Abstract
The nature of mean sea level variation over the global coastal ocean is considered based on 219 historical tide gauge records and three barotropic ocean circulation models forced by reanalysis surface air pressure and wind stress. The consistency of the models and their ability to reproduce the data are considered on nonseasonal timescales (seasonal cycles and linear trends removed) from bimonthly to multidecadal over 1900–2010. Models consistently simulate stronger sea level variability at higher latitude, higher frequency, between winters, and over broad shallow shelves and semi-enclosed marginal seas; standard deviations in modeled monthly sea level grow from 1–2 cm on average at low latitude (0°–30°) to 5–10 cm at high latitude (60°–90°), with larger values simulated over some shelf areas (e.g., North Sea). Models are more consistent over narrow shelf regions adjacent to deep basins and less consistent along the broad shallow continental shelf. On monthly timescales, discrepancies between models arise mostly from differences in model configuration (e.g., fine vs. coarse horizontal resolution), whereas model configuration and surface forcing (i.e., choice of atmospheric reanalysis) contribute comparably to model differences on annual timescales. Model solutions become more uncertain at earlier times (e.g., prior to 1950). The models show more skill explaining variance in tide gauge data at higher latitude, higher frequency, between winters, and over broad shallow shelves and within semi-enclosed marginal seas; at middle and high latitudes (poleward of 45°), model sea level solutions on average explain 30–50% of the monthly variance and 35–70% of the variance from one winter to the next in the tide gauge data records. Statistically significant relationships between the model solutions and observational data persist on long decadal periods. The relative skill of individual models is sensitive to region and timescale, such that no one model considered here consistently performs better than the others in all cases. Results suggest that barotropic models are useful for reducing noise in tide gauge records for studies of sea level rise and motivate additional model comparison studies in the context of sea level extremes.
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References
Adcroft A, Hill C, Marshall J (1997) Representation of topography by shaved cells in a height coordinate ocean model. Mon Weather Rev 125:2293–2315
Andres M, Gawarkiewicz GG, Toole JM (2013) Interannual sea level variability in the western North Atlantic: regional forcing and remote response. Geophys Res Lett 40:5915–5919. https://doi.org/10.1002/2013GL058013
Bingham RJ, Hughes CW (2008) The relationship between sea-level and bottom pressure variability in an eddy permitting ocean model. Geophys Res Lett 35:L03602
Bos MS, Williams SDP, Araújo IB, Bastos L (2014) The effect of temporal correlated noise on the sea level rate and acceleration uncertainty. Geophys J Int 196:1423–1430. https://doi.org/10.1093/gji/ggt481
Calafat FM, Chambers DP (2013) Quantifying recent acceleration in sea level unrelated to internal climate variability. Geophys Res Lett 40:3661–3666. https://doi.org/10.1002/grl.50731
Calafat FM, Chambers DP, Tsimplis MN (2012) Mechanisms of decadal sea level variability in the eastern North Atlantic and the Mediterranean Sea. J Geophys Res 117:C09022. https://doi.org/10.1029/2012JC008285
