 40' Suao -800 SO 60

0 Habn -80 -8 0 50 20′ 20' 0 80 HP 0 - Latitude

Latitude 8 00 40

0 0 -8

-800 25˚ 24°N N HL (%) coverage Data 30

20 40′ 40'

km 10

20′ 20' 0 102030 30′ 30' 122˚ 122°E E 30′ 30' 123˚ 123°E E 30′ 30' 124˚ 124°E E Longitude Longitude

Figure 1. The surface current data coverage in percentages (%) in 2013. Green squares indicate the Suao and Habn HFR Figure 1. The surface current data coverage in percentages (%) in 2013. Green squares indicate the Suao and Habn HFR stations. The red triangles indicate the tide-gauge stations along the coastline. The island in the center and the island closest stations. The red triangles indicate the tide-gauge stations along the coastline. The island in the center and the island closestto the to eastern the eastern edge ofedge the of domain the domain are the are Japanese the Japanese islands islands of Yonaguni of Yonaguni and Iriomote, and Iriomo respectively.te, respectively. The black The box black inside box the insideinset the at the inset bottom at the left bottom represents left represents the study the area. study area.

The main focus of this paper is to investigate the seasonal characteristics of the current patterns, the inﬂuence of wind forcing and the spatial distributions of tide constituents,

Remote Sens. 2021, 13, 3438 3 of 19

taking advantage of the continuous time and space data from the coastal radar systems. There are some seasonal mesoscale events that appear in this area, but they have not been comprehensively studied. This paper is divided in five parts. In Section2, this study describes the dataset and methods used. Selected data are compared with the HFR data depending on spatial and temporal availability, with Table1 providing a summary of the datasets used and their temporal and spatial resolutions. The analysis methods used in this article to study the flow field, wind influence and tide are introduced in Section3. Section4 presents the results. To understand the dynamic processes in the area, this study describes the main features of this region and then compares the relationships between the HFRs and the surface geostrophic velocities (SGVs) and wind stress using complex correlation analyses. Then, harmonic analyses are used to describe the characteristics of the tides. Finally, Section5 offers a discussion and conclusions.

Table 1. Summary of the key dataset characteristics.

HFR Altimeter (Aviso+) CCMP ETOPO1 Tide Gauge Sea surface Variable Geostrophic current Wind stress Bathymetry Sea level velocities Temporal Hourly Daily 6-hourly Hourly resolution Spatial resolution 1/13◦ 1/8◦ 1/4◦ 1/60◦ 1 m under the Instrument Vertical integration Surface 10 m above sea level Degree of depth surface reference level

2. Background There are existing, regional research results on the seasonal variations of the surface currents [6,7]. To characterize the regional marine environment in terms of ocean circulation, this study organized the available remote sensing data for comparison and analysis. We use the surface currents off of northeastern Taiwan derived from the HFRs. These observations are compared against two other datasets. First, the surface currents are correlated with the surface geostrophic currents obtained from satellite altimeter observations and extracted from the Archiving Validation and Interpretation of Satellite Oceanographic (AVISO+) database. Next, the surface currents are correlated against the wind field data from the source known as the Cross-Calibrated Multi-Platform (CCMP) database. To characterize the regional tidal fluctuations, the tidal currents and tide types analyzed and derived from the HFRs are compared with the tidal constituents derived from sea level measurements from the coastline tide-gauge stations. All of the data used in this study are summarized in Table1. In the following analysis of complex correlation of veering, this research is based on the shortest time resolution, i.e., daily, that Aviso+ can provide (as shown in Table1, the temporal resolutions of the datasets are as follows: HFR is hourly, SGV is daily, and wind is 6 h). Therefore, this study performs a long-term averaging of hourly HFR data and 6-hourly wind data and then analyzes the complex correlation of veering with these three remote sensing datasets to analyze the influence of wind.

2.1. Remote Sensing Data 2.1.1. High-Frequency Radar This study used HFR data from two long-range SeaSonde systems located at the Suao and Habn stations on the eastern coast of Taiwan, as shown in Figure1. The northeastern region of Taiwan, as well as the Yonaguni and Iriomote Islands of Japan, are all within the maximum radar coverage of 292 km. The long-range SeaSonde systems were operated with a chirp signal centered at 4.4 kHz with an 18.38 kHz sweep bandwidth and a sweep repetition time of 1 s (as shown in Table2). There is good correlation between the mean radial velocities measured by these two stations and the 20 m water-depth current data Remote Sens. 2021, 13, 3438 4 of 19

from the shipboard acoustic Doppler current profilers (SADCPs). It was also confirmed that there were no significant systematic deviations among these stations [8,9].

Table 2. Operating parameters of the study area HFRs.

Parameter Value Radar frequency (fc) 4.4 MHz Sweep bandwidth (B) 18.38 kHz Sweep period or sweep repetition time (Ts) 1 s Range resolution (c/2B) 8.16 km Maximum range 292 km Sampling time 243.2 µs

2.1.2. Aviso+ AVISO+ provides sea surface height (SSH) and SGV data in Mercator projection coor- dinates with a latitude range of 82◦ N to 82◦ S and a nominal cell size of 1/8◦. To maximize the accuracy of the spatial and temporal resolutions, this dataset merged observations from multiple satellites, including Topex/Poseidon, Jason-1, Jason-2, GFO, ERS-1, ERS-2, and EnviSat. The SGV used in this study was one of the gridded products from satellite altimetry data; other products also included wind speed modulus and significant wave height [10]. Altimeter-derived surface geostrophic velocities have been used to explore variations in the Kuroshio Current east of Taiwan over time periods from a few weeks to several years. Hsin et al., (2013) [11] verified that the altimeter-based velocities are compara- ble to shipboard ADCP velocity composites, including the turning position, magnitude and pathway of the Kuroshio Current. Figure2 shows the annual mean SGV around Taiwan in our study period. A significant meandering current with a high speed of approximately 70 cm/s was observed flowing northward along the eastern coast of Taiwan. The Kuroshio Current has been ascribed to the seasonal reversal of monsoonal winds via Ekman dynamics [12]. Sea surface currents derived by HFR contain wind, a mixture of geostrophic and ageostrophic constituents [13]. The satellite-derived current estimates, on the other hand, are limited to the geostrophic constituent by the physics of the measurement. Our approach, therefore, is to attempt to remove the geostrophic constituent from the HFR observations by subtracting the satellite-derived current estimates to form the residual currents. To understand the influence of wind forcing on HFR data, this study explored vector complex correlations between the HFR and satellite-derived SGV data and wind data to demonstrate high-frequency components in the following section.

2.1.3. CCMP Ocean Surface Wind Components The CCMP derives wind retrievals from a number of satellite-borne passive and active microwave instruments. The dataset primarily combines instrument observations and cross-calibrated satellite microwave wind using variational analysis methodology (VAM) to produce 1/4◦ high-resolution gridded analyses. This data source provides gap-free ocean surface wind data with high temporal and spatial resolutions, which are useful for the study of large-scale air–sea interactions affecting the atmosphere and ocean. Winds are dynamic and constantly evolve over short periods of time. Accordingly, the CCMP provides 6 h vector wind data at 10 m above the sea surface, which is useful for subsequent correlation studies of HFR and SGV data [14]. Remote Sens. 2021, 13, x FOR PEER REVIEW 5 of 19

provides 6 h vector wind data at 10 m above the sea surface, which is useful for subsequent Remote Sens. 2021, 13, 3438 correlation studies of HFR and SGV data [14]. 5 of 19

