The electromagnetic bias, or difference between the mean sea surface height measured
by an altimeter and the actual mean surface height, is among the largest source of
error in satellite altimetry. Our research project aims to understand the relationship
between the bias and properties of wind waves, and identify parameters which allow more
accurate modeling of the bias, so that it can be subtracted from altimeter data.
The goal of ocean satellite altimetry is to provide the sea surface height over the
oceans of the earth. Of course, the sea surface height varies on the scales of
centimetres and meters, due to wind-driven waves and ripples. It is less well
known that the mean surface height (if one were to smooth over the waves) also
varies, over tens or hundreds of kilometres. This gentle sloping of the surface
is produced by tides, seamounts, and currents. It is these larger scale effects
that users of altimeter data would like to study. The problem is, how do we average
out the small-scale waves and ripples to obtain the mean sea surface level?
The good news is that some of this averaging is done automatically. The footprint,
or illuminated area, seen by the altimeter signal on the sea surface, is much larger
than surface undulations due to wind-driven waves. Some of the altimeter's signal
arrives a bit early, due to the wave crests, and some arrives later, due to the
troughs. By adjusting the instrument to average these arrival times, we can determine
the mean surface height over the footprint area.
The bad news is that wind waves are not symmetric: if we compare the surface height
to a "sine wave" profile, the crests are sharper, and troughs longer (figure 1).
This makes the altimeter's measured height a few centimetres lower than the height
actually obtained if the wind stopped and the waves died out to leave a glassy smooth
surface. This error is the "electromagnetic (EM) bias."
Our research project is to understand the physical cause of this bias, and to model it
in terms of measurable properties of the ocean surface, such as wind speed and height
of the largest waves (the waves a surfer would ride on, also known as "swell", as opposed
to smaller ripples). A good bias model would allow altimeter data to be corrected, so
that geoscientists would have more accurate surface height information.
There are two approaches to modeling the EM bias. The first, empirical methods, compares
results from measurements and experiments to estimate the EM bias for given wind and sea
conditions. Empirical models using the wave height and wind speed are the most common
models currently in use. The other approach is to create mathematical models using
electromagnetic theory. These theoretical models are improving, but as yet have not
been able to be widely applied.
One result of our work so far is that by including a new parameter of the surface waves,
the slope of the swell, much more accurate models for the bias are obtained. For altimeter
data collected from altimeters mounted on towers, together with surface height data from
wave gauges, the bias can be estimated to less than a centimetre. Previous models also
work better for some regions of the ocean, and worse for others. Including the slope
reduces the error from region to region.
The drawback of this new model is that the slope parameter is not directly available
from the altimeter data. We are working on better surface models, which relate wind
to waves, and improved electromagnetic models, which relate the altimeter's received
signal to the surface height, which will help us learn how to use the data that is
available to better estimate the bias. We plan to use computer simulation of the
altimeter signal to model the bias without actually having to mount a radar on a tower
and collect data. Most bias models are based on the assumption that the ocean surface
only varies in one direction. We are investigating two-dimensional surface models as well.
Hopefully, with the progress that has been made so far, and a bit more effort, the bias
problem can be reduced so that, instead of being the largest source of error in altimeter
measurements, the bias will become only a minor part of the overall system error budget.