Calafat FM, Chambers DP, Tsimplis MN (2013) Inter-annual to decadal sea-level variability in the coastal zones of the Norwegian and Siberian Seas: the role of atmospheric forcing. J Geophys Res Oceans 117:1287–1301. https://doi.org/10.1002/jgrc.20106
Calafat FM, Chambers DP, Tsimplis MN (2014a) On the ability of global sea level reconstructions to determine trends and variability. J Geophys Res Oceans 119:1572–1592. https://doi.org/10.1002/2013JC009298
Calafat FM, Avgoustoglou E, Jordà G, Flocas H, Zodiatis G, Tsimplis MN, Kouroutzoglou J (2014b) The ability of a barotropic model to simulate sea level extremes of meteorological origin in the Mediterranean Sea, including those caused by explosive cyclones. J Geophys Res Oceans 119:7840–7853
Carrère L, Lyard F (2003) Modeling the barotropic response of the global ocean to atmospheric wind and pressure forcing: comparisons with observations. Geophys Res Lett 30(6):1275. https://doi.org/10.1029/2002GL016473
Chepurin GA, Carton JA, Leuliette E (2014) Sea level in ocean reanalyses and tide gauges. J Geophys Res Oceans 119:147–155. https://doi.org/10.1002/2013JC009365
Clarke AJ, Liu X (1994) Interannual sea level in the northern and eastern Indian Ocean. J Phys Oceanogr 24:1224–1235
Compo GP, Whitaker JS, Sardeshmukh PD, Matsui N, Allan RJ, Yin X, Gleason BE, Vose RS, Rutledge G, Bessemoulin P, Brönnimann S, Brunet M, Crouthamel RI, Grant AN, Groisman PY, Jones PD, Kruk MC, Kruger AC, Marshall GJ, Maugeri M, Mok HY, Nordli Ø, Ross TF, Trigo RM, Wang XL, Woodruff SD, Worley SJ (2011) The twentieth century reanalysis project. Q J R Meteorol Soc 137:1–28. https://doi.org/10.1002/qj.776
Csanady GT (1982) Circulation in the coastal ocean. D. Reidel Publishing Compeny, Dordrecht, p 279
Dangendorf S, Mudersbach C, Wahl T, Jensen J (2013) Characteristics of intra-, inter-annual and decadal sea-level variability and the role of meteorological forcing: the long record of Cuxhaven. Ocean Dyn 63:209–224. https://doi.org/10.1007/s10236-013-0598-0
Dangendorf S, Rybski D, Mudersbach C, Müller A, Kaufmann E, Zorita E, Jensen J (2014a) Evidence for long-term memory in sea level. Geophys Res Lett 41:5530–5537. https://doi.org/10.1002/2014GL060538
Dangendorf S, Müller-Navarra S, Jensen J, Schenk F, Wahl T, Weisse R (2014b) North Sea storminess from a novel storm surge record since AD 1843. J Climate 27:3582–3595
Dangendorf S, Marcos M, Müller M, Zorita E, Riva R, Berk K, Jense J (2015) Detecting anthropogenic footprints in sea level rise. Nat Commun 6:7849. https://doi.org/10.1038/ncomms8849
Dangendorf S, Marcos M, Wöppelmann G, Conrad CP, Frederikse T, Riva R (2017) Reassessment of 20th century global mean sea level rise. Proc Natl Acad Sci USA 114(23):5946–5951. https://doi.org/10.1073/pnas.1616007114
Featherstone WE, Penna NT, Filmer MS, Williams SDP (2015) Nonlinear subsidence at Fremantle, a long-recording tide gauge in the Southern Hemisphere. Geophys Res Lett 120:7004–7014. https://doi.org/10.1002/2015JC011295
Feng M, Li Y, Meyers G (2004) Multidecadal variations of Fremantle sea level: footprint of climate variability in the tropical Pacific. Geophys Res Lett 31:L16302. https://doi.org/10.1029/2004GL019947
Field CR, Bayard TS, Gjerdrum C, Hill JM, Meiman S, Elphick CS (2017) High-resolution tide projections reveal extinction threshold in response to sea-level rise. Glob Change Biol 23:2058–2070. https://doi.org/10.1111/gcb.13519
Forget G, Campin J-M, Heimbach P, Hill CN, Ponte RM, Wunsch C (2015) ECCO version 4: an integrated framework for non-linear inverse modeling and global ocean state estimation. Geosci Model Dev 8:3071–3104. https://doi.org/10.5194/gmd-8-3071-2015