26˚ N

25˚ N

24˚ N Latitude

23˚ N

22˚ N

120˚ E 121˚ E 122˚ E 123˚ E 124˚ E Longitude

Figure 2. Mean surface geostrophic velocity (SGV) in 2013. Figure 2. Mean surface geostrophic velocity (SGV) in 2013. 3. Methodology 3.1. Eddy Kinetic3. Methodology Energy Distribution To investigate3.1. Eddy the Kinetic time-varying Energy componentDistribution of the current, the distribution of mean and eddy energy was given by the velocity values, which grouped in time and area To investigate the time-varying component of the current, the distribution of mean boxes [15]. Eddy kinetic energy (EKE) values are time and space averages and commonly used to analyzeand theeddy velocity energy field. was For given this purpose,by the velocity it is necessary values, to which average grouped the currents in time and area boxes in few representative[15]. Eddy boxes kinetic and energy display (EKE) the time values evolution are time of theseand space spatially averages averaged and commonly used currents [16to]. However,analyze the this velocity definition field. contains For allthis processes purpos thate, it varyis necessary in time, including to average the currents in coherent mesoscalefew representative eddies, jets, waves,boxes and large-scaledisplay the motions. time evolution The EKE valueof these per spatially unit averaged cur- mass were givenrents by[16]. However, this definition contains all processes that vary in time, including co- 1 herent mesoscale eddies,EKE = jets,× waves,u02 + v0 2and large-scale motions. The(1) EKE value per unit 2 mass were given by where the mean velocity u, v in the horizontal and vertical directions and the departures u0, 0 1 v were calculated for each box. 𝐸𝐾𝐸 = ×(𝑢 +𝑣) (1) 2 3.2. Complex Correlation of Veering where the mean velocity 𝑢, 𝑣̅ in the horizontal and vertical directions and the departures Ocean currents can be depicted as a blend of geostrophic and ageostrophic terms, with 𝑢, 𝑣 were calculated for each box. the latter representing wind-driven ageostrophic currents [17]. HFRs have been utilized to derive wind-driven surface currents in many studies and to illustrate the connection between coastal3.2. Complex currents Correlation and wind. of Coastal Veering currents respond rapidly to wind effects, with currents changingOcean speedcurrents or reversingcan be depicted in response as a to blend changing of geostrophic wind patterns and and ageostrophic terms, wind stresseswith [17 –the20]. latter Since representing the angle between wind-driven two observed ageostrophic vectors (e.g., currents currents [17]. and HFRs have been uti- wind) can belized a function to derive of wind-driven time, one method surface to investigatecurrents in correlations many studies is to and find to the illustrate the connec- average angulartion between displacement coastal between currents two and vectors. wind. The Coasta averagel currents deviation respond between rapidly a to wind effects, pair of two-dimensional time series can be obtained from the phase angle of the complex with currents changing speed or reversing in response to changing wind patterns and correlation coefficient [21]. Thus, the correlation between the radar-derived surface current wind stresses [17–20]. Since the angle between two observed vectors (e.g., currents and

Remote Sens. 2021, 13, 3438 6 of 19

measurements, SGV, and overwater winds can be analyzed by the complex correlation of veering. In this case, the vectors are represented as complex variables such that

w(t) = u(t) + iv(t) (2)

where w is a complex representation of the velocity time series at time t. To estimate the mean veering by weights, the averaging process is in accordance with the magnitude of the instantaneous vectors and is given by

−1 < u1v2 − v1u2 > αav = tan 0 (3) < u1u2 − v1v2 >

where the phase angle of average veering is expressed as αav and the complex correlation coefﬁcient between two vector series is deﬁned as their normalized inner product as u1, v1 and u2, v2. The results using the complex correlation technique are presented in the next section.

3.3. Harmonic Analysis The tide is a phenomenon of periodic change in the sea water level, which heavily influences human activities at sea. Harmonic analysis is a time series analysis technique that can be applied to separate tidal components from other fluctuations at each observation grid location. Tidal patterns have been revealed using HFR observations [4,22,23]. Harmonic analysis is the process of calculating the amplitude and phase of the fundamental and higher-order harmonics of a periodic waveform and is sensitive to systematic signal changes [24]. The harmonic analysis in this study employed the T_Tide toolbox [25] to investigate and quantify tidally driven currents and thus explore coastal hydrodynamics. The procedure is dedicated to analysis phenomena of a periodically recurrent issue by the technique of breaking complicated mathematical curves into sums of comparatively simple components [26]. The technique was applied to locations on the HFR grid with more (75%) data coverage availability during the study period (Figure1). There are 45 astronomical and 101 shallow-water constituents that can be chosen from a list, with all constituents arranged in a predefined order. The program ranks the tidal constituents based on their equilibrium amplitude. Least-squares fitting can be used to determine the relative phase and amplitude of each frequency in the response [25]. The T_Tide toolbox can be corrected for the nodal modulation for each constituent k, which is converted into standard parameters to describe the tidal ellipse as follows: Lk = |ak| + |a−k| (4)

lk = |ak| + |a−k| (5) ang(a ) + ang(a ) θ = k −k mod180 (6) k 2

gk = vk − ang(ak) + θk (7)

where ak and a−k are a pair of complex values and Lk and lk are the lengths of the semimajor and semiminor axes of the ellipse, respectively. In addition, the inclination of the counterclockwise northern semimajor axis depends on east θk and Greenwich phase gk. These elliptical parameters are sufficient to further analyze the tidal elliptical properties of the specific field. The results using the T_Tide toolbox are presented in the next section.

4. Experimental Results 4.1. The Flow of Ocean Currents and Circulation In this section, this study analyzes the seasonal variability of surface circulation from HFR-derived current observations. One year is divided into four seasons (spring from March to May; summer from June to August; autumn from September to November; win- Remote Sens. 2021, 13, 3438 ter from December to February). Figure 3 shows the variability in seasonal currents7 of 19 in the study area. The waters around Taiwan are heavily influenced by the monsoon. The large- scale wind direction and speed for the four seasons are shown in Figure 4. In winter, the from December to February). Figure3 shows the variability in seasonal currents in the northeast monsoon has strong wind speeds starting in mid-September and reaching their study area. The waters around Taiwan are heavily influenced by the monsoon. The large- maximumscale wind from direction October and to speed January, for the after four whic seasonsh they are shown decrease. in Figure In 4summer,. In winter, the the southwest monsoonnortheast starts monsoon at the hasend strong of May, wind prevails speeds starting from June in mid-September to July and andends reaching in early their September. In summary,maximum the from strong October northeast to January, wind, after which whic theyh opposes decrease. the In summer,mean current, the southwest contributes to a reductionmonsoon in starts the surface at the end currents of May, prevailsmeasured from by June the to HFRs July and inends winter. in early In summer, September. the south- In summary, the strong northeast wind, which opposes the mean current, contributes westerlyto a reductionwind blows in the in surface the same currents direction measured as the by theKuroshio HFRs in Current winter. In and summer, thus increases the the velocitysouthwesterly of the Kuroshio wind blows surface in the samecurrents. direction Th ase thechange Kuroshio in the Current monsoon and thus drives increases the changes in surfacethe velocity currents. of the Under Kuroshio the surfaceinfluence currents. of complex The change ocean in thecurrent monsoon systems, drives the the monsoon and evenchanges topography, in surface currents. the mean Under current the influence values offor complex spring ocean and autumn current systems, are 46 theand 43 cm/s, monsoon and even topography, the mean current values for spring and autumn are 46 respectively.and 43 cm/s, Winter respectively. is the month Winter iswith the monththe lowe withst the average lowest averageflow rate flow of rate all of seasons all at 42 cm/s.seasons The average at 42 cm/s. flow The rate average in summer flow rate inis summer68 cm/s, is 68with cm/s, a maximum with a maximum velocity velocity of 162 cm/s (as shownof 162 cm/sin Figure (as shown 5). in Figure5).

(a) (b)

25°N 25°N

40′ 40′

20′ 20′

24°N 24°N

40′ 40′ Spring Summer 122°E 30′ 123°E 30′ 124°E 122°E 30′ 123°E 30′ 124°E (c) (d)

25°N 25°N

40′ 40′

20′ 20′

24°N 24°N

40′ 40′ Autumn Winter 122°E 30′ 123°E 30′ 124°E 122°E 30′ 123°E 30′ 124°E

Figure 3. Seasonal current velocities (vectors) in the region off of northeastern Taiwan. The green point in the north is the Figure 3. SeasonalSUAO station, current and thevelocities southern (v pointectors) is the in HABN the region station; off the of ﬂow northeastern direction is indicatedTaiwan. by The the green arrow vectors,point in and the the north is the SUAO station,contour and plots the of southern velocities are point for the is ﬂowthe HABN rates. (a) station; Spring, ( bthe) Summer, flow direction (c) Autumn, is andindicated (d) Winter by. the arrow vectors, and the contour plots of velocities are for the flow rates. (a) Spring, (b) Summer, (c) Autumn, and (d) Winter.

