京都大学防災研究所年報 第 64 号 B
DPRI Annuals, No. 64 B, 2021

Predicting the Risk Level of Guerrilla Heavy Rainfall by Using the Quantitative
Risk Prediction Method with Multiple Doppler Radar Analysis
Hwayeon KIM(1) and Eiichi NAKAKITA(1) Graduate School of Engineering, Kyoto University
Synopsis
Japan has suffered from devastating flood disasters caused by localized heavy
rainfall known as Guerrilla heavy rainfall recently. For reducing the damage, it isnecessary to predict the risk of GHR precisely. So, we aim to propose an accuratequantitative risk prediction method. One of the importance was that the relationshipbetween the predicted risk level and the variables was considered depending on eachrain stage because the variables showed different characteristics according to thedevelopment of the convective cloud. The other one was that the variables were
estimated with real wind field data by multiple Doppler radar analysis. Then, themultilinear regression was used for finding the correlation between the predicted risk
level and the variables with accuracy. The accuracy of multilinear regression was
estimated by a Receiver Operating Characteristic analysis. As the result, the mostappropriate regression among the relevant variables was composed of reflectivity,
vorticity, divergence, and updraft by multiple Doppler radar analysis. It is possible topredict the risk quantitatively with high accuracy of 90% at the early rain stage.
Keywords: Guerrilla heavy rainfall, Quantitative Risk Prediction, Multiple Doppler
Radar Analysis

1.

Introduction

Recently, localized severe heavy rainfalls,
which have not been experienced in the past, havefrequently occurred in Japan due to the effects ofclimate change (Miyasaka et al., 2020). In
particular,
the
Guerrillaheavy
rainfall(abbreviated as GHR), which is a rapidly growing
isolated single cumulonimbus when water vapor
rises to the upper atmosphere with the ascending
air current, could trigger flash floods in a small
river basin and caused extensive economic
damages and casualties. In 2008, more than fifty
people have washed away and five people were
killed by a tragic flash flood caused by GHR in
Toga River, Kobe city. It is quite difficult toobserve and predict the rapidly developed rainfalls.
If the risk of heavy rainfall can be identified andalerted in advance, it would be possible to safely
evacuate the danger. Nakakita et al. (2014)
developed qualitative risk prediction methods
based on the early detection of the rain cells aloft.
These methods can predict the risk of the localized
heavy rainfall qualitatively and track thedevelopment of convective cells by considering all
rain stages. Following this previous research, we
use the risk of terminology to represent theseverity of the localized heavy rainfall intensity.
To discriminate the risk quantitatively, we aim
to develop the early detection and quantitative risk
prediction method by considering the performanceof variables that have different characteristics― 217 ―

depending on each rain stage. Also, we deal withthe vertical vorticity, reflectivity, divergence, andupdraft to find the correlation with the predictedrisk level. Especially, the vorticity, divergence,and updraft are important variables at the
beginning of an isolated single cumulonimbus
cloud (Ulanski and Garstang, 1978). The vorticity
and divergence can be estimated by using Pseudo
radar analysis and multiple Doppler radar analysis.
On the other hand, the updraft can be calculated bymultiple Doppler radar analysis only because theanalysis can retrieve a three-dimensional windfield. Pseudo radar analysis uses only a single
Doppler radar observation which is a radial
component of wind field that flows toward or awayfrom the radar. To predict the risk level moreaccurately, it is necessary to estimate the threedimensional wind field by using multiple Doppler
radars. Therefore, in this study, we aim to propose
an accurate quantitative risk prediction method.
The objectives of this study are to (1) compare thetotal stage regression at all rain stages with thestage dependent regressions at each rain stage; (2)determine the multilinear regression with thehighest accuracy by finding the best combinationsof the variables (i.e. the reflectivity, vorticity,
divergence, and updraft) with Pseudo and multiple
Doppler radar analysis.
2.

Methodology

2.1 The process of Guerrilla heavy rainfall
occurrence
In Japanese media, the localized heavy rainfalls are denoted as “Guerrilla heavy rainfalls”. Fig.
1 illustrates the process from rain-cell into heavy
rainfall, which is classified into the development,
mature, and dissipation stages. In the early
development stage, water vapor in the lower
atmospheric layers rises and condenses to generate
a convective cloud in an atmospheric instability
condition. Cloud particles, however, are too small
to be detected by weather radars before
precipitation particles are formed. The detectedparticles can be defined as the first echo or a baby
rain-cell. When the baby rain-cell is detected, afirst rain stage is assigned. The rain stage is theprocess of convective cloud development. Then,the baby rain-cell develops gradually, and theheight of the cloud increases. However, anyraindrop is not observed on the ground at this stage.
In the mature stage, the volume of clouds increases
in an ascending air current and finally falls withthe descending air current. In the dissipation stage,as the ascending and descending air currents are
weakened, the rainfall intensity decreases.

Altitude Development stage Mature stage Dissipation stage

15km
10km

(10 – 15 min) (15 – 20 min)(5 – 10 min)

Convective cell

5km
Time
StrongWeak
Rainfall intensity

Wind direction

Fig. 1 The process of Guerrilla heavy rainfall
occurrence.
2.2 The early detection of convective cells
Early detection means to find out the existenceof the first echo in a convective cell on the upper
atmospheric layer. At the first rain stage, a volume
threshold, ranging from 0.125 km3 to 62.5 km 3, isutilized to search convective cells. The initialconvective cells can be identified by thresholds of
20 dBZ of radar reflectivity and verticalcomponent of vorticity. The vertical vorticity is ameasure of the local rotation of the flow. There are
two ways to calculate vertical vorticity. One is
Pseudo radar analysis; the other is multiple
Doppler radar analysis. The Pseudo verticalvorticity is roughly estimated by applying themethod proposed in Nakakita et al. (2017) with theradial velocity. From the radial velocity, thevorticity can be calculated by the following
formula.

― 218 ―

ζ = ( 𝑉2 − 𝑉1)/ΔX,(1)

where V 1 and V 2 (see definition in Fig. 2) are
moving toward and away from the radar in the
Cartesian coordinates and ΔX is the distance
between the center of the mesh. Because thevolume scanning observation using single Doppler
radar could not measure horizontal wind velocities
but the radial velocity. If we estimated thehorizontal wind velocities by multiple Doppler
radar analysis, the vertical component of vorticity
can be calculated by the following formula.
ζ = ∂v/∂x − ∂u/∂y,(2)where (u,v) are the horizontal wind velocities
in the Cartesian coordinates. Also, Nakakita et al.
(2017) proposed that the behavior of the vorticity
is related to the growth of rain-cell. However, notevery baby rain-cell aloft develops into severe
heavy rainfall. Therefore, it is important to trackthe detected baby rain-cell prone to generate
dangerous heavy rainfall. By using the early
detection method, Nakakita et al. (2013) haveclarified that the first echo was detected about 25
minutes on average before the maximum rainfall
near the surface occurred, and Katayama et al.
(2015) developed the qualitative risk prediction
system which is operationally used in the Kinki
region in Japan.
2.3 The multiple Doppler radar analysis
The multiple Doppler radar analysis could
retrieve the three-dimensional wind field. Shimizu(2012) emphasized that this analysis can improvethe understanding of the physical mechanisms
behind heavy rainfall and forecasting hazardous
weather. A variational method for the retrieval of
the three-dimensional wind field was developed.
To allow the measurement error, the Doppler
velocities as weak constraints and the continuity
formula as strong constraints are used in the costfunction. The weak constrain appropriately accepts
the observation errors from the radar data orassumptions in formulas. On the contrary, thestrong constraint demands all of the analyzed andretrieved variables satisfy the formula exactly.
Since the collected radar observation data could be
affected by noise, in the Cartesian coordinates theFig. 2 Conceptual diagram of calculating vorticity
and divergence by Pseudo and multiple Doppler
radar analysis.
horizontal wind components (u,v) are used as weak
constraints. By using the continuity formula, thevertical wind component (w) in multiple Doppler
analysis is estimated. The continuity formula isexpressed as follows:∂u/∂x+∂v/∂y+∂w/∂z = kw,(3)

