Non-Inertial Flow in NSCAT Observations of Tehuantepec Winds
Mark A. Bourassa and James J. O'Brien
Center for Ocean-Atmospheric Prediction Studies (COAPS), Florida State University
The first satellite images of Tehuantepec winds were observed with the NASA scatterometer (NSCAT) on the ADEOS satellite. Tehuantepec winds flow South through the Chivela Pass into the Gulf of Tehuantepec (Fig. 1), and often extend more than 5 degrees into the Pacific. These winds have a large impact on the local sea surface temperatures [Strumpf, 1975b; Stumpf and Legeckis, 1977; Legeckis, 1988; Barton et al., 1993; Trasviña et al., 1995; Schultz et al., 1997]. These winds also enhance fishing productivity by bringing nutrient rich waters to the surface [Fiedler, 1994]. NSCAT observations can be gridded and used to examine the strength, extent, and variability of wind related events on a wide range of scales: meso-scale events such as Tehuantepec winds, synoptic events such as hurricanes and typhoons, and planetary scale events such as El-Nino Southern Oscillation. NSCAT's fine temporal and spatial resolution is used herein to study features of the Tehuantepec winds (Tehuantepecers or Tehuanos) that have not been previously observed.
An averaging technique is developed to observe day by day changes in NSCAT surface wind patterns. The sampling characteristics of scatterometers, aboard polar orbiting satellites, are non-homogeneous on the time scales of interest [Chelton and Schlax, 1994]. A technique has been developed to fill gaps in coverage and to produce derivative fields (e.g., curl and divergence) that do not show the sampling pattern. Several characteristics of the averaging technique presented herein are investigated. The resulting fields are used to examine the trajectories of surface winds generated by Tehuanos in the presence of Hurricane Marco.
Previous observations of Tehuanos have been indirect (from sea surface temperatures and cloud motion) or interpolated from sparse ship observations. Relatively weak wind events that last for less than several days do not significantly modify the SSTs [Barton et al., 1993]. Therefore, SSTs cannot be used as a proxy for either the magnitude or location of short lived Tehuanos. It will be shown that, on the time scales of the influence of tropical storms, the gap winds can turn to the left, rather than to the right as would be expected from inertial flow in the northern hemisphere. In the extreme case of Hurricane Marco, the Tehuanos turns to the left and passes through the Gulf of Papagayo and over Nicaragua's lake district to enter the Caribbean Sea. NSCAT observations provide added insight to short term variations in the wind pattern, the extent of the influence of Marco on Tehuanos.
2.1 NASA Scatterometer
NSCAT is an active microwave sensor that measures the strength of signals backscattered from water waves. A preliminary comparison [Bourassa et al., 1997], of NSCAT winds to equivalent neutral winds determined from research vessel observations, found that the wind speeds were accurate to 1.5 m s-1, and (with some qualifying statements unique to scatterometry) the wind directions were accurate to 15° .
The processes that generate Tehuanos are reasonably well understood. The north American cold season is characterized by cold fronts traveling southward; and the route of these fronts is sometimes determined by continental topography. For example, when the cold fronts arrive to the Gulf of Mexico, they find that the Sierra Madre Mountains are a natural barrier. These mountains do not allow cold fronts to travel freely over the Mexican mainland. However, this barrier is broken by a low altitude narrow mountain gap, Chivela Pass, which runs north-south from the Gulf of Mexico's Bay of Campeche to the Pacific ocean's Gulf of Tehuantepec (Fig. 1). A pressure gradient drives strong winds along the mountain pass. On the South side of the pass, these winds can be intense, with maximum gusts around 60 m s-1 [Stumpf, 1975]. These winds blow offshore across the Gulf of Tehuantepec coast favoring strong near shore oceanic mixing and intense lowering of SSTs [Hurd, 1929; Roden, 1961; Stumpf, 1975; Lavin et al., 1992; Fiedler, 1994; Trasviña et al., 1995].
2.3 Previous Observations
There have been several direct observation of wind fields on the Gulf of Tehuantepec. The pioneer oceanographic cruises in the Gulf of Tehuantepec [Brandhorst, 1958; Blackburn, 1962] showed the presence of an anticyclonic eddy that is produced by the strong offshore winds. Roden (1961) used winds and SST from COADS data (10-30 observations in 2x2° grid boxes over periods of 10-30 days). In situ wind observations reported by Barton and Trasviña et al. are relatively dense for ship observations; however, sampling over several weeks prevented the study of day to day variability.