Remote Sens. 2021, 13, x FOR PEER REVIEW 8 of 19

RemoteRemote Sens. Sens.2021 2021, 13, ,13 3438, x FOR PEER REVIEW 8 of8 of 19 19

(a) (b)

25°(a)N 25°N (b)

25°N 25°N 30′ 30′

2430′°N 2430′°N

° 24°N 24 N 30′ 30′

Spring Summer 30′ 30′ 122°E 30′ 123°E 30′ 30′ 30′ 122°E 30′ 123°E 30′ Spring(c) Summer(d) 30′ 122°E 30′ 123°E 30′ 30′ 122°E 30′ 123°E 30′ (c) (d) 25°N 25°N

25°N 25°N30′ 30′

30′ 30′24°N 24°N

24°N 24°N30′ 30′

Autumn Winter 30′ 30′ 122°E 30′ 123°E 30′ 30′ 30′ 122°E 30′ 123°E 30′

Autumn Winter Figure 4. Wind fields30′ for122 °theE four30′ seasons123° Eoff eastern30′ Taiwan. The30′ wind 122direction°E 30′ reverses123 °betweenE 30′ winter and summer, whereas the wind is basically from the northeast in winter and autumn. (a) Spring, (b) Summer, (c) Autumn, and (d) Winter. FigureFigure 4. 4.Wind Wind ﬁelds fields for for the the four four seasons seasons off off eastern eastern Taiwan. Taiwan. The Th winde wind direction direction reverses reverses between between winter winter and and summer, summer, whereaswhereas the the wind wind is basically is basically from from the northeastthe northeast in winter in winter and autumn. and autumn. (a) Spring, (a) Spring, (b) Summer, (b) Summer, (c) Autumn, (c) Autumn, and (d) Winter and (.d) Winter. 160

140 160 120 140 100 120 80 100

Speed (cm/s) 60 80 40

Speed (cm/s) 60 20 40 0 20 Spring Summer Autumn Winter 0 Figure 5. Box plots of the sea-surface currents for the four seasons. A ﬁve-value summary is shown Figure 5. Box plots of the sea-surface currents for the four seasons. A five-value summary is shown for each dataset,Spring including Summer the minimum, Autumn ﬁrst (lower)Winter quartile, median (red line), third (upper) for each dataset, including the minimum, first (lower) quartile, median (red line), third (upper) quartile, and maximum. quartile, and maximum. Figure 5. Box plots of the sea-surface currents for the four seasons. A five-value summary is shown for Theeach EKEdataset, values including in the the four minimum, seasons first are shown(lower) inquartile, Figure median6. High (red variability line), third can (upper be ) seenquartile, in all and seasons maximum. in the region of the Kuroshio at approximately 122◦300 E and 24◦200 N.

Remote Sens. 2021, 13, x FOR PEER REVIEW 9 of 19

Remote Sens. 2021, 13, 3438 9 of 19 The EKE values in the four seasons are shown in Figure 6. High variability can be seen in all seasons in the region of the Kuroshio at approximately 122°30′ E and 24°20′ N. There is also a meandering and higher energetic area in the northeastern region. One pos- sibleThere reason is also can a meanderingbe attributed andto the higher Kuroshio energetic flow areabeing in fastest the northeastern in this area. region.The highest One EKEpossible values reason (orange can region), be attributed extending to the from Kuroshio the middle ﬂow being to the fastest southeast, in this occur area. in The the highest summer.EKE It values should (orange be noted region), that the extending amplitude from of the the averaged middle toEKE the is southeast,consistently occur smaller in thein thesummer. autumn It shouldand winter be noted months that thethan amplitude in the other of the months. averaged This EKE result is consistently is consistent smaller with Scharffenbergin the autumn and and Stammer winter months [27], who than found in the that other the months.maximum This EKE result level is in consistent the Kuroshio with extensionScharffenberg occurs and in Stammersummer, [while27], who the EKE found re thataches the its maximum minimum EKE there level in winter. in the KuroshioObvious mesoscaleextension occursevents inassociated summer, with while eddies the EKE at approximately reaches its minimum 123° E thereto 124° in E winter. and 23° Obvious N 40′ mesoscale events associated with eddies at approximately 123◦ E to 124◦ E and 23◦ N 400 to 24°◦ N 20′ 0occurred from autumn to winter. The main reason is that the strong Kuroshio flowingto 24 N from 20 occurred south to fromnorth autumn is suppressed to winter. by Thethe mainnortheasterly reason is wind, that the and strong the current Kuroshio is impededﬂowing fromby the south Japanese to north islands is suppressed of Yonaguni by the and northeasterly Iriomote, producing wind, and a theclockwise current mesoscaleis impeded eddy. by theThe Japanesespatial resolution islands ofof YonaguniHFRs not only and provides Iriomote, averaged producing current a clockwise values butmesoscale also reveals eddy. the The fast-evolving spatial resolution mesoscale of HFRs eddy not events only providesaround Taiwan. averaged current values but also reveals the fast-evolving mesoscale eddy events around Taiwan.

(a) (b)

25°N 25°N

40′ 40′

20′ 20′

24°N 24°N

40′ 40′ Spring Summer 20′ 20′ 30′ 122°E 30′ 123°E 30′ 124°E 30′ 122°E 30′ 123°E 30′ 124°E (c) (d)

25°N 25°N

40′ 40′

20′ 20′

24°N 24°N

40′ 40′ Autumn Winter 20′ 20′ 30′ 122°E 30′ 123°E 30′ 124°E 30′ 122°E 30′ 123°E 30′ 124°E

Figure 6. Seasonal current velocities (vectors) in the region off of northeastern Taiwan with the EKE (background color). Figure(a) Spring, 6. Seasonal (b) Summer, current (c) velocities Autumn, (vectors) and (d) Winter in the. region off of northeastern Taiwan with the EKE (background color). (a) Spring, (b) Summer, (c) Autumn, and (d) Winter. 4.2. Comparison of Various Spatial Data 4.2. ComparisonTo observe of the Various relationships Spatial Data among the three different variables investigated here, this studyTo calculated observe the complex relationships correlations among between the thr pairsee different of vector variables time series. investigated Figure7 shows here, thisthe study annual calculated SGV, HFR, complex and wind correlations vectors in between 2013, with pairs the of two vector grid time regions series. selected Figure for 7 showsvector the correlations annual SGV, indicated HFR, and in Figure wind7 vectorsa. The red in 2013, arrow with is the the SGV two ﬂowing grid regions from southselected to fornorth; vector the correlations black vector indicated is the HFR in measurement panel (a). The value red arrow of the sea-surfaceis the SGV flowing current. from The orangesouth cells are designated region of interest (ROI) 1, and the blue cells are designated ROI 2. The Kuroshio current velocity and wind speed are both relatively strong in these two areas, which is why they were selected. The wind ﬁeld is approximately northeasterly throughout,