where (u,v,w) are the three wind components in
Cartesian coordinates, k = − ∂(ln 𝜌)/𝜕 𝑧 , and 𝜌 isthe air density. With the continuity formula, thevertical wind component (w) is calculated by aweighted average of upward and downward
integrations. The variational method minimizes thecost function, which is the sum of discrepancies
between observations and analyses with weighting
matrices that depend on the strength of theconstraint (Protat and Zawadzki, 1999). In
summary, the procedures are to 1) set initial
control variables (u,v); 2) estimate the w informula (3); 3) calculate the gradient of the costfunction concerning control variables (Powell,1977); 4) finish if the predefined condition of costfunction was satisfied; otherwise, set new control
variables and return to the step 2. Additionally,
Ulanski and Garstang (1978) have proved that the
updraft, downdraft, an upward flux of water vapor,maximum divergence, vorticity, and rainfall arepresented in the convective cloud. So, the variables
are collected to find the relevance with the risk
level of localized heavy rainfall including GHR.

― 219 ―

where PRL is predicted risk level from rain stagei. Z , 𝜁, 𝑤, 𝐷 are reflectivity, vorticity, updraft,and divergence respectively. i ∈ 1, 6 is thenumber of rain stage which represents thedevelopment of a cumulonimbus cloud. The
variables would be extracted depending on eachrain stage (Fig. 4). There is a multilinear regression
which is performed with the variables (i.e. thereflectivity and vorticity) for all rain stages at once.
Moreover, the stage dependent regressions are also
considered to improve the accuracy of risk
prediction by including the variables (i.e. thedivergence and updraft), because the variables
have characteristics depending on each rain stage.
Fig. 3 Flowchart of improvement of thequantitative risk prediction accuracy. Z :Reflectivity, ζ : Pseudo Vorticity, D : Pseudo
Divergence, ζ : Vorticity of multiple Doppler
radar analysis, D : Divergence of multiple
Doppler radar analysis and 𝑤: updraft
2.4 Quantitative Risk Prediction
After we find out the existence of the first echo,
the rain stages from 2 to 6 are marked according to
the process of convective cloud development witha time interval of 5 minutes. To set the predictedrisk level, the predicted risk categories (risk levels)
are defined at the maximum rainfall intensity on
the ground, such as Risk 1(under 30mm/hr), Risk2(between 30mm/hr and 50mm/hr), Risk3(between 50mm/hr and 70mm/hr), and Risk
4(over 70mm/hr). Finding the relationship among
the predicted risk level and variables (i.e. thereflectivity, vorticity, divergence, and updraft) is
important within 30 minutes (from rain stage 1 to6) before the maximum rainfall intensity occurs on
the ground. Then, for predicting the risk levels byusing the observed and calculated variables, thecorrelation can be represented by using multilinear
regressions. Fig. 3 illustrates the process of how tofind the relationship and select the most accurate
multilinear regression by the quantitative risk
prediction method. The formulation of themultilinear regression becomes;

𝑃𝑅𝐿

𝐶
𝐶 ∙𝑍
𝐶 ∙𝜁
𝐶 ∙𝑤 𝐶 ∙𝐷 ,Fig. 4 The Early detection of the isolated
convective cell until the maximum rainfall occurs
on the ground. Extraction of variables dependingon each rain stage.
To check the accuracy between total stage andstage dependent regressions, we apply the
Receiver Operating Characteristic (ROC) analysis
and examine the Area Under ROC Curve (AUC).
The ROC analysis is a quantitative evaluation
method to assess the accuracy of the multilinear
regression. It divides values into observation andprediction as a contingency (Table 1). Also, it canestimate the ability of how many percent theanalysis predicted the occurrence of GHR. The
ROC curve plots the hit rate (HR) against the false
alarm rate (FAR), which are computed as formulas(5) and (6):Hit rate (HR) = H/(H+M),(5)

False alarm rate (FAR) = F/(F+N),

(6)

(4)

