Background
The mesoscale variability in the ocean spans the spatial-temporal scale of motion from tens to hundreds of km and tens to hundreds of days. Eddies with a diameter of about 200 km and sea surface height anomalies of up to 25 cm contribute the majority of mesoscale variability to the World Ocean (Chelton et al., 2007). The kinetic energy is one of the major characteristics of moving eddies, which is linked to sea surface topography. The ring-shaped negative sea surface height anomalies are used to be interpreted as cyclonic eddies (with counter-clockwise rotation in the northern hemisphere) in which the vertical component of current speed is directed upward injecting nutrients into the upper mixed layer (McGillicuddy et al., 1999). Positive sea surface height anomalies reflect the anticyclonic eddies with the downward motion resulting in a depleted concentration of nutrients in surface layers. The western Arabian Sea has a vigorous field of mesoscale eddies (Fisher et al., 2002). The kinetic energy of these eddies could exceed the mean kinetic energy of the oceanic current flows (Flagg and Kim, 1998). Eddies could markedly influence the heat balance of waters, as well as the variation of biological productivity in the region (Banse and Piontkovski, 2006). 

The era of remote sensing enabled one to estimate typical dimensions of mesoscale eddies in the western Arabian Sea, as well as to track their propagation and lifetime (Tang et al., 2002). However, an actual mechanism and quantitative relationships underlying physical-biological coupling are yet to be understood. We were aimed at evaluating the relationship between the energetic characteristics of eddies and chlorophyll-a concentration. 

1 Results and Discussion
Weekly time series of chlorophyll-a allowed us to analyze the seasonal cycle on the scale of the western Arabian Sea (Figure 1)

This cycle was bimodal, with two maxima corresponding to February and September. In comparing two modes, the summer peak tended to dominate in 80% of cases. The summer peak used to be wider compared to the winter peak and the variability of the summer peak (in terms of interannual variability) is pronounced greater than the variability of the winter peak. On average, the chlorophyll concentration during the summer peak as much as 2.5 times exceeded the background concentrations featuring the off-peak months. In case of the winter peak the difference between the modal and background concentration is about double.

The kinetic energy of eddies has experienced seasonal changes as well. However, the seasonal variation of kinetic energy was not pronounced as clear as for the chlorophyll concentration. The maps of chlorophyll and sea surface heights both showed marked spatial-temporal variability of the eddy field (Figure 2). 

 
One could notice the presence of cyclonic and anticyclonic eddies as well as their shifts characterizing propagation to the south, south-west, and south-east. The analysis of weekly time series of the sea surface height maps has implied that some of these eddies were keeping more or less stationary location while the others were actively moving. The stationary eddies were associated with the region of capes (in particular with the Ras al Hadd region of the Oman coast), where the confluence of two currents along the continental shelf form the paired system-with the cyclonic eddy to the north and the anticyclonic eddy to the south of this confluence. The other eddies have originated in the open ocean and propagated through the region.

The analysis of the relationship between the kinetic energy of eddies and chlorophyll concentration gave two types of statistically significant correlations- positive and negative (Figure 3). 

 
In maps and time series, the footprints of cyclonic eddies were denoted by negative values of sea surface heights whereas the anticyclonic eddies had positive values. 

We calculated the balance between negative and positive sea surface height anomalies in time series (Figure 4). For some years, the total annual balance of negative to positive sea surface heights (cyclonic to anticyclonic eddies) was negative. These years (Figure 3 A, B) were featured by positive correlation showing that the cyclonic eddies dominated throughout the year and the chlorophyll-a concentration was positively related to the sea surface heights acting as the indicator of the upward directed vertical component of currents of an eddy field.

For the other years, the total annual balance of negative to positive sea surface heights (cyclonic to anticyclonic eddies) was positive. These years (Figure 3 C, D) were featured by negative correlation showing that anticyclonic eddies dominated throughout the year and the chlorophyll-a concentration was negatively related to the kinetic energy (due to the dominating downward directed vertical component of currents of an eddy field). The ratio between positive and negative sea surface heights is exemplified in Figure 4 and Figure 5. 