Remote Sens. 2021, 13, x FOR PEER REVIEW 10 of 19

to north; the black vector is the HFR measurement value of the sea-surface current. The orange cells are designated region of interest (ROI) 1, and the blue cells are designated ROI 2. The Kuroshio current velocity and wind speed are both relatively strong in these two areas, which is why they were selected. The wind field is approximately northeasterly throughout, as shown in panel (b) of Figure 7. It is obvious that the orientation of the SGV is approximately the same as that of the current field derived by HFR, but the only difference is that HFR data include the influence of wind-driven forcing. The spatially averaged time series over the two ROIs are shown in Figure 8. The horizontal axis is time, the left vertical axis is velocity (cm/s) for the SGV and radar data, and the right vertical axis is the wind velocity (m/s). Figure 8a,b shows u component results; Figure 8c,d shows v component results. The blue line is HFR data, the red line is SGV data, and the green line is wind data. It is obvious that the component speed of the SGV (green line) behaves like a low- pass filter for the time series in Figure 8a,c due to the geostrophic effect taking place over Remote Sens. 2021, 13, 3438 a longer time scale. By comparison, the time series of the wind (red line) and HFR10 of data 19 (blue line) show high-frequency variations over shorter time scales, suggesting that wind plays an important role in directly forcing surface currents in this region. To investigate this hypothesis, this study produced a residual time series from the difference between as shown in Figure7b. It is obvious that the orientation of the SGV is approximately the the HFR and SGV data for surface currents. The u and v components of the wind exhibit same as that of the current field derived by HFR, but the only difference is that HFR data good visual agreement with the residuals, as shown in Figure 8b,d, except for some time include the influence of wind-driven forcing. The spatially averaged time series over the periods in June with missing radar data. two ROIs are shown in Figure8. The horizontal axis is time, the left vertical axis is velocity (cm/s)The for results the SGV of andthe complex radar data, correlation and the rightof the vertical mean wind axis istime the series wind against velocity the (m/s). mean FigureHFR,8 a,bSGV, shows and residualu component time series results; are Figure shown8c,d in shows Table v3 componentby season for results. both TheROI blue1 and lineROI is 2 HFR (see data,Figure the 7). red The line correlation is SGV data, between and thethe greenresidual line current is wind and data. the Itwind is obvious vector is thathigher the componentthan the SGV speed correlation of the SGV due (green to the line) geostrophic behaves likecomponents a low-pass being filter removed for the time from seriesthe time in Figure series.8a,c Relative due to to the the geostrophic correlation effect in spring taking in placeROI 1over and aROI longer 2, the time radar-to-wind scale. By comparison,correlations the are timehigher series in the of theother wind three (red seas line)ons anddue HFRto stronger data (blue winds. line) In showaddition, high- the frequencyaverage correlation variations over between shorter the time HFR scales, and wind suggesting in ROI that 1 is windlarger plays than anthat important in ROI 2, role with inmean directly correlations forcing surface of 0.57 currents and 0.49 in thisand region.standard To investigatedeviations this(STDs) hypothesis, of 0.11 and this 0.04 study be- producedtween the a residualradar and time wind, series respectively. from the difference The reason between for ρ1 being the HFR higher and than SGV ρ data2 is likely for surfacebecause currents. the islands The uaboveand v ROIcomponents 2 block northe of theasterly wind exhibit winds. good Short visual time-scale agreement wind with com- theponents residuals, produce as shown fast inand Figure variable8b,d, movements except for some in the time oceans, periods while in Junegeostationary with missing fields radarproduce data. low-frequency phenomena on larger scales.

(a) (b)

25°N 25°N

30′ 30′

24°N 24°N

30′ 30′

30′ 122°E 30′ 123°E 30′ 30′ 122°E 30′ 123°E 30′

Figure 7. Mean SGV, HFR, and wind vectors from 1 January 2013 to 31 December 2013. (a) The red arrows are the SGV ﬂowingFigure from 7. Mean south SGV, to north;HFR, and the blackwind vectorsvectors arefrom HFR 1 January measurements 2013 to 31 of December the sea-surface 2013. current.(a) The red The arrows two grid are regions the SGV flowing from south to north; the black vectors are HFR measurements of the sea-surface current. The two grid regions where complex correlations are computed for box-averaged currents are also shown with the orange cell designated ROI 1 where complex correlations are computed for box-averaged currents are also shown with the orange cell designated ROI and the blue cell designated ROI 2. (b) Mean wind velocities, which are from the northeast. 1 and the blue cell designated ROI 2. (b) Mean wind velocities, which are from the northeast. The results of the complex correlation of the mean wind time series against the mean HFR, SGV, and residual time series are shown in Table3 by season for both ROI 1 and

ROI 2 (see Figure7). The correlation between the residual current and the wind vector is higher than the SGV correlation due to the geostrophic components being removed from the time series. Relative to the correlation in spring in ROI 1 and ROI 2, the radar-to-wind correlations are higher in the other three seasons due to stronger winds. In addition, the average correlation between the HFR and wind in ROI 1 is larger than that in ROI 2, with mean correlations of 0.57 and 0.49 and standard deviations (STDs) of 0.11 and 0.04 between the radar and wind, respectively. The reason for ρ1 being higher than ρ2 is likely because the islands above ROI 2 block northeasterly winds. Short time-scale wind components produce fast and variable movements in the oceans, while geostationary ﬁelds produce low-frequency phenomena on larger scales. RemoteRemote Sens. Sens. 20212021, 13, ,x13 FOR, 3438 PEER REVIEW 11 of11 19 of 19

(a) 100 10 -1 Uradar (cm/s )

50 0 -1 Usvg (cm/s ) 0 -1 -10 (m/s) Uwind (cm/s ) (cm/s) -50 -20 (b) 100 10 -1 Uradar − Usvg (cm/s ) 50 0 -1 Uwind (cm/s ) 0 -10 (m/s) (cm/s)

-50 -20 (c)

200 20 -1 Vradar (cm/s ) 10 100 -1 Vsvg (cm/s ) 0 -1 0 (m/s) Vwind (cm/s ) (cm/s) -10

-100 -20 (d) 200 20 -1 Vradar − Vsvg (cm/s ) 10 100 V (cm/s-1) 0 wind

0 (m/s)

(cm/s) -10

-100 -20 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2013

Figure 8. Spatially averaged u and v components of the daily wind, SGV and HFR velocity time series related to box 1 (a,b) Figure 8. Spatially averaged u and v components of the daily wind, SGV and HFR velocity time series related to box 1 and box 2 (c,d). (a,b) and box 2 (c,d). Table 3. Complex correlation coefﬁcients and veering angles of the HFR, SGV, and residual data with the wind in Tablefour 3. seasons.Complex correlation coefficients and veering angles of the HFR, SGV, and residual data with the wind in four seasons. Geostrophic to Wind Radar to Wind Residual to Wind 2013 Geostrophic to Wind Radar to Wind Residual to Wind ρ1 ρ2 θ1 θ2 ρ1 ρ2 θ1 θ2 ρ1 ρ2 θ1 θ2 2013 Spring 0.35 0.34 −111.76 −128.99 0.42 0.44 −151.33 −87.26 0.46 0.48 110.46 −12.35 ρ1 ρ2 θ1 θ2 ρ1 ρ2 θ1 θ2 ρ1 ρ2 θ1 θ2 Summer 0.40 0.37 −47.57 −45.76 0.50 0.50 −81.79 −45.46 0.51 0.48 −178.66 −60.90 SpringAutumn 0.35 0.32 0.34 0.37 −111.76−163.51 −128.99−140.08 0.42 0.67 0.44 0.45 −151.33 177.87 −87.26−132.29 0.460.46 0.480.40 110.46 72.99 −12.35−100.76 Winter 0.40 0.39 −130.21 −110.70 0.69 0.55 −138.33 −105.91 0.48 0.50 112.58 −99.79 SummerMean 0.40 0.37 0.37 0.37 −47.57−113.26 −45.76−106.38 0.50 0.57 0.50 0.49 −81.79−48.40 −45.46−92.73 0.510.48 0.480.47 −178.66 29.34 −60.90−68.45 STD 0.03 0.02 42.22 36.54 0.11 0.04 133.22 31.63 0.02 0.04 121.12 31.16 Autumn 0.32 0.37 −163.51 −140.08 0.67 0.45 177.87 −132.29 0.46 0.40 72.99 −100.76

