Dynamic and regression modeling of ocean variability in the tide-gauge record at seasonal and longer periods
Hill, E. M., R. M. Ponte, and J. L. Davis (2007), Dynamic and regression modeling of ocean variability in the tide-gauge
record at seasonal and longer periods, J. Geophys. Res., 112, C05007, doi:10.1029/2006JC003745.
Comparison of monthly mean tide-gauge time series to corresponding model time
series based on a static inverted barometer (IB) for pressure-driven fluctuations and an
ocean general circulation model (OM) reveals that the combined model successfully
reproduces seasonal and interannual changes in relative sea level at many stations.
Removal of the OM and IB from the tide-gauge record produces residual time series with a
mean global variance reduction of 53%. The OM is mis-scaled for certain regions, and
68% of the residual time series contain a significant seasonal variability after removal of
the OM and IB from the tide-gauge data. Including OM admittance parameters and
seasonal coefficients in a regression model for each station, with IB also removed,
produces residual time series with mean global variance reduction of 71%. Examination of
the regional improvement in variance caused by scaling the OM, including seasonal terms,
or both, indicates weakness in the model at predicting sea-level variation for constricted
ocean regions. The model is particularly effective at reproducing sea-level variation for
stations in North America, Europe, and Japan. The RMS residual for many stations in
these areas is 25-35 mm. The production of "cleaner" tide-gauge time series, with
oceanographic variability removed, is important for future analysis of nonsecular and
regionally differing sea-level variations. Understanding the ocean model's s strengths and
weaknesses will allow for future improvements of the model.
High resolution images may be obtained by clicking the link above.
Selected time series for stations for which DT-OI > 70%. Tide gauge time series are shown in blue, and combined OM and IB time series shown in red. Time series (b) to (h) are offset by a constant value for the purposes of illustration. Only 10 years of data are shown, also for the sake of clarity, although the entire time series for each station was used for calculations (this is true for all time series plots). The time series are for stations (a) Venezia, Italy (45.4 ºN, 12.3ºE), (b) Ko Lak, Thailand (11.8ºN, 99.8ºE), (c) Zhapo, China (21.6ºN, 111.8ºE), (d) Lusi, China (32.1ºN, 121.6ºE), (e) Sogcho, South Korea (38.2ºN, 128.6ºE), (f) Kariya, Japan (33.5ºN, 129.9ºE), (g) St Petersburg, Florida, USA (27.8ºN, 82.6ºW), (h) Newport, Rhode Island, USA (41.5ºN, 71.3ºW).
Histogram showing the distribution of variance reduction of the residual time series after removing OM and IB (ΔT-OI).
Global distribution of ΔT-OI. Each dot represents a single tide-gauge station. Positive numbers indicate an improvement in the variance after the models were applied (see Equations (1) and (2)).
Period of peak periodogram power from Lomb spectral analysis [Lomb, 1976; Scargle, 1982] of the residual time series; (a) when IB and OM are removed from the tide-gauge record, (b) when IB and scaled OM are removed from the tide-gauge record, and (c) when IB, scaled OM, and an estimated annual and semiannual cycle are removed from the tide-gauge record.
Difference between the estimated annual phase for the tide-gauge time series (with IB removed) and the estimated annual phase for the OM time series. Open circles indicate locations where the phase uncertainty was ≥0.3 months.
Selected time series for stations for which scaling of the OM improves the variance of the residuals. Tide gauge time series are shown in blue, and combined OM and IB time series shown in red. Time series (a) to (c) are scaled down (admittance parameter <1)and time series (d) to (f) are scaled up (admittance parameter >1). Time series (b) to (f) are offset by a constant value for the purposes of illustration. Only 10 years of data are shown, also for the sake of clarity. Time series are for tide gauges at (a) Tregde, Norway (58.0ºN, 7.6ºE), (b) Odomari, Japan (31.0ºN, 130.7ºE), (c) Pusan, South Korea (35.1ºN, 129.0ºE), (d) Willipa Bay, Washington, USA (46.7ºN, 124.0ºW) (e) Tajiri, Japan (35.6ºN, 134.3ºE), and (f) Paradip, India (20.3ºN, 86.7ºE).
Estimated OM admittance parameters. Warm colors indicate that the OM values are estimated to need scaling up and cool colors indicate that the OM fits the tide-gauge time series better when it is scaled down. Tide gauges with an estimated admittance parameter that is not significantly different (within 2σ) from 1 are shown as white circles: these stations either have large errors, or the OM is estimated to be correctly scaled.
Histogram showing variance reduction of the residual time series after removing scaled OM and IB (a) with respect to the uncorrected tide gauge time series (ΔT-AOI) (b) with respect to residual time series produced using a model with no admittance parameter (ΔOI-AOI).
Variance reduction (ΔOI-AOI) for the residual time series after the removal of scaled OM and IB, with respect to the residual time series produced using the unscaled OM. Note that the upper end of the color bar (40%+) includes values as high as 74%.
Histogram showing variance reduction for the RAOIS(t) (a) relative to the variance of uncorrected tide-gauge time series (ΔT-AOIS) and (b) relative to the variance of residual time series produced using a model with no estimation of an admittance parameter or seasonal cycle (ΔOI-AOIS).
Reduction in variance (ΔOI-AOIS) of the residual time series, after removal of a scaled OM, IB and seasonal cycles.
Selected time series for stations where estimation of seasonal terms improves the variance of the residuals. Tide gauge time series are shown in blue, and combined OM and IB time series shown in red. Time series (b) to (d) have been offset by a constant for the purposes of illustration. Time series are for (a) Ofunato, Japan (39.0ºB, 141.8ºE), (b) Balboa, Panama (9ºN, 79.6ºW), (c) North Sydney, Canada (46.2ºN, 60.2ºW), and (d) Guaymas, Mexico (27.9ºN, 111ºW).
Estimated OM admittance parameters. Warm colors indicate that the OM values are estimated to need scaling up and cool colors indicate that the residuals are smaller when the OM is scaled down. The OM scaling factor for each tide gauge was estimated with simultaneous estimation of annual and semiannual terms. Tide gauges with an estimated admittance parameter that is not significantly different (within 1σ) from 1 are shown as white circles: these stations either have large errors, or the OM is estimated to be correctly scaled.
Estimated amplitude of the annual cycle at each tide gauge that is additional to annual cycle explained by the OM and IB. Annual cycle amplitudes were estimated in an inversion that also included semiannual amplitudes and OM admittance parameters.
Results of spectral analysis of the RAOIS(t). The plot shows the period of peak periodogram power. Many stations have additional spectral peaks that are only slightly smaller than those illustrated here.
K. Ueyoshi and D. Stammer provided the 50-year long OM output used in this paper. This work is a contribution to the Consortium for Estimating the Circulation and Climate of the Ocean (ECCO), funded by the National Oceanographic Partnership Program. Suggestions from two anonymous reviewers significantly improved this manuscript. We would also like to thank M. Tamisiea and P. Woodworth for useful discussions. This work was supported by the NASA Earth Science Enterprise's Earth Observing System Interdisciplinary Science Program (grant NNG04GL69G), the NASA Physical Oceanography Program (grant NAG5-12742), and the NSF Geophysics Program (grant EAR-0125518). Some figures were produced using the Generic Mapping Tools version 4 [Wessel and Smith, 1998].