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Use of data assimilation to initialize hydrometeors plays a vital role in numerical weather prediction (NWP). To directly analyze hydrometeors in data assimilation systems from cloud-sensitive observations, hydrometeor control variables are necessary. Common data assimilation systems theoretically require that the probability density functions (PDFs) of analysis, background, and observation errors should satisfy the Gaussian unbiased assumptions. In this study, a Gaussian transform method is proposed to transform hydrometeors to more Gaussian variables, which is modified from the Softmax function and renamed as Quasi-Softmax transform. The Quasi-Softmax transform method then is compared to the original hydrometeor mixing ratios and their logarithmic transform and Softmax transform. The spatial distribution, the non-Gaussian nature of the background errors, and the characteristics of the background errors of hydrometeors in each method are studied. Compared to the logarithmic and Softmax transform, the Quasi-Softmax method keeps the vertical distribution of the original hydrometeor mixing ratios to the greatest extent. The results of the D’Agostino test show that the hydrometeors transformed by the Quasi-Softmax method are more Gaussian when compared to the other methods. The Gaussian transform has been added to the control variable transform to estimate the background error covariances. Results show that the characteristics of the hydrometeor background errors are reasonable for the Quasi-Softmax method. The transformed hydrometeors using the Quasi-Softmax transform meet the Gaussian unbiased assumptions of the data assimilation system, and are promising control variables for data assimilation systems.

In this study, a multi-time-scale four-dimensional variational data assimilation (MTS-4DVar) scheme is developed and applied to the assimilation of radar observations. The MTS-4DVar employs multitime windows with various time lengths in the framework of incremental 4DVar in the Weather Research and Forecasting Data Assimilation (WRFDA). The objective of MTS-4DVar is to enable the 4DVar data assimilation system to extract multiscale information from radar observations, and the algorithm of MTS-4DVar is first discussed in detail. Using a heavy rainfall case, it is shown that the nonlinearity growth of reflectivity is faster than that of radial velocity, suggesting that the time window for assimilating reflectivity in the incremental 4DVar should be shorter than that of radial velocity. A series of single observation tests and observing system simulation experiments (OSSEs) are then presented to examine the physical characteristics and performance of MTS-4DVar. These experiments demonstrate that the MTS-4DVar is capable of combining the larger-scale information from a longer time window and the local-scale features from a shorter time window. With the OSSEs it is shown that the value of the cost function is reduced properly in the minimization of the MTS-4DVar with a combination of longer and shorter time windows. By assimilating the radar radial velocity alone, we found that the MTS-4DVar reduces the analysis and forecast errors and improves the precipitation forecasts in comparison with the normal incremental 4DVar. Additional assimilation of reflectivity further improved the precipitation forecasts, and the results show that the radar reflectivity can also be well assimilated by using MTS-4DVar.

Additional file 1: Table S1. The primers to construct mutants. Table S2. RMSD of the crucial residues between the constructed model and the crystal structure of muSCD1. Table S3. Evaluation of model quality. Table S4. Fatty acid composition of Micromonas pusilla delta 6 fatty acid desaturase (MpFADS6) mutants. Table S5. Sequence and structure alignment analysis of MpFADS6 models constructed by trRosetta and four mammalian FADS6 models constructed by Alphafold. Figure S1. Alignment of amino acid sequence between MpFADS6 and muSCD1(4YMK). Figure S2. (A). Structure-based phylogenetic analysis of models These models are the best among those constructed by the six methods. (B). Surface map of muSCD1 substrate tunnel composed of amino acids. (C). Main amino acids in the muSCD1 substrate tunnel. (D) and (E). Binding sites of muSCD1 and head group of stearoyl-CoA. (F). N148 gap between the actual structure and the two models. Figure S3. Quality assessment of models. (A). Ramachandran diagram of muSCD1 crystal. (B). Ramachandran diagram of model SCD_trR. (C). Ramachandran diagram of model MpFADS6 constructed by trRrosetta. Figure S4. Conformational changes in MpFADS6 due to mutation of M223A.

The probiotic bacterial strain Lactobacillus plantarum ZS2058 has been proven to alleviate colitis due to its ability to synthesize conjugated fatty acids (CFAs). To investigate the specific functions of CFAs produced by this probiotic bacterium, α-linolenic acid was isomerized by Lactobacillus plantarum ZS2058, and two different conjugated α-linolenic acid (CLNA) isomers were successfully isolated: c9, t11, c15-CLNA (CLNA1) and c9, t11, t15-CLNA (CLNA2). The effects and mechanism of CLNA crude extract and individual isomers on colitis were explored. CLNA significantly inhibited weight loss, the disease activity index, colon shortening. Additionally, CLNA improved histological damage, protected colonic mucous layer integrity and significantly upregulated the concentration of tight junction proteins (ZO-1, occludin, and claudin-3). CLNA significantly attenuated the expression of proinflammatory cytokines (TNF-α, IL-1β, and IL-6) while upregulating the expression of the colonic anti-inflammatory cytokine IL-10 and nuclear receptor PPARγ. Moreover, the activity of oxidative stress-related enzymes (superoxide dismutase, glutathione peroxidase and catalase) was increased by CLNA. The myeloperoxidase activity was significantly decreased by CLNA. Meanwhile, the concentrations of CLNA in the liver and colonic conjugated linoleic acid (CLA) were significantly increased in response to CLNA supplementation. Furthermore, CLNA could rebalance the gut microbial composition damaged by DSS, including increasing the α-diversity. CLNA1 and CLNA2 increased the abundance of Ruminococcus and Prevotella, respectively.