Winter 0.40 0.39 −130.214.3. Tidal−110.70 Flow 0.69 0.55 −138.33 −105.91 0.48 0.50 112.58 −99.79 4.3.1. Validation of Tidal Constituents Mean 0.37 0.37 −113.26 −106.38 0.57 0.49 −48.40 −92.73 0.48 0.47 29.34 −68.45 In terms of tidal analysis, the tidal variation from the shallow water to the continental STD 0.03 0.02 42.22shelf is36.54 nonlinear, 0.11 whereas 0.04 in the deep133.22 ocean, 31.63 it is less 0.02complex and0.04 can be121.12 analyzed 31.16 by using the dominant linear dynamics of astronomical tides [28]. Off of the eastern coast of Taiwan, the continental shelf is narrow, and the water reaches a depth of 1000 m within 1–2 km 4.3. Tidal Flow of shore. Hence, the tidal interactions can be conveniently expressed as simple harmonic 4.3.1.components Validation withof Tidal differences Constituents in phase and angular speed being multiples of astronomical constituentsIn terms of tidal of M analysis,2 and S2. the Tidal tidal ellipses variation are the from best the way shallow to represent water to tide-driven the continental changes shelfin is currents, nonlinear, thereby whereas describing in the deep the relationship ocean, it is between less complex the u and vcancomponents be analyzed [29 ].by This usingsection the dominant focuses onlinear validating dynami thecs of HFR-derived astronomical surface tides [28]. current Off componentsof the eastern against coast of those Taiwan,observed the continental by coastal tide-gaugeshelf is narrow, stations. and Harmonic the water analysis reaches ofa depth sea-surface of 1000 currents m within is used 1–2 tokm extract of shore. tidal Hence, components the tidal at interactio the differentns can locations be conveniently around the expressed HFR grid. as Thissimple study harmonicquantiﬁes components the major with tidal componentsdifferences in and phase analyzes and theangular tidal drivingspeed being currents multiples over the of four astronomicalseasons in constituents the region off of ofM northeastern2 and S2. Tidal Taiwan. ellipses are the best way to represent tide- driven changesThe largest in currents, semidiurnal thereby and describing diurnal tidal the ﬂuctuationsrelationship acrossbetween the the region u and observed v com- by ponentsthe HFRs [29]. This are shown section in focuses Figure 9on as valida tidal ellipsesting the resultingHFR-derived from surface harmonic current analyses. compo- These ◦ ◦ 0 ◦ 0 ◦ nentsellipses against are those largest observed at approximately by coastal tide-gauge 122 E to stations. 122 30 E Harmonic and 24 40 analysisN to 25 of sea-sur-N, which is facelocated currents east is used of the to Suao extract station. tidal compon The orientationsents at the of different the major locations axes tend around to be alignedthe HFR with grid.the This topography study quantifies on both the sides major of tidal the ridge components axis, particularly and analyzes for thethe dominanttidal driving M2 cur-and K1 rentsconstituents. over the four Harmonic seasons in analyses the region of coastal off of surfacenortheastern currents Taiwan. close to the diurnal period can

Remote Sens. 2021, 13, x FOR PEER REVIEW 12 of 19

The largest semidiurnal and diurnal tidal fluctuations across the region observed by the HFRs are shown in Figure 9 as tidal ellipses resulting from harmonic analyses. These ellipses are largest at approximately 122° E to 122°30′ E and 24°40′ N to 25° N, which is Remote Sens. 2021, 13, 3438 located east of the Suao station. The orientations of the major axes tend to be aligned12 with of 19 the topography on both sides of the ridge axis, particularly for the dominant M2 and K1 constituents. Harmonic analyses of coastal surface currents close to the diurnal period can be dominated by diurnal wind forcing [4]. Here, however, the K1 ellipse alignment argues be dominated by diurnal wind forcing [4]. Here, however, the K1 ellipse alignment argues againstagainst diurnal diurnal (sea (sea breeze) breeze) wind wind forcing, forcing, at at least least over over the the deep deep ocean ocean ridge ridge area. area. In In terms terms of rotation, the patterns corresponding to the semidiurnal M2 and diurnal K1 ellipses are of rotation, the patterns corresponding to the semidiurnal M2 and diurnal K1 ellipses are dominateddominated by by clockwise and anti-clockwiseanti-clockwise tides,tides, respectively. respectively. In In contrast, contrast, the the distribution distribution of the weaker semidiurnal S2 and diurnal O1 ellipses are observed to obtain their larg- of the weaker semidiurnal S2 and diurnal O1 ellipses are observed to obtain their largest est values in small patches (Figure 9c,d). Overall, the M2 tide is observed to have the high- values in small patches (Figure9c,d). Overall, the M 2 tide is observed to have the highest est amplitudes, and the tidal ellipses rotate in the opposite direction to K1 in the northern amplitudes, and the tidal ellipses rotate in the opposite direction to K1 in the northern and andcentral central portions portions of the of region.the region.

(a) (b)

25°N 25°N

40′ 40′

20′ 20′

24°N 24°N

40′ M240′ K1 30′ 122°E 30′ 123°E 30′ 30′ 122°E 30′ 123°E 30′ (c) (d)

25°N 25°N

40′ 40′

20′ 20′

24°N 24°N

40′ S240′ O1 30′ 122°E 30′ 123°E 30′ 30′ 122°E 30′ 123°E 30′

Figure 9. (a)M2,(b)K1,(c)S2, and (d)O1 tidal ellipses derived from harmonic analysis of the HFR current data. The red Figure 9. (a) M2, (b) K1, (c) S2, and (d) O1 tidal ellipses derived from harmonic analysis of the HFR (blue) ellipses indicate clockwisecurrent (anti-clockwise) data. The red (blue) rotation. ellipses The greenindicate ellipses clockwise indicate (anti-clockwise) tide speeds of rotation. less than The 5 cm/s. green The ellipses thick black line is the −800indicate m isobath. tide speeds of less than 5 cm/s. The thick black line is the −800 m isobath. The lunar synodic fortnightly (MSf) tides, with periods of 14.76 days, are typically the large tidal components at the 14-day period [30]. MSf are often contaminated with atmospheric forcing, which results in highly variable amplitudes and phases when comparing yearlong records from the same tidal station [30,31]. Schureman (1958) [32] provided the length of record (hour) with the frequency difference between neighboring constituents. Thus, the length of time needed to distinguish MSf constituents is 355 h. This study divided the data length of a year into four seasons (one season is equivalent to 3 months), so the data length is approximately 2160 h in one season, which is sufﬁcient to distinguish MSf by Remote Sens. 2021, 13, x FOR PEER REVIEW 13 of 19

The lunar synodic fortnightly (MSf) tides, with periods of 14.76 days, are typically the large tidal components at the 14-day period [30]. MSf are often contaminated with atmospheric forcing, which results in highly variable amplitudes and phases when comparing yearlong records from the same tidal station [30,31]. Schureman (1958) [32] provided the length of record (hour) with the frequency difference between neighboring con- Remote Sens. 2021, 13, 3438 stituents. Thus, the length of time needed to distinguish MSf constituents is 355 h.13 This of 19 study divided the data length of a year into four seasons (one season is equivalent to 3 months), so the data length is approximately 2160 h in one season, which is sufficient to distinguishseason. Seasonal MSf by tidal season. current Seasonal ellipses tidal for curre MSfnt are ellipses shown for in FigureMSf are 10 shown. It is worth in Figure noting 10. Itthat is worth the ellipse noting of that the summerthe ellipse MSf of the constituent summer (FigureMSf constituent 10b) at approximately (Figure 10b) at 122approxi-◦ E to mately122◦30 0122°E and E 24to ◦122°30400 N′ to E 25and◦ N 24°40 is signiﬁcantly′ N to 25° N larger is significantly than that inlarger any otherthan that location in any or otherseason, location and all or rotate season, counterclockwise. and all rotate counterclockwise. This may be related This may to the be three related land-proximal to the three land-proximaltyphoons (Figure typhoons 11) that (Figure passed 11) near that this passed study areanear during this study the summerarea during season: the SOULIK,summer season:KONG-REY, SOULIK, and TRAMI.KONG-REY, These and observations TRAMI. Thes showe thatobservations these strong show atmospheric that these systems strong atmosphericmay have had systems an outsized may have inﬂuence had an on ou thesetsized ellipses. influence on these ellipses.

(a) (b)

25°N 25°N

40′ 40′

20′ 20′

24°N 24°N

40′ 40′ Spring Summer 30′ 122°E 30′ 123°E 30′ 30′ 122°E 30′ 123°E 30′ (c) (d)

25°N 25°N

40′ 40′

20′ 20′

24°N 24°N

40′ 40′ Autumn Winter 30′ 122°E 30′ 123°E 30′ 30′ 122°E 30′ 123°E 30′

Figure 10. Current tidal ellipses for harmonic constituent MSf. (a) Spring, (b) Summer, (c) Autumn, and (d) Winter Figure 10. Current tidal ellipses for harmonic constituent MSf. (a) Spring, (b) Summer, (c) .Au- tumn, and (d) Winter.

