Assimilation of satellite altimeter data in a multilayer Indian Ocean circulation model

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Assimilation of satellite altimeter data in a multilayer Indian Ocean circulation model

Sujit Basu*, Vihang Bhatt, Raj Kumar & Vijay K. Agarwal

Oceanic Sciences Division, Meteorology and Oceanography Group,Space Applications Centre, Ahmedabad 380 015, India

*[ E-mail : rumi_jhim@yahoo.com ] Received 13 September 2002, revised 16 April 2003

The present study was dictated by a curiosity to examine whether the forecast capability of a multilayer Indian Ocean circulation model can be improved by assimilating satellite altimeter data into the model. In the present investigation we have studied the assimilation of Topex/Poseidon (T/P) altimeter observed sea level anomaly data in a 2 ¹/2 layer thermodynamic model of the Indian Ocean. The model has been spun up for 7 years with climatological winds and heat fluxes obtained by 5 years average of monthly mean winds and heat fluxes from the National Centre for Environmental Prediction (NCEP) to achieve steady annual cycle. Thereafter, the model has been run further for 5 years (1995-1999) with interannually varying daily NCEP winds and heat fluxes so as to reach the initial state corresponding to 1^st January of the experimental year 2000. Subsequently, the model has been run for the experimental year 2000. It has been able to produce the known patterns of current and SST in the Indian Ocean reasonably well. However, the model simulated sea level anomalies (SLA) do not compare well with observations. An attempt has been made to improve the simulation of SLA by assimilating highly accurate T/P altimeter data into the model using the techniques of blending and nudging. Both monsoon and non-monsoon cases have been studied. From the study it can be concluded that it is possible to provide reasonably accurate forecast of oceanic sea level variations in the short time scale (about 5 to 10 days) using this model of intermediate complexity forced by good quality forecast winds if satellite data can be properly assimilated into the model.

[ Key words: Altimeter data, assimilation, forecast, Indian Ocean circulation model ]

Ocean models can be used to examine how the ocean works¹. They also provide a reasonable scope for understanding and predicting various oceanic fields like currents, sea levels, SST etc., and their variabilities in space and time. However, another important aspect of ocean modeling is the work which seeks to combine models with data, a process known as data assimilation. This is important for testing models and forcing using models to extract maximum information from expensive data, and initializing coupled forecast models¹. Data assimilation is the name given to the process of optimally combining a physical model with observational data to provide a state analysis of the system which is better than could be obtained using just the data or physical model alone. There are good review papers describing this emerging field of physical oceanography^2,3. Although data assimilation has long been used by the meteorologists for the purpose of predicting the weather and climate, in the field of oceanography it was not used to a large extent mostly because of the scarcity of data over the oceans. However, the situation has changed dramatically after the launch of

dedicated ocean-observing satellites such as ERS-1 and Topex/Poseidon (T/P) with onboard altimeters as well as scatterometers (in the case of ERS-1). Since in-situ observations in the ocean are spatially confined to very limited regions and are also very infrequent in time, one is tempted to use the data from satellites which provide a dense spatio-temporal coverage over the oceans. Satellite-borne radiometers measure sea surface temperature⁴ while a satellite altimeter measures sea level⁵ which is extremely important as it is related to the subsurface structure of the ocean. The limits on the availability and type of oceanic data have stimulated considerable interest in the use of various data assimilation techniques in recent years.

It is imperative to explore assimilation of satellite data for improving the hindcast and forecast capabilities of Indian Ocean circulation models. Early studies^6-8 used relatively simple assimilation techniques together with idealized experiments. Later, researchers have assimilated actual data in various ocean models of different complexities. Most of the researchers have concentrated on the models of Pacific and Atlantic oceans. One can consult the

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review papers^2,3 which contain various references pertaining to the studies related to assimilation of satellite data in models of Atlantic and Pacific oceans.

