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  • View in gallery

    Observations of the Great Whirl and the Socotra Eddy from the TOPEX altimeter. The small squares indicate the estimated centers of these features based on in situ observations reported by Fischer et al. (1996). The contour interval is 5 cm

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    The model domain and major current systems of the North Indian Ocean during the two monsoon seasons

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    Values of the volume flux through the Indonesion Throughflow as prescribed in the model. Values are from Garternicht and Schott (1997)

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    Model results from both the synoptic and assimilation runs for 26 Dec 1993 along the 77°E section. The former shows a maximum velocity of 30 cm s−1, well below the reported observations. In the assimilation results, the maximum velocity is greater than 60 cm s−1, which is in much better agreement with observations

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    Currents at 25-m depth from the shipboard ADCP collected during Aug 1993. Reproduced from Journal of Geophysical Research, Fischer et al. (1996)

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    Sea surface temperature distribution on 13, 18 Aug 1993. The data are from Brown, Rosenstiel School of Marine and Atmospheric Sciences, University of Miami. Reproduced from Journal of Geophysical Research, Fischer et al. (1996)

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    Streak plots of the currents at 30 m in the Arabian Sea on 18 Aug 1993. The use of assimilation improves the model’s ability to capture the correct location of the Great Whirl

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    Time histories of the temperature at the mooring site of the (top) Arabian Sea Experiment from the model synoptic and (bottom) assimilation runs. Including assimilation in the upper layers degrades the model’s ability to capture the thermal structure of the upper ocean

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    Temperature observations from the Arabian Sea Experiment. The mooring is at 15°30′N, 61°30′E. The measurements provide an excellent opportunity to compare the model results to actual observations (Fischer and Weller 1996)

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    Time histories of the temperature at the mooring site of the Arabian Sea Experiment from the (top) model synoptic and (bottom) assimilation runs. In this case, there is no assimilation of TOPEX measurement above 100 m. By excluding the assimilation in the upper layers, the model obtains both an improved thermal structure and improved currents

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    Mean absolute error of the model results as a function of depth at the Arabian Sea mooring site. The solid line is from the data assimilative model and the dashed line is from the synoptically forced version of the model. Assimilation dramatically improves the temperature profile between 50 and 350 m while paying a slight penalty in the upper 50 m of the water column

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    Ten-day streak plots of the currents at 30-m depth from the data assimilative model on 30 May and 19 Jun 1993. The use of synoptic winds allows the model to capture the high variability of the currents which exist during the southwest monsoon

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    Time histories of the mixed layer depth from a simulated station in the central Arabian Sea and the central Bay of Bengal. These results are from the data assimilative version of the model. The mixed layer at 15.5°N, 61.5°E in the Arabian Sea shows strong seasonal modulation with a deep mixed layer during the southwest monsoon and a shallow one during the northeast monsoon. The seasonal modulation in mixed layer depth at 15°N, 90°E in the Bay of Bengal is much smaller

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A Data-Assimilative Numerical Model of the Northern Indian Ocean

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  • 1 Colorado Center for Astrodynamics Research, University of Colorado, Boulder, Colorado
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Abstract

A primitive equation, three-dimensional, baroclinic circulation model has been configured for use in the North Indian Ocean. After having been spun up by climatological winds, the model was used to generate a hindcast for 1993–95 under synoptic forcing, both with and without assimilation of multichannel sea surface temperature (MCSST) and altimetric sea surface height (SSH) anomaly data. Without data constraints, the model captures many of the salient oceanographic features in this region including equatorial surface and subsurface currents, the Laccadive High Eddy, the Great Whirl, and the reversing Somali Current. However, assimilation of altimetric data enables it to depict these features more accurately. MCSST data enable the near-surface layers to be simulated more accurately.

The National Aeronautics and Space Administration TOPEX precision altimeter has provided oceanographers with an important tool to study the variability in the circulation of the world’s oceans. The availability of SSH data from this altimeter provides a unique opportunity to assess the skill of a numerical model. More important, the assimilation of TOPEX altimetric observations, along with satellite-observed sea surface temperatures, greatly enhances the model’s ability to estimate the dynamical and thermodynamic state of the North Indian Ocean. The data-assimilative model provides therefore an additional tool for improving our understanding of the dynamical and thermodynamic processes in this region, through accurate hindcasts of the oceanic state. With the availability of real-time data streams, it also enables estimates of the oceanic state to be made in real-time nowcast/forecast mode.

Corresponding author address: Dr. Joseph W. Lopez, University of Colorado, Campus Box 431, Boulder, CO 80309-0431.

Email: lopezjw@colorado.edu

Abstract

A primitive equation, three-dimensional, baroclinic circulation model has been configured for use in the North Indian Ocean. After having been spun up by climatological winds, the model was used to generate a hindcast for 1993–95 under synoptic forcing, both with and without assimilation of multichannel sea surface temperature (MCSST) and altimetric sea surface height (SSH) anomaly data. Without data constraints, the model captures many of the salient oceanographic features in this region including equatorial surface and subsurface currents, the Laccadive High Eddy, the Great Whirl, and the reversing Somali Current. However, assimilation of altimetric data enables it to depict these features more accurately. MCSST data enable the near-surface layers to be simulated more accurately.

