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In preparation for possible higher frequency assimilation of ground-based Global Navigation Satellite System (GB-GNSS) Zenith Total Delay (ZTD) observations at Environment and Climate Change Canada (ECCC), two popular diagnostic methods are applied to observation-minus-background and observation-minus-analysis departures from the ECCC Global Deterministic Prediction System (GDPS) to estimate temporal ZTD observation error correlations within the 6 h assimilation window. The GDPS uses a four-dimensional ensemble-variational (4D-EnVar) data assimilation system with a background error covariance matrix (B-matrix) obtained from an equal blend of 3D static and 4D flow-dependent (ensemble-based) background error covariances. The two diagnostic methods, the Desroziers method and the Hollingsworth-Lonnberg method, are applied using ZTD observations from the North American NOAA network and the European EIG EUMETNET GNSS Water Vapour Programme (E-GVAP) network with similar results obtained for both networks. Correlations estimated with the Desroziers method drop off rapidly with time difference becoming significantly negative for observations separated by more than 2-3 h. The results are unexpected as there is no obvious physical basis for negative correlations. It is shown how suboptimal specification of the background error covariances in the 4D-EnVar assimilation system B-matrix could explain the unexpected aspects of the results obtained with this method. In contrast, diagnosed observation error covariances without negative temporal correlations are obtained with the Hollingsworth-Lonnberg method, where a decorrelation time-scale on the order of 4 h is found. Both methods capture some expected features of the error correlations, such as highly correlated errors between observations within the same 1 h data processing blocks. While considerable uncertainty is associated with the results due to the inherent assumptions and limitations of both methods, the results do suggest that ZTD observation error decorrelation time-scales are on the order of a few hours rather than days as suggested by early pioneering work with different error correlation estimation methods.