# Temperature correction and usefulness of ocean bottom pressure data from cabled seafloor observatories around Japan for analyses of tsunamis, ocean tides, and low-frequency geophysical phenomena

- Daisuke Inazu
^{1}Email author and - Ryota Hino
^{1}

**63**:6301101133

https://doi.org/10.5047/eps.2011.07.014

© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2011

**Received: **23 March 2011

**Accepted: **22 July 2011

**Published: **14 February 2012

## Abstract

Ocean bottom pressure (OBP) data obtained by cabled seafloor observatories deployed around Japan, are known to be significantly affected by temperature changes. This paper examines the relationship between the OBP and temperature records of six OBP gauges in terms of a regression coefficient and lag at a wide range of frequencies. No significant temperature dependency is recognized in secular variations, while substantial increases, at rates of the order of 1 hPa/year, are commonly evident in the OBP records. Strong temperature dependencies are apparent for periods of hours to days, and we correct the OBP data based on the estimated OBP-temperature relationship. At periods longer than days, the temperature corrections work well for extracting geophysical signals for OBP data at a station off Hokkaido (KPG2), while other corrected data show insufficient signal-to-noise ratios. At a tsunami frequency, the correction can reduce OBP fluctuations, due to rapid temperature changes, by as much as millimeters, and is especially effective for data at a station off Shikoku (MPG2) at which rapid temperature changes most frequently occur. A tidal analysis shows that OBP data at a station off Honshu (TM1), and at KPG2, are useful for studies on the long-term variations of tidal constituents.

### Key words

Ocean bottom pressure temperature correction tsunami ocean tide oceanic variation## 1. Introduction

Pressure sensor units for oceanographic applications have been employed since the late 1960’s (e.g., Munk and Zetler, 1967). Various types of pressure transducers have been investigated for obtaining high-quality ocean bottom pressure (OBP) records. These include vibrating wires, strain gauges, capacitance plates, and quartz-crystal resonators. The quartz-crystal resonator transducer is most commonly used at present because of its high sensitivity to pressure, high resolution, and long-term stability (Eble *et al.*, 1989; Joseph, 2011). Devices incorporating the quartz resonator manufactured by Paroscientific, Inc. (hereafter Paros), and by Hewlett-Packard, Inc. (hereafter HP), are currently used as water-depth sensors. In general, the physical pressure measurement is obtained from the vibrational frequency of the transducer, which changes with ambient pressure and temperature. Therefore, thermal effects must be accurately corrected to obtain a meaningful physical pressure value. A built-in thermometer is needed to accurately measure the temperature of the transducer. The manufacturers provide conversion equations, and tables of calibration coefficients, to calculate an accurate physical pressure value, with a thermal correction, from the vibrational frequency, for the respective sensors. The procedures to obtain the physical pressure value with a pressure-measurement system were introduced by Eble *et al.* (1989) for the Paros sensors, and by Takahashi (1981a) for the HP sensors.

After many field and laboratory experiments (e.g., Wearn and Larson, 1982; Wearn and Paros, 1988; Houston and Paros, 1998) partially conducted by the Scientific Committee on Oceanic Research (SCOR, 1975), the Paros sensor, incorporating the Bourdon tube (Filloux, 1970), was highly improved, and has been called the Digiquartz pressure sensor. The pressure gauges derived from the Paros measurement system have demonstrated good performances for observing tsunamis of the order of millimeters (Filloux, 1982), ocean tides (Mofjeld and Wimbush, 1977), and low-frequency (<1 day^{−1}) oceanic variations of the order of centimeters (Niiler *et al.*, 1993) (in general, a 1-cm sea-water height is equivalent to 1 hPa). At present, the Paros pressure gauges are widely used for oceanographic (e.g., Spencer and Vassie, 1997; Park and Watts, 2005; Park *et al.*, 2008; Uchida and Imawaki, 2008) and geodetic (e.g., Fox, 1990; Fujimoto *et al.*, 2003; Chadwick *et al.*, 2006; Matsumoto *et al.*, 2006; Nooner and Chadwick, 2009) applications. The Deep-ocean Assessment and Reporting of Tsunamis (DART) system, operated by the Pacific Marine Environmental Laboratory (PMEL) of the National Oceanic and Atmospheric Administration (NOAA), also utilizes Paros pressure gauges for the early monitoring of offshore tsunamis over the quasi-global ocean (González *et al.*, 2005).

