Numerical experiments using simulated altimeter data were conducted in order to examine the assimilation of altimeter-derived sea surface heights into numerical ocean circulation models. A reduced-gravity, primitive equation circulation model of the Gulf of Mexico was utilized; the Gulf of Mexico was chosen because of its amenability to modeling and the ability of low vertical-mode models to reproduce the observed dynamical features of the Gulf circulation. The simulated data were obtained by flying an imaginary altimeter over the model ocean and sampling the model sea surface just as real altimeter would observe the true ocean. The data were used to initialize the numerical model and the subsequent forecast was compared to the true numerical solution. Results indicate that for a stationary, circular eddy, approximately three to four tracks (either ascending or descending) across the eddy are sufficient to ensure adequate spatial resolution

Hurlburt, H. E.

Kindle, J. C.

Thompson, J. D.

English

NASA Technical Reports Server

cA_rPLINC _TN_.TE¢IES AND FOUR-D!?_NEIONAL A_.q/MII_TION OF ALTIMETR!C DATA
FOR OCEAN HONITORINC AND PREDICTION
John C. Kindle
J. Dana Thompson
f and H. E. HurlBurt
_i Dynamical Ocean Forecasting Branch
Code 324
Naval Ocean Research and Development Activity
NSTL, MS 39529
ABSTRACT
Numerical experiments using simulated altimeter data are conducted in order
to examine the assimilation of altimeter-derived sea surface heights into numerical
ocean circulation models. A reduced-gravity, primitive equation circulation model
of the Gulf of Mexico is utilized; the Gulf of Mexico is chosen because of its
amenability to modeling and the ability of low vertical-mode models to reproduce
the observed dynamical features of the Gulf circulation. The simulated data are
obtained by flying an imaginary altimeter over the model ocean and samplin_ the
model sea surface Just as a real altimeter would observe the true ocean. The
data are used to initialize the numerical model and the subsequent forecast is
compared to the true numerical solution. Results indicate that for a stationary,
circular eddy, approximately 3-4 tracks (either ascending or descending) across
the eddy are sufficient to ensure adequate spatial resolution.
I. INTRODUCTION
The satellite radar altimeter offers the most promising capability of
routinely providing global, timely observations suitable for initializing an
ocean circulation forecasting model. The inability, though, of a single nadir-
beam altimeter to provide a truly synoptic measurement which adequately resolves
the mesoscale eddy field, major current systems and fronts poses a serious
obstacle to the development of a skillful forecasting ability. A balance between
track spacing and period of the repeat tracks is necessitated. Hence, in
addition to the observational accuracy requirements, a viable oceanic forecast
will also depend on an innovative development of sampling strategies, four-
dimensional data assimilation techniques and initialization methods. The
thrust of this report is an ex_ination of sampling strategies which optimize
the usefulness of altimeter derived sea-surface heights in ocean monitoring
and prediction. In particular, we will attempt to determine the minimum track
spacing which adequately resolves the detectable meandering current systems
and eddies and to investigate the ability of numerical circulation prediction
models to fill in the resulting temporal gaps.
In addition to assimilating altlmetrlc data, numerical ocean models are
useful in simulation mode for generating "synthetic" sea surface heights to
=- investigate optimum sampling and initialization strategies and for comparison
,_ with actual altimeter data (Thompson et al., 1983). A reduced-gravity, primitive
equation circulation model of the Gulf of Mexico (Hurlburt and Thompson, 1980)
is utilized in order to examine the m thodology of incorporating satellite alti-
_l_. meter data into ocean forecasting models. Simulated altimeter measurements of
-_P sea surface height are obtained by: I) integrating the model to statisticalIG
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1984019194-595
https://ntrs.nasa.gov/search.jsp?R=19840019249 2020-03-22T09:26:25+00:00Z
" equilibrium, 2) flying ,'m ima_:inar,' altim('t,'r over tht, modt, 1 oct,an, 3) obiectivelv
mapping tilt, perfect (i.e., ,lnc,,ntnminatod t_v ,,,ec, id, tide or noi.qe) ,qnmpled data
",. onto a numerical arid. Tht' model is ";nitiatiz_.d ,ln¢] reqt;lrtod ,lsinv,, the
"observed" field, and the s, lb:_equent forecq:_t (ixp to several months) in compared
to the true solution. Thi._; approach allow,; us to inw,sti_,_ate the maximum ratio
of track spacin_ to eddv diameter for adequate mesoscale mappin_,_, the optimum
sampling period/track spacin?, for r_,T,_,at orbitq, in,N--dimensional dnta assimi-
lation methods , irtitializacion schomt, s and techniques for ,,pdatinv the
forecast. This, admtttedlv, antiseptic approach to studying the assimilation
problem is int_.nded as a first step. Fxp_,riments with contaminated data are
,,lso being conducted in order to :_,_sc,qs the accuracy requirements of altimeter
data for use _n ocean f_,recaqtln,,;. ".he r_,sults of these experiments will be
reported elsewhere.
2. TtlFi ClrLF OF MEXICO MODFT.
The Gulf of Mexico haq been chosen for thi._ study for several reasons.
As a semi-enclosed sea with well defined inflow and outflow ports, it is highly
amenable to model inc. The size of the, b;t.-, "'_ is small enough to permit a
relatively large number of experiments with fine resol_tion, and is sufficiently
large so that the dynamical features possess r_,,nv similarities to those found
in larger ocean basins. The primary forcing in the Culf is the intense Loop
Current which enters through the Yucatan Straits and exits through the Florida
Straits. Approximately once per year, the l,oop Current sheds an anti-cyclonic
eddy which propagates westward. Both the Loop Current and the associated eddies
have large sea-surface si_matures ( 30-50 cm). Additionally, the eddies propa-
x;ate slowlv (-- 3 cm/sec) and have larve horizontal scales (300-500 km in diameter).
Also, during a portion of the CEOSAT (a U. S. Navy spacecraft vhose primary
altimetric purpose is geodetic) mission there t_ _ pr,,posed field experiment
capable of providing verification data for the numerical forecast experiments.
The numerical simulations use the one-laver reduced-gravity version of
the Hurlburt and Thompson (1980) model of the C,ulf of Mexico circulation. This
formulation represents the ocean as two incompressible, homogeneous layers.
The lower layer is motionless been,.,c the pressure gradient generated by the
slope of the interface exactly balances that due to the surface slope. Hence,
the interface (model pycnocline) slope is an inverted representation of the surface
height field. This _s an advantageous formulation for altimeter applications
because the internal pressure field is uniquely determined by the sea-surface
height variations. In spite of its simpltcitv, the model has demonstrated a
remarkable ability t_ reproduce such observed features as the shedding of eddies •
from the Loop Current with realistic diameters, amplitudes and westward propagation
speeds (Hurlburt and Thompson, 1980). In addition, the two layer version of
/ the model was used in the study by Thompson et al. (1983) as an aid in identifying
the Loop Current system from collinear-traek altimetry from SEASAT.
3. EXPERIMENT DESIGN AND RESULTS
The simulation experlmet'ts described herein are motivated by a NORDA
research program to study ocean dynamics using the altimeter derived sea-surface
_ heights acquired during the C,EO,qAT mission. The satellite track sequence during
the first 18 months of C,EOSAT _s shown in Fig. I. This pattern produces an
b_ equatorial track separation of 40 km with global coverage in approximately 70
.,P days. The tracks, however, do not repeat and, hence, may be only marginally
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useful for mesoscale modeling. The geodetic portion uf GEOSAT may be followed
by an extended mission with exactly repenting tracks and a shorter repeat track
period.
As a first step in designing an optimum sampling strategy for mesoscale
modeling and forecasting, the track spacing required to resolve adequately
' a stationary eddy is examined. Figure 2(a) depicts the ascending and descending
tracks with a separation of I00 km superimposed on the numerical solution at Day
1120. The values of the model pycnocline depth are sampled every 20 km along
the tracks. Because, in general, the location of the ,,hservatlon points do not
coincide with the model grid points, the observation zs an interpolated value
from the numerical solution. The 'observed' data are mapped back to the numerical
grid in order to reconstruct the solution (Fig. 2(b)). The RMS error difference
between the true solution and the observed values is determined; the error is
calculated only within a square circumscribing the eddy and is normalized by
the standard deviation of the true solution within the square. For each value
of track separation, tw_ values of the RMS error are calculated: a) only one
set of tracks (i.e. ascending or descending are used in the analysis and b) both
ascending and descending tracks are used to reconstruct the height field. The
results (Fig. 3) reveal that if data from both tracks are used, track separation
as large as an eddy radius adequately resolves the features. Additional tracks
yield only a slightly improved representation. For cases in which the ascending
