Contributions of annual and semiannual tidal constituents to chart datum in the China seas and adjacent waters
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Abstract: Global uniform chart datum (CD) surface construction is the basic upon which to realize various vertical datums transformation, and is of great importance for geospatial data expression under the same vertical datum. Generally, the CD level is computed by developing the function between tidal constituents’ harmonic constants and time, i.e., the lowest astronomical tide is taken as the lowest predicted tide level by adopting the major constituents over a 19-a period. The CD surface prescribed in China is the theoretical lowest tide (TLT) and is calculated using 13 tidal constituents, i.e., short -period (Q1, O1, P1, K1, N2, M2, S2, K2, M4, MS4 and M6) and long-period (Sa and Ssa) tidal constituents. Although the accuracy in determining short-period tidal constituents has improved gradually, the long-period tide has not been studied thoroughly owing to nonstationary and temporal variations. Previous studies have intended to evaluate the effect of Sa and Ssa tides in the determination of the TLT level for the purpose of determining a more accurate CD surface for the China seas and adjacent waters. Here, the parameters of long-period tidal correction and long-period tidal correction rate were treated as the effect of both Sa and Ssa on the TLT, and the TOPEX/Poseidon and Jason series satellite altimetry data ranged from October 1992 to April 2022 were adopted to analyze the contribution of long-period tidal constituents. Results showed that the average long-period correction value is 10.10 cm (range from 8.57 cm to 14.98 cm), and that the average long-period tidal contribution rate is 14.56% (range from 9.09% to 23.97%) in the China seas and adjacent waters. Finally, data from 82 tide gauge station with at least a 1-a record of hourly observations were compared with satellite-derived result. We concluded that the long-period tidal contribution should not be neglected in TLT construction. Furthermore, to reduce tidal datum uncertainty, accurate extraction of long-period tidal constituents should receive closer attentions.
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Figure 1. Tide gauge station distribution in the China seas and adjacent waters. Red dots indicate the Chinese tide gauge stations considered in this study, black triangles identity locations of the GESLA-2 stations, and solid gray lines indicate the TOPEX/Poseidon and Jason primary mission tracks.
Figure 2. Histogram of the time length of tidal observations at the GESLA-2 tide gauge stations.
Figure 3. Satellite-derived tidal amplitudes and phase values of annual (Sa) and semiannual (Ssa) long-period tidal constituents.
Figure 4. Statistics of amplitude values of annual (Sa) and semiannual (Ssa) in offshore (depth < 200 m, a and c) and deep-sea (depth > 200 m, b and d) area.
Figure 5. Long-period tidal constants of annual (Sa) and semiannual (Ssa) tidal constituents at the 82 tide gauge stations.
Figure 6. Spatial distribution of satellite-derived long-period tidal contributions. Colored dots depict results from the tide gauge stations.
Figure 7. Distribution of the long-period tidal constituent contributions to the theoretical lowest tide (TLT).
Figure 8. Annual (Sa) and semiannual (Ssa) tidal amplitude differences as a function of the latitude of the tide gauge stations (a), and the distance between the tide gauge stations and the nearest satellite along-track point (b).
Figure 9. Comparison of long-period tidal contributions between tide gauge results and satellite-derived results.