The National Aeronautics and Space Administration TOPEX precision altimeter has provided oceanographers with an important tool to study the variability in the circulation of the world’s oceans. The availability of SSH data from this altimeter provides a unique opportunity to assess the skill of a numerical model. More important, the assimilation of TOPEX altimetric observations, along with satellite-observed sea surface temperatures, greatly enhances the model’s ability to estimate the dynamical and thermodynamic state of the North Indian Ocean. The data-assimilative model provides therefore an additional tool for improving our understanding of the dynamical and thermodynamic processes in this region, through accurate hindcasts of the oceanic state. With the availability of real-time data streams, it also enables estimates of the oceanic state to be made in real-time nowcast/forecast mode.

Corresponding author address: Dr. Joseph W. Lopez, University of Colorado, Campus Box 431, Boulder, CO 80309-0431.

Email: lopezjw@colorado.edu

1. Introduction

The North Indian Ocean is a region of considerable interest to oceanographers and atmospheric scientists principally due to its unique periodically reversing monsoon wind system (see the recent review by Webster et al. 1998). In addition to the scientific interest, the effects of ocean circulation on pollution transport, biological productivity, and commercial operations are also of practical interest. During the boreal winter, winds from the northeast drive the circulation of the North Indian Ocean. During this period, the equatorial circulation resembles that found in the Atlantic and the Pacific. The Somali Current along the Somali coast flows southwestward. With the onset of the southwest monsoon, the currents of the North Indian Ocean change dramatically. The Somali Current reverses and flows northeastward, and a large anticyclonic eddy, the Great Whirl, spins up off the Somali coast. The eastward flowing Indian Monsoon Current transports water masses from the Arabian Sea to the Bay of Bengal. It is the southwest monsoon that is responsible for most of the precipitation over South and Southeast Asia on which depend the food sources of nearly half the world population.

Recent improvements in computer technology have made it possible to apply comprehensive primitive equation ocean circulation models at meaningful resolutions to basinwide problems. The work described here is one of the few applications of a sigma coordinate primitive equation multilevel model to the North Indian Ocean basin. This model generates meaningful estimates of the oceanic state with relatively modest computational resources. The use of a multilevel model has two important advantages over layered models. First, the model has a high vertical resolution, which allows for the study to the vertical structure of the current system. Second, the comprehensive thermodynamics allow for the study of heat transports. Naturally, the overall CPU, storage, and memory requirements of these models are significantly greater than for purely dynamic layered models, which have been hitherto commonly used to investigate processes in the Indian Ocean (e.g., Jensen 1991, 1993;McCreary et al. 1993, 1996; Potemra et al. 1991) and the global circulation. This limits their horizontal resolution, especially when the models are implemented on a high-performance workstation. Fortunately, continuing progress in the development of more powerful computer systems at greatly reduced costs will allow higher-resolution versions of the model documented here to be employed in the very near future.

An altimeter is an important source of data for investigating the circulation of the Indian Ocean and other regions (see Wunsch and Stammer 1998). It measures the sea surface height (SSH) variability at points along ground tracks that are repeatedly visited at fixed intervals. The TOPEX precision altimeter has a repeat period of approximately 9.9 days and measures SSH fluctuations to an rms accuracy of 3–5 cm (Fu et al. 1994). The TOPEX data contain the signatures of many important oceanic mesoscale features. For example, the Great Whirl and Soccotra Eddy are both clearly visible in the gridded TOPEX data from cycles 33 and 34 shown in Fig. 1. The small squares indicate the estimated centers of these features based on in situ observations reported by Fischer et al. (1996). The observations of these featuers by altimetry and in situ observations are consistent, adding to the confidence we can place in the altimeters ability to locate and define mesoscale features. An obvious advantage of the altimeter is the greater spatial coverage relative to very limited in situ observations. An important use of altimetric data is as a check of numerical model results. Comparisons of SSH anomalies from the altimeter and model allow us to identify the situations in which the model successfully captures mesoscale features. While TOPEX data cannot provide estimates of quantities such as velocity directly, a dynamical model can and this is an important asset. However, the skill of even the best models in depicting the evolution of circulation and its variability is limited by the nonlinear nature of dynamical processes. Therefore, the assimilation of TOPEX data into the numerical model has the potential to improve the model skill and to make realistic estimates of the oceanic state in both hindcast and nowcast modes possible (e.g., Choi et al. 1995).

2. The numerical model

The model used in this study is the University of Colorado (CU) version of the sigma-coordinate, free surface, primitive equation Princeton Ocean Model (POM) originally developed by George Mellor’s group at Princeton (Blumberg and Mellor 1987). The core model has been previously documented by Blumberg and Mellor (1987) and Mellor (1992), and the curvilinear version by Kantha and Piacsek (1997). Ezer and Mellor (1994a) have applied this model to the North Atlantic. We refer to the University of Colorado version of the model as CUPOM. The CUPOM (Kantha and Piacsek 1993, 1997) differs from the original POM in that it has a better mixed-layer parameterization (Kantha and Clayson 1994), and has an optimal interpolation (OI)-based data-assimilation module (Choi et al. 1995;Bang et al. 1966; Kantha 1999) that is especially well suited to assimilating altimetric data [in addition to other remotely sensed data such as multichannel sea surface temperature (MCSST), and in situ data such as XBTs and CTDs]. The model also capable of incorporating river runoff. It has bean successfully applied at CU to nowcast/forecasts in the Gulf of Mexico (Choi et al. 1995; Kantha at al. 1999), studies in the tropical Pacific (Clayson 1995), the North Indian Ocean (Lopez 1998; Lopez and Kantha 2000), and the North Pacific (Engelhardt 1996). The operational versions of it are used at Naval Oceanographic Office (NAVO) for the Mediterranean Sea (Horton et al. 1997), the Red Sea (Clifford et al. 1997), the Baltic Sea and the Persian Gulf (Horton et al. 1991, 1992). A Yellow Sea version of it at the Naval Research Laboratory (NRL) has been transitioned recently to NAVO (Jacobs et al. 1998). In the Japan Sea itself, the model has been applied to studies of interannual variability (Suk and Kantha 1997) and for hindcast studies (Bang et al. 1966) using a nowcast/forecast system based on altimetric SSH and MCSST assimilation. Many details of the model and the modeling system can be found in the references cited above. The focus here is on model features that have not been previously documented and on those features specific to this implementation.

