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Abstract: The tide plays a pivotal role in the ocean, affecting the global ocean circulation and supplying the bulk of the energy for the global meridional overturning circulation. To further investigate internal tides and their impacts on circulation, it is imperative to incorporate tidal forcing into the eddy-resolving global ocean circulation model. In this study, we successfully incorporated explicit tides (eight major constituents) into a global eddy-resolving general ocean circulation model and evaluated its tidal simulation ability. We obtained harmonic constants by analyzing sea surface height through tidal harmonic analysis and compared them with the analysis data Topex Poseidon Cross-Overs v9 (TPXO9), the open ocean tide dataset from 102 open-ocean tide observations, and tide gauge stations from World Ocean Circulation Experiment. The results demonstrated that the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics/Institute of Atmospheric Physics (LASG/IAP) Climate System Ocean Model 3.0 (LICOM3.0) effectively simulated tides, with errors predominantly occurring in nearshore regions. The tidal amplitude simulated in LICOM3.0 was greater than that of TPXO9, and these high-amplitude areas exhibited greater errors. The amplitude error of the M2 constituent was larger, while the phase error of the K1 constituent was more significant. Furthermore, we further compared our results with those from other models.
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Key words:
- tide /
- eddy resolution /
- ocean general circulation models /
- harmonic analysis /
- LICOM3.0
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Figure 1. Changes in the sea surface caused by the equilibrium tide calculated by the LICOM3.0 tidal module: the results during a spring tide at 04:00, 10:00, 16:00, and 22:00 (a–d) and the results during a neap tide at 00:00, 06:00, 12:00, and 18:00 (e–h). Time in UTC+0.
Figure 2. Spatial patterns of the amplitude (colored, cm) and phase (contour, °) characteristics of the M2 constituent for TPXO (a) and LICOM3.0 (b) and of the K1 constituent for TPXO (c) and LICOM3.0 (d). The black solid lines are separated by 30°.
Figure 3. Errors of the simulated M2 constituent (a–c) and K1 constituent (d–f) relative to TPXO in LICOM3.0: amplitude error (a, d), phase error (b, e), and total error (c, f).
Figure 4. Spectral analysis of sea levels observed (obs) by Yap (
9.5083 °N,138.1283 °E) and Kodiak (57.7317 °N,152.511 7°W) in WOCE (Ponchaut et al., 2001) and simulated by LICOM3.0. Table 1. Calculation formulas for the nodal factor f and the nodal angle μ
Constituent f μ/(°) K1 1.0060 +0.1150 cos$ {N}_{0} $ –0.0088 cos(2$ {N}_{0} $) +0.0006 cos(3$ {N}_{0} $)–8.86° sin$ {N}_{0} $ + 0.68° sin(2$ {N}_{0} $) − 0.07° sin(3$ {N}_{0} $) O1 1.0089 +0.1871 cos$ {N}_{0} $ −0.0147 cos(2$ {N}_{0} $) +0.0014 cos(3$ {N}_{0} $)10.80° sin$ {N}_{0} $ − 1.34° sin(2$ {N}_{0} $) + 0.19° sin(3$ {N}_{0} $) P1 1 0 Q1 same as O1 same as O1 M2 1.0004 −0.0373 cos$ {N}_{0} $ +0.0003 cos(2$ {N}_{0} $)–2.14° sin$ {N}_{0} $ S2 1 0 N2 same as M2 same as M2 K2 1.0241 +0.2863 cos$ {N}_{0} $ +0.0083 cos(2$ {N}_{0} $) −0.0015 cos(3$ {N}_{0} $)–17.74° sin$ {{N}}_{0} $ + 0.68° sin(2$ {N}_{0} $) − 0.04° sin(3$ {N}_{0} $) 
