SATELLITE DERIVED SCATTEROMETER / ERS-1 SEA SURFACE WIND STRESS CURL IN THE OCEANS.

ABSTRACT

During January-July 1993 an experiment was conducted in the Southwestern Indian Ocean with the aim to analyze the relationship between oceanographic events and weekly satellite derived Sea Surface Wind Stress Curl (SSWSC) fields computed following the Rossby equation from the scatterometer ERS-1 data sets, and compared with satellite derived Sea Surface Temperature (SST) from AVHRR/NOAA imagery. SST and SSWSC imagery showed that variation in the ocean pattern occurs in apparent response to submesoscale oceanographic events such as fronts or eddies that varied on time scales of one week.

Keywords: Ocean wind stress, vorticity, scatterometer

INTRODUCTION

Nothing has been done until now related to the application of microwave sensors on board of satellite to the optimization of derived Sea Surface Wind Vorticity (SSWSC) from global measurements of the wind fields on the surface of the Indian Ocean provided by the scaterometter ERS-1 (Petit et al. 1994). The aim of this study is to provide the mesoscale and submesoscale zones of divergence and convergence on the sea surface to improve our understanding of the underlying factors affecting the onset and subsequent variation of the oceanic submesoscale events in this area.

METHODOLOGY

The model

Expressed simply, vorticity is a characteristic of the kinematic of fluids flow which expresses the tendency for portions of the fluid to rotate. In the cartesian (x,y,z) system we can define an ocean model which consists of two isopycnic layers 1 and 2 of density µ₁, µ₂ and depth h with zonal and meridional meridional velocity components V₁ (u₁,v₁,w₁), and V₂ (u₂,v₂,w₂) respectively. The equation of motion per unit of mass for the x, y components can be written as two components equations with the coordinates x, y, and z and their respective velocity components u, v and w being positive in the east, north and upward directions respectively and the origin of coordinates being at the sea surface as:

(1)

(2)

where ƒ is the coriolis parameter, p is the pressure, the density of the air and Fx, Fy are the wind force components.

If we cross-differentiate these equations, integrate between -h and 0, substract them and note that << ƒ, being the relative vorticity, the resulting equations can be written as:

(3)

This equations means that the velocities divergence (vorticity) in the xy plane is rqual to the z component of the wind stress, or in another way, a surface divergence or convergence will produce an upwelling or downwelling respectively.

From equation (3), (ƒh) represents the vertical coefficient of eddy viscosity (Kv).

The coriolis parameter ƒ is:

(4)

for &_ij the latitude in the Northern Hemisphere and = 0.000073. In the Equator, ƒ=0 so the function will not exists. However if we are working on the Southern Hemisphere, then

(5)

Using the equation (3), a novel technique based on weekly high spatial resolution - high density scatterometer ERS-1 wind was developed to calculate the ekman pump derived from the wind geostrophic vorticity field on the sea surface.

(6)

(7)

V and @ are the module and angle of the wind velocity respectively and the air density (1.3 kg/m³). From here and assuming a linear relationship (Smith 1980, Large and Pond 1981) of the drag coefficient Cd and V,

(8)

for a = 0.0006 and b = 0.00006 (Smith 1980). Substituing both into the equations (6) and (7),

(9)

(10)

If we derive related to x and y,

(11)

(12)

which result from deriving Tx related to y and Ty related to x, considering the sign of the projection (+ or -), between an space interval given by the resolution of the Scatterometer ERS-1 and equal to 25000 meters, and multiply by (1.3 kg/m³).

The sum between both will give us the SSWSC.

However we have to divide all the expression (12) by µ₁ (1024.8 kg/m³)

(13)

So the final expression will be for the Northern Hemisphere

(14)

or

(15)

In the Southern Hemisphere however,

(16)

or

(17)

In the geographical equator the function does not exist because ƒ = 0.

That means that the wind stress associated to the SSWSC on the surface of the ocean will be equilibrated with the divergence or convergence of water at the ocean surface.

Satellite derived scatterometer ERS-1 wind fields

The wind scatterometer ERS-1 uses three sideways looking antenna, continuously iluminating a swath of 500 km wide as the satellite advances along its orbit. Each antenna provides measurements of radar backscatter from the sea surface for overlapping 50 km spatial resolution cells using a 25 km grid spacing on the surface of the Sea. Weekly sea surface wind data base of the southwestern Indian Ocean were achieved by Meteo-France Reunion and processed at ORSTOM-SEAS.