Notable exception is a recent study⁹in which the authors have described assimilation of high quality TOPEX altimeter observations in a primitive equation three-dimensional baroclinic circulation model of the North Indian Ocean. Other authors¹⁰ have used a variational technique for assimilating more accurate Topex altimeter data in a reduced gravity model of the Northwestern Indian Ocean. Although the technique used was very sophisticated, the model used was linear and did not cover the entire Indian Ocean.

Thus, they ignored role of the remote forcing originating in the eastern half of the basin¹⁰. This deficiency was improved later¹¹ by studying the impact of satellite altimetry on the simulations of sea level variability by an Indian Ocean model. In this study a nonlinear reduced gravity model of the entire Indian Ocean was initialized by Topex/Poseidon (T/P) altimeter data and after running the model for various time periods the results were compared with independent T/P altimeter observations. It was found that altimeter data exhibit a significant positive impact on model simulations. This can be considered as a simple form of data assimilation at the model initial time. However, no data were assimilated at intermediate time steps. Also, since the model was 1¹/2 layer reduced gravity model it was rather easy to convert the altimeter sea level anomaly into anomaly of the interface depth, a dynamic variable of the model. More challenging is the task of assimilating altimeter data in a multilayer model. In the present paper we study the assimilation of satellite altimeter data in a 2^1/2 layer model¹² of the Indian Ocean using blending and nudging techniques and the present study thus can be considered as a logical extension of the earlier studies^10,11. There of course have been numerous studies of data assimilation using more sophisticated models, a recent example being the study using a primitive equation model by Lopez &

Kantha⁹ mentioned earlier. However, the selection of a relatively simpler model employed in the present study was dictated by the following considerations.

The most important point favouring the use of this model is that limited computer resources are required to run the model. Also, the model is reasonably good in simulating the basin scale variability of circulation and SST in the Indian Ocean on seasonal to

interannual scale and has been used successfully to simulate the upper layer circulation along the east coast of India¹³as also to simulate SST and currents in the North Indian Ocean¹⁴ during the onset phase of southwest monsoon. However, one major problem with the model is that it is not able to produce reasonably good simulations of sea level which will be shown in this article. It was thus felt that if this deficiency can be corrected using the tool of data assimilation, it will be possible to forecast the important oceanographic variables (currents, sea level and SST) using a single model and forecast winds from the National Centre for Medium Range Weather Forecast, New Delhi.

Materials and Methods Model description

The model employed in the study has been elaborately described by McCreary et al¹². The model ocean consists of two active layers overlying a deep motionless layer of infinite depth. The upper two active layers interact with each other through entrainment and detrainment while conserving mass and heat of the total system. The uppermost sublayer of the upper layer that can be termed as mixed layer entrains or detrains water in a process in which the mixing is maintained by turbulence generated by both wind stirring and cooling at the surface. The non- turbulent fossil layer, i.e., the lower sub-layer of the upper layer being formed by the detrainment of water from the upper mixed layer, is kept isolated from the surface turbulence. However, it can be engulfed into the mixed layer during the strong entrainment or upwelling regimes.

The equations of motion for the upper layer are (h1 v1)t +∇. (v1h1v1)+f k x h1v1 +h1 <∇p1>

=τ+υ∇² (h1v1)+v2weθ (we)+v1 weθ (−we)−γ h1u1i,

… (1a)

h1t +∇. (h1v1)=κh ∇²h1 + we … (1b) and for the lower layer are

(h2v2)t +∇.(v2 h2 v2)+fkxh2v2 +h2 <∇p2>=υ∇²(h2v2) – v2 we θ (we)–v1weθ (- we)−γ h2u2 i,… (2a)

h2t +∇. (h2 v2)=κ h∇²h2 – we + wc … (2b) where vi and hi are instantaneous values of layer

velocity and thickness respectively, <∇pi> is the

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depth averaged pressure gradient in a layer, and the subscript i=1,2 is a layer index. τ is the surface wind stress, f is the Coriolis parameter and i and k are unit vectors in the zonal and vertical directions. There is Laplacian mixing of momentum and layer thickness with coefficients υ and κh respectively. The terms associated with γ act to damp the ui fields near the southern boundary. The terms involving we ensure that momentum and mass are conserved when water moves between the layers. The term wc is a correction that keeps the total mass in the system fixed to its initial value and θ denotes Heaviside step function.

