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| Fig. 1. Model sea surface temperature and surface current on March 28, 2000. |
We have successfully implemented a new Gulf Stream (GS) data assimilation scheme into the NOAA Coastal Ocean Forecast System (COFS) as a part of the Coastal Marine Demonstration Project. The scheme is designed to augment the data assimilation method used operationally in COFS, aiming to improve the representation of the Gulf Stream path and structure in the model. The main thrust [RG1] of the implemented scheme is the use of the observed spatial and temporal stability of the GS density and velocity structure in the cross-stream coordinates. The technique employs the cross-stream temperature and velocity profiles derived from field experiments and the daily-available GS path data.
In this report, we outline the methodology, its implementation into COFS and the real-time data assimilation experiments. We demonstrate an improved skill in nowcasting the position and three-dimensional structure of the Gulf Stream in COFS.
The Coastal Ocean Forecast System produces nowcasts and 24-h forecasts of currents, salinity, temperature and water levels for the U.S. coastal waters. COFS uses the three-dimensional Princeton Ocean Model with the east coast version covering the region from the Florida Straits to Newfoundland.
In the current operational COFS a 24-h nowcast/data assimilation cycle takes place in several steps. It begins with an assimilation of satellite altimetry data. Altimetry data, such as those obtained from Geosat, are available every 7 km along each satellite track, which repeats every 17.05 days. In the COFS domain there are typically only two tracks per day from one satellite. For better coverage, altimetry is used the last 11 days. The altimetry data are interpolated horizontally into the model grid with an Optimal Interpolation (OI)-based algorithm. To project the surface information into the deep ocean model-derived surface to subsurface correlations are used (Mellor and Ezer, 1991, Ezer et al., 1991, Ezer and Mellor, 1994). The correlation functions statistically derived from the model are served for correction of the model's subsurface temperature and salinity fields. Assimilation of altimetry data is performed only at grid points with depths more than 2000 m. More recently, Mellor et al. (1998) implemented an elevation ‘feature’ model for the dynamic height anomaly across the Gulf Steam. Their scheme utilizes the GS path data from 75°W to 65°W provided daily by NAVOCEANO. From 65°W to 50°W a mean GS path obtained during a long-time integration of COFS is used.
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| Fig. 1. Model sea surface temperature and surface current on March 28, 2000. |
In the second step of the operational COFS cycle the assimilation of altimetry data is followed by assimilation of SST data from in-situ and satellite observing platforms (Kelley et al. 1999). In-situ observations are recovered from fixed and drifting buoys, C-MAN stations, and ships. Remotely-sensed observations are MCSST retrievals from the AVHRR sensor onboard the NOAA polar orbiting satellites. The assimilated SSTs are then projected into the mixed layer following the method of Chalikov et al. (1996). The SST assimilation procedure is repeated at each step of the model integration during 24 hours. During this time the velocity field is adjusted to the new temperature, salinity and elevation fields. This process completes the nowcast/data assimilation cycle and produces the initial conditions for the 24-h forecast.
The COFS data assimilation technology has demonstrated an improved representation of the Gulf Stream system in the model. However, there is still a limited skill in nowcasting and forecasting the structure and position of the Gulf Steam in the region which spans from approximately 74°W, where the Gulf Stream leaves the continental shelf at Cape Hatteras, to approximately 50°W. For illustration, consider the sea surface temperature and surface current fields (Fig. 1) and sea surface elevation (Fig. 2) after the 24-h COFS assimilation cycle on March 28, 2000. In the COFS model’s output we see a pronounced strong Gulf Stream only near Florida Straits where it is created by the advection of south boundary conditions (a very strong inflow is prescribed here) and where it flows along the east coast. However, once the Gulf Stream leaves the Cape Hatteras it weakens substantially and loses its continuity in some locations. This behavior is not consistent with observations (see below). Fig. 3 shows the Navy’s GS path from 75°W to 65°W (red crosses) on March 28, 2000. We see noticeable differences between the Gulf Stream location in the actual data and in COFS model output. While in the model, the Gulf Stream is more unstable and develops significant meandering, the observations indicate a substantially more stable jet. Our new GS data assimilation scheme, which we describe next helps to improve the representation of the Gulf Stream location and its dynamical structure in COFS.