Remote Sens. 2021, 13, x FOR PEER REVIEW 14 of 19 Remote Sens. 2021, 13, 3438 14 of 19

2828°N°N

13-Jul-2013 12:00:00 2626°N°N 29-Aug-2013 06:00:00

21-Aug-2013 03:00:00

2424°N°N SOULIK

11-Jul-2013 21:00:00 Latitude Latitude 2222°N°N KONG-REY

2020°N°N 27-Aug-2013 12:00:00

19-Aug-2013

200 km TRAMI 50 mi Esri, HERE 1818°N°N 118118°E°E 120 120°E°E 122 122°E°E 124 124°E°E 126 126°E°E 128 128°E°E 130 130°E°E Longitude Longitude

Figure 11. Three typhoonsFigure passed 11. Three to the typhoons east and passed north to of the the east study and area north during of the the study summer area period.during the summer period.

4.3.2.4.3.2. Tide Tide Type Type Classification Classification TidalTidal forces forces can can be convertedbe converted into into tidal tidal potentials, potentials, and and their their effects effects can can bemeasured be measured throughthrough sea sea level level fluctuations fluctuations and and equilibrium equilibriu tidem tide theory. theory. Most Most equilibrium equilibrium amplitudes amplitudes areare small, small, but but there there are are 11 major11 major tidal tidal constituents, constituents, and and of these, of these, tidal tidal analysis analysis has has shown shown that the four main tide constituents are M (principal lunar semidiurnal), S (principal that the four main tide constituents are M2 2 (principal lunar semidiurnal), S22 (principal so- solar semidiurnal), K (principal lunar diurnal), and O (main lunar diurnal constituent). lar semidiurnal), 1K1 (principal lunar diurnal), and1 O1 (main lunar diurnal constituent). ThroughThrough these these four four constituents, constituents, it is possibleit is possible to explain to explain in general in general terms terms the characteristics the characteris- of sea level variations, such as diurnal tides, semidiurnal tides, diurnal inequalities, spring tics of sea level variations, such as diurnal tides, semidiurnal tides, diurnal inequalities, tides and neap tides [33]. In the study region, there are five tide-gauge stations along spring tides and neap tides [33]. In the study region, there are five tide-gauge stations the coast of Taiwan that measure the presence of the 15 constituents with the greatest along the coast of Taiwan that measure the presence of the 15 constituents with the great- amplitude. Those amplitudes are displayed in Figure 12 for each of the five tide-gauge est amplitude. Those amplitudes are displayed in Figure 12 for each of the five tide-gauge locations. As expected, semidiurnal M2 and S2 and diurnal K1 and O1 exhibit the largest locations. As expected, semidiurnal M2 and S2 and diurnal K1 and O1 exhibit the largest amplitudes. LD and HL are the northernmost and southernmost tide-gauge stations in the amplitudes. LD and HL are the northernmost and southernmost tide-gauge stations in the study area. The amplitudes of semidiurnal M2 and S2 in the northern part were smaller study area. The amplitudes of semidiurnal M2 and S2 in the northern part were smaller than those in the southern part. This result means that the semidiurnal tides are more than those in the southern part. This result means that the semidiurnal tides are more pronounced in the south. The K1 amplitude was greater at the northern station than at the pronounced in the south. The K1 amplitude was greater at the northern station than at the two southern stations. twoTo revealsouthern the stations. tidal characteristics and type of tide in the study area, harmonic analysis of the spatially averaged HFR currents over the entire domain was conducted for the same 15 tidal constituents (Figure 13). The high amplitudes of the long-period SSA and MF tidal constituents in the figure are almost certainly due to meteorological rather than astronomical forcing [31]. The semidiurnal (M2 and S2) and diurnal (K1 and O1) constituents, as observed from HFR currents, were compared against results from the tide-gauge observations. In previous studies, the 2D tidal current model was used to analyze the tidal characteristics of the northern Taiwan coast, and the proportion of the elliptical tidal axis was used to determine the form of the tide [34,35].

Remote Sens. 2021, 13, x FOR PEER REVIEW 15 of 19 Remote Sens. 2021, 13, 3438 15 of 19

50 Longdong 45 Wushi Suao Hoping 40 Hualien

20 SeaLevel (cm)

2 2 A 2 2 4 1 2 M K1 S O1 N2 P1 K2 Q1 U MF M L Remote Sens. 2021, 13, x FOR PEER REVIEW SS NU M NO 16 of 19

Figure 12. AmplitudesAmplitudes of of sea sea level level height height (in (in cm) cm) based based on on instrument instrument reference reference level level (RL) (RL) for for 15 15constituents constituents from from five ﬁve tide-gauge tide-gauge stations stations from from no northrth to tosouth south in insequence. sequence.

50 To reveal the tidal characteristics and type of tide in the study area, harmonic analysis 45 of the spatially averaged HFR currents over the entire domain was conducted for the same 15 tidal constituents (Figure 13). The high amplitudes of the long-period SSA and MF tidal 40 constituents in the figure are almost certainly due to meteorological rather than astronom- 35 ical forcing [31]. The semidiurnal (M2 and S2) and diurnal (K1 and O1) constituents, as ob-

30 served from HFR currents, were compared against results from the tide-gauge observations. In previous studies, the 2D tidal current model was used to analyze the tidal char- 25 acteristics of the northern Taiwan coast, and the proportion of the elliptical tidal axis was 20 used to determine the form of the tide [34,35].

Mean amplitude (cm/s) Tidal characteristics are classified according to the form ratios given in Table 4. The 15 types of classifications based on the form ratio are taken from Courtier [36]. The form ratio 10 represents the ratio of the sum of the amplitudes of the major diurnal components (K1 and 1 2 2 5 O ) to the sum of the amplitudes of the major semidiurnal components (M and S ), as defined by [37] 0 2 1 2 1 A 2 1 2 1 𝐾 +𝑂 4 2 M K S O N P K Q U2 MF M L SS NU2𝑖= M NO1 (8) 𝑀 +𝑆 FigureFigure 13. 13. TheThe mean currentwhere ellipseellipse majorimajor is the axis axis form magnitude magnitude ratio, also (in (in cm/s) known cm/s) for for as 15 15 the constituents constituents tidal characteristics from from the the HFR HFR overof theover the criteria entirethe entire domain. index. domain. Tidal characteristics are classified according to the form ratios given in Table4. The The form ratios are given for each of the tide-gauge locations (first four columns) and Tabletypes 4. of Classification classifications types based of tidal on thecharacteristics. form ratio are taken from Courtier [36]. The form ratio the HFR surface current observations (last column) in Table 5. According to the form ratio, represents the ratio of the sum of the amplitudes of the major diurnal components (K and the tide in Taiwan is a mixed, mainly semidiurnal tide, and the results show that the1 tide- O1) to theForm sum Ratio of the amplitudes of the major semidiurnal Type components (M2 and S2), as gauge station and HFR observations yield the same result, which is consistent with Dai et defined by [37] al. (2018)0.00–0.25 [38]. Most of the ocean tides are mixed,Semidiurnal with predominan tide tly semidiurnal tides K1 + O1 in the northwestern Pacific Ocean andi =East China Sea, east of Taiwan. Moreover, these(8) M2 + S2 results confirm0.25–1.50 that HFR is a very good tool Mixed for tidalmainly observation. semidiurnal In tideaddition, the single where i is the form ratio, also known as the tidal characteristics of the criteria index. time series1.50–3.00 classification is shown in Figure 13 Mixed and Tablemainly 5. diurnal tide Table 4. Classification types of tidal characteristics. 3.00–∞ Diurnal tide Form Ratio Type Table 5. Results of the0.00–0.25 form ratio and tidal patterns from the tide-gauge Semidiurnal stations tide and HFR. 0.25–1.50 Mixed mainly semidiurnal tide 1.50–3.00LD WS SO MixedHP mainly diurnalHL tideCODAR 3.00–∞ Diurnal tide Form ratio 1.0690 0.67024 0.60599 0.46849 0.46057 0.91193

TidalThe types form ratios are given for each Mixed of themainly tide-gauge semidiurnal locations tide (ﬁrst four columns) and the HFR surface current observations (last column) in Table5. According to the form 5. Discussion and Conclusions The main focus of this paper was to investigate the current patterns, influence of wind forcing and spatial distributions of tide constituents off of northeastern Taiwan with coastal HFR systems. The results of the three subtopics are discussed below. This study analyzes the seasonal variability of surface circulation from HFR-derived current observations. The Kuroshio flows from south to north throughout the year. In winter, the strong northeast wind blows in the opposite direction, weakening the flow of the Kuroshio surface current; in summer, the southwesterly wind accelerates the speed of the Kuroshio surface current by blowing in the same direction as the Kuroshio current. Changes in the monsoon around Taiwan drive changes in surface ocean currents. EKE results are shown for the four seasons. A high degree of variability can be seen in all seasons in the Kuroshio area at approximately 122°30′ E and 24°20′ N. There is also a windy, high-energy area in the northeast portion of the measurement area. The highest EKE values (orange area) extend from the center to the southeast and occur in summer. It should be noted that the magnitude of the average EKE is always smaller in the autumn and

Remote Sens. 2021, 13, 3438 16 of 19

ratio, the tide in Taiwan is a mixed, mainly semidiurnal tide, and the results show that the tide-gauge station and HFR observations yield the same result, which is consistent with Dai et al. (2018) [38]. Most of the ocean tides are mixed, with predominantly semidiurnal tides in the northwestern Pacific Ocean and East China Sea, east of Taiwan. Moreover, these results confirm that HFR is a very good tool for tidal observation. In addition, the single time series classification is shown in Figure 13 and Table5.