The HP sensor, based on the quartz pressure transducer of Karrer and Leach (1969), was investigated by Irish and Snodgrass (1972), SCOR (1975), Culverhouse (1977), Hayes *et al.* (1978), and Wearn and Larson (1982). The Japan Meteorological Agency (JMA) has employed a pressure gauge, derived from the HP measurement system, to a real-time observatory cabled from land for monitoring offshore tsunamis and seafloor level changes (Isozaki *et al.*, 1980). Brief descriptions of the cabled observatory have been provided by Isozaki *et al* (1980) and Takahashi (1981a, b). Currently, seven cabled observatories utilizing HP pressure gauges around Japan are operated by JMA, the National Research Institute for Earth Science and Disaster Prevention (NIED), the Earthquake Research Institute of the University of Tokyo (ERI), and the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) (Hirata *et al.*, 2009). Although these HP pressure gauges show a fairly good ability to observe tsunamis of the order of millimeters (Hino *et al.*, 2001; Hirata *et al.*, 2003; Baba *et al.*, 2004; Tanioka *et al.*, 2004; Satake *et al.*, 2005; Saito *et al.*, 2010), there have been no reports of successful observations of low-frequency (<1 day^{−1}) oceanic variations of the order of centimeters. The HP measurement system possibly has a low detection capability for low-frequency variations. In this paper, pressure gauges, derived from the HP measurement system, deployed on cabled observatories are referred to as ocean bottom tsunami meters (OBTMs) (e.g., Matsumoto *et al.*, 2003; Tsushima *et al.*, 2009).

Baba *et al.* (2006) detected a large vertical seafloor elevation of tens of centimeters, related to the 2003 Tokachi-oki earthquake (M_{w} 8.0), from OBTMs off Kushiro operated by JAMSTEC (Hirata *et al.*, 2002). The detection capability was clearly improved by correcting the OBTM records using a regression coefficient to the temperature changes. Hirata and Baba (2006) estimated a response of OBTM output to transient temperature changes that can cause false pressure signals in the analysis of tsunamis. These supplementary thermal corrections are beyond the routine procedure to calculate the physical pressure value. So far, the dependency of OBTM data on temperature in other frequency bands has not been investigated, and its temporal changes have not been demonstrated. In addition, if an effective correction of OBTM data is possible, it is useful to discuss the detection capabilities of the OBTM data regarding various geophysical phenomena. In this study, the following are investigated: (1) long-term changes, including drifts in the OBTM records, using records of more than ten years; (2) dependency of the OBTM data on temperature in various frequency bands; and (3) the usefulness of the OBTM data for monitoring geophysical phenomena, after a correction based on the estimated relationship between the OBP and temperature in various frequency bands.

## 2. Data

*et al.*, 1997); and Kushiro: KPG1 and KPG2 (Hirata

*et al.*, 2002). OBTM records during periods ofmore than ten years are used to investigate long-term changes. For reference data to the OBTM data, we use seven sets of OBP data derived from two conductivity-temperature-depth measuring instruments (CTDs) (MCTD and KCTD) connected to the above-mentioned cabled observatories, one OBP gauge (HPG) connected to a cabled observatory (Iwase

*et al.*, 2003), and four autonomous OBP observations (GJT3, GJT4, PKMN06, and NMS09) conducted by Tohoku University. All of the OBP reference data were obtained by the Paros measurement system. Data from six tide gauges are also used for comparison. Details of the data used are listed in Table 1.

OBP and tide gauges used in this study.

