Dear Mercatorians,
The effects of this 7th stage of the quarterly newsletter
will make themselves felt. It begins with a first category
article in which assimilation climbers will be able to
express their talents in fairly steep transitions. The quiz
which follows is a deceptive flat stretch which should
suit observation rollers. Participants will probably bunch
up again before the final sprint of this stage which is
almost entirely devoted to satellite alitmetry.
1. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 1
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
The riddle
By Eric Greiner (5-7-2002)
Introduction
In 2001 (30 May and 6 June) the operational PSY1-v1 system team detected an anomaly in the level of the sea
analysed to the south of the Gulf of Guinea, near Ascension island. It appeared to be an isolated case to the
extent that the 1993-99 reanalysis did not reveal any such malfunction. However, in 2002 the phenomenon
occurred again in a spectacular way successively on the 1, 8, 15 and 22 May. Fishermen using MERCATOR
products and CATSAT products (maps showing sea level, surface temperature and chlorophyl content) also
observed the anomaly: in May 2002, the sea level analysed on day D and forecast for D+7 and D+14 was
systematically too high in the Gulf of Guinea when compared to satellite altimetery observations (Topex-Poseidon
and ERS-2). An explanation is therefore called for. Is there a problem with the projected atmospheric forcing? If
this were the case, how would this affect the analysis on day D? And would it not also affect the later analyses
(D+7 or D+14)? This is the riddle we shall now attempt to solve.
Initial observations
The rest of the discussion will deal with the analysis date of 8 May 2002, on which the most spectacular anomaly
was detected. It may be seen that the anomalies on the 1, 15 and 22 May are similar to those of 8 May, with a
few slight differences.
Editorial Contents
Dear Mercatorians,
The effects of this 7th stage of the quarterly newsletter
will make themselves felt. It begins with a first category
article in which assimilation climbers will be able to
express their talents in fairly steep transitions. The quiz
which follows is a deceptive flat stretch which should
suit observation rollers. Participants will probably bunch
up again before the final sprint of this stage which is
almost entirely devoted to satellite alitmetry.
The riddle
Introduction
Initial observations
A clue
Following the tracks
The gigantic stroboscope
What about the model's instability?
How did the anomaly affect the forecast?
What should be done?
A few lessons to be learnt
Quizz
A posteriori validation of hypotheses: correlation
radii
Notebook
2. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 2
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
The riddle (continued)
Our investigation begins with the abnormally high sea level in the Gulf of Guinea (figure 1). The figures are taken
from the 'assimilation technical report' which was published in real time with the ocean bulletin on 8 May.
We can see that the sea level analysed for day D is particularly high for the whole of the Gulf of Guinea and even
further to the south and west.
The predicted sea level at D+7 is lower, but is still abnormally high when compared to satellite observations.
The predicted sea level at D+7 is once again similar to observations in the Gulf of Guinea.
The anomaly sequence may thus be summed up as a rising of the Gulf of Guinea during the day D analysis
followed by a gradual return to normal at D+7 and D+14. This adjustment to the shock caused by the
analysis on 8 May 2002 was done at the expense of various ocean processes such as the coastal Kelvin wave
from the Ivory Coast to Morocco (shown in red in figure 1).
Figure 1: analysed sea level (on left), predicted at D+7 (middle) and predicted at D+14 (right)
3. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 3
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
The riddle (continued)
A clue
We will attempt to clarify what was happening during the 8 May analysis by looking closer at the sea level time
series at different places in the Gulf of Guinea (moorings 18, 19 and 22 of PSY1-v1). For the mooring at 8°W we
can see that the guess marked 'E' (forecast for day D or 'guess') has a value of about +5 cm. The analysis gives a
level of +15cm, which means an analysis jump of +10cm. The following forecast, as we have seen on the maps,
shows a drop in level up to 22 May. It may be observed as well that the forecast is consistently higher (we could
say 'warmer' to give a more vivid picture) than the hindcast from 1 May to 29 May. In short, the forecast is too
warm in May 2002. In 2001, this phenomenon only lasted 2 weeks.
