Fresh Water, the Ocean, and Sea Level Change

Carl WunschAustin November 2009

Excess or accelerated glacial ice melt is widely believed to be contributing about 2mm/y to apparent global sea level rise. Main data comes from observations, sometimes conflicting, of the ice sheets. Raises several interesting oceanographic issues:

Can it be independently, quantitatively, confirmed from oceanic observations?

Can the influence of additional fresh water on the ocean structure and circulation be quantified and understood? Includes the influence on sea level. Involves everything in physical oceanography, geodesy, hydrology, meteorology, geophysics, glaciology,….

Model Magic:

Fresh water layer covers entire subpolar basin. Is this possible? Leads to sometimes dramatic shifts in the ocean circulation. (Hosing)

Manabe and Stouffer, Nature, 1995

“Shutdown”Has garnered huge media attention, large field programs (RAPID), etc.

The context raises several immediate issues:

(1)There is a very active hydrologic cycle whose steady state values dominate the estimated increase, and whose interannual variations are poorly known, but likely large. Increased glacial input is a perturbation on the existing hydrological cycle.

(2) Ice melt (mainly) enters the oceans at the boundaries---one of the most complex and least-understood of all oceanic regions.

(3) Time scales of oceanic adjustment to fresh water disturbances range from hours to thousands of years. Disturbance time scales are similarly disparate.

How does fresh water enter the ocean?

Open ocean rainfallRiver runoffIce melt at boundariesIce melt in the ocean interior (icebergs)Percolation at depth through continental margins

How does fresh water leave the ocean?

EvaporationSubduction into the sea floorFormation of sea ice

These processes are both ongoing and subject to fluctuation.

Moore, 2009, Ann Rev EPS. Infers as large as river input.

Understanding how, where, and at what rate, fresh water is injected or removed from the oceans, and the consequences of those phenomena, raises a long series of difficult questions ranging from in situ to space observations and intricate modeling problems. Surprisingly little seems known.

Some useful numbers.1 Sv=106m3/s. (Florida Current carries about 30Sv.)1mm/y (of water) globally ~ 0.01Sv entering the ocean.

Mean annual precipitation ~ 1 m (of water)/year. About 10 Sv entering globally. Almost perfectly balanced by evaporation, runoff, and percolation---but with very different spatial patterns.

1km3/y~3x10-5Sv1Gt/y=1012kg/y=3x104kg/s=0.03Sv

Area of Greenland: 2.2x106km2 =2.2x1012m2

Area of Antarctica: 1.4x107km2 =1.4x1013m2

So 1 cm/y precip. over Greenland is about 6x10-4Sv and over Antarctica is about 0.003Sv

Global total P about 1m (Peixoto and Oort, 1992) and approximatelyequal to the net E-R.

Beranger et al., Oc. Dyn., 2006Note large disagreements

Greenland ice sheet mass balance (Box, Bromwich, & Bai, JGR,D, 2004) estimate , approximately, 600km3/y precip, 63 km3/y sublimation/evaporation, 40 blowing snow, 376 melt, to give balance within about 10% on average 1992-1998.

Very roughly then about 400km3/y would be discharged to the ocean, assuming most of the ice melt ultimately ends as runoff (?). Rignot and Kanagaratnam, Science, 2006, Chen et al., Science,, 2007, suggest an increase in ice discharge of about about 100 km3/y, which is a 25% increase. Can one detect this change? Note that interannually, Box et al. suggest a year-to-year range of about +/-145km3/y, and that the net increase in sl from Greenland, 1991-2000 was 0.22mm/y.

“…the natural variability in ice sheet mass balance appears to be too large to provide an indisputable assessment of positive or negative mass balance.” (published in Box et al., 2004). At least shows that the background variability is not negligible in this context.

“The large variability in moisture convergence presented in this study implies a dramatic impact on global sea level. Interannual oscillations of more than 30% in Antarctic annual net precipitation shown here represent a global sea level variability range of +/-1.2-1.5mm/y based on estimated continental ice accumulation…” Cullather et al. 1996.

