CARPE DIEM 5TH PROJECT MEETING DECEMBER 15-16 DUBLIN

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CARPE DIEM 5TH PROJECT MEETING DECEMBER 15-16
DUBLIN

• WP 4 Assessment of Nwp Model Uncertainty
  Including Models Errors
• Dott.ssa Riccardo Sara

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Carpe Diem 5th Project Meeting December 15-16
Dublin
ESTIMATION OF COVARIANCE PARAMETERS
Maximum likelihood approach suggested by Dee for
Hirlam data assimilation 1 Dee, D.P., 1991
Simplification of the Kalman filter for
meteorological data assimilation, Q.J.R.
Meteorol. Soc. 117,365-384. 2 Dee, D.P., 1995
On-line estimation of error covariance parameters
for atmospheric data assimilation, Mon. Wea. Rev.
123,1128-1145. 3 Todini, Ferraresi, 1996
Influence of parameter estimation uncertainty in
Kriging, J. Hydrol.175,555-566. 4 Todini, 2001
Influence of parameter estimation uncertainty in
Kriging. Part1 and Part2, Hydrol. Earth System
Sci. 5, 215-232.
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Carpe Diem 5th Project Meeting December 15-16
Dublin
DEFINITIONS AND MODELLING ERRORS
Errors must be unbiased and gaussian Observation
and backround errors are mutually uncorrelated
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Carpe Diem 5th Project Meeting December 15-16
Dublin
ALGORITHM
KRIGING TECNIQUE
MAXIMUM LIKEHOOD ESTIMATION
Estimation of innovation and background errors
covariances
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Carpe Diem 5th Project Meeting December 15-16
Dublin
ALGORITHM OF KRIGING METHOD
We have a set of innovation vector z
l interpolating weights
s2 variance of innovation
g variogram could be esponential, gaussian or
more and it is function of distance h between
measures
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Carpe Diem 5th Project Meeting December 15-16
Dublin
MAXIMUM LIKELIHOOD METHOD
In observation space we estimate covariance
innovation with a covariogram based on the
esponential variogram
Parameters p, w, a are estimated with ML tecnique
find the minimum of the gaussiam pdf or maximum
of the logaritmic function
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Carpe Diem 5th Project Meeting December 15-16
Dublin
MAXIMUM LIKELIHOOD METHOD
Parameters p, w, a are estimated with ML tecnique
find the minimum of the gaussiam pdf or maximum
of the logaritmic function
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Carpe Diem 5th Project Meeting December 15-16
Dublin
APPLICATIONS
Meteorological data was provided from HIRVDA
3D-var data assimilation process of HIRLAM (SMHI).

• For the entire calculation domain for each time
  step of analysis we use the following information
  of observations variables
• coordinates points si(x,y)
• innovation vector
• observations errors

Dimension domain is 202x178 grid-points Horizontal
resolution is roughly 44 km 
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Carpe Diem 5th Project Meeting December 15-16
Dublin
EXAMPLE OF APPLICATION
March 8, 2003 1 GMT
Temperature
Innovation covariance
Background error covariance
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Carpe Diem 5th Project Meeting 15-16 December
Dublin
EXAMPLE OF APPLICATION
v component wind velocity
Innovation covariance
Background error covariance
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Carpe Diem 5th Project Meeting 15-16 December
Dublin
CONCLUSIONS

• Set algorithm ML to estimate covariance
  parameters
• Application for some types of observations (es.
  wind and temperature)

FUTURE

• Application for other observations innovation
• Use algorithm for each time step analysis
• Application of covariance information in kalman
  filter