On the joint estimation of model and satellite sea surface height anomaly errors

Abstract

We describe a technique to estimate the error ®eld in the sea surface height (SSH) anomaly ®eld of an ocean model through the joint use of SSH anomaly ®elds measured from two satellites, Topex/Poseidon (T/P) and ERS-2. The joint error maps for the model, T/P and ERS-2 show distributions distinctly di erent from one another and globally inhomogeneous. Both sampling errors and instrument errors are represented in the mapped ®elds. Additionally, we compare the joint error estimation method to a technique using the model and only one satellite, and show the importance of the cross covariance between the measured SSH and the true SSH ®eld in the estimation of the error ®eld. Finally, we look at the distribution of the error versus the variance of the SSH at a location. This logged distribution suggests that the model errors are generally proportional to the model's variance (regression coe cient of 0.99, globally) while the satellites' errors do not exhibit this linear relationship (regression coe cients on the average of 0.60). The comparison of the two satellite distributions implies that ERS-2 has a lower sampling error than the T/P instrument except in the tropical region.