Applicability of ocean wave measurements based on high-frequency radar systems in an estuary region

ABSTRACT The applicability of high-frequency (HF) radar systems for wave measurement in an estuary was explored by extracting the significant wave height (${H_{sr}}$Hsr) using a traditional Barrick equation from the Doppler spectra observed by three radar systems installed in Ise Bay, Japan. The minimum value of ${H_{sr}}$Hsr estimated around each grid point was relatively consistent with the wave height observed with a wave gauge/buoy, except for a deterioration of wave measurement accuracy caused by a decrease in seawater conductivity from the freshwater inflow after flooding. Furthermore, the relationship between the accuracy and the signal-to-noise ratios for the first- and second-order peaks (SNR1 and SNR2, respectively) highlighted the difficulty in determining the threshold values of SNRs in the bay. Thus, we suggest the use of ${H_{sr}}$Hsr as a criterion for quality control when applying a nonlinear inversion method for estimating ocean wave spectra based on the Bayesian possibility theorem (BIM). Our suggestion is to select the appropriate Doppler spectra and increase the acquisition rates of wave data with low relative error compared to BIMs using SNR1 and SNR2. These results can promote the applicability of the nonlinear inversion in estuary regions.


Introduction
The 3-30 MHz high-frequency (HF) radar system is a powerful tool for continuous monitoring of ocean currents and waves within 200 km of the coast at high spatial (1-6 km) and temporal (hourly or higher) resolutions (Roarty et al. 2019).The radar system can provide the Doppler spectrum, which consists of first-and secondorder scattered powers (Barrick 1971(Barrick , 1972a(Barrick , 1972b)).These scattered powers are proportional to the scattered cross-section.According to Barrick's theoretical expression, the first-order cross-section is determined by the wave energy of a fundamental wave whose wavenumber is twice the wavenumber in the beam direction of the radio wave (i.e.Bragg scattering wave).Moreover, the second-order cross-section is expressed by a nonlinear integral function in which the wave energies of pairs of fundamental waves are included.Hasselmann (1971) first suggested that the secondorder Doppler sidebands around each first-order peak should be proportional to the wave frequency spectra, but a root-mean-square wave height (H rms ) estimated following this suggestion was not strictly true based on a comparison with buoy measurements for true wave height (Barrick 1977a).Thus, Barrick 1977aBarrick , 1977b) ) employed a weighting function for the second-order backscattered power, which was obtained from theoretical models of electromagnetic and hydrodynamic coupling factors, and derived an equation to extract H rms based on the ratio of the weighted second-order to the first-order powers, hereinafter referred to as the "Barrick equation."By applying the Barrick equation, Ramos, Graber, and Haus (2009) demonstrated the capability of phased-array HF radar systems to sample the spatial distribution of wave energy in different storm scenarios and coastal configurations.Subsequently, many algorithms have been proposed to invert the two-dimensional ocean wave spectrum based on a theoretical secondorder cross-section equation (Green and Wyatt 2006;Guiomar and Conley 2019;Hashimoto and Tokuda 1999;Hisaki 2015;Wyatt and Jim Green 2009).Green and Wyatt (2006) inverted theoretical first-and second-order crosssection equations proposed by Barrick and Weber (1977) and Weber and Barrick (1977) by several row-action methods.Hisaki (2015) developed an algorithm for inverting the wave spectrum by solving these theoretical equations using several constraints.In another approach, Hashimoto and Tokuda (1999) developed a technique for inverting the wave spectrum with the Bayesian theorem (BIM) by assuming that the wave spectrum is smooth in both wave frequency and direction planes.Kataoka and Nagamatsu (2016) modified the BIM to invert the wave spectrum in shallow water.
The availability of wave Information based on these algorithms is dependent on the significant backscattered power induced by ocean waves, but the power could be contaminated due to internal/external noise.
Thus, previous studies often used the signal-to-noise ratio (SNR) as a criterion for wave measurement (e.g.Tian et al. 2020;Wyatt et al. 2005Wyatt et al. , 2006)).The SNRs for first-and second-order scattering (hereinafter referred to as SNR 1 and SNR 2 , respectively) have been adopted as criteria.However, several threshold values existed in previous studies.Wyatt et al. (2005) asserted that wave measurement requires an SNR 2 of at least 10 dB.Thus, Wyatt et al. (2006) used Doppler spectra with SNR 2 >15 dB.Additionally, Tian et al. (2020) suggested that the threshold value of SNR 1 could be 20 dB for ocean current measurements.
However, these wave measurement algorithms have been rarely applied to monitor estuary regions because HF radio waves strongly attenuate due to the desalination of seawater, that is, the decline in seawater conductivity determined by the sea surface temperature (SST) and sea surface salinity (SSS) (Gurgel, Essen, and Kingsley 1999).In addition, the attenuation depends on the radio frequency and distance from the radar station (Gurgel, Essen, and Kingsley 1999).This could hinder HF radar-derived wave measurements in estuary regions.Nevertheless, monitoring waves is essential to manage marine transport, mitigate storminduced coastal disasters, and operate fisheries in estuary regions.In this case, HF radar systems can be potentially significant tools to provide wave data if their applicability is sufficiently validated.
In the present study, the applicability of HF radarderived wave measurements in estuary regions is validated in Ise Bay, which is a major estuary in Japan.For this purpose, the significant wave heights are computed by applying the Barrick equation to the Doppler spectra observed by three radar systems installed on the bay's coast.The calculated wave heights are evaluated by comparison with wave heights measured by a depth-mounted gauge and buoy.The deterioration of the wave measurement accuracy in the bay and the determinative factors are discussed.Following our findings, several criteria used to decide which Doppler spectra to invert using BIM are considered.This study provides suggestions for inverting the wave spectrum and insights into the deterioration of wave measurement accuracy in an estuary.

