A Method for Correlated Noise Modeling in Satellite

Radiance Simulation

 

Thomas J. Kleespies

David Crosby

NOAA/NESDIS

Thomas.J.Kleespies@noaa.gov

 

1.      Introduction

 

This work is motivated by an Observing Systems Simulation Experiment in which NESDIS is collaborating with NCEP/EMC and the NASA Data Assimilation Office.  The immediate goal is to determine the incremental improvement on the forecast of a Doppler Wind Lidar instrument over present day observing systems.  In order for the current satellite instruments to be accurately simulated, it is necessary to model instrument noise, both independent and correlated.  This paper presents such a method, and notes a high level of correlation in the inter channel noise in one of the High Resolution Infrared Sounder (HIRS) instruments.

 

2.      Methodology

 

A number of standard methods of modeling correlated noise are available.  We chose one such method presented in Searle (1982).  Let S be the sample covariance matrix from the measured noise, then the vector of simulated correlated noise is given by

 

                                                                                     1)

 

where

G is the eigenvectors of S

is a matrix whose diagonal is composed of the square root of the eigenvalues of S

X is a vector of gaussian random numbers with mean =0.0, variance=1.0

 

The sample of the measured noise is from HIRS space calibration observations for an entire day.  An example of inter channel noise for NOAA 11 is given in figure 1.  The gaussian random numbers are computed by (Box and Muller, 1958),

 

                                                                    2)

 

where U1 and U2 are numbers drawn from a uniform random distribution.  We used the FORTRAN RAN function for this purpose.  This approach was applied to a realization of size 100,000 and the inter channel correlation coefficients were computed.  Results for selected channel pairs are presented in Table 1.

 

 

 

 

 

 

 

 

 

Figure 1. HIRS 11 Space calibration radiances, Ch 10 vs Ch 15, n=16032, r=.492

units are mw /(cm2 sr cm-1)

 

 

 

 

Table 1.  Correlation coefficient for selected channels of NOAA 11 HIRS observed and simulated space calibration observations.

3.      Conclusions

 

We have presented a method for simulating correlated noise and applied it to radiances from the NOAA 11 HIRS instruments.  This method accurately reproduces the observed correlation structure.  The NOAA 11 HIRS exhibits inter channel noise correlations that approach 0.5 .  This fact has implications for the use of off diagonal elements in the observational error covariance matrix used in variational data assimilation.

 

4.   References

 

Box, G. E. P. and M. E. Muller, 1958: A note on the generation of random normal deviates. Annals of Mathematical Statistics, 29, pp 610-611.

 

Searle, S. R., 1982: Matrix Algebra Useful for Statistics, Ch. 13, Wiley&Sons.