Observation | Site | Latitude (°N) | Longitude (°E) | Depth (m) | Sensor | Data period | Sampling | Agency |
---|---|---|---|---|---|---|---|---|

Cabled OBP gauges | TM1 | 39.23 | 142.78 | 1563 | HP | Apr. 1997–Dec. 2009 | 10 Hz | ERI |

TM2 | 39.25 | 142.45 | 990 | HP | Apr. 1997–Dec. 2009 | 10 Hz | ERI | |

MPG1 | 32.39 | 134.48 | 2308 | HP | Mar. 1997–Dec. 2009 | 10 Hz | JAMSTEC | |

MPG2 | 32.64 | 134.36 | 1507 | HP | Mar. 1997–Dec. 2009 | 10 Hz | JAMSTEC | |

MCTD | 32.37 | 134.53 | 3303 | Paros | Jul. 2006–Jun. 2008 | 0.1 Hz | JAMSTEC | |

KPG1 | 41.70 | 144.44 | 2218 | HP | Jul. 1999–Dec. 2009 | 10 Hz | JAMSTEC | |

KPG2 | 42.24 | 144.85 | 2210 | HP | Jul. 1999–Dec. 2009 | 10 Hz | JAMSTEC | |

KCTD | 41.67 | 144.34 | 2540 | Paros | Jul. 2006–Feb. 2010 | 0.1 Hz | JAMSTEC | |

HPG | 35.00 | 139.22 | 1176 | Paros | May 2004–Dec. 2009 | 1 Hz | JAMSTEC | |

Autonomous OBP gauges | GJT3 | 38.29 | 143.48 | 3321 | Paros | Oct. 2008–Oct. 2009 | 1 min | Tohoku Univ. |

GJT4 | 38.40 | 142.77 | 1450 | Paros | Oct. 2008–Oct. 2009 | 1 min | Tohoku Univ. | |

PKMN06 | 33.64 | 136.60 | 2070 | Paros | Aug. 2006–Dec. 2007 | 30 min | Tohoku Univ. | |

NMS09 | 42.37 | 145.92 | 3315 | Paros | Jun. 2009–Feb. 2010 | 1 min | Tohoku Univ. | |

Tide gauges | OF | 39.02 | 141.08 | Jan. 2002–Dec. 2009 | 1 hr | JMA | ||

AY | 38.30 | 141.50 | Jan. 2002–Dec. 2009 | 1 hr | JMA | |||

MU | 33.27 | 134.17 | Jan. 2002–Dec. 2009 | 1 hr | JMA | |||

KC | 33.50 | 133.57 | Apr. 2003–Dec. 2009 | 1 hr | JMA | |||

KR | 42.98 | 144.37 | Jan. 2002–Dec. 2009 | 1 hr | JMA | |||

HN | 43.28 | 145.57 | Jan. 2002–Dec. 2009 | 1 hr | JMA |

In the following sections, we analyze one-minute time series obtained by averaging raw data with a one-minute window and by removing outliers. Ocean tide components in the one-minute OBP time series are removed by applying the NAO.99Jb model (Matsumoto *et al.*, 2000). On the other hand, hourly time series obtained by averaging the one-minute time series with a ten-minute window are used when tidal components are examined.

## 3. OBP Records and Remaining Temperature Dependency

*et al.*, 1999; Wunsch

*et al.*, 2009), are superimposed on the observations in Fig. 2(a). We can see that the detided OBP variations measured by the Paros pressure gauges and those of the ECCO-JPL model show a good spatio-temporal consistency within at least a 100-km scale. Similar results were also found by Matsumoto

*et al.*(2006). In addition, in the Kuroshio Extension region, Donohue

*et al.*(2010) remarked that OBP variations are spatially consistent within a scale of hundreds of kilometers for periods of 2–30 days. Since the ECCO-JPL model basically involves only geophysical fluid dynamics, the OBP observations, obtained using the Paros measurement system, have relatively low instrumental noise. However, the OBTM records show a low correlation with the other OBP observations, or the ECCO-JPL model. The variabilities are quite large and appear to be positively correlated with temperature (Fig. 2(b)). The OBTM data thus appear to be affected by temperature-induced noises relatively more than does the Paros pressure measurement system, at least for periods longer than a few days. These results indicate an insufficiency in the thermal correction calibration of the HP measurement system.