The North Indian Ocean model has a moderate horizontal resolution of ½° × ½° but a high vertical resolution consisting of 38 sigma levels. The majority of these levels are located in the upper layers to better depict the mixed-layer processes and the equatorial and near-equatorial surface current system. For example, in a water column 4000 m deep, the upper 250 m contains 29 levels. This approach differs from previous modeling efforts for this region, in that the emphasis is on the vertical structure of water masses and currents in the upper layers, whereas the earlier efforts using principally the layered model had generally greater horizontal resolution, but limited vertical resolution. In the near future, with improvements in available computing resources, the model will be run at ¼° × ¼° resolution.

The model domain, shown in Fig. 2, extends from 20°S to 26°N and 39° to 120°E. While the model domain includes the South China Sea, the results there are not as realistic as in the rest of the domain because of the closed eastern boundary along the South China Sea. The southern boundary is placed at 20°S so as to encompass the equatorial waveguide. The western boundary coincides roughly with the African coast and the eastern boundary with Australia and Indonesia. Because of the emphasis on surface layers, the Red Sea and the Persian Gulf are not included. Along the eastern boundary, velocities, temperature, and salinity are specified for the passage between Australia and Indonesia to account for the Indonesian throughflow. The mass entering through this passage, along with that from the rivers described below, is removed uniformly along the southern boundary. The volume flux through the Indonesian Throughflow is prescribed from values presented by Garternicht and Schott (1997) and are shown in Fig. 3. These values are monthly means derived from a global model encompassing 1987–89.

A simple river model has been added to account for the freshwater flux from the rivers in the region. These fluxes are especially important in the Bay of Bengal, where surface waters are significantly lower in salinity than those in the Arabian Sea. The Indus river in the Arabian Sea also carries a significant amount of freshwater. When possible, monthly average river flux values from a UNESCO database (UNESCO 1993) have been used. For the Irrawaddy, Salween, and Hong (Red) rivers, the fluxes are based on a yearly average (Berner and Berner 1987). The river fluxes are specified via lateral boundary conditions at the grid cells which contain the actual river locations. The rivers included in the model are shown in Table 1.

We do not include at present the saline water outflows from the Red Sea and the Persian Gulf. These are of obvious importance to the water mass structure in the Arabian Sea. However, since our focus is principally on the upper layers and their dynamics and thermodynamics, the omission is justified. It is unlikely that these outflows affect the upper mixed layer characteristics, although some studies using layered models with a limited number of layers and a simple embedded bulk type mixed layer appear to suggest that the mixed layer might be affected somewhat by these outflows. The most optimum way to include these outflows in this model is to explicitly resolve these marginal seas and this requires a higher spatial resolution than the ½° resolution currently used in the model.

The model bottom topography is derived from the 5′ resolution ETOP05 database. A nonlinear filter was used to mitigate the topographic gradients that could otherwise cause spurious along-slope currents in a sigma coordinate model (Haney 1991; Mellor et al. 1994; Mellor et al. 1998). During model spinup, the model was forced by the 2° resolution monthly climatological wind stress from Hellerman and Rosenstein (1983) and surface temperature and salinity were damped to the seasonal climatological sea surface temperature (SST) and sea surface salinity (SSS) values of Levitus. The model was initialized with temperature and salinity data from Levitus (1984). Starting from rest, the model was run for a period of 4 yr and 10 months using climatological forcing. In preparation for the 1993 model runs, the last two months of the spinup used 1992 winds from the European Centre for Medium-Range Weather Forecasts (ECMWF) and the surface temperature was damped to weekly MCSST observations. The ECMWF 10-m wind product is converted to a stress using the formulation from Smith (1980). For wind speeds less than 6 m s−1 drag coefficient (Cd) of 1.1 × 10−3 is used. For higher values, Cd = (0.61 + 0.063u) × 10−3 was used.

A longstanding challenge to numerical ocean modelers has been to accurately account for the exchange of heat and moisture between the air and sea. Inevitable biases in flux models and fluxes can lead to significant errors in the sea surface temperature and the density in the upper layers of the water column. Precipitation over the tropical oceans is now being measured by the NASA Tropical Rainfall Measuring Mission (TRMM), which will provide a means of better describing the air–sea moisture fluxes. At present, fluxes computed using bulk formulations are used to drive the model. However, the availability of observed sea surface temperatures, collected by satellites, in the form of MCSST products, provides a means of correcting or replacing the heat flux prescription in numerical models.