The equations (15) and (17) were then solved by latitude and longitude (25 km) for both Tx and Ty and the SSWSC fields were obtained. The area was also divided into a 520* 520 grid and a medium value was calculated for the overlapped SSWSC data calculated by the different orbits over the same window at different latitudes.

Satellite derived AVHRR/NOAA imagery

From the AVHRR sensor of NOAA satellites series, thermal infrared data values were converted to brightness temperature values using the inverse of Planck’s radiation equation. A geometric correction derived from knowledge of the characteristics of the sensors was applied (Saunders 1988, Barton and Cechet 1989). Data were then re-sampled onto a chart projection with a fixed resolution of one nautical mile. The validation was done with the eXpendable Bathy Thermogram (XBT), ARGOS buoys and fishing boats measures giving an standard error lower than 0.5º Celsius.

RESULTS

The major problem in developing remote sensing methods from model calculations is verification. A remote sensing method must be based on physical law (here the Rossby equation) which the model has to contain. Only in some cases is a direct verification possible. The capability of recognizing patterns with our eyes using artificial images from georeferencied digital records, helps with a subjective control of a filter depending on our purposes (purse seine tuna fishing ground SSWSC range location for example). Here, satellite data are superior to surface observations in density and space time consistency so ground oceanographic data bases are impracticable. For that and waiting for fishing data base further analysis implementation, SST images nowadays very well implemented at ORSTOM-SEAS, have been used to contrast the synoptic windows with positive and negative SSWSC. The Figure 1 shows the range of the maximum and minimum vorticity records for the hole 1994. Despite of the strong seasonal variability observed especially between January - march (summer in the southern hemisphere and the period of strong wind), a logic asimmetry between both, positive and negative SSWSC can be observed. From that, a scale including the range of maximum variability has been used to plot the digital records, in spite of the asimmetry between the positive and negative SSWSC (Figure 2) over 2.400.000 records.

Figure 1. Range of maximum and minimum vorticity during 1994.

Figure 2. Asimmetry between positive and negative SSWSC.

After that an animation in time was developed in order to see the seasonal dynamic of the SSWSC.

Different oceanographic events were observed and contrasted on satellite derived SST imagery:

a.-The coastal upwelling along the Somalian and Mozambique coast marked as a zone of strong positive vorticity (Figure 3).

Figure 3. Coastal upwelling along the Somalian and Mozanbique coast.

b.-The Odile Cyclone observed during april 1994 marked with an strong positive vorticity signal over the eye (Figure 4).

Figure 4. The Odile cyclon during April 1994.

c.-The synoptic Mass effect of Island observed at the north (warm) and south (cold) Madagascar (Figure 5), and the submesoscale eddy system observed at the north (warm) and south (cyclonic) Reunion Island (Figure 6).

Figure 5. The Mass Effect observed at the north and south of Madagascar.

Figure 6. Eddies observed at the north and south of Reunion Island.

d.- Week 46 of year 92. It is possible to appreciate the filament at the south of Gran Canaria (blue positive and red negative) and cold features to the west of La Palma (Fig. 7).

Figure 7. Satellite- derived scatterometer/ERS-1 sea surface vorticity in the NE Atlantic during week 46 of 92. Blue means positive vorticity and red negative vorticity.

e.- Week 26 of 94. The warm wake of La Palma and a cold eddie to the west of this island can be observed (Fig.8).

Figure 8. SSWSC during week 26 of 94.

REFERENCES

BARTON, I.J., and CECHET, R.P., 1989, Comparison and optimization of AVHRR sea surface temperature algorithms. Journal of Atmospheric and Oceanic Technology, 6, 1083-1089.

LARGE, W.G., and POND, S., 1981, Open ocean momentum flux measurements in moderate to strong winds. Journal of Physical Oceanography, 11, 324-336.

PETIT, M., DAGORN, L., LENA, P., SLEPOUKHA, M., RAMOS, A. and STRETTA, J.M., 1994, Oceanic and scape concept and operational fisheries oceanography, in Les nouvelles frontières de la télédétection océanique, edited by F. Doumenge (Monaco: Mémoires de l’Institut Océanographique de Monaco), pp. 85-97.

POND, S., and PICKARD, L., 1983, Introductory dynamical oceanography, (Great Britain: Pergamon Press).

SAUNDERS, R. W., 1988, An improved method for detecting clear sky and cloudy radiances from AVHRR data, International Journal of Remote Sensing, 9 (1), 123-150.

SMITH, S.D., 1980, Wind stress and heat flux over the ocean in gale-force winds. Journal of Physical Oceanography, 10, 709-726.

Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry