Technical Comments

Heat Content Changes in the Pacific Ocean

Science  11 Jun 1999:
Vol. 284, Issue 5421, pp. 1735
DOI: 10.1126/science.284.5421.1735a

The Acoustic Thermometry of Ocean Climate (ATOC) Consortium (1) showed a factor of 2 discrepancy between heat content changes from a numerical model assimilating ocean observations and changes expected from surface heat fluxes as measured by the daily National Center for Environmental Prediction (NCEP), averaged over the North Pacific. Their conclusion was that either the heat fluxes are too large by a factor of 2, or that half of the heat content changes are a result of advection of heat by ocean currents. We calculate that the most likely cause of the discrepancy is an underestimate of heat content changes by the numerical model.

Changes in oceanic heat content are caused by (diabatic) changes in the flux of heat from the atmosphere to the ocean, by (adiabatic) wind-forced vertical movement of isotherms, or by horizontal fluxes. Changes in heat content can be inferred from changes in sound speed by ATOC or calculated directly from an expendable temperature profiler (XBT). Changes in heat content can also be inferred from sea level measured by altimeter, longitudinally averaged to suppress adiabatic terms (2).

Advection is not large enough to account for the discrepancy. Previous studies showed that the contribution of advection is about 30% in the central North Pacific (3), about 50% near its western boundary (3, 4) (a region excluded from the comparisons), and negligible when averaged over the width of the Pacific (5). In addition, the discrepancy of 100 W m−2 for the entire North Pacific would require seasonally reversing heat transports that are four times larger than estimates of the mean meridional transport at 10°N (6), a highly unlikely scenario.

Errors in the heat fluxes are also not large enough to account for the discrepancy. Differences between heat content from climatological XBT data and from surface fluxes are only about 20% of the discrepancy (7), and some of those errors are in the XBT data. Advection and heat flux errors together could total 50%, but a compelling argument against this hypothesis is that the NCEP fluxes are consistent with the seasonal altimetric sea level variations (Fig. 1) within 20%, with no difference in phase. The careful reader may have deduced this agreement by noting that the altimetric estimates are double that of estimates from ATOC or the numerical model, but the authors of the report did not point out this remarkable consistency.

Figure 1

(A). Altimetric sea level (blue) and expected steric response from NCEP heat fluxes (red) for the North Pacific from 16° to 52°N and 168° to 240°E measured on days since 1 January 1992. (B) Same as (A), except that annual harmonics are shown.

Discrepancies between the altimeter and quarterly XBT estimates may be the result of the small number of samples. Annual harmonics computed from quarterly estimates of XBT and altimetric sea level showed comparable amplitudes; however, including all the altimetric data over the same time period increased the amplitude in the eastern Pacific by a factor of 2 (8). Therefore, although the XBT error estimates are formally small, the quarterly sampling can cause a factor of 2 underestimate in the amplitude of the annual harmonic.

In sum, seasonal heat flux estimates can be reconciled with both XBT data and altimetric data after accounting for adiabatic terms, without resorting to large advective contributions. This agreement suggests that the model and the ATOC estimates are too small by a factor of two.

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Response: A full response to the comment by Kellyet al. would require a technical discussion of the origins and interpretation of the error budgets of the altimeter, the acoustics, the XBTs, the meteorological center analyses, and the general circulation model.

The ATOC Consortium did not state that its estimates of North Pacific heat content change were exact. We distinguish between (i) errors along the acoustic paths, and (ii) errors associated with extrapolating the path integrals to the entire northeast Pacific. The most accurate calculations of heat content change come from the tomographic integrals. Acoustic travel times are measured with high precision, giving error estimates for heat content along the acoustic paths of about 1-cm equivalent sea level height, as depicted in figure 3 in our report (1). The model, XBTs, climatology, and altimetry are in general accord within their stated uncertainties with the acoustic measurements, as can be seen in the figure.

A greater uncertainty arises with regard to (ii), owing to the limited spatial coverage of the tomographic integrals available to us. Here the model is used to interpolate and extrapolate dynamically across the many different oceanographic regimes in figure 4 in our report (1). Estimates (2) are that the meteorological values of heat flux to and from the ocean, used to drive the model, have global average systematic errors of 35 W/m2, with probably much larger errors in different regions. It is difficult to evaluate the point or small regional in situ estimates cited by Kelly et al. against the very large-scale values of advective flux obtained from our combined model and data. Approximate local agreement between any two of the methods for calculating heat content change, for example, XBTs and altimeter data, does not imply that their overall uncertainties are smaller than what was estimated in our report (1).

We agree that the model may be underestimating the annual cycle of the heat flux, but within our uncertainty values, we have no conflict with the numbers provided by Kelly et al. With longer duration and (more important) a larger number of acoustic paths, the estimates of heat content change will be improved greatly.

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