Bromwich et al., 2007, JGR

Annual mean area-weighted P-E in Antarctica for various regions and different elevations.

Arrival of polar orbiters

Modeled precip. over all of Antarctica. Bromwich et al., 2004. Note large annual cycle,and interannual variability.

Box et al., 2004, Science,

Net precip. fraction liquid precip.

Accumulation 1991–2000, equal to precipitation minus surface snow and blowing-snow sublimation.

One way to determine whether more fresh water is entering the ocean is to answer the question of whether the ocean getting fresher?

A 1mm/y addition of fresh water corresponds to a global mean salinity change ΔS=S(0)hm/h(0) of about 10-5 y, (Salinity is a dimensionless quantity, on average about 35, meaning about 3.5% salt, by mass.)

1mm sea level change/y represents a volume or mass precision of 10-3m/4000m=0.25x10-6/y .

(Normally one seeks a precision 10 x better than the expected signal.)

Are such precisions possible either with available data or models?

Over a decade, the implied change is 10 times larger. Are precisions of that magnitude possible from the data, for the model, or the combination? The signal grows with time, but so do systematic and random errors.

Worthington, 1981, Evol. of Physical Oceanography

As of 1977, white squares had at least one acceptable deep station, Hatched had at least one intermediate depth station, and black had no acceptable station.

Consider the sampling problem for in situ hydrographic (temperatureand salinity) data.

Worthington threw out almost all data, as being inaccurate, except those obtainedby a small private club of trusted hydrographers. Contrasts greatly with some recent “data mining” activities. Are the errors in the data Worthington rejected random? Or systematic?

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sampling in 1960 WOA

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sampling in 2002

mainly MBTs(mechanical bathythermographs)To about 400 feet (sic)

More than 4 measurements in a 1 degree square in 50 years. “Recent” means WOCE & later. To 300m (recall that the mean ocean depth is 3800m).

G. Forget

Can one really compute global averages at useful accuracyfrom such data???

Examples of possible systematic errors in data leading to trends:(XBT fall rate errors have attracted much attention. But many others.)Salinity: the technology changed from water samples run by titration to water samples run on conductivity machines which evolved (toSchleicher/Bradshaw). The definition of salinity changed (not initself an issue). Samples were often drawn into poorly rinsed bottles;they were often stored for later measurement ashore, weeks oreven months later (evaporation was found to be a problem). Seasonaland latitudinal sampling biases.

Another issue is the depth inference, which shifted from reversingthermometers to pressure gauges. Gouretski and Jahncke (2001) foundin their climatology an inordinate number of samples at the nominalbottle depth---suggesting a failure to use uprotected thermometers.Seasonal and latitudinal sampling biases.

Temperature and salinity problems were what led Worthington to his data cull (failure to recover the deep T-S relationships).

How big is the ongoing hydrologic cycle? How much does it vary, naturally?

Peterson et al., Science, 2002

Arctic River Discharge

1mm/day is about40cm/y

Villar et al. J. Hydromet., 2009

The annual cycle. How does the ocean respond? A complex dynamical question.

Some Theoretical Problems:

What happens when fresh water is ejected from land into the ocean---either as liquid runoff, or as ice? Steady-state versus transient?

What is gravity (mass) signature, and how long does it take? What happens to earth rotation parameters, and how long does that take?

How does sea level adjust and on what time scale?

What does it do to the ambient ocean circulation?

initial mass injection

after about 1 day to---?

lateral displacement after about 1 day.

Surface Elevation. Geostrophically Adjusted.

If unblocked, would persist until diffusion acted.

A version of the classical “Rossby adjustment problem”.

Compensation occurs after order one day

Very little theory exists for the adjustment process to fresh water injection (or removal). Over shelves/slopes a complex wave process would be involved.

