Using Spatial Gradient Information to Extract Small Scale Information from Observations with Correlated Errors
The errors associated with dense observations can have significant spatial correlations due to various causes (e.g. correlated instrument noise, correlated representativeness error, correlated observation operator error). However, assimilation algorithms generally assume spatially uncorrelated observation errors because it is both prohibitively expensive to invert the full covariance matrix and it is difficult to estimate the real error correlations. It is common practice to spatially thin observations to reduce error correlation between remaining observations, however, this results in a loss of small-scale information. A practical assimilation approach will be presented that efficiently extracts small-scale information from observations with spatially correlated errors, while still assuming uncorrelated errors within the data assimilation algorithm. Results from idealized one-dimensional experiments show that the analysis error can be reduced by combining the original observations with spatial difference-observations. The analysis benefits from both the large-scale information of the original observations and the small scales of the difference-observations.
Dr. Joel Bedard Environment and Climate Change Canada