1. Using Profiling Float Trajectories to Estimate Ocean Circulation
A Presentation to the ARGO Workshop November 2003
Breck Owens
Woods Hole Oceanographic Institution

2. Collaborators
Mapping the circulation from profiling float trajectories Kara Lavender (SIO  WHOI  SEA) Russ Davis (SIO)
Mapping using variety of data types Bruce Cornuelle (SIO) Steve Jayne (WHOI) Jim McWilliams (UCLA)

3. Outline of Presentation
Procedure
Results from profiling floats for - the northern North Atlantic - the Indian and South Pacific
Combining with other data - combining with other floats for the North Atlantic - Using other data to get a 3 dimensional description - first results for the North Atlantic - comparisons with altimetry

4. Procedures
Ascent and descent positions used to compute average velocity at depth for that cycle. Time to surface << time at depth  Errors for at depth velocities are small O(1 cm/s).
Space and time averages computed over bins (nominal size 1º degree or larger)
Impose geostrophy and construct smoothed version of circulation using Optimal Interpolation (OI)
Future work can include other data or weak constraints as input into the OI procedure

5. Schematic of float cycle
- Surface Positions used to obtain best estimate of ascent and descent positions
- As long as travel time to surface << drift time, positions can be converted into average velocity at depth

6. - Time scale from temporal covariances
To estimate uncertainties in bin averages and to provide a priori statistics from observations (or analysis of modeling studies) requires
- Time scale from temporal covariances
- Space scales from spatial covariances (including noise)
Spatial Covariances
Temporal Covariances
Temporal and spatial covariances

7. Bin Averaging and Estimating Float Velocities
Bin size ~ 110 km square
Obtain mean and variance for velocities averaged over all floats that pass through bin
Using integral time scale (10 days), convert statistics to means + error estimates

8. Optimal Estimation
Objective Mapping uses a priori statistics (covariances) for spatial interpolation and takes into account estimated errors when drawing maps
Imposes dynamical balance (hard constraint) ie Geostrophy
Directly provides estimates of linearly related fields, for example, dynamic pressure from velocity estimates

9. Results from the Northern North Atlantic
Based on profiling float data collected from deployed in support of the Atlantic Climate and Circulation Experiment (ACCE) and Labrador Sea Deep Convection Experiment
Results described by Lavender, Owens and Davis (2003, DeepSea Research, accepted)

10. Path of Floats from pre-Argo Array
208 P-ALACE and SOLO floats
21,886 velocity measurements (arrows)
 578 years of drift velocity data

11. Number of Observations per bin

12. Bin Averaged Velocities
Bins nominally 1º square
Error ellipses based on degrees of freedom (10 day time scale)
All Bins
Bins with significant means

13. Objective Mapped Velocity, 700 m
Data from bin averages
Imposed Geostrophy
Guassian form for dynamic presssure covariance, scale = 150 km
Recirculation near boundaries
Interconnection between Labrador and Irminger Seas
Strong influence of topographic steering

14. Dynamic Pressure
Lavender, Owens, & Davis, 2003

15. Indian and South Pacific Oceans
Russ Davis has used WOCE and Argo float data for these two Oceans to estimate the circulation at 1000 m depth
Projections onto basis functions, assuming an a priori variances (spectra) for these functions, ie form of OI.
Bin size larger than Atlantic, O(300 km)

16. Indian Ocean
Velocities at 1000 m
From WOCE and Argo floats
1174 float years of data
Davis, 2003

17. Indian Ocean
Absolute Dynamic Pressure at 1000 m
From WOCE and Argo floats
1174 float years of data
Davis, 2003

18. South Pacific Ocean
Velocities at 1000 m
From WOCE and Argo floats
1332 float years of data
Davis, 2003

19. Absolute Dynamic Pressure at 1000 m From WOCE and Argo floats
South Pacific Ocean
Absolute Dynamic Pressure at 1000 m
From WOCE and Argo floats
1332 float years of data
Davis, 2003
South Pacific Dynamic Height

20. Expanded Analysis of North Atlantic
Used all float observations from North Atlantic SOFAR floats - RAFOS floats - Profiling floats
First maps from project to eventually combine subsurface and surface velocities, dynamic height, altimetry

21. North Atlantic - using all float data
Profiling and acoustically tracked floats
1540 float years of data from 1240 floats
Used same spatial scale, 150 km for  covariance, as earlier North Atlantic maps

22. Combining 700 m Floats and Shear from Hydrographic Climatology
Dynamic Height from Hydrobase
Sea surface relative to 700 m
700 m Floats + hydrography
Sea surface pressure

23. Comparing Float + Hydrography with Altimeter Estimates
Topex/Posidion mean relative to Geoid from Grace Mission
Floats + hydrography
Sea surface pressure

24. Another Estimate of Surface Circulation
Peter Niiler, Nikolai Maximenko and Jim McWilliams
Circulations estimated from surface drifter data (15 m drogue) and NCEP reanalysis for Ekman velocity estimate

25. Estimate of Surface Pressure from Surface Drifters
Niiler, Maximenko and McWilliams, 2003

26. Conclusions
Profiling float trajectories provide an excellent means of estimating ocean circulation
Broadly consistent with other measures of circulation. Examinations of differences should elucidate both physical processes and sampling issues.
Future work will combine velocities, Argo profiles, altimetry, surface drifters, and winds to give mean and low-frequency 3-D estimates of the ocean circulation