These figures show the dominance of cyclonic or anticyclonic eddies for the year 2002 and 1998 correspondently. So in terms of interannual variability, in the years with prevailing cyclonic eddies the chlorophyll-a concentration will be higher than normal (compared to interannual mean). In the years with prevailing anicyclonic eddies (suppressing injection of nutrients in the upper mixed layer) the chlorophyll concentration will be less than normal. Weekly time series of chlorophyll-a and kinetic energy have also allowed us to seek long-term trends in parameter variability. Apparently, no statistically significant rising or declining tendencies were found, for the time range from 1997 to 2008. The weekly time series subjected to spectral analysis have implied both parameters exerting fluctuations with some matching dominant periods. The annual and semiannual periodicity dominated the variability of chlorophyll-a concentration, whereas the kinetic energy spectrum had peaks at 4 years, 1 year, and the 6~7 month period. 

In tracing the passage of eddies through the region, we have noticed a diversity of directions represented by southward, eastward, and westward propagation. Global generalization of mesoscale eddies in the World Ocean has pointed out that these eddies propagate west at the phase speed of nondispersive baroclinic Rossby waves, with a general preference of the cyclonic eddies to move poleward, while anticyclonic eddies tend to move towards the equator (Chelton et al., 2007). It goes without saying, that the tendencies of tracks inferred through global generalization may not be the case for a number of regions. For instance, a cyclonic (highly productive) eddy tracked in the Northern Arabian Sea was about 100 km in diameter and has persisted for about 4 weeks (from November to December) moving towards the equator, accompanied by an anticyclonic eddy of the same size (Tang et al., 2002). The authors related the formation and decay of these eddies with variations of the input of wind stress vorticity.

The bimodal seasonal cycle of chlorophyll-a (Figure 1) is mediated by the reversal of the wind system over the region (Banse, 1994; McCreary et al., 2009). Seasonal development of the first and second peaks reflects the timing of the Northeast (winter) and the Southwest (summer) monsoons (Le´vy et al., 2007). 

It was believed that in the western Arabian Sea, mesoscale eddies are mostly associated with the summer monsoon. Our data showed that both monsoon periods could be accompanied by a well-developed field of mesoscale eddies in the region. These data and preceding publications-both imply a multilateral origin of eddies. Some of them were associated with the coastal circulation—the confluence of currents. For instance, a steady structure consisting of two eddies (cyclonic to the north and anticyclonic to the south of the frontal jet) might be annually observed in the region of Ras al Hadd cape of the Omani coast (Böhm et al., 1999). The system is formed by the confluence of two currents and persists through the time of the summer monsoon. Truly oceanic eddies observed in the region, were reportedly mediated by baroclinic instability of currents and planetary (Rossby and Kelvin) waves which generated densely packed eddy field (Subrahmanyam and Robinson, 2000). 

Gomes et al (2009) have noticed that years with high kinetic energy of eddies in the north Arabian Sea were associated with high chlorophyll-a concentration. We believe that the high value of kinetic energy does not characterize and is not associated with the type of eddy however; both types (cyclonic and anticyclonic) might possess a high level of the available potential energy or kinetic energy. In this regard, we provided insights into the relation between the type of eddies (characterized by the balance of positive to negative sea surface heights), and kinetic energy.

When the total annual balance of cyclonic to anticyclonic eddies is positive (Figure 4A), the correlation between kinetic energy of eddies and chlorophyll concentration is positive as well, showing that cyclonic eddies dominated throughout the year (reflected by the total negative balance of sea surface height anomalies), so chlorophyll values were higher than normal. In the case of the year with dominating anticyclonic eddies the situation is reversed, the balance is positive, so the kinetic energy of eddies and chlorophyll concentration is negatively related, showing that anticyclonic eddies dominated throughout the year (Figure 4B); the chlorophyll values were less than normal.

