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