Twentieth century sea level: an enigma

Abstract

Changes in sea level (relative to the moving crust) are associated with changes in ocean volume (mostly thermal expansion) and in ocean mass (melting and continental storage): zeta(t) = zeta(steric)(t) + zeta(eustatic)(t). Recent compilations of global ocean temperatures by Levitus and coworkers are in accord with coupled ocean/atmosphere modeling of greenhouse warming; they yield an increase in 20th century ocean heat content by 2 x 10(23) J (compared to 0.1 x 10(23) J of atmospheric storage), which corresponds to zeta(greenhouse)(2000) = 3 cm. The greenhouse-related rate is accelerating, with a present value zeta(greenhouse)(2000) approximately 6 cm/century. Tide records going back to the 19th century show no measurable acceleration throughout the late 19th and first half of the 20th century; we take zeta(historic) = 18 cm/century. The Intergovernmental Panel on Climate Change attributes about 6 cm/century to melting and other eustatic processes, leaving a residual of 12 cm of 20th century rise to be accounted for. The Levitus compilation has virtually foreclosed the attribution of the residual rise to ocean warming (notwithstanding our ignorance of the abyssal and Southern Oceans): the historic rise started too early, has too linear a trend, and is too large. Melting of polar ice sheets at the upper limit of the Intergovernmental Panel on Climate Change estimates could close the gap, but severe limits are imposed by the observed perturbations in Earth rotation. Among possible resolutions of the enigma are: a substantial reduction from traditional estimates (including ours) of 1.5-2 mm/y global sea level rise; a substantial increase in the estimates of 20th century ocean heat storage; and a substantial change in the interpretation of the astronomic record.

Figure 1

Cartoon of the assumed model of holocene sea level (see text). After the glacial maximum 20,000 years ago, global sea level rose by 125 m and has been within a few meters of the present level since 4000 B.P. After the little ice age early in the 19th century, sea level rose at 18 cm/cy (the historic rate) with no measurable acceleration until the mid-20th century, when thermal expansion associated with greenhouse warming became significant, contributing an additional 3 cm by the year 2000. Greenhouse-related sea level rise has accelerated to the present rate of 6 cm/cy, making the historic + greenhouse rate 24 cm/cy.

Figure 2

(Bottom) Global mean temperature changes θ(t) at stated depths. Vertical scales are amplified at increasing depths in the ratio 1:2:4. (Top) Relative heat content h(t). Solid red curves are measured temperatures [from The World Ocean Atlas (4, 5)] and associated heat content 0–3,000 m; dotted curves are model predictions; red from the Levitus et al. experiment GSSV (5) and blue from Barnett et al. (6). Parallel Coupled Model (PCM) decadal ensemble averaged (6). The scale (top right) gives the approximate sea level rise associated with the increased heat content. The line AB corresponds to a steric rise by 12 cm/cy.

Figure 3

The time difference ΔT derived from Babylonian, Chinese, Arabic, and Greek eclipses (18). The best-fitting parabola (dashed) is consistent with an increase in the length of day by 1.70 ± 0.05 ms/cy over the last 2,700 years. The solid curve is fitted by using cubic splines. The parabola associated with tidal friction (19) is represented by the ±1σ limits (dotted). The Inset shows the situation for the last 500 years with ×25 amplification.

Figure 4

Length of day, τ in milliseconds relative to 1900 (18, 19). The long-term observed rate 500 BC to AD 1990 is τ̇_millennium = +1.7 ms/cy. Tidal deceleration is associated with τ̇_tides = +2.3 ms/cy, indicating a long-term residual τ̇_rebound = −0.6 ms/cy associated with a viscous rebound of the solid Earth from a removal of the ice sheets. (Bottom) τ(t) for the last 170 years on an enlarged scale, together with the previously established linear trends: τ̇_tides = +2.3 ms/cy, τ̇_tides + τ̇_rebound = 2.3 − 0.6 = 1.7 ms/cy, and τ̇_tides + τ̇_rebound + τ̇_sealevel = 1.7 + 1.2 = 2.9 ms/cy for a 12 cm/cy eustatic rise in sea level.

Figure 5

Motion of the pole of rotation in milliarcseconds (mas) and in meters; x toward Greenwich and y toward 90° west of Greenwich (27, 28). The mean observed motion (dotted), together with that computed by Peltier (7) for rebound, is shown in Inset. The dashed arrow toward Greenland is the computed displacement for 12-cm eustatic sea level rise associated with Greenland melting. Changes in the length of day over the same interval are taken from Fig. 4.