Critical analysis of Mediterranean sea level limit cycles during the Messinian salinity crisis




Messinian Salinity Crisis, sea-level change, Mediterranean, Strait of Gibraltar


The Messinian Salinity Crisis (5.97-5.33Ma) may be one of the most significant periods of sea-level change in recent geologic history. During this period, evaporite deposition throughout the Mediterranean basin records a series of dramatic environmental changes as flow through the Strait of Gibraltar was restricted. In the first stage of evaporite deposition, cycles of gypsum appear in shallow basins on the margins of the Mediterranean. The complex environmental history giving rise to these cycles has been investigated for decades but remains controversial. Notably, whether the evaporites are connected to significant changes in Mediterranean sea level is an open question.

In one proposed model, competition between tectonic uplift and erosion at the Strait of Gibraltar gives rise to selfsustaining sea-level oscillations—limit cycles—which trigger evaporite deposition. Here I show that limit cycles are not a robust result of the proposed model and discuss how any oscillations produced by this model depend on an unrealistic formulation of a key model equation. First, I simplify the model equations and test whether limit cycles are produced in 64 million unique combinations of model parameters, finding oscillations in only 0.2% of all simulations. Next, I examine the formulation of a critical model equation representing stream channel slope over the Strait of Gibraltar, concluding that a more realistic formulation would render sea-level limit cycles improbable, if not impossible, in the proposed model.


Andrews, E.R., Billen, M.I., 2009. Rheologic controls on the dynamics of slab detachment. Tectono-physics, 464(1-4), 60-69. DOI: 10.1016/j.tecto.2007.09.004

Baum, M., 2021a. markmbaum/messinian-salinity-crisis v1. Version v1. DOI: 10.5281/zenodo.4571688. url: January, 2021b, wordsworthgroup/libode v1.0.3. Version v1.0.3.

doi: 10.5281/zenodo.4429314. URL: https: //

Commission Internationale pour l’Exploration Scientifique de la Méditerranée (CIESM), 2008. The Messinian Salinity Crisis

from Mega-deposits to Microbiology. A Consensus Report. In: Briand, F. (ed.). CIESM Workshop Monographs. Monaco, Commission Internationale pour l’Exploration Scientifique de la Méditerranée (CIESM), 16 bd de Suisse, MC-98000, 33, 1-168.

Coulson, S., Pico, T., Austermann, J., Powell, E., Moucha, R., Mitrovica, J., 2019. The role of isostatic adjustment and gravitational effects on the dynamics of the Messinian salinity crisis. Earth and Planetary Science Letters, 525, 115760, 1-9.

DOI: 10.1016/j.epsl.2019.115760

De Lange, G.J., Krijgsman, W., 2010. Messinian salinity crisis: A novel unifying shallow gypsum/deep dolomite formation mechanism. Marine Geology, 275(1-4), 273-277. DOI: 10.1016/j.margeo.2010.05.003.

Duggen, S., Hoernle, K., Morgan, J.P., 2003. Deep roots of the Messinian salinity crisis. Nature, 422, 602-606.

Duretz, T., Gerya, T.V., May, D.A., 2011. Numerical modelling of spontaneous slab breakoff and subsequent topographic

response. Tectonophysics, 502(1-2), 244-256. DOI: 10.1016/j.tecto.2010.05.024

EMODnet Bathymetry Consortium (2018). EMODnet Digital Bathymetry (DTM 2018). DOI: 10.12770/18ff0d48-b203-4a65-94a9-5fd8b0ec35f6. Last access: June 2020. Website:


Garcia-Castellanos, D., Villaseñor, A., 2011. Messinian salinity crisis regulated by competing tectonics and erosion at the Gibraltar arc. Nature, 480(7377), 359-363. DOI: 10.1038/nature10651. Last accessed: 7 February 2020. Website:

Gargani, J., Rigollet, C., 2007. Mediterranean Sea level variations during the Messinian salinity crisis. Geophysical Research

Letters, 34(10), 19-26. DOI: 10.1029/2007GL029885

Gerya, T.V., Yuen, D.A., Maresch, W.V., 2004. Thermomechanical modelling of slab detachment. Earth and Planetary Science Letters, 226(1-2), 101-116. DOI: 10.1016/j.epsl.2004.07.022.

