The Japan Meteorological Agency (JMA) has developed the third Japanese global atmospheric reanalysis, the Japanese Reanalysis for Three Quarters of a Century (JRA-3Q). The objective of JRA-3Q is to improve quality in terms of issues identified in the previous Japanese 55-year Reanalysis (JRA-55) and to extend the reanalysis period further into the past. JRA-3Q is based on the TL479 version of the JMA global Numerical Weather Prediction (NWP) system as of December 2018 and uses results of developments in the operational NWP system, boundary conditions, and forcing fields achieved at JMA since JRA-55. It covers the period from September 1947, when Typhoon Kathleen brought severe flood damage to Japan, and uses rescued historical observations to extend its analyses backwards in time about 10 years earlier than JRA-55. This paper describes the data assimilation system, forecast model, observations, boundary conditions, and forcing fields used to produce JRA-3Q as well as the basic characteristics of the JRA-3Q product. The initial quality evaluation revealed major improvements from JRA-55 in the global energy budget and representation of tropical cyclones (TCs). One of the major problems in JRA-55—global energy imbalance with excess upward net energy flux at the top of the atmosphere and at the surface—has been significantly reduced in JRA-3Q. Another problem—a trend of artificial weakening of TCs—has been resolved through the use of a method that generates TC bogus based on the JMA operational system. There remain several problems such that volcanic-induced stratospheric warming is smaller than expected. This paper discusses the causes of such problems and possible solutions in future reanalyses.

 It is well-known in rainfall ensemble forecasts that ensemble means suffer substantially from the diffusion effect resulting from the averaging operator. Therefore, ensemble means are rarely used in practice. The use of the arithmetic average to compute ensemble means is equivalent to the definition of ensemble means as centers of mass or barycenters of all ensemble members where each ensemble member is considered as a point in a high-dimensional Euclidean space. This study uses the limitation of ensemble means as evidence to support the viewpoint that the geometry of rainfall distributions is not the familiar Euclidean space, but a different space. The rigorously mathematical theory underlying this space has already been developed in the theory of optimal transport (OT) with various applications in data science.

 In the theory of OT, all distributions are required to have the same total mass. This requirement is rarely satisfied in rainfall ensemble forecasts. We, therefore, develop the geometry of rainfall distributions from an extension of OT called unbalanced OT. This geometry is associated with the Gaussian-Hellinger (GH) distance, defined as the optimal cost to push a source distribution to a destination distribution with penalties on the mass discrepancy between mass transportation and original mass distributions. Applications of the new geometry of rainfall distributions in practice are enabled by the fast and scalable Sinkhorn-Knopp algorithms, in which GH distances or GH barycenters can be approximated in real-time. In the new geometry, ensemble means are identified with GH barycenters, and the diffusion effect, as in the case of arithmetic means, is avoided. New ensemble means being placed side-by-side with deterministic forecasts provide useful information for forecasters in decision-making.

 The trend of strong typhoons over the recent 30 years was analyzed using Dvorak reanalysis data from 1987 to 2016 produced by Japan Meteorological Agency. The strong typhoons were defined in this study as tropical cyclones equivalent to category 4 and 5 on the Saffir-Simpson scale. The temporal homogeneity of the Dvorak reanalysis data is expected to be much better than that of best track data. Results showed no statistically significant increasing trend in strong typhoons with large inter-annual and multi-year scale variations. Meanwhile, the spatial distribution of the genesis locations of tropical cyclones, which could influence whether or not they develop into strong typhoons, varied locally during the analysis period. The changes in genesis locations may have influenced the overall trend of strong typhoons during the analysis period. The results with the new Dvorak reanalysis data highlight the need for the accumulation of high quality data over time as well as for careful interpretation of trend analysis results seen in previous studies.

 In a global numerical weather prediction (NWP) modeling framework we study the implementation of Gaussian uncertainty of individual particles into the assimilation step of a localized adaptive particle filter (LAPF). We obtain a local representation of the prior distribution as a mixture of basis functions. In the assimilation step, the filter calculates the individual weight coefficients and new particle locations. It can be viewed as a combination of the LAPF and a localized version of a Gaussian mixture filter, i.e., a Localized Mixture Coefficients Particle Filter (LMCPF).

 Here, we investigate the feasibility of the LMCPF within a global operational framework and evaluate the relationship between prior and posterior distributions and observations. Our simulations are carried out in a standard pre-operational experimental set-up with the full global observing system, 52 km global resolution and 10⁶ model variables. Statistics of particle movement in the assimilation step are calculated. The mixture approach is able to deal with the discrepancy between prior distributions and observation location in a real-world framework and to pull the particles towards the observations in a much better way than the pure LAPF. This shows that using Gaussian uncertainty can be an important tool to improve the analysis and forecast quality in a particle filter framework.

 A new operational seasonal forecast system, Japan Meteorological Agency (JMA)/Meteorological Research Institute (MRI) Coupled Prediction System (CPS) version 3 (JMA/MRI–CPS3), has been developed. This system represents a major upgrade of the former system, CPS2. CPS3 comprises atmosphere, land, ocean, and sea ice forecast models and the necessary initialization systems for these models. For historical reforecasts, the atmospheric reanalysis dataset JRA-3Q provides initial conditions for the atmosphere and the external forcings for land, ocean, and sea ice analysis. In the operational forecast, JMA's operational atmospheric analysis is used in conjunction with JRA-3Q to initialize the system in near-real time. The land surface model is initialized using an uncoupled free simulation, forced by the atmospheric analysis. The ocean and sea ice models are initialized with the global ocean data assimilation system MOVE-G3, which incorporates a newly developed four-dimensional variational method for temperature, salinity, and sea surface height and a three-dimensional method for sea ice concentration. Compared with the previous system, the CPS3 forecast model components have approximately 2-4 times higher resolution: the atmosphere and land models are configured with ∼ 55 km horizontal resolution, with 100 vertical atmosphere layers; and the ocean and sea ice models have a resolution of 0.25° × 0.25°, with 60 vertical ocean layers. The physical processes of the atmosphere are greatly refined in CPS3 relative to CPS2, resulting in improved representation of sub-seasonal to seasonal scale variability, including the eastward propagation of the Madden–Julian Oscillation, winter blocking highs in the North Atlantic, and coupled atmosphere–ocean variability during El Niño–Southern Oscillation events. Our historical reforecast experiment for 1991-2020 suggests that CPS3 has greater forecast skill than CPS2. The usability of the model output has been improved in CPS3 by reorganizing the operation schedule to provide daily updates of five-member ensemble forecasts.