Gas Transfer Velocity from Normalized Radar Backscatter

David M. Glover, Nelson M. Frew and Scott J. McCue

Dept. Marine Chemistry & Geochemistry

Woods Hole Oceanographic Institution

Woods Hole, MA 02543

508-289-2656

dglover@whoi.edu

Erik J. Bock

University of Heidelberg

Germany

Changes made to web page: 30 May 2002

Project Overview

The goal of this project is to develop an algorithm for estimating regional and global air-sea gas exchange rates using the dual-frequency TOPEX and Jason-1 altimeters. The approach is based on parameterization of the gas transfer velocity (k) using normalized radar backscatter as a direct measure of sea surface roughness due to small-scale waves. The mean square surface slope for waves in the gravity-capillary region of the slope spectrum is a robust predictor of transfer velocity. Mean square slope can be estimated from nadir-looking microwave altimeters using a geometric optics specular scattering model. Mean square slope is inversely related to the normalized backscatter. The differential scattering of the Ku-band and C-band pulses allows us to isolate the contribution of small-scale waves to mean square slope and gas transfer. The differenced mean square slope for the nominal wavenumber range 40-100 rad/m is estimated as:

where and are effective nadir reflectivities, and are normalized Ku-band and C-band backscatter coefficients and is an ad hoc adjustment to . The parameters for estimating the differenced mean square slope are optimized using in situ optical slope measurements. An empirical relationship between gas transfer velocity and differenced mean square slope is derived from field and laboratory measurements of gas flux and optical slope. The algorithm is used to construct monthly global maps of CO₂ transfer velocity and to estimate seasonal transfer velocity variations.

The Algorithm

The basic relationship (Eqn 1) between

and normalized radar backscatter is especially effective because of the dual frequency nature of the TOPEX altimeter. The dual frequency altimeter aboard TOPEX gives us normalized radar backscatter in the Ku (2.1 cm) and C (5.5 cm) bands. The effective wavelength of surface features sampled is approximately three times the incident wavelength or 6.3 and 16.5 cm. This range nicely brackets the gravity-capillary wave field, the portion of the surface wave filed thought to be most active in gas transfer.

In collaboration with our colleagues at the University of Heidelberg and the University of Rhode Island, NMF has made a comparison between field derived gas transfer velocities and mean square slope data. They found that when a rather broad spectrum of surface gravity-capillary waves (40-800 rad/m) are considered, the relationship between gas transfer velocity and mean square slope is linear. However, when the mean square slope data is binned to a wavenumber range commensurate (40-100 rad/m) with the wavelengths bracketed by the dual frequency altimeter TOPEX the relationship is quadratic.

Using the quadratic fit between and gas transfer velocity normalized to a Schmidt number of 660 (i.e. CO₂ in seawater at 20^o) and a Nelder-Mead simplex optimization to yield the best values for , , and we obtain the quadratic algorithm version 1.1:

where C₀ = 0.697, C₁ = 8.02x10⁵, = 0.402, = 0.510, and = 1.36.

Time Series Results

In what follows we present the results of applying the above algorithm to the multi-year record of TOPEX data starting with cycle 11 (Jan. 1993) and concluding (as of this writing) at the end of cycle 333 (Sep. 2001); 1 cycle equals a 10 day exact repeat orbit period. The results of 105 monthly, global maps of gas transfer velocity can be summarized as zonal averages and the main differences between the linear and quadratic relationships can be seen in the two figures below.

We also provide MPEG files for you to view the time series as a movie. To highlight the seasonal nature of the time varying transfer velocities these MPEG files start in Jan 1993 and end in Dec 2000, when the rest of 2001 has been processed we will extend these files to Dec 2001. A word of caution: these MPEG files are large (~4MB), so you may want to consider your bandwidth prior to downloading them.

Click here to view the linear (v3.1) time-series animation.

Click here to view the quadratic (v1.1) time-series animation.

The above zonal averages can be further collapsed into either a global, zonally averaged transfer velocity for the entire 8+ year time series (see upper panel in the figures below) or into an area weighted, global average time series of transfer velocity (lower panels). As can be seen in the zonal average time series plots above, the quadratic algorithm achieves higher high and lower low values than the linear algorithm.

Monthly Images and Data Sets

The individual image files (and the data files that went into making them) are also available (in tabular form: "img" is linked to the corresponding image and "data" to the corresponding data). We ask our colleagues to let us know if you have field data that either corroborates or contradicts these fields. Please click here to get the images and data.

The text, graphics, and other materials contained in this homepage and attached documents are intended solely for scholarly use by the scientific and academic community. No reproduction, re-transmission or linking of this page to any other page without the author's expressed written permission is permitted.