*et al.*, 1984; Tamura

*et al.*, 1991). For example, barometric effects can be well corrected in sea level, strain, and gravimetric data by referring to surface air pressure data at neighboring points. We then use the BAYTAP-G program to examine the OBTM data with, and without, reference to the temperature data (Fig. 3). In the case of referring to the temperature data, the effect of temperature is effectively removed in the OBTM data, more so than in the case without reference to the temperature data; however, discernible temperature effects still remain. The relationship between the OBP and temperature strongly depends on frequency, as will be described in the next section. Since the BAYTAP-G program models the effects of ambient data as an impulse-response function in the whole frequency domain, this approach may not effectively work when the correlation between the OBP and temperature strongly depends on frequency.

We will investigate the temperature dependency of the OBTM data in terms of temporal changes and frequencies in Section 4, and correct the OBTM data using the estimated temperature dependencies in Section 5.

## 4. Lagged Correlation Analysis of the OBTM Data: Relationship between OBP and Temperature

We examine the relationship between the OBP and temperature records obtained by the OBTMs. The detided OBP is compared with the temperature in terms of a regression coefficient and lag. The lag is defined by the maximum positive lagged correlation between the OBP and the temperature, and its sign is defined to be positive when the OBP variation lags behind the temperature. The regression coefficient is calculated based on a least-squares method with the maximum lagged correlation. The analysis is carried out in both the time and frequency domains.

### 4.1 Year to year change

For TM1, the mean OBP gradually increases at a rate of about 5 hPa/year, while no increase of the mean temperature is evident. Similar results are found for MPG1 and MPG2. The mean OBPs of KPG1 and KPG2 show sudden decreases from 2003 to 2004, corresponding to the co-and post-seismic uplift of seafloor due to the 2003 Tokachioki earthquake (Baba *et al.*, 2006). Gradual increases of the mean OBP are nonetheless distinct for the stations before the earthquake. The mean OBP and the mean temperature of TM2 show remarkable changes from 2005 to 2008: the mean OBP decreases at a rate of ∼100 hPa/year, and the bottom temperature decreases at a rate of 0.2°C/year at 1000-m depth without recovery. Since no evidence of vertical seafloor movements (e.g., large earthquake occurrences and/or systematic crustal movements detected by other geodetic measurements) has been reported, it is tentatively concluded that the TM2 data are very unstable and unreliable for studying long-term variations in OBP and temperature. Except for TM2, the mean OBPs show exponential-like increases. The long-term OBP changes seem unrelated to the temperature changes, and are possibly caused by aging due to creep of the pressure-transducer materials (e.g., Eble *et al.*, 1989) and/or burial of the instruments after deployment. Although similar exponential-like temporal changes are also found in the regression coefficients, it is unclear if there is any relationship between the temporal changes in the regression coefficients and those in the mean OBPs.

From the current evaluation, we suggest that these OBTM data point to difficulties in detecting seafloor deformation due to tectonic motions which are expected to show rates of a few cm/year (e.g., Fujita *et al.*, 2006; Matsumoto *et al.*, 2008; Watanabe *et al.*, 2009; Sato *et al.*, 2011). Yearly changes of the mean OBP recorded by the CTDs (Paros measurement system) also show similar long-term changes but their rates are relatively smaller (less than ±2 hPa/year). Drift rates of the Paros OBP data have been investigated and reported to be less than tens of hPa/year (e.g., Watts and Kontoyiannis, 1990; Polster *et al.*, 2009).

### 4.2 The relationship depending on frequency

Cutoff frequencies for high-pass, band-pass, and low-pass filters. *ω*_{
H
} and *ω*_{
L
} are the cutoff frequencies at the high- and low-frequency sides, respectively. Units are hours along time axis.