Study area and periods
Our study area was Ise Bay, in the center of Japan (Figure 1), with an average depth of 16.8 m.The eastern region of the bay is called Mikawa Bay, and the total basin area of Ise Bay and Mikawa Bay is 16,191 km 2 .The bay mouth is connected to the Pacific Ocean in the southern region of the bay.Seawater exchange is low because the bay mouth width is 12 km; the residence time is approximately one year.Freshwater flows into the bay from four rivers (Kiso, Nagara, Ibi, and Shounai Rivers) on the northern coast and four rivers (Suzuka, Kushida, Kumodzu, and Miya Rivers) on the western coast.The Kiso River is the largest river flowing into the bay, with a basin area of 5,275 km 2 .The basin areas of the Nagara, Ibi, and Shonai Rivers are 1,985 km 2 , 1,840 km 2 , and 1,010 km 2 , respectively.The bay's northern part of the catchment area is 10,110 km 2 , corresponding to 62% of the whole area (16,191 km 2 ).Moreover, the basin areas of four rivers (Suzuka, Kushida, Kumodzu, and Miya Rivers) in the western parts are 2,254 km 2 (323 km 2 , 461 km 2 , 550 km 2 , and 920 km 2 , respectively), which corresponds to 14% of the whole area.
In the present study, five periods for the significant growth of ocean waves due to the presence of typhoons in Japan were selected as targets (p1: 16-September 26 2016; p2: 18-October 28 2017; p3: 19-August 29 2018; p4: 31 August-September 10 2018; p5: 26 September-October 6 2018; see Table 1).To evaluate the influence of the freshwater inflow from the eight rivers on the HF radar-derived wave measurement, we collected data on hourly river discharges at nine river-discharge stations (stations D1 to D9 in Figure 1) that were not in the tidal reach in each river during the periods via the Water Information System operated by MLIT (http://www1.river.go.jp/).Note that station D5 was in the Utsube River, the major tributary of the Suzuka River.As station D6 was located upstream of the confluence point, the river discharge of the Suzuka River was evaluated by summing those measured at stations D5 and D6.The peaks of the total river discharge ranged between 7,501 and 20,661 m 3 /s in the five periods (Table 1); thus, the river discharge from three major rivers (Kiso, Nagara, and Ibi Rivers) in the Kiso River basin was predominant in the freshwater inflow.The largest flooding event occurred in period p1 (Figure 2).