In a hindcast mode, the model surface temperature could be damped to MCSST observations to obtain a realistic SST. However, this technique would not capture the temperature fluctuations which occur on short timescales, such as the daily fluctuation which results from incoming short wave radiation. Unfortunately, SSTs of models which rely solely on observed or modeled surface fluxes tend to drift from reality due to unavoidable biases in the forcing data. By assimilating observed MCSST and including surface heat fluxes from a simple model, a reasonable SST can be maintained while capturing short timescale fluctuations.

The observational sea surface temperature data assimilated into the model was obtained from the Physical Oceanography Distributed Active Archive Center (PO.DAAC) at the Jet Propulsion Laboratory. The dataset used here contains weekly composite MCSSTs from the NOAA Advanced High Resolution Radiometer (AVHRR). The data are on an equal angle grid (1024 × 2048) that has a resolution of approximately 18 km × 18 km at the equator. The data were prepared by the University of Miami/Rosenstiel School of Marine and Atmospheric Sciences (RSMAS). Additional information about the dataset is presented by McClain, et al. (1985) and Olson et al. (1988). The data are placed onto the model grid by evenly weighting all of the available observations within a model cell.

In some versions versions of this model and a similar one used in the Gulf of Mexico (Choi et al. 1995), surface temperatures were damped to MCSST observations in place of calculating surface energy fluxes. In those configurations, damping with 2–5-day timescales provided reasonable SSTs. However, with the inclusion of surface fluxes, where the observations are intended to remove long-term biases, the surface temperature must be nudged to the observations on shorter timescales. If timescales on the order of a day are not used, the fluxes overwhelm the assimilation of the MCSST observations, since the heat exchange due to surface damping is two orders of magnitude smaller than that due to surface fluxes.

A simple model, presented by Weare et al. (1980), is used to calculate the three components of the surface heat flux: latent heat, sensible heat, and longwave radiation. The advantage of this model is that the fluxes are only a function of the sea surface temperature. The long wave and sensible heat terms are modeled together as being proportional the surface temperature. The usual bulk formulation for the latent heat flux is used with the assumption of a constant humidity value. The latent heat (LH) flux is given by
QLHρaCELwδqs
where ρa is the density of air, CE is the exchange coefficient with a value of 1.5 × 10−3, L is the latent heat of evaporation, w is the wind speed, and qs is the saturation humidity of air evaluated at the ocean surface temperature. The long radiation and sensible heat (SH) fluxes are modeled by
QLR/SHαTsT
where Ts is the ocean surface temperature and T* is 0°C. The value of α is 1.67 W °C−1 m−2. These values are similar to those used by Chen et al. (1994). The value of T* was adjusted by trial and experiment to reduce the amount of damping required to maintain a reasonable SST.

The solar radiation portion of the Weare model is replaced with a more comprehensive model developed by Paul Martin at NRL. This model accounts for the time of day, time of year, cloud fraction, and surface albedo as a function of the incident angle.

The incoming shortwave radiation model requires an estimate of the cloud cover. Monthly cloud fraction statistics are available from the National Climatic Data Center. These statistics are derived from observation from the Special Sensor Microwave/Imager (SSM/I) used by the Defense Meteorological Satellite Program (DMSP). The 1° × 1° monthly averaged data were bi-linearly interpolated onto the model grid. The data set is describe in detail by Ferraro et al. (1996).

There are three external sources which affect the surface salinity. The modeling of the river fluxes has already been described. The other two sources are precipitation and evaporation. Monthly averaged precipitation data was provided by Ping Ping Xie at NOAA (Xie and Arkin 1995, 1997). The data are bilinearly interpolated from the original 2.5° × 2.5° onto the final model grid. The dataset contains the total rainfall for each month, which is converted into a constant rainfall rate for use with the ocean model. The latent heat flux model provides the mass of water that evaporates from the surface. The surface salinity is damped toward climatology using a 2-day timescale to prevent unreasonable salinity values, which could result from unavoidable errors in the salt flux model.

3. TOPEX assimilation

It is desirable, as is done with numerical weather forecasting models, to assimilate observed data into a model to nudge it toward reality. It has been demonstrated that anomalies in the vertical temperature profile can be estimated from altimeter measured surface height anomalies (Carnes et al. 1990). Since one of the obstacles to performing data assimilation has been a dearth of observational data, the use of pseudo-temperature profiles (BTs) from altimetric observations has important implications in numerical ocean modeling. Pseudo-BTs have been applied to a study of the Gulf of Mexico using a data assimilative numerical model (Choi et al. 1995) resulting in greatly improved estimates of the oceanic state. Ezer and Mellor (1994b) have also assimilated pseudo-temperatures into a sigma coordinate model of the Gulf Stream and have obtained encouraging results.

The functional relation between the satellite observed SSH anomaly and the synthetic temperature profile of the water column is determined through an empirical orthogonal function (EOF) analysis of historical temperature and salinity data in the region of interest. With the mean temperature profile removed, amplitude coefficients and the EOF modes of the temperature anomaly are determined using singular value decomposition. From the amplitude coefficients and the EOF modes, the original data set can be recovered. Only a few modes need be retained since over 96% of the variability is contained in the first six modes for the regions of the Indian Ocean investigated here, with the first mode contributing the lion’s share of this. From each temperature profile, the surface dynamic height is calculated. Using the amplitude coefficients from the EOF analysis and the surface dynamic height anomaly, a third-order polynomial regression is used to determine a functional relationship between the amplitude coefficients and the surface dynamic height anomaly.