When compared with the maps, it is clearer that the
forecast does not exactly 'match' the hindcast. In other
words, the analysis jump on day D not only introduced
a bias (shift) in the forecast but also affected the
dynamics. More precisely, the drops in level are less
significant in the forecast than in the hindcast,
which is true for all 3 moorings. There is thus a ripple
effect of the analysis on the forecast. This will be
discussed later.
What we especially have to note for the moment is the
difference between the analysis on day D and that,
deferred for day D+7. Thus, while the analysis jump on
day D for 8 May was +10cm, the hindcast jump (done
on D+7) for 8 May was nil. In other words, the real-
time analysis 'jumps' and the hindcast does not.
In fact the hindcast is continuous, as if it were perfect
or knew nothing of the observations. The problem
therefore is to find out what difference there is
between the real-time and the hindcasts.
Figure 2:
time series of sea level at 3 mooring points: 8°W-0°N
(18, top), 6.2°E-0.2°N (19, Sao Tomé, middle) and
14.3°W-7.6°S (22, Ascension island, bottom). The
unbroken curve shows the period preceding the
analysis (deferred time or 'hindcast' analysis) and the
dotted curve the forecast. The vertical lines show the
analysis dates. The colours correspond to the different
dates (dark blue for 17-4, blue-green (cyan) for 24-4,
aquamarine for 1-5).
4. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 4
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
The riddle (continued)
Following the tracks
The difference is in the amount of observations. For the week preceeding dat D (figure 3, on left), we only have
observations up to D-3 (which is what we call the 'cutoff' date): the data acquisition has to be cut off to start the
analysis). Analysis one week later is called a hindcast, and all satellite altimetry observations are fed into the
acquisition system. In passing we can see why analysis for day D is trickier than for D+7 as there are many more
gaps between the tracks. But how do these gaps throw the system off?
Figure 3: sea level: observations from D-7 to day D (8 May 2002)
in real time (on left) and hindcast (on right)
The gigantic stroboscope
The trick in fact is that the problem is not caused by spatial gaps, but by the time interval between tracks. To
understand this point, you have to look at the difference between the observations and the model (innovation or
misfit) in figure 4. In real time, from D-7 to D-3 (i.e. from 1 May to 5 May), the observations are almost all higher
than the model (shown in red, figure 4 on left). There is not much inconsistent information such as the two
neighbouring tracks around 15°W. In deferred time, from D-7 to D (from 1 May to 8 May), there are now as
many lower observations as for the model. In other words, the information for the periods [D-7 , D-3] and [D-3,
D] is the opposite. We may note in passing that the same phenomenon occurs around 40°W-15°N.
Figure 4: sea level: difference between observations minus model from D-7 to day D (8 May 2002)
in real time (on left) and hindcasting (on right)
5. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 5
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
The riddle (continued)
A synthesis of the anomaly is shown in figure 5. With a 7 day cycle and a cutoff of 3, with an oscillatory
phenomenon with a 7 day frequence, only half of the phenomenon can be observed in real time. For the analysis
tool , the model gives readings which are obviously much lower than the observations and it thus has to be 'lifted'
during analysis. The analysis jump is in itself a big one. It is quite natural even and is only wrong to the extent
that the phenomenon's frequency is slightly higher than the cutoff. During hindcasting, we can observe the low
and the high phases of the phenomenon at the same time, and the analysis tool does not, therefore, lift the
model, since, on average, the model's pseudo observations fall in the middle of the actual observations. There is
no analysis jump.
Figure 5: difference in observations between real time model (on left) and hindcast model (on right):
the 3 day cutoff creates aliasing for a phenomenon with a 7 day frequency.
We can finish the analysis of this anomaly by noting
that this type of malfunction can only occur in real time
and only for a narrow range of frequencies. Hence
figure 6 shows that the 3 day cutoff only creates
significant aliasing for frequencies from between 5 and
12 days.
Figure 6:
difference in observations - real time model: impact of
3 day cutoff on phenomenon with different frequencies.
6. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 6
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
The riddle (continued)
What about the model's instability?
LThe winds from the European Centre for medium range weather forecasting (ECMWF), which were used to force
the ocean model, revealed a clear change between the end of April and the beginning of May. Around 20 April,
the tradewinds were strong in the north (around 40°-50°W and 4°-14°N) and weak in the south, with a calm
zone on the equator and in the Gulf of Guinea.