The depth-averaged pressure gradients in each layer are:

<∇p1>=αg∇[h1(T1−Td)+h2(T2−Td)]−½α g h1∇T1,

… (3a)

<∇p2>=αg∇[(T2−Td)(h1+h2)]–αg(h1+ ½ h2)∇ T2,

… (3b)

where g is the acceleration due to gravity, T1 and T2

are layer temperatures and Td is the temperature of the deep ocean. The coefficient of thermal expansion α is assumed to have the constant value 0.00025/^oC throughout the study. The thermodynamic equations are the equations for the time evolution of the temperature in the two layers. There are additional equations for the time evolution of thickness and temperature of the mixed layer. Since our study is concerned with assimilation of sea level data from altimeters, we will be concerned mainly with the equations for the time evolution of the layer thicknesses h1 and h2 since the model sea level will be computed from these quantities. Hence we are not reproducing the thermodynamic equations in this article.

The model equations have been integrated numerically on a staggered Arakawa C-grid over the North Indian Ocean (29°S-25°N and 35°E-115°E) (Fig. 1) with a horizontal resolution of 55 km. Leap- frog scheme has been used for time integration with a time step of one hour. To inhibit time-splitting instability the fields are averaged between two successive time-levels every 41 time steps. Diffusive terms have been evaluated at the backward time level, and all other terms at the central time level. The conditions applied at the western, northern and eastern boundaries, as well as around Madagascar, are

no-slip conditions and at the open southern boundary, zero-gradient conditions have been applied.

Data used

The data used in the study can be classified into two types. The first type is data for forcing the model (winds and heat fluxes) and the second type is sea level anomaly (SLA) data for assimilating into the model. The model was forced by winds as well as by surface heat fluxes. The surface heat flux used as a thermal forcing in the model has been derived from the net solar radiation (incoming-outgoing), air temperature, specific humidity and scalar wind magnitudes. These fields have been derived from the daily NCEP data set¹⁵ for computation of sensible and latent heat fluxes. The drag coefficients for sensible and latent heat fluxes are as given by McCreary et al¹². The winds have also been taken from the same data set. The wind stress has been derived from the winds using a drag coefficient CD =1.5×10^-3 and air density ρ =1.175 kg m^-3. Linear interpolation has been carried out to get the NCEP winds and fluxes at model grid points and at model time step. The sea level anomaly (SLA) data set has been generated using sea level fields from T/P altimeter with respect to a 5-year mean calculated from the data. The data are 10-day averaged and are gridded over 1°×1°. The data set has been elaborately described in a study⁵. We have used few data sets in the months of March and June 2000 for studying the effects of data assimilation during non-monsoon and monsoon seasons respectively. The data were interpolated to the model grid points using linear interpolation.

Fig. 1 — Location map of the study area

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Assimilation methodology

Two types of assimilation techniques have been explored in this study. The first one is a simple blending technique. Since the model is of considerable complexity it is useful to start with a simple technique and progress gradually to more complicated ones. The blending technique³ is a highly simplified and localized version of optimum interpolation (OI), with purely empirical weights. At assigned times, the model forecast field at a given gridpoint is replaced by a new variable which is a blending of observation and model. We can represent this procedure in our case by the following equations: h1

new=βh1

obs+(1−β)h1 model

… (4a)

h2

new=βh2

obs+(1−β)h2 model

… (4b)

where β is the weight assigned to the observed value and h1obs

and h2obs

are the satellite altimeter observations of the model layer thicknesses. Actually, the satellite altimeter observes sea level anomaly which has been converted to observations of layer thicknesses using a procedure to be explained later in this paper. When β =1, the blending method reduces to direct insertion of the observed value in the place of model-predicted value. As mentioned earlier, this technique of direct insertion has been used earlier¹¹for assimilating satellite altimeter data in a 1½ layer model of the entire Indian Ocean, but the technique was used only at the model initial time.