Table 5. Results of the form ratio and tidal patterns from the tide-gauge stations and HFR.

LD WS SO HP HL CODAR Form ratio 1.0690 0.67024 0.60599 0.46849 0.46057 0.91193 Tidal types Mixed mainly semidiurnal tide

5. Discussion and Conclusions The main focus of this paper was to investigate the current patterns, influence of wind forcing and spatial distributions of tide constituents off of northeastern Taiwan with coastal HFR systems. The results of the three subtopics are discussed below. This study analyzes the seasonal variability of surface circulation from HFR-derived current observations. The Kuroshio flows from south to north throughout the year. In winter, the strong northeast wind blows in the opposite direction, weakening the flow of the Kuroshio surface current; in summer, the southwesterly wind accelerates the speed of the Kuroshio surface current by blowing in the same direction as the Kuroshio current. Changes in the monsoon around Taiwan drive changes in surface ocean currents. EKE results are shown for the four seasons. A high degree of variability can be seen in all seasons in the Kuroshio area at approximately 122◦300 E and 24◦200 N. There is also a windy, high-energy area in the northeast portion of the measurement area. The highest EKE values (orange area) extend from the center to the southeast and occur in summer. It should be noted that the magnitude of the average EKE is always smaller in the autumn and winter months. Regarding the observations of mesoscale events, it can also be noticed that in autumn and winter, there are obvious mesoscale eddy events in the vicinity of 123◦ E to 124◦ E and 23◦400 N to 24◦200 N. The main reason is that the strong Kuroshio current flowing from south to north is suppressed by the northeasterly wind, and the water hits Japan’s Yonaguni Island and Iriomote Island, producing a clockwise mesoscale vortex. Sea surface currents derived from the HFR data include both SGV and wind-driven components. The result of complex correlation analysis shows that the average correlation between radar and wind and residual and wind is higher than that between SGV and wind. In addition, the correlation ρ1 of ROI 1 is higher than ρ2 of ROI 2, which may be because the island above ROI 2 blocks the northeasterly wind. This reduces the impact of the wind on the ocean currents. Since the geostrophic effect occurs on a longer time scale, the component velocity of the SGV behaves like a low-pass filter on the time series. In contrast, the wind and HFR data show high-frequency changes on a shorter time scale, indicating that wind plays an important role in directly forcing surface water flow in the area. Overall, this approach is to attempt to remove the geostrophic constituent from the HFR observations by subtracting the satellite-derived current estimates to form the residual currents. A prior study [17] followed this same approach and found that the residual currents were much better correlated with the local wind forcing than either the satellite- or HFR-derived currents. In the case of this study, there is only slight improvement in the correlation with local wind forcing for the residual currents, which suggests that there is a more complex relationship between winds and geostrophic currents in this region and/or there is significant energy in mesoscale eddies that are not wind driven but are also not resolved by the satellite measurements. The spatial distributions of tidal ellipses in the study area were also revealed by the HFR observations. The results showed that the M2 tidal ellipses have the highest amplitudes, and the tidal ellipses rotate more than K1,S1, and O1 over the head of the I-Lan Remote Sens. 2021, 13, 3438 17 of 19

Ridge (122◦ E, 24◦400 N to 122◦300 E, 25◦ N), which is located off of the northeastern Suao station. The orientation of the major axis tends to be consistent with the topography on both sides of the ridge axis. It is worth noting that the ellipse pattern of the MSf constituent in summer is significantly larger and rotates counterclockwise at approximately 122◦300 E, 25◦ N. The literature records that tidal components with a period of approximately 14 days are often polluted by atmospheric forcing. The preliminary results of this study show that the three typhoons in the summer of 2013 may have forced the pattern of the MSf tidal ellipse in the summer to be different from those in the other three seasons. Moreover, according to the basic theory of tidal form ratio, the HFRs observed that the tides in Taiwan are mixed, mainly semidiurnal tides. This result is also consistent with the results from coastal tide-gauge stations. In summary, HFRs are very good remote sensing tools to observe the characteristic motion of surrounding seas. Analyzing the available data, with particular emphasis on the higher spatial and temporal resolution of the HFR observations, this study made use of HFR observations to confirm the seasonal characteristics of current patterns, the spatial distribution of the tidal components, and the occurrence of mesoscale recirculation in the region on annual time scales. Extended coverage through an expanded HFR network over longer time periods will reveal even more regional ocean dynamics. In future studies, circulation and vorticity analyses will be beneficial to reveal more mesoscale ocean flows in the study area.

Author Contributions: Writing—original draft, Y.-R.C.; writing—review and editing, Y.-R.C., M.S.C., J.D.P., L.Z.-H.C. and Y.-J.C.; conceptualization, Y.-R.C., M.S.C., J.D.P. and L.Z.-H.C.; data curation, Y.-R.C., M.S.C. and Y.-J.C.; formal analysis, Y.-R.C., M.S.C., J.D.P. and Y.-J.C.; funding acquisition, L.Z.-H.C.; investigation, Y.-R.C., J.D.P. and L.Z.-H.C.; methodology, Y.-R.C., M.S.C., J.D.P., L.Z.-H.C. and Y.-J.C.; resources, J.D.P., L.Z.-H.C. and Y.-J.C.; software, Y.-R.C., M.S.C. and Y.-J.C.; supervision, M.S.C., J.D.P., L.Z.-H.C. and Y.-J.C.; visualization, Y.-R.C., M.S.C., J.D.P., L.Z.-H.C. and Y.-J.C. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Ministry of Science and Technology under grants 109- 2221-E-006-101, 109-2623-E-006-002-D, 108-2611-M-012-002, Ministry of Science and Technology Overseas Project for Post Graduate Research under grants 108-2917-I-006-012, Ministry of Education PEE1090492 and Naval Postgraduate School contributions were supported by NOAA’s Integrated Ocean Observing System agreement MOU-2020-078/12015/NPS-21-400-2778. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available upon request from the corresponding author. The data are not publicly available due to security issues. Acknowledgments: We thank all the scientists and principal researchers who prepared and provided the research data. Thanks to Yung-Da Sun from the Naval Meteorological and Oceano-graphic (METOC) Office R.O.C, I-Fong Tsui from Chung Cheng Institute of Technology, Yiing-Jang Yang from NTU, Chi-Min Chiu, Li-Chung Wu from Coastal Ocean Monitoring Center (COMC), Jian-Wu Lai from Ocean Affairs Council (OAC) and António Carlos Gonçalves Tavares from the Hydrographic Institute in portugal for discussion and technique support. We would also like to thank the Cen- tral Weather Bureau (CWB), Ministry of Transportation and Communications who provided tide gauge data to our research. Last but not least, we also thank the anonymous reviewers for their constructive observations. Conflicts of Interest: The authors declare no conflict of interest.