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| Fig. 2. Model sea surface elevation on March 28, 2000. |
The Gulf Stream region from 74°W to approximately 50°W has been the subject for intensive observational studies. One of the important results of these studies is the discovery of a remarkable spatial and temporal stability of the stream structure. Despite of the vigorous meandering and considerable exchange of waters that takes place between the meandering jet and surrounding waters the dynamical structure of the Gulf Stream is preserved as far as 55°W.
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| Fig. 3. Gulf Stream path (red)
from the Navy’s north-wall data (crosses) combined with climatology on March 28, 2000. |
Based on the analysis of 16 sections of temperature and velocity at 73°W, collected during the Pegasus field experiment, Halkin and Rossby (1985) have concluded that the Gulf Stream has a very well defined dynamical structure which maintains its integrity regardless of its instantaneous position (Fig. 4). A similar dynamical structure of the Gulf Stream appears to persist further downstream as well. Hall and Fofonoff (1993) observed the same structure in a CTD section across the Gulf Stream at 68°W, acquired in late March of 1988. Johns et al. (1995) analyzed the structure of the Gulf Stream at 68°W using the direct current meter observations from 13-mooring array deployed from June 1988 to August 1990 (SYNOP Central Array). Their analysis was based on a "stream-coordinate" approach, in which velocities are rotated into a local, downstream coordinate frame and averaged according to their relative cross-stream location within the current. The along-stream velocity structure of the stream revealed by this analysis was found to be very similar to the velocity structure at 73°W obtained by Halkin and Rossby (1985).
Bower and Hogg (1996) performed a stream-coordinate analysis of the Gulf Stream synoptic structure at 55°W similar to that of Johns et al. (1995) at 68°W. The observations used for this analysis were obtained from an array of 13 current meter moorings deployed near 55°W (SYNOP Eastern Array). The resulting along-stream velocity structure was found to be similar to the structure at 68°W.
A remarkable temporal stability of the Gulf Stream structure was also observed during both Pegasus and SYNOP experiments. The long-term stability of the Gulf Stream was the primary focus of the Oleander project (Rossby and Gottlieb, 1998). Rossby and Gottlieb processed twice-weekly cross section data between New Jersey and Bermuda, in the upper 300 m and found that the maximum velocity of the GS, surface integral of the high velocity core, and width of the core had remained stable to within a few percent over 4.5 years.
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| Fig. 4 Cross-section of temperature and velocity from Pegasus data |
The new GS data assimilation scheme is based on a “feature modeling” approach that utilizes the observed spatial and temporal stability characteristics of the Gulf Stream. In particular, our main assumption is that the cross-stream temperature and velocity in the upper and main thermocline change insignificantly along the GS path.
We briefly outline here the essence of the scheme and its implementation into the COFS operational nowcast/data assimilation cycle described earlier. The present GS data assimilation procedure consists of several steps and is implemented after the SSH assimilation, but before the SST assimilation.
Once the SSH assimilation is completed, the temperature and salinity fields are interpolated from the COFS curvilinear horizontal grid and vertical sigma levels into a uniform 0.2° resolution grid and vertical 31 z-levels. This grid system is similar to that used by the Navy’s Optimum Thermal Interpolation System (OTIS). As illustrated above, the Gulf Stream structure east of 75°W is often poorly resolved in COFS. Therefore, we first apply a filtering procedure (Kurihara at el. 1993) to remove the temperature and salinity gradients associated with the Gulf Stream in the model. The following smoothing operator is applied in the latitudinal direction (similar operator is applied in the longitudinal direction)
(1)
where K is a filtering parameter defined as
(2)
In the course of successive applications of (1), m in (2) sequentially varies as 2, 3, 4, 2, 5, 6, 7, 2, 8, 9, 2. If the above filtering operator is applied to a field of sinusoidal waves, components with less than 1.8° wavelengths will be completely filtered out and the amplitudes of those with 3°, 4°, and 6° wavelengths will be reduced by 82%, 60%, and 32%, respectively. This filtering operator is applied for all z-levels.