― 220 ―

where H and M represent hits and misses when
GHR occurs. F and N represent false and negative
hits when GHR not occurs. The ROC curve isplotted with the resulting pairs of (FAR, HR) fromthe contingency table are plotted and connected byline segments from the origin point (0, 0), whichcorresponds to never prediction of the heavy
rainfall, and to the point (1, 1), which corresponds
to always prediction of the heavy rainfall. The
AUC can represent the accuracy of the multiple
linear regression formulas with a range of 0.5 to 1.
When the AUC value approaches unity, the ROC
curve goes up to the upper-left corner of the ROC
diagram and reflects better discrimination
performance. Therefore, the most appropriate
multiple linear regression formula is chosen by thehighest AUC value among the identified multiple
linear regression formulas. We analyzed theaccuracy at the early and late rain stages as well toreveal specific characteristics of variables during
each rain stage.
Table 1 ROC contingency table for 𝑅𝑃 (Risk
Prediction of radar) and 𝑅𝑃 (Risk Prediction ofregression).

and provides complete volume scan data every 5
minutes. The three-dimensional volume scan data
has a resolution of 250 and 500 m in the horizontal
and vertical directions, respectively. Also, toretrieve the three-dimensional wind field,
especially at upper levels, background information(i.e. Sounding data) is required. By using these
data, the variables (i.e. the vorticity, divergence,and updraft) were calculated. From August 2013 toAugust 2018, 10 GHR events were selected andtabulated in Table 2.

Fig. 5 The detection range of radars, study area,and distribution of Guerrilla heavy rainfall
events.

Observed Value (RPRD )Predicted
Value(RP RG )3.

GHR
occurred

GHR not
occurredGHR
occurredHit (H)

False (F)GHR not
occurred

Missing(M)

Table 2 List of Guerrilla heavy rainfall events

Negativehit (N)

Data and Study Area

To provide the high spatiotemporal observation
data throughout Japan, MLIT has been operating
the X-band polarimetric RAdar Network (XRAIN)
since 2010. As of now, the MLIT has installed 39
X-band multi-parameter (X-MP) radars. Fig. 5
illustrates the positions of the radar sites and theirobservation ranges in the Kinki region. In our
research target area, there are four radars which are
named Rokko, Katsuragi, Juubusan, andTanokuchi. The XRAIN in the Kinki region
produces composite radar images every one minute

4.

No.

Date

No.

Date

1

2013-08-06

6

2015-08-29

2

2013-08-07

7

2016-08-03

3

2014-08-23

8

2016-08-25

4

2014-08-23

9

2017-08-04

5

2015-08-07

10

2018-08-13

Result and Discussion

4.1 Accuracy comparison between total stage
regression and stage dependent regressions
To improve the quantitative risk prediction
method, it is necessary to make regressions
depending on each rain stage because thereflectivity
andvorticityholddifferent
characteristics in different development rain stagesof a cloud. First of all, the performance of stage
dependent regressions is compared with the total
stage regression as a three-dimension scatter and― 221 ―

Fig.6 a) The performance of stage dependent regressions is compared with the total stage regression by
three-dimension scatter and plane plot. b) The Comparison between total stage regression and stage
dependent regressions is conducted based on the accuracy by ROC curve.
plane plot (Fig. 6a). The plane plots are useful forshowing the relationship of regression analysis
among the dependent variable (i.e. predicted risk
level) and two independent variables (i.e.
reflectivity and vorticity). The warmer color of theplane plot, which is closer to the risk level 4.0,
corresponds to more severe risk levels. The total
stage regression (Fig. 6a, blue dashed box) showsa positive correlation between the dependent
variable and each independent variable. The stage
dependent regressions (Fig. 6a, red dashed box)
from rain stages 1 to 6 represent the relationshipamong the dependent variable and two
independent variables. The correlation between
predicted risk level and reflectivity shows morepositive correlations as the rain stage develops,
except rain stage 1. The correlation between
predicted risk level and vorticity shows positive
correlations at the early rain stage. However, at thelate rain stage, it becomes difficult to findcorrelations. For each event, there are cases withrain stages 1 to 6. When each case is compared, thepredicted risk level of stage dependent regressions
shows higher than the total stage regression mostly.