Table 1. Geographical information and harmonic constants of annual (Sa) and semiannual (Ssa) long-period tidal constituents at the Chinese tidal gauge stations
Station No. Latitude Longitude Sa Ssa Amplitude/cm Amplitude_err/cm Phase Phase_err Amplitude/cm Amplitude_err/cm Phase Phase_err 1 40.30°N 122.10°E 29.12 2.66 201.39° 5.44° 2.89 2.38 32.40° 52.58° 2 39.82°N 124.15°E 27.55 2.72 207.66° 5.83° 3.21 2.31 28.94° 49.13° 3 39.23°N 122.67°E 26.06 2.99 208.31° 11.45° 2.22 2.88 8.46° 31.01° 4 39.21°N 119.01°E 28.27 2.28 204.85° 4.76° 2.79 3.21 352.59° 44.48° 5 38.98°N 117.78°E 29.75 2.10 203.27° 10.51° 3.51 1.80 342.81° 19.70° 6 38.92°N 118.51°E 27.52 2.27 203.63° 10.18° 3.18 2.39 344.52° 38.74° 7 37.83°N 120.74°E 24.82 2.45 210.42° 2.08° 1.39 2.48 346.74° 53.38° 8 37.65°N 120.32°E 25.12 2.15 209.95° 5.45° 1.47 2.18 331.86° 78.95° 9 36.87°N 122.42°E 22.15 2.11 215.09° 6.37° 1.72 1.91 2.79° 47.21° 10 36.27°N 121.38°E 22.38 3.01 216.26° 11.97° 1.48 2.73 351.93° 31.51° 11 30.83°N 121.83°E 19.77 2.15 227.49° 5.44° 2.52 1.97 6.50° 85.80° 12 29.22°N 121.97°E 16.55 2.98 244.01° 11.50° 2.69 2.96 38.39° 33.42° 13 28.69°N 121.47°E 14.19 2.27 253.30° 5.06° 3.76 2.01 23.76° 89.55° 14 26.92°N 120.22°E 13.61 2.78 274.62° 10.96° 4.38 2.56 57.26° 36.11° 15 25.47°N 119.83°E 13.22 2.03 283.79° 8.64° 4.61 2.26 55.42° 17.03° 16 24.88°N 118.95°E 15.07 2.91 296.64° 11.98° 4.87 2.62 60.15° 30.16° 17 23.40°N 117.10°E 13.06 1.79 301.71° 5.08° 5.27 1.71 57.36° 68.61° 18 23.22°N 116.78°E 13.00 2.27 302.15° 8.59° 5.67 2.33 59.45° 52.76° 19 21.02°N 109.12°E 10.01 3.07 273.42° 6.16° 6.03 3.25 86.63° 48.57° 20 20.23°N 110.13°E 10.54 1.42 292.42° 9.10° 6.29 1.46 76.82° 14.69° 21 18.23°N 109.50°E 14.45 2.02 315.19° 4.75° 7.50 2.16 69.13° 60.72° Note: err represents standard error. 
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Table 2. Geographical correction models used for tidal constituent analysis
Geography correction Edit criteria Description min/m max/m Dry tropospheric correction −2.40 −2.10 ECMWF dry tropospheric correction Wet tropospheric correction −0.60 0.00 radiometer wet tropospheric correction Ionospheric correction −0.04 0.04 smoothed dual-frequency ionospheric correction Solid earth tide −1.00 1.00 Elastic response to tidal potential Load tide −0.50 0.50 FES2014a load tide
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Table 3. Length of TOPEX/Poseidon satellite-derived data required to fully separate the 13 tidal constituents (unit: a)
Constituent Ssa Q1 O1 P1 K1 N2 M2 S2 K2 M4 MS4 M6 Sa 1.00 0.23 0.14 0.32 0.90 0.16 0.21 0.19 0.31 0.09 1.51 0.06 Ssa 0.31 0.17 0.47 9.19 0.19 0.26 0.24 0.45 0.10 0.60 0.06 Q1 0.37 0.87 0.32 0.47 1.62 1.04 0.96 0.15 0.20 0.08 O1 0.26 0.17 1.63 0.47 0.57 0.27 0.27 0.13 0.10 P1 0.50 0.31 0.56 0.47 9.19 0.13 0.27 0.07 K1 0.19 0.27 0.24 0.47 0.10 0.56 0.06 N2 0.67 0.87 0.32 0.23 0.14 0.10 M2 2.94 0.60 0.17 0.18 0.09 S2 0.50 0.18 0.17 0.09 K2 0.13 0.26 0.07 M4 0.09 0.17 MS4 0.06
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Table 4. Differences in amplitude (cm) of long-period tidal constituents and theoretical lowest tide (TLT) value obtained from time series records of different time scales
Continuous time length Sa Ssa TLT min max err min max err min max err 1 a −8.53 9.94 2.69 −5.77 5.15 1.95 −26.80 19.06 5.69 2 a −7.25 5.08 1.79 −4.56 3.67 1.37 −26.76 18.61 5.09 3 a −6.40 4.51 1.44 −2.70 3.15 1.09 −23.80 18.12 4.72 5 a −3.46 3.18 1.06 −1.99 2.54 0.89 −12.38 14.47 4.22 10 a −2.05 1.99 0.60 −1.27 1.25 0.43 −8.34 7.40 2.81 18 a −1.06 0.74 0.29 −0.57 0.76 0.19 −1.48 1.68 0.43 Note: err represents standard error.
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Table 5. Average contribution of three types of tidal constituents to the theoretical lowest tide in the four regions of the China seas and adjacent waters
Sea area Eight major constituents contribution/% Shallow water tidal contribution/% Long-period tidal contribution/% Bohai Sea 77.08 2.18 23.97 Yellow Sea 85.78 1.96 15.06 East China Sea 91.80 0.63 10.12 South China Sea 92.87 1.28 9.09
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