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 Bi-decadal climate variation is dominant over the North Pacific on inter-decadal timescale; however the mechanism has not been fully understood. We here find that the bi-decadal variations in the North Pacific climate and intermediate waters possibly relate to the 18.6-year period modulation of diurnal tide. In the period of strong diurnal tide, tide-induced diapycnal mixing makes surface salinity and density higher and the upper-layer shallower along the Kuril Islands and the east coast of Japan. Simple model results suggest that the coastal depth adjustment by baroclinic Kelvin waves enhances the thermohaline circulation, the upper-layer poleward western boundary current and associated heat transport by about 0.05PW. This could also explain the warmer SST in the Kuroshio-Oyashio Extension regions, where positive feedback with Aleutian Low might amplify the bidecadal variations. The 18.6-year tidal cycle hence could play a role as a basic forcing for the bi-decadal ocean and climate variations.
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 Bi-decadal climate variability is known to be dominant on inter-decadal timescale over the North Pacific [e.g., Cook et al., 1997, hereinafter referred to as C97; Minobe et al., 2002, and references therein, hereinafter referred to as M02]. The bi-decadal fluctuation has been explained by mid-latitude air-sea interactions with oceanic Rossby waves and boundary current fluctuations [Latif and Barnett, 1994], oceanic subduction and thermal anomaly advection leading to ENSO-decadal modulation and solar 11/22-year cycles. However, ENSO does not have a bi-decadal spectrum peak, and the solar cycle does not follow the bi-decadal SST variability in the early 19th century [White et al., 1997]. We thus have had no definitive answer what causes the bi-decadal variation and what provides the time-scale. 18.6-year period nodal cycle found by James Bradley [Phil. Trans. XLV, 1, 1748] (henceforth “18.6-year cycle”) is one candidate for the bi-decadal climate variability.
 The 18.6-year cycle is caused by the lunar orbital fluctuation around the earth: the moon's orbital surface is inclined by the mean of 23.4 degrees to the earth equatorial surface and this inclination fluctuates from 18.3 to 28.6 degrees with the period of 18.613 years [Doodson, 1927; Loder and Garrett, 1978, hereinafter referred to as LG78]. The bidecadal signals that seem to be related with the 18.6-year cycle have been detected in the long-term records of atmosphere and ocean, particularly in mid-high latitudes [Maximov and Smirnov, 1965; Currie and O'brien, 1988; Royer, 1993; LG78]. However, since there has been no theory that bridges the nodal cycle with the climate bi-decadal variability, no one could have confidently insisted on the influence on the climate.
 The 18.6-year cycle causes the long-term fluctuations of oceanic tides, especially for the diurnal components of K1 and O1 whose amplitudes are modulated by up to 20% (LG78); the modulation takes maximum at 45 degrees latitude [Doodson, 1921]. Diurnal tidal flows are large around islands and straits in mid-high latitude oceans because of the resonance between coastally trapped waves and subinertial diurnal tidal waves [Chapman, 1989]. Around the Kuril Islands bordering the North Pacific and the Okhotsk Sea (see Figure 1 for locations), huge diapycnal mixing with the coefficient over 1000 cm2/s due to strong diurnal tidal flows is predicted using numerical models [Nakamura et al., 2000]. The strong tidal mixing around the Kuril Islands can be seen in spring-fall SST around Kuril Islands where the tidal mixing brings subsurface cold water into surface to cause the cold water distribution (not shown). The strong diapycnal mixing can drive the thermohaline circulation which has crucial roles in producing North Pacific Intermediate Water (NPIW) [Tatebe and Yasuda, 2004; Nakamura et al., 2004] that is characterized by intermediate salinity minimum and distributed widely in the subtropical North Pacific. Diurnal tidal flows and diapycnal mixing in the Okhotsk Sea and Bering Sea are reported to be strong [e.g., Nakamura et al., 2000]. Since the strong diurnal tidal flow changes its amplitude by 20%, it could be expected that the 18.6-year cycle changes the intermediate waters and large-scale oceanic circulation in the North Pacific.
Osafune and Yasuda [2006, hereinafter referred to as OY06] showed the bi-decadal variations in the intermediate waters and surface salinity in the north-western subarctic Pacific and the Okhotsk Sea, and the relationship between the bidecadal variations and the 18.6-year period nodal tidal cycle. They indicated that relatively new intermediate water formation with higher salinity and oxygen and lower nutrient is enhanced in the Okhotsk Sea, and its outflow transport to the Pacific is increased to make Oyashio intermediate water with higher oxygen and lower nutrient and colder temperature in years of strong diurnal tide. This consistently explains the bidecadal variations in the North Pacific subarctic intermediate waters reported by Ono et al. .