and descending tracks sample the eddy at slgnlflcantIy different times, it may
be advantageous to assimilate the observations from only one set of tracks.
In such instance_, Fig. 3 suggests that 3-4 tracks per eddy are required.
The non-stationarlty of the ocean adds a frustrating complexity to the
sampling problem. The inverse relationship between repeat track period and
track separs!tlon for a single, nadlr-beam altimeter demands a prudent sampling
and four-di_,.ensionalassimilation strategy for optimum results. If the dynamical
features of interest necessitate narrow track spacing, the temporal resolution
may be inadequate unless a numerical model is able to fill in the temporal gaps.
This problem is illustrated by Fig. 4 in which the interpolated Gulf of Hcxico
height fleld is shown for both a 72-day and a 39-day repeat track period. The
model ocean is sampled during the repeat period Just as a real altimeter would
observe the true ocean. The 72-day sampling period grossly distorts the west-
ward propagating eddy. The deformation is substantially reduced in the 39-day
repeat period case; the 21-day repeat period sanpling (not shown) exhibits very
little distortion of the eddy.
p
The 'observed' data are used to initialize a forecast of the Cull of Hexlco
circulation in order to measure the skill of a particular Qsnpllng strateby. The
forecast begins on day 1200 of the numerical slmulatlon and continues for 180 days.
, Initial conditions for the forecast are obtained by sampllng the model ocean with
an imaginary altimeter for a duration nearly equal to the repeat track period.
. ThIJ insures complete coverage of the basin. In each case, the last observation
occurs on day 1200. Hence, the 21-day repeat period case samples the model ocean
from day 1182 to day 120G while the 72-day case 'observes' the ocean from day I131
to day 1200. The height field is interpolated to the numerical grid and treated
as a synoptic data set. The results described below are based on _echnlques
i_ whlch exclude both four-dimenslonel asslml]ation and updatlnR of the forecast:
future experiments will Include these important aspects of the aasimilatlon
problem. The imltlal he ght fleld= re somewhat smoother than those shown in
_,e Fig. 4 due to the incorporation of data from both ascending _nd descending
.,r tracks. The imltlal velocity fleld is determined from the geo=trophlc 8pproxl-
_4= nation; the imltlal conditions are a=s_ned to be valld at approximately the uld-
604
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-;._.
Figure 2. a) Ascending and descending tracks
(separation equals I00 k=) of an imaginary altimeter
superimposed on the numerical solution of the Gulf
of Mexico. The contours are the model interface
_-'_ deviation from its initial flat position. The
contour interval is 10 m. Solid lines denote a
"--. deepening of the pycnocline while dashed lines
--_*. represen_ shoaling. The model is sampled every ;
_d= 20 k_, along each track. The solution is stationary
during the sa_pllng process, b) A recoustruction
'_ of the numerical solution at Day 1120 from the values "
sampled along the tracks in (a). Experiment R_8
fro= Surlburt and Thompson (1980) is the base
experiment.
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1984019194-599
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, 606 i
1984019194-600
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I _ I I _
Figure 4. The ascending tracks of an imaginary altimeter superimposed
--" on the interpolated height field. The values of the pycnocline height
anomaly were determined by sampling the numerical model every 20 km
along the tracks. The dashed track lines denote where the model was
sampled during the first half of the repeat track period and the solid
tracks depict where the model was sampled during the latter half.
;J Adjacent tracks sampled the model three days apart. The most recent
track (i.e. at Day 1200) is a solid track just to the left cf an
adjacent dashed track, a) 72-day repeat track period. The model was
-- observed from Day 1131 to Day 1200. The distortion of the eddy is
caused by westward propagation during the sampling period. The eddyis most distorted where two adjacent tracks differ by 69 days.
'_ b) 39-day repeat track period. The model is sampled from Day 1164 to
_p, Day 1200, The distortion of the eddy is not as large as in (a) because
the most recent and oldest tracks only differ by 36 days.
6071
] 9840 ] 9 ] 94-60 ]
gpoint of the sampling period. The skill of the forecast is determined by calcu-
. lating the RMS error difference between the predicted pycnocline depth and the
numerical solution throughout the basin. The results for three cases are shown
in Fig. 5. For the Gulf of Mexico simulation, the 21-day repeat track case