References 1. Yang, Y.; Liu, C.-T.; Hu, J.-H.; Koga, M. Taiwan Current (Kuroshio) and impinging eddies. J. Oceanogr. 1999, 55, 609–617. [CrossRef] 2. Liang, W.-D.; Tang, T.; Yang, Y.; Ko, M.; Chuang, W.-S. Upper-ocean currents around Taiwan. Deep Sea Res. Part II Top. Stud. Oceanogr. 2003, 50, 1085–1105. [CrossRef] Remote Sens. 2021, 13, 3438 18 of 19

3. Paduan, J.D.; Washburn, L. High-frequency radar observations of ocean surface currents. Annu. Rev. Mar. Sci. 2013, 5, 115–136. [CrossRef][PubMed] 4. Paduan, J.D.; Cook, M.S. Mapping surface currents in Monterey Bay with CODAR-type HF radar. Oceanography 1997, 10, 49–52. [CrossRef] 5. Lee, B.C.; Fan, Y.M.; Doong, D.J.; Kao, C.C. A study on the homogeneity of tides around coasts of Taiwan. J. Mar. Eng. 2005, 5, 67–83. 6. Yoshikawa, Y.; Masuda, A.; Marubayashi, K.; Ishibashi, M. Seasonal variations of the surface currents in the Tsushima Strait. J. Oceanogr. 2010, 66, 223–232. [CrossRef] 7. Yoshikawa, Y.; Masuda, A. Seasonal variations in the speed factor and deflection angle of the wind-driven surface flow in the Tsushima Strait. J. Geophys. Res. Oceans 2009, 114.[CrossRef] 8. Fang, Y.C.; Wang, J.; Yang, Y.J. Surface Current Measurement Using HF-Radar off Northeastern Taiwan: Preliminary Result and Validation. In Proceedings of the 1st Ocean Radar Conference for Asia, Seoul, Korea, 17–19 May 2012; pp. 45–48. 9. Chen, Y.-W.; Yang, Y.J.; Wang, J. A study on data filling from incomplete dataset of HF radar measured ocean currents—A case study of the flow field Northeast of Taiwan: Data filling from incomplete ocean currents dataset. In Proceedings of the OCEANS 2014, Taipei, Taiwan, 7–10 April 2014; pp. 1–4. 10. Picot, N.; Case, K.; Desai, S.; Vincent, P.; Bronner, E. AVISO and PODAAC User Handbook. IGDR and GDR Jason Products; Jet Propulsion Laboratory, California Institute of Technology: Pasadena, CA, USA, 2003. 11. Hsin, Y.C.; Qiu, B.; Chiang, T.L.; Wu, C.R. Seasonal to interannual variations in the intensity and central position of the surface Kuroshio east of Taiwan. J. Geophys. Res. Oceans 2013, 118, 4305–4316. [CrossRef] 12. Chao, S.-Y. Circulation of the East China Sea, a numerical study. J. Oceanogr. 1990, 46, 273–295. [CrossRef] 13. Roesler, C.J.; Emery, W.; Kim, S.Y. Evaluating the use of high-frequency radar coastal currents to correct satellite altimetry. J. Geophys. Res. Oceans 2013, 118, 3240–3259. [CrossRef] 14. Scott, J.; Wentz, F.; Hoffman, R.; Atlas, R. Improvements and Advances to the Cross-Calibrated Multi-Platform (CCMP) Ocean Vector Wind Analysis (V2. 0 release). Am. Geophys. Union 2016, 2016, PO54F-3322. Available online: https: //www.researchgate.net/publication/298552723_Improvements_and_Advances_to_the_Cross-Calibrated_Multi-Platform_ CCMP_Ocean_Vector_Wind_Analysis_V20_release (accessed on 27 August 2021). 15. Richardson, P.L. Eddy kinetic energy in the North Atlantic from surface drifters. J. Geophys. Res. Oceans 1983, 88, 4355–4367. [CrossRef] 16. Sikhakolli, R.; Sharma, R.; Basu, S.; Gohil, B.; Sarkar, A.; Prasad, K. Evaluation of OSCAR ocean surface current product in the tropical Indian Ocean using in situ data. J. Earth Syst. Sci. 2013, 122, 187–199. [CrossRef] 17. Reyes Suarez, N.C.; Cook, M.S.; Gaˇcić,M.; Paduan, J.D.; Drago, A.; Cardin, V. Sea Surface Circulation Structures in the Malta-Sicily Channel from Remote Sensing Data. Water 2019, 11, 1589. [CrossRef] 18. Kim, S.Y.; Cornuelle, B.D.; Terrill, E.J. Anisotropic response of surface currents to the wind in a coastal region. J. Phys. Oceanogr. 2009, 39, 1512–1533. [CrossRef] 19. Kohut, J.T.; Glenn, S.M.; Paduan, J.D. Inner shelf response to tropical storm Floyd. J. Geophys. Res. Oceans 2006, 111.[CrossRef] 20. Paduan, J.D.; Rosenfeld, L.K. Remotely sensed surface currents in Monterey Bay from shore-based HF radar (Coastal Ocean Dynamics Application Radar). J. Geophys. Res. Oceans 1996, 101, 20669–20686. [CrossRef] 21. Kundu, P.K. Ekman veering observed near the ocean bottom. J. Phys. Oceanogr. 1976, 6, 238–242. [CrossRef] 22. Kohut, J.T.; Glenn, S.M.; Chant, R.J. Seasonal current variability on the New Jersey inner shelf. J. Geophys. Res. Oceans 2004, 109. [CrossRef] 23. Rosenfeld, L.; Shulman, I.; Cook, M.; Paduan, J.; Shulman, L. Methodology for a regional tidal model evaluation, with application to central California. Deep Sea Res. Part II Top. Stud. Oceanogr. 2009, 56, 199–218. [CrossRef] 24. de Beurs, K.M.; Henebry, G.M. Spatio-temporal statistical methods for modelling land surface phenology. In Phenological Research; Springer: Berlin/Heidelberg, Germany, 2010; pp. 177–208. 25. Pawlowicz, R.; Beardsley, B.; Lentz, S. Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE. Comput. Geosci. 2002, 28, 929–937. [CrossRef] 26. Britannica, T. Harmonic Analysis. Available online: https://www.britannica.com/science/harmonic-analysis (accessed on 27 August 2021). 27. Scharffenberg, M.G.; Stammer, D. Seasonal variations of the large-scale geostrophic flow field and eddy kinetic energy inferred from the TOPEX/Poseidon and Jason-1 tandem mission data. J. Geophys. Res. Oceans 2010, 115.[CrossRef] 28. Madah, F.; Mayerle, R.; Bruss, G.; Bento, J. Characteristics of tides in the Red Sea region, a numerical model study. Open J. Mar. Sci. 2015, 5, 193. [CrossRef] 29. Subeesh, M.; Unnikrishnan, A.; Fernando, V.; Agarwadekar, Y.; Khalap, S.; Satelkar, N.; Shenoi, S. Observed tidal currents on the continental shelf off the west coast of India. Cont. Shelf Res. 2013, 69, 123–140. [CrossRef] 30. Ponte, R.M.; Chaudhuri, A.H.; Vinogradov, S.V. Long-period tides in an atmospherically driven, stratified ocean. J. Phys. Oceanogr. 2015, 45, 1917–1928. [CrossRef] 31. Crawford, W. Analysis of fortnightly and monthly tides. Int. Hydrogr. Rev. 1982, LIX, 132–141. 32. Schureman, P. Manual of Harmonic Analysis and Prediction of Tides; US Government Printing Office: Washington, DC, USA, 1958; Volume 4. Remote Sens. 2021, 13, 3438 19 of 19

33. Stewart, R.H. Introduction to Physical Oceanography; Texas A&M University: College Station, TX, USA, 2008. 34. Lin, S.F.; Yang, Y.J.; Tang, T.Y. Coastal Tidal Current Phenomena on Northern Taiwan. In Proceedings of the 27th Ocean Engineering Conference, Taichung, Taiwan, 1–2 December 2005. 35. Dietrich, G.; Kalle, K. General Oceanography; An Introduction; Interscience Pub.: New York, NY, USA, 1957. 36. Courtier, A. Classiﬁcation of tides in four types. Int. Hydrogr. Rev. 1939. Available online: https://journals.lib.unb.ca/index.php/ ihr/article/download/27428/1882520184 (accessed on 27 August 2021). 37. Hicks, S.D. Tidal wave characteristics of Chesapeake Bay. Chesap. Sci. 1964, 5, 103–113. [CrossRef] 38. Dai, C.F. Regional Oceanography of Taiwan Version II; National Taiwan University Press: Taipei, Taiwan, 2018.