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Annual cycle in coastal sea level from tide gauges and altimetry

Sergey V. Vinogradov1 and Rui M. Ponte1

Received 28 August 2009; revised 17 November 2009; accepted 4 December 2009; published 24 April 2010.

[1] Tide gauges provide a unique data set extending many decades back in time, butcoverage is restricted to continental boundaries and a few oceanic islands and the extentto which the tide gauge records can be used to infer lowfrequency, largescale sea level

behavior remains unclear. Since 1992, satellite altimetry provides nearglobal coverageof sea level variability, including coastal regions. We compare variability at 345continental and island tide gauge coastal locations and adjacent shallow and deep oceans,as inferred from altimetry. Initial focus is on the dominant annual cycle. On average,annual amplitudes in tide gauges are comparable to but larger than those in the nearbyshallow ocean (


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possible use in constraining models of the oceanic coastalregions.

2. Data and Methods

[5] For the temporal period of analysis, we used the initialyears of the TOPEX/POSEIDON (T/P) altimetry mission(1 January 1993 to 7 December 2001), during which thesatellite was in its nominal orbit. Spanning this period,monthly records from 345 tide gauges from the PermanentService for Mean Sea Level (http://www.pol.ac.uk [e.g.,Woodworth and Player, 2003]) yielded valid mean annualcycles. Based on their geographical location relative to thecontinental shelf, 204 tide gauges are defined as conti-

nental and 134 as island stations (Figure 1), dependingon whether a shelf break is present between the location anda nearest continent. As the focus is on dynamically relevantsignals in sea level, the inverted barometer (IB) correctionhas been applied by using the National Centers for Envi-ronmental Prediction/National Center for AtmosphericResearch reanalysis sea level pressure fields [Kalnay et al.,1996]. Each sea level time series was detrended and 12mean months were computed by averaging all the availablevalues for January,.., December; the mean annual fit wasfound from this set of 12 mean months. We only used therecords containing a complete mean annual fit, that is, atleast one mean month should exist for this time series foreach of the 12 months.

[6] Altimetric T/P data obtained from the PhysicalOceanography Distributed Active Archive Center, NASAJet Propulsion Laboratory, cover the ocean from 66S to66N, with repeat period of10 days andalongtrack samplingof 7 km. All standard environmental corrections (includingthe IB correction) are applied to the raw T/P data [e.g.,Benada, 1997]. The IB correction is essentially the same asthat used for the tide gauge records. We do not attempt anyspecial treatment of nearland retrievals, which are known tosuffer from noisier radar backscatter and radiometer readings.Ongoing efforts to improve radar tracking and wet tropo-spheric delay algorithms, along with better tidal and nontidal

dealiasing corrections, promise to deliver cleaner coastal al-timeter products in the near future. Here we assess presentstandard products, which can provide a baseline for analysisof forthcoming improved coastal data sets.

[7] Mean annual amplitudes and phases were computedfor monthly averaged altimetric sea level time series at everypoint along the track in a way similar to the tide gaugesannual fit. All suitable T/P alongtrack data were collected

in the proximity of every tide gauge (TG). The selectedspatial radius for this work was 134 km for every TG, asomewhat optimal coverage to include enough nearbyaltimetry tracks. The collected T/P data were split intoshallowand deepgroups relative to the 200 m isobath, atypical outer limit of the continental shelf (Figure 2). Alongtrack annual cycles within each T/P group were averaged asa sum of sine waves to produce mean shallow and deepannual cycles. As a result, annual cycle estimates of coastal(either continental or island TG), shallow, and deep sea levelhave been computed and collected in the vicinity of everyTG.

3. Analysis

[8] The scatter plots in Figures 36 show the amplitudesand phases of the annual cycle in both TG and correspondingshallow and deep T/P locations. The range associated witheach T/P value in Figures 36 denotes its respective standarddeviation and provides a measure of how spatially variablethe annual cycle is along track. The correlation coefficients

Figure 1. Locations of the tide gauge stations used in thisstudy.

Figure 2. An example of Humboldt Bay, California, tidalstation and averaging of the nearby altimetric data. Yellowdiamond is the location of the tide gauge. Color backgroundis the bathymetry. Blue (green) dots are alongtrack T/P ob-servations that are in water deeper (shallower) than 200 m.Annual signals at blue and green dots are averaged withineach group to produce mean deepand shallowoffshoreannual sea level cycles as observed by the altimeter. Dashedred circle shows the extent of the spatial averaging.

