Kaoru Sato, Professor, Department of Earth and Planetary Science

Takeya Kinoshita (Researcher, Japan Agency for Marine-Earth Science and Technology)

Masashi KOREI (Assistant Professor, Department of Earth and Planetary Science)

Key points of the presentation

• The theoretical equation for the three-dimensional Lagrangian flow ^{(Note 1)} was derived, and it was clarified that the "deep circulation" from the equatorial region to the polar regions in the winter stratosphere has a characteristic structure that is strong in Eastern Siberia and reversed in North America.
• The three-dimensional structure of stratospheric and mesospheric material circulation has often been discussed only in terms of an east-west averaged two-dimensional (latitude and altitude) structure due to the lack of a theory to describe it, but this study has developed a theory that makes this possible.
• Ozone is produced in the upper equatorial stratosphere and transported around the world by stratospheric circulation. This research has developed a theoretical tool to find the route of this flow. It can also be used to elucidate the three-dimensional structure of the Earth's mesosphere and the material cycles of the terrestrial planets Venus and Mars.

Summary of the Announcement

The stratospheric Lagrangian flow is an important flow that transports ozone produced in the equatorial upper stratosphere to the global atmosphere and maintains the Earth's ozone layer. The structure and driving mechanism of the material circulation in a two-dimensional (latitude-height) cross section have been discussed by using the deformed Euler mean equation system ^{(Note 2), etc., which} gives an approximate expression for the east-west averaged Lagrangian circulation. To investigate the three-dimensional structure including the longitude structure, a theoretical equation for three-dimensional Lagrangian flow is necessary, but it has been difficult to formulate the drift effect caused by waves with a fixed phase (standing waves) on the ground where the position of pressure troughs and ridges do not move, and the theory has not been constructed.

In response, Professor Kaoru Sato and his colleagues at the Graduate School of Science, The University of Tokyo, abandoned the assumption of the conventional formulation that the east-west mean zonal wind is the basic field, and by deforming the equation with good symmetry between east-west and north-south, they extended the deformed Euler mean equation system to three dimensions and successfully derived an approximate formula for the three-dimensional Lagrangian flow.

Using this equation, we analyzed the general circulation from low latitudes to the poles in the middle and upper stratosphere, called the deep circulation, which exists only in winter, and found that it is not uniformly east-west, but is strong over eastern Siberia and reversed over North America. In other words, the flow over Eastern Siberia toward the poles can be interpreted as the main route by which ozone is transported from the equatorial region to the mid- and high latitudes. This theoretical equation is highly versatile and can be used to elucidate not only the circulation in the mesosphere and lower stratosphere, but also the structure and driving mechanisms of atmospheric general circulation on terrestrial planets such as Venus and Mars.

Announcement

Research Background
The stratospheric general circulation is an important flow that carries ozone produced in the upper stratosphere in the equatorial region to the entire globe and maintains the ozone layer. Such a flow of air masses carrying ozone and other substances is called a Lagrangian flow. Large-scale Lagrangian flows in the stratosphere are driven by the redistribution of angular momentum by atmospheric waves called Rossby waves ^{(Note 3} ) and atmospheric gravity waves ^{(Note 4)}, which are generated in the troposphere and propagate upward, and by seasonal changes in solar radiation absorbed by the atmosphere. Theoretical equations for the east-west averaged two-dimensional Lagrangian circulation have been proposed and discussed using these equations. Figure 1 shows the zonally averaged Lagrangian circulation in stratospheric and mesospheric latitudinal height cross sections.

Figure 1: East-west averaged Lagrangian flow. In the stratosphere, there is a circulation from low latitudes to both poles, and in the mesosphere, there is a circulation from the summer pole to the winter pole. The stratospheric circulation is seen as a bi-hemispheric symmetric circulation in the lower troposphere (shallow circulation) and a deep circulation that exists only in the winter hemisphere.

In order to investigate the three-dimensional structure of this circulation, including its meridional structure, a theoretical equation for the three-dimensional Lagrangian flow is required. The system of equations often used to describe 2-dimensional Lagrangian flows is the deformed Eulerian mean system of equations. This system of equations provides a good approximation of the Lagrangian flow. Because of the predominance of the east-west jet stream in the earth's atmosphere, the zonal mean zonal wind is often treated as the basic field. Therefore, the extension of the deformed Euler mean equation system to three dimensions has often been attempted using the zonal mean zonal wind as the basic field.

Research Contents
In contrast, Professor Kaoru Sato and his colleagues at the Graduate School of Science, The University of Tokyo, have succeeded in extending the deformed Euler mean equation system to three dimensions by abandoning the assumption that the zonal mean zonal wind is the basic field and deforming the equation with good symmetry between east-west and north-south directions, and have derived an approximate expression for three-dimensional Lagrangian flow. The Lagrangian flow is a flow of air masses and is represented by the sum of the Eulerian mean flow averaged over a fixed location and the drift effect (Stokes drift) due to waves. The derived theoretical equation uses time averaging as the average, but describes the physical quantity without separating it into an average field and a wave field. This enables the formulation of the drift effect of waves with a fixed phase with respect to the ground (standing waves), which has been difficult. Another advantage of using this theoretical equation for data analysis is that there is no need to separate the waves.

