成層圏-対流圏結合系における

極端気象変動の現象論

余田 成男

京都大学 大学院理学研究科 地球惑星科学専攻

数学協働プログラム研究集会「地球科学における極端現象と疎構造」京都大学数理解析研究所 ２０１４年１１月１３・14日

極端気象変動（変化）

IPCC, 2012: Summary for Policymakers. In: Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation [Field, C.B., et al., Eds.]

Figure SPM.3: The effect of changes in temperature distribution on extremes.

Different changes in temperature distributions between present and future climate and their effects on extreme values of the distributions.

IPCC (2007;FAQ 3.3, Fig. 1)

極端な気温の日の出現頻度

寒い夜

寒い昼

暖かい夜

暖かい昼

1950 20001950 2000

成層圏－対流圏結合系における極端気象変動の現在・過去・未来

研究代表者： 余田 成男所属： 京都大学大学院理学研究科

平成２４～２８年度 基盤研究（Ｓ）

研究の学術的背景

成層圏突然昇温現象

極端気象変動の典型

周極渦の変形・崩壊非線型性の強い地球規模の力学的現象

その出現予測は大変難しい問題

北極上空 10hPa（～高度30 km）での気温 [K] の時間変化

70 K

Mukougawa et al. (2012)

5 日

2009年

突然昇温時の周極渦の時間変化 （３日間隔）

寒

寒北極

7/18

アニメーション： 2009年1月における北極域周極渦の3次元構造の時間発展

野口 峻佑 (2014)https://sites.google.com/a/dpac.dpri.kyoto-u.ac.jp/noguchi/Home/research

dynamical interpretation of SSWs with TEM equations TEM equations

generalized E-P relationship

Equator WinterPole

dA/dt > 0div F < 0W

W

C

CdU/dt < 0

V > 0

downward control(Haynes et al. 1991)

time

A

amplification

thermal gradient –windshear balance

成層圏－対流圏結合変動

成層圏極端気象シグナルが下方伝播

地表気候にまで影響

Baldwin and Dunkerton (2001)

成層圏

対流圏

経過日数

周極渦強度の時間‐高度コンポジット

成層圏-対流圏結合系の多重時間スケール変動像2008～11年の科学研究費基盤（Ａ）の成果

北半球では、冬季に大きな日々・季節内・年々の変動

月平均気温の頻度分布は、冬季には大きく歪み、バイモーダルにも

220 240 260 280 [K]

６月

７月

８月

９月

１０月

１１月

１２月

１月

２月

３月

４月

５月

北極上空での月平均気温の頻度分布１５,２００年分の力学モデル実験Nishizawa and Yoden (2005)

2000年代

1990年代

北極上空での気温の季節内変動・年々変動 Noguchi and Yoden (2012)

7 9 11 1 3 5 月

研究目的

本研究は、成層圏-対流圏結合系における

極端気象変動の力学的関連性の総合的な理解と

その予測能力の向上を目的とする

現在気候の観測・予報データ解析による

結合系変動の現状把握と、

過去気候の再現実験による

モデル検証・改良を踏まえて、

予測の不確実性を押さえて

未来気候の結合系変動に対する影響評価を行う

独創性及び革新性

① 成層圏突然昇温現象という極端気象を、

強非線型性な力学現象の不規則で稀な出現と認識

非ガウス型確率密度関数の先端部に関わる統計解析

複雑精緻な気候モデルではどうか ？

過去気候ではどうだったか ？

将来気候ではどうなるのか ？

220 240 260 280 [K]

１２月

１月

２月

Nishizawa and Yoden (2005)

出現間隔の統計：

ポアソン過程？

極端気象変動に関する統計則

従来の経験則風速： ワイブル分布

降雨量： ガンマ分布

雲特性： 対数正規分布

・・・・・・

周極渦崩壊の形態学観測事例数の不足

数値実験による代用

計算結果データに基づいて経験則をつくる

vs 演繹的な法則

強非線型現象の不規則で稀な出現

独創性及び革新性

② あらゆる階層の数値モデルを用いて系統的に実験

○ 理想化簡略化した低次元モデル(LOM)100～101自由度； 簡単概念・定性的

○ 全球３次元の力学モデル(MCM)104～106自由度； メカニズム理解

○ 大気大循環モデル(GCM),数値天気予報モデル(NPM),気候モデル(CGCM)106～109自由度； 複雑精緻・定量的

１９８０年代は低次元モデル、

１９９０年代からは３次元力学モデル、

これからは、複雑精緻モデルも総合的に活用

波及効果

① 過去気候の再現実験

古気候学・古環境情報学との融合研究の推進

京都大学理学研究科と気象研究所の間で共同研究契約を締結済

気候モデルによる縄文期気候再現実験Kitoh (2012)

１月 ５月 ９月

２月 ６月 １０月

３月 ７月 １１月

４月 ８月 １２月

月平均地表気温の現代気候との差

波及効果

② アンサンブル実験データを活用して、

極端気象変動の予測可能性に関する新たな枠組みを構築

異常天候の予測能力の向上に貢献

2009年成層圏突然昇温現象の気象庁１ヶ月アンサンブル予報結果 Mukougawa (2012)

