Multi-scale Incremental Analysis Update Scheme and Its Application to Typhoon Mangkhut(2018)Prediction

In the traditional incremental analysis update(IAU)process,all analysis increments are treated as constant forcing in a model’s prognostic equations over a certain time window.This approach effectively reduces high-frequency oscillations introduced by data assimilation.However,as different scales of increments have unique evolutionary speeds and life histories in a numerical model,the traditional IAU scheme cannot fully meet the requirements of short-term forecasting for the damping of high-frequency noise and may even cause systematic drifts.Therefore,a multi-scale IAU scheme is proposed in this paper.Analysis increments were divided into different scale parts using a spatial filtering technique.For each scale increment,the optimal relaxation time in the IAU scheme was determined by the skill of the forecasting results.Finally,different scales of analysis increments were added to the model integration during their optimal relaxation time.The multi-scale IAU scheme can effectively reduce the noise and further improve the balance between large-scale and small-scale increments in the model initialization stage.To evaluate its performance,several numerical experiments were conducted to simulate the path and intensity of Typhoon Mangkhut(2018)and showed that:(1)the multi-scale IAU scheme had an obvious effect on noise control at the initial stage of data assimilation;(2)the optimal relaxation time for large-scale and small-scale increments was estimated as 6 h and 3 h,respectively;(3)the forecast performance of the multi-scale IAU scheme in the prediction of Typhoon Mangkhut(2018)was better than that of the traditional IAU scheme.The results demonstrate the superiority of the multi-scale IAU scheme.

Use of Incremental Analysis Updates in 4D-Var Data Assimilation

The four-dimensional variational （4D-Var） data assimilation systems used in most operational and research centers use initial condition increments as control variables and adjust initial increments to find optimal analysis solutions. This approach may sometimes create discontinuities in analysis fields and produce undesirable spin ups and spin downs. This study explores using incremental analysis updates （IAU） in 4D-Var to reduce the analysis discontinuities. IAU-based 4D-Var has almost the same mathematical formula as conventional 4D-Var if the initial condition increments are replaced with time-integrated increments as control variables. The IAU technique was implemented in the NASA/GSFC 4D-Var prototype and compared against a control run without IAU. The results showed that the initial precipitation spikes were removed and that other discontinuities were also reduced, especially for the analysis of surface temperature.

Application of a Typhoon Initialization Scheme Based on the Incremental Analysis Updates Technique in a Rapid Update Cycle System

Initialization of tropical cyclones plays an important role in typhoon numerical prediction. This study applied a typhoon initialization scheme based on the incremental analysis updates (IAU) technique in a rapid refresh system to improve the prediction of Typhoon Lekima (2019). Two numerical sensitivity experiments with or without application of the IAU technique after performing vortex relocation and wind adjustment procedures were conducted for comparison with the control experiment, which did not involve a typhoon initialization scheme. Analysis of the initial fields indicated that the relocation procedure shifted the typhoon circulation to the observed typhoon region, and the wind speeds became closer to the observations following the wind adjustment procedure. Comparison of the results of the sensitivity and control experiments revealed that the vortex relocation and wind adjustment procedures could improve the prediction of typhoon track and intensity in the first 6-h period, and that these improvements were extended throughout the first 12-h period of the prediction by the IAU technique. The new typhoon initialization scheme also improved the simulated typhoon structure in terms of not only the wind speed and warm core prediction but also the organization of the eye of Typhoon Lekima. Diagnosis of the tendencies of variables showed that use of the IAU technique in a typhoon initialization scheme is efficacious in resolving the spurious high-frequency noise problem such that the model is able to reach equilibrium as soon as possible.

Implementation of the Incremental Analysis Update Initialization Scheme in the Tropical Regional Atmospheric Modeling System under the Replay Configuration

In traditional simulations of heavy rainfall events, the regional model is often initialized by using a global reanalysis dataset and a cold start method. An alternative to using global analysis data is to gradually introduce the analysis field via an incremental analysis update(IAU) method under the replay configuration. We found substantial differences in the forecast of a heavy rainfall event in southern China between a precipitation forecast using the traditional method and a forecast using the IAU method in the Tropical Regional Atmospheric Modeling System(TRAMS),based on the ECMWF global analysis. The IAU method is efficient in removing spurious high-frequency gravity wave noise, especially when the relaxation time is more than 90 min. The regional model needs to be pre-integrated for about 12 h to warm up the convective system in the background field. The improvement by the IAU method is supported by verification of simulations over 1 month(1–30 April 2019). In general, the IAU technique improves the initialization and spin-up process in the simulation of the heavy rainfall event.

Answering Reachability Queries on Incrementally Updated Graphs by Hierarchical Labeling Schema

We proposed a novel solution schema called the Hierarchical Labeling Schema （HLS） to answer reachability queries in directed graphs. Different from many existing approaches that focus on static directed acyclic graphs （DAGs）, our schema focuses on directed cyclic graphs （DCGs） where vertices or arcs could be added to a graph incrementally. Unlike many of the traditional approaches, HLS does not require the graph to be acyclic in constructing its index. Therefore, it could, in fact, be applied to both DAGs and DCGs. When vertices or arcs are added to a graph, the HLS is capable of updating the index incrementally instead of re-computing the index from the scratch each time, making it more efficient than many other approaches in the practice. The basic idea of HLS is to create a tree for each vertex in a graph and link the trees together so that whenever two vertices are given, we can immediately know whether there is a path between them by referring to the appropriate trees. We conducted extensive experiments on both real-world datasets and synthesized datasets. We compared the performance of HLS, in terms of index construction time, query processing time and space consumption, with two state-of-the-art methodologies, the path-tree method and the 3-hop method. We also conducted simulations to model the situation when a graph is updated incrementally. The performance comparison of different algorithms against HLS on static graphs has also been studied. Our results show that HLS is highly competitive in the practice and is particularly useful in the cases where the graphs are updated frequently.

Study and application of temporal index technology

This paper addresses the mathematical relation on a set of periods and temporal indexing construc- tions as well as their applications.First we introduce two concepts, i.e.the temporal connection and temporal inclusion, which are equivalence relation and preorder relation respectively.Second, by study- ing some basic topics such as the division of ＂large＂ equivalence classes and the overlaps of preorder relational sets, we propose a temporal data index model （TDIM） with a tree-structure consisting of a root node, equivalence class nodes and linearly ordered branch nodes.Third, we study algorithms for the temporal querying and incremental updating as well as dynamical management within the framework of TDIM.Based on a proper mathematical supporting, TDIM can be applied to researching some significant practical cases such as temporal relational and temporal XML data and so on.