- 著者
- Le DUC Yohei SAWADA
- 出版者
- Meteorological Society of Japan
- 雑誌
- 気象集誌. 第2輯 (ISSN:00261165)
- 巻号頁・発行日
- vol.102, no.1, pp.35-47, 2024 (Released:2023-12-12)
- 参考文献数
- 31
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.
- 著者
- Yohei Sawada Shinichi Okugawa Takayuki Kimizuka
- 出版者
- Japan Society of Hydrology and Water Resources (JSHWR) / Japanese Association of Groundwater Hydrology (JAGH) / Japanese Association of Hydrological Sciences (JAHS) / Japanese Society of Physical Hydrology (JSPH)
- 雑誌
- Hydrological Research Letters (ISSN:18823416)
- 巻号頁・発行日
- vol.16, no.4, pp.73-79, 2022 (Released:2022-10-27)
- 参考文献数
- 25
Verification processes of rainfall-runoff modeling are important to improve the skill of hydrological models to reproduce water cycles in river basins. It is ideal that newly developed models are compared with many benchmarking conventional models in many river basins as part of the verification process. However, this robust verification is time-consuming if model developers prepare data and models from scratch. Here we present a useful dataset which can accelerate the robust verification of hydrological models. Our newly developed dataset, Multi-model Ensemble for Robust Verification of hydrological modeling in Japan (MERV-Jp), provides runoff simulation by 44 calibrated conceptual hydrological models in 135 Japanese river basins as well as meteorological forcing which is necessary to drive conceptual hydrological models. By comparing simulated runoff with river discharge observations which are not used for the calibration of hydrological models, we find that the best models in the 44 models can reproduce observed river runoff with KGE larger than 0.6 in most of the 135 river basins, so that the runoff simulation of MERV-Jp is reasonably accurate. MERV-Jp is publicly available to support all hydrological model developers to robustly verify their model improvement.