A practical assimilation approach to extract smaller‐scale information from observations with spatially correlated errors: An idealized study

Abstract

It is still common to neglect the spatial error correlations of assimilated observations in numerical weather prediction systems because no practical approach is available to account for them when the number of observations with correlated error is large or when these observations are non‐uniformly distributed. Instead, it is common practice to inflate observation error variances to avoid overfitting large scales and spatially thin observations to reduce error correlations between remaining observations, although both methods generally sacrifice small‐scale information. Inspired by previous work on assimilating the difference between adjacent observations (so‐called spatial difference observations), this study aims at combining direct observations with spatial difference observations in the assimilation to extract both large‐ and smaller‐scale information from observations with spatially correlated errors, while still neglecting these error correlations. Experiments performed in a simplified 1D context over a periodic domain show that the combined approach is numerically equivalent to directly assimilating observations available at every grid point using non‐diagonal observation error covariances based on a first‐order autoregressive correlation function. In a case where observation error correlations have a different structure (e.g. Gaussian), the true observation error correlations are not perfectly taken into account by the combined approach, but it still efficiently extracts information to correct the scales that have the most errors. Combining direct observations with spatial difference observations proves complementary and experimental results show lower analysis errors for both large and intermediate scales. More specifically, while neglecting spatial observation error correlations, the combined approach provides results with lower analysis error than the direct approach, especially when spatial error correlations are large and when direct observations are spatially thinned.

The Impact of Assimilating Satellite Radiance Observations in the Copernicus European Regional Reanalysis (CERRA)

“…Given the short development period of the CERRA system and limited computational resources, it was not feasible to further enhance the assimilation of the radiance observations. The development of subsequent generations of the CERRA system can benefit from the results of this study and further continue the investigation of reducing the effect of high observation error correlations by combining the utilization of observation error inflation and observation thinning to preserve the small-scale information from observations, as discussed in [50].…”

“…Each subplot depicts the comparison at a specific analysis (F00) or forecast lengths (F03) that is initialized at a particular assimilation time. In order to address the high observation error correlation for radiance observations in the CERRA system, one can increase the thinning distance and/or inflate the observation error for these observations [22,50]. Consequently, three impact experiments with different thinning distance configurations for radiance observations were conducted, while rejecting IASI channels 104, 180, 2991, 3098, 3309 and 3506, due to its highly correlated observation errors.…”

Supermodding – A special footprint operator for mesoscale data assimilation using scatterometer winds

“…Therefore, when observation‐error correlation exists, but is ignored, more advanced error statistics or different practical solutions are required to improve the sub‐optimal DA system. For instance, Bédard and Buehner (2020) showed in a 1D simplified model that observations with spatially correlated errors can still be employed to extract more small‐scale information by the inflation of observation errors. In the area of ocean DA and altimetry, Brankart et al .…”

“…Therefore, when observation-error correlation exists, but is ignored, more advanced error statistics or different practical solutions are required to improve the sub-optimal DA system. For instance, Bédard and Buehner (2020) showed in a 1D simplified model that observations with spatially correlated errors can still be employed to extract more small-scale information by the inflation of observation errors. In the area of ocean DA and altimetry, Brankart et al (2009) investigated a parametrization of observation-error covariance matrix in Ensemble Kalman Filters and Ruggiero et al (2016) examined another way to account for observation-error correlations, which consists of the transformation of the observation vector allowing us to use errors that are spatially correlated.…”

Assimilating realistically simulated wide-swath altimeter observations in a high-resolution shelf-seas forecasting system

“…There has been work to extend data assimilation schemes to explicitly account for correlated observation errors. For example, Bédard and Buehner (2020) used a 1D model to demonstrate the combination of direct and spatial difference observations to account for observation error correlations, while Ruggiero et al (2016) and Guillet et al (2019) parameterised the observation error covariances using the diffusion equation to avoid the need to invert a non-diagonal covariance matrix. On the other hand, Metref et al (2020) used the correlatederror reduction (CER) method to account for correlated errors when assimilating SWOT observations in a one-and-a-half layer quasi-geostrophic model.…”