By looking at the equations of motion for the mean wind in the east-west and north-south directions using the obtained 3D Lagrangian flow, it was also possible to give a physical interpretation that the 3D Lagrangian flow is a flow balanced by the angular momentum carried by the waves, including the standing waves. The seasonal variation of the Lagrangian flow can also be analyzed by shortening the time average to about one month.

In the middle and upper stratosphere, there exists a circulation from the equator to the winter pole, called "deep circulation," only in winter. As an example of application of the derived theoretical equation, we focused on this circulation and analyzed it using the atmospheric reanalysis data ^{(Note 5)}. The obtained horizontal map is shown in Figure 2. The components perpendicular to the geostrophic wind ^{(Note 6} ), which is intrinsic to the material circulation, are plotted. It is clear that the deep circulation is not uniformly east-west, and that the flow from low latitudes to the poles is strong over East Siberia and reversed over North America. The flow over Eastern Siberia toward the poles can be interpreted as the main route by which ozone is transported from the equatorial regions to the mid and high latitudes.

Figure 2: Polar stereo diagram of the Lagrangian flow centered at the North Pole at a pressure surface of 7 hPa (altitude about 40 km) analyzed using the derived theoretical equation. Only the component perpendicular to the geostrophic wind is shown, indicating the longitude distribution of the flow shown in Figure 1.

Social Significance and Future Plans
The theoretical equation is highly versatile, and with global grid point data, the three-dimensional structure of the Lagrangian flow can be analyzed. We plan to analyze the circulation structure and its interannual variations in the mesosphere and lower stratosphere in each season. We also plan to apply this method to atmospheric circulations of terrestrial planets such as Venus and Mars, and to investigate their structures and driving mechanisms in detail.

This research was conducted under the research theme "Development and Application of Intelligent Measurement and Analysis Methods by Integrating Measurement Technology and Advanced Information Processing" of the Japan Science and Technology Agency (JST) Core Research for Evolutional Science and Technology (CREST) team research project (Research Director: Yoshiyuki Amemiya). The research was conducted as part of the JSPS Grant-in-Aid for Scientific Research (Kiban B) "Stochastic Behavior of Atmospheric Gravity Waves in the Antarctic Region by Advanced Balloon Observations" (Kiban B), Project No. 18H01276 (Research Director: Kaoru Sato). The research was conducted as part of the Grant-in-Aid for Scientific Research (Kiban B) "Stochastic Behavior of Atmospheric Gravity Waves in the Antarctic Region by Advanced Balloon Observations.

Journal

Journal name	Journal of the Atmospheric Sciences
Title of paper	A new three-dimensional residual flow theory and its application to Brewer-Dobson circulation in the middle and upper stratosphere
Author(s)	Kaoru Sato*, Takenari Kinoshita, Yuki Matsushita and Masashi Kohma
DOI number	https://doi.org/10.1175/JAS-D-21-0094.1

Terminology

1 Lagrangian flow

Flow of atmospheric masses (fluid particles). Describes the flow of atmospheric masses and atmospheric trace constituents such as water vapor, ozone, and carbon dioxide. ↑up

Note 2 Modified Euler mean system of equations

A type of system of equations that describes the time variation and balance of atmospheric motion and temperature in the east-west mean. It also gives approximate forms of the flow of air masses (Lagrangian flow) in the north-south and vertical directions. ↑up

Note 3 Rossby wave

Along with gravity waves, Rossby waves are one of the main waves in the atmosphere. Coriolis force, which is an apparent force due to the Earth's rotation, is stronger at higher latitudes for the same wind speed. The large spatio-temporal scale allows it to be resolved by climate models. ↑up

Note 4 Atmospheric gravity waves

Along with Rossby waves, these are one of the major waves in the atmosphere. Waves with a small spatio-temporal scale that use buoyancy as a restoring force. Also called gravity waves. Since climate models usually cannot resolve them, they are represented by parameterizing their momentum transport. The latest high-resolution climate models are able to resolve them. ↑up

Note 5 Atmospheric reanalysis data

Time series of uniform three-dimensional grid point data describing atmospheric conditions such as wind, temperature, pressure, water vapor, and radiation, obtained by the same atmospheric general circulation model and analysis method based on several decades of atmospheric observation data. It is produced by various meteorological organizations around the world, including the Japan Meteorological Agency. ↑up

Note 6 Geostrophic wind

The atmospheric pressure gradient force and Coriolis force (the apparent force caused by the earth's rotation. In the Northern Hemisphere, the Coriolis force acts to the right of the wind vector). In the mid-latitudes, winds associated with phenomena above a horizontal scale of about 1000 km, except near the earth's surface, are almost always geostrophic winds. ↑up