 In the present paper, we will study on the relationships between the 18.6-year period nodal tidal cycle and North Pacific climate variability and between the nodal cycle and thermohaline circulation related with North Pacific Intermediate Water formation. We then try to explain the bi-decadal climate variations by the nodal tidal cycle. We here show the evidences that the bidecadal ocean/climate variations are related with the 18.6-year cycle and propose a possible theory linking the 18.6-year cycle with the bi-decadal ocean/climate variations through the oceanic tidal mixing and the heat transport change through the changes in the oceanic western boundary currents and air-sea interaction.
 We compare the time-series of the band-passed filtered (11.6–25.6 year-period) bi-decadal component of winter (January–March)- NPI, PDO and MOI with the 18.6-year nodal tidal cycle, where NPI (North Pacific Index) is sea-level pressure (SLP) anomaly averaged in 30–65°N, 160°E–140°W, PDOI (Pacific Decadal Oscillation Index: first principal component of North Pacific sea surface temperature) and MOI (East-Asian Monsoon Index: SLP difference between Irkutsk and Nemuro). We found the bidecadal variations of the climate indices correspond to the 18.6-year nodal cycle (Figure 2a). These climate indices commonly have a bidecadal signal peak at around 17–20-year period surrounded by troughs at around 11 and 25-years periods during 1930–2000 (C97, M02). In years when the diurnal tide is strong, the wintertime Aleutian Low and the winter East-Asian Monsoon wind are weak, and PDO is negative. The maximal diurnal tide in mid-high latitude in 1932, 1951, 1969 and 1988 (LG78) corresponds to the positive-NPI, negative-MOI and negative-PDOI. The minimum in 1941, 1960, 1978/79 and 1997 also corresponds to the opposite sign of the climate indices. During 1900–1930, bidecadal signals were weak (C97, M02); this might be due to the superposition of the 18.6-year and the solar 22-year cycles (C97).
 Differences in winter- SST and SLP distributions between the periods of strong and weak diurnal tides are depicted in Figure 1 on the basis of bandpass-filtered (11.6–25.6-year period) February-SST and SLP data (SLP is from NCEP/NCAR reanalysis data [Kalnay et al., 1996] and SST from GISST.2.2). This distribution shows the pattern similar to the one in the negative-PDO phase where the winter-SST anomaly in the western-central North Pacific in 25°–45°N is positive and the Aleutian Low is weaker in years of the strong diurnal tide. The weaker Aleutian Low causes weaker north-westerly winter East-Asian Monsoon wind that can maintain the warm-SST anomalies in the Kuroshio-Oyashio Extension areas east of Japan (145–180°E, 35–45°N).
 The 18.6-year cycle is detected in the thickness of the upper and intermediate layers in the Okhotsk Sea, on the Pacific side of the Kuril Islands and in the Oyashio east of Japan (Figure 2b) using the individual profile data of temperature and salinity based on World Ocean Database 2001 [Conkright et al., 2002] and see OY06 for data processing. During the periods when the diurnal tide is stronger (weaker), the intermediate layer between 26.7–27.2σθ is thicker (thinner) whereas the upper layer thickness from surface to the depth at 26.7σθ is thinner (thicker). The increase of the intermediate layer thickness corresponds to the decrease in the thickness of the upper and deep layers. The shallower isopycnal depth at 26.7σθ distributed around the Kuril Islands and the east coast of Japan as depicted in Figure 3. The thinner deep layer in 27.2–27.4σθ is possibly caused by the enhanced diapycnal upwelling from deep to intermediate layers due to stronger tidal mixing.
 These thickness changes suggest that the oceanic thermohaline circulation could be strengthened in the period of strong diurnal tide: strong tidal mixing around the Kuril Islands and Aleutian Islands and along the coasts of Bering Sea and Okhotsk Sea makes upper layer salinity higher and denser. This suggests that the diapycnal transport from upper to intermediate layer is enhanced in the subarctic area and also suggests that dense shelf water formation around the north-western shelves in the Okhotsk Sea could also be enhanced [Nakamura et al., 2004]. This enhanced thermohaline circulation could be accompanied by the changes of the poleward heat transport, because the sinking from surface to intermediate layers (see vertical red arrow in Figure 4) could be compensated by the poleward warm-water transport in the upper layer (orange horizontal arrow) and equatorward cold-water transport in the intermediate layer (light-blue horizontal arrow) in the North Pacific.