ω | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 5 | 11 | 13 | 23 | 27 | 36 | 48 | 48 | 120 | 200 | 300 |

ω | 0.25 | 0.5 | 1 | 2 | 3 | 4 | 7 | 11 | 13 | 23 | 27 | 48 | 72 | 120 | ∞ | ∞ | ∞ | ∞ |

^{−1}, both the regression coefficients and the lags asymptotically approach zero. The regression coefficients and the lags gradually increase at frequencies from 10

^{0}to 10

^{−1}hour

^{−1}. At frequencies lower than 10

^{−2}hour

^{−1}, the regression coefficients are almost constant at their maxima, while the lags tend to flip and become negative with large error margins. A negative lag indicates that the temperature changes arise from the OBP changes. An oceanic process related to temperature may cause a negative lag. If the oceanic process involves substantial magnitudes of OBP, the OBP signals originating from temperature changes are identified with difficulty and have large error margins. A possible explanation for the negative lag will be given later.

The regression coefficients estimated at low frequencies (< ∼1 day^{−1}) may not be reliable because the estimated lags have large errors. Here, the regression coefficients are re-estimated assuming that the lag is zero (Fig. 5). At low frequencies, the re-estimated regression coefficients are equivalent to those estimated based on the maximum lagged correlation. So, the actual lags at low frequencies are expected to have maxima of tens to hundreds of minutes for the respective OBTMs. Compared with the periods of several days, the several-hour lags are relatively small in phase dimension. Thus, the regression coefficients are relatively constant at their maxima at low frequencies.

^{−1}). This feature is common for the other OBTMs. It is unclear why the regression coefficient, i.e., the relationship between the OBP and temperature, becomes interannually stronger at low frequencies.

At tidal frequency bands, the estimation based on the maximum lagged correlation is not robust probably due to remaining ocean tide components. The noise level at the tidal frequency bands will be examined by a tidal analysis in Section 6.

We speculate on the cause of the negative lag estimated at the low frequencies (< ∼1 day^{−1}). The negative lag is not expected to originate from the thermal response of the sensor with a finite delay time. At low frequencies, the effects of the thermal response may be relatively negligible compared to substantial oceanic signals. Niiler *et al.* (1993) remarked that barotropic OBP variations due to water convergence/divergence, with periods of days, are mainly induced by synoptic wind-stress curl fields. For example, water convergence related to a negative wind-stress curl field induces sea-level elevation. This water convergence results in an increase of OBP and a downward movement of water that may contribute to an increase of the bottom temperature, since the temperature of the upper layer is usually warmer than that of the bottom water. This succession could account for the negative lags, i.e. the increase (decrease) of OBP leading the increase (decrease) of the bottom temperature.

## 5. Usefulness of the OBTM Data after Temperature Corrections

*r*and τ are the regression coefficient and the lag, respectively.

*P*

_{corrected}(

*t*),

*P*

_{uncorrected}(

*t*), and

*T*(

*t*) denote the corrected pressure, uncorrected pressure, and the temperature time series, respectively. Figure 7 shows the amplitudes at the various frequency bands, like a variance-preserving power spectrum, of the corrected and uncorrected OBTM data, and those of the temperature data in 2009. The amplitudes of the Paros OBP data, obtained at the neighboring sites, are also shown for comparison. At low frequencies (<10

^{−2}hour

^{−1}), both the corrections yield a reduction in the amplitude of tens of a percent, and therefore the zero-lag correction works well in practice. The correction by Baba

*et al.*(2006) is equivalent to the zero-lag correction. At high frequencies (>10

^{−2}hour

^{−1}), the correction using the estimated pairs of the regression coefficient and the lag yields a greater reduction in the amplitude than does the zero-lag correction. However, the correction seems largely ineffective at frequencies higher than 10

^{0}hour

^{−1}. In the following subsections, we compare the corrected OBTM data with the Paros OBP data within distances of a few hundreds of kilometers from the OBTMs, and evaluate the utility of the OBTM data at low and tsunami frequencies (Fig. 7(a)).

### 5.1 Low frequency (<1 day^{−1})

^{−1}for which the correction is expected to be effective. Only the amplitude of the corrected KPG2 data is equivalent to that of the Paros data (KCTD). In Fig. 8, time series from KPG2, KCTD, and NMS09 are compared at frequencies of lower than 0.5 day

^{−1}. Similar variations are found among the Paros data (KCTD and NMS09) and the KPG2 data corrected by the zero-lag regression coefficient. Although the amplitude of the corrected KPG2 data is still a little greater than that of the Paros data, it can be concluded that the corrected KPG2 data enable the successful detection of low-frequency variations (days to weeks) of centimeters caused by oceans, or crustal level changes (e.g., Asano

*et al.*, 2008).

