Research overview
The computational program "atmospheric simulation model” reproduces the atmosphere in a computer, discretizes the atmosphere into grids, and performs calculations.
How high should the fineness of the grids (resolution) be so that the occurrence location and time, precipitation amount, and wind speed of cumulonimbus clouds that caused wind and flood damage can be depicted with the highest possible accuracy?
We aimed to derive the required resolution by solving related equations.
With this approach, we clarified the resolution and reproducibility required for estimating the probability and show the goals of atmospheric simulation model development.
Details of research
When atmospheric phenomena, such as typhoons and cumulonimbus clouds, are reproduced in an atmospheric simulation model, the atmosphere is discretized into grids, and the flow of heat and water vapor is calculated for each grid. The size of each grid is called the spatial resolution. This size is similar to the size of pixels in a photograph. A facial photo with a small number of pixels is vague, making it difficult to recognize the person in the photo. Even with the computation power of the atmospheric simulation models, the features of typhoons cannot be depicted if the resolution is low.
What level of resolution can reproduce atmospheric phenomena with high accuracy?
Mr. Miyamoto joined the RIKEN research team in 2011 and performed high-resolution atmospheric simulations via the “K computer,” which ranked first in the world’s supercomputer performance ranking (TOP500). He investigated the change in reproducibility when the weather of the entire Earth was simulated at increasingly finer spatial resolutions.
Results showed a change in reproducibility at a spatial resolution of approximately 2 km on one side of the grid, which made it possible to reproduce the rough structure of the cumulonimbus clouds that constituted a typhoon. The reason why it was 2 km remained unclear; however, Miyamoto et al. theoretically solved this mystery.
“Fluid dynamics,” which describes the atmospheric flow, is mainly used for calculating weather. The real atmosphere is, of course, continuously connected and not discretely divided by grids. The theory of fluid dynamics is built on the premise that the atmosphere is continuous.
Miyamoto et al. challenged this premise and decided to recreate the atmospheric representation by assuming that “the atmosphere is discretized into grids.” To simplify the problem, they created a series of hypothetically simplified conditions, including the exclusion of the occurrence of clouds. Solving the equations of the discretized atmospheric representation rendered it possible to determine the appropriate resolution to depict the thermal convection observed in a continuous atmosphere in reality by clarifying the relationship between resolution and reproducibility.
The relationship between reproducibility and resolution can be clarified by solving the equations on the left side, as shown in Figure 1 on the right, so that the resolution required for highly accurate reproducibility can be determined.
Miyamoto et al. published a study on this topic in 2015. They succeeded in developing a method for theoretically deriving the resolution necessary to reproduce atmospheric phenomena with extremely high accuracy. The hypothetical idea of "if the atmosphere is discretized into grids" was the key to success. This method can derive an answer from solving equations through manual calculations.
What is the resolution required to estimate the probability of occurrence location and time, precipitation amount, and wind speed of cumulonimbus clouds that caused wind and flood damage? This was determined in this study.
The horizontal diameter of cumulonimbus clouds is small, ranging from several hundred meters to several kilometers, and is an atmospheric phenomenon with a short life span of approximately 30–60 min until clouds begin to form due to updrafts, develop into cumulonimbus clouds, and eventually disappear. A theory describing the formation of clouds is necessary to reproduce the features of cumulonimbus clouds.
First, we determined the resolution required to estimate the probability of cumulonimbus cloud development under simplified conditions. For example, if the appropriate resolution is 100 m, there must be some important events of the 100-m scale related to cumulonimbus clouds. For example, turbulence of the 100-m scale generated around clouds may affect the generation and development of cumulonimbus clouds. Determining the required resolution enhances our understanding of atmospheric phenomena, such as cumulonimbus clouds, and provides important insights into improving atmospheric simulation models.
Cumulonimbus clouds occur in mountainous areas; owing to updrafts, they appear to climb up mountains. Therefore, the location where cumulonimbus clouds occur in mountains is greatly affected by the topography. A higher resolution is required to reproduce the position of cumulonimbus clouds in undulating mountains than in flat areas. The resolution required for reproduction may also differ depending on the location and time, precipitation amount, and wind speed of the cumulonimbus clouds.
The purpose of this study was to determine the resolution required for an atmospheric simulation model to accurately estimate the probability of atmospheric phenomena that cause wind and flood damage. With this current approach, we can evaluate the theoretical accuracy achieved by the atmospheric simulation model we have developed.