Figure 7: Zonal wind stress from the European Centre
In less than two weeks, we witnessed a shift in strength of the tradewinds from north to south. During this shift,
a small scale wave can be seen on the equator (figure 7) to the west around 23 April and then the east around 26
April. By the beginning of May the shift had been completed, with strong tradewinds in the south.
Figure 8: Zonal wind stress from the European Centre at 1°30'N from west to east on 23 April and 5 May
7. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 7
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
The riddle (continued)
If we look at the section of zonal wind stress at 1°30'N (figure 8) we can see quite clearly that there are
structures in the atmospheric forcing which are capable of generating equatorial waves (Kelvin) in the ocean
model. Nevertheless the model does not give a clear response at the equator.
On the other hand, around 12°S, we can see on the wind maps (figure 7) that the strengthening of the southerly
tradewinds is not homogeneous in longitude but occurs through (among others) a west to east rising propagation.
In this case the model's response is quite clear (figure 9). The sudden (7 days) drop in sea level in the Gulf of
Guinea (and beyond) is the basin response to the wind. We then check that the correlation between sea level and
zonal wind stress is satisfactory for the whole period (towards Ascension island).
Figure 9: sea level on 30 April and 4 May
Figure 11: change in sea level between 30 April and 5 May barocline height and barotrope height
The model response is thus mechanical and local.
Unfortunately we cannot compare the wind stresses
from the European centre with the PIRATE moorings
since the anemometers located at 10°W-6°S, 10°W-0°
N, 0°W-0°N were not in operation at the beginning of
2002 (which also means they were not available from
the European Centre). It is nevertheless possible to
confirm that there is no clear ocean response to this
atmospheric forcing (figure 10).
It is possible to confirm that the temperature time
series from the hindcast shows no significant
fluctuations and that is is comparable to the PIRATA
values. So where does the model's sea level response
come from? Figure 11 shows the change in sea level
between 30 April and 5 May in analytical terms. The
barocline height response (or dynamic height, deduced
from temperature and salinity) has been separated
from the barotrope height (deduced from the barotrope
current). It may be seen that the barocline response is
located near the equator It is a fairly moderate
response. On the other hand, the barotrope response is
very intense around 15°S, in other words, very near to
Ascension island and just above the mid-Atlantic
dorsal.
Figure 10: temperature time-series at the PIRATA
mooring at 10°W-6°S
8. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 8
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
The riddle (continued)
How did the anomaly affect the forecast?
We noticed at the beginning that the analysis did not only introduce a warm bias. We can also see that the
consecutive drops in level are less significant for the forecast than for the hindcast . This is very clear at
Ascension island and to a lesser extent at 8°W-0°N. We shall now attempt to determine which processes are
involved in this reaction.
To do this, we'll look at the temperature and meridianal speed time series at Ascension island (figure 12).
Figure 12: time series at Ascension island:
temperature (top) and meridianal speed (bottom), for hindcast (on left) and reanalysis (on right)
The first thing we notice is that there are no major differences between the hindcasst and that of the reanalysis.
There is no 7 day signal which could result in variations in sea level of about 25 cm. The two clear effects
revealed by an analysis of the forecast are on the one hand the lack of surface cooling (already noted) and on the
other an end to cooling at a depth of about 1000 m.
The meridianal speed of the hindcast has a very clear 7 day barotropic signal (from 1 to 15 May in particular).
This same signal is found in the barotropic height and in the sea level. In passing we can see the surface
advection is weak but oriented to the north (cold waters) in the reanalysis just after 8 May.
It may be seen that the 8 May analysis 'interrupts' the 7 day signal almost entirely. The forecast reveals a less
barotropic meridianal speed , whose signature in sea height is more neutral thus marking the end of oscillations
in this region.
Finally the surface advection is strong and oriented to the south (warm waters) in the forecast. Hence the surface
advection is the cause of heating in this region.
9. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 9
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
The riddle (continued)
At the equator we can confirm that at 8°W the 7 day signal comes from fluctuations in the position of the
Equatorial Under Current (EUC) The latter "surfaces" in the hindcast, bringing its cold waters to the surface.