Forsyth J, Gawarkiewicz G, Andres M, Chen K (2018) The interannual variability of the breakdown of fall stratification on the New Jersey shelf. J Geophys Res Oceans. https://doi.org/10.1029/2018JC014049
Frankignoul C, Müller P, Zorita E (1997) A simple model of the decadal response of the ocean to stochastic wind forcing. J Phys Oceanogr 27:1533–1546
Frederikse T, Simon K, Katsman CA, Riva R (2017) The sea-level budget along the Northwest Atlantic coast: GIA, mass changes, and large-scale ocean dynamics. J Geophys Res Oceans 122:5486–5501. https://doi.org/10.1002/2017JC012699
Fukumori I, Wang O, Llovel W, Fenty I, Forget G (2015) A near-uniform fluctuation of ocean bottom pressure and sea level across the deep ocean basins of the Arctic Ocean and the Nordic Seas. Prog Oceanogr 134:152–172
Gill AE (1982) Atmosphere-ocean dynamics. Academic Press, New York, p 662
Gill AE, Niiler PP (1973) The theory of the seasonal variability in the ocean. Deep See Res 20:141–177
Gille ST (2004) How nonlinearities in the equation of state of seawater can confound estimates of steric sea level change. J Geophys Res 109:C03005. https://doi.org/10.1029/2003JC002012
Gomis D, Tsimplis MN, Martín-Míguez B, Ratsimandresy AW, García-Lafuente J, Josey SA (2006) Mediterranean Sea level and barotropic flow through the Strait of Gibraltar for the period 1958–2001 and reconstructed since 1659. J Geophys Res 111:C11005. https://doi.org/10.1029/2005JC003186
Gomis D, Ruiz S, Sotillo MG, Álvarez-Fanjul E, Terradas J (2008) Low frequency Mediterranean sea level variability: the contribution of atmospheric pressure and wind. Glob Planet Change 63:215–229
Gonneea ME, Mulligan AE, Charette MA (2013) Climate-driven sea level anomalies modulate coastal groundwater dynamics and discharge. Geophys Res Lett 40:2701–2706. https://doi.org/10.1002/grl.50192
Greatbatch RJ, Lu Y, de Young B (1996) Application of a barotropic model to North Atlantic synoptic sea level variability. J Mar Res 54:451–469
Haigh ID, Wahl T, Rohling EJ, Price RM, Pattiaratchi CB, Calafat FM, Dangendorf S (2014) Timescales for detecting a significant acceleration in sea level rise. Nat Commun 5:3635. https://doi.org/10.1038/ncomms4635
Hay CC, Morrow E, Kopp RE, Mitrovica JX (2015) Probabilistic reanalysis of twentieth-century sea-level rise. Nature 517:481–484
Holgate SJ, Matthews A, Woodworth PL, Rickards LJ, Tamisiea ME, Bradshaw E, Foden PR, Gordon KM, Jevrejeva S, Pugh J (2013) New data systems and products at the permanent service for mean sea level. J Coast Res 29(3):493–504
Holton JR (1992) An introduction to dynamic meteorology. Academic Press, San Diego, p 507
Horton BP, Kopp RE, Garner AJ, Hay CC, Khan NS, Roy K, Shaw TA (2018) Mapping sea-level change in time, space, and probability. Annu Rev Environ Resour. https://doi.org/10.1146/annurev-environ-102017-025826
Jordà G, Marbà N, Duarte CM (2012a) Mediterranean seagrass vulnerable to regional climate warming. Nat Clim Change 2:821–824
Jordà G, Gomis D, Álvarez-Fanjul E, Somot S (2012b) Atmospheric contribution to Mediterranean and nearby Atlantic sea level variability under different climate change scenarios. Glob Planet Change 80–81:198–214
Karegar MA, Dixon TH, Engelhart SE (2016) Subsidence along the Atlantic Coast of North America: insights from GPS and late Holocene relative sea level data. Geophys Res Lett 43:3126–3133. https://doi.org/10.1002/2016GL068015
Kenigson JS, Han W, Rajagopalan B, Yanto Jasinski M (2018) Decadal shift of NAO-linked interannual sea level variability along the U.S. Northeast Coast J Clim 31:4981–4989
