Typically, the first step assumes a spatially and temporally constant e value (e.g., e = 0.04 m3/m3 everywhere). In the second step, this value is converted into e’ by rescaling e with the ratio of the time series standard deviations of the modeled and the observed near-surface soil moisture.

Here, we test combinations of different methods for specifying e, and for rescaling e to e’. For specifying e, we test four options:

i) constant in space and time,

ii) temporally invariant fraction of the local time series standard deviation of the observations,

iii) time series mean of the observation error estimates provided with the observations by the instrument/retrieval team, and

iv) instantaneous observation error estimate provided with the observations by the instrument/retrieval team.

For ii) and iii), e varies in space but not in time, while for iv) e varies in both space and time.

Moreover, we test two options for rescaling e to e’ based on:

i) the ratio of the standard deviations of the modeled and observed soil moisture time series, and

ii) the linear regression coefficient from regressing the modeled soil moisture onto the observed soil moisture time series.

While neither of these rescaling methods is optimal, theory suggests that the regression approach is less problematic.

The impact of different combinations of the above options were tested by evaluating the impact of assimilating ASCAT and SMOS soil moisture retrievals into the GMAO LDAS over the contiguous US and evaluating the results against ground-based observations from the USCRN and SCAN networks. The difference in skill between the assimilation experiments with different observation error specifications was insignificant (<0.01 differences in anomaly correlations). Given the substantial differences between the tested error estimation methods, including the introduction of spatial and temporal variability, and the introduction of much more realistic spatial patterns, this result suggests that, at least for the GMAO LDAS, the observation error specification is of little importance to the near-surface soil moisture analysis. This is thought to be because the observation errors are set relatively high in order to prevent the assimilation from introducing noise into the modeled root-zone soil moisture.