Effects of Observation‐Operator Nonlinearity on the Assimilation of Visible and Infrared Radiances in Ensemble Data Assimilation

Abstract Numerical weather prediction is becoming increasingly reliant on the assimilation of cloud‐affected satellite observations. Their assimilation implicitly linearizes nonlinear observation operators in ensemble Kalman filters. The linearization causes the posterior to deviate from its linear approximation, which is often used for analysis verification. We investigate the linearization error for visible and infrared radiances in the ensemble adjustment Kalman filter (EAKF) using observing‐system simulation experiments (OSSEs). We found that increments can be detrimental for small first‐guess departures, but they are beneficial on average. The increments were typically about half of their linear approximation. Similarly, the ensemble spread reduction was smaller than its linear approximation, and sometimes negative (spread increase), but overall the mean nonlinear variance adjustment was consistent with the mean nonlinear squared error reduction. Lastly, the linear approximation overestimated the analysis mean absolute error (MAE) reduction by 37% for visible reflectance and 71% for infrared brightness temperature. Thus, the linear approximation of the posterior of observed variables, such as satellite radiances, should not be used for verification.