### 5.2 Tsunami frequency (>2 hour^{−1})

At frequencies higher than 1 hour^{−1}, no significant amplitude reduction in the corrected OBTM data is perceived compared with the uncorrected OBTM data, and the corrected, or uncorrected, OBTM data show noise levels equivalent to those of the Paros data (Fig. 7(a)). So, this overall correction seems ineffective and, therefore, unnecessary at high frequencies. Meanwhile, Hirata and Baba (2006) remarked that the OBTM data should be carefully corrected for the analysis of small tsunamis, since rapid temperature changes (e.g., ±0.005^{°}C/min) frequently occur. They analyzed the effects of the rapid temperature changes for KPG1 and KPG2 using a convolution method. In the present study, the effectiveness of the correction using the regression method is re-evaluated for a tsunami frequency band when the temperature rapidly changes.

^{−1}(<30 minutes) is defined as the tsunami frequency (e.g., Ward, 2001). (3) The regression analysis and the correction are performed on the highpass filtered time series of the OBP and the temperature data during a two-day interval including each rapid-temperature-change event. A suite of these analyses is carried out for all the OBTM data. Table 3 summarizes the regression analysis and compares this with the results of the overall analysis shown in Fig. 7. First, we consider the temperature variations and then indicate the results of the correction.

Results of the correction applied to the OBTM data at the tsunami frequency (>2 hour^{−1}). The results of the overall correction based on the analysis shown in Fig. 7 are also shown at the second line of each OBTM site. Temperature increase and decrease denotes total numbers of the rapid temperature increases and decreases that occurred during the entire observing periods. Numbers in brackets are standard deviations of the estimates. Reduction rates are defined as

Site | Temperature | Regression coefficient | Lag | Uncorrected SD | Reduction rate | |
---|---|---|---|---|---|---|

Increase | Decrease | (hPa/°C) | (min) | (hPa) | (%) | |

TM1 | 0 | 21 | 15.609 (6.120) | 10.2 (3.4) | 0.117 (0.031) | 5.1 |

10.349 (3.225) | 8.0 (0.9) | 0.118 (0.014) | 0.8 | |||

TM2 | 3 | 42 | 11.147 (6.356) | 8.9 (4.8) | 0.146 (0.053) | 2.1 |

5.774 (2.119) | 7.6 (1.4) | 0.133 (0.020) | 0.8 | |||

MPG1 | 10 | 469 | 25.352 (6.928) | 8.9 (4.0) | 0.102 (0.048) | 6.9 |

21.057 (2.991) | 9.5 (0.3) | 0.098 (0.029) | 2.0 | |||

MPG2 | 2037 | 4904 | 18.442 (4.114) | 9.4 (2.4) | 0.109 (0.092) | 10.1 |

17.441 (1.320) | 9.3 (0.3) | 0.110 (0.015) | 6.4 | |||

KPG1 | 29 | 441 | 10.381 (2.154) | 11.2 (5.1) | 0.081 (0.033) | 3.7 |

9.033 (0.250) | 10.1 (0.2) | 0.084 (0.005) | 1.2 | |||

KPG2 | 1 | 31 | 18.286 (4.172) | 2.1 (5.4) | 0.088 (0.027) | 5.7 |

17.588 (1.075) | 0.0 (0.1) | 0.086 (0.007) | 1.2 |

The rapid temperature changes appear as decreases more frequently than as increases at all the stations. This tendency is probably general, rather than found only at KPG1 and KPG2, as pointed out by Hirata and Baba (2006). It is plausible that cold, dense water penetrates to the sea bottom more easily than does warm, less dense water, after mixing processes near the bottom boundary layer, although the detailed mechanism is poorly understood. Of the six OBTMs, the MPG2 records experience rapid temperature changes most frequently of the order of once a day. This result is anticipated from Fig. 7(b). The MPG2 data show the largest amplitude of temperature variations at the tsunami frequency. In addition, we can see that the variabilities in temperature indeed differ from station to station. The temperature variabilities may be strongly localized by instrument installation: small-scale seafloor undulations (e.g., Hirata and Baba, 2006), depths, seafloor sediments, and the possible burial of sensors.