Another popular technique of assimilation is known as Newtonian relaxation or nudging^3,16. In this method there is preforecast integration period during which the model variables are driven towards observations by including extra forcing terms in the model equations. These terms are nothing but difference of observation and model multiplied by suitable nudging coefficient. When the model initial time is reached, the extra forcing terms are dropped from the model equations and the forecast proceeds without extra forcing. This technique has been used in the present study. The nudging scheme employed here can be given as:

h1t +∇. (h1v1)=κh ∇²h1 + we +λ(h1

obs –h1) … (5a) h2t +∇. (h2 v2)=κh ∇2

h2 – we +wc +λ(h2obs

–h2)

… (5b)

It can be seen that these equations are nothing but the time evolution equations for the layer thicknesses with an extra nudging term in the right hand side, and λ is the nudging coefficient which determines the strength of nudging.

The data to be used in the assimilation procedure are gridded sea level anomaly data observed by Topex/Poseidon altimeter described previously.

Unfortunately, there are no prognostic equations for this variable in the model employed here. Thus one has to distribute this sea level anomaly to the individual layer thicknesses using some assumption.

In this study we have used a type of reduced gravity updating¹⁷ which updates only the pressure in the upper layer and the correction to the pressure in the lower layer is set equal to zero.

The following equations were used for calculating the corrections Δh1 and Δh2 to h1 and h2 where h1

and h2 are the thicknesses of the upper and lower active layers of the model.

Δh1 =(ρ /Δρ)Δη … (6)

Δh2 = Δη-Δh1 … (7)

Here ρ is the mean density of the ocean, Δρ is the density difference between the layers and Δη is the difference between the observed and model sea level anomaly. Since the model is a thermodynamic one and without salinity we compute the upper and lower layer densities using the formula

ρi = ρ0 (1−αTi) … (8)

where

ρ

0 = 1 g cm^–3, i=1,2 and α is the coefficient of thermal expansion.

As the model calculates layer temperatures at each time step the densities can be easily calculated. As regards the model sea level anomaly (SLA) it has been calculated using

η

model = SLVL-MSL … (9a)

SLVL=[(

ρ

d-

ρ

1)h1 + (

ρ

d-

ρ

2)h2]/

ρ

d … (9b) In Eq. (9a), SLVL and MSL are respectively the instantaneous and mean sea levels computed by the model. To compute the mean sea level the model has to be run for a long time and the instantaneous sea levels have to be averaged. Accordingly, the model has been run for five years (1995-1999) after establishment of the steady annual cycle.

Instantaneous sea levels computed by the model

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during this run were averaged to obtain MSL in Eq. (9a). This was done for the following reason. The altimeter derived sea level anomaly data used in the study is the deviation of the measured sea level from a 5 year mean. Hence it was felt that the model derived SLA also should be computed relative to a 5 year mean.

Control run of the model

The model was spun up for 7 years with winds obtained by 5 years average of monthly mean NCEP winds and heat fluxes for the period 1992 to 1996.

The numerical solution reached a quasi-equilibrium state after 6^th year. Thereafter, the model equations were integrated further for 5 years from 1st January 1995 to 1st January 2000 with interannually varying daily NCEP winds and heat fluxes. The model was also run for the experimental year 2000 to see the general features of ocean circulation. It was able to produce the known patterns of current and SST reasonably well. This fact was already established by other researchers, most recently in the study by Salvekar et al.¹⁴ in their numerical simulations of the North Indian Ocean state prior to the onset of SW monsoon using the same model. However, in this study we are concerned with assimilation of sea level data, hence refrain from a discussion of the simulation of currents and SST.

Results

Earlier, we have briefly described the methodology of data assimilation adopted in our study. We made a first attempt to use the simple technique of blending.