Ice sheet time scales---one piece of the overall system (courtesy, P. Heimbach). Represents the time scales of forcing of the ocean:

• Minutes to hours: – wave/ice-shelf interaction from swell, tides, calving icebergs– stick/slip behavior of ice motion (revealed from seismography)

• Weeks: – Larsen B ice shelf break-up 2002 (WAIS)

• Monthly to seasonal: – Speedup/slowdown of Greenland outlet glaciers– seasonal accumulation

• Inter-annual to multi-decadal/centennial(?): – Speedup/slowdown of Greenland outlet glaciers– Speedup/slowdown of West Antarctic ice streams

• Multi-centennial:– Speedup/slowdown of West Antarctic ice streams– circumpolar deep water (CDW) age reaching the Antarctic ice

shelves• Multi-millennial:

– surface-to-bottom heat conduction– ice sheet deglaciation

Wunsch & Heimbach, Quat. Sci. Rev.

Cessi et al., 2004. Time in years for a North Atlantic disturbance to penetrate the world ocean (sea level). Many decades are required for its evolution and many more required to fully observe it. What can one say after 15 years?

Idealized

“Realistic”

Because of the long memory times intrinsic to ice sheets and the ocean, what we observe today of fresh water injection/removal is a consequence, at least in part, of long-ago events and disturbances.

As a corollary, disturbances occurring today will excite modes of response extending far into the future (the system is not in equilibrium).

Human populationdoubling

To origins of oceans, atm. oxygen, life; continental drift, evolution, weathering chemistry,…

Some of the intrinsic timescales of climate change.Human populationdoubling

Can one model global sea level change?

Calculation of the mean sea surface in an ocean model of mean depth of 4000m to an accuracy of 0.1mm/yr requires a volumetric accuracy of 1 part in 107. Are models that good?

What can change global mean sea level?:Net temperature change (heat exchange with the atmosphere)Addition or subtraction of fresh water (exchange with atmosphere, land, ice)Change in volume of the ocean (post glacial rebound; spreading rate changes)Melting or formation of sea ice with non-zero salinity

What can change regional mean sea level?Global contributions plus:

Temperature shiftsAddition or removal of fresh waterDisplacement of ocean circulation featuresTectonic upliftGravity field modification (melting of glacial ice)Change in ocean load (local atm. pressure)….

There exist serious modelling questions in a context where submillimeter/year accuracy is needed.For most models:

Boussinesq approximation---conserves volume, not mass; conserves salinity, not salt.Surface boundary condtions for salt---at least 3 in use, including virtual salt flux (Huang, 1993) as well as incomplete treatment of surface layer dynamics. Numerical treatment of the moving free surface.

Approximations in the equation of state.

Errors in the meteorological forcing including large-scale imbalances.

Incomplete sea ice models, volume/mass inconsistencies when ice is formed.

Models generally lack self-attraction and pressure load corrections….

And these models must be run for decades. Many of these errors will necessarily be cumulative.

Mitrovica et al., Nature, 2001

Fractional variation of sea levelfrom melting ice, assumed uniformover restricted areas. 0 meansno change.

Antarctica

Greenland

Mountain glaciers

There are many more complications notyet accounted for, e.g.:

How well do we know long term ice volume changes? Is a 5 year record meaningful? Can one predict with skill? if so, what is it? How is that known?

GCMs do not yet usually include effects of water displacement self-attraction and sea floor load.

Regional estimates in global models reflect imposed global constraints---e.g., global volume conservation implies regional compensations occur.

Oceanic baroclinic memories, and hence spatial distribution of sea level change signals, extend to thousands of years.

Trend in sl from model and all data m/y

Trend in column integrated density from temperature Trend in column integrated density frrom salt

Red means increasing density (decreasing temperature, increasing salinity

Trend in sl from altimetry data mm/y

Global mean removed from the sl results

Vertical integrals of net density change & ratio from temperature

ratios to the top-to-bottom integral

What is the vertical distribution?

Cannot ignore the deep ocean

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Understood? Tipping points?

Understanding where, how, and what rates fresh water enters the ocean, and what the consequences are for sea level and the circulation are fundamental science issues----ones with extremely important societal implications. Little is now known about any of these problems.

Solving these problems brings together, perhaps uniquely, physical oceanography, geodesy, glaciology, geophysics, hydrology, numerical modeling, meteorology, …,and with all the societal implications. A nice challenge for everyone.

Thank you.