MITSUBISHI-B project
Title:
Multi-objective optimization for best early prediction of extreme weather events
Industrial Partner: Information Technology R&D Center of Mitsubishi Electric Corp.
Mitsubishi Electric is one of the world's leading names in the manufacture and sales of electricaland electronic products and systems used in a broad range of fields and applications. As a global,
leading green company, we are applying our technologies to contribute to society and daily lifearound the world. The Information Technology R&D Center is actively creating new businessthrough our basic research and development in the fields of information technology, media
intelligence, electro-optics microwave and communication technologies. We are also searching out
technologies that enable us to be the leader, and are working to renew existing business throughthe fruits of our R&D in the field of IT.
Industry Mentors:
Shumpei Kameyama Ph.D.
Hidenobu Tsuji Ph.D.
Yusuke Ito Ph.D.
Information Technology R&D Center, Mitsubishi Electric Corp., Kamakura, Japan.
Project Description:
1. Motivation for the project~ Early prediction of extreme weather events is vital ~Climate change and global warming has increased extreme weather events. This includes, forexample, heavy rains, tornados, and more. Concretely, you know the tragic heavy rain disaster in
New York this September [1], and the big landslide caused by heavy rain in Atami this July [2]. Suchdisasters make the early prediction of weather events vital for disaster mitigation [3]. The
mathematical problem to be solved here is related to this scientific field. The goal of this project ismulti-objective optimization [9] on locations of meteorological sensing instruments for the best early
prediction of extreme weather events. This will be explained in more detail in the following
2. Toward the early prediction of heavy rain
~ Sensing of water vapor and wind is effective ~As many people know, we can predict heavy rain after the appearance of the cumulonimbus.

However, for the purpose of disaster mitigation one needs to be able to make this prediction before
the appearance ofthe cumulonimbus. For this early prediction, accurate and wide-area

meteorological sensing within a certain time interval is necessary of course.
Especially, the “distributions of the water vapor and wind in the atmosphere" are very important,since these often become the signs for the cumulonimbus and eventually heavy rain [3].
2.1. The attractive meteorological sensor "LiDAR"
For the sensing of the water vapor and wind, the “LiDAR (Light Detection And Ranging)” is an
attractive instrument, and its deployment has recently grown. This instrument (LiDAR) transmits alaser light to the atmosphere, and detects the light that is scattered (reflected) by the aerosols(particles) drifting in the air. The distribution of the water vapor and wind can be measured(visualized) by analyzing the received light [3-5] (see Fig. 1). The detection of light scattered by theaerosols is similar to what one
observes when one illuminates asearch light at midnight; in thatcase, you can see the path of thelight in the air [6], and your eyes
are exactly detecting the scattered
light by the aerosols.
The LiDAR instruments canmeasure the water vapor and wind“remotely” from the ground. This isa very big advantage compared to“in-situ”

humidity

and

wind

Fig. 1. Measurement principle using LiDAR[3].

sensors [7-8] especially for themeasurement in the high-altitude
regions. Furthermore, the LiDAR
can work especially well in clearsky

conditions

beforetheappearance of the cumulonimbus
and can catch the sign of that. Thisis also a significant advantage
compared to the electro-magnetic
wave RADAR (RAdio Detection
And Ranging) which works only
after the appearance of clouds andFig. 2. LiDAR system for early weather predictions[3].

rain (see, Fig. 2). How the LiDAR contributes to the early prediction of heavy rain is roughly shownin Fig. 2. Note again that what is important is the detection of the first signs before the appearanceof the cumulonimbus. This project focuses on how to improve this early detection of water vapor
that might lead to catastrophic rain events.
2.2. "The sky is the limit"
The LiDAR is an attractive meteorological instrument. But unfortunately, it also hassomeweaknesses. In investigating these weaknesses, one English phrase comes to mind: “The sky is
the limit.” This phrase means “no limitation in your future”, or “your possibilities are unlimited.” Thisphrase was recently used by Shohei Otani, the two-way major-league baseball player, and is true
for all of you. This is also true for the LiDAR instruments in another meaning. For example, what
happens when the sky is very clear? (see, Fig. 1) In this case, the aerosol loading is very low andtherefore there is only a low scattering signal from the atmosphere. If there is no signal, the LiDAR
data cannot be used. Similar issues arise when it is foggy: The laser light from the LiDAR cannot
pass through the atmosphere and cannot reach to the measurement volume. This also leads tolimitations of the LiDAR performance. Therefore, the LiDAR measurement performance is always
affected and limited by the atmospheric conditions in the sky. The atmospheric conditions here
include the visibility (aerosol loading) and more, and they highly depend on the locations andaltitudes. For example, the aerosol loading is high at the ground (which is good for the LiDAR
measurement), and it is low at the higher altitudes. It is also high in urban areas and low in the
countryside.
3. What is the best meteorological sensing?
One can improve the performance of the LiDAR instrument in different ways: one strategy is the
deployment of higher grade instruments (i.e., with high-grade laser components, Fig. 3(a)).
However, this comes with a higher
cost. Alternatively, one can alsouse multiple sensors with low
specification (Fig. 3(b)), but thisalso increases the deployment
cost. This means that there is an
optimization

problemforthenumberof

instruments

andlocationstoobtainbest

measurements

the

while

also

considering the deployment cost.

