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The diurnal cycle in GERB data

GIST 23 27 th -29 th April DWD, Germany. 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

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The diurnal cycle in GERB data

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  1. GIST 23 27th-29th April DWD, Germany 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

  2. 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

  3. 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

  4. y j i x 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

  5. space time The maths bit Consider the data in matrix form with the overall mean at each location removed 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)

  6. What does this mean? To illustrate, suppose we choose corresponding to a single point in the domain Then Gives a mean diurnal cycle at that point. But we want to represent the whole domain

  7. What does this mean? We could represent each location equally i.e. Then Mean diurnal cycle over the whole domain The first EOF is a with more weighting given to locations with more variation…

  8. We do this by giving greater weighting to the areas that vary the most EOF1= a What does this mean? PC1= c To understand the variation of the data set we want to give c maximum variance

  9. First EOF & PC PC1 describes 83.1% of the total variance • Strong signal over deserts suggests surface heating response • Note some small negative signals around African coast

  10. Contribution from PC1 Contribution from PC1 Mean curve Comparison of PC1 with Sahara mean EOFs/PCs do not necessarily describe physical modes in the data, however

  11. Subsequent EOFs To find the second EOF and PC we remove the contribution of the first from our data and repeat the process. i.e. (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:

  12. Convective cloud Stratus Second EOF & PC PC2 describes 9.6% of the total variance Hence first 2 PCs describe 92.7% Provides modification to PC1 for cloud

  13. Contribution from PC2 Contribution from PC2 Mean curve Southern Atlantic

  14. Atlas Mountains Hoggar Tibesti Marra Plateau Ethiopian highlands Topography visible in second EOF

  15. Cloudy Mean curve Mean curve Mean curve Contribution from PC1 Contribution from PC1 Combined contributions from PCs 1&2 TRMM shows maximum precip here (Nesbitt & Zipser 2002) Clear sky Central Africa

  16. Mean curve Contribution from PC1 Contribution from first 2 PCs Contribution from first 3 PCs EOF3 PC3 Gulf of Guinea

  17. 0 6 12 18 24 Gulf of Guinea Debois et al (1988) suggest diurnal cycle of cloud here is forced by land-sea breeze effects

  18. 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

  19. Future Work • Comparison of GERB with other data • TRMM • RADAGAST • Investigation of models • Met Office NWP model • HiGEM • Cloud resolving models

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