As shown in Table 3, the regression coefficients and the lags estimated event-by-event are quantitatively equivalent to those based on the overall regression analysis, the results of which are shown in Fig. 5. The regression coefficients calculated here may be a little greater on average than those based on the overall regression analysis, but their differences are within the error margins. The regression coefficients and the lags listed in Table 3 are expected to be useful in practice, not only for tsunami analyses but also in a correction procedure for real-time OBTM data processing to help avoid false tsunami alarms in an early tsunami warning system (Tsushima *et al.*, 2009).

## 6. Tidal Frequency Bands—Evaluating Seasonal Variations of Tidal Constituents

_{2},S

_{2},K

_{1}, and O

_{1}) are calculated by the BAYTAP-G program (Fig. 11). A time series of three months is used to calculate the amplitude and phase of the tidal constituents for the middle month. The tidal analysis using the BAYTAP-G program preliminarily calculates equilibrium tides correcting the effect of an 18.6-year nodal modulation (Tamura, 1987). We can note pronounced seasonal variations of the tidal constituents rather than interannual variations. The range of the seasonal variations is of the order of 1 hPa for amplitude and 1 degree for phase.

Seasonal variations of ocean tides have been reported in terms of sea level by a number of studies (e.g., Tamura, 1985; Pugh, 1987; Kang *et al.*, 1995, 2002; Leeuwenburgh *et al.*, 1999; Blanton *et al.*, 2004) and, in spite of limited studies, in terms of OBP (e.g., Tamura *et al.*, 1986; Blanton *et al.*, 2004). Tamura *et al* (1986) used the OBTM data of JMA (Isozaki *et al.*, 1980) and pointed to a seasonal variation of the M_{2} constituent, without detailed discussions. Blanton *et al* (2004) used sea level and OBP data, and noted a seasonal variation of the M_{2} constituent of the sea level, but hardly described the seasonal variation of the OBP tide because of the short duration of the observations. Although the effects of stratification (Kang *et al.*, 2002) and tide-surge interaction (e.g., Pugh, 1987; Leeuwenburgh *et al.*, 1999; Bernier and Thompson, 2007) have been suggested as causes of the seasonal variation of ocean tides in coastal regions, critical mechanisms have not yet been proposed (Woodworth, 2010). Although, investigating the mechanism of the seasonal modulation of ocean tides is beyond the scope of the present study, we assume that the seasonal variations of the OBP tide should be observed ubiquitously and their detectability is regarded as a measure of the quality of the OBP data at the tidal frequency bands.

Correlation coefficients of monthly variations of tidal constituents calculated from a pair of neighboring stations. The correlation coefficient is calculated by weighting the amplitude of four major tidal constituents (M_{2}, S_{2}, K_{1}, and O_{1}). The correlation coefficients in excess of a 99.5% confidence level are marked. The correlation coefficient between KCTD and NMS09 is blank due to the short data length.

Sites | Data number | Correlation coefficient | 99.5 % confidence level | |
---|---|---|---|---|