VINOGRADOV AND PONTE: COASTAL VS OPEN OCEAN ANNUAL SEA LEVEL C04021C04021

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inferred from the amplitude and phase scatter plots are sum-marized in Table 1.

3.1. Annual Amplitudes

[9] Tide gauges annual amplitudes are comparable withnearby shallow altimetry data with correlation coefficientR = 0.85 (Figure 3a). The observed amplitudes generallyrange from just a few mm to 0.2 m, with some TG signalsreaching 0.40.5 m. The mean T/P annual amplitudes do notexceed 0.26 m. The standard deviation of the estimatedmean T/P values may reach 60 mm but is usually smallerthan 50 mm.

[10] Continental TG amplitudes (red dots in Figure 3a) areusually higher than nearby shallow T/P, particularly inplaces where amplitudes are larger than 100 mm. The largestdiscrepancies are found in the vicinity of the Ganges Riverdelta, where coastal amplitudes range from 0.3 to 0.5 m dueto extremely high monsoonaldriven river outflow, whereasaltimetry observes amplitudes of only 0.20.25 m over theshallow continental shelf. The TG amplitudes are signifi-cantly larger than the shallow ocean amplitudes along the USWest Coast (up to 80 mm differences, with TG amplitudesranging from 100 to 150 mm), where the strong alongshoreCalifornia Currentisolates coastal seasonal variability from

Figure 3. Scatter plots of the mean annual sea level amplitudes in TG (x axis) versus average (a) shallowand (b) deep ocean annual cycles in T/P (y axis). Range plotted for each T/P value represents 1 standarddeviation of the alongtrack T/P shallow and deep values and can be interpreted as a measure of the re-spective spatial variability of the annual cycle as observed by T/P. The 1:1 line is also plotted.


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the open ocean. Some TG stations in Singapore (the south-ernmost tip of Malaysia Peninsula) observe 140 mm am-plitudes whereas nearby altimetry measures only 6070 mmannual signal in Malacca/Singapore Strait. There is a no-

ticeable latitudinal change of the difference between coastaland continental shelf annual amplitudes along the US EastCoast, associated with Gulf Stream moving further offshore;TG amplitudes exceed nearby shallow T/P annual signal inmost TG stations in Florida, but this difference reversesstarting from Fort Pulaski, GA, and northward. Other areaswhere offshore sea level has noticeably larger annual ampli-tudes relative to TG records are found at some stations in theGulf of Mexico, where persistent coastal jets separate rela-tively stable nearshore environments from the significantmesoscale seasonal variability.

[11] Most island TG stations are located in the openocean, and they do not have a shallow T/P counterpart forthis analysis, because the ocean in proximity is mostly

deeper than 200 m. Those island locations that have shallowT/P data in their vicinity are plotted as blue dots inFigure 3a. Annual amplitudes do not exceed 150 mm. Witha few exceptions, shallow T/P annual mean amplitudes nearisland TG stations have standard deviations smaller thanthose near most continental TG; however the statistics forthe former are less significant due to a smaller number ofalongtrack points that constitute the shallow T/P groupsnear island TG.

[12] Comparison of TG amplitudes with T/P data degradeswith increase in depth (R = 0.53). As expected, continentalTG have much smaller correlation (0.36) with deep than with

shallow T/P amplitudes. Most continental TG have annualamplitudes higher than nearby deep ocean (red dots inFigure 3b). The relative differences between continental TGand deep T/P amplitudes have geographical patterns similar

to the previous comparison with shallow T/P, but in someareas like California/Oregon/Washington coast, the dis-crepancies become larger. Another area of substantial dif-ferences is the South Australian coast, where deep ocean hasmuch smaller annual variability than coastal TG.

[13] The overall correlation between island TG (blue dotsin Figure 3b) and deep T/P values (0.79) is much higherthan that for continental TG. The most noticeable outlier isthe station at MinamiTorishima Atoll (153.98E, 24.30N);TG records at this small Pacific island indicate an amplitudeof 162 mm compared to a T/P value no larger than 50 mm,therefore implying a possible land locking of the tidegauge, probably due to geomorphologic changes of theinstrument location (e.g., changes in geometry of the basin

and connections with open ocean), or some sort of hardwareproblem. A similar discrepancy is found for Benoa station,Indonesia (115.21E, 8.74S), which is positioned within ashallow harbor and not expected to represent deep oceanmeasurements, whereas midocean atolls like MinamiTorishima are usually considered suitable for direct mea-surements of sea level variability in the open ocean.