Sea state monitoring stations in Ise Bay
Three HF radar systems (Nagano Japan Radio Company (NJRC)) were installed by the Ministry of Land, Infrastructure, Transport and Tourism, Japan (MLIT) in November 2005.Their central frequency for the transmission signal was 24.515 MHz with a sweep bandwidth of 100 kHz along the coast of Ise Bay (Figure 1).Doppler spectra with a spatial resolution of 1.5 km and an azimuth of 7.5° were observed in the bay.The beam directions of radars N, T, and O ranged between 164° and 246.5°, between 47° and 167°, and between −26.6° and 93.4°, respectively, in the clockwise direction from the north, and the numbers of beams were 12, 17, and 17, respectively.The three HF radar systems were operated at 10 min intervals, on the hour (Radar N), 10 min later (Radar T), and 20 min later (Radar O) every hour to avoid unexpected radio interference between the HF radars, for which the hourly Doppler spectra were available from the three HF radar systems.
Two monitoring stations were situated in the inner bay where surface waves provided in the Nationwide Ocean Wave information network for Ports and Harbours (NOWPHAS: https://www.mlit.go.jp/kowan/ nowphas/index_eng.html) and water quality parameters (e.g.salinity and temperature) provided by MLIT were observed (black circles in Figure 1).Stn.A (Stn.B) was located at distances of 11.1 km (39.3 km) from radar N, 27.2 km (29.7 km) from radar T, and 44.5 km (18 km) from radar O.The depths at Stns.A and B were 27 m and 30 m, respectively.The seawater conductivity was calculated from SSS and SST observed at each station by the International Thermodynamic Equation of Seawater-2010 (IOC, SCOR, and IAPSO 2010) (Figure 2).Note that the pressure was negligible in the conversion of the seawater conductivity because the skin depth of radio waves at 25 MHz is on the order of a few centimeters (Halverson, Pawlowicz, and Chavanne 2017).

Extraction of significant wave height from Doppler spectra
First-order backscattering of the incident radio waves on the sea surface is induced by a Bragg scattering wave with 2k 0 in the same direction, where k 0 is the radio wavenumber (Crombie 1955).In addition, second-order backscattering is induced by a bound wave that satisfies the following resonance condition: where k i i ¼ 1; 2 ð Þ and k 0 are the wavenumber vectors of the fundamental and radio waves, respectively.The first-and second-order cross-sections (σ 1 and σ 2 ) can be normalized by ω b (i.e. (2) and (3), respectively (Hisaki 1996;Lipa and Barrick 1986).where ω DN and ω iN are the Doppler angular frequency and wave angular frequency, respectively, normalized by the Bragg angular frequency ω b , and k iN is the wavenumber vector normalized by 2k 0 .m i is the sign (�1) determined from the range of Doppler angular frequency ω DN (Hisaki 1996).n is the unit vector, and is the normalized form of the wave spectrum for wavenumber vector k i , which is written as Γ TN is the total coupling coefficient, which can be divided into the electromagnetic (Γ EN ) and hydrodynamic (Γ HN ) components normalized by 2k 0 (i.e.Γ TN ¼ Γ EN À iΓ HN ) (Hisaki 1996;Lipa and Barrick 1986) as follows: where Δ is the sea surface impedance, which is often 0:011 À 0:012i according to Lipa and Barrick (1986).Eq. ( 5) is the normalized hydrodynamic component of the coupling coefficient for shallow water while considering the effect of wave refraction (i.e. the fourth term of Eq. ( 5)).For deep water (i.e.k iN h N !1), the fourth term of Eq. ( 5) is neglected because csch k iN h N ð Þ !0, and k diN is the wavenumber for deep water, which is equal to k iN when k iN h N ! 1 according to the following linear dispersion relation normalized by ω B (Hisaki 1996).
Following Barrick 1977aBarrick , 1977b), H rms is available from the Barrick equation derived from a ratio of the weighted second-order powers to the first-order powers.
where w ω DN ð Þ is a dimensionless weighting function for each ω DN , which averages the total coupling coefficient Γ TN for deep water over the radar-towave direction (Barrick 1977a(Barrick , 1977b)).When calculating H sr by Eq. ( 7), the second-order scattering is normalized by the first-order scattering peak in the same frequency domain; thus, the integral range is defined as 1.8% *1 The value in the parenthesis was the coefficient of variation (CoV).*2 Percent decrease means the ratio of the decrease in mean conductivity after river discharge peaks to that before the peaks.

