Predicting indices of climate extremes using eigenvectors of

SST and MSLP

Malcolm Haylock, CRU

Predictands

• 601R Mean climatological precipitation (mm/day)

• precXXp XXth percentile of rainday amounts (mm/day)

• fracXXp Fraction of total precipitation above annual XXth percentile

• 606R10 No. of days precip >= 10mm

• 641CDD Max no. consecutive dry days

• 642CWD Max no. consecutive wet days

• pww Mean wet-day persistence

• persist_dd Mean dry-day persistence

• persist_corr Correlation for spell lengths

• wet_spell_mean mean wet spell lengths (days)

• wet_spell_perc median wet spell lengths (days)

• wet_spell_sd standard deviation wet spell lengths (days)

• dry_spell_mean mean dry spell lengths (days)

• dry_spell_perc median dry spell lengths (days)

• dry_spell_sd standard deviation dry spell lengths (days)

• 643R3d Greatest 3-day total rainfall

• 644R5d Greatest 5-day total rainfall

• 645R10d Greatest 10-day total rainfall

• 646SDII Simple Daily Intensity (rain per rainday)

• 691R90N No. of events > long-term 90th percentile

• 692R90T % of total rainfall from events > long-term 90th percentile

33 rainfall indices calculated seasonally for 27 stations in SE England

Predictors• Eigenvectors of Nth Atlantic SST and

MSLP

• Calculated using all months together with seasonal cycle removed

• Significant components rotated (VARIMAX) 9 SST 9 MSLP

1960 1970 1980 1990 2000 2010

-3

-2

-1

0

1

2

3

4

SST Scores PC: 1

1960 1970 1980 1990 2000 2010

-6

-4

-2

0

2

4

6

SST Scores PC: 2

1960 1970 1980 1990 2000 2010

-4

-3

-2

-1

0

1

2

3

SST Scores PC: 3

1960 1970 1980 1990 2000 2010

-4

-3

-2

-1

0

1

2

3

4

SST Scores PC: 1

1960 1970 1980 1990 2000 2010

-4

-3

-2

-1

0

1

2

3

4

SST Scores PC: 2

1960 1970 1980 1990 2000 2010

-4

-3

-2

-1

0

1

2

3

4

SST Scores PC: 3

The Model• 1960-2000

• Multiple linear regression using singular value decomposition

• Best predictors selected using cross-validation For each combination of predictors (2n):

• Remove a year

• Find MLR coefficients

• Hindcast missing year

• Assess skill using all hindcasts

Skill of model

• Build model using all years except 1979-93 then hindcast these years and compare

• Double cross-validation For each year in 1960-2000:

• Remove a year

• Use cross-validation to find best model

• Hindcast missing year

• Assess skill using all hindcasts

LEPS - Linear Error in Probability Space

0

0.25

0.5

0.75

1

Predictand

Cu

mu

lati

ve F

req

ue

ncy

Obs. Forecast

abs(pf - pv) LEPS=1- abs(pf - pv)1 is perfect forecast0 is worst possible forecast

pf

pv

…LEPS• For single forecast

LEPS' = LEPS - LEPS(climatology)= abs(pv - 0.5) - abs(pf - pv)

• For set of forecasts

pS

LEPSLEPS

'

'%

pSS ',0' If = LEPS'(perfect forecast)

pSS ',0' If = LEPS'(worst case)

100 = all perfect forecasts 0 = all climatology-100 = all worst case forecasts

-100 -80 -60 -40 -20 0 20 40 60 80 100

-100

-80

-60

-40

-20

0

20

40

60

80

100

LEPS(hindcast)

LEP

S(d

x-va

l)

LEPS(hindcast) vs LEPS(dx-val) SST onlySST only. LEPS(hindcast) vs LEPS(dx-val)

-100 -80 -60 -40 -20 0 20 40 60 80 100

-100

-80

-60

-40

-20

0

20

40

60

80

100

MSLP

SS

T

Hindcast LEPS(MSLP) vs LEPS(SST)Hindcast LEPS(MSLP) vs LEPS(SST)

Where to...

• NW England

• Other European stations

• Combined SST and MSLP (trim predictors)

• Other predictors?