[14] Comparing mean T/P annual amplitudes over shallowand deep areas in vicinity of TG locations yields a corre-lation of 0.64, with shallower waters usually having largeramplitudes (Figure 4). From the standard deviations dis-played in Figure 4, spatial variability of annual cycle over

Figure 4. Annual amplitudes in T/P observations over the shelf and nearby open ocean. Range bars areplotted as in Figure 3, depicting spatial variability associated with shallow and deep T/P values.


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the shelf is generally larger than over the deep ocean. Thelargest difference in the annual amplitudes between shallowand deep data are found near the continental TG stations(correlation is 0.58). Most notable differences occur at theU.S./Canadian Pacific Northwest, where amplitudes candecrease (on the scales of selected spatial radius) from120 mm at the TG, to 80 mm in shallow areas, and to lessthan 10 mm in deep ocean. Other sharp differences between

shallow and deep annual amplitudes are found along theSouth Australian coast (e.g., for Esperance, amplitudesdecrease from 107 mm at the coast to 92 mm in shallow T/Pdata, and to 47 mm in deep waters). The correlation betweenshallow and deep amplitudes near islands (0.85) is muchhigher than that for nearcontinental locations. Large spatialvariability over the continental shelf at Cilacap, SouthIndonesian coast (standard deviation of 45 mm), is due toinclusion of a few T/P data points on the north side ofIndonesia and reflects the difference of about 60 mm inmean annual amplitudes on the opposite shores. Locationswith higher shallow T/P standard deviation (60+ mm) are

likely due to land contamination from small islands inshallow altimetric data.

3.2. Annual Phases

[15] In most places, the difference between mean sea levelannual phases in TG and nearby shallow T/P data does notexceed 1 month (Figure 5a). The total correlation is 0.92.There is more phase discrepancy near continental TG than

near island TG, with some outliers having phase differencesof 35 months. Among continental stations (red dots inFigure 5a, R = 0.92), most notable outlier is Puerto Quetzaon the Pacific coast of Guatemala (the leftmost point inFigure 5a), where the time of the annual maximum changesfrom September offshore to early March at the coast andnearby shallow waters. Similar changes are observed at twoSouth African stations (Saldanha Bay on the Atlantic coast,and East London on the Indian Ocean coast). For the islandstations (blue dots in Figure 5a, R = 0.94), the largest dis-crepancy of about 3 months between TG and shallow T/Pannual phases is found at Jolo Island, Philippines, whichessentially reflects mean annual sea level phase differencebetween Sulu and Celebes Seas. Other large outliers are

found near the Antarctic Peninsula, where altimetry valuesshow large standard deviations, probably due to ice returncontamination.

[16] Larger phase discrepancies are seen between conti-nental TG and deep T/P values (red dots in Figure 5b, R =0.88), reflecting high spatial variability at places likeCharleston and Tofino in west North American coast,Durban in South African East coast, Termisa in Brazil, inaddition to locations mentioned above in the coastal versusshallow ocean comparison. Most island locations correlatevery well (0.93, blue dots in Figure 5b). Notable exceptionis San Felix Island off the coast of Chile (80.13W 26.28S),which lies near an area of large phase changes in the annualcycle [e.g., seeVinogradov et al., 2008, Figures 3b and 3d].

Another large outlier is Macquarie Island midway betweenAntarctica and New Zealand (158.96E 54.48S), in the areaof the Southern Ocean that has significant smallscale fluc-tuations in sea level annual phase as observed by altimetry.

Figure 5. Same as in Figure 3 but for annual phases,shown as the time of the annual maximum. Dashed linesshow 3 month phase difference, whereas solid lines show6 month phase difference. Axis tick marks correspond to themiddle of the month.

Figure 6. Same as in Figure 4 but for annual phases. Axistick marks correspond to the middle of the month.