OF | AY | 94 | 0.66 | X |

MU | KC | 74 | 0.60 | X |

KR | HN | 94 | 0.48 | X |

GJT3 | GJT4 | 15 | 0.96 | X |

GJT3 | TM1 | 15 | 0.78 | X |

GJT3 | TM2 | 15 | 0.60 | |

MCTD | PKMN06 | 13 | 0.77 | X |

MCTD | MPG1 | 20 | 0.25 | |

MCTD | MPG2 | 20 | 0.26 | |

KCTD | NMS09 | 6 | _ | |

KCTD | KPG1 | 39 | 0.46 | |

KCTD | KPG2 | 39 | 0.76 | X |

## 7. Summary

We investigated the six OBTM data that include significant dependency on the change of the built-in thermometer output. The OBTM data show spurious signals which are positively correlated with the temperature and lag behind the temperature by tens of minutes. In the present study, this relationship was characterized by the regression coefficient and the lag between the OBP and the temperature. The relationship depends on frequency, and becomes stronger at periods from hours to days. The relationship at frequencies lower than ∼1 day^{−1} secularly becomes strong. These relationships differ from station to station. The yearly mean OBPs gradually increase at rates of the order of 1 hPa/year, possibly due to aging of the measurement system. Thus the OBTM data involve difficulties in detecting seafloor deformation due to tectonic motions.

The OBTM data were corrected based on the estimated relationship. The usefulness of the corrected OBTM data was evaluated by comparison to the Paros OBP data which have relatively low instrumental noises. At frequencies of lower than ∼1 day^{−1}, the corrected data show a reduction in amplitude of the order of a few tens of a percent, but are several times noisier than the Paros data. Only the corrected KPG2 data show amplitudes almost equivalent to that of the Paros data, and could be useful for detecting several-centimeter variations of the ocean, and seafloor deformation, at low frequencies. At frequencies higher than 1 hour^{−1}, the noise levels of the OBTM data were found to be equivalent to those of the Paros data, without the correction. At a tsunami frequency range (>2 hour^{−1}), however, rapid temperature changes in excess of ±0.003^{°}C/min frequently occur, resulting in spurious signals in the OBTM records. The rapid temperature changes occur typically as decreases in temperature. Focusing on the rapid temperature changes, the effectiveness of the correction was re-evaluated, and noise related to the temperature can be reduced by millimeters. We need to carefully analyze tsunamis in OBTM records by correcting the effects of rapid temperature changes, especially for the MPG2 data in which a number of rapid temperature changes occur.

A correction for tidal frequency bands has not been proposed in this study. However, tidal analyses have suggested that the TM1 and KPG2 data could be used to study temporal variations of tidal constituents in excess of 1 hPa, even though they are a little noisier than the Paros data. The tidal constituents are known to change seasonally (e.g., Kang *et al.*, 2002), interannually (e.g., Munk *et al.*, 1965), and secularly (e.g., Ray, 2006, and references therein) although their mechanisms are still poorly understood. Even the theoretically expected 18.6-year nodal modulation has recently been paid attention in relation to bi-decadal climate changes (e.g., Osafune and Yasuda, 2006; Ray, 2007). It is expected that such OBTM data in excess of 10-year durations will yield valuable information for tidal studies.

Similar investigations of other OBTM data from the cabled systems around Japan (see Hirata *et al.*, 2009) will be awaited in order to examine their potential applicability to oceanography and geodesy, as well as seismology. In addition, the recent cabled systems of HPG, other CTDs, and the Dense Oceanfloor Network System for Earthquakes and Tsunamis (DONET) (Araki *et al.*, 2008) using the Paros sensors, as well as the DART system, are expected to be of use in a wide range geophysical applications.

## Declarations

### Acknowledgements

We thank Ichiro Takahashi and Toshitaka Baba of JAMSTEC for kindly providing the data obtained from the cabled systems operated by JAMSTEC, and Hiromi Fujimoto and Yukihito Osada of Tohoku University for providing the OBP data obtained from their observations. Hiroaki Tsushima of MRI/JMA (Meteorological Research Institute) and Syuichi Suzuki of Tohoku University helped for handling the OBTM data operated by ERI. We also thank JMA for the presentation of the tide gauge data. The author, Daisuke Inazu, thanks Tadahiro Sato of Tohoku University for gracious discussions on tidal analyses. Comments and suggestions from William W. Chadwick Jr. and an anonymous reviewer improved this presentation. This study was funded by a MEXT (Ministry of Education, Culture, Sports, Science and Technology of Japan) project entitled “Research concerning Interaction between the Tokai, Tonankai and Nankai Earthquakes”. All the figures in this paper were produced using Generic Mapping Tools.

## Authors’ Affiliations

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