An elevated convection initiation (CI) of a quasi-linear mesoscale convective system (MCS) that occurred in a weak-lifting environment in the early morning on 23 June 2016 in central-eastern China was investigated using observational analysis and convection-permitting numerical simulations. This MCS gradually developed into a surface-based MCS and eventually produced a strong supercell that spawned an EF4 tornado in Yancheng City of Jiangsu Province and killed 98 people. This elevated MCS was initiated ahead of a surface front without identifiable boundaries at the surface. An elevated moist absolutely unstable layer (MAUL) was found to be conducive to the CI. The MAUL provided negligible convective inhibition and contributed to CI without strong-lifting mechanisms. Numerical simulation results showed that the formation of the elevated MAUL was mainly attributed to adiabatic cooling by weak vertical ascent and sufficient horizontal moisture transport near the terminus of a low-level jet. The weak vertical ascent before the CI was sloping and was likely to be relevant to the layer-lifting process associated with the realization of potential instability. The results showed that the MAUL in this weak-lifting environment was characterized by a shallower depth, a weaker lapse rate, and a longer sustaining period than the conditions in a strong-lifting environment. The predictability of this elevated CI case was examined using a 10-member ensemble forecast. A total of 80% of the ensemble members captured the CI. Rather than a difference in lifting, whether having an elevated MAUL or not was the major difference between CI and non-CI members in the present case.

Recognizing the importance and challenges inherent in the remote sensing of precipitation in typhoon monitoring, a study of the Advanced Geosynchronous Radiation Imager (AGRI) data from Feng-Yun 4A on typhoon precipitation was conducted. First, Typhoon Maria was selected to statistically analyze the AGRI infrared brightness temperature in the “precipitation” and “nonprecipitation” channels of the field of view. When there was precipitation, the brightness temperature of the AGRI channel changed significantly. Second, the shrunken locally linear embedding algorithm (SLLE) was adopted to carry out the retrieval of precipitation based on the brightness temperatures of AGRI infrared channels 8–14. The contribution rate of the brightness temperature at different channels to the objective function of precipitation retrieval model was obtained by the Bayesian model averaging (BMA). Based on the preliminary experimental “quantification” evaluation index, we concluded that the method adopted in this paper can be used to retrieve precipitation in infrared data and to retrieve the spiral cloud rain bands of a typhoon. Finally, based on the AGRI channel brightness temperature of a 10.8-micron window channel, we applied the membership degree information of a typhoon’s dominant cloud system from the fuzzy c-means (FCM) clustering method to modify precipitation retrieval results. The results were used to obtain the main morphological structure of typhoon precipitation. By further analyzing the temporal variation of dominant cloud system development using the FCM method, we concluded that the brightness temperature gradient can assist in the analysis of the variation of a typhoon’s intensity. This method can be applied to the continuous retrieval of large-scale precipitation. Precipitation retrieval via the AGRI can yield indicators for typhoon precipitation warnings and forecasts, thus providing a reliable reference tool for disaster prevention and mitigation.

The vertical evolution of the cloud effective radius (R e ) reflects the precipitation-forming process. Based on observations from the first Chinese next-generation geostationary meteorological satellites (FY-4A, Feng Yun 4), we established a new method for objectively obtaining the vertical temperature vs. R e profile. First of all, R e was calculated using a bispectral lookup table. Then, cloud clusters were objectively identified using the maximum temperature gradient method. Finally, the R e profile in a certain cloud was then obtained by combining these two sets of data. Compared with the conventional method used to obtain the R e profile from the subjective division of a region, objective cloudcluster identification establishes a unified standard, increases the credibility of the R e profile, and facilitates the comparison of different R e profiles. To investigate its performance, we selected a heavy precipitation event from the Integrative Monsoon Frontal Rainfall Experiment in summer 2018. The results showed that the method successfully identified and tracked the cloud cluster. The R e profile showed completely different morphologies in different life stages of the cloud cluster, which is important in the characterization of the formation of precipitation and the temporal evolution of microphysical processes.

High order spatial derivatives and stiff reactions often introduce severe temporal stability constraints on the time step in numerical methods. Implicit integration method (IIF) method, which treats diffusion exactly and reaction implicitly, provides excellent stability properties with good efficiency by decoupling the treatment of reactions and diffusions. One major challenge for IIF is storage and calculation of the potential dense exponential matrices of the sparse discretization matrices resulted from the linear differential operators. Motivated by a compact representation for IIF (cIIF) for Laplacian operators in two and three dimensions, we introduce an array-representation technique for efficient handling of exponential matrices from a general linear differential operator that may include cross-derivatives and non-constant diffusion coefficients. In this approach, exponentials are only needed for matrices of small size that depend only on the order of derivatives and number of discretization points, independent of the size of spatial dimensions. This method is particularly advantageous for high dimensional systems, and it can be easily incorporated with IIF to preserve the excellent stability of IIF. Implementation and direct simulations of the array-representation compact IIF (AcIIF) on systems, such as Fokker-Planck equations in three and four dimensions and chemical master equations, in addition to reaction-diffusion equations, show efficiency, accuracy, and robustness of the new method. Such array-presentation based on methods may have broad applications for simulating other complex systems involving high-dimensional data.

Robust multiple-fate morphogen gradients are essential for embryo development. Here, we analyze mathematically a model of morphogen gradient (such as Dpp in Drosophila wing imaginal disc) formation in the presence of non-receptors with both diffusion of free morphogens and the movement of morphogens bound to non-receptors. Under the assumption of rapid degradation of unbound morphogen, we introduce a method of functional boundary value problem and prove the existence, uniqueness and linear stability of a biologically acceptable steady-state solution. Next, we investigate the robustness of this steady-state solution with respect to significant changes in the morphogen synthesis rate. We prove that the model is able to produce robust biological morphogen gradients when production and degradation rates of morphogens are large enough and non-receptors are abundant. Our results provide mathematical and biological insight to a mechanism of achieving stable robust long distance morphogen gradients. Key elements of this mechanism are rapid turnover of morphogen to non-receptors of neighoring cells resulting in significant degradation and transport of non-receptor-morphogen complexes, the latter moving downstream through a “bucket brigade” process.