Computation of significant wave height derived by the HF radar system
In the present study, H sr at polar grids on beams around Stns.A and B (Figure 1) were computed by Eq (7) and were then compared with those observed by the wave gauge/buoy at both stations.
A single HF radar system provided the four Doppler spectra at the polar grids around each station; thus, up to twelve Doppler spectra around them were obtained from the three HF radar systems (Figure 3).The Doppler shift induced by surface ocean currents was removed as preprocessing for extracting wave information.Furthermore, the abnormal peaks that are of about the same power as the first-order peak (mainly, ship-induced noise) were simply removed by comparing them with a smoothed Doppler spectrum in each of negative and positive frequency domains (e.g.Chuang, Chung, and Tang (2015)).Then the backscattered powers were linearly interpolated.However, since this simple removal process is not robust, several ship-derived noise remain.We discussed the negative effect of the residual noise on wave measurement in 3.1.Then, the Doppler spectrum was divided into first-and second-order scattered components by identifying the local minimum around the first-order peak.H sr was computed using the first-and second-order backscattered powers in the negative and positive frequency domains of the Doppler spectrum, which means that two H sr values were extracted from a single Doppler spectrum.Finally, up to 24 H sr values around the 1.5-km grid point (4 polar grids/radar × 3 radars × 2 (negative and positive) frequency domains of Doppler spectrum) were extracted by applying Eq (7).Doppler spectra that do not follow Barrick's theory should be discarded in advance to avoid incorrectly estimating wave heights.Thus, the Doppler spectra with SNR 2 ≤10 dB were removed according to Wyatt (2005) when extracting H sr (Figure 3).SNR 2 was evaluated using the second-order peak in the outer band of each frequency domain against a noise floor level in the same domain.The noise floor level was determined by averaging the noise power over the outer edge of each domain (i.e.1:79 < ω DN j j < 1:94) beyond 60 km from each radar station at each time point.Note that the noise floor levels were defined from a range-Doppler map but not from a single Doppler spectrum.This removes the effect of wave-induced powers and/ or local external noises from the noise floor level.Furthermore, SNR 1 was also computed with the ratio of the first-order peak to the noise floor level in each domain to assess the capability as a criterion for the wave spectrum inversion.

Statistical analysis
The HF radar-derived significant wave height (H sr ) was compared with that measured by the wave gauge/ buoy (H so ).The measurement accuracy was evaluated with four indexes, that is, Pearson's correlation coefficient (r), bias, root mean square error (RMSE) without bias, and scatter index (SI), as follows.
where hH sr i and hH so i are the temporal averages during each computing period for comparison, and N denotes the amount of data.The python package "scipy (ver 1.4.1)" was used in the statistical analysis.
Furthermore, Pearson's correlation coefficient was also adopted to discuss the effect of environmental factors (freshwater inflow volume, seawater conductivity) on the measurement accuracies (i.e.Eq (9) and Eq (11)) and was then tested with a 95% confidence level using a t test.

Extraction of significant wave height from Doppler spectra in Ise Bay
Up to 24 H sr values were computed at each time by Eq (7) and then compared with H so values at Stns.A and B during the five periods (Figure 4).Overall, H sr greatly fluctuated against H so .A possible cause of the large fluctuation in H sr could be the decline in SNR 2 and/or the occurrence of unexpected peaks in the second-order domain.These unexpected peaks occur due to various factors.One factor is temporary obstructions in the working range of the HF radar (e.g.ship) (Maresca et al. 2011).Many ships operate in Ise Bay because of activity in the Ports of Nagoya and Yokkaichi, with more than 50,000 domestic/ international ships entering Ise Bay each year as well as fishery ships that operate in the bay.The strong ship-derived echoes contaminate the Doppler spectrum.Another factor is radio interference, which can have a major impact on the performance of HF radar measurements (Gurgel, Barbin, and Schlick 2007).In Ise Bay, the operation times of the three radar systems were shifted by 10 min to avoid interference among these systems (see 2.2); however, several unexpected echoes induced by radio interference were confirmed, especially radar N.These echoes in the Doppler spectrum extended over a measurable distance from the radar station.These unexpected peaks would yield an overestimation of H sr .
Interestingly, the minima among the estimated H sr (H sr;min ) values at Stn. B were relatively consistent with H so (black solid line in Figure 4), although several abnormal variabilities were observed (n = 1200, r = 0.71, bias = 0.18 m, SI = 0.82; see Table 2).In contrast, H sr;min at Stn.A greatly fluctuated against H so (n = 1184, r = −0.01,bias = 1.23 m, SI = 6.45; see Table 2); in particular, the accuracy of H sr;min worsened after peak river discharge (arrows of each panel in Figure 4).The temporal variability of H sr;min before the peak was relatively consistent with that of H so at Stn.A as well as Stn.B (Stn.A: n = 610, r = 0.74, bias = 0.28 m, SI = 0.83; Stn.B: n = 611, r = 0.85, bias = 0.11 m, SI = 0.53; see Table 2).The correlation between H so and H sr at each radar station before the river discharge peak is shown in Figure 5. Basically, H sr was overestimated against H so (Figure 5), while H sr;min was relatively correlated with H so .H sr;min values at Stns.A and B were often extracted from radar N (Stn.A -radar N: 11.1 km; Figure 5a) and radar O (Stn.B -radar O: 18 km; Figure 5f) depending on the distance from the radar stations.The accuracy of H sr;min at Stn.A deteriorated compared with Stn.B (Figure 5) regardless of whether the monitoring site was closer to the radar station (Figure 1).