The EOFs for the North Indian Ocean were determined through analysis of measured temperature and salinity casts contained in the World Ocean Atlas 1994 from the National Oceanographic Data Center (NODC 1994). The data for each cast are available at both observed depths and standard depths. For this analysis, the standard level data were used. The dataset was checked for duplicate profiles and quality controlled. Since the water properties vary greatly in different regions of the North Indian Ocean, a separate analysis was performed for the Arabian Sea, Bay of Bengal, and the Equatorial Indian Ocean regions. Unfortunately, there is not sufficient data presently available to perform the analysis on smaller regions. Since water properties vary spatially, it would be desirable to perform a separate analysis over 5° or 10° boxes. This could be especially important in regions such as the extreme northern Bay of Bengal where the water properties vary greatly over relatively short distances due to the large influx of fresh water from rivers.

Along-track observations from the TOPEX altimeter were assimilated into the model on a continuous basis. No Poseidon observations are used. Pseudo-BT profiles were derived at each along track point from the TOPEX sea surface height anomaly measurements. A pseudo-BT profile at each model grid point with a depth of 1000 m or greater is determined from the along track profiles using optimal interpolation. Using OI requires the inversion of a matrix for each model grid point. To limit the size of the matrix, and therefore save computing resources, the OI procedure used only the 10 most correlated along track points. Once a pseudo-BT profile has been found for each model grid point, the model temperature field is nudged toward the TOPEX derived temperature profile. The assimilated temperature field is given a weight of 0.02. The assimilation routine begins every 6 h and is continued for a period of 2.4 h. Only TOPEX measurements that are within ±5 days of the current time step are used. Based on an analysis of the dynamic height anomalies used to derive the pseudo-BT coefficients, TOPEX SSHA outliers with a magnitude of 30 cm or more are discarded. The details of the assimilation strategy are shown in an appendix to this paper.

4. Computational requirements

It is only within the past few years that it has become practical to run comprehensive basin scale ocean models on desktop workstations. Prior to this, a super computer, such as a Cray T-90, was required to do any significant work with this type of model. The North Indian Ocean code, with a 163 × 93 × 38 model grid, is run on a DEC Alpha workstation with a clock speed of 433 MHz, and 512 MB of system memory. With this configuration, the model without assimilation runs at a rate of 8.2 model days per CPU hour. On a Cray C-90, the approximate rate is 40 model days per CPU hour. The inclusion of data assimilation increases the run time by roughly 50%. The model requires 130 MB of RAM in the stand-alone mode and 180 Mbytes of RAM in the data assimilative mode.

Regardless of the platform on which the model is executed, sufficient storage for the results is also required. For the Indian Ocean configuration, each three dimensional field requires 2.3 MB per time step saved. Clearly, the frequency of model output and the model fields to be saved must be judiciously chosen. The strategy shown in Table 2 was employed to retain sufficient data to conduct meaningful analysis while minimizing the amount of data retained. Ideally, the three dimensional model fields would be saved at frequent enough intervals that processes at all timescales could be analyzed at any model location. However, the size of the resulting dataset makes this impractical. In an effort to retain enough data to perform analysis of processes with short timescales, high-frequency saves are made of 37 vertical profiles and three cross sections of interest.

5. Example model results

With regards to currents, the use of data assimilation has to important effects. The first is to improve the currents below the mixed layer. The second is to properly locate, and in some cases strengthen the circulation about, important circulation features. Examples of these improvements are briefly described here.

The use of assimilation improves the definition of subsurface features, such as the Equatorial Undercurrent. For example, at 70°E, Molinari et al. (1990) report westward zonal velocities in the undercurrent on the order of 75 cm s−1 during the month of December. Figure 4 shows the model results from both the no-assimilation and assimilation runs for 26 December of 1993 at a nearby section. The former shows a maximum velocity of 30 cm s−1, well below the observations reported by Molinari et al. (1990). In the assimilation results, the maximum velocity in the undercurrent is greater than 60 cm s−1, which is in much better agreement with observations. Note that core of the undercurrent is found within ±3° of the equator.

Fischer et al. (1996) have reported observed currents and water mass properties in the Somali basin collected over the period 11–22 August 1993. Extensive measurements were made in the regions of the Great Whirl and the Socotra Eddy. This dataset provides an opportunity to assess the improvements that result from data assimilation. Figure 5 shows the near surface currents (25 m) measured by ADCP during the cruise. Also shown is the 25°C isotherm contour, which roughly defines the locations of the Great Whirl and Socotra Eddy. Figure 6 shows SST contours for two time periods during the cruise. The two cold wedges shown in the SST plot identify the location where currents from the Southern Gyre and Great Whirl separate from the coast.

Figure 7 shows the currents at 30 m from the no-assimilation and the assimilation runs for 18 August 1993. This falls into the time period during which the observations were made. Numerous differences between the two model runs are evident. Perhaps the most significant difference is that the Great Whirl and Southern Gyre are more distinct features in the assimilation run. The Southern Gyre is not always present, but observations over numerous years show that when it is, a portion of the Somali Current turns offshore between 4° and 6°N (Knox 1987). Although no acoustic doppler current profiler (ADCP) measurements were made in the region of the Southern Gyre, a wedge of cold water along the African coast near 5°N shows the northern edge of the Southern Gyre. This is consistent with the currents from the assimilation runs.

The northward extent of the Somali Current is also modified by the assimilation procedure. Without assimilation, the maximum northward extent of the current is about 10°N. The current between the African coast and the island of Socotra is to the southeast. With assimilation, the northward current extends to 14°N before turning to the east. The current between the continent and Socotra is to the north. The ADCP measurements show that the current flows to the north-northwest. Therefore, the assimilation run is in better agreement with the observations.