(a)(b)
Fig. 3. High-grade (a) and low-grade (b) LiDARs [10].

4. The ProjectIn this project students will use a mathematical approach to develop an optimization strategy forthe number and location of instruments, to get the best early prediction of the extreme weather
events.
4.1. What we can provide before solving the problem
We can give you the atmospheric conditions in three dimensional meshes which depends on thelocation and altitudes. The importance of the measurement for the weather prediction depends on
the location of the atmospheric mesh in the three-dimensional space. This is defined as the“measurement score”, which can be obtained with the knowledge of simple meteorology. Formulasof the score have not yet been reported in the literature, but we can provide examples of the score(simple formulas with exponential functions). If the students in the project team have someknowledge of meteorology, they might also work on the score formula to be more accurate and to
fit more realistic situations.
An example of an atmospheric mesh and measurement scores is depicted in Fig. 4. The area
size of 70 km × 30 km is roughly equal to the area of Tokyo. The terrain can be expressed with aformula as schematically shown in the figure, but real terrain models for specific areas can be used
if you like.

Fig. 4. Example of atmospheric mesh and measurement scores.
(The pictures of LiDARs are the ones in [10])Examples of scores are also shown in Figs. 4 and 5. Generally speaking, measurements at the
ground are very easy with in-situ wind sensors and humidity sensors, but the importance of themeasurement at the ground level is not so high from the view point of meteorology. This meansthat the “measurement score” is low at the ground level. On the other hand, measurements at highaltitude (especially around the height of 1 ~ 3 km) have a high “measurement score”, since this isimportant for the early prediction of heavy rain. The measurements at high altitudes are impossible
with in-situ sensors, but are possible with LiDAR (i.e., a remote sensor).

Measurements inmountainous regions with living areas have also high “measurement scores”.

Fig. 5. Examples for measurement and cost scores
The “cost score” is defined by considering the financial cost of each instrument as shown in Fig.
5. The in-situ sensors (for example, a humidity sensor) are also available in addition to the LiDAR
as cheaper instruments. It should be noted again that the in-situ sensors can measure the windand humidity only at the ground and cannot measure them at high altitudes. The LiDARs (especially,high grade one) can measure them remotely even though they make the cost score large (i.e.,
worse).
Further, we also give you the specification of the LiDAR instruments and the equation to derive
their measurement performance named "LiDAR equation". You can calculate the measurement
performance of water vapor and wind by using the above-mentioned LiDAR equation and theatmospheric conditions.
Formulas and parameters shown in Figs. 4 and 5 are just examples and are expected to be
improved during the project.
4.2. What should be optimized
The students will perform a multi-objective optimization [9] on (i) where we should place theLiDAR instruments, (ii) how many instruments we should use for each type of the instruments. The
goal is to maximize the measurement score SM and to minimize the cost score SI.
Recommended interests, skills, and knowledge
The ideal students for this project have an interest in the social issue of climate change, naturalscience, and mathematics. Knowledge of the following items is necessary.
-

Basic knowledge of optimization-

Programing skill (MATLAB or Python)
Knowledges on the following items will be helpful.

-

Topology, Bayesian inference, meteorology
We highly recommend that students read the references [4-5] before starting this project. The

equations (10) – (16) in [5] are what we call the set of LiDAR equations. The example of theatmospheric parameters has been shown in Fig. 7 in [4]. At the beginning of the project we will give
additional lectures about the LiDAR instrument and how to derive the LiDAR equation, if necessary.
References[1] https://www.bbc.com/news/world-us-canada-58417442[2] https://www.asahi.com/sp/ajw/articles/14386694[3] https://www.mitsubishielectric.com/news/2018/1011-a.html[4] M. Imaki, K. Hirosawa, T. Yanagisawa, S. Kameyama, and H. Kuze, “Wavelength selection andmeasurement error theoretical analysis on ground-based coherent differential absorption lidar
using 1.53 µm wavelength for simultaneous vertical profiling of water vapor density and wind speed,”
Applied Optics, 59(8), 2238-2247 (2020).
[5] M. Imaki, H. Tanaka, K. Hirosawa, T. Yanagisawa, and S. Kameyama, “Demonstration of the
1.53-µm coherent DIAL for simultaneous profiling of water vapor density and wind speed,” Optics
Express, 28(18), 27078-27096 (2020).
[6] https://en.m.wikipedia.org/wiki/Searchlight[7]

https://www.vaisala.com/en/products/instruments-sensors-and-other-measurement-

devices/instruments-industrial-measurements/hmt330[8] https://www.vaisala.com/en/products/weather-environmental-sensors/wind[9] https://en.wikipedia.org/wiki/Multi-objective_optimization[10] http://www.mitsubishielectric.co.jp/lidar/products/index.html#DopplerLidarSystems