326 Martin Fischer
sea surf ace height data directly into the model. This would affect the barotropic
mode only, and the information would be lost within a few time steps. Sea surf ace
elevation is an integral quantity that contains information about the vertical density
structure. To assimilate SSH observations, the information contained in the data
must be transformed into a correction of the mass field. Different methods have
been developed to solve this problem (Mellor and Ezer 1991, Cooper and Haines
1996). In the following the method of (Fischer et al. 1997) is presented.
For the tropics, a linear relation between small changes in sea level and the corresponding changes in the vertical mass structure is a reasonable assumption. Further, salinity variations can be neglected, which yields a linear relation between
small changes in the vertical temperature stratification and sea level. This relationship can be estimated from a long ocean model integration (here 10 years) using a
linear regression method. For each horizontal grid point, an EOF analysis (compare
appendix 1) of the anomalous vertical temperature profile was performed. Five
EOFs were retained, explaining about 95% of the local variance in most of the
model domain. Regression coefficients An between SSH anomalies and the principal components 1 of the EOFs G n(z) were computed and stored separately for every
horizontal grid point. To insert the sea level observations into the model, first a correction field for the sea surface height anomalies A~' was computed. The principal
components of the EOF expansion of the vertical temperature corrections are
obtained by multiplying the sea level corrections by the An (eq. 6). To obtain the
desired temperature correction field, the principal components must be inserted
into the EOF expansion ofthe anomalous temperature profile (eq. 7):
(6)
5
(AT'(Z))j = L (1)j· (G(z)n)j
(7)
n = 1
The index i denotes the actual horizontal model grid point. Finally, the temperature corrections were added to the original model solution, and a convective adjustment routine was applied to avoid unstable stratifications. Thus, the surf ace height
correction was transformed into a correction ofthe vertical temperature structure.
The extension of this method to include salinity is straight forward. Then for
each grid point a combined EOF analysis of (T,S) has to be performed.
16.4.2 Results of ENSO prediction experiments
In this section prediction results obtained with different models and with different initialization methods are presented and compared to each other. In Fig.16.12
The forecast skill obtained from two statistical models is compared with the persistence of a slightly smoothed Southem Oscillation Index (SOI). Both statistic al
models use the time history of one year of sea level pressure anomalies as predictors. The POP model (thick line) is based on monthly predictions ofthe southem
sea surf ace height data directly into the model. This would affect the barotropic
mode only, and the information would be lost within a few time steps. Sea surf ace
elevation is an integral quantity that contains information about the vertical density
structure. To assimilate SSH observations, the information contained in the data
must be transformed into a correction of the mass field. Different methods have
been developed to solve this problem (Mellor and Ezer 1991, Cooper and Haines
1996). In the following the method of (Fischer et al. 1997) is presented.
For the tropics, a linear relation between small changes in sea level and the corresponding changes in the vertical mass structure is a reasonable assumption. Further, salinity variations can be neglected, which yields a linear relation between
small changes in the vertical temperature stratification and sea level. This relationship can be estimated from a long ocean model integration (here 10 years) using a
linear regression method. For each horizontal grid point, an EOF analysis (compare
appendix 1) of the anomalous vertical temperature profile was performed. Five
EOFs were retained, explaining about 95% of the local variance in most of the
model domain. Regression coefficients An between SSH anomalies and the principal components 1 of the EOFs G n(z) were computed and stored separately for every
horizontal grid point. To insert the sea level observations into the model, first a correction field for the sea surface height anomalies A~' was computed. The principal
components of the EOF expansion of the vertical temperature corrections are
obtained by multiplying the sea level corrections by the An (eq. 6). To obtain the
desired temperature correction field, the principal components must be inserted
into the EOF expansion ofthe anomalous temperature profile (eq. 7):
(6)
5
(AT'(Z))j = L (1)j· (G(z)n)j
(7)
n = 1
The index i denotes the actual horizontal model grid point. Finally, the temperature corrections were added to the original model solution, and a convective adjustment routine was applied to avoid unstable stratifications. Thus, the surf ace height
correction was transformed into a correction ofthe vertical temperature structure.
The extension of this method to include salinity is straight forward. Then for
each grid point a combined EOF analysis of (T,S) has to be performed.
16.4.2 Results of ENSO prediction experiments
In this section prediction results obtained with different models and with different initialization methods are presented and compared to each other. In Fig.16.12
The forecast skill obtained from two statistical models is compared with the persistence of a slightly smoothed Southem Oscillation Index (SOI). Both statistic al
models use the time history of one year of sea level pressure anomalies as predictors. The POP model (thick line) is based on monthly predictions ofthe southem