Kundu PK, Cohen IM (2004) Fluid mechanics, 3rd edn. Elsevier Academic Press, Amsterdam, p 759
Kopp RE, Hay CC, Little CM, Mitrovica JX (2015) Geographic variability of sea-level change. Curr Clim Change Rep 1(3):192–204
Krueger O, Schenk F, Feser F, Weisse R (2013) Inconsistencies between long-term trends in storminess derived from the 20CR reanalysis and observations. J Clim 26:868–874
Laloyaux P, Balmaseda M, Dee D, Mogensen K, Janssen P (2016) A coupled data assimilation system for climate reanalysis. Q J R Meteorol Soc 142:65–78. https://doi.org/10.1002/qj.2629
Marcos M, Tsimplis MN (2007) Forcing of coastal sea level rise patterns in the North Atlantic and the Mediterranean Sea. Geophys Res Lett 34:L18604. https://doi.org/10.1029/2007GL030641
Marcos M, Tsimplis MN (2008) Coastal sea level trends in Southern Europe. Geophys J Int 175:70–82. https://doi.org/10.1111/j.1365-246X.2008.03892.x
Marcos M, Calafat FM, Berihuete Á, Dangendorf S (2015) Long-term variations in global sea level extremes. J Geophys Res Oceans 120:8115–8134. https://doi.org/10.1002/2015JC011173
Marshall J, Adcroft A, Hill C, Perelman L, Heisey C (1997) A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J Geophys Res 102(C3):5753–5766. https://doi.org/10.1029/96JC02775
Merrifield MA, Thompson PR (2018) Interdecadal sea level variations in the Pacific: distinctions between the tropics and extratropics. Geophys Res Lett. https://doi.org/10.1029/2018GL077666
Milne GA, Gehrels WR, Hughes CW, Tamisiea MA (2009) Identifying the causes of sea-level change. Nat Geosci 2:471–478
Pascual A, Marcos M, Gomis D (2008) Comparing the sea level response to pressure and wind forcing of two barotropic models: validation with tide gauge and altimetry data. J Geophys Res 113:C07011. https://doi.org/10.1029/2007JC004459
Pedlosky J (1987) Geophysical fluid dynamics, 2nd edn. Springer, New York, p 710
Peixoto JP, Oort AH (1992) Physics of Climate. American Institute of Physics, New York, p 520
Philander SGH (1978) Forced oceanic waves. Rev Geophys 16(1):15–46
Piecuch CG, Ponte RM (2014) Mechanisms of global-mean steric sea level change. J Clim 27:824–834
Piecuch CG, Ponte RM (2015a) Inverted barometer contributions to recent sea level changes along the northeast coast of North America. Geophys Res Lett 42:5918–5925. https://doi.org/10.1002/2015GL064580
Piecuch CG, Ponte RM (2015b) A wind-driven nonseasonal barotropic fluctuation of the Canadian inland seas. Ocean Sci 11:175–185. https://doi.org/10.5194/os-11-175-2015
Piecuch CG, Fukumori I, Ponte RM, Wang O (2015) Vertical structure of ocean pressure variations with application to satellite-gravimetric observations. J Atmos Ocean Technol 32:603–613
Piecuch CG, Dangendorf S, Ponte RM, Marcos M (2016a) Annual sea level changes on the North American Northeast Coast: influence of local winds and barotropic motions. J Clim 29:4801–4816
Piecuch CG, Thompson PR, Donohue KA (2016b) Air pressure effects on sea level changes during the twentieth century. J Geophys Res Oceans 121:7917–7930. https://doi.org/10.1002/2016JC012131
Poli P, Hersbach H, Tan D, Dee D, Thépaut J-N, Simmons A, Peubey C, Laloyaux P, Komori T, Berrisford P, Dragani R, Trémolet Y, Hólm E, Bonavita M, Isaksen L, Fisher M (2013) The data assimilation system and initial performance evaluation of the ECMWF pilot reanalysis of the 20th-century assimilating surface observations only (ERA-20C). ERA report series 14
Ponte RM (1992) The sea level response of a stratified ocean to barometric pressure forcing. J Phys Oceanogr 22:109–113