Then, the accuracy is evaluated by using the ROC
and AUC analysis. Fig. 6b represents the ROC
curves at the early (i.e. rain stage 1 to 2) and laterain stages (i.e. rain stage 3 to 6), which isestimated by the total stage and stage dependent
regressions with vorticity and reflectivity. At theearly rain stage, the accuracy of stage dependent
regressions is 76% (AUC=0.76), which is higher
than the total stage regression (AUC=0.73).
Because the number of cases about stage
dependent regressions is smaller than the total
stage regression statistically, the stage dependent
regressions deviate from the limited number ofcases. The stage dependent regressions arestrongly affected by cases, so they have lessstatistical stability than total stage regression
relatively. However, if we collect more events, theproblem could be solved. Physically, the variables
show different characteristics according to thedevelopment of the cloud. Also, the stage
dependent regressions calculate higher accuracy atthe early rain stage. For saving lives by alerting thewarning at the beginning of GHR, this research is
focused on stage dependent regressions.

― 222 ―

4.2 Determination of the most appropriate
regression among the variables
The development processes of the convective
cloud at the rain stage 1, 2, and 5 are plotted in Fig.
7 with the variables calculated by Pseudo andmultiple Doppler radar analysis. Depending oneach rain stage, the three-dimensional vorticity anddivergence are calculated. Then, the pair ofvorticity, divergence, and convergence increase
while the rain-cell developed into heavy rainfall.
The divergence and convergence can be an
explanatory variable because at the beginning of
the cumulonimbus cloud the strong convergenceoccurred at the lower layer (Houze, 1997). In
addition, when the vorticity is detected in thedevelopment of cumulonimbus cloud, a verticalvortex tube is formed by the strong updraft, and it
brings the water vapor. According to the results,
we consider that the vorticity, divergence, andupdraft are related to the predicted risk level ofheavy rainfall.
To analyze the characteristics of variables
depending on each rain stage, the multilinear
regressions are expressed by combining thedivergence and updraft based on reflectivity andvorticity. In this paper, we use the part correlation
coefficient (Huber, 1981) of variables because thepart correlation coefficient shows how the
explanatory variables explained the predicted risk
level. A partial correlation coefficient shows asimilar explanation with the part correlation
coefficient. The differences are presented in the
Appendix. The part correlation coefficientindicates that only the variable (i.e. vorticity) by
eliminating the influence of the other variables can
explain the dependent variable (i.e. predicted risk
level). Fig. 8 illustrates the part correlation
coefficient of variables affecting the predicted risk
level depending on each rain stage by Pseudo andmultiple Doppler radar analysis. It represents thatthe most explanatory variable is changed
depending on each rain stage. In Pseudo andmultiple Doppler radar analysis, the combinationsof variables have conditions in common that thereflectivity and vorticity are very important at theearly and late rain stage respectively. We focus on
the early rain stage for saving evacuation time toescape from danger because the Guerrilla heavy
rainfall occurs within a few minutes. So, vorticity
is the most explanatory variable to estimate thepredicted risk level before the maximum rainfall
reached the ground. Moreover, the inclusion ofdivergence and updraft can better describe thepredicted risk level. By the way, the part
correlation coefficient of updraft suddenly
decreases at rain stage 3. The reason is that atransition occurs in which the direction of the
updraft is changed to the downdraft.

Fig.7 The reflectivity, updraft, vorticity, anddivergence calculated by Pseudo and multiple
Doppler radar analysis. The circle represents theexistence of divergence and convergence at rain
stage 1.

