Abstract
The observation error covariance (R) matrix is a key component in the data assimilation (DA) process for retrieval of atmospheric state parameters (ASPs), also impacting the subsequent numerical weather forecast. However, one commonly used type of R matrix depends on instrument noise, which contravenes reality because the retrieved ASPs would depend on the instrument used. Other types of R matrix rely on the observation operator (H), analyzed state ( x a ), background error covariance (B) matrix or the background state ( x b ), and the selected forecast ensemble. All these dependences reduce the representativeness of the R matrix, since the correctness of H needs verification and no true values exist for x a or x b . As such, a better method to correctly specify the R matrix is needed. Through the physical mechanism occurring between incident radiation and particles in the atmosphere, which complies with the phenomena of energy absorption and emission, correlations among bands or channels in a detected atmospheric radiance spectrum occur. This paper thus proposes a data-derived R matrix based on a large number (N) of detected atmospheric radiance spectra constructed from N real-time measurements, where N real-time measurements can be acquired by staring at some observation location of interest during a short amount of time. This data-derived R matrix for satellite radiance observations does not rely on any assumed quantities and is unambiguous. Technically, recording N real-time measurements is achievable by modifying the trigger configuration of data recording from ground.
Highlights
Modern numerical weather prediction (NWP) systems require accurate determination of the initial atmospheric state to produce a reliable weather forecast
Since a single measurement is used in atmospheric research analyses and operational weather forecast (ARWF), correct variance and covariance cannot be obtained for the R matrix
The diagonal Rd matrix arranged with instrument noise in the diagonal elements to serve as variances by leaving zeros in off-diagonal has been used in ARWF for years
Summary
Modern numerical weather prediction (NWP) systems require accurate determination of the initial atmospheric state to produce a reliable weather forecast. Following the path of radiation through the atmosphere up to the radiation received by sensors and transformed to radiance, the correlations among the channels or bands in a detected atmospheric radiance spectrum allows us to propose a data-derived R matrix. These are used to form the theoretical basis of the data-derived R matrix using N real-time measured radiances.
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