Ponte RM (1993) Variability in a homogeneous global ocean forced by barometric pressure. Dyn Atmos Oceans 18:209–234
Ponte RM (1994) Understanding the relation between wind- and pressure-driven sea level variability. J Geophys Res 99(C4):8033–8039
Ponte RM (2006) Low-frequency sea level variability and the inverted barometer effect. J Atmos Ocean Technol 23:619–629
Ponte RM, Dorandeu J (2003) Uncertainties in ECMWF surface pressure fields over the ocean in relation to sea level analysis and modeling. J Atmos Ocean Technol 20:301–307
Ponte RM, Quinn KJ, Piecuch CG (2018) Accounting for gravitational attraction and loading effects from land ice on absolute sea level. J Atmos Ocean Technol 35:405–410
Proshutinsky AY, Johnson MA (1997) Two circulation regimes of the wind-driven Arctic Ocean. J Geophys Res 102(C6):12493–12514
Proshutinsky A, Pavlov V, Bourke RH (2001) Sea level rise in the Arctic Ocean. Geophys Res Lett 28(11):2237–2240
Proshutinsky A, Ashik IM, Dvorkin EN, Häkkinen S, Krishfield RA, Peltier WR (2004) Secular sea level change in the Russian sector of the Arctic Ocean. J Geophys Res 109:C03042. https://doi.org/10.1029/2003JC002007
Proshutinksy A, Ashik I, Häkkinen S, Hunke E, Krishfield R, Maltrud M, Maslowski W, Zhang J (2007) Sea level variability in the Arctic Ocean from AOMIP models. J Geophys Res 112:C04S08. https://doi.org/10.1029/2006JC003916
Permanent Service for Mean Sea Level (PSMSL) (2018) Tide gauge data. http://www.psmsl.org/data/obtaining/. Retrieved 5 Mar 2018
Qiu B, Chen S (2006) Decadal variability in the large-scale sea surface height field of the South Pacific Ocean: observations and causes. J Phys Oceanogr 36:1751–1762
Qiu B, Chen S (2010) Interannual-to-decadal variability in the bifurcation of the North Equatorial Current off the Philippines. J Phys Oceanogr 40:2525–2538
Qiu B, Chen S (2012) Multidecadal sea level and gyre circulation variability in the northwestern tropical Pacific Ocean. J Phys Oceanogr 42:193–206
Richter K, Nilson JEØ, Drange H (2012) Contributions to sea level variability along the Norwegian coast for 1960–2010. J Geophys Res 117:C05038. https://doi.org/10.1029/2011JC007826
Royston S, Watson CS, Legrésy B, King MA, Church JA, Bos MS (2018) Sea-level trend uncertainty with Pacific climatic variability and temporally-correlated noise. J Geophys Res Oceans 123:1978–1993. https://doi.org/10.1002/2017JC013655
Sandstrom H (1980) On the wind-induced sea level changes on the Scotian shelf. J Geophys Res 85(C1):461–468
Sasaki YN, Minobe S, Miura Y (2014) Decadal sea-level variability along the coast of Japan in response to ocean circulation changes. J Geophys Res 119:266–275. https://doi.org/10.1002/2013JC009327
Sasaki YN, Washizu R, Yasuda T, Minobe S (2017) Sea level variability around Japan during the twentieth century simulated by a regional ocean model. J Clim 30:5585–5595
Stammer D, Hüttemann S (2008) Response of regional sea level to atmospheric pressure loading in a climate change scenario. J Clim 21:2093–2101
Stammer D, Cazenave A, Ponte RM, Tamisiea ME (2013) Causes for contemporary regional sea level changes. Annu Rev Mar Sci 5:21–46
Stammer D, Ray RD, Andersen OB, Arbic BK, Bosch W, Carrère L, Cheng Y, Chinn DS, Dushaw BD, Egbert GD, Erofeeva SY, Fok HS, Green JAM, Griffiths S, King MA, Lapin V, Lemoine FG, Luthcke SB, Lyard F, Morison J, Müller M, Padman L, Richman JG, Shriver JF, Shum CK, Taguchi E, Yi Y (2014) Accuracy assessment of global barotropic ocean tide models. Rev Geophys 52:243–282. https://doi.org/10.1002/2014RG000450
Sturges W, Douglas BC (2011) Wind effects on estimates of sea level rise. J Geophys Res 116:C06008. https://doi.org/10.1029/2010JC006492
Sündermann J, Pohlmann T (2011) A brief analysis of North Sea physics. Oceanologia 53(3):663–689
Theuerkeuf EJ, Rodriguez AB, Fegley SR, Luettich RA (2014) Sea level anomalies exacerbate beach erosion. Geophys Res Lett 41:5139–5147. https://doi.org/10.1002/2014GL060544
Thompson PR, Mitchum GT (2014) Coherent sea level variability on the North Atlantic western boundary. J Geophys Res 119:5676–5689. https://doi.org/10.1002/2014JC009999
Thompson PR, Mitchum GT, Vonesch C, Li J (2013) Variability of winter storminess in the eastern United States during the twentieth century from tide gauges. J Clim 26:9713–9726
Thompson PR, Merrifield MA, Wells JR, Chang CM (2014) Wind-driven coastal sea level variability in the northeast Pacific. J Clim 27:4733–4751
Thompson PR, Hamlington BD, Landerer FW, Adhikari S (2016) Are long tide gauge records in the wrong place to measure global mean sea level rise? Geophys Res Lett 43:10403–10411. https://doi.org/10.1002/2016GL070552
Thorne K, MacDonald G, Guntenspergen G, Ambrose R, Buffington K, Dugger B, Freeman C, Janousek C, Brown L, Rosencranz J, Holmquist J, Smol J, Hargan K, Takekawa J (2018) U.S. Pacific coastal wetland resilience and vulnerability to sea-level rise. Sci Adv 4:eaao3270
Tsimplis MN, Álvarez-Fanjul E, Gomis D, Fenoglio-Marc L, Pérez B (2005) Mediterranean Sea level trends: atmospheric pressure and wind contribution. Geophys Res Lett 32:L20602. https://doi.org/10.1029/2005GL023867
Vinogradova NT, Ponte RM, Stammer D (2007) Relation between sea level and bottom pressure and the vertical dependence of oceanic variability. Geophys Res Lett 34:L03608
Willebrand J, Philander SGH, Pacanowski RC (1980) The oceanic response to large-scale atmospheric disturbances. J Phys Oceanogr 10:411–429
Woodworth PL, Pouvreau N, Wöppelmann G (2010) The gyre-scale circulation of the North Atlantic and sea level at Brest. Ocean Sci 6:185–190
Woodworth PL, Morales Maqueda MÁ, Roussenov VM, Williams RG, Hughes CW (2014) Mean sea-level variability along the northeast American Atlantic coast and the roles of the wind and the overturning circulation. J Geophys Res Oceans 119:8916–8935. https://doi.org/10.1002/2014JC010520
Woodworth PL, Morales Maqueda MÁ, Gehrels WR, Roussenov VM, Williams RG, Hughes CW (2017) Variations in the difference between mean sea level measured either side of Cape Hatteras and their relation to the North Atlantic Oscillation. Clim Dyn 49(7–8):2451–2469
Woodworth PL, Melet A, Marcos M, Ray RD, Wöppelmann G, Sasaki YN, Cirano M, Hibbert A, Huthnance JM, Montserrat S, Merrifield MA (2019) Forcing factors affecting sea level changes at the coast. Surv Geophys. https://doi.org/10.1007/s10712-019-09531-1
Wunsch CW, Stammer D (1997) Atmospheric loading and the oceanic ”inverted barometer” effect. Rev Geophys 35(1):79–107
Acknowledgements
This work was supported by National Science Foundation awards OCE-1558966 and OCE-1834739 as well as the J. Lamar Worzel Assistant Scientist Fund and the Penzance Endowed Fund in Support of Assistant Scientists at the Woods Hole Oceanographic Institution. This paper is an outcome of the ISSI Workshop on, “Understanding the Relationship between Coastal Sea Level and Large-Scale Ocean Circulation,” held on 5–9 March 2018 in Bern, Switzerland. Helpful comments from Magdalena Andres and an anonymous reviewer are acknowledged.