Later, we used the more advanced technique of nudging for assimilating satellite altimeter data. The altimeter derived SLA data have been used to calculate the corrections to the model layer thicknesses in the manner outlined earlier.

Non-monsoon case

The model was initialized on 6^th March 2000 with a mixture of model and observations [see Eq. (4)]. The blending coefficient β was chosen to be 0.65. This value was arrived at in the following manner. The blending coefficient was slowly increased starting from low values and after running the model for 5, 10 and 15 days the model forecast SLAs were compared with altimeter observed SLAs of the corresponding days. The blending coefficient which produced maximum correlation between model forecast SLAs

and altimeter observed SLAs was finally retained.

Here by initialization we mean the following. Using Eqs (6) and (7) we calculated the corrections Δh1 and Δh2 to the model simulated layer thicknesses. They were added to h1 and h2 to obtain h1

obs and h2 obs . Afterwards, Eq (4) were used to initialize the model with a blending of model simulated values and observations. The model transports were found by multiplying these values by the upper and lower layer currents computed by the model. In an earlier study¹¹, the authors experimented with choice of currents in a 1¹/2 layer reduced gravity model without thermodynamics. They found that their model was insensitive to choice of currents. This time, however, it was found that the model is extremely sensitive to the choice of currents and best results were obtained by using the model computed currents. With this initialization the model was run for periods of 5, 10 and 15 days. Model computed SLAs were stored daily for the first five days of forecast and later, after 10 and 15 days for subsequent comparison with altimeter observed SLAs. For finding out the degree of improvement in the model simulation due to this initialization we also ran the model from 6^th March for periods of 5, 10 and 15 days without initialization and again stored the model computed SLAs daily for first five days and also after 10 days and 15 days. We found that the correlation between the model without initialization and observations is extremely low. In fact it was negative (-0.07) after first day forecast (Table 1). The RMS difference between the model forecast SLA and observed SLA was also very high after first day forecast (9.06 cm). The correlations and RMS differences between the uninitialized model forecast SLAs after various days of forecast and altimeter observed SLAs were computed. The same quantities were computed for the initialized model also. It can be seen that correlation has improved significantly as a result of blending on each day of forecast (Table 1). However, after 2 days the correlation does not vary much and is almost constant till 5 days. The RMS difference is 3.98 cm after first day of forecast. After 5 days of forecast the correlation is 0.68, improved from -0.1 and the RMS difference is 4.31 cm, still quite low compared to the case without blending (8.86 cm). In fact the RMS difference is about half of what it was for the model without assimilation. In Fig. 2 we show the various SLAs on 11^th March as well as on 16 th March (5^th day forecast).

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It can be seen that blending has significantly enhanced the forecast potential of the model. In fact even after 10 days the correlation between blended model and data is quite high (0.58). However, the RMS difference is still quite high (4.95 cm). It was thus felt that alternative tool of data assimilation should also be explored which can enhance further the forecast capability of the model. We used the technique of nudging. As mentioned earlier, in this technique a model is nudged towards observations using artificial terms in the time evolution equation for the appropriate variables. These terms are nothing but the difference of observations and model multiplied by suitable nudging coefficients. In present case, we introduced these terms in the evolution equations for the model layer thicknesses h1 and h2. The model counterparts of observations were found from the altimeter SLA in the same way as in the case of blending. The corrections calculated by Eqs. (6 and 7) were added to the model computed layer thicknesses to arrive at the model counterpart of observations.

