Seasonal forecasting of Ethiopian spring rains

Seasonal Forecasting of EthiopianSpring rains

Gulilat Tefera DiroSupervisors: David Grimes and Emily Black

Department of Meteorology

University of Reading

Africa group 2007 – p. 1/20

Outline of the talk

Large scale controls

Homogeneous rainfall zones

Predictors

Forecasting Models

Skill Assessment

Conclusions


Large scale controlsUpper Level

Longitudes

Latit

ude

Climatology (1969-2001) of wind at 200mb for FMAM season

0° 30° E 60° E

30° S

15° S

0°

15° N

30° N

Longitude

Latit

ude

Composite of wind at 200mb based on excess-deficit of zone IV rainfall

0° 30° E 60° E

30° S

15° S

0°

15° N

30° N

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Low-Level

Longitude

Latit

ude

FMAM climatology (1969-2001) of wind at 850mb

30° W 0° 30° E 60° E

30° S

15° S

0°

15° N

30° N

2

4

6

8

10

12

14

Longitude

Latit

ude

Composite of wind at 850mb based on excess-deficit of zone IV rainfall

30° W 0° 30° E 60° E

30° S

15° S

0°

15° N

30° N

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2


Identifying homogeneous rainfall zones

Determining and selecting of predictors

Model development

Skill Assessment


Seasonal Cycle

Feb Apr Jun Aug Oct Dec0

50

100

150

200

250

300

350

Month

Ra

infa

ll(m

m)

Zone I

35 40 45

4

6

8

10

12

14

LongitudeLatitu

de

I


Seasonal Cycle


50

100

150

200

250

300

350

Month

Ra

infa

ll(m

m)

Zone IZone II

35 40 45

4

6

8

10

12

14

LongitudeLatitu

de

I

II


Seasonal Cycle


50

100

150

200

250

300

350

Month

Ra

infa

ll(m

m)

Zone IZone IIZone III

35 40 45

4

6

8

10

12

14

LongitudeLatitu

de

I

IIIII


Seasonal Cycle


50

100

150

200

250

300

350

Month

Ra

infa

ll(m

m)

Zone IZone IIZone IIIZone IV

35 40 45

4

6

8

10

12

14

LongitudeLatitu

de

I

IIIII

IV


Seasonal Cycle


50

100

150

200

250

300

350

Month

Ra

infa

ll(m

m)

Zone IZone IIZone IIIZone IVZone V

35 40 45

4

6

8

10

12

14

LongitudeLatitu

de

I

IIIII

IV

V


Seasonal Cycle


50

100

150

200

250

300

350

Month

Ra

infa

ll(m

m)

Zone IZone IIZone IIIZone IVZone VZone VI

35 40 45

4

6

8

10

12

14

LongitudeLatitu

de

I

IIIII

IV

V

VI


Inter-annual variability (cross-correlation)

Belg Z I Z II Z III Z IV Z V Z VI

Zone I 0.34 0.30 0.15 0.26 0.17 0.10

Zone II 0.30 0.33 0.23 0.24 0.23 0.09

Zone III 0.15 0.23 0.55 0.47 0.48 0.26

Zone IV 0.26 0.24 0.47 0.53 0.42 0.21

Zone V 0.17 0.23 0.48 0.42 0.43 0.27

Zone VI 0.10 0.09 0.26 0.21 0.27 0.25

35 40 45

4

6

8

10

12

14

Longitude

Latit

ude

I

IIIII

IV

V

VI


Inter-annual variability (cross-correlation)

Belg Z I Z II Z III Z IV Z V Z VI

Zone I 0.34 0.30 0.15 0.26 0.17 0.10

Zone II 0.30 0.33 0.23 0.24 0.23 0.09

Zone III 0.15 0.23 0.55 0.47 0.48 0.26

Zone IV 0.26 0.24 0.47 0.53 0.42 0.21

Zone V 0.17 0.23 0.48 0.42 0.43 0.27

Zone VI 0.10 0.09 0.26 0.21 0.27 0.25

35 40 45

4

6

8

10

12

14

Longitude

La

titu

de

I

IIIII

IV

V

VI

⇒

Belg Z I Z II Z III Z IV Z V

Zone I 0.50 0.30 0.10 0.21 0.09

Zone II 0.30 0.36 0.19 0.21 0.11

Zone III 0.10 0.19 0.51 0.44 0.27

Zone IV 0.21 0.21 0.44 0.50 0.26

Zone V 0.09 0.11 0.27 0.26 0.40

35 40 45

4

6

8

10

12

14

Longitude

Latitu

de

I

II III

IV

V




Model development

Skill Assessment


Predictors Identification

Longitude

Latit

ude

Correlation of FMAM Zone V ranfall with October SST

60° E 120° E 180° E 120° W 60° W 0° 90° S

60° S

30° S

0°

30° N

60° N

90° N

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Longitude

Latit

ude

Correlation of FMAM Zone V ranfall with November SST

60° E 120° E 180° E 120° W 60° W 0° 90° S

60° S

30° S

0°

30° N

60° N

90° N

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Longitude

La

titu

de

Correlation of FMAM Zone V ranfall with December SST

60° E 120° E 180° E 120° W 60° W 0° 90° S

60° S

30° S

0°

30° N

60° N

90° N

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Longitude

Latit

ude

Correlation of FMAM Zone V ranfall with January SST

60° E 120° E 180° E 120° W 60° W 0° 90° S

60° S

30° S

0°

30° N

60° N

90° N

-0.6 -0.4 -0.2 0 0.2 0.4 0.6


Selection procedure

Four sets of Predictors (A’, B’,A and B) are createdusing:

A’: stepwise regression and including predictorsfrom contemporaneous season

B’: stepwise discriminant analysis and includingpredictors from contemporaneous season

A : stepwise regression and excluding predictorsfrom contemporaneous season

B : stepwise discriminant analysis and excludingpredictors from contemporaneous season


Selected Predictors

Longitude

Latitu

de

Belg zone I predictors

Feb

Jan

Dec

Aug

Sep

Jul

Jul

Jun

JunMay

Dec

Oct

Dec

60° E 120° E 180° E 120° W 60° W 0° 90° S

60° S

30° S

0°

30° N

60° N

90° N

Longitude

Latitu

de

Belg zone II predictors

MayNov

OctJul

Aug

Sep

Jun

Sep

Aug

Feb

60° E 120° E 180° E 120° W 60° W 0° 90° S

60° S

30° S

0°

30° N

60° N

90° N

Longitude

Latitu

de

Belg zone III predictors

Mar

Mar

Oct

Dec

Jun

Jul

Jun

Jun

Jul

60° E 120° E 180° E 120° W 60° W 0° 90° S

60° S

30° S

0°

30° N

60° N

90° N

Longitude

Latitu

de

Belg zone IV predictors

Dec

Dec

Nov

Jun

Sep Jul

60° E 120° E 180° E 120° W 60° W 0° 90° S

60° S

30° S

0°

30° N

60° N

90° N

Longitude

Latitu

de

Belg zone V predictors

Oct

Oct

Dec

Sep

Aug

Jul

Sep

Sep

60° E 120° E 180° E 120° W 60° W 0° 90° S

60° S

30° S

0°

30° N

60° N

90° N

35 40 45

4

6

8

10

12

14

Longitude

Latitu

de

I

II III

IV

V

Stepwise regression Stepwise discriminant analysis Common to both Including FMAM predictors




Model development

Skill Assessment


Forecasting Models

Multiple Linear Regression (MLR)

Pr(Y|X) ∼ N(Y, var(Y )); Y = βX; var(Y ) = σ2

o [1 + X′(X′X)−1X]

Linear Discriminant Analysis (LDA)

Pr(Wi|X) =Pr(Wi)fi(X)

P

j Pr(Wj)fj(X); ln(fi(X)) = αi1x1+αi2x2+· · ·+αinxn+Γi

Pr(Wi|X) =edi

P

j edj

; where di = αi1x1+αi2x2+· · ·+αinxn+Γi+ln(Pr(Wi))

Y = Rainfall ; X= predictors (SSTA); β = regression parameter

Where αij = S−1

ij xi and Γi = − 1

2xT

i S−1xi

d=discriminant score, Pr(Wi) = apriori probability, W = category, f = density function




Model development

Skill Assessment


Hindcastleaving out 3 years cross-validation

2002

1971

1972

1970

2000

2001

1969

2003

OmitForecastTraining

1973


Skill Assessment-I1. Relative Operational Characteristics (ROC) score

compare with a random forecastFor a skillful forecast→ ROC score (0.5,1]

Dry Normal Wet

Predictors MLR LDA MLR LDA MLR LDA

Set A’ 0.87 0.84 0.69 0.69 0.89 0.85Set B’ 0.86 0.86 0.69 0.74 0.87 0.84Set A 0.87 0.83 0.63 0.64 0.88 0.84Set B 0.83 0.82 0.66 0.72 0.83 0.80

Lower skill in the near Normal categoryHigher ROC score for models with predictors set B(including contemporaneous season)


Skill Assessment -II2. Ranked Probability Skill Score (RPSS)

compare with climatologyFor a skillful forecast→ RPSS(0,1]

RPSS

0.00.2

0.40.6

0.81.0

RPSS for FMAM quint LDA forecast

Zone_I

Zone_II

Zone_IIIZone_IV

Zone_V

Stepwise MLR including FMAMStepwise LDA including FMAMStepwise MLR excluding FMAMStepwise LDA excluding FMAM

RPSS

0.00.2

0.40.6

0.81.0

RPSS for FMAM quint MLR forecast

Zone_I

Zone_II

Zone_IIIZone_IV

Zone_V


RPSS

0.00.2

0.40.6

0.81.0

RPSS for FMAM tercile LDA forecast

Zone_I

Zone_II

Zone_IIIZone_IV

Zone_V


RPSS

0.00.2

0.40.6

0.81.0

RPSS for FMAM tercile MLR forecast

Zone_I

Zone_II

Zone_IIIZone_IV

Zone_V


If we exclude contemporaneous predictors, the highest skillis over Zone V (where spring is the main rainy season)

35 40 45

4

6

8

10

12

14

Longitude

La

titu

de

I

II III

IV

V


Conclusions

Due to high spatial variation forecasting should be done foreach homogeneous rainfall zones separately

Linear approach yield a better skill compared to climatology orrandom forecast

The skill in the outer categories (above normal and belownormal) is better that that of the inner one (near normal)

Models with predictor set A’ and B’ (includingcontemporaneous season) have got higher skill than modelswith predictor set A and B (excluding contemporaneous season)

The skill of the forecast is better for zone V where Spring is themain rainy season.


Future work

Modify the seasonal forecast by using additional atmosphericparameter and compare with the one already done

Carry out idealised SST experiments for different regions ofoceans to understand the mechanisms


Thanks


Seasonal forecasting of Ethiopian spring rains

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