Assimilation shifts the center of the Socotra Eddy north to 11°N and east to 57°E in a manner consistent with the ADCP observations. In the assimilation results, a cyclonic eddy is present between the Great Whirl and the Socotra Eddy. While this eddy is not clearly shown in the ADCP measurements, its location is consistent with the current shear observed near 55°E on the 8°N section shown in Fig. 5.

The formation of an anticyclonic feature in the South Arabian Sea called Laccadive High during the northeast monsoon off the west coast of India (Bruce et al. 1994, 1998) is an important aspect of the circulation in the Arabian sea. The model simulation of the Laccadive Eddy and its variability has been reported elsewhere (Lopez and Kantha 2000).

The technique used here improves the circulation through adjustments to the temperature gradients and hence density gradients. While this has the desired effect of improving the model’s skill in capturing realistic circulation features, the procedure can be detrimental to the upper-ocean thermodynamics and mixed-layer response. Figure 8 shows the time histories of the temperature in the upper 250 m at 15.5°N, 61.5°E from each of the model runs. This location coincides with a mooring from the Arabian Sea Experiment which was in place from October 1994 through October 1995. The observational data for temperature and salinity are shown in Fig. 9 (Fischer and Weller 1996).

The temperature results from the run with no data assimilation show general agreement with the observational data. Throughout the time period of the observations, the model obtains thermocline depths similar to those seen in the observations. Generally, the model temperatures are higher than is seen in the observations. The model and observations both show deep mixing during the 1995 southwest monsoon and an abrupt shoaling of the mixed layer in August of 1995. The results from assimilation show that at depths below 100 to 150 m, the model temperature field is in better agreement with the observations than that from the model without data constraints. However, in the near-surface waters, the temperature profile is clearly degraded by assimilation. Additionally, mixing is suppressed.

With one of the long-term goals of this modeling effort being to couple the data assimilative ocean model to an atmospheric model, the degraded upper-ocean thermal structure is unacceptable. For a coupled model to give good results, the SST, the upper-ocean heat content, and mixed layer depth must be accurately captured by the ocean model (Bao et al. 2000). Also, reliable estimates of oceanic heat transports cannot be made with the degraded temperature field.

The assimilation results in an improvement in the currents and in the subthermocline thermal structure. It is desirable to retain these benefits without degrading the near surface temperature structure. Therefore, the assimilation of the TOPEX derived temperature anomalies was restricted to depths greater than 100 m. The weight of the assimilation changes linearly from zero to the full weight in a transition zone between 100 and 200 m. Figure 10 shows the results from a run in which the assimilation is turned off in the upper 100 m of the water column. Without the TOPEX assimilation in the upper 100 m of the water column, the temperature results adjust to the surface flux forcing and the assimilation of MCSST observations. The thermal structure of the upper layers is greatly improved over the run in which TOPEX assimilation was performed all the way to the surface. Additionally, the benefits of assimilation in improving the model’s skill in capturing mesoscale features are retained, and likely improved.

By restricting the TOPEX assimilation to depths greater that 100 m, the model makes the best use of all the observational data available for assimilation. Recall that the determination of temperature anomalies from TOPEX measured SSHAs is an inverse problem. The relationship between the derived temperature anomalies and height anomalies depends on the statistics of the sample profiles that were used to determine the regression coefficients. Since direct observations of the subsurface temperature structure are not dense enough in time or space, TOPEX derived temperature anomalies are the best information about the thermal structure of the deep waters available for assimilation. However, at the surface, MCSST provides a much more direct means of measuring the water temperature. While there are uncertainties in MCSST observations, a MCSST observation is more reliable than a TOPEX derived temperature anomaly in the upper water column, principally because of the large scatter in the near-surface data that affects the EOF analyses.

Figure 11 shows the mean of the absolute error of the model results relative to the temperature observations at the Arabian Sea mooring site. The solid line is from the data assimilative model and the dashed line is from the synoptically forced version of the model. The assimilation results show the greatest improvement between 50- and 350-m depth. In this region, the reduction in error is significant. Between 100 and 200 m, the reduction in error is on the order of 3°. The synoptically force model still has a small advantage over the assimilation model in the upper 50 m. This is only a single point check. However, the assimilation procedure is clearly improving the results at this point. As more data becomes available, similar comparisons will be conducted at other locations.

Figure 12 shows sample results from the data-assimilative model. Intraseasonal variability in circulation depicted by the model can be seen in plots of the surface current snapshots for 30 May 1993 and 19 June 1993 in Fig. 12. A rich spectrum of variability due to the synoptic nature of the wind forcing can be seen. In future work, we will examine fluxes of heat and salt in the Northern Indian Ocean. The models ability to capture intraseasonal variability in circulation will be fundamental in studying the intraseasonal variability of heat and salt fluxes.