 To confirm the influence of the layer-thickness variations on the ocean circulation and heat transport, we performed simplified layered numerical model experiments. Of course, more realistic models would be desirable; but we here keep the story as simple as possible to be able to be checked by future detailed studies. We employed a three-layer primitive equation ocean model with horizontal 0.25° by 0.25° grids in 120°E–75°W and 10°S–65°N, realistic coastal and bottom topography, and forced by annual mean NCEP/NCAR reanalysis wind-stress data. See Tatebe and Yasuda  for the details of the model configurations. In the Okhotsk Sea, the thickness of the surface and intermediate layers are restored to the observed ones, and the diapycnal transport is evaluated. The observed thickness differences are 50 m and 100 m for the upper and intermediate layers respectively between the periods of strong and weak diurnal tide as observed in Figure 2b. The diapycnal transport is compensated by the meridional transport across the southern open boundary at 10°S. Based on the model poleward velocity field multiplied by the corresponding temperature field from World Ocean Atlas 1994 [Levitus and Boyer, 1994], we estimated poleward heat transports and its difference between in the cases of strong and weak tide.
 The diapycnal transports in the Okhotsk Sea in the model experiments are as follows. In the case of strong diurnal tide, the sinking transport from upper to intermediate layers across 26.7σθ isopycnal surface W1 = 2.8 Sv and the diapycnal upwelling transport from deep to intermediate layer across 27.2σθ surface W2 = 1.0 Sv (roughly corresponds to the diapycnal coefficient of 50 cm2/s around Kuril Straits); whereas in the case of weak diurnal tide W1 = 1.2 Sv and W2 = 0.5 Sv. The increased sinking rate of 1.6 Sv and upwelling rate of 0.5 Sv both indicate the enhanced equatorward intermediate water transport. This corresponds to the enhanced circulation of North Pacific Intermediate Water in the real ocean. These results are obtained from variable thicknesses restored in the Okhotsk Sea with the same wind-stress fields.
 The poleward heat transport estimated from the model results (Figure 5) suggests that the heat transport is increased by about 0.05PW south of 40°N between in the cases of strong and weak diurnal tide. Increased poleward transport of upper-layer warm water and equatorward transport of cold intermediate layer (Figure 4) both indicate the increased poleward heat transport in the North Pacific. The 0.05 PW increase in the poleward heat transport possibly influences climate variations, because this amount is about 10% of the North Pacific poleward heat transport in the model (Figure 5) and observations (0.45–0.76 PW across 24°N in the North Pacific [e.g., Bryden and Imawaki, 2001]). It is also noted that this enhanced poleward heat transport is concentrated near the western boundary current regions (WBC) (not shown) where large heat exchanges occur between the ocean and atmosphere.
 The enhanced northward WBC in the upper layer can be alternatively explained by the Kelvin-wave adjustment of the shallower upper-layer thickness along the western boundary as seen in the observation (Figure 3) and in the model (not shown). In the period of strong diurnal tide, the signal of the shallower upper-layer thickness due to strong tidal mixing propagates as baroclinic Kelvin waves along the coasts (Figure 4) and leads to the intensification of the poleward WBC (black vertical arrow).
 The change in the poleward heat transport along the WBC associated with the 18.6-year cycle could be related with the bi-decadal climate variability. During the period when the diurnal tide is stronger, greater poleward oceanic heat transport could bring about warmer-SST as observed in the Kuroshio-Oyashio Extension regions east of Japan (Figures 1 and 4). Since the weaker Aleutian Low and East-Asia winter monsoon winds can make the SST further warmer, a positive feedback possibly amplifies the 18.6-year period signal (Figure 4). Although the mechanism of the co-variation between the SST and Aleutian Low is still not fully understood, the recent analysis that the autumn warmer SST leads to winter weaker Aleutian Low through the changes of storm-track activity and associated eddy heat transport (A. Gotoh and H.Nakamura, personal communication, 2005) and air-sea coupled model results [e.g., Latif and Barnett, 1994] suggest the positive feedback plays a role in the mid-latitude ocean-atmosphere system. Air-sea coupled model experiments with variable tidal mixing coefficients around the Kuril Islands are now going on to elucidate the influence of 18.6-year cycle on climate.
Cerveny and Shaffer  reported a statistical link between the lunar nodal modulation and ENSO; large El Nino events occurred within a few years of the minimum diurnal tides. The large ENSO events might occur in association with the observed deeper isopycnal depth at 26.7σθ due to the weaker tidal mixing and Kelvin-wave adjustment along the western boundary. This needs further studies.
 We have focused on the North Pacific. The 18.6-year tidal cycle generally occurs in the mid-high latitude oceans and possibly influences on the large-scale oceanic circulations and climate variability as shown in the present study. If the present hypothesis is validated, we will have a precise time-table for the bi-decadal climate variations because the nodal cycle is accurately predictable. This would greatly contribute to improving climate predictability. To validate the hypotheses, we need to further explore many issues: tidal mixing hot spots, oceanic tidal mixing versus atmospheric influences, boundary currents changes, air-sea interactions in the Kuroshio Extension regions related to Aleutian Low, and relation with ENSO, ecosystem and carbon cycles etc.
 This work was supported from KAKEN (#17253004) and also from the ODATE and DEEP. The authors thank Dr. Skip Mackinnel for valuable discussion on the 18.6-year tide.