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[17] Scatter plot in Figure 6 shows the discrepancies andrelative spatial variability in shallow and deep sea levelannual phases from T/P. Overall correlation is 0.92; alongtrack standard deviations are mostly higher in shallowwaters than in deep ocean. Most locations identified inprevious comparisons of altimetry with coastal sea level ashaving noticeable differences or large spatial variability inthe annual phase also stand out in Figure 6. Large dis-crepancies in mean sea level annual phases are found nearsome continental TG stations (R = 0.90, red dots in Figure 6),in particular, along the US/Canada West coast, some nearSouth African and Kenyan TG, Imbituba in Brazil, and SanJuan station in Peru. Deep and shallow areas near island

TG are better correlated (R = 0.97, blue dots in Figure 6),and they mostly have smaller alongtrack phase variations.Largest discrepancies between deep and shallow phases arefound near some Indonesian islands, accompanied by largespatial variability in both shallow and deep estimates.

4. Discussion and Conclusions

[18] Our findings indicate significant variability in annualsea level cycle across the coastal ocean, from the immediatecoastline to the adjacent shallow and deep waters. Thecomplexity of coastal annual sea level patterns can beillustrated by the example of the US/Canadian West Coast(Figure 7). On the scale of 7 km sampled by the altimeter,

alongtrack amplitudes and phases exhibit consistent andgradual changes that are still quite different from the coastalTG. Approaching from the ocean, annual amplitudes in thealtimetry (Figure 7a) tend to increase to 7080 mm in thevicinity of 100200 m isobaths, and decrease below 40 mmcloser to the coast, whereas all TG in this region north ofSan Francisco have considerably larger amplitudes (90140 mm). The annual cycle on the coast and over theCalifornian continental shelf peaks during winter (Figure 7b),but there is a distinct smallscale complete phase reversal inaltimetry data transitioning from the open ocean to shallowwaters just 7 to 30 km offshore. Although some of the fea-tures in the alongtrack data can be attributed to instrumenterrors, such spatial variability is consistent with the complex

ocean circulation in the area, including a combination of thestrong alongshore California Current system and winddriven coastal upwelling, which has been a subject of detailedstudy [Strub and James, 2000; Veneziani et al., 2009]. Thelarge difference between TG and altimeter annual cycles rightnear the coast is, however, quite striking and has not yet beenaddressed in any detail.

[19] The annual cycle in sea level appears to have mostlylarger amplitudes and spatial variability in shallow areas,with largest amplitudes right at the coast, except in thevicinity of strong western boundary currents located justoffshore. These and other differences across the coastal

oceans can be attributed to many physical factors, resultingfrom a combination of local and remote atmospheric, oce-anic and terrestrial processes. The land/ocean boundaryexhibits sharp gradients in atmospheric fluxes and windpatterns, the important drivers for sea level variability. Thedifferences in the atmosphere over land and water occur onall scales, and can provide different annual forcing for theocean in the immediate vicinity of land and just offshore[e.g.,Haack et al., 2005]. Surface heating and cooling havedifferent impact on shallow (mixed from top to bottom)circulation and offshore (more stratified) dynamics. Theseasonal upwelling also provides fine spatial details to theoffshore profile of annual sea level and does not necessarily

occur right at the coastline. Upwelling associated withmesoscale ocean circulation may exhibit quasiannualperiodicity (e.g., Gulf of Mexico), and appear at some dis-tance from the coast, depending on eddy dynamics and shapeof the continental shelf [Vinogradov et al., 2004]. The riverinput is another significant factor, which relates to hydro-logical and atmospheric regimes far upstream (and inland)from the river mouths. A good example is the Ganges Riverdelta with the largest annual amplitudes observed in TG data.In addition to hydrological and atmospheric factors, thedynamics of inner harbors, fjords and basins where TG aresometimes located can be very different from the nearby openocean. Terrestrial impacts through sedimentation, coastlinechanges, harbor construction, etc., can also affect the coastal

sea level measurement, but they are likely to be less importantthan the hydrological and atmospheric factors mentionedabove.

[20] Observational errors in the TG and altimetry esti-mates contribute to some of the differences highlighted inFigures 36. The two systems have very different samplingproperties in time, and the various data proce ssing steps(e.g., original smoothing, gap filling, and filtering of theTG hourly records) can affect the annual fit computations.In addition, the TG measures sea level with respect to afixed geolocation, whereas altimetry measures absolutesea level relative to the geoid. Any land motions with anannual component (e.g., from tidal or atmospheric pres-sure loading) could give rise to differences between the

TG and altimeter measurements. Annual amplitudes of afew millimeters are possible [van Dam et al., 2007].