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Table 2. Total (d), amplitude (da), and phase (dp) errors of the four major constituents of LICOM3.0 relative to TPXO
Experiment Error/cm M2 S2 K1 O1 d da dp d da dp d da dp d da dp wd0.5 9.86 7.21 5.37 5.12 4.00 2.47 3.58 2.36 2.25 2.59 1.26 1.99 wd1 10.70 8.16 5.45 5.38 4.25 2.57 3.77 2.49 2.36 2.57 1.25 1.94 wd1.5 11.39 8.88 5.59 5.59 4.43 2.67 3.92 2.59 2.45 2.57 1.26 1.91
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Table 3. Phases-dependent
$ {V}_{0}+\mu $ and nodal factor f values of each constituent calculated by DFO, tidal harmonic analysis program UTIDE and LICOM3.0 tidal module in 2016, corresponding to the dates of January 1 and July 1 of that yearConstituent ($ {V}_{0}+\mu $) (Jan. 1)/(°) f (Jul. 1) DFO UTIDE LICOM3.0 DFO UTIDE LICOM3.0 M2 210.745 210.729 210.857 1.037 1.037 1.037 K1 9.242 9.227 9.299 0.886 0.886 0.886 O1 202.050 202.106 202.000 0.809 0.809 0.813 S2 0.001 0 0 0.998 0.998 1.000 P1 349.847 349.852 349.903 1.011 1.011 1.000 Q1 43.050 43.384 41.752 0.821 0.823 0.813 N2 50.690 50.690 50.610 1.037 1.037 1.037 K2 198.451 198.412 198.722 0.752 0.752 0.755
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Table 4. Errors relative to TPXO in LICOM3.0 and ICON-O (von Storch et al., 2023), including total error
$ d $ , amplitude error$ {d}_{\mathrm{a}} $ , and phase error$ {d}_{\mathrm{p}} $ Constituent Error/cm LICOM3.0 ICON-O $ d $ $ {d}_{\mathrm{a}} $ $ {d}_{\mathrm{p}} $ $ d $ $ {d}_{\mathrm{a}} $ $ {d}_{\mathrm{p}} $ M2 10.19 6.83 6.09 14.25 10.63 9.39 K1 2.85 1.66 1.92 4.60 3.26 3.25 O1 4.30 2.55 2.98 5.19 3.89 3.43 S2 5.37 3.12 3.84 7.90 4.71 1.50 P1 1.12 0.52 0.86 1.49 1.08 1.02 Q1 0.77 0.47 0.56 0.86 0.48 0.72 N2 1.51 0.87 1.06 2.30 1.50 1.74 K2 1.19 0.78 0.73 2.30 1.19 1.96
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Table 5. Signal
$ S $ , total error$ d $ , amplitude error$ {d}_{\mathrm{a}} $ , and phase error$ {d}_{\mathrm{p}} $ of the eight major constituents of LICOM3.0 relative to st102 data, the percentages of captured sea surface height variance$ {V}_{\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{t}} $ for each constituent of LICOM3.0, STORMTIDE (Müller et al., 2014), and HYCOM (Arbic et al., 2010), and the root square sum (RSS) values of the eight major constituentsConstituent and RSS Error/cm $ {V}_{\mathrm{capt}} $/% $ S $ $ d $ $ {d}_{\mathrm{a}} $ $ {d}_{\mathrm{p}} $ LICOM3.0 STORMTIDE HYCOM M2 33.22 13.85 9.56 8.12 82.62 93.9 93.8 K1 11.26 3.44 1.89 2.39 90.67 95.0 95.1 O1 7.76 6.21 3.31 4.62 35.89 83.2 89.7 S2 12.62 6.35 4.33 4.03 74.66 86.9 83.2 P1 3.62 1.61 0.73 1.26 80.22 94.7 95.2 Q1 1.62 1.06 0.66 0.73 57.19 64.7 82.1 N2 6.86 2.02 1.36 1.21 91.07 96.0 95.9 K2 3.43 1.58 1.23 0.74 78.78 89.7 76.9 RSS 39.04 17.11 11.36 10.64 80.76 92.8 92.6
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