Decrease in wave measurement accuracy due to freshwater inflow
A possible cause for a decrease in the accuracy at Stn.A is the attenuation of HF radio waves due to seawater desalination induced by the freshwater inflow (Gurgel, Essen, and Kingsley 1999).Seawater desalination yields a decline in seawater conductivity and thus results in a reduction in SNRs (Gurgel, Essen, and Kingsley 1999;Forget and Broche 1991).In fact, the seawater conductivity around Stn.A showed dramatic changes due to the freshwater inflow (Figure 2) because Stn.A was close to the mouth of the Kiso River, which is the largest river in the Ise Bay basin (Figures 1 and 2).In contrast, the conductivity at Stn. B slightly changed.As expected, the mean conductivity at Stn.A after the river discharge peak significantly decreased between 16% and 75%, yielding a larger variance in the conductivity, while that at Stn. B was only a 0.2% to 6.7% decrease with a smaller variance (Table 1).The percent decrease in mean conductivity at Stn.A (Stn.B) was the largest in p1 (p2), resulting from the large river discharge from the northern (western) part of the bay (Table 1).In fact, the percent decrease in mean conductivity at Stn.A strongly correlated with the freshwater inflow volume from the northern rivers (n = 5, r = 0.801, p = 0.103), whereas the decrease at Stn. B strongly correlated with the volume from western rivers (n = 5, r = 0.853, p = 0.066).Unfortunately, a statistically significant correlation at the 95% confidence level was not found because of a few data points (i.e.n = 5).However, in contrast to these correlations, the relationship of the percent decrease at Stn.A (Stn.B) with freshwater volume from western (northern) rivers was weak (n = 5, r = 0.320, p = 0.600 for percent decrease at Stn.A vs. freshwater volume from western rivers; n = 5, r = 0.240, p = 0.697 for percent decrease at Stn. B vs. freshwater volume from northern rivers).These results suggest that the freshwater inflow from northern and western rivers leads to the decrease in seawater conductivity at Stns.A and B, respectively.
The percent decrease in mean seawater conductivity determined the wave measurement accuracy.Comparing bias and SI for each period at Stns.A and B (Table 2) with the percent decrease (Table 1), the percent decrease at Stn.A showed a statistically significant correlation with both bias and SI (n = 5, r = 0.970, p < 0.01 for bias; n = 5, r = 0.971, p < 0.01 for SI), but a significant correlation at Stn. B was not found (n = 5, r = 0.133, p = 0.832 for bias; n = 5, r = 0.090, p = 0.886 for SI).This verifies the deterioration of wave measurement accuracy at Stn.A caused by the decrease in seawater conductivity, as the measurement accuracy at Stn. B was not always dependent on conductivity.This is because the attenuation pattern of radio waves at a distance from a radar station affects the signal level in the far zone (Forget and Broche 1991).Even if the conductivity at a target point was high, the radio waves could be highly attenuated in the low-conductivity region, which is close to a radar station such as Stn.N (Figure 1).

Requirement of signal-to-noise ratio (SNR) for wave measurement
Here, a question arises: How should we select the Doppler spectra to extract ocean wave information?As mentioned above, the minimum value among the estimated significant wave heights (i.e.H sr;min ) before flooding was relatively consistent with H so (Figure 4).This implies that various noises yielded unexpected peaks in the secondorder frequency domain and thus basically worked toward the overestimation of H sr (Figure 5).To answer the above question, we consider a criterion for selecting the Doppler spectra for wave measurement.
In the present study, SNR 1 and SNR 2 were considered criteria for wave measurement.To examine the requirements of SNR 1 and SNR 2 , relative errors (RE) in all periods were computed by H sr;min À H so � � � � =H so .Note that SNR 1 and SNR 2 were evaluated in the positive/negative domain  from which H sr;min was computed.Figure 6 shows a twodimensional density plot in the SNR 1 -SNR 2 plane when RE < 50% (Figure 6a and b) and RE > 50% (Figure 6c and d).
The acquisition rate of H sr;min with RE < 50% at Stn. B was 60%, which was higher than that at Stn.A (33%) (Figure 2).H sr;min with RE < 50% at both sites was likely to be available with SNR 1 >40 dB (Figure 6a and b).In the case of RE > 50%, SNR 1 at Stn.A was less than 40 dB (Figure 6c), while SNR 1 at Stn. B was greater than 40 dB (Figure 6d).The deterioration of H sr;min at Stn. B was seen even if SNR 1 >40 dB (Figures 6d).The density plots also indicate that wave measurement requires an SNR 2 of at least 10 dB, which is consistent with Wyatt et al. (2005) (Figure 6a and  b).On the other hand, H sr;min with RE > 50% was often estimated at Stn. B even if SNR 2 >10 dB.This implies that such a higher SNR 2 would be derived from not only waveinduced echoes but also noise-induced echoes which were unrelated to Barrick's theory.