― 223 ―

Reflectivity 0.6
Vorticity00Part Correlation Coefficient

0.2

𝑍

1

𝜁

3
4
Rain stage

5

0.8

0.6 Vorticity

Reflectivity

0.4

0Divergence1

2 3 4
Rain stage

5

Divergence
1

2

𝑤

Reflectivity
Vorticity

0.8
0.8
0.6
0.6

𝑤

0.2
0.2

0.2

0.00

0
0.0

Updraft
1

2

AUC
76%
75%
79%
82%

0.20.2

Divergence

0.4

0.60.6

3
4
Rain stage

5

The ROC analysis is applied to select the best
multilinear regression with the highest accuracy.
The predicted risk level is defined at the maximum
rainfall intensity on the ground according to thepredicted risk categories. To make the ROC curve,
the HR, FAR, and AUC are estimated among the
combinations of independent variables of themultilinear regression. Fig. 9 represents the ROC
curves of the stage dependent regressions. As aresult of the highest accuracy, the multilinear
regression of reflectivity, vorticity, divergence,and updraft has 82% accuracy (AUC= 0.82). The
regression by using multiple Doppler radar
analysis and adding more independent variables
has brought remarkable improvement rather than
the total stage regression. Moreover, the inclusionof divergence and updraft can better describe thepredicted risk level. The AUC analysis isconducted at the early and late rain stages andconfirms higher accuracy at the early rain stage(90% accuracy). Therefore, by using the improved
regression, the risk level of localized heavy
rainfall could be predicted with high accuracy.
Conclusions

In order to minimize human injury such as
isolation, death, and disappearance due to heavy

0.2
0.2 0.4
0.4

0.6
0.6

0.8
0.8

76%
89%
85%
90%

0.4
0.4
0.00
0.00

0.40.4

Fig.8 The impact of variables affecting thepredicted risk level by Pseudo and multiple
Doppler radar analysis.

5.

𝐷
𝐷
𝐷

0.80.8

0.6

0

𝜁
𝜁
𝜁
𝜁

⑥

1.01

1.01

3
4 5
Rain stage
𝐷 Multiple Doppler Radar analysis 𝑍 𝜁 𝐷
1

0.8

0.2

𝑍
𝑍
𝑍
𝑍

Vorticity
Reflectivity

0.4

0.2
2

𝐷

HIT RATE (HR)

0.6

𝜁

1
1.0

1-FALSE ALARM RATE (FAR)

0.2

0.4

0.6

0.8

1

0.2
0.4
0.6
1-FALSEALARM
RATE 0.8(FAR) 1.0

① ② ③ ④ ⑤⑥

1.01

HIT RATE (HR)

0.8

1

𝑍

1

0.8

0.4

① ② ③ ④ ⑤Pseudo Radar analysis

𝜁

HIT RATE (HR)Part Correlation Coefficient

1 𝑍

0.8
0.8
0.6
0.6

76%
68%
96%
96%

0.4
0.4
0.2
0.2
0.00

0 0.2
0.4
0.6
0.8
11.0
0.2
0.4
0.6
0.8

0.0

1-FALSE ALARM RATE (FAR)

Fig.9 The accuracy of multilinear regression
among the combination of dependent variables by
AUC. By Pseudo radar analysis, the purple andblue lines were the regressions of 1) reflectivity,
pseudo vorticity and 2) those with added pseudo
divergence. By multiple Doppler radar analysis,
the green and red lines were the regressions of 3)
reflectivity, vorticity, divergence and 4) thosewith the added updraft.
rainfall, this study has proposed the quantitativerisk prediction method which accurately alerts therisk of localized heavy rainfall. First, the stage
dependent regressions depending on each rain
stage are compared with the total stage regression
by the performance of variables and accuracy since
the reflectivity and vorticity show different
characteristics. Then, by using Pseudo radar
analysis and multiple Doppler radar analysis, themultilinear regression with the highest accuracy is
chosen among the combinations of variables. If
this regression is applied to the field, it is possible
to secure more evacuation time and predict thedisasters with high accuracy.
However, there still exists some points toimprove. When we formulate the stage dependent
regressions, the number of cases is less than the
total stage regression. This condition could cause
the stage dependent regressions to be over-fitted
due to data insufficiency. If more cases areincluded, this problem should be resolved.
Furthermore, it is still unclear to determine which― 224 ―

convective cell would be developed. Even if a baby
rain-cell can be detected, it is difficult to predict inwhich direction the rain-cell would move andwhere heavy rainfall would occur. So, it
necessitates finding more explanatory variables
that affect the localized heavy rainfall to improvereliability and accurate risk prediction, such asreflectivity, rainfall intensity, Doppler wind speed,
vorticity, the velocity of vertical invigoration,echo amplitude difference, convergence, etc. In
addition, it is expected to carry out a study to
predict the movement of convective cells by
extrapolation to estimate the risk in long-term leadtimes.
The improved quantitative risk prediction(meteorology)
and
flash
flood
warning(hydrology) will be combined in the next step of
this research. Flash floods happened whenmeteorological and hydrological circumstances
coexist. Therefore, future research is promising tobridge the gap between this study and the flash
flood prediction system.
Acknowledgements
The authors are grateful to the Publishing
Committee members who made the previous
versions of this instruction.