We know that the real-time analysis introduces a warm bias in the model. In practice this results in a lowering of
the thermohaline structure in the Gulf of Guinea at the equator. But this means a decrease in the zonal density
gradient. As this gradient drives the EUC at the centre of the basin, the EUC is interrupted by the analysis. This
then enables the southern equatorial current (SEC) to renew its intensity at the surface. This current oriented
towards the west advects the warm waters of the Gulf of Guinea. Hence the surface advection is also behind the
heating in this region.
What should be done?
The anomaly which has just been described can only occur for a very specific case of the analysis/forecasting
system. We can diminish the probability of this combination by improving each weak point. The first step is to try
and make the model more stable for this region for May.
In the number 3 Quarterly letter we already saw that the tropical instability waves (TIW) are too great as shown
by the summer surface temperatures in this configuration of the model. This is partly explained by an EUC which
is too fast by approximately 20 cm/s.
Some improvements have already been made to the next multi-variate PSY2-V1 operational system: increased
vertical diffusion at the bottom, shorter spin-up, new altimetry reference level. Via either the model or the
assimilation, this should help to limit shearing between SEC, EUC and NECC and hence reduce instability in this
region. Other possibilities are being considered (aerodynamic formulae for the ocean/atmosphere flux, increased
vertical turbulence during heating periods, types of water, etc.).
Another improvement is the cut-off which can be reduced. The orbit determination however requires a minimum
of time and so it is not easy to solve the cut-off problem. On the other hand, it is possible to lessen its impact by
using an extra satellite (Geosat Follow On for instance).
It is in fact possible that with only two satellites, the last track for any given region would be for J-4 or J-5.
Adding a satellite means we don't have to artificially increase the cut-off. The use of in-situ observations affected
by a 24h cut-off would also help matters.
A few lessons to be learnt
The model is too unstable in May, with a resonance peak at 7 days.
For May 2002, the real-time analysis degrades the projected fields by introducing a warm bias. The
hindcast does not correct the model's resonance at 7 days.
The cut-off is too far removed (J-3) from the analysis date. It would be a good idea to reduce it to
improve real-time analysis for frequencies of approximately 7 days. The use of a third satellite such as
Geosat Follow ON (GFO) would enable more observations just before cutoff.
There may be an alias for the observation/analysis system for phenomena whose period is between 5 and
12 days (which gives a poor sampling due to the cut-off during an analysis cycle).
It would be better to use hindcasts for applications which are not constrained to real-time.
The PSY1-v1 operational system with hindcasting (J-21) rather than just using the last analysis (J-7)
guarantees the system's stability.
This study was triggered by precise feedback from users. This shows the importance of feedback for
measuring and improving system performance.
10. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 10
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
Quizz
More than 30 years after humans first walked on the moon, they've rolled on MERCATOR. This can be seen from
the 'tyre tracks' found at 40°W on the analysis increment for 11-9-2002:
sea level: analysis increment (correction)
on 11-9-2002 for 11-9-2002
Who dared to do such a thing?
You'll find the answer on the next page
11. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 11
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
Quizz: Answer
Luckily, it was ERS-2 which rolled on MERCATOR. What happened was that an error crept in during processing of
altimetry observations from JASON, which has replaced Topex/Poseidon for the analysis since July. Delivery of
these observations to MERCATOR was delayed beyond the cut-off and the observations did not therefore arrive in
time to be taken into account by the analysis/forecasting system:
sea level: the week's observations for 11-9-2002
This was the first time this had occurred since the commissioning of PSY1-v1 in January 2001. It allowed us to
measure the impact of the operational system on a reduced altimetry coverage. We can clearly see how the
analysis was limited to the neighbourhood of the satellite tracks as the increment was nil in the 'gaps'. Where
there was too much space between the tracks in relation to the correlation radii, the altimetry plots can be seen
in the analysis increment. We should however note that the amplitude of the increment is fairly moderate and
that the tyre tracks are less visible in the absolute height field.
The following week, all of the week's observations on 11-9-2002 were entered into the system to produce a much
higher quality analysis increment in hindcasting.
12. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 12
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
A posteriori validation of hypotheses:
correlation radii
By Eric Greiner
When defining a configuration for a numerical ocean model some algorithms have to be defined, for instance for
diffusion formulae, atmospheric forcing, physical parameter settings, etc. The relevance of these algorithms are
then assessed by validating the results of the numerical simulation, possibly by adjusting the algorithms. This
same validation may be done for the analysis part of the forecasting analysis system. This is because certain
choices also have to be made when defining the analysis tool, in particular for statistical hypotheses.