Capability of the wave height estimated by Barrick's equation as a criterion for nonlinear inversion of ocean wave spectrum
Based on these results, we formulated a hypothesis that H sr is helpful in selecting the Doppler spectrum with low contamination by noise when applying an inversion of the wave spectrum.This idea was originated by Hisaki (2015), but its capability was not sufficiently validated.Furthermore, the applicability of wave measurements in estuary regions such as Ise Bay is unknown.As a method of wave spectrum inversion, the BIM for shallow water established by Kataoka and Nagamatsu (2016) was applied, which is modified from the BIM for deep water originally proposed by Hashimoto and Tokuda (1999), as concisely described in Appendix A.
To demonstrate the hypothesis, we compared three algorithms with different criteria for selecting the Doppler spectra in the BIM.The first criterion was H sr (BIM Barrick ), and the second and third criteria were SNR 1 (BIM SNR1 ) and SNR 2 (BIM SNR2 ), respectively.In BIM Barrick , the Doppler spectra were used when the relative difference of up to 24 H sr against H sr;min (i.e.H sr À H sr;min � � � � =H sr;min ) was lower than 50% (BIM Barrick ).Meanwhile, the Doppler spectra in BIM SNR1 and BIM SNR2 were selected when SNR 1 and SNR 2 in the Doppler frequency domain with the strongest firstorder peak were greater than 40 dB and 10 dB, respectively.Hereinafter, these quality controls before applying BIM are referred to as "prior quality control."The significant wave height (H s ) was computed by Eq (A8) using the inverted wave spectrum.Then, as "posterior quality control," the abnormal wave heights estimated by the three algorithms were neglected if H s À H sr;min � � � � =H sr;min > 50%.Finally, the acquisition rate was evaluated by a ratio of the number of H s with RE < 50% to the total data.
The measurement accuracy of H s was evaluated in the durations before the river discharge peaks (Table 3).For reference, the measurement accuracies of H sr;min are also described in Table 3.At Stn. A, H s estimated by BIM Barrick was more accurate than the others.At Stn. B, there were no significant differences in measurement accuracy among the three algorithms.However, we found that the acquisition rates of BIM Barrick  H sr was a functional criterion for the prior quality control.For example, Figure 7 shows the Doppler spectra around Stn. B at 13:00 JST on August 21 2018.Initially, a Doppler spectrum (Figure 7b) was rejected because SNR 2 ≤10 dB (see 2.4), and thus, the eleven Doppler spectra with SNR 2 >10 dB observed by three radar systems were used for BIM SNR2 .The three Doppler spectra with SNR 2 ≤40 dB (Figure 7a, c,  d) were rejected for BIM SNR1 , and furthermore, three Doppler spectra (Figure 7e, f, h) with H sr À H sr;min � � � � =H sr;min > 50% where H sr;min ¼ 0:82m (see Figure 7i) were rejected for BIM Barrick .Based on the prior quality control, the wave spectra were estimated using the five Doppler spectra for BIM Barrick , the eight for BIM SNR1 and the eleven for BIM SNR2 (Figure 8).The wave spectra estimated by the three BIMs show that the wind waves predominantly came from the southeast, which is consistent with the wind direction observed at Stn. B, that is, southwesterly winds (135°Clockwise from the north).The significant wave height computed by BIM Barrick (H s ¼ 0:58 m, RE = 19%) was reasonable with the observed height at Stn. B (H so ¼ 0:72 m) compared  to H s computed by BIM SNR1 (H s ¼ 1:09 m, RE = 51%) and BIM SNR2 (H s ¼ 1:13 m, RE = 57%).BIM SNR2 estimated high wave energies at low frequencies (Figure 8c).The six Doppler spectra with SNR 2 >10 dB (Figure 7a, c, d, e, f, h) caused the overestimation of H s compared to H so .The criteria suggested by Wyatt et al. (2006) (SNR 2 >15 dB) can reject three of those spectra (Figure 7a, c, d), which was consistent with the SNR 1 -based selection, whereas it was difficult to reject the remaining Doppler spectra.They were successfully rejected by using H sr as the prior quality control in BIM Barrick .This demonstrates that H sr effectively functions as a criterion to reject inappropriate Doppler spectra in the BIM.

