Assimilation of Satellite Altimetry in Ocean Models
127
ple, be large changes in surface heat flux associated with the altered frontal paths
shown in Fig. 7.6e,f, although we have not yet diagnosed these from the run.
(ii) Sea level Tendency and error analysis
There is little point in using a model for data assimilation if that model is unable
to interpolate data correctly in time over some period. To test this ability Fig. 7.7a
shows the observed sea level change over the Atlantic during the 20 days from 30th
January 1993 to 19th February 1993. This is simply the difference between the
TOPEX maps from AVISO (without accounting for errors in the maps). Twenty
days is the shortest period for which the maps contain entirely independent satellite
data. Fig. 7.7b shows a model prediction ofthe same quantity (sea level change)
based on assimilating data up to 30th January and thereafter allowing the model to
run free for 20 days. If we compare Figs. 7a,b we tind many features in common.
Similar tigures could be shown from any time during the assimilation run and also
from most regions ofthe globe, even away from the Tropics. It is possible to detine
more quantitative comparison methods. The rms difference between the model predicted height anomaly and the observed TOPEX map on 19th February 1993 was 8
cm while the difference between the 30th January and 19th February TOPEX maps
was 10 cm. The anomaly correlations for the above comparisons give 0.8 for the
model prediction and 0.6 for the persistence tield. Thus the model forecast can beat
sea level persistence over 20 day periods.
The updating of model sea level was carried out as follows;
a 2
11a = 11f+ ~(11T-11f)'
(3)
a f + a T
where aT is the current TOPEX error map, afis the model forecast error, 11T is the
current TOPEX sea level anomaly and 11.r is the model forecast sea level anomaly
and 11a is the analysis sea level. Other tields are calculated from this update using
the Cooper and Haines (1996) method. The model-data mistit, M, at analysis time
is calculated as;
M = L -\(11T-11f,a)2
a T
(4)
where 11f,a may be the forecast or the analysed model sea level, and the sum represents an area weighted average. Fig. 7.8a shows M through the 1993 run.
In the tirst few timesteps M is greatly reduced but thereafter the growth in M
every 10 days is approximately equal to the reduction in M when new data is
assimilated. The current af is being set equal to the global mean of aT which is
very crude and does not allow for a reduction in af which would be necessary for
convergence. An important future step will be to improve this error treatment.
Finally Fig. 7.8b shows the kinetic energy during the assimilation run. The
assimilation is seen to increase the kinetic energy over the tirst 2 months but this
127
ple, be large changes in surface heat flux associated with the altered frontal paths
shown in Fig. 7.6e,f, although we have not yet diagnosed these from the run.
(ii) Sea level Tendency and error analysis
There is little point in using a model for data assimilation if that model is unable
to interpolate data correctly in time over some period. To test this ability Fig. 7.7a
shows the observed sea level change over the Atlantic during the 20 days from 30th
January 1993 to 19th February 1993. This is simply the difference between the
TOPEX maps from AVISO (without accounting for errors in the maps). Twenty
days is the shortest period for which the maps contain entirely independent satellite
data. Fig. 7.7b shows a model prediction ofthe same quantity (sea level change)
based on assimilating data up to 30th January and thereafter allowing the model to
run free for 20 days. If we compare Figs. 7a,b we tind many features in common.
Similar tigures could be shown from any time during the assimilation run and also
from most regions ofthe globe, even away from the Tropics. It is possible to detine
more quantitative comparison methods. The rms difference between the model predicted height anomaly and the observed TOPEX map on 19th February 1993 was 8
cm while the difference between the 30th January and 19th February TOPEX maps
was 10 cm. The anomaly correlations for the above comparisons give 0.8 for the
model prediction and 0.6 for the persistence tield. Thus the model forecast can beat
sea level persistence over 20 day periods.
The updating of model sea level was carried out as follows;
a 2
11a = 11f+ ~(11T-11f)'
(3)
a f + a T
where aT is the current TOPEX error map, afis the model forecast error, 11T is the
current TOPEX sea level anomaly and 11.r is the model forecast sea level anomaly
and 11a is the analysis sea level. Other tields are calculated from this update using
the Cooper and Haines (1996) method. The model-data mistit, M, at analysis time
is calculated as;
M = L -\(11T-11f,a)2
a T
(4)
where 11f,a may be the forecast or the analysed model sea level, and the sum represents an area weighted average. Fig. 7.8a shows M through the 1993 run.
In the tirst few timesteps M is greatly reduced but thereafter the growth in M
every 10 days is approximately equal to the reduction in M when new data is
assimilated. The current af is being set equal to the global mean of aT which is
very crude and does not allow for a reduction in af which would be necessary for
convergence. An important future step will be to improve this error treatment.
Finally Fig. 7.8b shows the kinetic energy during the assimilation run. The
assimilation is seen to increase the kinetic energy over the tirst 2 months but this