CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Optimal Merging of Water Vapour Retrievals from Different Instruments Ralf Lindau Bonn University

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Data  Merging daily water vapour fields from: AMSU and SSM/I over sea only ATOVS  NOAA-15  NOAA-16

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Data Example NOAA15 NOAA16 Number of observations Swath-oriented data is averaged on a 150 km grid (Sinosuidal projection) 4 independent observations per day at maximum

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Kriging Approach n observations x i at the locations P i are given. Perform a prediction x 0 for the location P 0, where no obs is available. Construct the prediction by a weighted average of the observations x i. Take into account the observation errors  x i. Determine the weights i.

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Kriging Equations To determine the weight i we need: the spatial covariances [ x i x j ] the error variance [  x i  x i ]

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Spatial Correlation Correlation as a function of distance Fitting of: r = exp (a 0 + a 1 x) Handy characteristics: Correlation length: 645 km ordinate intercept: 0.969

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Error of daily means AMSU SSM/I

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Ready to run

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 TPW on 4 th April 2004 Anomaly on 4.April Mean and Stddev. in April

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Raw Data / Results

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Conclusion  Daily fields of Total Water Vapour: ATOVS Spatial correlation function Error of daily grid averages  For each TPW field an error field is provided

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Error Covariance D = ((x 1 +  x 1 ) – (x 2 +  x 2 )) 2 D = 2 Var – 2 Cov + Err1 + Err2 - 2 ErrCov

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Error Covariance D = ((x 1 +  x 1 ) – (x 2 +  x 2 )) 2 S = (x 1 +  x 1 ) 2 + (x 2 +  x 2 ) 2 D = 2 Var – 2 Cov + Err1 + Err2 - 2 ErrCov S = 2 Var + Err1 + Err2

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 Error Covariance D = ((x 1 +  x 1 ) – (x 2 +  x 2 )) 2 S = (x 1 +  x 1 ) 2 + (x 2 +  x 2 ) 2 D = 2 Var – 2 Cov + Err1 + Err2 - 2 ErrCov S = 2 Var + Err1 + Err2 S – D = 2 Cov + 2 ErrCov

CMSAF 2 nd CMSAF U&T Workshop – Nürnberg, 30. August 2005 TPW anomaly on 4 th April