Suggestion of a methodology for providing reliable HF radar-derived wave data in the estuary region
We summarize a methodology for providing reliable HF radar-derived wave data in an estuary region.The most specific issue in this region is the attenuation of radio waves propagating on the sea surface due to the decline in seawater conductivity induced by freshwater inflow (Figure 2).Accordingly, both SNR 1 and SNR 2 significantly decreased after the river discharge peak corresponding to seawater conductivity, which yielded a deterioration in the measurement accuracy of H sr;min (Figure 4).HF radar-derived wave data are unavailable under seawater desalination, which is a limitation of HF radar-derived wave observations (Gurgel, Essen, and Kingsley 1999).
Nevertheless, further research is necessary to define the threshold values of the conductivity because the attenuation of radio waves is dependent on the distance from the radar station and radio frequency as well (Gurgel, Essen, and Kingsley 1999;Toguchi and Fujii 2023).Figure 9 shows the dependence of the RE of H s estimated by BIM Barrick on the conductivity.At Stn. B with the higher conductivity (mostly conductivity >4 S/m), the acquisition rate of H s (percentage of RE < 50% in the total number) was 67%.On the other hand, the acquisition rate at Stn.A with the lower conductivity significantly decreased depending on the deterioration of the conductivity (Figure 9), but the acquisition rate at Stn.A (71%) was slightly greater than that at Stn. B (67%) when the conductivity >4 S/m because of the shorter distance from the radar station.Moreover, even if the conductivity ranged between 3 and 4 S/m at Stn. A, the acquisition rate of H s was 52%.
In addition, the first-order and second-order Doppler spectra in the bay were often contaminated by other external noises.This noise occurs in the nonwave-induced peaks in those frequency domains, which could overestimate SNR 1 and SNR 2 .Although SNR 1 and SNR 2 are important criteria to evaluate the quality of Doppler spectra, these criteria could not select the appropriate Doppler spectra for the wave spectrum inversion in the bay (see 3.4).
Here, our suggestion is to employ H sr as the criterion for the inversion.The present study demonstrates that H sr could select adequate Doppler spectra from those affected by desalination and containing noise.Consequently, the wave measurement accuracy and acquisition rates of the BIM Barrick -derived H s were improved compared with those of BIM SNR1 and BIM SNR2 (Table 3).Although the present study only focused on the significant wave height, we need to further validate other wave parameters, such as wave period and direction.Additionally, it is necessary to consider the applicability of the suggestion listed in the present study in other estuary regions and radar systems with different radio frequencies.

Summary
To explore the applicability of high-frequency (HF) radar systems in estuary regions for wave measurement, we validated the significant wave height in Ise Bay, Japan, by applying a traditional equation formulated by Barrick (1977a) and then assessing the deterioration of the measurement accuracy of the wave height and factors that influence it.Moreover, the capability of using the wave height derived by the Barrick equation in a nonlinear inversion for the twodimensional wave spectrum from Doppler spectra was considered.
The minimum (H sr;min ) of up to 24 significant wave heights computed by the Barrick equation to the Doppler spectra observed by three radar systems around a 1.5-km regular grid point was consistent with the wave height measured by wave gauges/ buoys at two sites (Stns.A and B) in the bay.The measurement accuracy at Stn. A, which was close to the mouth of the major rivers, notably deteriorated due to the decrease in seawater conductivity from the inflow of freshwater, as indicated by the significant correlation between the accuracy indexes (bias and SI) and the percent decrease in the conductivity.
Furthermore, the requirement for wave measurement was assessed by computing the signal-to-noise ratios of the first-order (SNR 1 ) and second-order peaks (SNR 2 ) against a noise floor level.The significant wave height at Stn.A tended to be accurately measured when SNR 1 >40 dB, while that at Stn. B deteriorated even if SNR 1 >40 dB.In addition, there were no significant differences in SNR 2 .These results highlight the difficulty in determining the threshold values of SNR 1 and SNR 2 for measuring ocean waves in estuary regions.
To explore more suitable criteria for wave measurement in estuary regions, nonlinear inversion methods using H sr (BIM Barrick ), SNR 1 (BIM SNR1 ), and SNR 2 (BIM SNR2 ) were applied.BIM Barrick successfully selected appropriate Doppler spectra, whereas BIM SNR1 and BIM SNR2 had difficulty selecting the Doppler spectrum observed in the estuary due to desalination and noise contamination.Consequently, BIM Barrick showed better performance than BIM SNR1 and BIM SNR2 in terms of a high acquisition rate, although there was difficulty in determining the best method in terms of measurement accuracy.Therefore, our results demonstrate that H sr can select appropriate Doppler spectra from those deteriorated in the estuary regions.