Assimilating MCSST observations at the surface, and TOPEX observations in the subsurface waters, as demonstrated here, improves the model skill with respect to both circulation and the water column thermal structure. More accurate estimates of oceanic state are possible and this enables studies of aspects such as the heat and mass transports and circulation variability. While analyses are routinely used in the atmosphere to study atmospheric processes, until recently, oceanographers have relied primarily on numerical models running without data assimilation for studies of oceanic processes. With the availability of more data for assimilation, the situation is changing and data-assimilative models are being used for such studies (e.g., Horton et al. 1997). Studies of the variability in the circulation in the North Indian Ocean, and the heat and salt transports during 1993–98, based on the results of the data-assimilative model described in this paper, are under way and will be reported elsewhere (Lopez and Kantha 1999, personal communication). This period includes the 1997–98 ENSO event that led to the most anomalous warming seen this century in the North Indian Ocean (Webster et al. 1999). Figure 13 from this simulation illustrates the differing characteristics of the mixed layer in the Arabian Sea and Bay of Bengal. The mixed layer at 15.5°N, 61.5°E in the Arabian Sea shows strong seasonal modulation with a deep mixed layer during the southwest monsoon and a shallow one during the northeast monsoon, while the seasonal modulation in mixed layer depth at 15°N, 90°E in the Bay of Bengal is much smaller. The influence of freshwater is likely to be the reason for this contrasting behavior.

6. Concluding remarks and future work

A primitive equation baroclinic circulation model has been configured for use in the North Indian Ocean. The results of the model provide additional insight into the oceanic processes of the Indian Ocean. With synoptic forcing, the model captures many of the significant oceanographic features of the region including equatorial surface and subsurface currents, the Laccadive High, the Great Whirl, and the reversing Somali Current. With the proper use of data assimilation, the model depiction of these circulation features is markedly improved.

The data generated are suitable for studying a wide variety of oceanographic processes. One of the advantages of the model used here is the inclusion of salinity. This has made it possible to investigate the exchange of salt between saline Arabian Sea and the unusually fresh Bay of Bengal via the currents of the Equatorial Indian Ocean. The equatorial currents of the Indian Ocean, both at the surface and below, are unique among the world’s equatorial oceans. The high vertical resolution of the model allows for the investigation of the vertical structure of these currents, with special attention being paid to the Equatorial Undercurrent.

The technique used here to assimilate TOPEX SSHA observations improves the circulation through adjustments to the temperature gradients and hence density gradients. While this has the desired effect of improving the model’s skill in capturing realistic circulation features, without proper care, the procedure can be detrimental to the upper ocean thermodynamics and mixed layer response. Since the SST signature is related to the thermodynamic structure of the upper mixed layer, and the altimetric height with the baroclinic structure of the entire water column, we find that it is advisable to assimilate altimetry-derived subsurface temperature anomalies only in the water column below the mixed layer, while the influence of SST on the ML structure is taken into account by an accurate embedded mixed layer model. Assimilating MCSST observations at the surface, and TOPEX observations in the subthermocline waters provides an improvement in the model’s skill with respect to both circulation and thermal structure.

Significant effort was required to configure the model, process the supporting data, and develop the analysis tools that were used to generate and study the datasets presented here. This work provides the foundation for continuing modeling efforts in the North Indian Ocean. Some of this work has already begun. For example, the model has been coupled to the Mesoscale Meteorological (MM5) atmospheric research model. This coupled model provides an excellent opportunity to examine the air–sea exchange processes which play a critical role in the evolution and variability of the southwest monsoon. The ocean model’s ability to capture the dynamics and thermodynamics of the mixed layer will be critical to the success of any coupled model. Figure 13 from this simulation illustrates the differing characteristics of the mixed layer in the Arabian Sea and Bay of Bengal. The mixed layer at 15.5°N, 61.5°E in the Arabian Sea shows strong seasonal modulation with a deep mixed layer during the southwest monsoon and a shallow one during the northeast monsoon, while the seasonal modulation in mixed layer depth at 15°N, 90°E in the Bay of Bengal is much smaller. The influence of freshwater is likely to be the reason for this contrasting behavior.

While the model results currently provide good representation of the ocean state, there are undoubtedly improvements that can be made to the model. One area worthy of additional investigation is with regards to the precipitation forcing. The greatest deficiencies in the data set used for this research were found to be in the extreme northern Bay of Bengal. Improved results can also be obtained by running the model at a higher horizontal resolution. The computational power and physical memory of the workstations available to researchers today are significantly greater than was available when the resolution was selected for the current configuration of the model. At that time, a supercomputer was required to run the model. Today, a desktop workstation is capable of running the current model version or an improved ¼° version of the model.

The example results presented here are from running the model in a hindcast mode. It is a relatively straightforward procedure to transition the model into a real-time nowcast/forecast mode. The greatest challenge is to obtain the required forcing data and prepare it for use by the model in a timely fashion. The details of using the model in the nowcast mode, and some example results, will be presented in a follow-up paper.

Finally, a comprehensive circulation model, such as that used in this study, generates voluminous amounts of data that present difficulties in interpretation solely in the form of static snapshots and averages. Many of these results are best visualized as animations. The interested reader can find these animations online at http://www-ccar.colorado.edu/∼lopezjw.

Acknowledgments

JWL acknowledges with pleasure the support by NASA Graduate Student Fellowship Program Contract NGT-70389, and LHK, the support by NOMP program of the Office of Naval Research under Contract N00014-95-1-0343. The authors also wish to thank Jim Hendricks for his assistance in the processing of the TOPEX data used here.

