| 03 Aug 2026
1D-VAR system for a ground-based microwave radiometer: application of an inter-channel observation-error covariance matrix
Abstract. This study presents the specification of an inter-channel observation-error covariance matrix (R) and evaluates its effects on One-Dimensional Variational (1D-VAR) retrievals from a ground-based microwave radiometer (MWR) using RTTOV-gb as the observation operator. In the 1D-VAR, the accurate characterization of the background error covariance matrix and R is crucial, as they determine the relative weighting of background and observational uncertainties and thus directly control retrieval performance. However, realistic specification of R remains challenging due to the complexity of error sources, including instrument noise, forward-model error, and representativeness error. Consequently, many previous studies have adopted a simplified diagonal approximation. In this study, a correlated R is specified and compared with its diagonal configuration to quantify the effects of inter-channel error correlations on 1D-VAR performance. Radiosonde validation shows root mean square error (RMSE) reductions of 1.02 % for temperature and 4.52 % for humidity relative to the diagonal configuration below 1000 m. Using the correlated configuration, the 1D-VAR retrieval outperforms the Numerical Weather Prediction (NWP) model used as the background in the lowest 1000 m, achieving RMSE reductions of up to 23 % for temperature and 12 % for humidity, indicating an improved representation of near-surface variability during the intensive observation periods. The correlated configuration improves convergence efficiency, with 5.7 % of successful retrievals converging in a single iteration (compared to 0.1 % for the diagonal configuration), reducing the total processing time by approximately 2.6 %. In addition to enhanced computational efficiency, the correlated R maintains comparable retrieval accuracy in the lower troposphere. Overall, explicitly accounting for inter-channel observation-error correlations enhances convergence efficiency and provides modest improvements in retrieval accuracy below 1000 m, highlighting the importance of realistic observation-error covariance specification for lower-tropospheric thermodynamic profiling.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Atmospheric Measurement Techniques.
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Overview:
This paper is a nice continuation of previous studies on 1D-VAR retrievals using HATPRO MWR observations, particularly in its examination of an observation error covariance matrix that accounts for inter-channel error correlations. The authors carefully applied data screening to the MWR measurements collected in Seoul, Korea, and developed a 1D-VAR retrieval procedure that includes the 1D-VAR framework, an observation error covariance matrix incorporating radiometric noise from the instrument, radiative transfer model error, and representativeness error, as well as a background error covariance matrix for the retrieval of temperature and water vapor profiles. They used LDAPS data as the background and radiosonde observations to validate the retrieval results.
The main objective of this study is to demonstrate the need to account for correlations between MWR channels when constructing the observation error covariance matrix. Given the important role of the observation error covariance matrix in the retrieval procedure, how to construct an observation error covariance matrix that properly accounts for off-diagonal terms is one of the key aspects of this study.
The authors’ efforts are appreciable, and the subject is suitable for publication in Atmospheric Measurement Techniques. However, more details should be adjusted and included in the manuscript. I recommend publication after major revisions.
Comments on the manuscript: