At frequencies below 1 kHz sound absorption coefficients in the ocean are
a function of pH, and at higher frequencies are dependent upon MgSO
.
The pH dependent terms are attributable to relaxation of B(OH)
and
MgCO
species, and the ensemble effect has been approximated (
Mellen et al. [1987]) as:
where 
is the absorption coefficient (dB/km) and
where S is the salinity, 
is the amplitude of each component and
depends on pH, f is the frequency and 
is the relaxation frequency.
Overall accuracy of 
15% in 
requires that pH be known to 0.05
pH units.
The presently used oceanic pH field for sound absorption models is derived
from a combination of GEOSECS data and Soviet data from the Gorshkov atlas
( Gorshkov [1978]) for the North Atlantic where GEOSECS data are
absent. We compare the North Atlantic fields with the well constrained TTO
North Atlantic CO
data set and find large differences. We further show
that sufficiently strong correlations exist between CO
system variables
and other more commonly available hydrographic properties that improved
renditions of the pH field in other regions of the ocean are possible once
equivalent local correlations are established, thus leading to greatly
improved estimates of the sound absorption field.
Accurate measurement of the oceanic CO
system on a global scale has
long been a goal of ocean chemists and has a confusing history.
Complexities in representing the pH scale, uncertainties in thermodynamic
constants, and the need for an adequate chemical model of sea water have
all contributed to the problem. The first large scale data set was that
obtained during the GEOSECS program (1972--1978); the details of the
CO
system measurements made then are to be found in Bradshaw et al.
[1981], and the data are recorded in the GEOSECS atlases.
Early work on the North Atlantic segments of GEOSECS did not produce a useful
CO
data set due to problems with sensor readiness, and thus a large
data gap existed. This deficiency was remedied in the Transient Tracers
in the Ocean (TTO) North Atlantic cruise of 1981 where, following the work
of Bradshaw et al. [1981] a large and well documented data set was
obtained. The uses for oceanic CO
data are many, and among them is
the estimation of the oceanic sound absorption coefficient 
(dB/km) at low frequencies. This problem is the focus of this paper.
The history of elucidating the oceanic chemical properties responsible for
sound absorption is a fascinating one. An excellent account is to be found
in the Naval Underwater Systems Center (NUSC) report by Mellen et al.
[1987]. Early work by Leonard et al. [1949] established that
MgSO
was responsible for the absorption anomaly, relative to fresh
waters, at frequencies in the 10 --- 100 kHz range. Eigen and Tamm
[1962] formally established the two-step equilibrium and relaxation process
involved.
Schulkin and Marsh [1962] provided the first practical formula for sound absorption in sea water, and Thorp [1965] was able to show that an absorption anomaly, one order of magnitude greater than that predicted by the Schulkin and Marsh formula, existed for frequencies about 3 kHz. The pH dependence of this low frequency anomaly was subsequently confirmed by resonator experiments, and thus predictions of the low frequency sound absorption in sea water depend upon a knowledge of the pH field.
Mellen et al. [1987] have combined the chemical terms responsible for acoustic losses into a global absorption formula model of the form:
where
and
in which S is the salinity, 
is the amplitude of each component, K
is a pH dependent parameter (
), 
is the
relaxation frequency (kHz) of the corresponding term, f is the frequency
for which the sound absorption coefficient is being evaluated, T is
temperature (
C), d is depth (km), and consequently 
and 
are pH dependent terms of the form:
is a constant. They note that pH is clearly the major limiting
factor in the accuracy of the absorption formula, and that errors of
15% in 
require that pH be known to 
0.05 pH units.
Although Qiu [1991] has shown that this model may need to include the
effects of pressure on B(OH)
, revision of the acoustic absorption model
is beyond the scope of this paper.
We recognize that many other terms contribute to acoustic losses in the
ocean. Guoliang and Worcester [1989] recently investigated the obverse
of this problem by examining the possibility of determining pH from the
acoustic signals. They found that surface scattering introduced considerable
complexity and concluded that differential acoustic transmissions at
550 
100 Hz over a 750 km path would require about 60 independent
samples in order to estimate mean pH in the Atlantic acoustic path to a
precision of 
0.05 pH units.
The problem then is not easy. However, if reliable estimates of the oceanic pH field on a common, and well defined, scale are achievable, then a consistent oceanic matrix for interpreting long range acoustic losses can be provided. In this paper we examine this problem.
Our research was stimulated by the observation that, in order to provide full North Atlantic coverage, Mellen et al. [1987] were forced to resort to combining GEOSECS data and Soviet data from the Gorshkov atlas [1978]. We are aware of the difficulties here and undertook to examine the reliability of this approach through comparison of the Gorshkov data with the more recently available TTO data set. In addition, we were compelled to ask to what extent the pH field is predictable from regressions with hydrographic chemistry master variables that have been more widely measured in the global ocean.
After a long history of difficulties in both developing a sound absorption
model and measuring CO
system variables in sea water, the results
presented here for the North Atlantic ocean suggest that the oceanic pH field
can now be defined on a dense geographic grid within the a precision of
0.05 pH unit, as required for determining the sound absorption
coefficient to within 
15%. The extension of this result from the North
Atlantic ocean to other regions is currently under investigation. The results
of the present and planned measurements of the carbonate system in the world
ocean within the international programs such as JGOFS and WOCE are enlarging
the present CO
database and will further allow us to refine and extend
the validity of these concepts.
In summary we have evaluated the usefulness of prediction of the ocean pH
field from other hydrographic chemical variables. We have further reviewed
the various pH scales currently in use by geochemists. We show that the
purely non-CO
system variables of the TTO North Atlantic data set gives
an estimate of the pH field that is superior to the direct estimate provided
by the Gorshkov atlas. We suggest our estimates of K be adopted for the
North Atlantic. We extend our work by presenting multiple linear regression
formulae representing C
and A
as linear combinations of
more commonly measured hydrographic and nutrient variables in the North
Atlantic. Finally, we are ascertaining similar relationships in other ocean
basins.
Table: Stepwise Multiple Linear Regression Parameters and Statistics for A
Table: Stepwise Multiple Linear Regression Parameters and Statistics for C