offers the best compromise between track separation and repeat period.
As a more stringent test of the optimum sampling strategy for the Gulf, the
experiments are repeated with a very fine-resolution Gulf of Mexico si_nulation.
The grid spacing and eddy viscosity are reduced from 20 km and 300 m2/sec to 10 kn,
and i00 m2/sec, respectively. Although the essential elements of the Gulf circu-
lation are still present, the fine scale solution is also charactecized b7 a
larger number of eddies exhibiting a wide range of shape, amplitude and horizontal
scale. Moreovez, the dynamical features bebave in a much more irregular manner.
The methodology of the forecast is identical to the process described above
except that the prediction begins on day 1530 instead of day 1200. This is due
to the longer spin-up time of the fine-scale simulation. Forecasts are again
performed for the 21, 39 and 72-day repeat periods. In addition, a 40-day
repeat track case is conducted in which the adiacent tracks are laid down one
day apart instead of three days. For a given track separation, this scheme has
the advantage of sampling a given feature in the shortest time. A comparison
of the true solution and the forecast initialized from the 40-day repeat period
case is shown in Fig. 6. The _S error plots of the forecasts are given in Fig.
7. Clearly, the 72-day repeat track period is inadequate. The relatively minor
differences between the other cases is supported by Fig. 3. The track separation
of the 21-day repeat period (~ 120 km) is sufficient to resolve the primary
dynamical features. Hence, additional tracks do not significantly improve the
spatial error of the measurement. The propagation speed of the eddies is slow
enough that the 39 and 40 day repeat periods yield reasonably synoptic
_bservations.
$. CONCLUSIONS
Simulated altimeter data have been incorporated into numerical ocean circu-
lation models in order to examine optimum sampling strategies of a single nadir-
)eam altimeter. The numerical experiments suggest that approximately 3-4 tracks
[either ascending or descending) across an eddy provide adequate resolution.
_or the Gulf of Mexico the track separation of the 20-day repeat r :od resolves
:he Loop Current and the westward propagating anti-cyclonlc eddies ampling
7ith a smaller track separation does not improve the forecast. In _ ._eroceanic
•egions, however, the 20-day repeat period yields a track separation unable
_ .o resolve the energetic mesoscale field. In wester, boundary systems, where
_ddies have smaller horizontal scales and propagate more rapidly, simultaneously
,braining adequate spatial and temporal resolution is more difficult. As part
,f this research program, numerical experiments using simulated altimeter data
: ,Ill also be conducted for the Gulf Stream region.
The experiments described in this report are merely a first step towards
he development of a methodology for assimilating altimeter data into ocean
-_orecast models. The utilization of contaminated data, optimal interpolation
_m_nd initialization schemes, forecast updating methods and multi-layer models need to
_)Im--e examined. These studies may substantially alter any quantitative conclusions
,_,w hich might be derived from the results presented here.
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1984019194-60:3
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.---, -.. ..__
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. Figure 6. a) Contours of pycnociine height anomaly for the fine
_- scale numerical simulation of the Gulf of Mexico circulation.
-_ b) Forecast of PHA in which simulated altimeter data are used teinitialize the model. The forecast, which begins on Day 1530, Is
for the 40-day repeat track period case.
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1984019194-605
ACKNOWLEDGEMENTS
Funding is from the Office of Naval Research under the Special Focus
Program, "Ocean Dynamics for GEOSAT". The computation8 were performed on the
Texas Instruments Advanced Scientific Computer at the Naval Research Laboratory
in Washington, D.C. The authors are grateful for the technical a3slstance
provided by Monty Peffley. Thanks are also due to Charlene Parker for typing
the manuscript.
REFERENCES
Hurlburt, H. E. and J. D. Thompson, 1980: A numerical study of Loop Current
intrusions and eddy shedding. J. Phys. Oceanogr., IO, 1611-1651.
Thompson, J. D., G. H. Born and G. A. M_ul, 1983: Collinear-Track Altimetry
in the Gulf of Mexico from SEASAT: measurements, models and surface
truth. Geophys. Res., 8_88,1625-1636.
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Sampling strategies and four-dimensional assimilation of altimetric data for ocean monitoring and prediction

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