Altimetry Beyond 2010: Where Do We Go From Here? A sketch. Carl Wunsch Scripps Institution of Oceanography April 2008

15+ years since the flight of TOPEX/POSEIDON. It was first discussed 35 years ago (1974). First near-global, continuous measurements. Covered the frequency/ wavenumber spectrum from (very approximately) 20 days to 15 years periods, 200km to 20,000km wavelengths and the first direct determination of absolute sea surface topography. “Solved” the tidal problem; gave hugely improved marine geoid; global wave and ionosphere measurements; permitted (unexpectedly) estimates of global mean sea level change,….. Showed enormous ENSO signal (we were lucky). Was “sold” in part by designing WOCE to support and exploit it--- independent of NASA---made it appear that a major scientific community would actually use the data. Much of the appeal was descriptive/exploration---no one had ever observed oceanic variability on time scales longer than a few days except in a few isolated (e.g., MODE/POLYMODE, FDRAKE, ISOS,…) regions.

When proposing new technical developments the most compelling arguments tend to concern questions where the measurements provide qualitatively new information: no one could ever measure those space-time scales before, no one ever measured in that region before, theory says something important should exist that we have never seen, or all of these things. In 1980, this was almost easy. It’s much harder now as we know so much more.

For climate studies, pure duration is probably the highest priority: a 15-year record is pathetically short compared to the known time scales/memories present in the ocean. Need open-ended, indefinite duration measurements. Chief lacunae in existing T/P-class altimetry are: (1)High southern latitudes---with sea ice being a major problem. Depending upon Arctic sea ice behavior, may badly want altimetry there. (2)Shallow water tides and lower frequencies (3)Scales shorter than about 200km (Stammer, Zang, Scott, Arbic,…) down to order 1 km (latter perhaps beyond reach by radar methods). (4)Sea ice freeboard determination (5)Glacial ice volume (a major sea level issue) (6)More convincing understanding of low frequency variability versus trends Going forward:

TOPEX Science Working Group, 1980 (Note---this was not the Science Team) Spectra are useful summaries as they provide simple summaries and sampling requirements. Not intended to diminish the importance of phase information e.g., for the study of coherent structures. Approx. coverage by T/P

Stammer, 1997, altimetric power density and slope power density estimates Scott and Wang, 2005 Does energy move up or downscale? (Yes?) A crucial element in modelling longterm climate behavior.

Ferrari and Wunsch, 2009 Overlapping wave numbers of common frequencies

Zang and Wunsch, 2001 Disclaimed any skill below 200km wavelengths. What is the behavior at very low frequencies? Trends? Red noise? White noise? Schematic frequency/wavenumber at low frequency. Have Garrett-Munk at high (>f) frequencies.

Katz, JPO, 1979 Main thermocline wavenumber spectrum. Interpreted as internal waves. Why not mesoscale? Gage & Nastrom, 1986, for atmosphere Interpretation of frequency spectra is that they are predominantly advected by larger scales. See also Pinkel, JPO, 2008 Some things that seemed settled long ago suddenly seem open to question.

Risien and Chelton, 2008, time mean wind-curl from scatterometer. Must account for the fact that the system is a forced one---not at all obvious that theories of a “free” ocean are very relevant. Forcing exists at all frequencies and wavenumbers, everywhere.

Known (to me) physics on scales shorter than about 200km: “Mesoscale” or geostrophic eddies (quasi-geostrophic physics) Internal/inertial waves Vortical modes [?] Wind-forced, negative equivalent depth, surface trapped modes Neutral and unstable modes of surface-intensified shear (Eady/Charney) Frontal physics, some near balanced Long surface gravity waves (What are the surface pressure signatures of all these phenomena?) Direct separation appears to depend on the ability to distinguish different frequencies having common wavenumbers. What is possible with next- generation altimeters? Or is it possible to be clever about phases/velocities versus pressure, etc.?

Strass et al., 2002 Southern Ocean. All spatial scales present. Two different times

SOSE Animation Here From Matt Mazloff PhD Thesis, MIT/WHOI, in preparation, 2008 Part of ECCO-GODAE effort at MIT/AER (NOPP/NASA)

Zero-order physics questions remaining: At what spatial scale is energy injected into geostrophic eddies? How is it partitioned between barotropic and baroclinic structures? Are there significant up and down-scale energy/enstrophy fluxes in the real ocean and to what degree are they functions of the vertical structure? Most of the kinetic energy in the ocean lies in the geostrophic eddies: how is that dissipated---bottom stress, wind stress, lateral stress/fluxes, interaction with larger scales? It’s always troubling when models produce unobservable/untestable structures. Was one of the major arguments for TOPEX, circa that global models would soon outstrip any observational capability. It is the situation with motions on scales below about 200km and time scales beyond 15 years.

Part of the “selling” of TOPEX was the construction of WOCE, to simultaneously exploit and augment the hoped-for data. Supporting field programs are both attractive to agencies and are also (often) good science.

Exploitation/Support: A strawman experiment to determine the upper ocean frequency/wavenumber content: Regional, for later global inference. Region: open ocean, moderate eddy energy level, significant wind variability. Position, size to be worked out. Observational mix could include: Altimetry (direct velocity inferences??) Scatterometry SST (satellite) Color (satellites are ultimately justified by their global coverage) Armada of gliders. Nominally 3 cm/s velocity. Depths 0-200m. Shipboard ADCP Shipborne tows Moorings (IWEX-type to obtain short horizontal scales?) Shipboard over-horizon radar Seismic imaging of water column Aircraft-borne laser altimeters State estimation for open ocean boundaries; non hydrostatic, extremely high spatial resolution (next generation of SOSE)

An interesting challenge. Good luck to us all. Thank you.