[21] The typical RMS errors for TG monthly mean dataare believed to be within 10 mm [Pugh, 2004]. Instrumenterrors may also have a seasonal dependence. As for altim-etry observations, besides instrument noise, a plethora ofcorrections are applied to the raw data, including wet tro-posphere correction, IB removal, and tidal dealiasing thatare important for the coastal sea level observations.Ponte etal.[2007] offer spacedependent RMS estimates of 24 cmfor the total altimetry error; uncertainties for the annualperiod per se are likely to be much smaller. Present work to

Table 1. Correlations in Annual Amplitudes and Phases Between Tide Gauges and Nearby Altimetry

TG

Shallow T/P Versus TG Deep T/P Versus TG Shallow Versus Deep T/P

No. Amplitudes Phases No. Amplitudes Phases No. Amplitudes Phases

Continental 152 0.84 0.92 114 0.36 0.88 89 0.58 0.90Island 42 0.82 0.94 113 0.79 0.93 41 0.85 0.97All 194 0.85 0.92 227 0.53 0.91 130 0.64 0.92


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improve corrections and dealiasing models and techniquespromises to deliver in the near future better altimetric esti-mates in the nearcoastal waters.

[22] Taking the uncertainty in the mean annual cycleestimates from TG and altimeter data to be 12 cm, muchof the differences seen in Figures 36 are hard to explainsimply in terms of data noise and represent to some degreethe true spatial variability of the annual cycle in the coastalocean. We notice also that, in most of the areas studied, thestandard deviation of T/P mean amplitudes exceeds 23 cm.Thus, the spatial variability sensed by the altimeter instru-

ment particularly in the shallow continental shelves seems tobe a robust feature of the annual sea level patterns.

[23] Land contamination and aliasing effects, typically aconcern in altimetric coastal measurements, are less of anissue for our study of the annual cycle. The altimetric orbitswere designed to specifically reduce tidal aliasing at theannual period and Ponte and Lyard [2002] show that theannual cycle in sea level is probably less contaminated(aliased) by other variability. Similarly, although we did notapply any special algorithms to detect land contamination inaddition to what was performed on the original T/P data

Figure 7. California, Oregon, and Washington coast: (a) annual amplitudes (mm) and (b) time of annualmaximum in TG and T/P. Isobaths shown are 200 m (gray curve) and 1000 m (black curve).


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processing, we have found only a few locations where landreturns may contribute outliers to the altimetry data, mostlyin the areas with many small islands (e.g., Indonesia, SouthFlorida). The results in Figures 36 and Table 1 suggest thatthe altimeter measurements are still very useful in mostshallow regions, even very close to the land boundaries.

[24] The differences in annual sea level cycle between TGand nearby altimetry limit the use of TG data for inferring

mean annual cycle in the adjacent shallow and open ocean.One implication is that TG data can only provide a weakconstraint on coarseresolution ocean circulation models, asthey fail to capture physical processes behind fine spatialgradients in annual sea level cycle that we found in alongtrack altimetry data. Highresolution ocean data assimilationsystems will benefit most from TG input, if they are capableof resolving both oceanic and atmospheric shortscaledynamics along the sea/land boundary. On the other hand,alongtrack T/P sea level data have quite robust, stable andconsistent annual cycles in shallow waters, and can providestrong constraints for both coarseand highresolution modelsof the coastal regions.

[25] High spatial variability of the annual sea level cycle

in shallow areas indicates strong seasonally varying featuresin local ocean and atmospheric circulation that need to bestudied in detail in a coupled highresolution modelingframework. Coastal modeling systems that combine ocean,atmosphere and terrestrial input (hydrology, inner basins,land motion) can benefit from both altimetry and tide gaugedata in simulating the complexity of the nearcoastal cir-culation on annual and lower frequencies. Such integratedmodeling efforts will be essential for predictions of thecoastal environment on climate time scales.

[26] Acknowledgments. This work is supported by NASA PhysicalOceanography program through contract NNH08CD67C. The authorsthank Charmaine King from the Massachusetts Institute of Technology

for helping with initial data processing.

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