Numerical weather forecast models have biases caused by insufficient grid resolution and incomplete physical processes, especially near the land surface. Therefore, the Japan Meteorological Agency (JMA) has been operationally post-processing the forecast model outputs to correct biases. The operational post-processing method uses a Kalman filter (KF) algorithm for surface temperature prediction. Recent reports have shown that deep convolutional neural networks (CNNs) outperform the JMA operational method in correcting temperature forecast biases. This study combined the CNN-based bias correction scheme with the JMA operational KF algorithm. We expected that the combination of CNNs and a KF would improve the post-processing performance, as the CNNs modify large horizontal structures, and then, the KF corrects minor spatiotemporal deviations. As expected, we confirmed that the combination outperformed both CNNs and the KF alone. This study demonstrated the advantages of the new method in correcting coastal fronts, heat waves, and radiative cooling biases.

 A historical atmospheric reanalysis from 1850 to 2015 was performed using an atmospheric general circulation model assimilating surface pressure observations archived in international databases, with perturbed observational sea surface temperatures as a lower boundary condition. Posterior spread during data assimilation provides quantitative information on the uncertainty in the historical reanalysis. The reanalysis reproduces the evolution of the three-dimensional atmosphere close to those of the operational centers. Newly archived surface pressure observations greatly reduced the uncertainties in the present reanalysis over East Asia in the early 20th century. A scheme for assimilating tropical cyclone tracks and intensities was developed. The scheme was superior to the present several reanalyses in reproducing the intensity close to the observations and the positions. The reanalysis provides possible images of atmospheric circulations before reanalyses with full-scale observations become available, and opportunities for investigating extreme events that occurred before World War II. Incorporating dynamical downscaling with a regional model that includes detailed topography and sophisticated physics is an application of historical reanalysis to reveal the details of past extreme events. Some examples of past heavy rainfall events in Japan are shown using a downscaling experiment, together with dense rainfall observations over the Japanese islands.

 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.