Equivalent altimeter observation at each time step was generated by linear interpolation between two altimeter observations ten days apart. Nudging was

carried out for 10 days prior to the actual forecast. A nudging coefficient of 2.2 E- 06was used. This value was arrived at by the same procedure as in the case of blending, i.e., by gradually increasing the coefficient and computing the correlation between model forecast SLAs and observed SLAs. The power of this technique can be judged from Fig. 2C. The match between the observations and model results with the use of nudging on 11^th March (after 5 days of forecast) is better (Fig. 2) than that between the observations and model results with the use of blending. In quantitative terms the correlation between the model (with the use of nudging) and observations after first day is now as high as 0.79 and the RMS difference is 3.48 cm. The results of this phase (correlations and the RMS differences) are also summarised in Table 1. The superiority of the nudging technique can be judged from the fact that on each day of forecast the correlation between the nudged model and observations is higher than that between the blended model and observations and the corresponding RMS differences are lower. As expected, the quality of forecast degrades as the forecast progresses. The degradation in quality can also be seen by comparing the results of 10^th day forecast and the results of 15^th day forecast appearing in Figs. 2 and 3 with the results of 5^th day forecast in Fig. 2. To supplement these observations we have also plotted the time series of the SLAs (Fig. 4) from the model without assimilation, from altimeter and from blended and nudged models for selected points in the Arabian Sea, Bay of Bengal and the Southern Indian Ocean. The strength of data assimilation is apparent from these figures. The superiority of nudging compared to blending is also quite clear.

However, at the Southeastern Indian Ocean (Fig. 4D)) blending performs better. The reason for this is not clear. It may be possible that for more efficient nudging, the nudging coefficient should be selected as a function of space. However, this will be a subject of separate research. It is however clear that assimilation improves the forecast capability of the model at all the points.

Monsoon case

The blending was performed on 14^th June 2000 and the model was subsequently run for periods of 5, 10 and 15 days as in the previous case. However, this time a blending coefficient of 0.52 was found to be suitable. The model was unable to adjust with higher

Table 1—Correlation and RMS difference between model SLA and T/P SLA (During Non-Monsoon)

Forecast date Remarks Correla- RMS

tion difference

(cm)

7 March 2000 Without assimilation -0.07 9.06

With blending 0.73 3.98

With nudging 0.79 3.48

With blending 0.58 4.95.

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Fig. 2—Sea level anomaly (SLA) for the non-monsoon case on 11th & 16th March 2000 (A) observed by T/P altimeter (B) 5th and 10th day forecast by the blended model (C) 5th and 10th day forecast by the nudged model.

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values of β. The reason for this is not quite clear. It might be because of the difference in winds and fluxes in the case of monsoon compared to the case of non-monsoon. Again the model forecasts were compared with observations after each day of forecast up to 5 days and after 10 and 15 days. It can be seen from Table 2 that though blending improves the correlation between model forecast SLAs and altimeter observed SLAs compared to the case without blending, the improvement in correlation is not as much as in the non-monsoon case. This may again be ascribed to the strong monsoon winds. In fact, the RMS differences remain quite high (always more than 5 cm) although they are significantly lower (almost by a factor of 2) than the case without blending. It is thus more imperative to use the nudging method of data assimilation in this case.

Accordingly, the model was nudged by altimeter SLA for 10 days prior to the actual forecast. The nudging coefficient employed was 5.0E-05. Again this difference might be due to the difference in winds and fluxes during monsoon and non-monsoon cases. The strength of the nudging technique can be judged from the fact that the correlations between model and

Table 2—Correlation and RMS difference between model SLA and T/P SLA (During Monsoon)

Forecast date Remarks Correlation RMS

difference

(cm)

15 June 2000 Without assimilation -0.18 10.83

With nudging 0.89 3.00 19 June 2000 Without assimilation -0.17 10.82

Fig. 3—SLA for the non-monsoon case on 21st March 2000 (A) observed by T/P altimeter (B) 15th day forecast by the blended model (C) 15th day forecast by the nudged model.

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No assimilation

Nudging

Altimeter Altimeter

Blending

No assimilation

Blending

Nudging

Altimeter

No assimilation Altimeter

Nudging Blending

No assimilation Blending

Nudging Altimeter A

B

C

D

Fig. 4—Time series of sea level anomaly at—(A) 10ôN, 55ôE, (B) 10ôS, 55ôE, (C) 15ôN, 90ôE, (D) 15ôS, 90°E, during non-monsoon.