ー 観測結果ー アンサンブル予報

（５０メンバー）

SPARC / SNAPStratospheric Network for the Assessment of Predictability

初期時刻

初期時刻

初期時刻に依存した予測可能性

観測結果

アンサンブル予報

The 6th IAGA/ICMA/CAWSES workshop on "Long-Term Changes and Trends in the Atmosphere" NCAR, Center Green Conference Center, Boulder, Colorado, USA, June15–18, 2010 -alpha

1. Introduction2. Spurious trend in a finite-length dataset3. Seasonally dependent detectability 4. Concluding remarks

Long-term trends in stratospheric temperatureand their detectability in future simulations

under the situation of large natural variability

YODEN ShigeoDept. of Geophysics, Kyoto Univ., JAPAN

stratospheric temperature trends Randel, W. J., et al. (2009, JGR )

“An update of observed stratospheric temperature trends” limited time period of observations

• radiosonde network (1958~)• NOAA operational satellites (MSU:1979~2007, SSU:1979~2005)

homogeneity adjustment is necessary

1. Introduction

Radiosonde stations for RATPAC-lite dataset

large seasonal dependence large latitudinal dependence large height dependence

Temperature trends:1979–2005SSU & MSU4; 60N–60S

El Chichon Pinatubo

RATPAC-lite

T(solar max) – T(solar min) [K]

anthropogenic influences (mostly?)• increase of CO2, H2O, …; decrease of O3, …

natural influences• large volcanic eruptions, 11-year solar cycle

large natural variability

South Pole(NCEP)

North Pole(NCEP)

North Pole(Berlin)

courtesy ofDr. Labitzke

natural variability in the stratosphere Labitzke diagram

histograms of the monthly mean T (p=30 hPa)Length of the observed dataset isat most 50 years.

Only numerical experimentscan supply much longer datasets

to obtain statistically significant results,although they are not real but virtual.

7 models with volcanic aerosol heating Temperature trends:1980–1999global mean

numerical simulations with high-end climate models Austin, J., et al. (2009, GRL ) “Coupled chemistry climate

model simulations of stratospheric temperatures and their trends for the recent past”

In this talk Nishizawa and Yoden (2005, JGR )

“Distribution functions of a spurious trend in a finite length data set with natural variability: Statistical considerations and a numerical experiment with a global circulation model”

analysis with a simple linear trend model with non-Gaussian natural variability (Edgeworth expansion)

seasonally dependent detectability of a linear trend

linear trend+

random variability

N=5N=5N=10N=20N=50

Linear trend We assume a linear trend

in a finite-length dataset with random variability

Spurious trend We estimate the linear trend

by the least square method

We define a spurious trend as

( ) ( ), 1, ,i iX n an b n n Nε= + + =

ˆˆ ˆ( )i i iX k a k b= +

1

ˆ'12'

( 1)( 1)1 ( )

2

i i

i

N

in

a a a

aN N N

Nn n　　　 ε=

= −

=+ −

+ × −

∑

( )i nε

N = 5 10 20

N = 50

2. Spurious trend in a finite-length dataset

Moments of the spurious trend Mean of the spurious trend is 0

Standard deviation of the spurious trend is

Skewness is also 0

Kurtosis is given by

32

'12 12

( 1)( 1)a NN N N ε εσ σ σ

−= ≈

+ −

standard deviation ofnatural variability

kurtosis ofnatural variability

+ Monte Carlo simulationwith Weibull (1,1) distribution

Probability density function (PDF)of the spurious trend

When the natural variability is Gaussian distribution

When it is non-GaussianEdgeworth expansion of the PDF Cf. Edgeworth expansion of sample mean (e.g., Shao 2003)

( )

2

'2

'

12

' 0,'

1( ) ( ) .2

a

a

x

a Na

f x f x e σσ πσ

−

= =

Distribution function of the spurious trend Edgeworth expansion

where and are PDF and CDF of , respectivelyand

where is k-th Hermite polynomialand is k-th cumlant of ( )

For further details, see Nishizawa and Yoden (2005; JGR)

(0,1)N

An example of Weibull(1,1),of which

seasonal dependence of internal interannual variabilityis large in temperature at the North Pole due to the occurrence of SSWs in winter stratosphere breakdown of the polar vortex is a highly nonlinear process

3. Seasonally dependent detectability

Real atmosphere (Berlin data) MCM(15,200years)30hPa 2.6hPa

Labitzke diagram of the polar stratospheric [T] (Nishizawa and Yoden, 2005, JGR )

stratosphere troposphere

Different dynamical processes produce these seasonally

dependent internal variability↓

“Annual mean” may introduceextra uncertainty or danger

into trend studies

non-Gaussian nature of internal interannual variability Nishizawa and Yoden (2005, JGR ) normalized pdfs of monthly [T] at the north pole

Example of cooling trend run- 96 ensembles of 50-year integration- with external linear trend

-0.25K/year around 1hPa

Natural variability small in summer (July) large in winter (Feb.)

a cooling trend experiment 96 ensembles of 50-year integration

with external linear trend -0.25K/year around 1hPa

necessary data length [years]to detect a linear trend of- 0.5K/decade with 90% conf.

month

pres

sure

[hPa

]

0.1

Jan Dec100

necessary magnitude of the trend [K/decade] todetect with a 20-year dataset

seasonally dependent detectability How many years do we need to get a statistically significant

trend ? How small trend can we detect in finite length data with a

statistical significance ?