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| Fig.5 Model sea surface temperature
and surface velocity on March 28, 2000 after the Gulf Steam data assimilation. |
We then construct a continuous GS path for the entire COFS domain from 81°W to 50°W. This is done by combining the climatological GS path data from 81°W to 75°W (Leaman et al. 1989), the NAVOCEANO daily GS path data from 75°W to 65°W, and a mean GS path obtained from a long-term integration of COFS east of 65°W (Mellor et al., 1998).
In the next step we generate a sequence of cross-sections normal to the GS path with 0.1° increments along the GS path. Each cross-section is divided by 40 points separated by 0.1° (20 points on each side of the Gulf Stream). The temperature and salinity fields are then interpolated onto these points at each z-level using a bi-linear interpolation. After creating the cross-stream sections we sharpen the temperature and salinity gradients along each cross-section according to the observational data obtained in the PEGASUS and SYNOP field experiments as shown in Fig. 4. Note that the gradients are modified only in the region limited by ±0.8° from the GS path. Finally, we use an iterative procedure to further adjust the temperature and salinity fields in order to make the downstream surface velocity in each cross-section the same as the one observed at 68°W (Johns et al., 1995). We assume here that the density and velocity fields are in the geostrophic balance and have zero velocity at the bottom. The obtained temperature and salinity fields are then interpolated back into the COFS grid system. Our scheme makes no adjustments to the COFS velocity field. We have found that the velocity field adjusts to the new density field quite rapidly.
Once we create the new three-dimensional temperature and salinity fields we proceed with the 24-h SST assimilation cycle as described in section 2.
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| Fig. 6 Model sea surface elevation
on March 28, 2000 after the Gulf Steam data assimilation. |
We have successfully tested our scheme in real-time during the CMDP Demo 2 in February and March of 2000. The model was run in parallel to the operational COFS. The nowcast SST, SSH and current fields were evaluated daily and compared to the operational products.
The implementation of the GS data assimilation scheme has demonstrated significant improvement in nowcasting the position and three-dimensional dynamical structure of the Gulf Stream. For illustration, Fig. 5-6 show surface temperature, velocity and surface elevation fields for March 28, that are analogous to Fig. 1-2. One could see that the representation of the Gulf Stream has been improved significantly by the new scheme compared to the operational COFS. The Gulf Stream shown in Fig. 5-6 is continuous and strong over the entire COFS domain, which is consistent with the observations. Also the GS path in the model is in good agreement with the Navy’s north-wall data shown in Fig. 4. Thus, we can conclude that the data assimilation methodology based on the “natural” features of the Gulf Stream offers a better skill of field nowcasting and improves the initial conditions for the GS forecasting.
Gulf Stream data assimilation technique demonstrates a significantly better model representation of the Gulf Stream using COFS. We plan to implement this method into the operational version of COFS after some final testing. Additional work will be required to make the integrated system work in a fully automated mode. Some improvements under consideration include the initialization of not only the Gulf Stream structure but also the Deep Western Boundary Current, the Southern and Northern Recirculation gyres, the Slope water gyre and the Rings as suggested by Robinson and Gangopadhyay (1998), Gangopadhyay et al. (1997).
The melding of data and dynamics via assimilation of observations into coastal ocean observing and prediction systems provides a powerful new methodology of field estimation. We believe such systems would significantly accelerate progress in coastal ocean science as well as enhance the capabilities for efficient and comprehensive coastal zone management and operations.
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