The balance between positive and negative sea surface heights might be also partly driven by the general switch between anticyclonic circulations dominating the Arabian Sea during summer monsoon to a cyclonic one, in winter. Interannually, the pronouncement of mesoscale sea surface height anomalies as well as the ratio of cyclonic-to-anticyclonic eddies could markedly depend on how strong or weak the latest monsoon was. Further development of this hypothesis and its testing might contributes to the understanding of the sign switch in the kinetic energy-chlorophyll relationship.

As far as the interannual variability is concerned, the time series and their statistical analysis does not allow us to vote for the concept of rising productivity of the Arabian Sea reported earlier (Goes et al., 2005). It seems that in a given time range, we are dealing with a balanced pelagic ecosystem exhibiting no pronounced interannual trends (as far as the chlorophyll-a tend to be used as the indicator of productivity) underlined by the absence of interannual trends in variations of the kinetic energy of eddies-partly driving the chlorophyll variations. Moreover, we analyzed interannual changes in chlorophyll-a over the whole Arabian Sea subdivided into 61 2-degree regions. For each region, remotely sensed chlorophyll-a, sea surface temperature, and wind speed time series were retrieved, from appropriate databases (Piontkovski and Claereboudt, 2012). The spatial and temporal trend analysis showed physical-biological oscillations with dominant periods of 12 and 6 months (reflecting the seasonality of monsoonal winds) with a globally warming trend but no overall increase in chlorophyll over the past 12 years (1997~2009).

Overall, the evaluated relationship between the sea surface height anomalies, kinetic energy, and chlorophyll concentration contributes to our understanding of the mechanism mediating mesoscale variability of the chlorophyll-a in regions with vigorous eddy fields.

2 Data and Methods 
Satellite derived (9-km spatial resolution SeaWIFS and MODIS-Aqua) weekly and monthly Level-3 products for chlorophyll-a concentration were employed, to assemble time series for the western Arabian Sea (18-25ºN, 58-62ºE), for the period of 1997~2008. These products are available from the National Aeronautics and Space Administration (NASA) Ocean Color Group (http://oceancolor.gsfc.nasa.gov). Monthly time series were acquired using the GES-DISC Interactive Online Visualization and Analysis Infrastructure (GIOVANNI) software as part of NASA's Goddard Earth Sciences Data and Information Services Center. Maps for sea surface height anomalies were produced from TOPEX/Poseidon, Jason-1 and Jason-2 altimeter data and acquired from the Archiving, Validation and Interpretation of Satellite Oceanographic Data Center website (http://www.aviso.oceanobs.com) and the CCAR Global Near Real-Time SSH Anomaly/Ocean Color Data Viewer (http://argo.colorado.edu/~realtime/modis/).

The construction of the kinetic energy time series was based on the altimeter–derived sea surface heights for the western Arabian Sea (18º~25ºN, 58º~62ºE), for the period of 1997~2008. The methodology of calculations of eddy kinetic energy per unit mass (EKE) was given by Sharma et al (1999).

The spectral analysis (from the “Statistica” v9 package) has been applied to estimate dominant periods in weekly time series of chlorophyll-a concentration (with N=524) and kinetic energy of eddies (with N=624 and the Hamming window weights: 0.357, 0.241, 0.446, 0.241, 0.357 applied to both parameters). 

Author’s Contributions
SP performed the statistical analysis and drafted the manuscript. NN retrieved time series from appropriate databases and carried out the estimates of the kinetic energy. All authors read and approved the final manuscript.

Acknowledgement 
The present work was supported by the Research Council grant No. ORG/EBR/09/004 (Sultanate of Oman). 

References
Banse K., 1994, Seasonality of Coastal Zone Colour Scanner phytoplankton pigment in the offshore oceans, J. Geophys. Res., 99: 7323-7345
http://dx.doi.org/10.1029/93JC02155  

Banse K., and Piontkovski S.A., (eds.), 2006, The mesoscale structure of the epipelagic ecosystem of the open northern Arabian Sea, Universities Press, Hyderabad.

Böhm E., Morrison J.M., Manghnani V., Kim H.S., and Flagg C.N., 1999, The Ras al Hadd jet: remotely sensed and acoustic Doppler current profiler observations in 1994-1995, Deep-Sea Res. II, 46: 1531-1549