In addition to the direct observations, the effects of the Tehuanos on the ocean and the atmosphere have already been studied through satellite images. Parmenter  reported the first visible satellite image of the Gulf of Tehuantepec (an ESSA 9 photograph) which shows the quickly westward movement of a cold front. Thermal infrared sensors aboard the NOAA-2 and NOAA-4 satellites have been used to describe upwelling formation related to the onset of Tehuanos [Stumpf, 1975; Stumpf and Legeckis, 1977]. The NOAA-9 satellite images of sea surface temperature has been used to indirectly estimate that the wind usually follows a near inertial path [Clarke, 1988].
Recently, Schultz et al.  following the 1993 superstorm cold surge, observed clouds proceeding from the Chivela Pass which turned anticyclonicly, consistently with the inertial path. The studies to that date suggested that conditions which cause large deviations from the inertial path are relatively rare or short lived. For inertial flow (1) the centrifugal acceleration balances the Coriolis force:
, and (1a,b)
where u is the zonal velocity component, v is the meridional velocity component, and f is the Coriolis parameter. A recent modeling study using the PSU-NCAR MM5 meso-scale model [Steenburgh et al., 1998] indicated that the trajectories differed substantially from inertial flow: the pressure gradient was non-negligible. Prior to accurate and high temporal resolution remote sensing the trajectories could not be verified.
3. Gridding nscat winds
Daily wind products are used to study a wide range of meteorological and oceanographical phenomena with time scales from days to seasons. Observations over oceans are typically sparse in both space and time. Consequently, the initialization fields from GCMs (e.g., ECMWF and NCEP winds) have often been utilized as surface winds. Alternatively, fields have been developed from long term averages (at least monthly) of ship and buoy observations [Roden, 1961; Hellerman and Rosenstien, 1983; Legler et al., 1989]. In both cases the spatial resolution is course, typically 2 to 5 degrees. Better temporal and spatial resolutions are desirable.
3.1 Previous fields of scatterometer winds
Spaceborne scatterometers provide a high spatial resolution (~25 to 50 km) within their observation swaths, but no observations outside the swaths. The time taken to completely cover the world's oceans has been limited by the choice of orbits and operational restrictions. For example, without operational restrictions, the ERS-1/2 scatterometers cover the globe in approximately six days. The sampling time required to remove sampling biases related to the orbital pattern has been found to be greater than one month for the ERS scatterometers [Zeng and Levy, 1995]. The construction of daily surface wind fields, based on oceanic observations, has not been practical prior to the period of NSCAT observations.
3.2 NSCAT winds
NSCAT equivalent neutral wind observations cover most of the Earth in one day, and have nearly 100% coverage in two days. The advantages over ERS scatterometers are duo swaths (one on each side of the orbital trajectory), nearly continual operation (no mission constraints), and a lack of dropout. Additional advantages are improved accuracy in equivalent neutral wind speed and direction [Bourassa et al., 1997; Freilich and Dunbar, 1988], and superior ambiguity selection. For most open ocean conditions and/or high wind speeds, equivalent neutral winds [Tang and Liu, 1996; Verschell et al., 1998] are similar to winds. Differences between equivalent neutral winds and winds are related to variations from neutral atmospheric stability, and a typically less than 0.5 m s-1.
The production of daily wind fields, appropriate for forcing ocean models, requires that gaps in the coverage are filled by accurate estimates of the wind. The wind fields must also be smooth at the edges of these gaps. The evidence of swath patterns in wind fields, and derivative fields of wind curl and vorticity, can be greatly reduced by averaging with reasonable proxy winds filling the observational gaps [Zeng and Levy, 1995]. Our solution to this problem is to use observations from closely related times to smoothly fill the gaps. Observations closer in time to the day of interest are weighted much more heavily than those further away in time. This approach retains the dominance of winds observed on the day in question, and it also allows for a relatively smooth transition into regions where there were no observations.
3.3.1 Binning and weighting
The bin size for the winds was chosen to include sufficient observations such that incorrectly selected ambiguities were unlikely to have a large influence, and so that the landmask about small islands does not cause gaps in the wind field. For the 50 km resolution NSCAT wind product, which is used in this study, this condition is satisfied with a 1° x 1° bin size. Without additional spatial averaging, the landmask of 25 km from any land would result in substantial gaps for any resolution finer than 50 km.
The weighting procedure is analogous to a weighted vector average of one, two, four, and eight day averages. Each of these averaging periods is centered on 12Z of the day in question. The weighting mechanism is designed to favor observations in the short averaging periods. The eight day averaging period was sufficiently long that there are observations in each grid box despite occasional 12 to 24 hour gaps in the observations. The effective averaging window is then reduced through a weighted average () of the eight day () and four day () fields; and then further reduced by averaging the product () with two day and one day averages. The key equations are
where the numerical subscript is the number of days used in determining the average wind vector , and n is the number of observations in cell i, j. The superscript '*' indicates that observations from longer time periods have been included in the wind field. Increasing the value of the weighting parameter (b) sharpens the fit to at the expense of smooth fields near swath edges. No additional smoothing is applied. We have found a value of b =5 to be sufficiently large that the field is dominated by winds observed on the day of interest, and sufficiently small that the field is reasonably smooth where swaths intersect.
There is usually little loss of information from the daily observations. This point is illustrated in the differences between the filled winds () and mean winds for one day (). The sampling related rms differences in velocity are estimated using only the points where there were observa-tions in the one-day average (). For the region examined herein (0 to 30° N, 80 to 120° W), there is a rms difference of 1.2 m s-1 in the East-West wind component (u), 1.1 m s-1 in the North-South wind component (v), and 1.7 m s-1 in speed. There is little spatial bias in these differences. These differences are similar to the observational uncertainty in NSCAT equivalent neutral wind speeds [Bourassa et al. 1997; Freilich and Dunbar, 1988].
3.3.2 Temporal Sampling Characteristics
The non-homogenous sampling results in non-homogenous temporal averaging characteristics (Chelton and Schlax, 1994). The temporal sampling is examined for seven days, May 25 - 31, 1996. The weighted mean absolute difference from 12Z on the day corresponding to the wind field is determined, with the same weighting procedure as the wind field components. Areas with good sampling have mean characteristic time ranging from a quarter day to greater than two days. A histogram (Fig. 2) shows the probability density distribution of values over the seven days, split into eighth of a day bins. The effective averaging period is approximately double this characteristic time. The peak characteristic time is at one day. In most cases the characteristic time is between 0.75 and 1.75 days, indicating that this averaging technique is appropriate for examining wind field evolution on a daily scale.
3.3.3 Animations and Trajectories
The above wind fields were used to produce animations of the winds and derivative fields. Animations with moving wind vectors were used to identify Tehuanos. The motion of the vectors is Lagrangian, and the vector lengths indicate the wind speed. The vector positions (i.e., motion) were calculated by interpolating the daily wind fields to one hour time steps, and integrating with a fourth order Runge-Kutta method. The Runge-Kutta technique used an adaptive time step, with a first guess of ten minutes. The optimal time interval between animation frames is dependent on the highest wind speeds; however, we found a time step of three hours to be effective for most conditions. The same motion calculation is used to determine wind traces (pseudo-trajectories).
A Tehuano is examined around the times that hurricane Marco was in the Caribbean (Nov. 15 to 21, 1996). The airflow will be shown to evolve from the typical flow to highly non-inertial flow. The daily gridded wind fields and trajectories show the evolution of the field. Initially, there is a strong Tehuanos with trajectories (colored lines) that noticeably depart from inertial flow. The initial points for each track are along 15.5° N, spaced in 0.3 degree intervals form 95.7° W to 93.9° W. Each day along the parcel trajectory is marked by an arrowhead, which indicates 24 hours of travel, except for the first arrowhead, which indicates three hours.
For the days shown in the animation the winds peak on Nov. 9, 1996. The gap flow then weakens until Nov. 12, after which they remain relatively constant for the shown period (Nov. 12 to Nov. 19). The trajectories turn to the right from the eighth through the tenth. The influence of hurricane Marco is first shown on the eleventh, when the two easternmost trajectories turn to the left. From the 12th through the 15th the wind field adjusts to the point where all the gap flow is turning the east. The trajectories from the 11th through the 16th indicate that much of the flow through Chivela Pass is exiting the Pacific through the wide gap at Nicaragua's lake district, and entering the Caribbean Sea. From the 15th through the 19th it is also apparent that air is flowing from the Pacific Ocean, over the Isthmus of Panama, and into the Caribbean Sea. The direction of gap flow through the southern passes is reversed from the usual westward flow. The tighter cyclonic circulation pattern of hurricane Marco is most evident on the 18th and 19th, prior to it's rapid departure from the region. On these days the trajectories are highly confused because Marco does not remain in the area sufficiently long for the air parcels to reach Central America.
NSCAT provided sufficient high quality wind observations to study the daily evolution of flow through Chivela Pass. This is the first set of high spatial and temporal resolution winds that can be compared to theory or model results. The trajectories appear to be similar to those modeled with MM5 [Steenburgh et al., 1998]; however, further study will be required to validate the model results. The remainder of the discussion will be focused on accuracy of several assumptions that have been used in modeling Tehuanos and their influence on the ocean.
5.1 Non-Inertial flow
Non-inertial flows indicate that terms other than the Coriolis 'force' are significantly influencing the motion. In our example, this additional forcing is a pressure gradient across the Gulf of Tehuantepec and neighboring Pacific Ocean. The flow shown for Nov. 11th through 19th curves to the left, rather than the right as would be expected of inertial flow in the northern hemisphere. The low pressure of hurricane Marco sets up the atypical pressure gradient. The cyclone also changes the local airflow pattern, causing the inter-tropical convergence zone (ITCZ) to move North of its usual position. Interaction with the ITCZ also creates a weak pressure gradient the alters the trajectories.
There are several additional causes for non-inertial flow, near Chivela Pass, prior to the influence of the hurricane. There is little reason to believe that near surface (10 m) wind will follow an inertial trajectory: surface drag has a substantial impact on the balance of forces determining motion. In comparison to geostrophic winds, surface drag causes the surface wind to be roughly 15 to 30 degrees counter-clockwise (in the northern hemisphere) and reduced in speed be a factor of 0.6 to 0.9 [Clarke and Hess, 1975; Harlan and O'Brien, 1996]. These factors appear to account for a substantial portion of the differences; however, it is also clear that horizontal pressure gradients can play an important roll in determining the trajectories. Some of these gradients are likely to be due to pressure differences with respect to that at the center of the gap flow, which causes the trajectories to fan out as they exit the Gulf of Tehuantepec. Another factor is the evolving circulation pattern, which (among other things) changes the pressure gradient across the Chivela Pass.
5.2 Direction of Flow Exiting Chivela Pass
In previous modeling studies, flow exiting Chivela Pass has often been approximated as perpendicular to the shoreline [Crépon and Richez, 1982; McCreary et al., 1989]. A more recent study with a high resolution meso-scale model found substantial departure from this assumption [Steenburgh et al., 1998]. They found the flow exiting Chivela Pass fanned out to have substantial along shore components on each side of the pass. This finding is supported in the trajectories determined from the NSCAT gridded wind fields. The rapid evolution of the gap flow, and along shore wind components, are likely to induce along shore Kelvin waves that could play a role in coastal bio-productivity.
A technique has been developed to fill gaps in NSCAT observations, and produce a 1x1° daily gridded wind fields. The characteristic time is non-homogenous in space and time, with a peak at one day, and most values between five-eighths and 1.75 days. The effective averaging period is approximately double this characteristic time. This technique is found to effectively show Tehuanos, except within roughly 25 km of the coast where the NSCAT land mask prevents observations.
NSCAT wind fields provide a valuable insight into daily wind variations and into wind patterns for regions with otherwise sparse observations. The spatial and temporal resolutions are more than an order of magnitude finer than those used in previous observational studies of Tehuanos. The fine spatial resolution shows that near coastal surface wind could have significant components parallel the coastline. Furthermore, NSCAT observations show the full extent of Tehuanos, sometimes near 2000 km, as well as the areas where tropical storms and hurricanes can influence the flow pattern.
The NSCAT observations indicate that SSTs are not a good proxy for short term (daily to weekly) variations in the wind flow. Animations of wind field showed one example of winds flowing South through the Chivela Pass, turning to there left, flowing through the Gulf of Papagayo, over Nicaragua lake district, and entering the Caribbean Sea. The non-inertial motion was induced by pressure gradients across the trajectory track, and also by a cyclone off the Caribbean coast of Nicaragua. The hurricane related non-inertial flow was not observed in previous studies of the region.
Acknowledgments. We thank Kathy Verzone and Al Davis for their contributions developing the moving vector code, Jiraporn Whalley for animation graphics. Funding for this project is from the NASA JPL NSCAT Project (contracts 957649 and 980646). COAPS receives its base funding from ONR's Secretary of Navy Grant to Dr. James J. O'Brien.
Barton, E. D., M. L. Argote, J. Brown, P. M. Kosro, M. Lavin, J. M. Robles, R. L. Smith, A. Trasviña, and H. S. Velez, Supersquirt: Dynamics of the Gulf of Tehuantepec, Mexico, Oceanography, 6(1), 23 - 30, 1993.
Blackburn, M., An oceanography study of the Gulf of Tehuantepec, U. S. Fish Wildl. Serv. Spec. Sci. Rep. Fish., 404, 28 pp., 1962.
Bourassa, M. A., M. H. Freilich, D. M. Legler, W. T. Liu, and J. J. O'Brien, Wind observations from new satellite and research vessels agree, EOS, 78, 597-602, 1997.
Brandhorst, W., Thermocline topography, zooplankton standing crop, and mechanisms of fertilization in the eastern tropical Pacific. Conseil Permanent International Exploration de la Mer, Journal du Conseil, vol. 24, no. 1, p. 16 - 31, 1958.
Chelton, D. B., and M. G. Schlax, The resolution capability of an irregularly sampled dataset: with application to Geosat altimeter data. J. Atmos. Oceanic Technol., 11, 534-550, 1994.
Clarke, A. J., Inertial wind path and sea surface temperature patterns near the Gulf of Tehuantepec and Gulf of Papagayo, J. Geophys. Res., 93(C12), 15,491 - 15,501, 1988.
Clarke, R. H., and G. D. Hess, On the relation between surface wind and pressure gradiant, especially in lower latitudes, Boundary Layer Meteorology, 1975, 9, 325-339.
Crépon, M., and C. Richez, Transient upwelling generated by two-dimensional atmospheric forcing and variability in the coastline, J. Phys. Oceanogr., 13, 1012-1033, 1982.
Fiedler, P. C., Seasonal and interannual variability of coastal zone color scanner phytoplankton pigments and winds in the eastern tropical Pacific, J. Geophys. Res., 99,18371 - 18384, 1994.
Freilich, M. H., and R. S. Dunbar, The Accuracy of the NSCAT-1 Vector Winds: Comparisons with NDBC Buoys, J. Geophys. Res., 1998, submitted.
Harlan, J. Jr., and J. J. O'Brien, Assimilation of scatterometer winds into surface pressure fields using a veriation method, 1986.
Hellerman, S. and M. Rosenstien, normal monthly wind stress over the world oceans with error estimates, J. Phys. Oceanogr.,13, 1093 - 1104, 1983.
Hurd, W. E., Northers of the Gulf of Tehuantepec, Mon. Weather Rev., 57, 192, 194, 1929.
Lavín, M. F., J. M. Robles, M. L. Argote, E. D. Barton, R. Smith, J. Brown, M. Kosro, A. Trasviña, H. S. Vélez Muñoz and J. García, Fisica del Golfo de Tehuantepec. Ciencia y Desarrollo, Vol XVIII, 103, 97-108, 1992.
Legeckis, R., Upwelling off the Gulfs of Panama and Papagayo in the tropical Pacific during March 1985, J. Geophys. Res., 93, 1988.
Legler, D. M., I. M. Navon, and J. J. O'Brien, Objective analysis for psuedostress over the Indian ocean using a direct-minimization approach, Mon. Wea. Rev., 117, 709 - 720, 1989.
McCreary, J. P., and J. S. Allen, The generation and propagation of sea level variability along the Pacific coast of Mexico. J. Phys. Oceanogr., 13, 1012-1033, 1989.
Parmenter, F. C., A 'Tehuantepecer', Mon. Wea. Rev., 98, 479, 1970.
Roden, G. I., On the wind-driven circulation in the Gulf of Tehuantepec and its effect upon surface temperatures, Geofis. Int., 1, 55 - 72, 1961.
Schultz, D. M., W. E. Bracken, L. F. Bosart, G. J. Hakim, M. A. Bedrick, M. J. Dickinson, and K. R. Tyle, The 1993 superstorm cold surge: frontal structure, gap flow, and tropical impact, Mon. Wea. Rev., 125, 5 - 39, 1997.
Steenburgh, W. J., D. M. Schultz, and B. A. Colle, The structure and evolution of gap outflow over the Gulf of Tehuantepec, Mexico, Mon. Wea. Rev., 1998, in press.
Stumpf, H. G., Satellite detection of upwelling in the Gulf of Tehuantepec, Mexico, J. Phys. Oceanogr., 5, 383 - 388, 1975.
____, and R. V. Legeckis, Satellite observations of mesoscale eddy dynamics in the eastern tropical Pacific Ocean, J. Phys. Oceanogr., 7, 648-658, 1977.
Tang, W., and W. T. Liu, Equivalent Neutral Wind, JPL Publication 96-17, 1996.
Trasviña, A., E. D. Barton, J. Brown, H. S. Velez, P. M. Kosro, and R. L. Smith, Offshore wind forcing in the Gulf of Tehuantepec, Mexico: The asymmetric circulation, J. Geophys. Res., 100(C10), 20,649, 20,663, 1995.
Verschell, M. A., M. A. Bourassa, D. E. Weissman, and J. J. O'Brien, Model validation of the NASA scatterometer winds, J. Geophys. Res., 1998, submitted.
Zeng, L., and G. Levy, Space and time aliasing structure in monthly mean polar-orbiting satellite data. J. Geophys. Res., 100, 5133 - 5142, 1995.