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APPENDIX

The Data Assimilation Scheme

Temperature anomalies are computed from the TOPEX measured SSH anomalies and the first six EOF modes. The weight of each mode (An) is a function of the measured SSH anomaly. The relationship between the SSH anomaly and the weight is a fourth-order polynomial with coefficients determined by analysis of the dynamic heights of each cast used in the EOF computations:
i1520-0426-17-11-1525-ea1
At the location of each TOPEX observation, model sigma level temperatures are converted to z level by interpolation. The residuals relative to the model temperatures are computed using Eq. (A2):
Tresn, zTanomn, zTn, zTmodeln, z
The bias in Tres(n, z) is computed at each model grid point. The bias is then removed from the residual:
i1520-0426-17-11-1525-ea3
where Rn is the e-folding weight. The OI values at each grid point will be found from Tunbias(n, k).
Rni, jed2/a2et2/b2
In Eq. (A5), the spatial decay scale is a, the temporal decay scale is b, the distance between the observation point and the model grid point is d, and the time difference between the observation time and the model time is t.
The N most correlated observations are found by sorting Rn(i, j). In this implementation, the 10 most correlated points are used. The covariance matrix between all pairs of the retained observations is computed using Eq. (A6):
Clmi, jep2/a2eq2/b2l, mN.
In Eq. (A6), p is the distance between observations and q is the time between observations. After computing the inverse of Clm, Toi is computed using Eqs. (A7) and (A8):
i1520-0426-17-11-1525-ea7
Tres(i, j, k) is computed by adding Tbias(i, j, k) to Toi(i, j, k)
Tresi, j, kToii, j, kTbiasi, j, k
Here, Tres(i, j, k) is converted back to sigma levels and then used to compute the new model temperature, Tnew(i, j, k):
Tnewi, j, kTmodeli, j, kαTmodeli, j, kTresi, j, k
In Eq. (A10), α is the insertion rate. Here we use an insertion rate of 0.02.

Fig. 1.
Fig. 1.

Observations of the Great Whirl and the Socotra Eddy from the TOPEX altimeter. The small squares indicate the estimated centers of these features based on in situ observations reported by Fischer et al. (1996). The contour interval is 5 cm

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Fig. 2.
Fig. 2.

The model domain and major current systems of the North Indian Ocean during the two monsoon seasons

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Fig. 3.
Fig. 3.

Values of the volume flux through the Indonesion Throughflow as prescribed in the model. Values are from Garternicht and Schott (1997)

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Fig. 4.
Fig. 4.

Model results from both the synoptic and assimilation runs for 26 Dec 1993 along the 77°E section. The former shows a maximum velocity of 30 cm s−1, well below the reported observations. In the assimilation results, the maximum velocity is greater than 60 cm s−1, which is in much better agreement with observations

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Fig. 5.
Fig. 5.

Currents at 25-m depth from the shipboard ADCP collected during Aug 1993. Reproduced from Journal of Geophysical Research, Fischer et al. (1996)

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Fig. 6.
Fig. 6.

Sea surface temperature distribution on 13, 18 Aug 1993. The data are from Brown, Rosenstiel School of Marine and Atmospheric Sciences, University of Miami. Reproduced from Journal of Geophysical Research, Fischer et al. (1996)

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Fig. 7.
Fig. 7.

Streak plots of the currents at 30 m in the Arabian Sea on 18 Aug 1993. The use of assimilation improves the model’s ability to capture the correct location of the Great Whirl

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Fig. 8.
Fig. 8.

Time histories of the temperature at the mooring site of the (top) Arabian Sea Experiment from the model synoptic and (bottom) assimilation runs. Including assimilation in the upper layers degrades the model’s ability to capture the thermal structure of the upper ocean

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Fig. 9.
Fig. 9.

Temperature observations from the Arabian Sea Experiment. The mooring is at 15°30′N, 61°30′E. The measurements provide an excellent opportunity to compare the model results to actual observations (Fischer and Weller 1996)

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Fig. 10.
Fig. 10.

Time histories of the temperature at the mooring site of the Arabian Sea Experiment from the (top) model synoptic and (bottom) assimilation runs. In this case, there is no assimilation of TOPEX measurement above 100 m. By excluding the assimilation in the upper layers, the model obtains both an improved thermal structure and improved currents

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Fig. 11.
Fig. 11.

Mean absolute error of the model results as a function of depth at the Arabian Sea mooring site. The solid line is from the data assimilative model and the dashed line is from the synoptically forced version of the model. Assimilation dramatically improves the temperature profile between 50 and 350 m while paying a slight penalty in the upper 50 m of the water column

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Fig. 12.
Fig. 12.

Ten-day streak plots of the currents at 30-m depth from the data assimilative model on 30 May and 19 Jun 1993. The use of synoptic winds allows the model to capture the high variability of the currents which exist during the southwest monsoon

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Fig. 13.
Fig. 13.

Time histories of the mixed layer depth from a simulated station in the central Arabian Sea and the central Bay of Bengal. These results are from the data assimilative version of the model. The mixed layer at 15.5°N, 61.5°E in the Arabian Sea shows strong seasonal modulation with a deep mixed layer during the southwest monsoon and a shallow one during the northeast monsoon. The seasonal modulation in mixed layer depth at 15°N, 90°E in the Bay of Bengal is much smaller

Citation: Journal of Atmospheric and Oceanic Technology 17, 11; 10.1175/1520-0426(2000)017<1525:ADANMO>2.0.CO;2

Table 1.

Maximum river discharge and type of data available for the 16 rivers included in the model. Monthly averages are calculated using all available data from the UNESCO database (see references). Yearly averages are from Berner and Berner (1987).

Table 1.
Table 2.

Data archival strategy

Table 2.
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