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Fig. 5—SLAfor the monsoon case on 19th and 24th June 2000 (A)observed by T/P altimeter, (B) 5th and 10th day forecast by the blended model, (C) 5th and 10th day forecast by the nudged model.

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observations have improved quite significantly as a result of nudging. The correlation is more than 0.8 even after 10 days. The RMS differences are also quite low compared to the case of blending. After 5 days of forecast the RMS difference is 3.15 cm.

Figures 5 and 6 present the results for the monsoon case. As usual the left panel in each of these figures shows the altimeter observed SLA, the middle panel shows the SLA forecast by the model as a result of blending and the right panel shows the SLA forecast by the model as a result of nudging. Again we show the time series of various SLAs at the same selected points (Fig. 7). A curious observation (Fig. 7D) is that SLA from model without assimilation is closer to observations after 10 days. However, in practice, forecast has to be carried out by forecast winds from medium range weather prediction centers. These winds are known not to be accurate beyond a period of ten days. Thus it can be safely concluded that assimilation of satellite data improves the forecast capability of the Indian Ocean circulation model studied by us in the realm of predictability.

Discussion

We have investigated assimilation of satellite altimeter data in a 2¹/2 layer model of the Indian Ocean. This study is a logical extension of the studies done earlier^10,11 using 1¹/2 layer reduced gravity model of the Indian Ocean. The choice of the present model¹² was dictated by the fact that it is known to produce realistic simulations of SST and currents in the Indian Ocean. Also, the model can be run with limited computing resources. The only deficiency is that the model simulated sea level values do not agree well with observations. It was thus felt that if assimilation of satellite altimeter data can lead to a better forecast of sea levels then a single model can be used for operational forecast of the three oceanic parameters of interest (currents, sea levels and SSTs) in the Indian Ocean in the near future. We have initialized the model with altimeter data using blending³ and have found that the sea level forecast by the model can be significantly improved using data assimilation. The sea level measured by altimeter has been spread to the two model layers using reduced gravity updating¹⁷. Both non-monsoon and monsoon cases have been studied. Also, data have been assimilated during the course of model run using nudging¹⁶. Again, it has been found that data assimilation is able to enhance forecast capability of

Fig. 6—SLAfor the monsoon case on 29th June 2000 (A=observed by T/P altimeter, B=15th day forecast by the blended model, C=15th day forecast by the nudged model).

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Fig. 7—Same as in Fig. 4 except during monsoon.

No assimilation

Blending

Altimeter

Nudging No assimilation

Blending

Altimeter

No assimilation

Blending Nudging

Altimeter

No assimilation

Blending

Nudging

Altimeter A

C B

D

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the model. The overall performance of nudging is much better than simple blending, particularly so in the case of monsoon, as a result of assimilation, although this might not be so at specific points of the ocean. Thus, use of space-dependent nudging coefficient can be explored in future research to further enhance the strength of nudging.

Thus, as demonstrated, it is possible, in principle, to forecast oceanic variations in the short time scale (about 10 days) using a model of intermediate complexity if good quality forecast winds are available and if satellite data can be assimilated in the model.

In the diagnostic mode the model can also be used to generate reliable values of gridded currents, sea level anomaly and SST using a combination of winds, fluxes and assimilation of altimeter data. Needless to mention that these types of data are useful for many atmospheric and oceanographic applications.

Acknowledgement

The authors are indebted to Prof. J. P. McCreary, Director, International Pacific Research Center, Honolulu, USA, for providing the ocean model used in the study . They also thank Dr. D. Sengupta, Indian Institute of Science, for providing the daily NCEP winds and fluxes for the years 1995-2000 and to Dr. C. M. Kishtawal for programming assistance in the initial stage of this study. Discussions with Dr. M. S. Narayanan and Dr. A. Sarkar are gratefully acknowledged. The authors express their deep gratitude to Mr. H. I. Andharia for computer support.

Finally, the authors are deeply indebted to the Department of Ocean Development for funding under DOD/SATCORE project.

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