In an analysis system based on optimal interpolation (OI), the most important hypotheses are those for
observation and forecasting error covariance (guess). To reduce the numerical cost of OI, the covariances are
separated into variances and correlations. Each of the hypotheses for observation and guess variances and
correlation can and must be validated a posteriori. We shall now look at the case of correlation radii for the guess
error.
The PSY1-v1 radii were calculated a priori from sea level anomalies (SLA) observed by Topex/Poseidon. There are
several ways of calculating the correlation scale at a given location.
This scale is defined here as the furthest point at which the temporal correlation with the origin falls within the
interval [0.4-0.6]. Below this scale, the correlation is significant, beyond it we find decorrelation (in the form of a
bell).
The radius thus determines a circle within which the signal is significantly correlated, while signals outside the
circle are decorrelated.
The scales were calculated for each of 5 Topex/Poseidon years from 1993 to 1997, including the seasonal cycle,
then averaged over the 5 years and finally filtered to eliminate the small scales (Figure 2a).
The longitude correlation radii of the SLA observed (Figure 2a) can be seen in the SLA analysed for 2001 (Figure
2b).
The correlation radii deduced from the 3 months of summer in 2001 (Figure 2c) reveal a few significant
differences from the imposed radii. The same is true for the three months of winter in 2001.
The correlation radii deduced from the SLA analysis increments in 2001 (Figure 2d) are clearly different from
those imposed.
In PSY1-v1, the correlation structure for the guess has
the form of a spatio-temporal bell which varies in
shape according to the geographical position. Thus the
correlation is approximately 0.2 between two points
separated by a distance 'dx' which would be twice the
correlation radius (Figure 1). This correlation function
does not have a negative lobe as is often the case in
meteorology. This means that the analysis is less
'refined' (smoother). The advantage is that it limits
errors due to extrapolation between satellite tracks.
In PSY1-v1, the correlation radius of the guess
determines the sphere of influence of an individual
observation, since the observations are assumed to not
be correlated among themselves (observation error
correlation in the form of a dirac distribution).
Hence, in the riddle, the width of the 'tyre tracks' is
determined by the correlation radius of the guess. Figure 1: function of the correlation of PSY1-v1
as a function of 'dx', the distance normalized by the
zonal correlation radius.
13. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 13
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
A posteriori validation of hypotheses: correlation radii (continued)
The same may be said for the meridianal correlation radii observed (Figure 3a) which can be seen in the SLA
analysed for 2001 (Figure 3b).
Although there appears to be a meridianal correlation maximum off the coasts of Portugal and Africa, which looks
like an ERS satellite track, this is in fact not the case. This strong consistency of the correlation is related to the
coherent structure of the meridian current between 1000 m and 2000 m, a current which is strongly constrained
by the bathymetrics on the edge of the continental shelf.
The correlation radii deduced from the analysis increments in 2001 (Figure 3c) are clearly different from those
imposed.
Figure 2: Zonal correlation radii deduced from Topex/Poseidon (a, top left),
calculated a posteriori from the hindcast for 2001 (b, top right),
calculated a posteriori for July to September 2001 (c, bottom left),
calculated a posterior from the analysis increments for 2001 (d, bottom right).
Figure 3: Zonal correlation radii deduced from Topex/Poseidon (a, left),
calculated a posteriori from the hindcast for 2001 (b, right),
calculated a posterior from the analysis increments for 2001 (c, right).
14. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 14
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
A posteriori validation of hypotheses: correlation radii (continued)
Figure 4: zonal correlation radius (on left) and meriain correlation radius (on right)
calculated a posteriori on hindcast increments for 2002 and averaged in longitude.
The correlation radii for the guess are an important
part of this system. However, most of the analysis
tools similar to the OI tool have to specify, in one way
or another, statistics which describe the error
covariances for the guess . The important thing is to
choose a 'good' set of system states, in other words
one which has realistic statistics. The first solution
consists in using a constant correlation radius
(~200km). This value is often deduced from a set of
empirical experiments.