Figure 1 .
Figure 1.Study area.The stars are the three HF radar stations.The contour in the sea indicates the depth with 5 m intervals (thin line) and 10 m intervals (thick line).The squares are the monitoring sites of river discharge in nine major rivers flowing into the bay.The circles are locations where water quality parameters (seawater temperature and salinity) and wave heights are observed.

Figure 2 .
Figure 2. Time series of river discharge from each river basin and seawater conductivity.From the top, the time series in p1 to p5 are described.Notably, the river discharge in the Kiso (Suzuka) river basin is summed up by those of the Kiso, Nagara and Ibi Rivers (utsube and Suzuka Rivers).The seawater conductivity is calculated from the SSS and SST observed at Stn.A and B (see Figure1).

Figure 3 .
Figure 3. Schematic image of the selection of Doppler spectra to extract significant wave heights.The filled (white) circles indicate the parallel grid point at which the Doppler spectrum with SNR 2 >10 dB (SNR 2 ≤10 dB) is observed.The square indicates the 1.5-km grid point at which the significant wave height is calculated.In this case, the eight Doppler spectra are utilized to compute the significant wave height.

Figure 4 .
Figure 4. Time series of significant wave heights extracted from the Doppler spectra.The color dots indicate H sr estimated from up to 24 Doppler spectra.The black solid line indicates H sr;min among up to 24 H sr , and the gray solid line indicates H so observed by wave gauge/buoy.The arrow on the upper edge of each panel denotes the time at which the peak of total river discharge occurred (see Figure 2).From the top, the time series in p1 to p5 are described.The left and right panels are the time series at Stns.A and B, respectively.

Figure 5 .
Figure 5.Comparison between the significant wave heights estimated by applying the Doppler spectrum observed by three radar systems to Barrick's equation (H sr ) and observed by wave gauge/buoy (H so ) in the duration before the river discharge peak.The upper and lower panels denote the scatter plots at Stns.A and B, and the left, center and right panels denote those from radar N, T and O, respectively.The colors show the calculation periods, and the outlined circles show the minima of H sr (H sr;min ).Their legend is shown in the upper right of each panel.

Figure 7 .
Figure 7. Example of the normalized Doppler spectra observed around Stn. B (13:00 JST, 21 August 2018).The Doppler spectra are normalized by the first-order peaks.The upper, middle and lower panels are for radar N, T and O, and the four columns are for the four polar grids.The title of each panel describes the radar station, cell number of range and beam directions and beam angle ϕ clockwise from the north.H sr , SNR 1 , SNR 2 and normalized noise floor level, which were evaluated in the positive/negative frequency domain, are described in each panel.Note that the noise floor level is also normalized by the first-order peaks to be consistent with the normalized Doppler spectra.The gray and light gray areas denote the first-order and second-order domains, respectively.The blue lines show the normalized Doppler spectrum computed from the optimum solution of ocean wave spectra inverted by BIM Barrick , BIM SNR1 , and BIM SNR2 described in Figure 8, whose legends are shown in the bottom box.

Figure 8 .
Figure 8. Example of the ocean wave spectra inverted by BIM Barrick , BIM SNR1 , and BIM SNR2 at Stn. B at 13:00 JST, 21 October 2018.The Doppler spectra selected in the three BIMs are described in Figure 7.The significant wave heights computed from the inverted spectrum are shown at the upper-left of each panel.

Table 1 .
Summary of river discharge peak, freshwater inflow volume from northern and western rivers and mean sea water conductivity at Stns.A and B in the five periods.

Table 2 .
Accuracy of H sr;min in total duration and only before the river discharge peak.

Table 3 .
Comparison of measurement accuracies of significant wave height estimated by Barrick's equation (H sr;min ) and BIMs with three types of criteria (BIM Barrick , BIM SNR1 , and BIM SNR2.).