Influence of salinity on the interannual heat storage trends in the Atlantic estimated from altimeters and Pilot Research Moored Array in the Tropical Atlantic data

Changes in the oceanic heat storage (HS) can reveal important evidences of climate variability related to ocean heat fluxes. Specifically, long-term variations in HS are a powerful indicator of climate change as HS represents the balance between the net surface energy flux and the poleward heat transported by the ocean currents. HS is estimated from sea surface height anomaly measured from the altimeters TOPEX/Poseidon and Jason 1 from 1993 to 2006. To characterize and validate the altimeter-based HS in the Atlantic, we used the data from the Pilot Research Moored Array in the Tropical Atlantic (PIRATA) array. Correlations and rms differences are used as statistical figures of merit to compare the HS estimates. The correlations range from 0.50 to 0.87 in the buoys located at the equator and at the southern part of the array. In that region the rms differences range between 0.40 and 0.51 x 10(9) Jm(-2). These results are encouraging and indicate that the altimeter has the precision necessary to capture the interannual trends in HS in the Atlantic. Albeit relatively small, salinity changes can also have an effect on the sea surface height anomaly. To account for this effect, NCEP/GODAS reanalysis data are used to estimate the haline contraction. To understand which dynamical processes are involved in the HS variability, the total signal is decomposed into nonpropagating basin-scale and seasonal (HS(l)) planetary waves, mesoscale eddies, and small-scale residual components. In general, HS(l) is the dominant signal in the tropical region. Results show a warming trend of HS(l) in the past 13 years almost all over the Atlantic basin with the most prominent slopes found at high latitudes. Positive interannual trends are found in the halosteric component at high latitudes of the South Atlantic and near the Labrador Sea. This could be an indication that the salinity anomaly increased in the upper layers during this period. The dynamics of the South Atlantic subtropical gyre could also be subject to low-frequency changes caused by a trend in the halosteric component on each side of the South Atlantic Current.

Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere

We obtain explicit formulas for the eigenvalues of integral operators generated by continuous dot product kernels defined on the sphere via the usual gamma function. Using them, we present both, a procedure to describe sharp bounds for the eigenvalues and their asymptotic behavior near 0. We illustrate our results with examples, among them the integral operator generated by a Gaussian kernel. Finally, we sketch complex versions of our results to cover the cases when the sphere sits in a Hermitian space.