A second solution involves deducing correlation radii
directly from observations: which is what was done for
PSY1-v1.
Figures 2a and 2 b, or 31 and 3b show that this choice
is compatible with the analysis tool and the ocean
model. The correlation radii for the observed SLA and
the analysed SLA are similar, even though the
observed variance remains much higher than the
analysed variance. Regions for which there are
differences are Ascension island, the north of the West
Indies Arc and also the continental shelves of Iceland,
Greenland and Labrador. This model configuration
(bathymetric trapping , sea ice) only gives a poor
reproduction of all these regions.
It may be noted that the radii deduced a posteriori
from the summer months (Figure 2c) are different to
those deduced for a whole year. They are generally
smaller. This is due to the fact that the steric signal
(dilatation due to summer warming) is a large scale
signal which accounts for a lot of the annual signal.
By choosing a set from a single season we are able to
filter out a goodly proportion of the steric signal for the
statistics to be deduced from this set. Likewise, it may
be noted that the correlation radius maximum around
40°W-4°N, deduced for 2001 (figure 2b) disappears
from the radius deduced from the summer months
(figure 2c). This is normal since the signal comes from
the meridianal migration of structures in this region,
which is very clearly visible between October and
January.
A third solution consists in using seasonal sets or in
filtering a seasonal signal or even a frequency band we
might not want to correct from a multi-annual set.
A fourth solution consists in using a set of analysis
increments. The assumption then is that the analysis is
sufficiently realistic for the increments to be
representative of the forecasting error. We can also
use a seasonal set of increments. The correlation radii
deduced from SLA increments (figures 2d, 2c) are
often much smaller than in the analysed SLA (figures
2b, 3b). For the zonal average of increment correlation
radii (figure 4) we can see that the increment
correlation structures are almost isotropic except for
the 5°N-10°S equatorial strip.
We then check a posteriori to ensure that 220-250km
is in fact a good mean value for a correlation radius.
15. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 15
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
A posteriori validation of hypotheses: correlation radii (continued)
It may be noted that while the increment correlation radii are generally smaller than those for the analysed SLA
(for instance around 25°W-39°N) the opposite may also hold (for instance around 25°W-0°N). We can explain
these differences in system behaviour by means of SLA time series and SLA increments near to the two locations
(figure 5).
Figure 5: SLA time series (on left) and SLA increments (on right)
around 25°W-0°N (top) and around 25°W-39°N (bottom) for the hindcast for 2001.
Around 25°W-0°N there is a slight bi-annual signal. The increments have the same amplitude as the signal which
means that there is a significant relative error. Paradoxically the increments are better correlated than the SLA.
Due to local effects (meridianal migration) increment correlation for September, October and November is
lessened and modulated at a smaller scale.
Around 25°W-39°N there is a clear annual cycle and approximately a one month delay between 25°W and 20°W.
The increment has a lower amplitude than the signal and the relative error is thus small. In spite of specifying
fairly large radii, the resulting increments are on a smaller scale than the SLA.
This is due to the high density of satellite observations in this region (Topex-Poseidon and ERS-2).
The analysis tool thus does not really have to extrapolate between the tracks.
The correlation structure is thus less significant since the observations are used locally.
Conclusion
The compared observed SLA and analysed SLA scales are coherent. On the other hand, an a posteriori check
shows that the correlation radii imposed by the analysis tool are often too great.
The zonal radius is over-estimated by a factor of two, with the exception of the equatorial strip where we can
even see a slight under-estimation around 2°-3° in latitude. The meridianal radius is over-estimated by about
40% north of 20°N and slightly under-estimated between 5°N and 15°S.
We thus intend to adjust the radii for future versions of the analysis/forecasting systems.
There is still some uncertainty as to the correlation structure (function and radii) and this field has to be
investigated further.
It appears that there is a lot of potential for improving the performance of the analysis/forecasting system.
16. The MERCATOR
Quarterly newsletter
#7- October 2002 - page 16
CNES
CNRS/INSU
IFREMER
IRD
METEO-FRANCE
SHOM
- Notebook -
Address
Please send us your comments to the following e-mail address: webmaster@mercator.com.fr
Next issue: January 2003
Editor
Eric Greiner
Authors :
Article 1 : E. Greiner
Article 2 : E. Greiner