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

CMSAF

Optimal Merging of Water Vapour Retrievals from Different Instruments

Ralf LindauBonn University

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

CMSAF

Data

Merging daily water vapour fields from:

• AMSU and SSM/I over sea only

• ATOVS NOAA-15 NOAA-16

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

CMSAF

Data ExampleNOAA15 NOAA16

Number of observations

• Swath-oriented data is averaged on a 150 km grid (Sinosuidal projection)

• 4 independent observations per day at maximum

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

CMSAF

Kriging Approach

• n observations xi at the locations Pi are given.

• Perform a prediction x0 for the location P0 , where no obs is available.

• Construct the prediction by a weighted average of the observations xi.

• Take into account the observation errors xi.

• Determine the weights i.

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

CMSAF

Kriging Equations

To determine the weight i we need:

• the spatial covariances [ xi xj ]

• the error variance [ xi xi ]

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

CMSAF

Spatial Correlation

Correlation as a function of distance

Fitting of:

r = exp (a0 + a1x)

Handy characteristics:Correlation length: 645 kmordinate intercept: 0.969

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

CMSAF

Error of daily meansAMSU

SSM/I

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

CMSAF

Ready to run

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

CMSAF

TPW on 4th April 2004

Anomaly on 4.AprilMean and Stddev. in April

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

CMSAF

Raw Data / Results

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

CMSAF

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

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

CMSAF

Error Covariance

D = ((x1 + x1) – (x2 + x2))2

D = 2 Var – 2 Cov + Err1 + Err2 - 2 ErrCov

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

CMSAF

Error Covariance

D = ((x1 + x1) – (x2 + x2))2

S = (x1 + x1)2 + (x2 + x2)2

D = 2 Var – 2 Cov + Err1 + Err2 - 2 ErrCov

S = 2 Var + Err1 + Err2

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

CMSAF

Error Covariance

D = ((x1 + x1) – (x2 + x2))2

S = (x1 + x1)2 + (x2 + x2)2

D = 2 Var – 2 Cov + Err1 + Err2 - 2 ErrCov

S = 2 Var + Err1 + Err2

S – D = 2 Cov + 2 ErrCov

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

CMSAF

TPW anomaly on 4th April