0.525

T(North Pole)

10

J F M A M J J A S O N D

[hPa]1

10

100

1000

[years]

20

4060

6080

80100

100

100

120

120

120

120

140 140

140

140

140160

160 160180

220

180

stratosphere- 0.5K/decade(MCM; 15,200years)

troposphere+0.05K/decade

(AOGCM; 1,000years)

North Pole

seasonally dependent detectability in the troposphere a natural variability run of AOGCM for 1,000 years necessary data length [years] to detect a linear trend of

+0.05K/decade with 90% statistical significanceNishizawa, Yoden & Nozawa (unpublished)

4. Concluding remarks Advancement in computing powers has enabled us to

do parameter sweep experiments with 3D MCMs

Very long-time integrations give reliable PDFs non-Gaussian, bimodal, ...nonlinear perspectives on climatic variations and trend

Statistics of natural variability are important to assess the detectability of a linear trend should be estimated well by the state-of-the-art GCMs

Thank you !June 14, 2010 Mt. Rainier

J F M A M J J A S O N D

[hPa]1

10

100

1000

[years]

20

4060

6080

80100

100

100

120

120

120

120

140 140

140

140

140160

160 160180

220

180

stratosphere- 0.5K/decade(MCM; 15,200years)

troposphere+0.05K/decade

(AOGCM; 1,000years)

North Pole

seasonally dependent detectability in the troposphere a natural variability run of AOGCM for 1,000 years necessary data length [years] to detect a linear trend of

+0.05K/decade with 90% statistical significanceNishizawa, Yoden & Nozawa (unpublished)

第５期結合気候プロジェクト(CMIP5)のpiControl実験

500年のデータ

外部強制力が一定

気象研究所地球システムモデル第1版の構成図

Yukimoto et al(2011）

Shinhara(2014)

第５期結合気候プロジェクト(CMIP5)のpiControl実験

北極での月平均気温の進行・季節内変動

成層圏 対流圏

Shinhara(2014)

第５期結合気候プロジェクト(CMIP5)のpiControl実験

北極での月平均気温の頻度分布(10hPa)

『衆瞽撫象之図』 英 一蝶 (1652‐1724)

July 2, 2010, way to Visakhapatnam from Delhi, India

Dependence ofmodel-simulated heavy rainfall

on the horizontal resolutionduring the Jakarta flood event

in January-February 2007SOLA, vol.7, p.193-196 (2011)

Shigenori Otsuka, Nurjanna J. Trilaksono,Shigeo Yoden,

Kyoto University, JAPANKazuo Saito, and Shugo Hayashi

MRI-JMA, JAPAN

Heavy rainfall during the Jakarta Flood event in 31 January--2 February, 2007Wu et al. (2007, SOLA)repeated torrential with pronounced two peaks in a day:

midnight (4 - 5 hours) and morning (3 - 4 hours)torrential rains coincided with a strong and persistent

trans-equatorial monsoon flow from the N. Hemisphere

1. Introduction

01:0

0

01:0

0

01:0

0

01:0

0

01:0

0

01:0

0

13:0

0

13:0

0

13:0

0

13:0

0

80

60

40

20

0

13:0

0

13:0

0

29/01 30/01 31/01 01/02 02/02 03/02

Date and Time (Local time)

Rain

fall

(mm

/hr)

Hourly precipitationat Jakarta

Computational domainshorizontal domainDomain 01

∆x = 20 km115 x 103 grids

Domain 02∆x = 4 km

150 x 150 grids

∆x = 5 km120 x 120 grids

Domain 02’∆x = 2 km

250 x 250 grids

vertical dimain0 ≤ z* ≤ 22.1 km

40 levels

Domain 01

Domain 02’(inside)

Domain 02

horizontal map of TBB at 03 LT 1 Feb, 2007for the best member of each resolution

A: Ocean

B: Northern coast

C: Mountain

D: Southern coast

A

B

C

D

2-km model 4-km model MTSAT IR1

5-km model 20-km model

Statistics on rain rateCumulative Distribution Functions (CDFs)

2-km model 4-km model TRMM

5-km model 20-km model

histogram of model-simulated precipitation

July 2, 2010, way to Visakhapatnam from Delhi, IndiaThank you !!

成層圏－対流圏結合系の主要力学過程

大気波動重力波/プラネタリー波/傾圧擾乱

大気波動の砕波に誘起された子午面循環のダウンワードコントロール

地表の気候状態にまで影響Son et al. (2008, 2010)Thompson et al. (2011)

Son et al. (2010)