The diurnal cycle in GERB data

• The diurnal cycle represents one of the most significant modes of atmospheric forcing

• OLR provides information about surface heating response and cloud variation

• Diurnal variation of OLR is greatest over the Sahara, making GERB an ideal data source

Ruth Comer, Tony Slingo & Richard Allan

Environmental Systems Science CentreUniversity of Reading

GIST 23 27th-29th April DWD, Germany

Background

This type of diurnal cycle study has a long history. Recent publications include:

• G Yang & J Slingo 2000– Fourier analysis in CLAUS Data

• L Smith & D Rutan 2002– EOF analysis in ERBS Data

• B Tian, B Soden & X Wu 2004– Time series and Fourier analysis comparing Satellite

observations with GCM

Processing

• One Month of GERB OLR Barg data from July 2004

• Simple time series mean plots and histograms• Average Month onto single day

– Mean plots/histograms

– EOF Analysis

– Fourier Analysis

What is EOF analysis?

• Method for looking at time- and space-dependent variables

• Finds an orthonormal basis to efficiently describe the variation in a data set

• Empirical Orthogonal Functions (EOFs)– Describe variation of data over area

• Principle Components (PCs)– Describe variation of data with time

x

y

i

j

The maths bit

EOF analysis finds a vector a such that the variance of c=Xa is maximised

(Each entry in a corresponds to a location in our physical domain

Each entry in c corresponds to a time-step)

NPNpN2N1

nPnpn2n1

2P2p2221

1P1p1211

xxxx

xxxx

xxxx

xxxx

X

space

time

Consider the data in matrix form with the overall mean at each location removed

What does this mean?

Np

np

2p

1p

NPNpN2N1

nPnpn2n1

2P2p2221

1P1p1211

x

x

x

x

0

0

1

0

0

xxxx

xxxx

xxxx

xxxx

aXc

To illustrate, suppose we choose corresponding to a single point in the domainThen

T01000a

Gives a mean diurnal cycle at that point. But we want to represent the whole domain

What does this mean?

N

n

2

1

P1

P1

P1

P1

NPNpN2N1

nPnpn2n1

2P2p2221

1P1p1211

x

x

x

x

xxxx

xxxx

xxxx

xxxx

aXc

We could represent each location equally i.e.Then

P1

P1

P1

a

Mean diurnal cycle over the whole domain

The first EOF is a with more weighting given to locations with more variation…

What does this mean?

PC1= c

To understand the variation of the data set we want to give c maximum variance

EOF1= a

We do this by giving greater weighting to the areas that vary the most

First EOF & PCPC1 describes 83.1% of the total variance

• Strong signal over deserts suggests surface heating response

• Note some small negative signals around African coast

Contribution from PC1

Comparison of PC1 with Sahara mean

EOFs/PCs do not necessarily describe physical modes in the data, however

Contribution from PC1

Mean curve

Subsequent EOFsTo find the second EOF and PC we remove the contribution of the first from our data and repeat the process. i.e.

pnpnnextpn

Tnext

acxx

acXX

(xpn is data point at location p, time-step n)

The number of EOFs required to describe the entire variation of the data is less than or equal to the number of time-steps (cf Fourier analysis)

We can reconstruct the original data from the EOFs: TacX

Second EOF & PC

PC2 describes 9.6% of the total varianceHence first 2 PCs describe 92.7%

Provides modification to PC1 for cloud

StratusConvective cloud

Contribution from PC2Contribution from PC2

Mean curve

Southern Atlantic

Topography visible in second EOFAtlas Mountains

Ethiopianhighlands

Hoggar

Tibesti

MarraPlateau

Mean curve

Central Africa

Mean curveContribution from PC1Mean curveContribution from PC1Combined contributions from PCs 1&2

TRMM shows

maximum precip here (Nesbitt &

Zipser 2002)

Clear sky

Cloudy

Contributionfrom PC1Contributionfrom first 2 PCs

Gulf of Guinea

Mean curve

Contributionfrom first 3 PCs

EOF3

PC3

Gulf of Guinea

Debois et al (1988) suggest diurnal cycle of cloud here is

forced by land-sea breeze effects

Local Times of minimum

0

2

4

6

8

1 4 7 10 13 16 19 22

Hour

freq

uen

cy

0 6 12 18 24

Conclusions

• EOF Analysis on GERB OLR data appears to pick up surface heating and cloud responses well (with certain exceptions)

• PC1 describes surface response to heating• PC2 describes cloud development

– Convective

– Stratus

– Shows significance of topography

Future Work

• Comparison of GERB with other data– TRMM

– RADAGAST

• Investigation of models– Met Office NWP model

– HiGEM

– Cloud resolving models