Hsü, K.J., Ryan, W.B.F., Cita, M.B., 1973. Late Miocene Desiccation of the Mediterranean. Nature, 242(5395), 240-244. DOI: 10.1038/242240a0

Hunter, J.D., 2007. Matplotlib: A 2D graphics environment. Computing in Science & Engineering, 9.3, 90-95. DOI: 10.1109/MCSE.2007.55

Just, J., Hübscher, C., Betzler, C., Lüdmann, T., Reicherter, K., 2011. Erosion of continental margins in the Western Mediterranean due to sea-level stag-nancy during the Messinian Salinity Crisis. Geo-Marine Letters, 31(1), 51-64. DOI: 10.1007/s00367-010-0213-010-0213-z

Krijgsman, W., Hilgen, F.J., Raffi, I., Sierro, F.J., Wilson, D.S., 1999. Chronology, causes and progression of the Messinian salinity crisis. Nature, 400(6745), 652-655. DOI: 10.1038/23231

Krijgsman, W., Fortuin, A.R., Hilgen, F.J., Sierro, F.J., 2001. Astrochronology for the Messinian Sorbas basin (SE Spain) and orbital (pre-cessional) forcing for evaporite cyclicity. Sedimentary Geology, 140(1-2), 43-60. DOI: 10.1016/S0037-


Lugli, S., Manzi, V., Roveri, M., Schreiber, C., 2010. The Primary Lower Gypsum in the Mediterranean: A new facies interpretation for the first stage of the Messinian salinity crisis. Palaeogeography, Palaeoclimatology, Palaeoecology, 297(1), 83-99. DOI: 10.1016/j.palaeo.2010.07.017

Manzi, V., Gennari, R., Hilgen, F., Krijgsman, W., Lugli, S., Roveri, M., Sierro, F., 2013. Age refinement of the Messinian salinity crisis onset in the Mediterranean. Terra Nova, 25(4), 315-322. DOI: 10.1111/ter.12038

Meijer, P., Krijgsman, W., 2005. A quantitative analysis of the desiccation and re-filling of the Mediterranean during the Messinian Salinity Crisis. Earth and Planetary Science Letters, 240(2), 510-520. DOI: 10.1016/j.epsl.2005.09.029

NOAA, 2010. Volumes of the World’s Oceans from ETOPO1. Last accessed: 4 June 2020. Website:, 2012.

Hypsographic Curve of Earth’s Surface from ETOPO1. Last accessed: 4 June 2020. Website:

Ohneiser, C., Florindo, F., Stocchi, P., Roberts, A., DeConto, R., Pollard, D., 2015. Antarctic glacio-eustatic contributions to late Miocene Mediterranean desiccation and reflooding. Nature Communications, 6(1), 8765, 1-10. DOI: 10.1038/ncomms9765

Rohling, E., Schiebel, R., Siddall, M., 2008. Controls on Messinian Lower Evaporite cycles in the Mediterranean. Earth and Planetary Science Letters, 275(1-2), 165-171. DOI: 10.1016/j.epsl.2008.08.022

Roveri, M., Flecker, R., Krijgsman, W., Lofi, J., Lugli, S., Manzi, V., Sierro, F., Bertini, A., Camerlenghi, A., De Lange, G., Gobers,

R., Hilgen, F., Hubscher, C., Meijer, P., Stoica, M., 2014. The Messinian Salinity Crisis: Past and future of a great challenge for marine sciences. Marine Geology, 352, 25-58. DOI: 10.1016/j.margeo.2014.02.002

Simon, D., Meijer, P., 2017. Salinity stratification of the Mediterranean Sea during the Messinian crisis: A first model analysis. Earth and Planetary Science Letters, 479, 366-376. DOI: 10.1016/j.epsl.2017.09.045

Strogatz, S.H., 1994. Nonlinear Dynamics And Chaos. New York (NY), Perseus Books Publishing L.L.C., 498.

Turowski, J.M., Lague, D., Hovius, N., 2007. Cover effect in bedrock abrasion: A new derivation and its implications for the modeling of bedrock channel morphology. Journal of Geophysical Research, 112.F4, F04006. DOI: 10.1029/2006JF000697

Verner, J.H., 2010. Numerically optimal Runge–Kutta pairs with interpolants. Numerical Algorithms 53(2-3), 383-396. DOI:


Virtanen, P., Gommers, R., Oliphant, T.E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W.,

Bright, J., van der Walt, S.J., Brett, M., Wilson, J., Millman, K.J., Mayorov, N., Nelson, A.R.J., Jones, E., Kern, R., Larson, E., Carey, C.J., Polat, I., Feng, Y., Moore, E.W., VanderPlas, J., Laxalde, D., Perktold, J., Cimrman, R., Henriksen, I., Quintero, E.A., Harris, C.R., Archibald, A.M., Ribeiro, A.H., Pedregosa, F., van Mulbregt, P., SciPy 1.0 Contributors, 2020. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17, 261-272. DOI: 10.1038/s41592-019-0686-2