Sampling errors of the global mean sea level derived from TOPEX/Poseidon altimetry

Sampling errors of the global mean sea level derived from TOPEX/Poseidon (T/P) altimetry are explored using 341 a of eddy-resolving numerical model outputs for sea level. By definition, the sampling errors would not exist if data were available everywhere at all times. Four problems with increasing and progressively added complexities are examined to understand the causes of the sampling errors. The first problem (P1) explores the error incurred because T/P with turning latitudes near 66\textdegree latitudes does not cover the entire globe. The second problem (P2) examines, in addition, the spatial sampling issue because samples are only available along T/P ground tracks. The third problem (P3) adds the additional complexity that sea level at any along track location is sampled only once every 10 d versus every 3 d for the model (i.e., the temporal sampling issue). The fourth problem (P4) incorporates the full complexity with the addition of real T/P data outages. The numerical model (Los Alamos POP model Run 11) conserves the total water volume, thus generating no global mean sea level variation. Yet when the model sea level is sampled in the four problems (with P4 using the real T/P sampling), variations occur as manifestations of the sampling errors. The results show root-mean-squares (rms) sampling errors for P1 of 0.67 (0.75) mm for 10 d (3 d) global mean sea level, 0.78 (0.86) mm for P2, 0.79 mm for P3, and 1.07 mm for P4, whereas the amplitudes of the sampling errors can be as large as 2.0 (2.7) mm for P1, 2.1 (2.7) mm for P2,2.2 mm for P3, and 2.5 mm for P4. The results clearly show the largest source of the sampling errors to be the lack of global coverage (i.e., P1), which the model has actually underestimated due to its own less-than-global coverage (between latitudes about 77\textdegree latitudes). We have extrapolated that a truly global model would show the rms sampling error to be 1.14 (1.28) mm for P1, thus implying a substantially larger sampling error for P4.