Improved Atmospheric State Analysis for Reanalysis and Reforecast: Suppressing Fast-Growing Error Modes

Atmospheric state analysis is a difficult scientific problem because of the chaotic nature of the atmosphere. Even the most accurate atmospheric state analysis by state-of-the-art data assimilation (DA) for numerical weather prediction (NWP), NWP-DA, still exhibits errors that grow rapidly with the time evolution of the atmosphere. Atmospheric state analysis with much higher accuracy than that by NWP-DA is essential for atmospheric sciences but is a scientific challenge. We call such a highly accurate analysis a pseudo-truth (PT) of the atmospheric state. Although some existing methods can generate analyses that significantly reduce forecast errors by correcting the NWP-DA analyses using forecast error information, three shortcomings disqualify them as PT: (1) inconsistency with observations, (2) ambiguity of analysis, and (3) unclearness of relationships with DA. The purpose of this study is to overcome the three shortcomings of the existing methods and construct a PT of the atmospheric state based on the DA theory. We proposed a new method as an extension of the four-dimensional variational DA with an extended DA window in the future direction. Therefore, the proposed method has the following properties as PT: (a) it can consistently integrate all our knowledge about the atmosphere, observations, a background field (forecast from previous analysis), physical laws and forecast error information; (b) its analysis is guaranteed to be a maximum posterior probability state under the Gaussian approximation; and (c) fast-growing modes of analysis errors are significantly suppressed. Moreover, the forecast error information is assimilated in two alternative forms—future analyses and future observations—which are the analyses of NWP-DA and observations in the extended part of the data assimilation window, respectively. We performed numerical experiments using the proposed method on the global NWP system of the Japan Meteorological Agency. The experimental results showed that the proposed method can generate analyses that significantly suppress fast-growing error modes, where forecast error reduction for height fields is greater than 25% and fitting to observations is achieved according to error covariance matrices based on the DA theory. This means that the analysis accuracy of fast-growing modes is significantly improved without degrading other modes. We conclude that an analysis generated by the proposed method can be considered a PT, and our design approach is useful for atmospheric sciences, including reanalysis for climatological studies and future earth-observing system design.