References
Houze, R. A., Jr. (1997): Stratiform Precipitation
in Regions of Convection: A Meteorological
Paradox?, Bulletin of the American MeteorologicalSociety, Vol.78, No.10, pp.2179-2196.
Huber, J. (1981): Partial and part (semipartial)
correlation-A vector approach, The Two-Year
College Mathematics Journal, Vol.12, No.2,
pp.151-153.
Katayama, M., Yamaji, A., Nakamura, F., Morita,
H. and Nakakita, E. (2015): Development ofdetection system for a local rain storm,
Proceedings
of
the
River
Engineering
Symposium(Japanese).
Miyasaka, T., Hiroaki, K., Tosiyuki, N., Yukiko, I.
and Izuru, T. (2020): Future projections of heavy
precipitation in Kanto and associated weather

patterns using large ensemble high-resolution
simulations, Scientific Online Letters on the
Atmosphere, Vol. 16, pp. 125-131.
Nakakita, E., Nishiwaki, R., Yamabe, H. andYamaguchi, K. (2013): Research on the prognostic
risk of baby cell for guerilla-heavy rainfall
considering by vorticity with Doppler velocity,
Journal of Japan Society of Civil Engineers,
Vol.69, No.4, pp.325-330(Japanese).
Nakakita, E., Sato, H., Nishiwaki, R., Yamabe, H.,
and Yamaguchi, K. (2017): Early Detection of
Baby-Rain-Cell Aloft in a Severe Storm and Risk
Projection for Urban Flash Flood, Advances in
Meteorology, Article ID 5962356, pp.15.
Protat, A., and Zawadzki, I. (1999): A Variational
Method for Real-Time Retrieval of ThreeDimensional Wind Field from Multiple-Doppler
Bistatic Radar Network Data, Journal of
Atmospheric and Oceanic Technology, Vol.16,
No.4, pp.432-449.
Powell, M. J. D. (1977): Restart procedures for the
conjugate-gradient method. Math. Prog., Vol.11,
pp.42–49.
Ulanski, S. L. and Garstang, M. (1978): The roleof surface divergence and vorticity in the life cycleof convective rainfall. Part II: Descriptive model,
Journal of Atmospheric Sciences, Vol.35, No.6,
pp.1063-1069.
Shimizu, S. (2012): Multiple Doppler Radar
Analysis for Retrieving the Three-Dimensional
Wind Field Within Thunderstorms, Doppler Radar
Observations, InTech.

Appendix A. Differences between part andpartial coefficient
The partial correlation coefficient shows asimilar explanation with the part correlation
coefficient. However, in this paper, we use the part
correlation coefficient of variables because thepart correlation coefficient shows how the
explanatory variables explained the predicted risk
level.
― 225 ―The part correlation (Fig.S1) is the correlation
between independent variable (X1) and thedependent variable (Y) after the linear effects

of the other independent variables (X2) havebeen removed from the independent variable(X 1) only. It can be calculated by the following
formula.

𝑟,(|) = B/(A+B+C+D) = B

Y
X1

𝑟 ( ,

X2

A
B

(S.1)

removed from both the independent variable(X 1) and the dependent variable (Y). For
example, there are the dependent variable (Y)and independent variables (X1, X 2). The part
correlation coefficient indicates the amount of
unique explanatory power in Y explained by
X 1. It can be calculated by the following
formula.

)|D= B/(A+B)

Y

C
X1

A

(S.2)

X2

B

Fig.S1 The part correlation coefficient

The partial correlation (Fig.S2) is thecorrelation between independent variable (X1)
and the dependent variable (Y) after the linear
effects of the other variables (X 2) have been

― 226 ―

Fig.S2 The partial correlation coefficient(Received August 31, 2021)