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Appendix: Scaling of the Relative Influences of Barotropic and Baroclinic Effects on \(\zeta\) Variability
Appendix: Scaling of the Relative Influences of Barotropic and Baroclinic Effects on \(\zeta\) Variability
Following past works (Gill and Niiler 1973; Willebrand et al. 1980; Frankignoul et al. 1997), we perform a scaling analysis to establish the basic controls on the relative contributions of barotropic and baroclinic processes on \(\zeta\) variability. The words “barotropic” and “baroclinic” have various usages and meanings in physical oceanography and geophysical fluid dynamics (Holton 1992; Pedlosky 1987). Here, we use these words in a similar sense to the separation of variables and normal vertical modes in a continuously stratified fluid (Gill 1982; Kundu and Cohen 2004). We define the barotropic component of a depth-dependent variable as the depth-averaged value, and the baroclinic component at a given depth as the deviation from the depth average. In the case of \(\zeta\), which has no explicit depth dependence, we define the barotropic component as the scaled depth-averaged hydrostatic pressure p (cf. Gill 1982),
where H is ocean depth, \(\rho _0\) a constant reference density, and g gravitational acceleration. The baroclinic \(\zeta\) component is defined as the difference between total and barotropic components,
Usage of angled brackets and double primes to denote the barotropic and baroclinic components follows Peixoto and Oort (1992). It can be shown that, by applying the hydrostatic equation,
\(\zeta ^{\prime\prime}\) can be rewritten in terms of a double integral of ocean density \(\rho\),
See Piecuch et al. (2015) for more details on how (14) can be derived from (13) and (12).
To compare the magnitudes of \(\left\langle \zeta \right\rangle\) and \(\zeta ^{\prime\prime}\) variations, we consider basic ocean dynamics. Given the timescales of interest to this study (monthly to decadal), we generally expect an equilibrium (time-independent) barotropic response to surface atmospheric forcing, while we anticipate a transient (time-dependent) baroclinic adjustment. For simplicity, we suppose that the only surface forcing is by a variable wind stress \(\varvec{\tau }\). (Indeed, the above expressions for \(\left\langle \zeta \right\rangle\) and \(\zeta ^{\prime\prime}\) neglect any surface loading by barometric pressure.) Thus, to scale the p integrand in Eq. (11), we assume that the equilibrium barotropic adjustment takes the form of a Sverdrup balance,
where \({\mathbf J}\) is the Jacobian operator, \(\nabla \times\) is the vertical component of the curl operator, and f is the Coriolis parameter. Eq. (15) represents a balance between vertical stretching of the water column by the curl of \(\varvec{\tau }\) and advection of the water column across contours of ambient potential vorticity by geostrophic flows (Pedlosky 1987). Combining Eqs. (11) and (15), we find that \(\left\langle \zeta \right\rangle\) is of order,
where \(\beta\) is the meridional derivative of f.
To scale the \(\rho\) integrand in Eq. (14), we assume the transient baroclinic response is such that density changes arise solely due to heaving of the mean stratification by an anomalous velocity w,
where \(N^2\) is the square of the buoyancy frequency. For simplicity, we assume a vertical structure for w such that it is equal to the Ekman pumping velocity,
within some shallow upper layer of vertical thickness \(\delta\), and zero everywhere below that depth. Combining Eqs. (14), (17), and (18), we find that \(\zeta ^{\prime\prime}\) scales as
where \(\omega\) is the angular frequency of the density variation and L is a representative length scale of the surface forcing. Thus, the ratio of the barotropic to the baroclinic \(\zeta\) term is on the order of
That is, barotropic response becomes increasingly important relative to baroclinic adjustment for progressively higher latitude (\(f^2/\beta\) increases in magnitude with latitude), higher frequency, larger spatial scale, weaker stratification, and shallower water column thickness. These simple arguments are borne out and corroborated by more realistic ocean general circulation model experiments (Vinogradova et al. 2007; Bingham and Hughes 2008).
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Piecuch, C.G., Calafat, F.M., Dangendorf, S. et al. The Ability of Barotropic Models to Simulate Historical Mean Sea Level Changes from Coastal Tide Gauge Data. Surv Geophys 40, 1399–1435 (2019). https://doi.org/10.1007/s10712-019-09537-9
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DOI: https://doi.org/10.1007/s10712-019-09537-9